Single-storey Steel Buildings - Steel Buildings in Europe

STEEL BUILDINGS IN EUROPE

Single-Storey Steel Buildings

Part 1: Architect’s Guide



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FOREWORD

This publication is part one of the design guide, Single-Storey Steel Buildings.

The 11 parts in the Single-Storey Steel Buildings guide are:

Part 1: Architect’s guide

Part 2: Concept design

Part 3: Actions

Part 4: Detailed design of portal frames

Part 5: Detailed design of trusses

Part 6: Detailed design of built up columns

Part 7: Fire engineering

Part 8: Building envelope

Part 9: Introduction to computer software

Part 10: Model construction specification

Part 11: Moment connections

Single-Storey Steel Buildings is one of two design guides. The second design guide is Multi-Storey Steel Buildings.

The two design guides have been produced in the framework of the European project “Facilitating the market development for sections in industrial halls and low rise buildings (SECHALO) RFS2-CT-2008-0030”.

The design guides have been prepared under the direction of Arcelor Mittal, Peiner Träger and Corus. The technical content has been prepared by CTICM and SCI, collaborating as the Steel Alliance.


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Contents Page No

FOREWORD i

SUMMARY v

1 INTRODUCTION 1 1.1 Steel as a construction material 1 1.2 Steel in single storey buildings 7

2 ADVANTAGES OF CHOOSING A STEEL STRUCTURE 8 2.1 Low weight 8 2.2 Minimum construction dimensions 9 2.3 Speed of construction 9 2.4 Flexibility and adaptability 10 2.5 A sustainable solution 11

3 FORM OF PRIMARY STEEL STRUCTURE 12 3.1 Structure types 12 3.2 Connections between columns and beams 26

4 BUILDING ENVELOPE 28 4.1 Cladding systems 29 4.2 Secondary steelwork 30 4.3 Roofs 30

5 FIRE SAFETY 33

6 OVERHEAD CRANES 34

7 CONCLUSIONS 36

8 FURTHER READING 37


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SUMMARY

This publication presents an introduction for architects to the use of steel in single storey steel-framed buildings. The primary application of such buildings is for industrial use but single storey solutions are appropriate for many other applications. The advantages of the use of steel, in terms of low weight, minimum construction dimensions, speed of construction, flexibility, adaptability and sustainability are explained. The primary forms of steel structure and the methods of cladding them are introduced. It is noted that the requirements for fire resistance are usually modest, since occupants can usually escape quickly in the event of fire. The influence of providing a crane inside a single storey building, in terms of the structural design, is briefly addressed.


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1 INTRODUCTION

1.1 Steel as a construction material Steel is synonymous with modern architecture. Throughout the twentieth century, the material has inspired architects and engineers, for it combines strength and efficiency with unparalleled opportunities for sculptural expression.

The key attribute of steel is its high strength to weight ratio, which gives remarkable spanning and load carrying ability. Steel lends itself to prefabrication. Whole structures can be created in a factory environment and then constructed quickly on site. Steel buildings are highly adaptable, in that frames can be modified and altered. Costs are low, recycling simple and aesthetic opportunities rich and varied. As designers, fabricators and constructors continually advance the boundaries of steel design, both technically and expressively, steel has a crucial role in modern architecture.

Steel is basically a simple alloy of iron and carbon, but its properties can be enhanced and modified by the addition of other alloying elements and by the manufacturing process. The material is then made into sections, plate, or sheet, and these simple products used to produce structures and building components.

Standard approaches have evolved for many types of single storey structures but they are not constraining: departures from norms are commonplace, for steel lends itself to creative solutions. Modern architecture is rich with solutions that defy simple categorization, even in single storey structures. These do not have to be utilitarian. They can be formed into gentle arcs or startling expressed structure. Although greatest economy is often achieved with regular grids and standardization, steel structures offer outstanding opportunity for architectural expression and outstanding design opportunities. Some illustrations of the dramatic structural forms that are possible in steel construction are shown in Figure 1.1 to Figure 1.5.


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Figure 1.1 Single storey structure with curved roof

Figure 1.2 Single storey warehouse with exposed steelwork truss


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Figure 1.3 Single storey curved and cranked steelwork for an art gallery

Figure 1.4 Modern industrial building with curved steel roof


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Figure 1.5 Roof steelwork for a transport museum

Structural steel frames generally rely on the use of hot rolled steel sections: for such sections, the material is heated and passed as a billet or blank through heavy rollers that gradually reduce and shape the cross-section whilst at the same time increasing the length; the final shape is generally in a standardised range. Typical cross section ranges are shown in Figure 1.6.


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Section IPE UPE HD HE HL Height (mm) 80 - 750 80 - 400 260 - 400 100 - 1000 620 - 1100

Figure 1.6 Typical hot rolled profiles

For larger spans, deep beams or other structural members can be fabricated from hot rolled sections and plate to form geometrically complex members. Hot rolled sections can be curved after manufacture, using bending equipment, or be converted to perforated web profiles using a variety of approaches, some of which split the beam into two in such a way that the two parts can be welded together as a deeper beam, with its spanning ability much increased.

Lighter steel sections can be formed by bending thin sheet steel into C or Z profiles. Normally this is done using either a cold rolling line (for standard sections) or by using a press or folding machine (for special sections). Common structural profiles range from around 80 mm to 350 mm deep, as shown in Figure 1.7, and are particularly suitable for roof purlins and side rails that support cladding, for lightweight frames, and as support to internal walls and partitions.

Wide thin sheets can be formed by cold rolling into profiled cladding for roofs and walls (see typical profiles in Figure 1.8) and into profiled floor decking.


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Sheet thickness 1,5 – 3 mm

HH

H 175 mm 195 mm 210 mm 240 mm 260 mm

Z shape


min. 30 mm max. 100 mm

max. 350 mm

min. 80 mm

H

C shape


max. 100 mmmin. 30 mm

H

max. 350 mm

min. 80 mm

U shape

Figure 1.7 Typical cold-rolled section profiles


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Flat

Wide Profile

Narrow profile

Micro profile

Trapezoidal

Corrugated

Figure 1.8 Typical cladding profiles

Steel members can be joined using a wide variety of techniques including welding and bolting; connection design is an important part of any structural system. Connection arrangements can be highly standardised or unique to suit a complex form. In expressed steelwork, connections often become important architectural elements in their own right.

1.2 Steel in single storey buildings A steel building for commercial, industrial or agricultural use is typically a single storey, single span or multi-span building. Both building length and building width are much larger than the height of the building. Building functions include warehouses, distribution centres, retail outlets, exhibition spaces, sports halls and a wide range of commercial premises.

Each building type has its own specific requirements with regard to the internal space, though most require a space that is either entirely clear of structural members, or has internal columns reduced to a minimum. Usually, the structure is specifically designed for its purpose. For manufacturing and warehouse structures, economics and flexibility often have a greater influence than the appearance of the building. For other buildings, the appearance of the structure is more important and fabricated steelwork may be used to form architecturally appealing structures.

Buildings which are designed to be adaptable retain their value, as it is possible to divide, combine or extend them in the future. The re-usability of the building is a major factor when deciding between renovation and rebuilding.

Depending on the function of the building, the architect’s brief will determine the basic layout of the structure. The structural engineer will have a wide choice of structural concepts, including simple frames, portal frames, trusses and arches. These solutions may range from the entirely functional for greatest economy to rather more adventurous architecture and external appeal.


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2 ADVANTAGES OF CHOOSING A STEEL STRUCTURE

A very large proportion of all industrial and commercial single storey buildings utilise a steel structure, which demonstrates the cost-effectiveness of a steel solution. Architects and engineers use steel not only as an economical solution but also to achieve:

low structural weight

minimum construction dimensions

a short construction time

flexibility in use

a sustainable solution

2.1 Low weight A steel structure has a relatively low self-weight compared to masonry or concrete structures. This advantage not only reduces the foundations required for the structure, but also means that the structure is lightweight, reducing material delivery to the site. The off-site prefabrication of steel construction is a significant contribution to reduced transport of materials to site and reduced site activities, minimising construction disruption and environmental impact.

Figure 2.1 The relatively low self weight of steel structures reduces material

delivery to site


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2.2 Minimum construction dimensions Steel enables large spans to be constructed with relatively small construction depths. The typical construction solution of an insulated external envelope supported on steel secondary members is a very well-developed solution, optimised over many years, leading to a structurally efficient and cost effective solution.

For pitched roofs or short span flat roofs, the construction depth of the roof beams or rafters can be as low as 1/40 of the span between columns. If internal columns are required for multi-span structures, they may be chosen to be small members, or the internal columns may be provided on every second (or every third) frame, maximising internal space and flexibility. Steelwork supporting the external envelope may be very slender, as shown on Figure 2.2, providing the opportunity for maximum natural lighting.

Figure 2.2 Slender construction takes up less space and results in

transparent buildings.

2.3 Speed of construction Structural steel components are pre-fabricated off site by a steelwork contractor; any protective coating that is required is applied at this stage. The site activity is primarily an assembly operation, bolting steelwork parts together, which leads to short construction periods. The building can be made weather tight quickly, allowing the following trades early access to commence their work.

Modern fabrication is achieved using numerically controlled machines, with data from three-dimensional electronic models of the complete structure. Modern fabrication is therefore extremely accurate, and errors that need rectification on site are rare. Three-dimensional building models can be used by other trades to ensure that their own contribution (for example, the cladding, or the mechanical and electrical services) can be properly co-ordinated with the structural frame before the building is constructed. All these facilities contribute to minimizing the period from conception to completion.


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Figure 2.3 Prefabricated components are easily and rapidly connected on site

2.4 Flexibility and adaptability A steel structure is both flexible and adaptable – design in steel is certainly not limited to rectangular grids and straight members, but can accommodate dramatic architectural intent, as shown in Figure 2.4.

Figure 2.4 Dramatic, expressed steelwork

Thanks to the numeric control of modern fabrication, components may be designed and fabricated to almost any shape desired. In most cases, a structure with an irregular floor plan or curved components is manufactured as easily as a rectilinear design, although there will be cost implications of the more complex fabrication.


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The building can also be made adaptable for future changes in use. Column-free floor space facilitates future changes in internal layout, which is likely to happen several times in the life of a structure. The building structure can be modified, strengthened and extended. The facility to extend the structure at some future stage can be incorporated into the original design and construction details. The external envelope maybe renewed, upgraded or modified. Future owners/users with different requirements can readily adapt a steel building to their requirements.

2.5 A sustainable solution Steel can be recycled any number of times without loss of quality or strength. Significant quantities of recycled steel are used in the manufacture of new steel products and there is a commercial value in scrap steel for this reason. Figure 2.5 shows scrap material being recycled to make new steel.

Steel building components are fabricated under controlled conditions with minimal waste (off-cuts are recycled as scrap). As the site activity is mainly assembly, there is rarely any waste on site.

Steel structures can often be dissembled, as they are primarily bolted skeletal structures. The steel members may reused in other structures – portal frames and similar structures are frequently dismantled and used at other locations.

Figure 2.5 Modern steel making technology has the ability to recycle scrap


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3 FORM OF PRIMARY STEEL STRUCTURE

Single storey steel buildings are generally built with an external cladding envelope, supported in many cases on relatively short span secondary steel members, which are in turn supported on the primary steel structure. This Section describes the structural possibilities that may be considered and comments on the type of structural sections that can be used.

3.1 Structure types There are four basic structural configurations that provide a clear interior space for a single storey building:

Rigid framed structures (portal frames and rigid-frame trusses)

Pinned frame beam-and-column structures

Cable-supported roofs

Arched roofs

For the first three configurations, the designer has the option of providing either a flat roof or a pitched roof.

Typical spans and span/depth ratios for the primary roof members in pinned and rigid framed buildings are given in Table 3.1.

Table 3.1 Typical spans and structural depths for single storey structures

Structure type Roof beam depth Typical span range

Pinned frames

Simple beam span/30 to span/40 Up to approximately 20 m

Fabricated Beam span/20 to span/25 Up to approximately 30 m

Perforated web beam span/20 to span/60 Up to approximately 45 m

Truss roof (pitched) span/5 to span/10 Up to approximately 20 m

Truss roof (flat) span/15 to span/20 Up to approximately 100 m

Rigid frames

Portal frame span/60 15 m – 45 m

Truss roof (flat) span/15 to span/20 Up to approximately 100 m

3.1.1 Rigid-framed structures

Rigid frames are achieved by providing a rigid (moment resisting) connection between the ends of the roof beams (or trusses) and the columns. The stiff frame that is created is much more efficient in carrying the imposed loads on the roof than a simply supported roof member (with nominally pinned connections at its ends) and the frame also provides resistance against wind forces on the sides of the building. Because the frames are self-supporting in the plane of the frame, the bracing in the roof can be reduced, compared to a structure with simply supported roof beams.

Rigid framed structures broadly fall into two categories, portal framed structures and truss framed structures.


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Portal frames

Portal frames typically use hot-rolled I-section beams and columns for the roof rafters and supporting columns, although cold formed sections may be adequate for small span structures. Portal frames come in a variety of different shapes and sizes, with flat and pitched roofs.

A typical configuration is shown in Figure 3.1. The roof and wall cladding is supported on purlins and side rails that span between the portal frames. Bracing is not needed between every frame but is needed in at least one bay to transfer longitudinal forces (normal to the frames) to the side walls and thus to ground level.

In some special design situations, the cladding can be used as the bracing – this is known as stressed skin design. The design of the cladding and the fixings to the supporting members will be assessed by the structural engineer. In most cases, bracing will be provided that does not rely on the sheeting.

Figure 3.1 Typical structural configuration of a portal frame structure


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25 - 40 m

6 m

6°

6 m

25-30 m (a) Portal frame – medium span (b) Curved portal frame

8 m

8 m 9 m 8 m

3.5 m

25 m

8 m

6°

(c) Portal frame with mezzanine floor (d) Portal frame with overhead crane

25 m

6 m

6°

(e) Two bay portal frame

10 m

8 m3.5 m

6°6°

(f) Portal frame with integral office

40 m

6 m

10° 3.00°

(g) Mansard portal frame

Figure 3.2 Forms of portal frame

Portal frames typically have straight rafters, as shown in Figure 3.3. The same structural principles can be followed to form a portal frame with a curved rafter, as shown in Figure 3.4. In each case, the connection of the rafter to the column is substantial, and usually the rafter is haunched locally to the column. The dimensions of the haunch should be allowed for when considering the clear height requirements.


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Figure 3.3 Pitched roof portal frame

Figure 3.4 Curved roof portal frame


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Figure 3.5 Typical roof and wall bracing in portal framed structures

In most cases, the rafter (and possibly the column) will need local restraints, as shown on Figure 3.6. In some countries, special provision must be made when using this form of restraint, to ensure that the purlins align with the roof bracing system. The location of these restraints will be specified by the structural engineer.

Figure 3.6 Stabilizing the bottom flange of a roof beam

Rigid framed trusses

When flat trusses are used, both top and bottom chords can easily be connected to the supporting columns, thus creating a rigid frame. For larger spans, roof trusses provide an effective and economic alternative. Typical flat truss shapes are shown in Figure 3.7, and a truss roof is illustrated in Figure 3.8.


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Figure 3.7 Typical truss shapes

Figure 3.8 Rigid frame flat truss (N-type)

In some situations, the columns are also of lattice form and then the building configuration is typically as shown in Figure 3.9.

Figure 3.9 Rigid frame flat truss with lattice columns


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The lateral stability of the top chords of trusses is usually provided by the purlins (and by one panel of bracing, as for portal frames) but where stressed skin design is permitted, it may provide the restraint without bracing, as shown in Figure 3.10.

Figure 3.10 Roof cladding acting as stressed skin in a rigid-framed truss roof

3.1.2 Pinned frame beam and column structures

In a pinned frame beam and column structure, the basic configuration is a series of parallel beams, each supported by columns at its ends, with a pinned or flexible connection between the beam and the column. Bracing has to be provided in the roof to transfer horizontal forces due to wind loads to the end and side walls; the walls are braced to transfer the forces to the foundations. (Alternatively, some countries allow the roof cladding to act as a ‘stressed skin’, thus largely eliminating the need for separate bracing.) A typical structural configuration is shown in Figure 3.11.

Figure 3.11 Typical structural configuration for a beam and column structure


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There are numerous options for the beams:

Hot rolled sections (I-beams)

Plate girders

Fabricated beams with holes in the webs

Trusses

Hot rolled I section beams

The most common type of beam and column structure uses hot rolled steel I sections for both beams and columns. These sections are produced in accordance with international standards and there are design tables available to allow for an easy selection of section size to suit the loading. The most common section sizes are readily available from stockists and can be ordered at short notice.

Deep sections with relatively narrow flanges are preferred for roof beams, as shown in Figure 3.12, where they primarily resist bending. Columns, which primarily resist compression, are usually thicker, shallower sections with wider flanges.

The span/depth ratio for the roof beams is typically 30 to 40 for spans up to 20 m.

Figure 3.12 Pinned frame beam and column structure

Plate girders

Plate girders are built up beams consisting of two flange plates, welded to a web plate to form an I-section. This type of beam offers a solution when the standard I and H beams are not suitable. The section dimensions are chosen to suit the design bending moments and shear forces; the beams can be profiled in elevation, as shown in Figure 3.13.

The span/depth ratio is typically 20 to 25 for spans up to 30 m.

An alternative that is sometimes used for large spans, to reduce the thickness of the web plate, is the use of a corrugated plate (profiled in plan). The span/depth ratio with a profiled web plate is typically 30 to 40 for spans up to 100 m.


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Figure 3.13 Tapered plate girders

Plate girders are likely to be more expensive than hot-rolled standard sections.

Beams with web openings

Because roof beams generally carry relatively light uniformly distributed loads, beam sections that span large distances can be created by fabricating sections with openings in the webs. Historically, the first beam of this type was the castellated beam, with hexagonal holes. Now beams with circular openings are commonly used.

In both cases, the beam is fabricated from a rolled I section by cutting along the web, to a special profile, separating the two halves and then displacing one half relative to the other and welding them back together. This is illustrated in Figure 3.14. The major advantage of this type of beam is the weight reduction: approximately 30% less than a beam with a solid web of similar depth and bending resistance.

An example of the use of beams with circular openings is shown in Figure 3.15.

Beams with web openings are less suitable for heavy concentrated loads.

The span/depth ratio is typically 30 for spans up to 50 m.

Hexagonal holes

Circular holes

Figure 3.14 Fabrication of beams with web openings


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Figure 3.15 Beams with circular web openings

Trusses

Trusses are a triangulated assembly of members. Two basic configurations are used in single storey buildings – pitched roof trusses and ‘flat’ trusses of near uniform depth.

Pitched roof trusses

A variety of pitched roof truss forms are used in pinned frames, as illustrated in Figure 3.16.

The trusses illustrated in Figure 3.16 are commonly fabricated from T and angle sections, and are used to create a sloped roof. The large (mostly unused) space between the trusses may be considered a disadvantage, requiring heating and raising the overall height of the structure, but it is a cost effective solution for modest spans and provides space for services.

Because these trusses are used with a steeply sloping roof, the span/depth ratio is typically 5 to 10 for spans up to 20 m


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Fink or Polonçeau truss (small span)

Fink or Polonçeau truss (large span)

Belgian truss

English truss

Mansard truss

Figure 3.16 Types of pitched roof truss

Flat trusses

Flat trusses are used mainly in rigid frames (see Section 0 for a more comprehensive description) but they are also employed in pinned frames – an example is shown in Figure 3.17.

Figure 3.17 Flat truss in pinned frame building

Trusses typically have a greater depth than single beams or plate girders. The deflection of a truss is modest, and can be controlled, making trusses especially suitable when significant loads have to be supported from the roof structure, or when a flat (or nearly flat) roof is to be provided. The larger depth of the trusses increases the dimensions of the façade, but also provides space for services to be placed in the roof structure instead of below.

The weight of a trussed roof structure per unit area of roof in general is less than that of single beam girders, but the fabrication costs are higher. Trusses


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may be exposed in the completed structure, which may increase the fabrication costs if, for example, hollow sections are used for the members.

The span/depth ratio for flat trusses is typically 15 to 20 for spans up to 100 m.

Trusses are usually planar and will generally require bracing of some form to provide stability. As an alternative, three-dimensional trusses can be created, as shown in cross section in Figure 3.18 and illustrated in Figure 3.19. This form of truss is generally expensive to fabricate, because of the complex intersections of the internal members.

The span/depth ratio for three-dimensional trusses is typically 16 to 20 for spans over 50 m.

Triangular truss (with circular hollow sections) Triangular truss (with rectangular hollow sections)

Figure 3.18 Three dimensional triangular trusses

Figure 3.19 Three-dimensional trusses supporting a roof

3.1.3 Cable stayed roofs

In a cable-stayed structure, tensile members (wire ropes or bars) are provided to give intermediate support to members such as roof beams, thus allowing those members to be reduced in size. The stays need to be supported by columns or masts and those members need to be anchored or braced with other stays. The bracing arrangement is usually very conspicuous and the aesthetics


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of the building must be considered carefully. An example of a cable stayed building structure is shown in Figure 3.20.

Figure 3.20 Cable stayed roof beams of a storage facility

Alternative configurations for a flat roof building are shown in Figure 3.21.

Cable stayed configurations are most economical for spans between 30 m and 90 m.

As most of the structure is outside of the building, maintenance costs can be high. Care must be taken in detailing the waterproofing where the stays pass through the cladding.

1

2

3

1 2 3

Roof beam Bending moment

+ ++ +

Compression force

-- - +

Anchorage Tensile force ++ -- --

Figure 3.21 Comparison of the three main configurations for cable stayed

structures

The arrangement of the structure has a significant effect on the internal forces and therefore the member sizes. The building arrangement should be developed in collaboration with the structural engineer.


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3.1.4 Arches

Arches have a parabolic or circular form, as illustrated in Figure 3.22. Uniform loading is carried by compression in the arch members; modest bending moments are induced by non-uniform loading and point loads. The compression forces must be resisted by horizontal forces in the foundation of the building – or by tie members between the foundations, as shown in Figure 3.22.

Arch members can be formed by cold bending I-section beams.

The span/depth ratio for the arch members is typically between 60 and 75 for spans up to 50 m.

An example of an arched roof building is shown in Figure 3.23.

Tie rod connecting supports

Both supports fixed

Figure 3.22 Methods of supporting arch members

Figure 3.23 Fire brigade station


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3.2 Connections between columns and beams 3.2.1 Moment-resisting connections

In a portal frame structure, the connections between beams and columns transfer bending moments, as well as shear and axial forces, and they must be designed as rigid connections.

A rigid connection typically has a full depth end plate. The roof beam is often haunched locally and the column web is stiffened in order to resist the local forces from the end of the roof beam. In general, stiffeners should be avoided if possible, as they add significant fabrication cost.

1

2

3

1 Extended end plate 2 Extended end plate with stiffener3 Haunched connection with

stiffener

Figure 3.24 Rigid bolted connections between roof beams and columns

Connections between trusses and columns are usually achieved by end plates on the top and bottom chords, bolted to the face of the column. A typical example is illustrated in Figure 3.25.


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Figure 3.25 Truss-column connection in a rigid framed structure

3.2.2 Nominally pinned connections

In a beam and column structure, the connections are nominally pinned and are not assumed to transfer any moments between the connected members. Externally applied actions, such as wind forces, must be resisted by bracing systems. The bracing system may be steel bracing, or a stiff core. For single storey structures, a system of steel bracing is almost universally adopted.

Pinned connections are relatively easy (and cheap) to fabricate. Typical connections use partial depth end plates, fin plates or angle cleats; the members are bolted together on site.

2

1

3

1 End plate connection 2 Angle cleat connection 3 Fin plate connection

Figure 3.26 Nominally pinned bolted connections


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4 BUILDING ENVELOPE

The steel structure of a single storey building generally comprises three principal components: a primary construction (roof beams and columns, with bracing); secondary steelwork, such as purlins and side rails that support the roof panels and wall cladding; and the roof panels and cladding themselves. The roof panels and cladding are generally referred to as the building envelope.

The building envelope provides a weather-tight enclosure to the building space. In most cases, it also provides thermal insulation from the exterior environment. The exterior appearance is often a major consideration in the choice of the form of the envelope. The architect must therefore choose a system that balances the demands of sustaining actions such as wind pressure and (on flat or near-flat-roofs) imposed loads, of achieving thermal performance that meets criteria for low energy use, and of producing an appearance that meets the client’s aspirations.

A single type of cladding system is often used for both roof and walls.

Detailing will be an important element of envelope design. Drainage systems that do not block or leak are essential and the integration of openings (windows and doors) with the cladding must not compromise thermal insulation.

A striking example of using coloured profiled sheeting is shown in Figure 4.1.

Figure 4.1 Car repair workshop with steel roof and façade


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4.1 Cladding systems The principal options for cladding systems are:

Profiled steel sheeting

- Single-skin

- Double-skin, built up on site from a liner panel, insulation and an outer sheet

- Composite sandwich panels, pre-fabricated off site from an inner sheet, and outer sheet and insulation.

Steel sheeting with insulation, covered by a waterproof membrane – commonly used on flat roofs.

Wooden panels/decking

Precast concrete slabs

Blockwork (for walls)

4.1.1 Profiled sheet cladding

The basic types of profiled steel sheeting system, used in roofs and walls, are summarized in Table 4.1.

Table 4.1 Basic types of cladding system

System Insulated? Benefits

Built up systems

yes free choice for exterior profiled sheeting high fire resistance good sound proofing and good sound absorption fast construction, with simple mechanical fasteners

Composite panels

yes fast construction fully prefabricated

single sheeting

no cheap and fast construction easy to dismantle large freedom of form

4.1.2 Precast concrete slabs

For flat roofs with significant imposed loads, cellular concrete slabs provide both a relatively easily installed building component and a thermal insulation layer.

Precast concrete slabs (either hollow core or sandwich panel) provide the necessary strength where there are heavy snow loads or a heavy roof is required for safety reasons (e.g. resisting explosive pressures in accidental situations). However, precast slabs are much heavier than profiled steel cladding and the primary steel structure must be correspondingly stronger.

4.1.3 Blockwork

Blockwork construction is often used for the walls of single storey buildings, either full height or partial height (with sheet cladding for the top of the wall). The blockwork provides insulation and robustness; it may also be chosen for appearance.


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4.2 Secondary steelwork Secondary beams are used when the spacing of the main beams or trusses is too large for the cladding or roof panels to span between them, or where the cladding spans parallel to the main beams, which is usually the case with pitched roofs.

For these secondary members, there is a choice between cold-formed and hot-rolled steel sections. The profiles of typical cold formed sections are shown in Figure 4.2. A cold formed section can be up to 30% lighter than a hot rolled section.

1 2 3 4 C profile

ℓmax = 10 m

140 mm < h < 300 mm

profile

ℓmax = 12 m

140 mm < h < 300 mm

profile

ℓmax = 16 m

250 mm < h < 420 mm

Z profile

ℓmax = 12 m

120 mm < h < 400 mm

Figure 4.2 Typical cross sections of cold formed beams

Cold formed sections are manufactured from galvanized steel and this normally provides sufficient protection against corrosion in the internal environment of the building (an exception might be, for example, in aggressive environments such as cattle sheds, where ammonia is present).

Secondary members of cold-formed sections are used at relatively low spacing, typically between 1,6 m and 2,5 m. Very long secondary members can be fabricated as small trusses.

4.3 Roofs The choice between a flat roof and a pitched roof often depends on the particular preferences in the local or national region. Some countries favour flat roofs that are able to sustain significant imposed loading, other countries favour pitched roofs that facilitate drainage and which are subject to only very modest imposed loading. Clearly, the type of cladding that is appropriate depends on those choices and circumstances.

4.3.1 Pitched roofs

The slope of a pitched roof also depends on local circumstances and custom. A slope of at least 10% (6°) is normally provided.

Where profiled sheeting is used, the profiles run down the slope, to facilitate drainage. Insulation must therefore be below the outer sheeting (possibly as a composite panel). The sheeting is supported on purlins spanning between the


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roof beams and is fastened with screws or bolts. The lapped sheets do not require a waterproof membrane; the panels are simply lapped, the higher above the lower on the slope.

A typical arrangement of a pitched roof at the eaves is shown in Figure 4.3. It is important that the drainage system is adequate for the run-off from the whole roof.

1

1

3

2

1 Sandwich roof panel and sandwich façade panel 2 Roof slope > 6 3 Hot rolled or cold formed section

Figure 4.3 Insulated sloped roof

4.3.2 Flat roofs

Where the roof is flat, it must be fully watertight against standing water and it is therefore usual to apply a waterproofing membrane on its top surface.

Where profiled steel sheeting is used, it is typically a deep profile, spanning between the primary structural members. Insulation is then placed on top of the sheeting, fixed with bolts or screws. The waterproof membrane is then applied on top of the insulation. An example is shown in Figure 4.4.

Where flat roofs are provided, there is a risk of ponding. Water can accumulate in the central area if the roof deflects significantly. If there is inadequate drainage, water can also be retained by kerbs or other details around the edge of the roof. It is vitally important to minimise the risk of ponding by precambering the roof and providing adequate drainage.


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1

2

3

7

6

5

4

1 Insulation 2 Liner panel 3 Exterior profiled sheeting 4 Screw

5 Insulation 6 Additional metal strip 7 Single roof sheeting

Figure 4.4 Insulated flat roof


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5 FIRE SAFETY

Requirements for fire safety are defined by national regulations but there are recognised international rules for assessing the fire resistance of steel structures. The minimum level of safety for structural fire design aims to provide an acceptable risk associated with the safety of building occupants, fire fighters and people in the proximity of the building. Levels of safety can be increased to protect the building contents, the building superstructure, heritage, business continuity, corporate image of the occupants or owner, and the environmental impact.

Requirements are usually expressed in relation to:

Spread of fire: combustibility of the materials expressed in relation to time until flashover. It is classified as A1 (flashover not possible) down to E (flashover in less than 2 minutes) and F (not tested).

Smoke intensity: materials are classified from class A2 to F depending on the smoke produced on combustion.

Fire resistance: the period of time for which a structural component can perform in a standardized fire test. The three criteria of load-bearing capacity, integrity and insulation (commonly expressed as R, E and I) are considered and the rating is expressed as R30, R60 etc. where the number refers to the period in minutes.

In order to achieve the required fire safety level in a single storey building the following items should be taken in account:

regulatory requirements

fire partitioning

fire spreading

escape routes

Single storey buildings often have very modest requirements for fire resistance because occupants can escape quickly. The main requirement is often the prevention of fire spread to adjacent properties.

To protect contents, especially in large production facilities and warehouses, partitioning may be needed or, where that is not feasible, alternative measures may be taken, such as the installation of a sprinkler system.


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6 OVERHEAD CRANES

Certain industrial buildings require overhead cranes – examples are printing shops (for moving rolls of paper) and engineering shops (for moving heavy equipment and components). An example is shown in Figure 6.1.

Most overhead cranes use single or twin beams spanning across the building and with a hoist mounted on the beams. The crane beams are supported on runway beams that run the length of the building. The crane serves the whole floor by moving along the runway beams and by moving the hoist along the crane beams (Figure 6.2).

Incorporating an overhead crane in a building always influences the design of the building structure, even when the hoisting capacity is very modest. A key design consideration is to limit the spread of the columns at the level of the crane. For this reason, portal frames are not appropriate for heavy cranes as limiting the column movement becomes uneconomic. Crane use also results in horizontal forces from movement of the loads, so additional bracing is usually provided.

A crane with a lifting capacity up to a safe working load of about 10 tons (100 kN) can usually be carried on runway beams that are supported off the columns that support the roof. For larger cranes, it is more economical to use separate columns (or vertical trusses) to support the runway beams and avoid excessive loads on the building structure.

Figure 6.1 Heavy crane in a large industrial building


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2 13

7

6

45

13

8910

1211

min. 500 mm

1 Lifting 2 Hoist drive 3 Crane drive 4 Motor drive 5 Hoist

6 Crane beams 7 Wheel cabinet 8 Hoist 9 Crane beam

10 Runway beam 11 Console 12 Hook 13 Crane operation

Figure 6.2 Typical overhead crane with gantry and hoist


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7 CONCLUSIONS

Steel is a versatile material that allows the architect and engineer to design any type of structure, ranging from orthodox portal frames for industrial use to state of the art buildings with architectural features, unorthodox shapes or any other requirements the stakeholders might have.

Structural steel design is familiar and efficient, providing elegant cost effective solutions. Structural steel can be combined with other materials to achieve the desired look, properties or functionality.

Fabrication of a steel building is carried out in a workshop, ensuring a high quality product and contributing to a low waste, sustainable solution. Standardised details and forms of construction are available which allow fast erection on site, with minimised disruption to the surroundings.

Steel has a very high resistance to weight ratio, resulting in a light, attractive solution with minimal intrusion into the working area of the structure. The transportation of highly prefabricated elements reduces deliveries to site, which is especially important in congested areas, such as city centres. The structural efficiency of steelwork results in lower loads being transferred to the foundations, leading to further economy.

Long span buildings can easily be designed in steel, resulting in large clear areas. This increases the functionality of the structure, offering flexibility of building use. Steel buildings are adaptable and may be easily extended, making refurbishment of the building a realistic solution for future use, instead of demolition.

Steel has excellent sustainability credentials. Steel buildings can easily be dismantled and reused. The steel can always be recycled without any loss of strength, minimising the amount of raw material required.

Steel’s low weight, sustainability and versatility, make steel the optimum choice for any type of building.


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8 FURTHER READING

Best Practice in Steel Construction: Industrial Buildings, Guidance for Architects, Designers and Constructors RFCS project deliverable for Euro-Build Available from the Steel Construction Institute, UK It can be downloaded from www.eurobuild-in-steel.com



Part 2: Concept Design



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FOREWORD

This publication is a second part of a design guide, Single-Storey Steel Buildings.




Part 3: Actions













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Contents Page No

FOREWORD iii

SUMMARY vi

1 INTRODUCTION 1 1.1 Hierarchy of design decisions 1 1.2 Architectural design 2 1.3 Choice of building type 6 1.4 Design requirements 9 1.5 Sustainability 12

2 CASE STUDIES ON SINGLE STOREY BUILDINGS 14 2.1 Manufacturing hall, Express Park, UK 14 2.2 Supermarket, Esch, Luxembourg 15 2.3 Motorway Service station, Winchester, UK 16 2.4 Airbus Industrie hanger, Toulouse, France 17 2.5 Industrial hall, Krimpen aan den Ijssel, Netherlands 17 2.6 Distribution Centre and office, Barendrecht, Netherlands 18

3 CONCEPT DESIGN OF PORTAL FRAMES 19 3.1 Pitched roof portal frame 20 3.2 Frame stability 22 3.3 Member stability 23 3.4 Preliminary Design 25 3.5 Connections 27 3.6 Other types of portal frame 29

4 CONCEPT DESIGN OF TRUSS BUILDINGS 35 4.1 Introduction 35 4.2 Truss members 36 4.3 Frame stability 38 4.4 Preliminary design 39 4.5 Rigid frame trusses 40 4.6 Connections 40

5 SIMPLE BEAM STRUCTURES 42

6 BUILT-UP COLUMNS 43

7 CLADDING 45 7.1 Single-skin trapezoidal sheeting 45 7.2 Double-skin system 45 7.3 Standing seam sheeting 47 7.4 Composite or sandwich panels 47 7.5 Fire design of walls 47

8 PRELIMINARY DESIGN OF PORTAL FRAMES 49 8.1 Introduction 49 8.2 Estimation of member sizes 49

REFERENCES 52


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SUMMARY

This publication presents information necessary to assist in the choice and use of steel structures at the concept design stage in modern single storey buildings. The primary sector of interest is industrial buildings, but the same information may also be used in other sectors, such as commercial, retail and leisure. The information is presented in terms of the design strategy, anatomy of building design and structural systems that are relevant to the single storey buildings. Other parts in the guide cover loading, the concept design of portal frames, the concept design of trusses and cladding.


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1 INTRODUCTION

Single storey buildings use steel framed structures and metallic cladding of all types. Large open spaces can be created, which are efficient, easy to maintain and are adaptable as demand changes. Single storey buildings are a “core” market for steel. However, the use of steel in this type of construction varies in each European country.

Single storey buildings tend to be large enclosures, but may require space for other uses, such as offices, handling and transportation, overhead cranes etc. Therefore, many factors have to be addressed in their design.

Increasingly, architectural issues and visual impact have to be addressed and many leading architects are involved in modern single storey buildings.

This section describes the common forms of single storey buildings that may be designed and their range of application. Regional differences may exist depending on practice, regulations and capabilities of the supply chain.

1.1 Hierarchy of design decisions The development of a design solution for a single storey building, such as a large enclosure or industrial facility is more dependent on the activity being performed and future requirements for the space than other building types, such as commercial and residential buildings. Although these building types are primarily functional, they are commonly designed with strong architectural involvement dictated by planning requirements and client ‘branding’.

The following overall design requirements should be considered in the concept design stage of industrial buildings and large enclosures, depending on the building form and use:

Space use, for example, specific requirements for handling of materials or components in a production facility

Flexibility of space in current and future use

Speed of construction

Environmental performance, including services requirements and thermal performance

Aesthetics and visual impact

Acoustic isolation, particularly in production facilities

Access and security

Sustainability considerations

Design life and maintenance requirements, including end of life issues.

To enable the concept design to be developed, it is necessary to review these considerations based on the type of single storey building. For example, the requirements for a distribution centre will be different to a manufacturing


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facility. A review of the importance of various design issues is presented in Table 1.1 for common building types.

Table 1.1 Important design factors for single storey buildings

Type of single storey buildings

Spa

ce

req

uire

men

ts

Fle

xibi

lity

of u

se

Spe

ed

of c

onst

ruct

ion

Acc

ess

and

Se

curit

y

Sta

ndar

diza

tion

of c

ompo

nen

ts

Env

ironm

enta

l per

form

anc

e

Aes

thet

ics

and

vis

ual i

mpa

ct

Aco

ustic

iso

latio

n

Des

ign

life,

ma

inte

nan

ce a

nd r

e-us

e

High bay warehouses

Manufacturing facility

Distribution centres

Retail superstores

Storage/cold storage

Office and light manufacturing

Processing facility

Leisure centres

Sports halls

Exhibition halls

Aircraft hangars

Legend: No tick = Not important = important = very important

1.2 Architectural design Modern single storey buildings using steel are both functional in use and are designed to be architecturally attractive. Various examples are presented below together with a brief description of the design concept. A variety of structural solutions are possible, which are presented in Sections 2 and 3.

1.2.1 Building form

The basic structural form of a single storey building may be of various generic types, as shown in Figure 1.1. The figure shows a conceptual cross-section through each type of building, with notes on the structural concept, and typical forces and moments due to gravity loads.


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Simple beam

Portal frame

Truss

Portal truss

Figure 1.1 Structural concepts

The basic design concepts for each structural type are described below:

Simple roof beam, supported on columns.

The span will generally be modest, up to approximately 20 m. The roof beam may be pre-cambered. Bracing will be required in the roof and all elevations, to provide in-plane and longitudinal stability.

Portal frame

A portal frame is a rigid frame with moment resisting connections to provide stability in-plane. A portal frame may be single bay or multi bay as shown in Figure 1.2. The members are generally plain rolled sections, with the resistance of the rafter enhanced locally with a haunch. In many cases, the frame will have pinned bases.

Stability in the longitudinal direction is provided by a combination of bracing in the roof, across one or both end bays, and vertical bracing in the elevations. If vertical bracing cannot be provided in the elevations (due to industrial doors, for example) stability is often provided by a rigid frame within the elevation.

Trusses

Truss buildings generally have roof bracing and vertical bracing in each elevation to provide stability in both orthogonal directions, as in Figure 1.4. The trusses may take a variety of forms, with shallow or steep external roof slopes.


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A truss building may also be designed as rigid in-plane, although it is more common to provide bracing to stabilise the frame.

Other forms of construction

Built–up columns (two plain beams, connected to form a compound column) are often used to support heavy loads, such as cranes. These may be used in portalised structures, but are often used with rigid bases, and with bracing to provide in-plane stability.

External or suspended support structures may be used, as illustrated in Figure 1.6, but are relatively uncommon.

Figure 1.2 Multi bay portal frame structure


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Figure 1.3 Use of curved cellular beams in a portal frame

Figure 1.4 Roof trusses and built-up columns


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Figure 1.5 Curved cellular beams used in a leisure centre

Figure 1.6 External structure supporting a single storey building

1.3 Choice of building type Portal frames are considered to be a highly cost-effective way to provide a single storey enclosure. Their efficiency depends on the method of analysis, and the assumptions that are made regarding the restraint to the structural members, as shown in Table 1.2. The assumptions about member stability may vary between countries.


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Table 1.2 Efficient portal frame design

Most Efficient Less Efficient

Analysis using elastic-plastic software Elastic analysis

Cladding considered to restrain the flange of the purlins and side rails

Purlins and side rails unrestrained

Purlins and side rails used to restrain both flanges of the hot-rolled steelwork

The inside flange of the hot rolled steelwork is unrestrained

Nominal base stiffness utilised Nominal base stiffness ignored

The reasons for choosing simple beam structures, portal frames or trusses are shown in Table 1.3.

Table 1.3 Comparison of basic structural forms for single storey buildings

Simple beam Portal frame Truss

Advantages

Simple design Long span Very long spans possible

Designed to be stable in-plane

Heavy loads may be carried

Member sizes and haunches may be optimised for efficiency

Modest deflection

Disadvantages

Relatively short span Software required for efficient design

Generally more expensive fabrication

Bracing needed for in-plane stability

Limited to relatively light vertical loading, and modest cranes to avoid excessive deflections

Generally bracing is used for in-plane stability

No economy due to continuity

1.3.1 Cladding types

The main types of roofing and wall cladding used in single storey buildings are described as follows:

Roofing

‘Built-up’ or double layer roofing spanning between secondary members such as purlins.

Composite panels (also known as sandwich panels) spanning between purlins.

Deep decking spanning between main frames, supporting insulation, with an external metal sheet or waterproof membrane.

Walls

Sheeting, orientated vertically and supported on side rails.

Sheeting or structural liner trays spanning horizontally between columns.

Composite or sandwich panels spanning horizontally between columns, eliminating side rails.

Metallic cassette panels supported by side rails.


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Different forms of cladding may be used together for visual effect in the same façade. Examples are illustrated in Figure 1.7, Figure 1.8 and Figure 1.9. Brickwork is often used as a “dado” wall below the level of the windows for impact resistance, as shown in Figure 1.8.

Figure 1.7 Horizontal spanning sheeting

Figure 1.8 Large windows and use of composite panels with “dado” brick wall


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Figure 1.9 Horizontal composite panels and ‘ribbon’ windows

1.4 Design requirements Design requirements for single-span buildings are presented as follows:

1.4.1 Actions

Permanent actions

Permanent actions are the self weight of the structure, secondary steelwork and cladding. These may be calculated from EN 1991-1-1.

Typical weights of materials used in roofing are given in Table 1.4.

If a roof only carries normal imposed roof loads (i.e. no suspended machinery or similar) the self weight of a steel frame is typically 0,2 to 0,4 kN/m2 when expressed over the plan area of the roof.


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Table 1.4 Typical weights of roofing materials

Material Weight (kN/m2)

Steel roof sheeting (single skin) 0,07 – 0,12

Aluminium roof sheeting (single skin) 0,04

Insulation (boards, per 25 mm thickness) 0,07

Insulation (glass fibre, per 100 mm thickness) 0,01

Liner trays (0,4 mm – 0,7 mm thickness) 0,04 – 0,07

Composite panels (40 mm – 100 mm thickness) 0,1 – 0,15

Steel purlins (distributed over the roof area) 0,03

Steel decking 0,2

Three layers of felt with chippings 0,29

Slates 0,4 – 0,5

Tiling (clay or plain concrete tiles ) 0,6 – 0,8

Tiling (concrete interlocking) 0,5 – 0,8

Timber battens 0,1

Variable actions

Variable actions should be determined from the following Eurocode parts:

EN 1991-1-1 for imposed roof loads EN 1991-1-3 for snow loads EN 1991-1-4 for wind actions

EN 1991-1-1 recommends a uniform load of 0,4 kN/m2 for roofs not accessible except for normal maintenance and repair (category H). A point load of 1,0 kN is also recommended, but this will only affect the design of the sheeting and not the main structural elements.

EN 1991-1-3 includes several possible load cases due to snow, including uniform snow and drifted snow, which typically occurs in valleys, behind parapets etc. There is also the possibility of exceptional snow loads.

The value of the snow load depends on the building’s location and height above sea level.

EN 1991-1-4 is used to determine wind actions, which depend on altitude, distance from the sea and the surrounding terrain.

The determination of loads is covered in detail in a separate chapter of this guidance.

Loading due to services will vary greatly, depending on the use of the building. A typical service loading may be between 0,1 and 0,25 kN/m2 as measured on plan, depending on the use of the building. If air handling units or other significant equipment loading is to be supported, the service load should be calculated accurately.

1.4.2 Temperature effects

In theory, steel frames expand and contract with changes in temperature. Often, the temperature change of the steelwork itself is much lower than any change


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in the external temperature, because it is protected. It is generally accepted that the movement available when using bolts in clearance holes is sufficient to absorb any movement due to temperature.

It is recommended that expansion joints are avoided if possible, since these are expensive and can be difficult to detail correctly to maintain a weather-tight external envelope. In preference to providing expansion joints, the frame may be analysed including the design effects of a temperature change. The temperature actions may be determined from EN 1991-1-5, and combinations of actions verified in accordance with EN 1990. In most cases, the members will be found to be adequate.

Common practice for industrial buildings in Northern Europe, in the absence of calculations, is that expansion joints do not need to be provided unless the length of the building exceeds 150m. In warmer climates, common practice is to limit the length to around 80m. Although it is good practice to position the vertical bracing mid-way along the length of the structure, to allow free expansion at both ends of the structure, this is not always possible or desirable. Many orthodox industrial structures have bracing at each end, or at intervals along the length of the structure, with no expansion joints, and perform perfectly well.

1.4.3 Thermal performance and air-tightness

The thermal performance of single storey buildings and enclosures is increasingly important because of their large surface area. Thermal performance also includes prevention of excessive heat loss due to air infiltration, known as ‘air-tightness’.

There is a strong inter-relationship between the types of cladding and thermal performance. Modern steel cladding systems, such as composite panels, can achieve U-values of less than 0,2 W/(m2K).

Air-tightness is assessed based on full-scale tests after completion of the structure in which the internal volume is pressurised - generally to 50 Pa (this may vary in different countries). The volume of air that is lost is measured and must be less than a given figure – typically 10m3/m2 /hour.

1.4.4 Fire resistance

Fire resistance requirements are dependent on a wide range of issues, such as the combustible contents of the building, effective means of escape and occupation density (e.g. for public spaces). Generally, in single storey buildings, the means of escape is good and most enclosures are designed for fire resistance periods of 30 minutes or less. An exception may be office space attached to these buildings.

National regulations are often more concerned to limit fire spread to adjacent structures, rather than the performance of the particular structure, especially if the structure is an industrial building. The determining factor is often the distance to the adjacent boundary. If such regulations apply, the usual solution is to ensure the integrity of the elevation that is adjacent to the boundary. This is commonly ensured by providing cladding with fire resistance, and ensuring that the primary supporting structure remains stable – by protecting the


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steelwork on that elevation, and designing the elevation steelwork to resist the forces applied by any other parts of the structure that have collapsed.

For many building types, such as exhibition halls, fire engineering analysis may be carried to out demonstrate that active protection measures are effective in reducing fire temperatures to a level where the structure is able to resist the applied loads in the fire scenario without additional fire protection.

1.5 Sustainability Sustainable construction must address three goals:

• Environmental criteria

• Economic criteria

• Social criteria

These three criteria are met by construction in steel:

Environmental criteria

Steel is one of the most recovered and recycled materials. Some 84% is recycled with no loss of strength or quality, and 10% reused. Before demolishing a structure, extending a building’s life is generally more beneficial. This is facilitated by steel construction, since large column-free spaces give flexibility for change in use. Advances in the manufacturing of raw materials means that less water and energy is used in production, and allows for significant reductions in noise, particle and CO2 emissions.

Economic criteria

Steel construction brings together the various elements of a structure in an integrated design. The materials are manufactured, fabricated and constructed using efficient production processes. The use of material is highly optimised and waste virtually eliminated. The structures themselves are used for all aspects of modern life, including logistics, retail, commercial, and manufacturing, providing the infrastructure on which society depends. Steel construction provides low investment costs, optimum operational costs and outstanding flexibility of building use, with high quality, functionality, aesthetics and fast construction times.

Social criteria

The high proportion of offsite fabrication in steel buildings means that working conditions are safer, controlled and protected from the weather. A fixed location for employees helps to develop communities, family life and the skills. Steel releases no harmful substances into the environment, and steel buildings provide a robust, safe solution.

Single storey structures

The design of low-rise buildings is increasingly dependent on aspects of sustainability defined by criteria such as:

Efficient use of materials and responsible sourcing of materials

Elimination of waste in manufacturing and in construction processes


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Energy efficiency in building operation, including improved air-tightness

Measures to reduce water consumption

Improvement in indoor comfort

Overall management and planning criteria, such as public transport connections, aesthetics or preservation of ecological value.

Steel framed buildings can be designed to satisfy all these criteria. Some of the recognised sustainability benefits of steel are:

Steel structures are robust, with a long life. Properly detailed and maintained, steel structures can be used indefinitely

10% of structural steel sections are re-used[1]

Approximately 95% of structural steel sections are recycled

Steel products can potentially be dismantled and reused, particularly modular components or steel frames

Steel structures are lightweight, requiring smaller foundations than other materials

Steel is manufactured efficiently in factory controlled processes

All waste is recycled in manufacture and no steel waste is produced on site

Construction in steel maximises the opportunity and ease of extending buildings and change of use

High levels of thermal insulation can be provided in the building envelope

Prefabricated construction systems are rapidly installed and are much safer in terms of the construction processes.

Different sustainability assessment measures exist in various European countries[2].


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2 CASE STUDIES ON SINGLE STOREY BUILDINGS

The following case studies illustrate the use of steel in single storey buildings, such as show rooms, production facilities, supermarkets and similar buildings.

2.1 Manufacturing hall, Express Park, UK

Figure 2.1 Portal frame during construction

The portal frame shows in Figure 2.1 forms part of a new production facility for Homeseeker Homes, who manufacture portable homes for residential parks. The project comprises a 150 m long production hall, an adjacent office building and a separate materials storage building.

The production hall is a duo-pitch portal frame with a 35 m clear span and a height of 9 m to the underside of the haunch. The production hall has to accommodate four overhead gantry cranes, each with a safe working load of 5 t. Two cranes may be used in tandem, and the forces arising from this loading case had to be carefully considered. The longitudinal surge from the cranes is accommodated by bracing in the elevations, which also provides longitudinal stability. There are no expansion joints in the production hall – the bracing was designed to resist any loads from thermal expansion.

To control the lateral deflection at the level of the crane rail, the frames, at 6 m centres, are rather stiffer than an equivalent structure without cranes. The columns are 762 mm deep and the rafters 533 mm deep.

The gable frames are portal frames instead of a braced gable frame constructed from columns and simply-supported rafters, to reduce the differential deflection between the end frame and the penultimate frame.


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The facility is relatively close to the site boundary, which meant that the boundary elevations had to have special consideration. A fire load case was analysed and the column bases designed to resist the overturning moment from grossly deformed rafters. The cladding on the “boundary” elevations was also specified to prevent fire spread.

The 380 t of steelwork in the project was erected in six weeks.

2.2 Supermarket, Esch, Luxembourg

Figure 2.2 Supermarket in Esch , Luxembourg using curved cellular beams

Curved 20 m span cellular beams were used to provide an exposed steel structure in a supermarket in Esch, Luxembourg, as shown in Figure 2.2. The beams used HEB 450 sections that were cut and re-welded to form beams with 400 mm diameter openings. The curved cellular frames were placed 7,5 m apart and the columns were also 7,5 m high and are illustrated in Figure 2.3. The structure was designed using fire engineering principles to achieve an equivalent 90 minutes fire resistance without additional fire protection.


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Figure 2.3 Portal frame structure using curved cellular beams

2.3 Motorway Service station, Winchester, UK Cellular beams provide an attractive solution for long span public spaces, as in this motorway service restaurant in Winchester, UK, shown in Figure 2.4. The 600 mm deep doubly curved cellular beams spanned 18 m onto 1,2 m deep cellular primary beams that spanned 20 m between H section columns. The cellular beams also provided for service distribution above the kitchen area.

Figure 2.4 Double curved cellular beams and primary beams


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2.4 Airbus Industrie hanger, Toulouse, France The Airbus production hall in Toulouse covers 200000 m2 of floor space and is 45 m high with a span of 117 m. It consists of 8 m deep lattice trusses composed of H sections. Compound column sections provide stability to the roof structure. The building is shown in Figure 2.5 during construction. Sliding doors create a 117 m 32 m opening in the end of the building. Two parallel rolling cranes are installed each of 50 m span and 20 tonnes lifting capacity.

Figure 2.5 View of Airbus Industrie hanger during construction

2.5 Industrial hall, Krimpen aan den Ijssel, Netherlands This production hall is 85 m in length, 40 m wide and 24 m high with full height doors at the end of the building, as shown in Figure 2.6. The roof structure consists of an inclined truss. Because of the lack of bracing in the end walls, the structure was designed to be stabilised through the columns assisted by in-plane bracing in the roof and side walls.

Figure 2.6 View of doors being lifted into place in Hollandia’s building in Krimpen aan den Ijssel


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2.6 Distribution Centre and office, Barendrecht, Netherlands This 26000 m2 distribution centre for a major supermarket in the Netherlands comprises a conventional steel structure for the distribution area and a two storey high office area that is suspended above an access road, as shown in Figure 2.7. This 42 m long office building comprises a 12 m cantilever supported by a two storey high internal steel structure with diagonal bracing. The structure uses H section beams and columns with tubular bracing.

Both the warehouse and office buildings are provided with sprinklers to reduce the risk of fire, and the steelwork has intumescent coating so that it can be exposed internally. The warehouse internal temperature is 2°C and the steelwork of the office is thermally isolated from the warehouse part.

Figure 2.7 Distribution centre, Barendrecht, NL showing the braced cantilever office structure


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3 CONCEPT DESIGN OF PORTAL FRAMES

Steel portal frames are widely used because they combine structural efficiency with functional form. Various configurations of portal frame can be designed using the same structural concept as shown in Figure 3.1.

1 2

43

5

6

1 Duo-pitch portal frame 2 Curved portal frame (cellular beam) 3 Portal with internal offices 4 Portal with crane 5 Two-span portal frame 6 Portal with external offices

Figure 3.1 Various types of portal frame


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3.1 Pitched roof portal frame A single-span symmetrical portal frame (as illustrated in Figure 3.2) is typically of the following proportions:

A span between 15 m and 50 m (25 m to 35 m is the most efficient)

An eaves height (base to rafter centreline) of between 5 and 10 m (7,5 m is commonly adopted). The eaves height is determined by the specified clear height between the top of the floor and the underside of the haunch.

A roof pitch between 5 and 10 (6° is commonly adopted)

A frame spacing between 5 m and 8 m (the greater frame spacings being used in longer span portal frames)

Members are I sections rather than H sections, because they must carry significant bending moments and provide in-plane stiffness.

Sections are generally S235 or S275. Because deflections may be critical, the use of higher strength steel is rarely justified.

Haunches are provided in the rafters at the eaves to enhance the bending resistance of the rafter and to facilitate a bolted connection to the column.

Small haunches are provided at the apex, to facilitate the bolted connection

1

34

5

6

7

2

1 Eaves 2 Roof pitch 3 Apex 4 Rafter 5 Eaves haunch 6 Apex haunch 7 Column

Figure 3.2 Single-span symmetric portal frame

The eaves haunch is typically cut from the same size rolled section as the rafter, or one slightly larger, and is welded to the underside of the rafter. The length of the eaves haunch is generally 10% of the span. The length of the haunch means that the hogging bending moment at the “sharp” end of the haunch is approximately the same as the maximum sagging bending moment towards the apex, as shown in Figure 3.3.


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3

h

h

1

2

1 Moment at the “sharp” end of the haunch 2 Maximum sagging moment 3 Haunch length

Figure 3.3 Rafter bending moment and haunch length

The final frames of a portal frame are generally called gable frames. Gable frames may be identical to the internal frames, even though they experience lighter loads. If future extension to the building is envisaged, portal frames are commonly used as the gable frames, to reduce the impact of the structural works. A typical gable frame is shown in Figure 3.4.

4

3 5

1

2

1 Rafter 2 Column 3 Personnel door 4 Roller shutter door 5 Dado wall (brickwork)

Figure 3.4 Typical details of an end gable of a portal frame building


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Alternatively, gable frames can be constructed from columns and short rafters, simply supported between the columns as shown in Figure 3.5. In this case, gable bracing is required, as shown in the figure.

Figure 3.5 Gable frame (not a portal frame)

3.2 Frame stability In-plane stability is provided by frame continuity. In the longitudinal direction, stability is provided by vertical bracing in the elevations. The vertical bracing may be at both ends of the building, or in one bay only. Each frame is connected to the vertical bracing by a hot-rolled member at eaves level. A typical bracing arrangement is shown in Figure 3.6.

1

2

2

3

1 Vertical bracing in the gable 2 Vertical bracing in the walls 3 Roof bracing

Figure 3.6 Typical bracing in a portal frame

The gable columns span between the base and the rafter, where the reaction is carried by bracing in the plane of the roof, back to the eaves level, and to the foundations by the vertical bracing.


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If diagonal bracing in the elevations cannot be accommodated, longitudinal stability can be provided by a rigid frame on the elevation, as shown in Figure 3.7.

1

2

1 Eaves strut 2 Rigid frame

Figure 3.7 Rigid frame alternative to vertical bracing

3.3 Member stability Member stability should be checked using expressions 6.61 and 6.62 of EN 1993-1-1. For economic design, restraints to the rafter and column must be considered. The purlins and side rails are considered adequate to restrain the flange that they are attached to, but unless special measures are taken, the purlins and side rails do not restrain the inside flange. Restraint to the inside flange is commonly provided by bracing from the purlins and side rails, as shown in Figure 3.8. The bracing is usually formed of thin metal straps, designed to act in tension, or from angles designed in compression if bracing is only possible from one side.

If the bracing shown in Figure 3.8 is not permitted by national regulations, restraint may be provided by a system of hot-rolled members.

This form of bracing will be required whenever the inside flange is in compression. This situation arises:

On the inside of the column and the inside of the rafter in the haunch region, in the gravity load combination

Towards the apex of the rafter, in the uplift combination.


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1

2

1 Restraint to inside flange 2 Purlin or side rail

Figure 3.8 Typical bracing to the inside flange

The arrangement of restraints to the inside flange is generally similar to that shown in Figure 3.9. In some instances, it may not be possible to restrain the inside of the column flange. In these circumstances, a larger column section may have to be chosen, which is stable between the underside of the haunch and the base.

1

1

1 Restraint to inside flange of rafter and column

Figure 3.9 General arrangement of restraints to the inside flange

In all cases, the junction of the inside face of the column and the underside of the haunch, as shown in Figure 3.10, must be restrained. The restraint may be of the form shown in Figure 3.8, or may be by a hot-rolled member provided for that purpose.

1

1 Restraint position

Figure 3.10 Restraint at the haunch / column junction


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3.4 Preliminary Design 3.4.1 Main frames

Although efficient portal frame analysis and design will use bespoke software, preliminary design is simple. In most circumstances, a reasonable estimate of the maximum bending moments will be obtained by considering only the vertical loads. Combinations of actions including wind actions must be validated in the final design, and may be important for preliminary design if the wind actions are onerous (e.g. near the sea, or if the portal frame is tall).

Based on the vertical load alone, charts that provide initial sizes are given in Section 8.

As an alternative to the sizes given in Section 8, the bending moment at the eaves and apex can be calculated based on an elastic analysis.

L

SM

I

I I

I

f

h

M

W

WL32

E

C

RR

C

2A

/ m

Figure 3.11 Details of a pinned base portal frame

For the pinned base frame shown in Figure 3.11, the bending moment at the eaves, ME and at the apex MA can be calculated as follows:

N

mwLM

16

532

E

and E

2

A 8Mm

wLM

where:

N = B + mC

C = 1 + 2m

B = 2(k + 1) + m

m = 1 +

= hf

s

h

I

Ik

C

R


2 - 26

It may be assumed for preliminary design that IC = 1,5 IR

Given the bending moments around the frame, the rafter should be chosen so that the moment resistance exceeds both the moment at the “sharp” end of the haunch and the maximum sagging moment (a little larger than the moment at the apex).

3.4.2 Gable columns

Gable columns are generally designed as simply supported from base to rafter. The primary loads are the wind actions. The internal pressure or suction will contribute to the loading on the gable column. Often, the critical design case will be pressure inside the building and suction on the outside, when the inside flange of the gable post is unrestrained. If national regulations allow, a restraint to the inside flange may be provided from a sheeting rail to increase the buckling resistance.

3.4.3 Bracing

At the preliminary design stage, it is convenient to calculate the overall longitudinal load on the structure. This shear must be the horizontal component of the load carried by the vertical bracing. The most heavily loaded roof bracing will be the member nearest the eaves. The longitudinal eaves member carries the load from the roof bracing to the vertical bracing. Bracing members may be hollow sections, angle sections or flat steel. Flat steel is assumed to resist tension forces only.


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3.5 Connections 3.5.1 Eaves connection

A typical eaves connection is shown in Figure 3.12. In almost all cases a compression stiffener in the column (as shown, at the bottom of the haunch) will be required. Other stiffeners may be required to increase the bending resistance of the column flange, adjacent to the tension bolts, and to increase the shear resistance of the column web panel. The haunch is generally fabricated from a similar size beam to the rafter (or larger), or fabricated from equivalent plate. Typically, the bolts may be M24 8.8 and the end plate 25 mm thick S275.

2

1

1 Haunch 2 Compression stiffener

Figure 3.12 Typical eaves connection

3.5.2 Apex connection

A typical apex connection is shown in Figure 3.13. The apex connection primarily serves to increase the depth of the member to make a satisfactory bolted connection. The apex haunch is usually fabricated from the same member as the rafter, or from equivalent plate. Typically, the bolts may be M24 8.8 and the end plate 25 mm thick S275.

Figure 3.13 Typical apex connection


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3.5.3 Bases

A typical pinned base is shown in Figure 3.14. The base plate is generally at least as thick as the flange of the column. Most authorities accept that even with four holding down bolts as shown in Figure 3.14, the base is still pinned. Alternatively, the base may have only two holding down bolts, on the axis of the column, but this may make the erection of the steelwork more difficult.

Columns are normally located on a number of steel packs, to ensure the steelwork is at the correct level, and the gap between the foundation and the steelwork filled with cementicious grout. Large bases should be provided with an air hole to facilitate complete grouting.

Holding down bolts are generally embedded in the foundation, with some freedom of lateral movement (tubes or cones) so that the steelwork can be aligned precisely. The holes in the base plate are usually 6 mm larger than the bolt diameter, to facilitate some lateral alignment.

~

5

4

3

2

1

1 Holding down bolts 2 Base plate 3 Grout 4 Tube (or cone) 5 Anchor plate

Figure 3.14 Typical portal base detail

3.5.4 Bracing Connections

Forces in portal frame bracing are generally modest. Typical connections are shown in Figure 3.15. Gusset plates should be supported on two edges, if possible.


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Figure 3.15 Typical bracing connections

3.6 Other types of portal frame The features of an orthodox portal frame were described in Sections 3.1 to 3.5. The basic structural concept can be modified in a number of ways to produce a cost effective solution, as illustrated below.

3.6.1 Portal frame with a mezzanine floor

1

1 Mezzanine

Figure 3.16 Portal frame with internal mezzanine floor

Office accommodation is often provided within a portal frame structure using a mezzanine floor (as illustrated in Figure 3.17). The mezzanine floor may be partial or full width. It can be designed to stabilise the frame. Often, the internal floor of the office space requires fire protection.


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Figure 3.17 Portal frame with intermediate floor

3.6.2 Portal frame with external mezzanine

1

1 Mezzanine

Figure 3.18 Portal frame with external mezzanine

Offices may be located externally to the portal frame which creates an asymmetric portal structure (as illustrated in Figure 3.18). The main advantage of this framework is that large columns and haunches do not obstruct the office space. Generally, this additional structure depends on the portal frame for its stability (the members often have nominally pinned connections to the main frame) and the members can be relatively lightweight.


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3.6.3 Portal frame with overhead crane

Figure 3.19 Crane portal frame with column brackets

For cranes of relatively low capacity (up to say 20 tonnes), portal frames can be used to support the crane beam and rail, as illustrated in Figure 3.19. The outward movement (spread) of the frame at the level of the crane rail is likely to be of critical importance. Use of a horizontal tie member or fixed column bases may be necessary to reduce this spread.

For larger cranes, a structure with a roof truss will be appropriate (see Section 4) as the column spread is minimised. For very heavy loads, built-up columns are appropriate, as introduced in Section 6. Detail design guides cover both the design of trusses[3] and the design of built-up columns[4].

3.6.4 Tied portal frame

1

2

1 Tie 2 Hangers (required for longer spans)

Figure 3.20 Tied portal frame

In a tied portal frame, as illustrated in Figure 3.20, the spread of the eaves and the bending moments in the frame are greatly reduced. Large compression forces will develop in the rafters, which reduce the stability of the members. Second-order software must be used for the design of tied portals.


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3.6.5 Mansard or curved portal frames

Figure 3.21 Mansard portal frame

A mansard portal frame consists of a series of rafters and haunches, as illustrated in Figure 3.21, which creates a pseudo-curved frame. The connections between the members may also have small haunches to facilitate the bolted connections.

Curved rafter portals as illustrated in Figure 3.22 are often used for architectural applications. The rafter can be curved to a radius by cold bending. For spans greater than approximately 18 m, splices may be required in the rafter because of limitations of transport.

Alternatively, a curved external roof must be produced by varying the lengths of purlin brackets supported on a rafter fabricated as a series of straight elements, as shown in Figure 3.23.

Figure 3.22 Curved beams used in a portal frame


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Figure 3.23 Quasi- curved portal frame

3.6.6 Multi bay portal frame

Multi-bay portal frames may be designed by using intermediate columns, as shown in Figure 3.24. If the number of internal columns must be minimised it is possible to remove every second internal column, or to only leave one internal column every third frame. Where the internal column is removed, a deep beam (often known as a “valley” beam) is designed to span between the remaining columns. Continuity of the rafters is achieved by using a haunch connection to the valley beam, as shown in Figure 3.25.

Figure 3.24 Multi-bay portal frame


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12

1 Valley beam 2 Rafter

Figure 3.25 Connection to valley beam


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4 CONCEPT DESIGN OF TRUSS BUILDINGS

4.1 Introduction Many forms of truss are possible. Some of the common types of truss for single storey buildings are shown in Figure 4.1.

Trusses are used for long spans, and particularly when significant loads must be carried by the roof structure, as the vertical deflection can be controlled by varying the member sizes.

For industrial buildings, the W-truss N-truss and duo-pitch truss are common. The Fink truss is generally used for smaller spans. Comparing the W-truss and N-truss:

The W-truss has more open space between the internal members

The internal members of the W-truss may be larger, because a long diagonal member must carry compression – the compression members in the N-truss are short.

1 2

3 4

5 1 W-truss 2 N-truss 3 Duo-pitch truss 4 Fink truss 5 Curved truss

Figure 4.1 Various forms of lattice truss used in industrial buildings


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4.2 Truss members Unless there are special architectural requirements, truss members are chosen to produce a simple connection between the chords and the internal members. Common combinations as shown in Figure 4.2 are:

Tees used as chords, with angles used as web members. The angles may be welded or bolted to the stem of the Tee.

Double angle members as chords, and single (or double) angles as internal members. The connections are made with a gusset plate welded between the angles forming the chords.

Rolled sections as chords, with the web in the plane of the truss. The internal members are usually angle members, connected via a gusset plate welded to the chord.

Rolled sections as chords, but with the web perpendicular to the plane of the truss. The connections to the chord members may be via gusset plates welded to the web, although the connections will need careful detailing. A simple, effective alternative is to choose chords that have the same overall depth, and connect the internal members to the outside of both flanges, generally by welding.

For heavily loaded trusses, rolled I or H sections, or channel sections may be used as the internal members. In such a large truss, developing economic connections will be important and both the members and internal members should be chosen with this in mind.

The detailed design of trusses is covered in Single-storey steel buildings. Part5: Detailed design of trusses[3].


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1

2

3

4

3

3

1 Tee section 2 Angle members 3 Gusset plate 4 Double angle chord

Figure 4.2 Typical truss members

A truss fabricated from rolled sections is illustrated in Figure 4.3.


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Figure 4.3 Truss fabricated from rolled sections

4.3 Frame stability In most cases, frame stability is provided by bracing in both orthogonal directions, and the truss is simply pinned to the supporting columns. To realise a pinned connection, one of the chord members is redundant, as shown in Figure 4.4, and the connection of that redundant member to the column is usually allowed to slip in the direction of the axis of the chord.

1

1 Redundant member

Figure 4.4 Redundant member in a simply supported truss

In the longitudinal direction, stability is usually provided by vertical bracing.


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4.4 Preliminary design At the preliminary design stage, the following process is recommended:

1. Determine the loading on the truss. See Section 1.4.1. At the preliminary design stage it is sufficient to convert all loads, including self weight, to point loads applied at the nodes and assume that the entire truss is pin-jointed. This assumption is also generally adequate for final design. As an alternative, the roof loads may be applied at the purlin positions and the chords assumed to be continuous over pinned internal members, but the precision is rarely justified.

2. Determine a truss depth and layout of internal members. A typical span : depth ratio is approximately 20 for both W- and N-trusses. Internal members are most efficient between 40° and 50°.

3. Determine the forces in the chords and internal members, assuming the truss is pin-jointed throughout. This can be done using software, or by simple manual methods of resolving forces at joints or by taking moments about a pin, as shown in Figure 4.5.

d

d

d

p

p

p

V

V

V

V

L

L

L

L

x

x

Resolving forces at joints

VL

A B C

DC

1p

Taking moments around node D determines the force CB

Figure 4.5 Calculation of forces in a pin-jointed truss

A very simple approach is to calculate the maximum bending moment in the truss assuming that it behaves as a beam, and divide this moment by the distance between chords to determine the axial force in the chord.

4. Select the compression chord member. The buckling resistance is based on the length between node points for in-plane buckling. The out-of-plane


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buckling is based on the length between out-of-plane restraints – usually the roof purlins or other members.

5. Select the tension chord member. The critical design case is likely to be an uplift case, when the lower chord is in compression. The out-of-plane buckling is likely to be critical. It is common to provide a dedicated system of bracing at the level of the bottom chord, to provide restraint in the reversal load combination. This additional bracing is not provided at every node of the truss, but as required to balance the tension resistance with the compression resistance.

6. Choose internal members, whilst ensuring the connections are not complicated.

7. Check truss deflections.

4.5 Rigid frame trusses The structures described in Sections 4.1 and 4.4 are stabilised by bracing in each orthogonal direction. It is possible to stabilise the frames in-plane, by making the truss continuous with the columns. Both chords are fixed to the columns (i.e. no slip connection). The connections within the truss and to the columns may be pinned. The frame becomes similar to a portal frame. For this form of frame, the analysis is generally completed using software. Particular attention must be paid to column design, because the in-plane buckling length is usually much larger than the physical length of the member.

4.6 Connections Truss connections are either bolted or welded to the chord members, either directly to the chord, or via gusset plates, as shown in Figure 4.6.

3

Figure 4.6 Truss connections

Trusses will generally be prefabricated in the workshop, and splices maybe required on site. In addition to splices in the chords, the internal member at the splice position will also require a site connection. Splices may be detailed with cover plates, or as “end plate” type connections, as shown in Figure 4.7.


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Figure 4.7 Splice details

Ordinary bolts (non-preloaded) in clearance holes may give rise to some slip in the connection. If this slip is accumulated over a large number of connections, the defection of the truss may be larger than calculated. If deflection is a critical consideration, then friction grip assemblies or welded details should be used.


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5 SIMPLE BEAM STRUCTURES

For modest spans, (up to approximately 20 m) a simple beam and column structure can be provided, as illustrated in Figure 5.1. The roof beam is a single rolled section, with nominally pinned connections to the columns. The roof beam may be straight, precambered, perforated or curved. The roof may be horizontal, or more commonly with a modest slope to assist drainage. Ponding of water on the roof should be avoided with a slope, or precambered beam.

Figure 5.1 Simple beam and column frame

Frame stability for this form of structure is provided by bracing in each orthogonal direction. The beam is designed as simply supported, and the columns as simple struts, with a nominal moment applied by the beam connection. It is common to assume that the shear force from the beam is applied 100 mm from the face of the column.


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6 BUILT-UP COLUMNS

Heavily loaded columns, or columns in tall industrial buildings may be in the form of built-up sections. Built-up columns often comprise HE or UPE sections in which battens (flat plate) or lacing (usually angles) are welded across the flanges, as shown in Figure 6.1.

Built-up columns are not used in portal frames, but are often used in buildings supporting heavy cranes. The roof of the structure may be duo-pitch rafters, but is more commonly a truss, as illustrated in Figure 1.4.

Figure 6.1 Cross-sections of built-up columns

To support the roof above the level of the crane, a single member may project for several meters. This is often known as a “bayonet” column. The projecting member may be a continuation of one of the two primary sections in the built-up section, or may be a separate section located centrally to the built-up section. Examples of built-up columns are shown in Figure 6.2. Buildings that use built-up columns are invariably heavily loaded, and commonly subjected to moving loads from cranes. Such buildings are heavily braced in two orthogonal directions.

The detailed design of built-up columns is covered in Single-storey steel buildings. Part 6: Detailed design of built-up columns[4] of this guide.


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Laced column Battened column Column withcrane girder

Figure 6.2 Examples of built-up columns in single storey buildings


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7 CLADDING

There are a number of generic types of cladding that may be used in single storey buildings, depending on the building use. These fall into four broad categories, which are described in the following sections.

7.1 Single-skin trapezoidal sheeting Single-skin sheeting is widely used in agricultural and industrial structures where no insulation is required. It can generally be used on roof slopes as low as 4° providing the laps and sealants are as recommended by the manufacturers for shallow slopes. The sheeting is fixed directly to the purlins and side rails, as illustrated in Figure 7.1 and provides positive restraint. In some cases, insulation is suspended directly beneath the sheeting.

Figure 7.1 Single-skin trapezoidal sheeting

7.2 Double-skin system Double skin or built-up roof systems usually use a steel liner tray that is fastened to the purlins, followed by a spacing system (plastic ferrule and spacer or rail and bracket spacer), insulation and the outer profiled sheeting. Because the connection between the outer and inner sheets may not be sufficiently stiff, the liner tray and fixings must be chosen so that they alone will provide the required level of restraint to the purlins. This form of construction using plastic ferrules is shown in Figure 7.2.

As insulation depths have increased, there has been a move towards “rail and bracket” solutions as they provide greater lateral restraint to the purlins. This system is illustrated in Figure 7.3.

With adequate sealing of joints, the liner trays may be used to form an airtight boundary. Alternatively, an impermeable membrane on top of the liner tray should be provided.


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24

3

1

5

1 Outer sheeting 2 Z spacer 3 Insulation 4 Liner tray (inner sheet) 5 Plastic ferrule

Figure 7.2 Double-skin construction using plastic ferrule and Z spacers

4

2

3

5

1

1 Outer sheet 2 Insulation 3 Rail 4 Liner tray (inner sheet) 5 Bracket

Figure 7.3 Double-skin construction using ‘rail and bracket’ spacers


2 - 47

7.3 Standing seam sheeting Standing seam sheeting has concealed fixings and can be fixed in lengths of up to 30 m. The advantages are that there are no penetrations directly through the sheeting that could lead to water leakage and fixing of the roof sheeting is rapid. The fastenings are in the form of clips that hold the sheeting down but allow it to move longitudinally (see Figure 7.4). The disadvantage of this system is that less restraint is provided to the purlins than with a conventionally fixed system. Nevertheless, a correctly fixed liner tray should provide adequate restraint.

3

1

2

1 Outer sheet 2 Insulation 3 Standing seam clip

Figure 7.4 Standing seam panels with liner trays

7.4 Composite or sandwich panels Composite or sandwich panels are formed by creating a foam insulation layer between the outer and inner layer of sheeting. Composite panels have good spanning capabilities due to composite action of the core with the steel sheets. Both standing seam (see Figure 7.4) and direct fixing systems are available. These will clearly provide widely differing levels of restraint to the purlins. The manufacturers should be consulted for more information.

7.5 Fire design of walls Where buildings are close to a site boundary, most national Building Regulations require that the wall is designed to prevent spread of fire to adjacent property. Fire tests have shown that a number of types of panel can perform adequately, provided that they remain fixed to the structure. Further guidance should be sought from the manufacturers.


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Some manufacturers provide slotted holes in the side rail connections to allow for thermal expansion. In order to ensure that this does not compromise the stability of the column by removing the restraint under normal conditions, the slotted holes are fitted with washers made from a material that will melt at high temperatures and allow the side rail to move relative to the column under fire conditions only. Details of this type of system are illustrated in Figure 7.5.

3

1

2

1 Side rail 2 Slotted hole for expansion 3 Cleat

Figure 7.5 Typical fire wall details showing slotted holes for expansion in fire


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8 PRELIMINARY DESIGN OF PORTAL FRAMES

8.1 Introduction The following methods of determining the size of columns and rafters of single-span portal frames may be used at the preliminary design stage. Further detailed calculations will be required at the final design stage. It should be noted that the method does not take account of:

Requirements for overall stability

Deflections at the Serviceability Limit State.

8.2 Estimation of member sizes The guidance for portal frames is valid in the span range between 15 to 40 m. and is presented in Table 8.1. The assumptions made in creating this table are as follows:

The roof pitch is 6.

The steel grade is S235. If design is controlled by serviceability conditions, the use of smaller sections in higher grades may not be an advantage. When deflections are not a concern, for example when the structure is completely clad in metal cladding, the use of higher grades may be appropriate.

The rafter load is the total factored permanent actions (including self weight) and factored variable actions and is in the range of 8 to 16 kN/m.

Frames are spaced at 5 to 7,5 m.

The haunch length is 10% of the span of the frame.

A column is treated as restrained when torsional restraints can be provided along its length (these columns are therefore lighter than the equivalent unrestrained columns).

A column should be considered as unrestrained when it is not possible to restrain the inside flange.

The member sizes given by the tables are suitable for rapid preliminary design. However, where strict deflection limits are specified, it may be necessary to increase the member sizes.

In all cases, a full design must be undertaken and members verified in accordance with EN 1993-1-1.

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Part 2: C

oncept Design

Table 8.1 Member sizes for single-span portal frame with 6° roof pitch

Span of frame (m) Rafter load (kN/m)

Eaves height(m) 15 20 25 30 35 40

Rafter 8 8 8

6 8

10

IPE 240 IPE 240 IPE 240

IPE 330 IPE 330 IPE 330

IPE 360 IPE 360 IPE 360

IPE 400 IPE 400 IPE 400

IPE 450 IPE 450 IPE 450

IPE 450 IPE 450 IPE 450

Restrained column

8 8 8

6 8

10

IPE 300 IPE 300 IPE 300

IPE 360 IPE 360 IPE 400

IPE 450 IPE 450 IPE 450

IPE 550 IPE 550 IPE 550

IPE 550 IPE 600 IPE 600

IPE 600 IPE 600

IPE 750 137

Unrestrained column

8 8 8

6 8

10

IPE 360 IPE 450 IPE 450

IPE 450 IPE 550 IPE 550

IPE 550 IPE 600 IPE 600

IPE 550 IPE 600

IPE 750 137

IPE 0 600 IPE 750 137 IPE 750 173

IPE 750 137 IPE 750 173

HE 800

Rafter 10 10 10

6 8

10

IPE 270 IPE 270 IPE 270

IPE 330 IPE 330 IPE 360

IPE 400 IPE 400 IPE 400

IPE 450 IPE 450 IPE 450

IPE 0 450 IPE 0 450 IPE 0 450

IPE 550 IPE 550 IPE 550

Restrained column

10 10 10

6 8

10

IPE 360 IPE 360 IPE 360

IPE 450 IPE 450 IPE 450

IPE 450 IPE 550 IPE 550

IPE 550 IPE 550 IPE 600

IPE 600 IPE 600 IPE 600

IPE 750 137 IPE 750 137 IPE 750 173

Unrestrained column

10 10 10

6 8

10

IPE 400 IPE 450 IPE 450

IPE 450 IPE 550 IPE 600

IPE 550 IPE 600

IPE 750 137

IPE 600 IPE 750 137 IPE 750 173

IPE 750 137 IPE 750 173

HE 800

IPE 750 137 HE 800 HE 800

Rafter 12 12 12

6 8

10

IPE 270 IPE 270 IPE 270

IPE 360 IPE 360 IPE 60

IPE 400 IPE 400 IPE 400

IPE 450 IPE 450 IPE 450

IPE 550 IPE 550 IPE 550

IPE 550 IPE 550 IPE 600

Restrained column

12 12 12

6 8

10

IPE 360 IPE 360 IPE 360

IPE 450 IPE 450 IPE 450

IPE 550 IPE 550 IPE 550

IPE 600 IPE 600 IPE 600

IPE 750 137 IPE 750 137 IPE 750 137

IPE 750 173 IPE 750 173 IPE 750 173

Unrestrained column

12 12 12

6 8

10

IPE 450 IPE 450 IPE 550

IPE 550 IPE 600 IPE 600

IPE 600 IPE 600

IPE 750 173

IPE 600 IPE 750 173

HE 800

IPE 750 137 HE 800 HE 800

IPE 750 173 HE 800 HE 900

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Part 2: C

oncept Design

Table 8.1 (Continued) Single-span portal frame with 6° roof pitch

Span of frame (m)

Rafter load (kN/m)

Eaves height(m) 15 20 25 30 35 40

Rafter 14 14 14

6 8

10

IPE 330 IPE 330 IPE 330

IPE 400 IPE 400 IPE 400

IPE 450 IPE 450 IPE 450

IPE 450 IPE 450 IPE 450

IPE 550 IPE 550 IPE 550

IPE 600 IPE 600 IPE 600

Restrained column

14 14 14

6 8

10

IPE 360 IPE 400 IPE 400

IPE 450 IPE 450 IPE 450

IPE 550 IPE 550 IPE 600

IPE 600 IPE 600

IPE 750 137

IPE 750 173 IPE 750 173 IPE 750 173

IPE 750 173 HE 800 HE 800

Unrestrained column

14 14 14

6 8

10

IPE 450 IPE 550 IPE 550

IPE 550 IPE 600

IPE 750 137

IPE 600 IPE 750 137 IPE 750 173

IPE 750 137 IPE 750 173

HE 800

IPE 750 173 HE 800 HE 800

HE 800 HE 800 HE 900

Rafter 16 16 16

6 8

10

IPE 330 IPE 330 IPE 330

IPE 400 IPE 400 IPE 400

IPE 450 IPE 450 IPE 450

IPE 550 IPE 550 IPE 50

IPE 550 IPE 600 IPE 600

IPE 600 IPE 600 IPE 600

Restrained column

16 16 16

6 8

10

IPE 400 IPE 400 IPE 450

IPE 550 IPE 550 IPE 550

IPE 600 IPE 600 IPE 600

IPE 750 137 IPE 750 137 IPE 750 137

IPE 750 173 IPE 750 173

HE 800

HE 800 HE 800 HE 800

Unrestrained column

16 16 16

6 8

10

IPE 450 IPE 550 IPE 600

IPE 550 IPE 600

IPE 750 137

IPE 600 IPE 750 173

HE 800

IPE 750 137 HE 800 HE 800

IPE 750 173 HE 800 HE 900

HE 800 HE 900 HE 900


2 - 52

REFERENCES

1 SANSOM, M. and MEIJER, J.

Life-cycle assessment (LCA) for steel construction European commission, 2002

2 Several assessement methods are used. For example:

BREEAM in the UK

HQE in France

DNGB in Germany

BREEAM-NL, Greencalc+ and BPR Gebouw in the Netherlands

Valideo in Belgium

Casa Clima in Trento Alto Adige, Italy (each region has its own approach)

LEED, used in various countries

3 Steel Buildings in Europe Single-storey steel buildings. Part 5: Design of trusses

4 Steel Buildings in Europe Single-storey steel buildings. Part 6: Design of built-up columns



Part 3: Actions


Part 3: Actions

3 - ii

Part 3: Actions

3 - iii

FOREWORD

This publication is part three of a design guide, Single-Storey Steel Buildings.




Part 3: Actions












Part 3: Actions

3 - iv

Part 3: Actions

3 - v

Contents Page No

FOREWORD iii

SUMMARY vi

1 INTRODUCTION 1

2 SAFETY PHILOSOPHY ACCORDING TO EN 1990 2 2.1 General format of the verifications 2 2.2 Ultimate limit states and serviceability limit states 2 2.3 Characteristic values and design values of actions 3

3 COMBINATIONS OF ACTIONS 4 3.1 General 4 3.2 ULS combinations 4 3.3 SLS combinations 6

4 PERMANENT ACTIONS 8

5 CONSTRUCTION LOADS 9

6 IMPOSED LOADS 10 6.1 General 10 6.2 Actions induced by cranes according to EN 1991-3 10 6.3 Horizontal loads on parapets 15

7 SNOW LOADS 16 7.1 General 16 7.2 Methodology 16

8 WIND ACTIONS 22 8.1 General 22 8.2 Methodology 22 8.3 Flowcharts 31

9 EFFECT OF TEMPERATURE 32

REFERENCES 33

Appendix A Worked Example: Snow load applied on a single-storey building 35

Appendix B Worked Example: Wind action on a single-storey building 45

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SUMMARY

This document provides guidelines for the determination of the actions on a single-storey building according to EN 1990 and EN 1991. After a short description of the general format for limit state design, this guide provides information on the determination of the permanent loads, the variable actions and the combinations of actions. The determination of the snow loads and the calculation of the wind action are described and summarized in comprehensive flowcharts. Simple worked examples on the snow loads and the wind action are also included.

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1 INTRODUCTION

This guide provides essential information on the determination of the design actions on a single-storey building. It describes the basis of design with reference to the limit state concept in conjunction with the partial factor method, according to the following parts of the Eurocodes:

EN 1990: Basis of structural design[1].

EN 1991: Actions on structures

- Part 1-1: General actions – Densities, self-weight, imposed loads for buildings[2].

- Part 1-3: General actions – Snow loads[3]

- Part 1-4: General actions – Wind actions[4]

- Part 1-5: General actions – Thermal actions[5]

- Part 3: Actions induced by cranes and machinery.[6]

The guide is a comprehensive presentation of the design rules applied to single-storey buildings with reference to the appropriate clauses, tables and graphs of the Eurocodes.

Additional information can be found in the references [7][8].

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2 SAFETY PHILOSOPHY ACCORDING TO EN 1990

2.1 General format of the verifications A distinction is made between ultimate limit states (ULS) and serviceability limit states (SLS).

The ultimate limit states are related to the following design situations:

Persistent design situations (conditions of normal use)

Transient design situations (temporary conditions applicable to the structure, e.g. during execution, repair, etc.)

Accidental design situations (exceptional conditions applicable to the structure)

Seismic design situations (conditions applicable to the structure when subjected to seismic events). These events are dealt within EN 1998[9], and are outside the scope of this guide.

The serviceability limit states concern the functioning of the structure under normal use, the comfort of people and the appearance of the construction.

The verifications shall be carried out for all relevant design situations and load cases.

2.2 Ultimate limit states and serviceability limit states 2.2.1 Ultimate limit states (ULS)

The states classified as ultimate limit states are those that concern the safety of people and /or the safety of the structure. The structure shall be verified at ULS when there is:

Loss of equilibrium of the structure or any part of it (EQU)

Failure by excessive deformation, rupture, loss of stability of the structure or any part of it (STR)

Failure or excessive deformation of the ground (GEO)

Failure caused by fatigue or other time-dependent effects (FAT).

2.2.2 Serviceability Limit States (SLS)

The structure shall be verified at SLS when there is:

Deformations that affect the appearance, the comfort of users or the functioning of the structure

Vibrations that cause discomfort to people or that limit the functional effectiveness of the structure

Damage that is likely to adversely affect the appearance, the durability or the functioning of the structure.

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2.3 Characteristic values and design values of actions

2.3.1 General

Actions shall be classified by their variation in time as follows:

Permanent actions (G), e.g. self-weight of structures, fixed equipment, etc.

Variable actions (Q), e.g. imposed loads, wind actions, snow loads, etc.

Accidental actions (A), e.g. explosions, impact from vehicles, etc.

Certain actions may be considered as either accidental and/or variable actions, e.g. seismic actions, snow loads, wind actions with some design situations.

2.3.2 Characteristic values of actions

The characteristic value (Fk) of an action is its principal representative value. As it can be defined on statistical bases, it is chosen so as to correspond to a prescribed probability of not exceeding on the unfavourable side, during a ‘reference period’ taking into account the design working life of the structure.

These characteristic values are specified in the various Parts of EN 1991.

2.3.3 Design values of actions

The design value Fd of an action F can be expressed in general terms as:

Fd = f Fk

where:

Fk is the characteristic value of the action

f is a partial factor for the action

is either 1,00, 0, 1 or 2

2.3.4 Partial factors

Partial factors are used to verify the structures at ULS and SLS. They should be obtained from EN 1990 Annex A1, or from EN 1991 or from the relevant National Annex.

2.3.5 factors

In the combinations of actions, factors apply to variable actions in order to take into account the reduced probability of simultaneous occurrence of their characteristic values.

The recommended values for factors for buildings should be obtained from EN 1990 Annex A1 Table A1.1, or from EN 1991 or from the relevant National Annex.

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3 COMBINATIONS OF ACTIONS

3.1 General The individual actions should be combined so as not to exceed the limit state for the relevant design situations.

Actions that cannot occur simultaneously, e.g. due to physical reasons, should not be considered together in a same combination.

Depending on its uses and the form and the location of a building, the combinations of actions may be based on not more than two variable actions – See Note 1 in EN 1990 § A1.2.1(1). The National Annex may provide additional information.

3.2 ULS combinations 3.2.1 Static equilibrium

To verify a limit state of static equilibrium of the structure (EQU), it shall be ensured that:

Ed,dst ≤ Ed,stb

where:

Ed,dst is the design value of the effect of destabilising actions

Ed,stb is the design value of the effect of stabilising actions

3.2.2 Rupture or excessive deformation of an element

To verify a limit state of rupture or excessive deformation of a section, member or connection (STR and/or GEO), it shall be ensured that:

Ed ≤ Rd

where:

Ed is the design value of the effect of actions

Rd is the design value of the corresponding resistance

Each combination of actions should include a leading variable action or an accidental action.

3.2.3 Combinations of actions for persistent or transient design situations

According to EN 1990 § 6.4.3.2(3), the combinations of actions can be derived either from expression (6.10) or from expressions (6.10a and 6.10b – whichever is more onerous). The choice between these two sets of expressions may be imposed by the National Annex.

In general, expression (6.10) is conservative in comparison to the pair of expressions (6.10a and 6.10b), but it leads to a reduced number of combinations to consider.

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Permanent

actions

Leading variable action

Accompanying variable actions

Ed = 1

jk,jG,j

G + k,1Q,1Q + 1

ik,i0,iQ,i

Q (6.10)

Ed = 1

jk,jG,j

G + k,1Q,10,1 Q + 1

ik,i0,iQ,i

Q (6.10a)

Ed = 1

jk,jG,j

G + k,1Q,1Q + 1

ik,i0,iQ,i

Q (6.10b)

Gk and Qk are found in EN 1991 or its National Annex.

G and Q are found in Table A1.2(A) for static equilibrium (EQU); Tables A1.2(B) and A1.2(C) for rupture (STR and/or GEO) of EN 1990 or in the National Annex. Table 3.1 gives the recommended values of the partial factors.

Table 3.1 Recommended values of partial factors

Table (EN 1990)

Limit state Gj,inf Gj,sup Q,1 = Q,I Q,1 = Q,I

A1.2(A) EQU 0,90 1,10 1,50 1,50

A1.2(B) STR/GEO 1,00 1,35 1,50 1,50

A1.2(C) STR/GEO 1,00 1,00 1,30 1,30

0 factors are found in EN 1990 Table A1.1 or in its National Annex. This factor varies between 0,5 and 1 except for roofs of category H (0 = 0).

ξ is a reduction factor for permanent loads. According to EN 1990 Table A1.2(B), the recommended value for buildings is ξ = 0,85. The National Annex may specify a different value.

For example, according to expression 6.10:

1. With snow as the leading variable action:

Ed = 1,35 G + 1,5 S + (1,5 0,6) W = 1,35 G + 1,5 S + 0,9 W

2. With wind as the leading variable action:

Ed = 1,35 G + 1,5 W + (1,5 0,5) S = 1,35 G + 1,5 W + 0,75 S

3.2.4 Combinations of actions for accidental design situations

Combinations of actions for accidental design situations should either involve an explicit accidental action or refer to a situation after an accident event.

Permanent

actions

Accidental action

Leading variable

action


Ed = 1

jk,j

G + Ad +( 1,1 or 2,1 )

k,1Q +

1ik,i0,iQ,

i

Q

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The choice between 1,1Qk,1 or 2,1Qk,1 should be related to the relevant accidental design situation. Guidance is given in EN 1990 or in the National Annex to EN 1990.

3.3 SLS combinations 3.3.1 Serviceability Limit State

To verify a serviceability limit state, it shall be ensured that:

Ed ≤ Cd

where:

Ed is the design value of the effects of actions specified in the serviceability criterion,

Cd is the limiting design value of the relevant serviceability criterion.

3.3.2 Characteristic combination

The characteristic combination is normally used for irreversible limit states.

Permanent

actions



Ed = 1

jk,j

G + k,1Q + 1

ik,i0,i

Q

For example:

Ed = G + S + 0,6 W

Ed = G + W + 0,5 S

3.3.3 Frequent combination

The frequent combination is normally used for reversible limit states.

Permanent

actions



Ed = 1

jk,j

G + k,11,1Q + 1

ik,i2,i

Q

For example:

Ed = G + 0,2 S (2 = 0 for the wind action)

Ed = G + 0,2 W (2 = 0 for the snow load)

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3.3.4 Quasi-permanent combination

The quasi-permanent combination is normally used for long-term effects and the appearance of the structure.

Permanent

actions

Variable actions

Ed = 1

jk,j

G + 1

ik,i2,i

Q

For example:

Ed = G (since 2 = 0 for both the wind action and the snow load)

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4 PERMANENT ACTIONS

The self-weight of construction works is generally the main permanent load. It should be classified as a permanent fixed action. In most cases, it should be represented by a single-characteristic value.

The total self-weight of structural and non-structural members, including fixed services, should be taken into account in combinations of actions as a single action.

Non-structural elements include roofing, surfacing and coverings, partitions and linings, hand rails, safety barriers, parapets, wall claddings, suspended ceilings, thermal insulation, fixed machinery and all fixed services (heating, ventilating, electrical and air conditioning equipment, pipes without their contents, cable trunking and conduits).

The characteristic values of self-weight should be defined from the dimensions and densities of the elements.

Values of densities of construction materials are provided in EN 1991-1-1 Annex A (Tables A.1 to A.5).

For example:

Steel: = 77,0 to 78,5 kN/m3

Aluminium: = 27,0 kN/m3

For manufactured elements (façades, ceilings and other equipment for buildings), data may be provided by the manufacturer.

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5 CONSTRUCTION LOADS

EN 1991-1-6 gives rules for the determination of the actions during execution. Verifications are required for both serviceability limit states and ultimate limit states.

Table 4.1 defines construction loads that have to be taken into account:

Personnel and hand tools (Qca)

Storage of movable items (Qcb)

Non permanent equipment (Qcc)

Moveable heavy machinery and equipment (Qcd)

Accumulation of waste material (Qce)

Loads from parts of structure in a temporary state (Qcf).

Recommended values are provided in the same table but values may be given in the National Annex.

In single-storey buildings, an example of construction load would be the weight of cladding bundles on the structure prior to fitting.

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6 IMPOSED LOADS

6.1 General Generally, imposed loads on buildings shall be classified as variable actions. They arise from occupancy. They include normal use by persons, furniture and moveable objects, vehicles, anticipating rare events (concentrations of persons or of furniture, momentary moving or stacking of objects, etc.). Movable partitions should be treated as imposed loads.

Imposed loads are represented by uniformly distributed loads, line loads or point loads applied on roofs or floors, or a combination of these loads.

Floor and roof areas in buildings are sub-divided into categories according to their use (EN 1991-1-1 Table 6.1). The characteristic values qk (uniformly distributed load) and Qk (concentred load) related to these categories are specified in EN 1991-1-1 Table 6.2 or in the relevant National Annex.

For the design of a single floor or a roof, the imposed load shall be taken into account as a free action applied at the most unfavourable part of the influence area of the action effects considered.

For imposed loads for floors and accessible roofs, the characteristic value qk may be multiplied by reduction factors due to the loaded area and the number of storeys (EN 1991-1-1 § 6.3.1.2). More information is provided in Section 6 of Multi-storey steel buildings. Part 3: Actions[10].

Characteristic values of imposed loads are specified in EN 1991-1-1 Section 6.3 as follows:

6.3.1 Residential, social, commercial and administration areas

6.3.2 Areas for storage and industrial activities

6.3.3 Garages and vehicle traffic areas

6.3.4 Roofs.

6.2 Actions induced by cranes according to EN 1991-3

6.2.1 General

Most industrial buildings have to be equipped with handling devices to allow movement and carriage of loads through the building. A typical crane used in industrial buildings is shown in Figure 6.1 with the main technical terms.

One of the convenient solutions is the installation of cranes. The structure is subject to loads acting both vertically and laterally. Such actions can become the dominant ones for the structure.

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The determination of the actions induced by cranes is complex, as they include many parameters such as:

Weight of the crane and safe working load

Stiffness of both the crane structure and the runway girders

Speed and acceleration of the crane

Design of the crane (wheel drives, guidance systems, etc.).

The characteristics of the crane generally have to be supplied by the crane manufacturers.

2

3

4

5

6

1

2

7

7

77

1

8

8

1 Axis of wheels 2 Bogies 3 Main girders of the crane 4 Crab

5 motor drive unit 6 Hook 7 Axes of runway beams 8 Axis of track wheels

Figure 6.1 Main components of a crane

The relevant standard which specifies these actions is EN 1991-3 ‘Actions on structures – Actions induced by cranes and machinery’.

The variable crane actions are separated into:

Variable vertical crane actions caused by self weight of the crane and the hoist load

Variable horizontal actions caused by acceleration or deceleration or by skewing or other dynamic effects.

6.2.2 Vertical actions

Vertical actions include dead loads (self weight of the crane, safe working load, hook block, etc.)

The distribution of these dead loads is generally assumed on the basis of simply supported beams, considering both the main girders and the secondary beams over the bogies.

Two positions of the crab are generally considered to obtain the worst load arrangement on the crane runway: crab located in the middle of the crane span or crab located at the minimum distance of hook approach from the runway.

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Considering both crab positions leads to the maximum and minimum loads per wheel acting on the crane runway.

An eccentricity of application for these loads, generally taken as ¼ of the rail head, also has to be considered.

In order to consider some features such as impact of wheels at rail joints, wear of rail and wheels, release or lifting of the working load etc., dynamic factors are applied to the above static action values.

For vertical action, the dynamic factors are called 1 to 4 (refer to Table 2.4 of EN 1991-3).

6.2.3 Horizontal actions

The following types of horizontal forces should be taken into account:

Horizontal forces caused by acceleration and deceleration of the crane in relation to its movement along the runway beams

Horizontal forces caused by acceleration and deceleration of the crab in relation to its movement along the crane bridge

Horizontal forces caused by skewing of the crane in relation to its movement along the runway beam

Buffer forces related to crane movement

Buffer forces related to movement of the crab.

Only one of the 5 types of the above horizontal forces should be considered at the same time. The third one is generally assumed to be covered by the fifth one. The two last ones are considered as accidental forces.

The following details considering the first two types are generally those that lead to dimensioning configurations for the crane runway:

1. Forces that result from acceleration and deceleration of the crane along its crane way.

They act at the contact surface between the rail and the wheel. They have to be amplified by a dynamic factor 5 (see Table 2.6 of EN 1991-3) whose value may vary from 1,0 to 3,0, the value 1,5 being generally relevant. These forces consist of longitudinal forces (K1 and K2) and transverse forces (HT,1 and HT,2) as shown in Figure 6.2.

The longitudinal forces correspond to the resultant drive force K; such force must be transmitted through the driven wheels without skidding even when the crane carries no working load.

The resultant of the drive force does not pass through the centre of mass ‘S’, generating a couple that causes a skewing moment each time the crane accelerates or brakes. This moment is distributed on each runway according to their distance from the centre of mass.

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1 2

l

1 l 2 l

HT,1

HT,1

HT,2

HT,2

K1 K2 K=K1+K2

S M

ls 3 3

1 Rail 2 Rail 3 Driven wheels

Figure 6.2 Acceleration forces

2 Forces that result from skewing of the crane in relation to its movement along the runway beam

The forces described hereunder are due to the oblique travel of the crane when it assumes a skew position, for any reason, and then continues obliquely until the guidance mean comes in contact with the side of the rail.

The lateral force on the side of the rail increases to reach a peak value ‘S’; due to the action of this force, the crane returns to its proper course, at least temporarily.

Guidance systems can be either specific guide roller or the flanges of the track wheels.

The calculation of the corresponding forces depends on the type of drive system (drive units without synchronisation of the driven track wheels or central drive unit coupled to the wheels), the fixing of wheels according to lateral movement and the location of the instantaneous centre of rotation.

Forces resulting from skewing consist of longitudinal and transverse forces such as indicated in Figure 6.3.

These loads act at each wheel (HS,i,j,k) and a guide force S (also called steering force) acts at the guidance system.

In the forces HS,i,j,k the indexes refer to:

S for ‘skewing’

i for beam runway

j for wheel pair (the number 1 refers to the farthest from the centre of rotation)

k for direction of the force, L if acting longitudinally or T if acting transversally.

The force S equilibrates the sum of the transverse forces.

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i=1

x

h

HS,2,j,T

y

HS,2,j,L HS,1,j,L

HS,1,j,T a

ext

ej

i=2

j

1 l 2 l 1

1

x 2

3

i = 1

HS,1,1,T

6

i = 2

j = 1

j = 2 HS,1,2,T

HS,2,1,T

HS,2,2,T

HS,1,2,L HS,2,2,L

4

5

S

1 Guidance system

2 Direction of motion

3 Instantaneous centre of rotation

is the skew angle

i = Rails

j = Pairs of wheels

Figure 6.3 Forces resulting from skewing

6.2.4 Other loads or forces

To give an overall picture of the loads induced by cranes, it is necessary to mention:

1. The wind actions on the structure of the crane and on the payload

The wind is generally considered at a speed of 20 m/s if considered together with the payload (external use).

2. Test loads

- Dynamic test load: at least 110% of the nominal hoist load, amplified by a dynamic factor 6 (see EN 1991-3 §2.10 (4)).

- Static test load: at least 125% of the nominal hoist load without dynamic factor.

3. Accidental forces

- Tilting force: when the load or lifting attachments collides with an obstacle.

- And if relevant: Mechanical failure (failure of a single brake, wheel axle failure, etc.).

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6.2.5 Multiple crane action

There is often more than one crane in one building; they can move either on the same runway or on several levels in a same bay or in multi-bay buildings.

Multiple cranes have to be considered in the most unfavourable position for:

The crane runway

The supporting structure.

Table 6.1 Recommended maximum number of cranes to be considered in the most unfavourable position

Cranes to each runway

Cranes in each shop bay

Cranes in multi-bay buildings

Crane action

Vertical 3 4 4 2

Horizontal 2 2 2 2

For horizontal crane actions, it is acceptable to limit the number of cranes acting with their payload to two; for vertical actions, the number of cranes varies from two to four.

The cranes which are unloaded have nevertheless to be considered, if unfavourable.

6.3 Horizontal loads on parapets The characteristic values of the line loads qk acting at the height of the partition walls or parapets but not higher than 1,20 m should be taken from EN 1991-1-1 Table 6.12 or from the National Annex.

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7 SNOW LOADS

7.1 General This document gives guidance to determine the values of loads due to snow to be used for a typical single-storey building according to EN 1991-1-3. The design procedure is summarized in a flowchart (Figure 7.5). A worked example dealing with the determination of the snow loads on a single-storey building is given in Appendix A.

The guidance does not apply to sites at altitudes above 1500 m (unless otherwise specified).

Snow loads shall be classified as variable, fixed actions, unless otherwise stated in EN 1991-1-3. For particular conditions like exceptional snow loads and/or loads due to exceptional snow drifts, they may be treated as accidental actions depending on geographical locations.

Snow loads should be classified as static actions.

Two design situations may need to be considered:

Transient/persistent situation should be used for both the undrifted and drifted snow load arrangements for locations where exceptional snow falls and exceptional snow drifts are unlikely to occur.

Accidental design situation should be used for geographical locations where exceptional snow falls and/or exceptional snow drifts are likely to occur.

The National Annex may define which design situation to apply.

7.2 Methodology 7.2.1 Snow load on the ground

Different climatic conditions will give rise to different design situations. The possibilities are:

Case A: Normal case (non exceptional falls and drifts)

Case B1: Exceptional falls and no exceptional drifts

Case B2: Exceptional drift and no exceptional falls (in accordance with EN 1991-1-3 Annex B)

Case B3: Exceptional falls and exceptional drifts (in accordance with EN 1991-1-3 Annex B)

The National Authority may choose the case applicable to particular locations for their own territory.

The National Annex specifies the characteristic value sk of snow load on the ground to be used.

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For locations where exceptional snow loads on the ground can occur, they may be determined by:

sAd = Cesl sk

where:

sAd is the design value of exceptional snow load on the ground for the given location

Cesl is the coefficient for exceptional snow loads (the recommended value is = 2,0)

sk is the characteristic value of snow load on the ground for the given location.

The National Annex may recommend another value of Cesl, or the design value of exceptional snow load on the ground sAd.

7.2.2 Snow load on roofs

The load acts vertically and refers to a horizontal projection of the roof area. Snow can be deposited on a roof in many different patterns.

Two primary load arrangements shall be taken into account:

Undrifted snow load on roofs

Drifted snow load on roofs.

Snow loads on roofs are derived from the snow loads on the ground, multiplying by appropriate conversion factors (shape, exposure and thermal coefficients). They shall be determined as follows:

Persistent (conditions of normal use)/transient (temporary conditions) design situations:

s = i Ce Ct sk

Accidental (exceptional conditions) design situations where exceptional snow load is the accidental action:

s = i Ce Ct sAd

Accidental design situations where the accidental action is the exceptional drift and where EN 1991-1-3 Annex B applies:

s = i sk

where:

i is the snow shape coefficient. It depends on the angle of pitch of roof (Table 6.1)

Ce is the exposure coefficient (Ce = 1,0 is the default value)

Ct is the thermal coefficient (Ct ≤ 1; Ct = 1,0 is the default value).

The National Annex may give the conditions of use for Ce and Ct.

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Table 7.1 Snow load shape coefficients

Angle of pitch of roof 0° 30° 30° < < 60° 60°

1 0.8 0.8 (60 – )/30 0

2 0.8 + 0.8 /30 1.6 -

These values 1 and 2 apply when the snow is not prevented from sliding off the roof (no snow fences or other obstructions like parapets). If obstructions exist, the snow load shape coefficient should not be reduced below 0.8.

The snow load shape coefficient that should be used for monopitch roofs is shown in Figure 7.1, where 1 is given in Table 7.1.

The load arrangement should be used for both the undrifted and drifted load arrangements.

1()

Figure 7.1 Snow load shape coefficient – Monopitch roof

The snow load shape coefficients that should be used for pitched roofs are shown in Figure 7.2, where 1 is given in Table 7.1.

Case (i) corresponds to the undrifted load arrangement.

Cases (ii) and (iii) correspond to the drifted load arrangements.

0,5 )

)

1 2

(i)

(ii)

(iii)

(i) Undrifted load arrangement

(ii) and (iii) Drifted load arrangement

Figure 7.2 Snow load shape coefficient – Pitched roof

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The snow load shape coefficients that should be used for multi-span roofs are shown in Figure 7.3, where 1 and 2 are given in Table 7.1.

Case (i) corresponds to the undrifted load arrangement.

Case (ii) corresponds to the drifted load arrangement.

1 2

(i)

(ii)

1 (2) 1 (1) 1 (2)

1 2

1 (1) 2 [(1+2)/2]

1 (2)

(i) Undrifted load arrangement

(ii) Drifted load arrangement

Figure 7.3 Snow load shape coefficient – Multi-span roof

The snow load shape coefficients that should be used for roofs abutting to taller construction works are shown in Figure 7.4, where 1, 2, s, w are given by the following expressions:

1 = 0,8 This value assumes that the lower roof is flat. If it is not, a specific study should be carried out by taking into account the direction of the slope.

2 = s + w

where:

s is the snow shape coefficient due to sliding of snow from the upper roof.

For ≤ 15°, s = 0

For > 15°, s = half the snow load on the adjacent slope of the upper roof

w is the snow load shape coefficient due to wind

w = (b1 + b2)/2h with w ≤ h / sk

And the recommended range is (it may be given in the National Annex):

0,8 ≤ w ≤ 4

b1, b2 and h are defined in Figure 7.4

is the weight density of snow for this calculation (2 kN/m3)

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ls is the drift length determined as :

ls = 2 h

The recommended limits of the drift length are (they may be given in the National Annex):

5 m ≤ ls ≤ 15 m

If b2 < ls, the coefficient 2 is truncated at the end of the lower roof.

The cases (i) corresponds to with the undrifted load arrangement.

The cases (ii) corresponds to with the drifted load arrangements.

h

b2b1

h

b1 b2 < ls

(i)

(ii)

1 (i)

(ii)1

1

2 2 s s

w w

ls ls

Figure 7.4 Snow load shape coefficient – Roofs abutting to taller construction

works

7.2.3 Local effects

The design situations to be considered are persistent/transient. EN 1991-1-3 Section 6 gives forces to be applied for the local verifications of:

Drifting at projections and obstructions (EN 1991-1-3 § 6.2)

The edge of the roof (EN 1991-1-3 § 6.3)

Snow fences (EN 1991-1-3 § 6.4).

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7.2.4 Flowchart

Characteristic value of the snow load sk on the ground

Shape coefficients i

Location of the constructionNational map

Pe

rsis

ten

t / t

ran

sien

t de

sig

n s

itua

tion

s

Snow load on the roof: s = I Ce Ct sk

Acc

ide

nta

l de

sig

n si

tuat

ion

s N

o d

rift

due

to lo

cal e

ffect

Exceptional load on the ground sAd = Cesl sk

Coefficient Cesl for exceptional snow load

Snow load on the roof: s = I Ce Ct sAd

(including drifts, except local effects)

Exceptional drifts Snow load on the roof:

s = I sk

Shape of the roof

Exposure coefficient Ce Thermal coefficient Ct

Location of the constructionNational map

National Annex

EN 1991-1-3 § 5.3

EN 1991-1-3 § 5.2(3) a)

EN 1991-1-3 Annex B

EN 1991-1-3 § 4.3

EN 1991-1-3 § 4.3

EN 1991-1-3 § 5.2(3) b)

Figure 7.5 Determination of the snow loads

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8 WIND ACTIONS

8.1 General This Section provides guidance to determine the values of the wind action to be used for the design of a typical single-storey building according to EN 1991-1-4. The design procedure is summarized by a flowchart in Figure 8.6 and Figure 8.7. A worked example dealing with the determination of the wind action on a single-storey building is given in Appendix B.

The rules apply to the whole structure or part of the structure, e.g. components, cladding units and their fixings.

A simplified set of pressures or forces whose effects are equivalent to the extreme effects of the turbulent wind represent the wind action.

Wind actions should be classified as variable fixed actions.

The relevant wind actions shall be determined for each design situation identified.

Where, in design, windows and doors are assumed to be shut under storm conditions, the effect of these being open should be treated as an accidental design situation.

8.2 Methodology The response of the structure to the effect of wind depends on the size, shape and dynamic properties of the structure. This response should be calculated from the peak velocity pressure qp and from the force and/or pressure coefficients.

8.2.1 Peak velocity pressure

The peak velocity pressure qp(z) is the velocity pressure used in the calculations.

It depends on the wind climate, the reference height, the terrain roughness and orography. It is equal to the mean velocity pressure plus a contribution from short-term pressure fluctuations.

The peak velocity pressure can be calculated using the following procedure.

1. Fundamental value of the basic wind velocity vb,0

The fundamental value of the basic wind velocity is the characteristic 10 minutes mean wind velocity, irrespective of wind direction and time of year, at 10 m above ground level, in open country terrain. It corresponds to a mean return period of 50 years (annual probability of exceedence of 0,02).

The National Annex specifies the fundamental value of the basic wind velocity.

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2. Basic wind velocity vb

vb = cdir cseason vb,0

where:

cdir is the directional factor

cseason is the seasonal factor

The recommended value is 1,0 for both cdir and cseason but the National Annex may give other values.

3. Basic velocity pressure

The basic velocity pressure qb is calculated as follows:

qb 2b

2

1v

where:

is the air density

= 1,25 kg/m3 (recommended value but the National Annex may give another value)

4. Terrain factor kr 07,0

II,0

0r 19,0

z

zk

where:

z0 is the roughness length according to the terrain category

z0,II is the roughness length for the terrain category II:

z0,II = 0,05 m

zmax = 200 m

Terrain categories and terrain parameters are defined in EN 1991-1-4 Table 4.1, but the National Annex may give other values.

5. Roughness factor cr(z)

cr(z) = kr ln(z/z0) for zmin ≤ z ≤ zmax

cr(z) = cr(zmin) for z ≤ zmin

where:

z is the reference height defined by EN 1991-1-4 Figure 7.4.

zmin depends on the terrain category, EN 1991-1-4 Table 4.1.

6. Orography factor co(z)

The orography consists of the study of the shape of the terrain in the vicinity of the construction.

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The effects of orography may be neglected when the average slope of the upwind terrain is less than 3°. The recommended value of co(z) is 1,0, but the National Annex may give the procedure to calculate the orography factor.

Annex A3 of EN 1991-1-4 gives the recommended procedure to determine co for hills, cliffs, etc.

7. Turbulence factor kl

The recommended value is 1,0 but the National Annex may give other values.

8. Peak velocity pressure qp(z)

)( 2

1)(71)( 2

mvp zvzIzq

where:

Iv(z) is the turbulence intensity which allows to take into account the contribution from short-term fluctuations

)/ln()(

)(0o

lv zzzc

kzI for zmin ≤ z ≤ zmax

)()( minvv zIzI for z < zmin

zmax = 200 m

vm(z) is the mean wind velocity at height z above the terrain:

vm(z) = cr(z) co(z) vb

Alternative for step 8:

For single-storey-buildings, the determination of the mean wind velocity vm(z) is not absolutely necessary. The peak velocity pressure can be directly obtained from the exposure factor ce(z):

bep )()( qzczq

where:

)( )()( )(

71)( 2

r2o

ro

rle zczc

zczc

kkzc

For flat terrain (co(z) = 1) and for turbulence factor kl = 1, the exposure factor ce(z) can be directly obtained from Figure 4.2 of EN 1991-1-4, as a function of the height above terrain and a function of terrain category.

8.2.2 Wind pressure on surfaces – Wind forces

There are three types of wind forces acting on a building:

External forces Fw,e (see 8.2.2.1)

Internal forces Fw,i (see 8.2.2.2)

Friction forces Ffr (see 8.2.2.3).

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The external and internal forces result in pressures perpendicular to the walls (vertical walls, roofs, etc.). By convention, pressure directed towards the surface is taken as positive, and suction, directed away from the surface as negative (Figure 8.1).

q < 0 q > 0

Figure 8.1 Sign convention for the pressure

As stated in EN 1991-1-4 § 5.3(2), the resulting wind force Fw acting on a structure, or a structural component, can be determined by the vector summation of Fw,e, Fw,i and Ffr. It can be globally expressed as follows:

Fw = cscd cf qp(ze) Aref

where:

cscd is the structural factor (for buildings with a height less than 15 m, it may be taken as 1)

Note: the mean wind velocity vm(z) is necessary to calculate the structural factor cscd.

cf is the force coefficient for the structure (or structural element)

Aref is the reference area of the structure (or structural element). Here it can be defined as the area of the projection of the structure or the structural component, on a vertical plan perpendicular to the wind direction.

Practical approach

In practice, the designer needs to evaluate the resulting pressure on the walls in order to determine the actions on the structural members. The resulting pressure can be expressed as follows:

Fw/Aref = cscd we – wi

where:

we is the wind pressure acting on the external surface (see 7.2.1.2),

wi is the wind pressure acting on the internal surface (see 7.2.1.3).

In addition the effects of the friction forces (see 7.2.1.4) have to be considered when necessary.

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8.2.2.1 External forces

The external forces are obtained from:

surfaces

refedsew, AwccF

where:

cscd is the structural factor (see 7.2.1.1)

we is the wind pressure acting on the external surface:

we = qp(ze) cpe

qp(ze) is the peak velocity pressure at the reference height ze

ze is the reference height for the external pressure (generally, the height of the structure). It depends on the aspect ratio h/b, where h is the height of the building and b is the crosswind dimension.

Generally, h is lower than b for single-storey buildings. In this case, ze is taken equal to the height of the building and the velocity pressure qp(z) is uniform on the whole structure: qp(ze) = qp(h).

cpe is the pressure coefficient for the external pressure. See § 8.2.3 for vertical walls and § 8.2.4 for roofs.

Aref is the reference area. Here it is the area of the surface under consideration for the design of the structure or the structural component.

8.2.2.2 Internal forces

The internal forces are obtained from:

surfaces

refiiw, AwF

where:

wi is the wind pressure acting on the internal surface:

wi = qp(zi) cpi

zi is the reference height for the internal pressure (generally: zi = ze)

qp(zi) is the peak velocity pressure at the height zi (generally: qp(zi) = qp(ze))

cpi is the pressure coefficient for the internal pressure, see § 8.2.5.

8.2.2.3 Friction forces

The friction force results from the friction of the wind parallel to the external surface. Friction is allowed for when the total area of all surfaces parallel to the wind is higher than four times the total area of all external surfaces perpendicular to the wind (windward and leeward), which is the case for long structures.

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W

d

b

h

Min(2b ; 4h)

Figure 8.2 Friction forces

The friction forces are obtained from:

frepfrfr AzqcF

where:

cfr is the friction coefficient. It can be taken equal to:

0,01 for smooth surface (steel, smooth concrete, etc.)

0,02 for rough surface (rough concrete, tar-boards, etc.)

0,03 for very rough surface (ripples, ribs, folds, etc.).

qp(ze) is the peak velocity pressure at the reference height ze.

Afr is the reference area. Friction forces are applied on the part of the external surfaces parallel to the wind Afr, located beyond a distance from the upwind eaves or corners, equal to the smallest value of 2b or 4h, b and h as defined in Figure 8.2.

8.2.3 External pressure coefficients on vertical walls

The values of the external pressure coefficients, given in tables in the Eurocode are attached to defined zones. The coefficients depend on the size of the loaded area A that produces the wind action in the zone under consideratiion. In the tables, the external pressure coefficients are given for loaded areas of 1 m2 (cpe,1) and 10 m2 (cpe,10). In this guide, only the values cpe,10 are taken into account, because they are used for the design of the overall load bearing structure of buildings.

Zones for vertical walls are defined in EN 1991-1-4 Figure 7.5 and the external pressure coefficients cpe,10 are given in EN 1991-1-4 Table 7.1. For intermediate values of h/d, linear interpolation may apply.

The values of the external pressure coefficients may be given in the National Annex.

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b

d

D E1

2 Plan

h A B C

e/5 4/5 e d – e

1

h A B C 1

Elevation for e < d

h A B

e/5 d – e/5

1

h A B1

Elevation for e ≥ d

1 Wind direction 2 Elevation

h A

d

1

h A 1

Elevation for e ≥ 5d

e = min(b ; 2h) b is the crosswind dimension

Figure 8.3 Key for vertical walls

For buildings with h/d > 5, the total wind loading may be determined by the force coefficients cf.

In cases where the wind force on building structures is determined by application of the pressure coefficient cpe on windward and leeward side (zones D and E) of the building simultaneously, the lack of correlation of wind pressures between the windward and leeward side may have to be taken into account as follows:

For buildings with h/d ≥ 5, the resulting force is multiplied by 1

For buildings with h/d ≤ 1, the resulting force is multiplied by 0,85

For intermediate values of h/d, linear interpolation may be applied.

8.2.4 External pressure coefficients on roofs

Zones for roofs and external coefficients cpe,10 attached to these zones are defined in EN 1991-1-4 as follows:

Flat roofs: Figure 7.6 and Table 7.2

Monopitch roofs: Figure 7.7 and Tables 7.3a and 7.3b

Duopitch roofs: Figure 7.8 and Tables 7.4a and 7.4b

Hipped roofs: Figure 7.9 and Table 7.5

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Multispan roofs : Figure 7.10 and the coefficients cpe are derived from Tables 7.3 to 7.4.

Figure 8.4 of this guide shows the zones for duopitch roofs.

b

e/10

G

F

1

e/10

F

H J I

2 4

e/4

e/4

3

b

e/10

G

F

1

e/2

F

H I

I

2

e/4

e/4

G

H

Wind on the long side (perpendicular to the ridge line)

1 Wind direction 2 Ridge line 3 Upwind face 4 Downwind face

Wind on the gable (parallel to the ridge line)

e = min(b ; 2h) b is the crosswind dimension

Figure 8.4 Zones for duopitch roofs

8.2.5 Internal pressure coefficients

The internal pressure coefficient cpi depends on the size and distribution of the openings in the building envelope.

When in at least two sides of the building (façades or roof) the total area of openings in each side is more than 30 % of the area of that side, the structure should be considered as a canopy roof and free-standing walls.

A face of a building should be regarded as dominant when the area of openings in that face is at least twice the area of openings in the remaining faces of the building considered.

Where an external opening would be dominant when open but is considered to be closed in the ultimate limit state, during severe windstorms (wind used for the design of the structure), the condition with the opening open should be considered as an accidental design situation.

For a building with a dominant face, the internal pressure should be taken as a fraction of the external pressure at the openings of the dominant face:

Area of the openings on the dominant face = 2 area of openings in the remaining faces: cpi = 0,75 cpe

Area of the openings in the dominant face = 3 area of openings in the remaining faces: cpi = 0,90 cpe

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Area of the openings at the dominant face between 2 and 3 times the area of the openings in the remaining faces: Linear interpolation for calculating cpi.

When the openings are located in zones with different values of cpe, an area weighted average value should be used.

For buildings without a dominant face, the coefficient cpi should be determined from a function of the ratio h/d and the opening ratio for each direction, as shown in Figure 8.5.

where:

openings all of area

0 whereopenings of area pecμ

Figure 8.5 Internal pressure coefficients for uniformly distributed openings

For values between h/d = 0,25 and h/d = 1,0, linear interpolation may be used.

Where it is not possible or not considered justified to estimate for a particular case, then cpi should be taken as the more onerous of + 0,2 and – 0,3.

The reference height zi for the internal pressures should be equal to the reference height ze for the external pressures on the faces which contribute by their openings to the creation of the internal pressure. Generally, for single-storey buildings, zi = ze = h and the velocity pressure qp(z):

qp(zi) = qp(ze) = qp(h)

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8.3 Flowcharts

Fundamental value of the basic wind velocity vb,0

Construction location National map

Directional factor cdir Season factor cseason

Basic wind velocity vb

Terrain category

Roughness factor cr(z)

Peak velocity pressure qp(z)

Orography factor co(z)

Basic velocity pressure qb Air density

Terrain factor kr

Turbulence factor kl

EN 1991-1-4 § 4.2(1)

(See National Annex)

EN 1991-1-4 § 4.5(1)

EN 1991-1-4 § 4.3.2

EN 1991-1-4 § 4.3.3 and A.3


EN 1991-1-4 § 4.4


Reference height z

EN 1991-1-4 § 4.5(1)

Figure 8.6 Flowchart A: calculation of the peak velocity pressure

Type of surface

External pressure coefficients cpe on vertical walls

Wind forces Fw,e and Fw,i

Peak velocity pressure qp(z)

Friction coefficient cfr Reference area Afr

External pressure coefficients cpe on roof

Internal pressure coefficients cpi

See Flowchart A

EN 1991-1-4 § 5.3

EN 1991-1-4 § 7.2.9

EN 1991-1-4 § 7.5

Table 7.10

EN 1991-1-4 § 7

Structural factor cs cd EN 1991-1-4

§ 6 and Annexes B, C, D (See National Annex)

Friction forces Ffr EN 1991-1-4 § 5.3

Dimensions of the building

Figure 8.7 Flowchart B: Calculation of the wind forces

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9 EFFECT OF TEMPERATURE

Buildings not exposed to daily or seasonal climatic changes may not need to be assessed under thermal actions. For large buildings, it is generally good practice to design the building with expansion joints so that the temperature changes do not induce internal forces in the structure. Information about the design of expansion joints is given in Section 1.4.2 of Single-storey steel buildings Part 2: Concept design[11].

When the effects of temperature have to be taken into account, EN 1993-1-5 provides rules to determine them.

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REFERENCES

1 EN 1990:2002: Eurocode Basis of structural design

2 EN 1991-1-1:2002: Eurocode 1 Actions on structures. General actions. Densities, self-weight, imposed loads for buildings.

3 EN 1991-1-3:2003: Eurocode 1 Actions on structures. General actions. Snow loads

4 EN 1991-1-4:2005: Eurocode 1 Actions on structures. General actions. Wind actions

5 EN 1991-1-5:2003: Eurocode 1 Actions on structures. General actions. Thermal actions

6 EN 1991-3:2006: Eurocode 1 Actions on structures. Actions induced by cranes and machinery

7 CLAVAUD, D. Exemple de détermination des charges de neige selon l’EN 1991-1-3. Revue Construction Métallique n°2-2007. CTICM.

8 CLAVAUD, D. Exemple de détermination des actions du vent selon l’EN 1991-1-4. Revue Construction Métallique n°1-2008. CTICM.

9 EN 1998-1:2004: Eurocode 8 Design of structures for earthquake resistance. General rules, seismic actions and rules for buildings.

10 Steel Buildings in Europe Multi-storey steel buildings. Part 3: Actions

11 Steel Buildings in Europe Multi-storey steel buildings. Part 2: Concept design

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APPENDIX A

Worked Example: Snow load applied on a single-storey building

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APPENDIX A. Worked Example: Snow load applied on a single-storey building

1 of 8

Made by DC Date 02/2009

Calculation sheet Checked by AB Date 03/2009

1. Data

This worked example deals with the single-storey building shown below.

B

A’

A

25,00 m

B’

Plan view

3,00 m

10%

25,00 m

15%

b2 = 10,00 m b1 = 40,00 m

1

1,25 m

6,00 m10,25 m

0,75 m

1

Cross-section BB’ Cross-section AA’

1 Parapets Figure A.1– Geometry of the building

2. Snow load on the ground

Characteristic value sk of snow load on the ground:

sk = 0,65 kN/m2

Coefficient for exceptional snow load:

Cesl = 2

EN 1991-1-3 § 4.3

Exceptional snow on the ground:

sAd = Cesl sk = 2 0,65 = 1,30 kN/m2

Title APPENDIX A. Worked Example: Snow load applied on a single-storey building

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3. Snow load on the roof

3.1. General

The loads act vertically and refer to a horizontal projection of the roof area.

Two primary load arrangements shall be taken account:

undrifted snow load on roofs

drifted snow load on roofs

EN 1991-1-3 §5.2(1)

Snow loads on roofs are determined as follows:

Persistent (conditions of normal use)/transient (temporary conditions) design situations:

s = i Ce Ct sk

EN 1991-1-3 § 5.2(3) a)

Accidental design situations (exceptional snow fall) where exceptional snow load is the accidental action:

s = i Ce Ct sAd

§ 5.2(3) b)

Accidental design situations (exceptional snow drift) where the accidental action is the exceptional drift and where Annex B applies:

s = i sk

§ 5.2(3) c)

where:

i is the snow shape coefficient

EN 1991-1-3 § 5.3

Ce is the exposure coefficient, Ce = 1,0 § 5.2(7)

Ct is the thermal coefficient, Ct = 1,0 § 5.2(8)

3.2. Upper roof (duo pitch roof)

Angle of the roof (15%):

= arc tan (0,15) = 8,5°

0 30°

Persistent /transient design situations

- Case (i) : undrifted load arrangement

1( = 8,5°) = 0,8

s = 0,8 0,65 = 0,52 kN/m2

EN 1991-1-3 § 5.3.3 Figure 5.3

- Case (ii): Drifted load arrangement

0,5 1 (= 8,5°) = 0,4

s = 0,4 0,65 = 0,26 kN/m2

- Case (iii): Drifted load arrangement

The case (iii) is symmetrical about the case (ii) because of the symmetry of the roof (1 = 2 = 8,5°).


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0,52 kN/m2

Case (i)

0,26 kN/m2 0,52 kN/m2

Case (ii)

0,52 kN/m2 0,26 kN/m2

Case (iii)

Figure A.2 Snow load arrangements on the upper roof in persistent design

situation

EN 1991-1-3 Figure 5.3

Accidental design situations – exceptional load on the ground

- Case (i): Undrifted load arrangement

1( = 8,5°) = 0,8

s = 0,8 1,30 = 1,04 kN/m2


0,5 1(= 8,5°) = 0,4

s = 0,4 1,30 = 0,52 kN/m2

- Case (iii): Drifted load arrangement

The case (iii) is symmetrical about the case (ii) because of the symmetry of the roof (1 = 2 = 8,5°)

1,04 kN/m2

Case (i)

0,52 kN/m2 1,04 kN/m2

Case (ii)

1,04 kN/m2 0,52 kN/m2

Case (iii)

Figure A.3 Snow load arrangements on the upper roof in accidental design

situation

Accidental design situations – exceptional drift:

This case is not applicable. There are no parapets or valleys.


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3.3. Lower roof: duo pitch roof abutting to taller construction works

Angle of the roof (10%):

= arc tan (0,10) = 5,7°

0 30°

EN 1991-1-3 § 5.3.6(1)

Persistent /transient design situations


1(5,7°) = 0,8

s = 0,8 0,65 = 0,52 kN/m2

0,52 kN/m2

0,52 kN/m2

Figure A.4 – Undrifted snow load arrangement on the lower roof in persistent

design situation

- Case (ii): drifted load arrangement

1(5,7°) = 0,8

s = 0,8 0,65 = 0,52 kN/m2

2 = s + w

where:

s is the snow shape coefficient due to sliding of snow from the upper roof.

For 15°: s = 0

w is the snow load shape coefficient due to wind

w = (b1 + b2) / 2h

with: w h/sk

b1 = 10 m

b2 = 40 m

h varies between 3 m at ridge to 4,25 m at eaves

= 2 kN/m3


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The recommended range is: 0,8 w 4

At ridge: h/sk = 2 3/0,65 = 9,2

w = (10 + 40)/(2 3) = 8,3 h/sk

At eave: h/sk = 2 4,25/0,65 = 13,1

w = (10 + 40)/(2 4,25) = 5,9 h/sk

But w should be maximum 4, so:

w = 4

Therefore:

s = 4 0,65 = 2,60 kN/m2

ls is the drift length determined as:

ls = 2h

This drift length varies between 6 m at ridge to 8,50 m at eaves.

The recommended restriction is: 5 m ≤ ls ≤ 15 m

EN 1991-1-3 § 5.3.6(1)

2,60 kN/m26,00 m

8,50 m

2,60 kN/m2

0,52 kN/m2

0,52 kN/m2

Figure A.5 Drifted snow load arrangement on the lower roof in the case of abutting to taller construction works in persistent design situation

EN 1991-1-3 Figure 5.7

Accidental design situations – exceptional load on the ground:


1(5,7°) = 0,8

s = 0,8 1,3 = 1,04 kN/m2

The arrangement is the same as Figure A.4 with: s = 1,04 kN/m2


The arrangement is the same as Figure A.5 with: s1 = 1,04 kN/m2


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where:

1 = 0,8

and s2 = 5,20 kN/m2 where w = 4

3.4. Lower roof: drifting at obstructions (parapets)

Only persistent/transient design situations are to be considered.

Angle of the roof (10%): = 5,7°

1(5,7°) = 0,8

s = 0,8 0,65 = 0,52 kN/m2

EN 1991-1-3 § 6.2(2)

2 = h/sk

where:

h is the height of parapet. It varies between 0 m at ridge and 1,25 m at low eaves.

= 2 kN/m3

At ridge: 2 = 0

At low eaves: 2 = 2 1,25/0,65 = 3,8

With the restriction: 0,8 ≤ 2 ≤ 2

2 varies between 0,8 at ridge, and 2 at eave.

s varies between 0,52 kN/m2 at ridge, and 2 0,65 = 1,30 kN/m2 at low eaves.

The drift length ls is determined by: ls = 2 h

This drift length varies between 0 m at ridge and 2,50 m at low eaves.

The recommended restriction is: 5 m ≤ ls ≤ 15 m. Therefore:

ls = 5 m at low eaves.

5,00 m

5,00 m

0,52 kN/m2

5,00 m

1,30 kN/m2

0,52 kN/m2

0,52 kN/m2

1,30 kN/m2 1,30 kN/m2

5,00 m 5,00 m

Figure A.6 Drifted snow load arrangement on the lower roof in the case of

obstruction in persistent design situation


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3.5. Exceptional snow drifts

3.5.1. Roofs abutting and close to taller structures

1 = 2 = 3 = Min(2h/sk ; 2b/ls ; 8)

where b is the larger of b1 or b2

ls = Min(5h ; b1 ; 15 m)

h = 4,25 m

b1 = 40,00 m

b2 = 10,00 m

sk = 0,65 kN/m2

5 h = 21,25m; ls = 15,00 m; 2h/sk = 13,08; 2b/ls = 5,3

1 = 2 = 3 = 5,3

And: s = 3 sk = 3,45 kN/m2

EN 1991-1-3 Annex B § B.3

15,00 m

3,45 kN/m2

Figure A.7 Exceptional snow drifted on the lower roof in the case of roofs

abutting and close to taller building


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3.5.2. Roofs where drifting occurs behind parapets at eaves

1 = Min(2 h/sk ; 2 b2/ls ; 8)

where: ls = Min(5h ; b1 ; 15 m)

h = 3,00 m

b1 = 12,50 m

b2 = 25,00 m

sk = 0,65 kN/m2

5h = 15,00 m ; ls = 12,50 m ; 2h/sk = 9,23 ; 2b2/ls = 4,00

1 = 4,00

And: s = 1 sk = 2,60 kN/m2

EN 1991-1-3 Annex B § B.4

3.5.3. Roofs where drifting occurs behind parapets at gable end

1 = Min(2 h/sk ; 2 b2/ls ; 8)

where: ls = Min(5h ; b1 ; 15 m)

h = 3,00 m

b1 = 40,00 m

b2 = 25,00 m

sk = 0,65 kN/m2

5h = 15,00 m ; ls = 15,00m ; 2h/sk = 9,23 ; 2b2/ls = 5,33

1 = 5,33

And: s = 1 sk = 3,46 kN/m2

EN 1991-1-3 Annex B § B.4

0,00 kN/m2

12,50 m 12,50 m

15,00 m

2,60 kN/m2 2,60 kN/m2

3,46 kN/m2

Snow behind the parapet at gable end Snow behind the parapets at eaves

Figure A.8 Exceptional snow drifted on the lower roof in the case of roofs where drifting occurs behind parapets at eaves

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APPENDIX B

Worked Example: Wind action on a single-storey building

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APPENDIX B. Worked Example: Wind action on a single-storey building

1 of 11



1. Data This worked example deals with the calculation of the wind action on a single-storey building according to EN 1991-1-4. The overall dimensions of the building are given in Figure B.1.

14 °

5 m

5 m

6 m

6 m 4,8 m

6 m

16 m

16 m 60 m

Figure B.1 Geometry of the building

The doors are assumed to be shut during severe gales.

The fundamental value of the basic wind velocity is:

vb,0 = 26 m/s

2. Peak velocity pressure The peak velocity pressure is determined according to the step-by-step procedure given in this guide.

1. Fundamental value of the basic wind velocity

vb,0 = 26 m/s

2. Basic wind velocity

For cdir and cseason, the recommended values are:

cdir = 1,0

cseason = 1,0

Then: vb = vb,0 = 26 m/s

EN 1991-1-4 § 4.2(2)

Title APPENDIX B. Worked Example: Wind action on a single-storey building

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3. Basic velocity pressure

2b 2

1bvq

where:

= 1,25 kg/m3 (recommended value)

Then: qb = 0,5 1,25 262 = 422,5 N/m2

EN 1991-1-4 § 4.5(1)

4. Terrain factor

07,0

II0,

0r 19,0

z

zk

EN 1991-1-4 § 4.3.2(1) Table 4.1

The terrain category is category III, then:

z0 = 0,3 m

zmin = 5 m

215,005,0

30,019,0

07,0

r

k

5. Roughness factor

0rr ln)(

z

zkzc

z is taken equal to the height of the building:

z = 8 m

Then: 706,03,0

0,8ln215,0)(r

zc

EN 1991-1-4 § 4.3.2(1)

6. Orography factor

The building is erected on a suburban terrain where the average slope of the upwind terrain is very low (< 3°), so:

co(z) = 1

EN 1991-1-4 § 4.3.3(2)

7. Turbulence factor

The recommended value is used:

kl = 1,0

EN 1991-1-4 § 4.4(1)


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3 - 48

8. Peak velocity pressure (alternative for a single-storey building)

qp(z) = ce(z) qb

where:

)( )()( )(

71)( 2

r2o

ro

rle zczc

zczc

kkzc

EN 1991-1-4 § 4.5(1)

56,1706,00,1706,00,1

215,00,171)( 22

e

zc

Then: qp(z) = 1,56 423 = 659 N/m2

qp(z) = 0,659 kN/m2 for z = 8 m

3. Wind pressure on surfaces

3.1. External pressure coefficients cpe,10

3.1.1. Vertical walls

1. Wind on gable

h = 8 m

b = 32 m (crosswind dimension)

h < b, so ze = reference height = h = 8 m

EN 1991-1-4 7.2.2 (1) Figure 7.4

d = 60 m

h/d = 8/60 = 0,13 (h/d < 0,25)

EN 1991-1-4 7.2.2 (2) Table 7.1

2h = 16 m

e = 16 m (b or 2h, whichever is smaller)

EN 1991-1-4 § 7.2.2 (1) Figure 7.5

e < d

e/5 = 3,2 m

4/5 e = 12,8 m

d – e = 44 m

Figure B.2 defines the external pressure coefficients cpe,10 on vertical walls for zones A, B, C, D and E with wind on the gable.

EN 1991-1-4 § 7.2.2(2) Table 7.1


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3 - 49

+ 0,7 - 0,3

Wind

44 m

h = 8 m

3,2 m 12,8 m

- 0,5 - 0,8

- 1,2 DD

BB CCEE

AA

Figure B.2 cpe,10 for zones A, B, C, D and E with wind on gable

2. Wind on the long side

h = 8 m


h < b, so ze = reference height = h = 8 m

d = 32 m

EN 1991-1-4 7.2.2 (1) Figure 7.4

h/d = 8/32 = 0,25

2h = 16 m

EN 1991-1-4 § 7.2.2(2) Table 7.1


e < d

e/5 = 3,2 m

4/5 e = 12,8 m

d – e = 16 m

EN 1991-1-4 § 7.2.2(1) Figure 7.5

Figure B.3 defines the external pressure coefficients cpe,10 on vertical walls for zones A, B, C, D and E with wind on the long side.

EN 1991-1-4 § 7.2.2(2) Table 7.1


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3 - 50

h = 8 m

3,2 m

- 0,3+ 0,7 - 1,2

12,8 m

DD AA BB

EE

- 0,8

16 m

CC

- 0,5

Wind

Figure B.3 cpe,10 for zones A, B, C, D and E with wind on long side

3.1.2. Roofs

1. Wind on gable

Ridges are parallel to the wind direction: = 90°

Pitch angle: = 14°

h = 8 m


EN 1991-1-4 § 7.2.5(1) Figure 7.8

The reference height is: ze = h = 8 m

2h = 16 m

EN 1991-1-4 § 7.2.7(3)


e/4 = 4 m

e/10 = 1,6 m

e/2 = 8 m

EN 1991-1-4 § 7.2.5(1) Figure 7.8

Figure B.4 defines the external pressure coefficients cpe,10 on roofs for zones F, G, H and I with a wind on gable.

EN 1991-1-4 § 7.2.2(2) Table 7b


6 of 11

3 - 51

Trough

Ridge

- 1,3

- 1,3

- 0,6

- 0,6

- 1,3

Ridge

- 1,3

- 1,3

4 m

4 m

8 m

1,6 m

d = 60 m

- 1,3

- 0,6

Wind

b = 32 m

- 0,5

- 0,5

- 0,6 - 0,5

- 0,5

FF

GG

GG

GG

II

II

II

II

HH

HH

HH

HH

GG

FF

Figure B.4 cpe,10 for zones F, G, H and I with wind on gable

2. Wind on long side

i. Ridges are perpendicular to the wind direction: = 0°

ii. Pitch angle = 14°

iii. h = 8 m

iv. b = 60 m (crosswind dimension)

v. h < b, so the reference height is: ze = h = 8 m

EN 1991-1-4 § 7.2.5(1) Figure 7.8

vi. d = 32 m

vii. 2h = 16 m

viii. e = 16 m (b or 2h, whichever is smaller)

ix. e/4 = 4 m

x. e/10 = 1,6m

EN 1991-1-4 § 7.2.5(1) Figure 7.8

Figure B.5 defines the external pressure coefficients cpe,10 on roofs for zones F, G, H, I and J with a wind on long side.

EN 1991-1-4 § 7.2.7(2) Figure 7.10c


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3 - 52

Trough

Trough

- 0,9+ 0,2 - 0,8

+ 0,2

- 0,5

- 0,9 + 0,2

Ridge

1,6 m

4 m4 m

b = 60 m

Wind

d = 32 m

- 0,3 + 0,2

- 0,5 HH

HH

GG

FF FF

HH - 0,9

II

Figure B.5 cpe,10 for zones F, G, H and I with wind on long side

3.2. Internal pressure coefficients cpi

3.2.1. Persistent or transient design situation

The doors are assumed to stay shut during severe gales:

cpi = + 0,2

And cpi = -0,3

with reference height for the internal pressure: zi = ze = h = 8 m

EN 1991-1-4 § 7.2.9(6) § 7.2.9(7)

3.2.2. Accidental design situation

A door opens upwind (wind on gable): this face is dominant and area of the openings at the dominant face = 3 area of the openings in the remaining faces:

cpi = 0,90 cpe

cpi = 0,90 (+0,7) = +0,63

A door opens downwind (wind on long side): this face is dominant and area of the openings at the dominant face = 3 area of openings in the remaining faces.

EN 1991-1-4 § 7.2.9(3) § 7.2.9(5)


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3 - 53

The most severe case is when the opening is in a zone where |cpe| is the highest (the door is completely in zone B).

cpi = 0,90 cpe

cpi = 0,90 -0,8 = -0,72

EN 1991-1-4 § 7.2.9(6)

4. Friction forces 4.1. Wind on gable

The area of the external surfaces parallel to the wind is calculated by:

60 2 (6 + 8,25 2) = 2700 m2

The area of the external surfaces perpendicular to the wind is:

2 2 16 (6 + 1) = 448 m2

The area of the external surfaces parallel to the wind is higher than 4 area of external surfaces perpendicular to the wind: friction forces should be taken into account:

EN 1991-1-4 § 5.3(4)

4 h = 32 m

2 b = 64 m

4 h < 2 b

The friction forces apply on the area Afr:

Afr = 2 (60 – 32) (6 + 8,25 2) = 1260 m2

EN 1991-1-4 § 7.5(3)

For a smooth surface (steel):

cfr = 0,01

and the friction force Ffr (acting in the direction of the wind):

Ffr = cfr qp(ze) Afr = (0,01 66 1260) 10-2 = 8,316 kN

EN 1991-1-4 § 5.5(3)

4 h < 2 b

The friction forces apply on the area Afr:

Afr = 2 (60 – 32) (6 + 8,25 2) = 1260 m2

EN 1991-1-4 § 7.5(3)

For a smooth surface (steel):

cfr = 0,01

and the friction force Ffr (acting in the direction of the wind):

Ffr = cfr qp(ze) Afr = (0,01 66 1260) 10-2 = 8,316 kN

EN 1991-1-4 § 5.5(3)

4.2. Wind on long side

Area of external surfaces parallel to the wind < 4 area of external surfaces perpendicular to the wind: friction forces should not be taken account

EN 1991-1-4 § 5.3(4)


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3 - 54

5. Wind forces on surfaces

F/Aref = cscd qp(ze) cpe – qp(zi) cpi

with: cscd = 1 (height < 15 m)

qp(ze) = qp(zi) = 0,66 kN/m2

The figures below show the wind forces per unit surfaces:

F/Aref = 0,66 (cpe – cpi) (in kN/m2)

EN 1991-1-4 § 6.2(1)b

Wind

+0,33

-0,99

-0,53 -0,46

-0,33

-0,92

-0,66

-0,46

Ffr = 8,32 kN

Figure B.6 Wind on gable with cpi = +0,2

Wind

+0,66

-0,66

-0,20 -0,13

0

-0,59

-0,33

-0,13

Ffr = 8,32 kN

Figure B.7 Wind on gable with cpi = -0,3


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3 - 55

-0,73

Wind

+0,33

-0,73 (+ 0)

-0,33(+ 0)

-0,46

-0,33

-0,92

-0,66

-0,46 -0,73(+ 0)

-0,66(+ 0)

Figure B.8 Wind on long side with cpi = +0,2

The values in brackets should be used together.

Wind

+0,66

-0,40 (+0,33)

-0 (+0,33)

-0,13

0

-0,59

-0,33

-0,13 -0,40(+0,33)

-0,33(+0,33)

-0,40

Figure B.9 Wind on long side with cpi = -0,3

Values in brackets should be used together.


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3 - 56

Wind

+0,07

-1,25

-0,79 -0,73

-0,59

-1,19

-0,92

-0,73

Ffr = 8,32 kN

Figure B.10 Accidental design situation: door open upwind (wind on gable)

with cpi = +0,6

Wind

+0,92

-0,13 (+0,59)

-0,26(+0,59)

+0,13

+0,26

-0,33

-0,7

+0,13 -0,13 (+0,59)

-0,07(+0,59)

+0,13

Figure B.11 Accidental design situation: door open downwind (wind on long

side) with cpi = -0,7

Values in brackets should be used together



Part 4: Detailed Design of Portal

Frames


Part 4: Detailed Design of Portal

Frames

4 - ii

Part 4: Detailed Design of Portal Frames

4 - iii

FOREWORD

This publication is part four of the design guide, Single-Storey Steel Buildings.




Part 3: Actions













4 - iv


4 - v

Contents Page No

FOREWORD iii

SUMMARY vii

1 INTRODUCTION 1 1.1 Scope 1 1.2 Computer-aided design 1

2 SECOND ORDER EFFECTS IN PORTAL FRAMES 3 2.1 Frame behaviour 3 2.2 Second order effects 4 2.3 Design summary 5

3 ULTIMATE LIMIT STATE 6 3.1 General 6 3.2 Imperfections 8 3.3 First order and second order analysis 13 3.4 Base stiffness 16 3.5 Design summary 18

4 SERVICEABILITY LIMIT STATE 20 4.1 General 20 4.2 Selection of deflection criteria 20 4.3 Analysis 20 4.4 Design summary 20

5 CROSS-SECTION RESISTANCE 21 5.1 General 21 5.2 Classification of cross-section 21 5.3 Member ductility for plastic design 21 5.4 Design summary 22

6 MEMBER STABILITY 23 6.1 Introduction 23 6.2 Buckling resistance in EN 1993-1-1 24 6.3 Out-of-plane restraint 26 6.4 Stable lengths adjacent to plastic hinges 28 6.5 Design summary 31

7 RAFTER DESIGN 32 7.1 Introduction 32 7.2 Rafter strength 32 7.3 Rafter out-of-plane stability 33 7.4 In-plane stability 37 7.5 Design summary 37

8 COLUMN DESIGN 38 8.1 Introduction 38 8.2 Web resistance 38 8.3 Column stability 38 8.4 In-plane stability 41 8.5 Design summary 41

9 BRACING 42 9.1 General 42


4 - vi

9.2 Vertical bracing 42 9.3 Plan bracing 48 9.4 Restraint to inner flanges 50 9.5 Bracing at plastic hinges 51 9.6 Design summary 52

10 GABLES 53 10.1 Types of gable frame 53 10.2 Gable columns 53 10.3 Gable rafters 54

11 CONNECTIONS 55 11.1 Eaves connections 55 11.2 Apex connections 56 11.3 Bases, base plates and foundations 57 11.4 Design summary 62

12 SECONDARY STRUCTURAL COMPONENTS 63 12.1 Eaves beam 63 12.2 Eaves strut 63

13 DESIGN OF MULTI-BAY PORTAL FRAMES 64 13.1 General 64 13.2 Types of multi-bay portals 64 13.3 Stability 65 13.4 Snap through instability 66 13.5 Design summary 66

REFERENCES 67

Appendix A Practical deflection limits for single-storey buildings 69 A.1 Horizontal deflections for portal frames 69 A.2 Vertical deflections for portal frames 71

Appendix B Calculation of cr,est 73 B.1 General 73 B.2 Factor cr,s,est 73

Appendix C Determination of Mcr and Ncr 76 C.1 Mcr for uniform members 76 C.2 Mcr for members with discrete restraints to the tension flange 77 C.3 Ncr for uniform members with discrete restraints to the tension flange 79

Appendix D Worked Example: Design of portal frame using elastic analysis 81


4 - vii

SUMMARY

This publication provides guidance on the detailed design of portal frames to the Eurocodes.

An introductory section reviews the advantages of portal frame construction and clarifies that the scope of this publication is limited to portal frames without ties between eaves. Most of the guidance is related to single span frames, with limited guidance for multi-span frames.

The publication provides guidance on:

The importance of second order effects in portal frames

The use of elastic and plastic analysis

Design at the Ultimate and Serviceability Limit States

Element design: cross-section resistance and member stability

Secondary structure: gable columns, bracing and eaves members.

The document includes a worked example, demonstrating the assessment of sensitivity to second order effects, and the verification of the primary members.


4 - viii


4 - 1

1 INTRODUCTION

Steel portal frames are very efficient and economical when used for single-storey buildings, provided that the design details are cost effective and the design parameters and assumptions are well chosen. In countries where this technology is highly developed, the steel portal frame is the dominant form of structure for single-storey industrial and commercial buildings. It has become the most common structural form in pitched roof buildings, because of its economy and versatility for a wide range of spans.

Where guidance is given in detail elsewhere, established publications are referred to, with a brief explanation and review of their contents. Cross-reference is made to the relevant clauses of EN 1993-1-1[1].

1.1 Scope This publication guides the designer through all the steps involved in the detailed design of portal frames to EN 1993-1-1, taking due account of the role of computer analysis with commercially available software. It is recognised that the most economic design will be achieved using bespoke software. Nevertheless this document provides guidance on the manual methods used for initial design and the approaches used in software. The importance of appropriate design details is emphasised, with good practice illustrated.

This publication does not address portal frames with ties between eaves. These forms of portal frame are relatively rare. The ties modify the distribution of bending moments substantially and increase the axial force in the rafter dramatically. Second order software must be used for the design of portal frames with ties at eaves level.

An introduction to single-storey structures, including portal frames, is given in a complementary publication Single-storey steel buildings. Part 2: Concept design[2].

1.2 Computer-aided design Although portal frames may be analysed by manual methods and members verified by manual methods, software is recommended for greatest structural efficiency. Bespoke software for portal frame design is widely available, which will:

undertake elastic-plastic analysis

allow for second order effects

verify members

verify connections.

Generally, a number of different load combinations will have to be considered during the design of a portal frame. Software that verifies the members for all load combinations will shorten the design process considerably.


4 - 2

Whilst manual design may be useful for initial sizing of members and a thorough understanding of the design process is necessary, the use of bespoke software is recommended.


4 - 3

2 SECOND ORDER EFFECTS IN PORTAL FRAMES

2.1 Frame behaviour The strength checks for any structure are valid only if the global analysis gives a good representation of the behaviour of the actual structure.

When any frame is loaded, it deflects and its shape under load is different from the un-deformed shape. The deflection causes the axial loads in the members to act along different lines from those assumed in the analysis, as shown diagrammatically in Figure 2.1 and Figure 2.2. If the deflections are small, the consequences are very small and a first-order analysis (neglecting the effect of the deflected shape) is sufficiently accurate. However, if the deflections are such that the effects of the axial load on the deflected shape are large enough to cause significant additional moments and further deflection, the frame is said to be sensitive to second order effects. These second order effects, or P-delta effects, can be sufficient to reduce the resistance of the frame.

These second order effects are geometrical effects and should not be confused with non-linear behaviour of materials.

As shown in Figure 2.1, there are two categories of second order effects:

Effects of deflections within the length of members, usually called P- (P-little delta) effects.

Effects of displacements of the intersections of members, usually called P- (P-big delta) effects.

1 4

32

1

2

3

Figure 2.1 Asymmetric or sway mode deflection


4 - 4

Figure 2.2 Symmetric mode deflection

The practical consequence of P- and P- effects is to reduce the stiffness of the frames and its elements below that calculated by first-order analysis. Single-storey portals are sensitive to the effects of the axial compression forces in the rafters and columns. These axial forces are commonly of the order of 10% of the elastic critical buckling loads of the rafters and columns, around which level the reduction in effective stiffness becomes important.

2.2 Second order effects Second order effects increase not only the deflections but also the moments and forces beyond those calculated by first-order analysis. Second order analysis is the term used to describe analysis methods in which the effects of increasing deflection under increasing load are considered explicitly in the solution, so that the results include the P- and P- effects described in Section 2.1. The results will differ from the results of first-order analysis by an amount dependent on the magnitude of the P- and P- effects.

The effects of the deformed geometry are assessed in EN 1993-1-1 by calculating the factor cr, defined as:

Ed

cr

FF

cr

where:

Fcr is the elastic critical load vector for global instability, based on initial elastic stiffnesses

FEd is the design load vector on the structure.

Second order effects can be ignored in a first order analysis when the frame is sufficiently stiff. According to § 5.2.1 (3), second order effects may be ignored when:

For elastic analysis: cr 10

For plastic analysis: cr 15


4 - 5

cr may be found using software or (within certain limits) using Expression 5.2 from EN 1993-1-1. When the frame falls outside the limits, an alternative expression may be used to calculate an approximate value of cr. Further details are given in Section 3.3.

When second order effects are significant, two options are possible:

Rigorous 2nd order analysis (i.e. in practice, using an appropriate second order software)

Approximate 2nd order analysis (i.e. hand calculations using first-order analysis with appropriate allowance for second order effects).

In the second method, also known as ‘modified first order analysis’, the applied actions are amplified, to allow for second order effects while using first order calculations. This method is described in Section 3.3.

2.3 Design summary Second order effects occur in the overall frame (P- ) and within elements

(P-).

Second order effects are quantified by the factor cr.

For portal frames, the expression given to calculate cr in EN 1993-1-1 § 5.2.1(4) may be used within certain limits. Outside the limits prescribed by the Standard, an alternative calculation must be made, as described in Appendix B.

Second order effects may be significant in practical portal frames.

Second order effects may be accounted for by either rigorous second order analysis using software or by a first order analysis that is modified by an amplification factor on the actions.


4 - 6

3 ULTIMATE LIMIT STATE

3.1 General Methods of frame analysis at the Ultimate Limit State fall broadly into two types – elastic analysis (see Section 3.2.2) and plastic analysis (see Section 3.2.3). The latter term covers both rigid-plastic and elastic-plastic analyses.

The formation of hinges and points of maximum moment and the associated redistribution of moment around the frame that are inherent to plastic analysis are key to the economy of most portal frames. They ‘relieve’ the highly stressed regions and allow the capacity of under-utilised parts of the frame to be mobilised more fully.

These plastic hinge rotations occur at sections where the bending moment reaches the plastic moment or resistance at load levels below the full ULS loading.

An idealised ‘plastic’ bending moment diagram for a symmetrical portal under symmetrical vertical loads is shown in Figure 3.1. This shows the position of the plastic hinges for the plastic collapse mechanism. The first hinge to form is normally adjacent to the haunch (shown in the column in this case). Later, depending on the proportions of the portal frame, hinges form just below the apex, at the point of maximum sagging moment.

A portal frame with pinned bases has a single degree of indeterminacy. Therefore, two hinges are required to create a mechanism. The four hinges shown in Figure 3.1 only arise because of symmetry. In practice, due to variations in material strength and section size, only one apex hinge and one eaves hinge will form to create the mechanism. As there is uncertainty as to which hinges will form in the real structure, a symmetrical arrangement is assumed, and hinge positions on each side of the frame restrained.

1 11

1 Position of plastic hinges

Figure 3.1 Bending moment diagram resulting from the plastic analysis of a

symmetrical portal frame under symmetrical vertical loading


4 - 7

Most load combinations will be asymmetric because they include either equivalent horizontal forces (EHF; see Section 3.2) or wind loads. A typical loading diagram and bending moment diagram are shown in Figure 3.2. Both the wind and the EHF can act in either direction, meaning the hinge positions on each side of the frame must be restrained.

11

1 Position of plastic hinges

Figure 3.2 Bending moment diagram resulting from plastic analysis of a

symmetrical portal frame under asymmetric loading

A typical bending moment diagram resulting from an elastic analysis of a frame with pinned bases is shown in Figure 3.3. In this case, the maximum moment (at the eaves) is higher than that calculated from a plastic analysis. Both the column and haunch have to be designed for these larger bending moments. The haunch may be lengthened to around 15% of the span, to accommodate the higher bending moment.

Figure 3.3 Bending moment diagram resulting from the elastic analysis of a

symmetrical portal frame under symmetrical loading (haunch at 10% of span is denoted by solid line; that for 15% of span is denoted by a dotted line)


4 - 8

3.2 Imperfections Frame imperfections are addressed in EN 1993-1-1§ 5.3.2. Generally, frame imperfections must be modelled. The frame may be modelled out-of-plumb, or alternatively, a system of equivalent horizontal forces (EHF) may be applied to the frame to allow for imperfections. The use of EHF is recommended as the simpler approach.

3.2.1 Equivalent horizontal forces

The use of equivalent horizontal forces (EHF) to allow for the effects of initial sway imperfections is allowed by § 5.3.2(7). The initial imperfections are given by Expression 5.5, where the initial imperfection (indicated as an inclination from the vertical) is given as:

= 0 h m

where:

0 is the basic value: 0 = 1/200

0,132

but2

hh h

h is the height of the structure in metres

m1

15,0m

m is the number of columns in a row – for a portal the number of columns in a single frame.

For single span portal frames, h is the height of the column, and m = 2.

It is conservative to set h = m = 1,0.

EHF may be calculated as multiplied by the vertical reaction at the base of the column (including crane loads as appropriate). The EHF are applied horizontally, in the same direction, at the top of each column.

§ 5.3.2(4) states that sway imperfections may be disregarded when HEd 0,15 VEd.

It is recommended that this relaxation is tested by comparing the net total horizontal reaction at the base with the net total vertical reaction. In many cases, the expression given in 5.3.2(4) will mean that EHF are not required in combinations of actions that include wind actions. However, EHF will need to be included in combinations of only gravity actions.

3.2.2 Elastic analysis

Elastic analysis is the most common method of analysis for general structures, but will usually give less economical portal structures than plastic analysis. EN 1993-1-1 allows the plastic cross-sectional resistance to be used with the results of elastic analysis, provided the section class is Class 1 or Class 2. In addition, it allows 15% of moment redistribution as defined in EN 1993-1-1 § 5.4.1.4(B)


4 - 9

Designers less familiar with steel design may be surprised by the use of plastic moment of resistance and redistribution of moment in combination with elastic analysis. However, it should be noted that, in practice:

Because of residual stresses, member imperfections, real inertias that differ from those assumed, real connection stiffness that differs from that assumed and lack of fit at connections, the true distribution of moments in any frame is likely to differ substantially from that predicted by elastic analysis.

Class 1 and 2 sections are capable of some plastic rotation before there is any significant reduction in capacity due to local buckling. This justifies a redistribution of 15% of moments from the nominal moments determined from the elastic analysis.

The results of elastic analysis should therefore be regarded as no more than a reasonably realistic system of internal forces that are in equilibrium with the applied loads.

In a haunched portal rafter, up to 15% of the bending moment at the sharp end of the haunch can be redistributed, if the bending moment exceeded the plastic resistance of the rafter and the moments and forces resulting from redistribution can be carried by the rest of the frame. Alternatively, if the moment at the midspan of the portal exceeded the plastic resistance of the rafter, this moment can be reduced by up to 15% by redistribution, provided that the remainder of the structure can carry the moments and forces resulting from the redistribution.

If an elastic analysis reveals that the bending moment at a particular location exceeds the plastic moment of resistance, the minimum moment at that point after redistribution should be the plastic moment of resistance. This is to recognise that a plastic hinge may form at that point. To allow reduction below the plastic resistance would be illogical and could result in dangerous assumptions in the calculation of member buckling resistance.

3.2.3 Plastic analysis

Plastic analysis is not used extensively in continental Europe, even though it is a well-proven method of analysis. However, plastic analysis is used for more than 90% of portal structures in the UK and has been in use for 40 years.

Traditionally, manual calculation methods were used for a plastic analysis (the so-called graphical method, or the virtual work method, etc.). These manual methods are not discussed in this publication, because plastic analysis is usually undertaken with software, most of the time using the elastic-perfectly-plastic method. The principle of this method is illustrated in Figure 3.4 and Figure 3.5.


4 - 10

M

M

M

y

p

1

1

23

2

1 True behaviour 2 Elastic-perfectly-plastic model 3 Unloading behaviour

Figure 3.4 Moment/rotation behaviour and elastic-perfectly-plastic model for

a Class 1 section

(4)

2

63

5

1

VEd

Ed

EdH

HEd,V (7)

1 Elastic response 2 First hinge forms 3 Second hinge forms 4 Horizontal displacement

5 True behaviour 6 Elastic/perfectly plastic model 7 Increasing vertical and (in proportion)

horizontal load

Figure 3.5 Simple model of a portal frame subject to increasing vertical and

horizontal loads, with failure governed by a sway mechanism


4 - 11

The elastic-perfectly-plastic model, Figure 3.4, assumes that the members deform as linear elastic elements until the applied moment reaches the full plastic moment Mp. The subsequent behaviour is assumed to be perfectly plastic without strain hardening.

With elastic-perfectly-plastic analysis, the load is applied in small increments, with hinges inserted in the analysis model at any section that reaches its full plastic moment, Mp as illustrated in Figure 3.6. If the appropriate computer software is used, it should be possible to predict hinges that form, rotate, then unload or even reverse. The final mechanism will be the true collapse mechanism and will be identical to the lowest load factor mechanism that can be found by the rigid-plastic method.

The elastic/perfectly-plastic method has the following advantages:

The true collapse mechanism is identified.

All plastic hinges are identified, including any that might form and subsequently unload. Such (transient) hinges would not appear in the final collapse mechanism but would nevertheless need restraint.

Hinges forming at loads greater than ULS can be identified. Such hinges do not need restraint, as the structure can already carry the ULS loads. This may produce economies in structures where the member resistance is greater than necessary, as occurs when deflections govern the design or when oversize sections are used.

The true bending moment diagram at collapse, or at any stage up to collapse, can be identified.

3.2.4 Elastic vs. plastic analysis

As discussed in Section 3.1, plastic analysis generally results in more economical structures because plastic redistribution allows smaller members to carry the same loads. For frames analysed plastically, haunch lengths are generally around 10% of the span.

Where deflections (SLS) govern design, there is no advantage in using plastic analysis for the ULS. If stiffer sections are selected in order to control deflections, it is quite possible that no plastic hinges form and the frame remains elastic at ULS.

The economy of plastic analysis also depends on the bracing system, because plastic redistribution imposes additional requirements on the restraint to members, as discussed in Section 6.3. The overall economy of the frame might, therefore, depend on the ease with which the frame can be restrained.

Plastic analysis should only be contemplated if commercial software is available. The more sophisticated software packages carry out second order (P-∆) elastic-plastic analysis directly, significantly simplifying the overall design process. The ready availability of elastic/plastic design software makes it as easy to adapt full plastic analysis. The resulting limitation to Class 1 sections, which are required at potential hinge positions, is not significant.


4 - 12

(a)

First hinge forms

1

(b)

Load increases – rafter approaches yield

1

(c)

Load increases, second hinge forms and a mechanism leads to collapse

11

(d)

1 Plastic resistance moment

Figure 3.6 Elastic-perfectly-plastic method of analysis, showing state of

frame as horizontal and vertical loads are increased proportionally a) Elastic throughout; (b) Plastic hinge at eaves;(c) Rafters approaching plasticity; (d) Plastic hinge in rafter

It is recognised that some redistribution of moments is possible, even with the use of elastic design. EN 1993-1-1 § 5.4.1.4(B) allows 15% redistribution, as discussed in Section 3.2.2, although this is uncommon in practice.

Where haunch lengths of around 15% of the span are acceptable and the lateral loading is small, the elastic bending moment diagram will be almost the same as the plastic collapse bending moment diagram. As illustrated in Figure 3.3, the maximum hogging moment at the end of the haunch is similar to the maximum sagging moment in the rafter. In such cases, an elastic analysis may provide an equivalent solution to a plastically analysed frame.


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3.3 First order and second order analysis For both plastic analysis and elastic analysis of frames, the choice of first-order or second order analysis may be governed by the in-plane flexibility of the frame, measured by the factor cr (see Section 3.3.1). In practice, the choice between first and second order analysis is also dependent on the availability of software. Even if a portal frame was sufficiently stiff that second order effects were small enough to be ignored, it may be convenient still to use second order analysis software.

When a second order analysis is required but is not available, modified first order methods can be useful for calculations. A modified first order approach is slightly different for elastic and plastic analysis, and is described in Sections 3.3.2 and 3.3.3. In elastic analysis, the horizontal actions are amplified; in plastic analysis, all actions are amplified.

3.3.1 cr factor

Expression 5.2 of EN 1993-1-1 § 5.2.1(4)B gives cr as:

EdH,Ed

Edcr

h

V

H

Note 1B and Note 2B of that clause limit the application of Expression 5.2 to roofs with shallow roof slopes and where the axial force in the rafter is not significant. Thus:

a roof slope is considered as shallow at slopes no steeper than 26°

axial force in the rafter may be assumed to be significant if Ed

y3,0N

Af .

A convenient way to express the limitation on the axial force is that the axial force is not significant if:

crEd 09.0 NN

Where

Ncr is the elastic critical buckling load for the complete span of the rafter

pair, i.e. 2

2

crL

EIπN

L is the developed length of the rafter pair from column to column, taken as span/Cos θ (θ is the roof slope)

If the limits are satisfied, then Expression 5.2 may be used to calculate cr. In most practical portal frames, the axial load in the rafter will be significant and Expression 5.2 cannot be used.

When the axial force in the rafter is significant, Appendix B provides an alternative, approximate method to calculate the measure of frame stability, defined as cr,est. In many cases, this will be a conservative result. Accurate values of cr may be obtained from software.


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3.3.2 Modified first order, for elastic frame analysis

The ‘amplified sway moment method’ is the simplest method of allowing for second order effects for elastic frame analysis; the principle is given in EN 1993-1-1, § 5.2.2(5B).

A first-order linear elastic analysis is first carried out; then all horizontal loads are increased by an amplification factor to allow for the second order effects. The horizontal loads comprise the externally applied loads, such as the wind load, and the equivalent horizontal forces used to allow for frame imperfections; both are amplified.

Provided cr 3,0 the amplification factor is:

cr11

1

If the axial load in the rafter is significant, and cr,est has been calculated in accordance with Appendix B, the amplifier becomes:

estcr,111

If cr or cr,est is less than 3,0 second order software should be used.

3.3.3 Modified first order, for plastic frame analysis

Design philosophy

In the absence of elastic-plastic second order analysis software, the design philosophy is to derive loads that are amplified to account for the effects of deformed geometry (second order effects). Application of these amplified loads through a first-order analysis gives the bending moments, axial forces and shear forces that include the second order effects approximately.

The amplification is calculated by a method that is sometimes known as the Merchant-Rankine method. Because, in plastic analysis, the plastic hinges limit the moments resisted by the frame, the amplification is performed on all the actions that are applied to the first-order analysis (i.e. all actions and not only the horizontal forces related to wind and imperfections).

The Merchant-Rankine method places frames into one of two categories:

Category A: Regular, symmetric and mono-pitched frames

Category B: Frames that fall outside of Category A but excluding tied portals.

For each of these two categories of frame, a different amplification factor should be applied to the actions. The Merchant-Rankine method has been verified for frames that satisfy the following criteria:

1. Frames in which 8h

L for any span

2. Frames in which 3cr


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where:

L is span of frame (see Figure 3.7)

h is the height of the lower column at either end of the span being considered (see Figure 3.7)

cr is the elastic critical buckling load factor.

If the axial load in the rafter is significant (see Section 3.3.1), cr,est should be calculated in accordance with Appendix B).

Other frames should be designed using second order elastic-plastic analysis software.

Amplification factors

Category A: Regular, symmetric and nearly symmetric pitched and mono-pitched frames (See Figure 3.7).

Regular, symmetric and mono-pitched frames include single span frames and multi-span frames in which there is only a small variation in height (h) and span (L) between the different spans; variations in height and span of the order of 10% may be considered as being sufficiently small.

In the traditional industrial application of this approach, first-order analysis may be used for such frames if all the applied actions are amplified by

cr11

1

, or

estcr,111

if the axial force in the rafter was found to be

significant.

h

L L

h

1 2

L L

h

3 1 Mono-pitch 2 Single-span 3 Multi-span

Figure 3.7 Examples of Category A frames


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Category B: Frames that fall outside of Category A (See Figure 3.8), but excluding tied portals.

For frames that fall outside of Category A, first-order analysis may be used if all the applied loads are amplified by:

cr11

1,1

or

estcr,111,1

if the axial force in the rafter was found to be

significant.

1 2

L LL1 12(>> )

3 1 Asymmetric 2 Sloping site 3 Multi-span with unequal spans

Figure 3.8 Examples of Category B frames

3.4 Base stiffness Analysis should take account of the rotational stiffness of the bases. The following simple rules in this section are recommended. These recommendations might not be accepted in certain countries; the relevant National Annex and the local regulatory authorities should be consulted.

It is important to distinguish between column base resistance and column base stiffness. Column base resistance is only relevant to elastic-plastic or rigid-plastic calculations of frame resistance, not to deflections. Column base stiffness is relevant to elastic-plastic or elastic frame analysis for both resistance and deflection.

If any base stiffness is assumed in ULS design, the base details and foundation must be designed to have sufficient resistance to sustain the calculated moments and forces.

In many general analysis computer programmes, these base stiffnesses are most conveniently modelled by the introduction of a dummy member, as shown in Figure 3.9.


4 - 17

h

0.75 h

Figure 3.9 Dummy member to model nominally rigid column base

Note that the reaction at the pinned end of the dummy member will affect the reaction at the column base. This must be corrected by taking the base reaction equal to the axial force in the column, which equals the sum of the reactions at the base and the pinned end of the dummy member.

3.4.1 Pinned and rocker bases

Where a true pin or rocker is used, as illustrated in Figure 3.10, the rotational stiffness is zero. The use of such bases is rarely justified in practice. Where they are adopted, careful consideration needs to be given to the transfer of shear into the foundation, and temporary stability of the column during erection.

Figure 3.10 Examples of zero stiffness column bases

3.4.2 Nominally rigid column bases

If a column is rigidly connected to a suitable foundation, the following recommendations should be adopted:

Elastic global analysis:

For Ultimate Limit State calculations the stiffness of the base can be taken as equal to the stiffness of the column.

For Serviceability Limit State calculations the base can be treated as rigid to determine deflections under serviceability loads.


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Plastic global analysis:

Any base moment capacity between zero and the plastic moment capacity of the column may be assumed, provided that the foundation is designed to resist a moment equal to this assumed moment capacity, together with the forces obtained from the analysis.

Elastic - plastic global analysis:

The assumed base stiffness must be consistent with the assumed base moment capacity, but should not exceed the stiffness of the column.

3.4.3 Nominally semi-rigid column bases

A nominal base stiffness of up to 20 % of the column may be assumed in elastic global analysis, provided that the foundation is designed for the moments and forces obtained from this analysis.

3.4.4 Nominally pinned bases

If a column is nominally pin – connected to a foundation that is designed assuming that the base moment is zero, the base should be assumed to be pinned when using elastic global analysis to calculate the other moments and forces in the frame under Ultimate Limit State loading.

The stiffness of the base may be assumed to be equal to the following proportion of the column stiffness:

10% when calculating cr or cr,est

20% when calculating deflections under serviceability loads.

Column base plates with a relatively thin base plate and four bolts outside the profile of the column section are considered in some countries as nominally pinned if they have sufficient deformation capacity, although in fact they will exhibit semi-rigid behaviour. Such bases have the additional practical advantage that they provide sufficient base stiffness to enable the column to be free-standing during erection, and assist in the aligning of the column.

3.5 Design summary Analysis for the Ultimate Limit State:

may be carried out either by elastic analysis or by plastic analysis

should take account of second order (P-) effects, when cr or cr,est is less an 10 (elastic analysis) or 15 (plastic analysis)

if necessary, second order effects can be accounted for either directly (using a second order analysis) or by the use of a modified first order analysis with an amplification factor.

For most structures, greatest economy (and ease of analysis and design) will be achieved by the use of software that:

is based on elastic/perfectly plastic moment/rotation behaviour

takes direct account of second order (P-) effects.


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A summary of the assessment of sensitivity to second order effects and the amplification to allow for second order effects is given in Table 3.1.

Table 3.1 Second order effects: assessment and amplification factors

Restrictions Elastic analysis Plastic analysis

shallow slopes, and rafter axial force not significant

cr cr Measure of sensitivity to second order effects

steep slopes, and rafter axial force significant

cr,est cr,est

Regular frames

cr11

1

or

estcr,111

cr11

1

or

estcr,111

Amplifier to allow for second order effects Irregular frames, but

excluding tied portals

cr11

1

or

estcr,111

cr

,

11

11or

estcr,111,1

Amplifier applied to: Horizontal loads only

All loads


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4 SERVICEABILITY LIMIT STATE

4.1 General The Serviceability Limit State (SLS) analysis should be performed using the SLS load cases, to ensure that the deflections are acceptable at ‘working loads’.

4.2 Selection of deflection criteria No specific deflection limits are set in EN 1993-1-1. According to EN 1993-1-1 § 7.2 and EN 1990, Annex A1.4, deflection limits should be specified for each project and agreed with the client. The relevant National Annex to EN 1993-1-1 may specify limits for application in individual countries. Where limits are specified’ they have to be satisfied. Where limits are not specified, Appendix A of this document presents typical limits.

If the structure contains overhead travelling cranes, the spread of the columns at the level of the crane is likely to be an important design criterion. In many cases, it will be necessary to provide stiffer steel sections than are necessary for the ULS design, or to provide some fixity in the base and foundation. An alternative is a tied portal (when second order analysis must be used) or a truss.

4.3 Analysis The SLS analysis is normally a first-order (elastic) analysis. The designer should verify plastic hinges do not form at SLS, simply to validate the deflection calculations.

4.4 Design summary The Serviceability Limit State (SLS):

Is assessed by first order analysis

Uses deflection criteria defined in the relevant National Annex or agreed with the client.


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5 CROSS-SECTION RESISTANCE

5.1 General EN 1993-1-1 requires that the resistance of cross-sections and the member buckling resistance are checked by separate calculations. Additional checks are required for the resistance of webs to shear buckling and buckling due to transverse loads.

The calculated resistance depends on the classification of the cross-section. Cross-section resistance is treated in Section 6.2 of EN 1993-1-1.

5.2 Classification of cross-section In EN 1993-1-1, cross-sections are classified according to the relative thickness of the flanges and web, together with the magnitude of the bending moment and axial compression on the section. The classification according to the slenderness of flange or web elements is given in EN 1993-1-1 Table 5.2. EN 1993-1-1 covers sections under axial load alone, under pure bending and under combined axial load and bending moment. The class of a section is the highest class of either the flanges or the web.

It is important to note that the classification depends on both the geometry of the cross-section and the ratio of the moments and axial force at the cross-section. For example, a typical I-beam might be Class 1 under pure moment but Class 2 or 3 under pure axial loading; under combined loading it might then be Class 1, 2, or 3, depending on the proportions of axial force and bending moment at the cross-section under consideration.

The classes indicate the following structural behaviour:

Class 1 can support a rotating plastic hinge without any loss of resistance from local buckling.

Class 2 can develop full plastic moment but with limited rotation capacity before local buckling reduces resistance.

Class 3 can develop yield in extreme fibres but local buckling prevents development of plastic moment.

Class 4 has proportions such that local buckling will occur at stresses below first yield.

5.3 Member ductility for plastic design As specified in EN 1993-1-1:2005 § 5.6, all members formed from rolled sections (and therefore uniform apart from haunches) containing plastic hinges that rotate prior to reaching the ULS loading must have a Class 1 cross-section. Elsewhere, they may be Class 2.


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§ 5.6(3) provides additional requirements for non-uniform sections, i.e. the rafters and their haunches. These will automatically be satisfied by the general requirement for uniform sections in the paragraph above where the haunch is formed from a cutting from the rafter section, or cut from a slightly larger rolled section.

5.4 Design summary Cross-section classification depends on the ratio of moment and axial load.

All critical cross-sections need to be checked for cross-section resistance in accordance with Section 6.2 of EN 1993-1-1.

For plastic design, all sections containing plastic hinges must be Class 1.


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6 MEMBER STABILITY

6.1 Introduction Members must be checked for the combined effects of axial load and buckling. In general, this will be by satisfying Expressions 6.61 and 6.62 of EN 1993-1-1, as described in Section 6.2. In the special circumstances where there are plastic hinges in members, EN 1993-1-1 gives particular requirements, as described in Section 6.4.

In-plane buckling is buckling about the major axis of the member. As explained in Section 6.1.1, there are no intermediate restraints when considering in-plane buckling of a member in a portal frame.

Out-of-plane buckling concerns buckling about the minor axis of the member. In a portal frame the secondary steelwork can be used to provide restraints, and so increase the buckling resistance, as described in Section 6.3.

6.1.1 Member buckling in portal frames

N

N

1

4

3

2M

M

1

2

1 Intersection with column at eaves 2,3 Intersection with purlins (typical) 4 Apex of frame

Figure 6.1 Diagrammatic representation of a portal frame rafter

Figure 6.1 shows a simple representation of the issues that need to be addressed when considering the stability of a member within a portal frame, in this example a rafter between the eaves and apex. The following points should be noted:

There can be no intermediate points of restraint for in-plane buckling between the main nodes of the frame, 1 and 4.

Intermediate restraints may be introduced (nodes 2 and 3) against out-of-plane buckling.


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Practical design addresses this interaction in several ways:

Out-of-plane stability near plastic hinges is generally addressed by the concept of stable lengths, Lstable, Lm, Lk and Ls. These are assumed to be independent of any interaction with in-plane stability effects (see Section 6.4.).

Interaction between bending moment and axial load is addressed by simultaneously satisfying Expressions 6.61 and 6.62 of EN 1993-1-1. This is usually undertaken by considering the most onerous out-of-plane check (from any part of the member) with the relevant in-plane check.

6.2 Buckling resistance in EN 1993-1-1 The verification of buckling resistance of members is addressed by several clauses in EN 1993-1-1. The clauses of primary interest in portal frame design are described below.

6.3.1 Uniform members in compression. This clause covers strut buckling resistance and the selection of buckling curves. The clause is primarily concerned with flexural buckling, but also addresses torsional and torsional-flexural buckling. These latter modes of failure will not govern the IPE sections and similar cross-sections adopted for portal frames.

6.3.2 Uniform members in bending. This clause covers lateral-torsional buckling of beams.

The distribution of bending moments along an unrestrained length of beam has an important influence on the buckling resistance. This is accounted for by the choice of C1 factor when calculating Mcr (See Appendix C).

6.3.3 Uniform members in bending and axial compression. This clause addresses the interaction of axial load and moment, in-plane and out-of-plane.

The clause requires the following checks to be carried out unless full second order analysis, including all member imperfections (P–, torsional and lateral imperfections), is utilised.

1

M1

Rkz,

Edz,Edz,yz

M1

Rky,LT

Edy,Edy,yy

M1

Rky

Ed

M

ΔMMk

M

ΔMMk

NN

(6.61)

1

M1

Rkz,

Edz,Edz,zz

M1

Rky,LT

Edy,Edy,zy

M1

Rkz

Ed

MΔMM

kM

ΔMMk

NN

(6.62)

For Class 1, 2, 3 and bi-symmetric Class 4 sections, 0Edz,Edy, MM

It is helpful to define M1

y.Rky

N

as Nb,y,Rd and LT M1

Rky,

M

as Mb,Rd.

Mz.Ed is zero because the frame is only loaded in its plane.


4 - 25

The expressions therefore simplify to:

Rdb,

Edy,yy

Rdy,b,

Ed

M

Mk

N

N 1.0 (from Expression 6.61)

and Rdb,

Edy,zy

Rdz,b,

Ed

M

Mk

N

N 1.0 (from Expression 6.62).

Values of kyy and kzy may be obtained from EN 1993-1-1, either Annex A or Annex B. Annex A generally provides higher design strength for the rafters and columns in portal frames than Annex B. The choice of Annex may be defined in some countries by their National Annexes. The worked example within this publication adopts Annex B values.

The buckling resistances will normally be based on the system length of the rafter and column. Some national regulatory authorities may allow the use of a reduced system length and a buckling length factor. The buckling length factor is 1.0 or smaller, and reflects the increased buckling resistance of members with a degree of end fixity. The buckling length is the product of the length and the buckling length factor, and will be less than the system length. This approach will result in an enhanced buckling resistance.

Clause 6.3.5 Lateral torsional buckling of members with plastic hinges. This clause provides guidance for the members in frames that have been analysed plastically. The clause requires restraint to hinge locations and verification of stable lengths between such restraints and other lateral restraints. Both topics are addressed in more detail in Section 6.4.

6.2.1 Influence of moment gradient

A uniform bending moment is the most onerous loading system when calculating the lateral torsional buckling resistance of a member. A non-uniform moment is less onerous. Annexes A and B in EN 1993-1-1 allow for the effect of the moment gradient, via coefficients Cmi,0 and CmLT etc. These C factors influence the kyy and kzy factors in Expressions 6.61 and 6.62, used when verifying the member.

Although it is conservative to take C factors as 1.0, this is not recommended.


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6.3 Out-of-plane restraint

(a)

(b)

(c)

Figure 6.2 Types of restraint to out-of-plane buckling

Figure 6.2 shows the three basic types of restraint that can be provided to reduce or prevent out-of-plane buckling:

(a) Lateral restraint, which prevents lateral movement of the compression flange.

(b) Torsional restraint, which prevents rotation of a member about its longitudinal axis.

(c) Intermediate lateral restraint to the tension flange. Such restraints are only of limited benefit, but do modify the out-of-plane buckling mode and may therefore allow the distance between torsional restraints to be increased.

As shown in Figure 6.3, practical details may provide more than one type of restraint.


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1 Stay

Figure 6.3 Example of combined lateral and torsional restraint

Purlins attached to the top flange of the rafter and side rails attached to the outer flange of the column provide stability to the rafter in a number of ways:

Direct lateral restraint, when the outer flange is in compression.

Intermediate lateral restraint to the tension flange between torsional restraints, when the outer flange is in tension.

Torsional and lateral restraint to the rafter when the purlin is attached to the tension flange and used in conjunction with rafter stays to the compression flange.

In all cases, the purlins and side rails should be tied back into a system of bracing in the plane of the rafters (see Section 9). Generally, the assumption that the forces are carried back to the bracing system via the roof diaphragm is accepted in many countries, even without supporting calculations. In other countries calculations are necessary, or the purlins can only be assumed to provide restraint if they are aligned directly with the bracing system.

The position of the purlins and side rails will be a balance between the capacity of the purlins themselves, and the necessary spacing required to restrain the primary steel members. The maximum spacing will usually be determined from manufacturers’ load tables. Spacing may have to be reduced to provide restraint to the inside flange at strategic points along the rafter or column, so it would be common to provide purlins at reduced spacing in zones of high bending moment, such as around the eaves haunch.

Normal practice is to locate one purlin at the ‘sharp’ end of the haunch, and one near the apex. The intervening length is split at regular spacing – typically about 1,6 to 1,8 m. A purlin is often located near the end plate of the rafter, and depending on the length of the haunch, one, two or more purlins in the length to the ‘sharp’ end of the haunch, usually at lesser spacing than the main length of rafter.

Additional purlins may be required to carry drifted snow – these may also be used to provide restraint.

Side rails are usually located at positions to suit the cladding, doors and windows. The inside of the flange at the underside of the haunch always requires restraint – it is common to position a side rail at this level.

Purlins and side rails must be continuous in order to offer adequate restraint, as shown in Figure 6.3. A side rail that is not continuous (for example, interrupted by industrial doors) cannot be relied upon to provide adequate restraint.


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6.4 Stable lengths adjacent to plastic hinges 6.4.1 Introduction

EN 1993-1-1 introduces four types of stable length, Lstable, Lm, Lk and Ls. Each is discussed below. Lk and Ls are used to verify member stability between torsional restraints and recognise the stabilising effects of intermediate restraints to the tension flange.

Lstable (Clause 6.3.5.3(1)B)

Lstable is the basic stable length for a uniform beam segment under linear moment and without ‘significant’ axial compression. This simple base case is of limited use in the verification of practical portal frames.

In this context, ‘significant’ may be related to the determination of αcr in EN 1993-1-1 § 5.2.1 4(B) Note 2B. The axial compression is not significant if

crEd 09,0 NN , as explained in Section 3.3.1

Lm (Appendix BB.3.1.1)

Lm is the stable length between the torsional restraint at the plastic hinge and the adjacent lateral restraint. It takes account of both member compression and the distribution of moments along the member. Different expressions are available for:

Uniform members (Expression BB.5)

Three flange haunches (Expression BB.9)

Two flange haunches (Expression BB.10).

Lk (Appendix BB.3.1.2 (1)B)

Lk is the stable length between a plastic hinge location and the adjacent torsional restraint in the situation where a uniform member is subject to a constant moment, providing the spacing of the restraints to either the tension or compression flange is not greater than Lm. Conservatively, this limit may also be applied to a non-uniform moment.

Ls (Appendix BB.3.1.2 (2)B) and (3)B

Ls is the stable length between a plastic hinge location and the adjacent torsional restraint, where a uniform member is subject to axial compression and linear moment gradient, providing the spacing of the restraints to either the tension or compression flange is not greater than Lm.

Different C factors and different expressions are used for linear moment gradients (Expression BB.7) and non-linear moment gradients (Expression BB.8).

Where the segment varies in cross-section along its length, i.e. in a haunch, two different approaches are adopted:

For both linear and non-linear moments on three flange haunches – BB.11

For both linear and non-linear moments on two flange haunches – BB.12.


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6.4.2 Application in practice

The flowcharts in Figures 6.4, 6.5 and 6.6 summarise the practical application of the different stable length formulae for any member segment adjacent to a plastic hinge. In the absence of a plastic hinge, the member segment is verified by conventional elastic criteria using Expressions 6.61 and 6.62.

Figure 6.4 Decision tree for selecting appropriate stable length criteria for

any segment in a portal frame – Sheet 1


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Figure 6.5 Decision tree for selecting appropriate stable length criteria for

any segment in a portal frame – Sheet 2


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Figure 6.6 Decision tree for selection of appropriate stable length criteria in a

portal frame – Sheet 3

6.5 Design summary Before proceeding to the detailed verification of rafter and column stability, designers should appreciate that:

Torsional and lateral restraints need to be provided at all hinge positions, as required by § 6.3.5.2.

EN 1993-1-1 recognises four different types of stable lengths, Lstable, Lm, Lk and Ls, adjacent to plastic hinge positions. Lateral restraints must be provided adjacent to the hinge at no greater distance than Lstable or Lm and torsional restraints at no greater distance than Lk or Ls, as appropriate.

In zones where there is no plastic hinge, each member must satisfy the simplified forms of Expressions 6.61 and 6.62. These consider in-plane and out-of-plane stability and their potential interaction.


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7 RAFTER DESIGN

7.1 Introduction Portal frame design is usually governed by the verification of members at ULS. Although SLS checks are important, orthodox frames are generally sufficiently stiff to satisfy the SLS deflection limits. Economy in the overall frame can usually be achieved by the use of plastic analysis; this requires Class 1 or 2 sections throughout and Class 1 where there is a hinge which is predicted to rotate.

1

2

1 Bottom flange in compression 2 Top flange in compression

Figure 7.1 Portal frame bending moments, gravity actions

As shown in Figure 7.1, rafters are subject to high bending moments in the plane of the frame, that vary from a maximum ‘hogging’ moment at the junction with the column to a minimum sagging moment close to the apex. They are also subject to overall compression from the frame action. They are not subject to any minor axis moments.

Although member resistance is important, stiffness of the frame is also necessary to limit the effects of deformed geometry and to limit the SLS deflections. For these reasons, high strength members are generally not used in portal frames, but lower steel grades with higher inertias. Optimum design of portal frame rafters is generally achieved by use of:

A cross-section with a high ratio of Iyy to Izz that complies with the requirements of Class 1 or Class 2 under combined major axis bending and axial compression.

A haunch that extends from the column for approximately 10% of the frame span. This will generally mean that the maximum hogging and sagging moments in the plain rafter length are similar.

7.2 Rafter strength The resistances of all critical cross-sections of the rafter must be verified in accordance with Section 6 of EN 1993-1-1.


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7.3 Rafter out-of-plane stability 7.3.1 Rafter and haunch stability under maximum hogging moment

Both in-plane and out-of-plane checks are required. Initially, the out-of-plane checks are completed to ensure that the restraints are located at appropriate positions and spacing.

BA

23

14

56

7

7

8M

2

C

M

p

p

1 Tapered length between torsional restraints2 Tapered length, between lateral restraints 3 Length between lateral restraints 4 Length between torsional restraints

5 Elastic section of rafter 6 Elastic section of rafter 7 Torsional restraint to the rafter 8 Torsional restraint to the column

Figure 7.2 Typical portal frame rafter with potential plastic hinges at tip of

haunch and first purlin down from apex

Figure 7.2 shows a typical moment distribution for permanent plus variable actions and typical purlin positions and typical restraint positions.

Purlins are placed at about 1,8 m spacing but this spacing may need to be reduced in the high moment regions near the eaves. Three stability zones are noted on Figure 7.2 (zones A, B, and C), which are referred to in the following sections.

The presence of plastic hinges in the rafter will depend on the loading, geometry and choice of column and rafter sections.

The selection of the appropriate check depends on the presence of a plastic hinge, the shape of the bending moment diagram and the geometry of the section (three flanges or two flanges). The objective of the checks is to provide sufficient restraints to ensure the rafter is stable out-of-plane.

Haunch stability in Zone A

In Zone A, the bottom flange of the haunch is in compression. The stability checks are complicated by the variation in geometry along the haunch.

The junction of the inside column flange and the underside of the haunch (point 8 in Figure 7.2) should always be restrained. The ‘sharp’ end of the haunch (point 7 in Figure 7.2) usually has restraint to the bottom flange, from a purlin located at this position, forming a torsional restraint at this point. If a


4 - 34

plastic hinge is predicted at this position, a restraint must be located within h/2 of the hinge position, where h is the depth of the rafter. In Figure 7.2, a hinge is predicted at point 7, and a restraint to the bottom flange has been provided. The restraints to each flange in the haunch region are shown in Figure 7.3.

1

2

4

53

6

1. Zone A 2. Depth of haunch 3 Intermediate restraint between torsional restraints 4. Torsional restraints 5. Depth of rafter 6. Restraints to flange

Figure 7.3 Restraints in the haunched region of a portal frame

It is necessary to check that the distance between torsional restraints (in Figure 7.2 this is indicated as ‘1’ in zone A) on both sides of a plastic hinge does not exceed Ls as given in § BB.3.2.2. In zone A, the member is tapered, and the bending moment is not constant.

Ls is given in § BB.3.2.2 Expression BB.11 for a three flange haunch and Expression BB.12 for a two-flange haunch. In both cases, a factor Cn (given in BB.3.3.2) takes account of non-linear moment gradients by calculating relevant parameters at the five cross-sections, as shown in Figure 7.4. The parameter c is a taper factor, given in § BB.3.3.3(1)B. § BB.3.2.2 also demands that the spacing of intermediate lateral restraints satisfies the requirements for Lm given in § BB.3.2.1. In Figure 7.2, both lengths indicated ‘2’ must satisfy this check.

Expression BB.9 is used for a three flanged haunch and BB.10 for a two-flanged haunch. A three flanged haunch would be the common situation when the haunch is fabricated from a section cutting and welded to the underside of the rafter.


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= = = =

Figure 7.4 Cross-sections to be considered when determining Cn

Rafter stability in Zone B

Zone B generally extends from the ‘sharp’ end of the haunch to beyond the point of contraflexure (see Figure 7.2). The bottom flange is partially or wholly in compression over this length. Depending on the overall analysis, this zone may or may not contain a plastic hinge at the ‘sharp’ end of the haunch.

In this zone, torsional and lateral restraint will be provided at the ‘sharp’ end of the haunch. At the upper end, restraint will be provided by a purlin beyond the point of contraflexure. Some national authorities allow the point of contraflexure to be considered as a restraint, provided the following conditions below are satisfied.

The rafter is a rolled section

At least two bolts are provided in the purlin-to-rafter connections

The depth of the purlin is not less than 0,25 times the depth of the rafter.

If a plastic hinge is predicted at the ‘sharp’ end of the haunch, a torsional restraint must be provided within a limiting distance in accordance with BB.3.1.2. The limiting distance may be calculated assuming:

A constant moment – use Expression BB.6

A linear moment gradient – use Expression BB.7

A non-linear moment gradient – use Expression BB.8.

In addition, the spacing between the intermediate lateral restraints (indicated as ‘3’ in Figure 7.2) must satisfy the requirements for Lm as given in § BB.3.1.1.

If there is no plastic hinge, and in elastic regions, the member must be verified in accordance with Expressions 6.61 and 6.62 (see Section 6.2 of this document).

Rafter stability in Zone C

In Zone C, the purlins can be assumed to provide lateral restraint to the top (compression) flange provided they are tied into some overall restraint system. In many countries, it is simply assumed that the diaphragm action of the roof sheeting is sufficient to carry restraint forces to the bracing system; in other


4 - 36

countries any purlins providing restraint must be connected directly to the bracing system.

The out-of-plane checks require the verification of the member in accordance with Expressions 6.61 and 6.62 (see Section 6.2 of this document). Normally, if the purlins are regularly spaced, it is sufficient to check the rafter between restraints assuming the maximum bending moment and maximum axial load.

If a plastic hinge is predicted to form adjacent to the apex, it must be restrained. In addition, the usual requirements for stability near a plastic hinge must be satisfied:

The distance between the restraint at the plastic hinge and the next lateral restraint must not exceed the limiting distance Lm.

The distance to the next torsional restraint each side of the hinge must not exceed the limiting distance Lk, or Ls, with the spacing of intermediate restraints satisfying the requirements for Lm, all as described for zone B.

Even if there is no plastic hinge adjacent to the apex, it is normal practice to provide a torsional restraint at this point, as this will be necessary when considering the uplift combinations of actions – the bottom flange will be in compression.

7.3.2 Rafter and haunch stability for uplift conditions

Under uplift, most of the bottom flange of the rafter is in compression. A typical reversal bending moment diagram is shown in Figure 7.5.

1

1

2

E

F

3

1 Torsional restraint 2 Torsional restraint to column 3 Possible additional torsional restraint required for the uplift condition.

Figure 7.5 Typical purlin and rafter stay arrangement for wind uplift

This type of bending moment diagram will generally occur under internal pressure and wind uplift. Normally, the bending moments are smaller than the gravity load combinations and the members will remain elastic. The stability checks recommended below assume that plastic hinges will not occur in this uplift condition.


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Haunch stability in Zone E

In Zone E, (see Figure 7.5) the top flange of the haunch will be in compression and will be restrained by the purlins.

The moments and axial forces are smaller than those in the gravity load combination. The members should be verified using Expression 6.62 (see Section 6.2 of this document). By inspection, it should be clear that the rafter in this zone will be satisfactory.

Stability in Zone F

In Zone F, the purlins will not restrain the bottom flange, which is in compression.

The rafter must be verified between torsional restraints. A torsional restraint will generally be provided adjacent to the apex, as shown in Figure 7.5. The rafter may be stable between this point and the virtual restraint at the point of contraflexure. If the rafter is not stable over this length, additional torsional restraints may be introduced, and each length of the rafter verified.

This verification may be carried out using Expression 6.62.

The beneficial effects of the restraints to the tension flange (the top flange, in this combination) may be accounted for using a modification factor Cm, taken from § BB.3.3.1(1)B for linear moment gradients and from § BB.3.3.2(1)B for non-linear moment gradients. If this benefit is utilised, the spacing of the intermediate restraints should also satisfy the requirements for Lm, found in § BB.3.1.1.

7.4 In-plane stability In addition to the out-of-plane checks described in Section 7.3, in-plane checks must be satisfied using Expression 6.61.

For the in-plane checks, the axial resistance M1

Edy

N

is based on the system

length of the rafter. The buckling resistance M1

Rky,LT

M

should be taken as the

least resistance from any of the zones described in Section 7.3.

7.5 Design summary Rafters should be IPE or similar sections with Class 1 or Class 2

proportions under combined moment and axial load. Sections containing plastic hinges must be Class 1.

Cross-sections should be checked to Section 6 of EN 1993-1-1.

Detailed checks must be carried out to ensure adequate out-of-plane stability under both gravity and uplift conditions – see Sections 7.3.1 and 7.3.2.

In-plane stability of the rafters and interaction with out-of-plane stability must be verified, using Expressions 6.61 and 6.62 – see Section 6.2.


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8 COLUMN DESIGN

8.1 Introduction As shown in Figure 8.1, the most highly loaded region of the rafter is reinforced by the haunch. By contrast, the column is subject to a similar bending moment at the underside of the haunch. The column will therefore need to be a significantly larger section than the rafter – typically proportioned to be 150% of the rafter size.

Figure 8.1 Typical bending moment diagram for frame with pinned base

columns subject to gravity loading

The optimum design for most columns is usually achieved by the use of:

A cross-section with a high ratio of Iyy to Izz that complies with Class 1 or Class 2 under combined major axis bending and axial compression

A plastic section modulus that is approximately 50% greater than that of the rafter.

The column size will generally be determined at the preliminary design stage on the basis of the required bending and compression resistances.

8.2 Web resistance The column web is subject to high compression at the level of the bottom flange of the haunch. In addition, EN 1993-1-1 § 5.6(2) requires that web stiffeners are provided at plastic hinge locations, if the applied transverse force exceeds 10% of the member’s shear resistance. For these reasons, full depth stiffeners are usually required to strengthen the web.

8.3 Column stability 8.3.1 Column stability under maximum gravity combinations

Whether the frame is designed plastically or elastically, a torsional restraint should always be provided at the underside of the haunch. Additional torsional restraints may be required within the length of the column because the side rails are attached to the (outer) tension flange rather than to the compression flange. As noted in Section 6.3, a side rail that is not continuous (for example, interrupted by industrial doors) cannot be relied upon to provide adequate


4 - 39

restraint. The column section may need to be increased if intermediate restraints cannot be provided.

Restraint may be provided by stays to the inside flange, as shown in Figure 8.2 shows stiffeners in the column, which are only typical at the level of the underside of the haunch where they act as compression stiffeners. At other locations, stiffeners are generally not required.

2

1

1 Side rail 2 Column

Figure 8.2 Typical eaves detail using a column stay

At the underside of the haunch level, it may be convenient to provide a hot-rolled member, typically a hollow section, to provide restraint. It is essential to connect the bracing on the inner flange to the outer flange at some point in the length of the building.

2

1

1 Cold rolled member supporting the cladding and gutter 2 Circular hollow section

Figure 8.3 Typical eaves detail using a circular hollow section as a

longitudinal bracing member

Figure 8.4 shows a typical moment distribution for permanent and variable actions and indicates the positions of restraints on a typical column. The presence of a plastic hinge will depend on loading, geometry and choice of column and rafter sections. In a similar way to the rafter, both out-of-plane and in-plane stability must be verified.


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1

2

3

4

1 Torsional restraint 2 Stay from side rail forming torsional restraint

3 Segment must satisfy Ls (if elastic) or Lm (if plastic) 4 Segment must satisfy elastic buckling checks

Figure 8.4 Typical portal frame column with plastic hinge at underside of

haunch

8.3.2 Out-of-plane stability under gravity combinations

If there is a plastic hinge at the underside of the haunch, the distance to the adjacent torsional restraint must be less than the limiting distance Ls as given by EN 1993-1-1 § BB.3.1.2. Expression BB.7 should be used when the moment is linear, and BB.8 when the moment is not linear.

In addition, the spacing between intermediate lateral restraints should satisfy the requirements for Lm as given in BB.3.1.1.

If the stability between torsional restraints cannot be verified, it may be necessary to introduce additional torsional restraints. In Figure 8.4, the check between the torsional restraint (indicated as ‘1’ in the figure) and the base was not satisfied – an additional torsional restraint was introduced at location ‘2’. If it is not possible to provide additional intermediate restraints, the size of the member must be increased.

In all cases, a lateral restraint must be provided within Lm of a plastic hinge.

If there is no plastic hinge, the stability of the column should be checked in accordance with Expression 6.62 (See Section 6.2 of this document) Account may be taken of the benefits of tension flange restraint as described in Appendix C of this document.


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8.3.3 Stability under uplift combinations

When the frame is subject to uplift, the column moment will reverse. The bending moments will generally be significantly smaller than those under gravity loading combinations, and the column will remain elastic.

Out-of-plane checks should be undertaken in accordance with Expression 6.62 (See Section 6.2 of this document).

8.4 In-plane stability In addition to the out-of-plane checks described in Section 8.3, in-plane checks must be satisfied using Expression 6.61.

For the in-plane checks, the axial resistance M1

Edy

N

is based on the system

length of the column. The buckling resistance M1

Rky,LT

M

should be taken as

the least resistance from any of the zones described in Section 8.3.

8.5 Design summary Columns should be IPE or similar sections with Class 1 or Class 2

proportions under combined moment and axial load.

The section should ideally be able to resist the high shears within the depth of the eaves connection, without shear stiffening.

Critical cross-sections should be checked to Section 6 of EN 1993-1-1.

Detailed stability checks, as defined in Sections 8.3 and 8.4 must be carried out to ensure adequate stability.


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9 BRACING

9.1 General Bracing is required to resist longitudinal actions, principally wind actions and provide restraint to members. The bracing must be correctly positioned and have adequate strength and stiffness to justify the assumptions made in the analysis and member checks.

9.2 Vertical bracing 9.2.1 General

The primary functions of vertical bracing in the side walls of the frame are:

To transmit the horizontal loads to the ground. The horizontal forces include forces from wind and cranes.

To provide a rigid framework to which side rails may be attached so that they can in turn provide stability to the columns.

To provide temporary stability during erection.

According to EN 1993-1-1, the bracing will have to satisfy the requirement of § 5.3.1, 5.3.2 and 5.3.3 for global analysis and imperfections within the bracing system.

The bracing system will usually take the form of:

A single diagonal hollow section

Hollow sections in a K pattern

Crossed flats (usually within a cavity wall), considered to act in tension only

Crossed angles.

The bracing may be located:

At one or both ends of the building, depending on the length of the structure

At the centre of the building (See Section 9.2.5)

In each portion between expansion joints (where these occur).

Where the side wall bracing is not in the same bay as the plan bracing in the roof, an eaves strut is required to transmit the forces from the roof bracing into the wall bracing.

9.2.2 Bracing using circular hollow sections

Hollow sections are very efficient in compression, which eliminates the need for cross bracing. Where the height to eaves is approximately equal to the spacing of the frames, a single bracing member at each location is economic (Figure 9.1). Where the eaves height is large in relation to the frame spacing, a K brace is often used (Figure 9.2).


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An eaves strut may be required in the end bays, depending on the configuration of the plan bracing (see Section 9.3.2).

1

2 1 Eaves level 2 Position of plan bracing

Figure 9.1 Single diagonal bracing for low rise frames

1


Figure 9.2 K bracing arrangement for taller frames

9.2.3 Bracing using angle sections or flats

Cross braced angles or flats (within a masonry cavity wall) may be used as bracing (as shown in Figure 9.3). In this case, it is assumed that only the diagonal members in tension are effective.

1


Figure 9.3 Typical cross bracing system using angles or flats as tension

members

9.2.4 Bracing in a single bay

For vertical bracing provided in a single bay, an eaves strut is required to transmit wind forces from the roof bracing into the vertical bracing (Figure 9.4). Further details of eaves struts are given in Section 12.2.


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1

32

1 Eaves strut/tie 2 Position of plan bracing 3 Vertical bracing acting as strut/tie

Figure 9.4 Bracing in a single end bay with an eaves strut

9.2.5 Single central braced bay

The concept of providing a single braced bay near the centre of a structure (Figure 9.5) is unpopular because of the need to start erection from a braced bay and to work down the full length of a building from that point. However, bracing in the middle of the building has the advantage that it allows free thermal expansion of the structure, which is particularly valuable in locations such as Southern Europe and the Middle East where the diurnal temperature range is very large. In most of Europe, the expected temperature range is more modest, typically 5°C to +35°C, and overall expansion is not generally considered to be a problem. If a central braced bay is used, it may be necessary to provide additional temporary bracing in the end bays to assist in erection.

3

1 12

1 Free expansion 2 Eaves strut 3 Position of plan bracing

Figure 9.5 Typical cross bracing at centre of the structure to allow free

thermal expansion

9.2.6 Bracing using moment-resisting frames

Where it is difficult or impossible to brace the frame vertically by conventional bracing, it is necessary to introduce moment-resisting frames in the elevations. There are two basic possibilities:

A moment-resisting frame in one or more bays, as shown in Figure 9.6.

Use of the complete elevation to resist longitudinal forces, with moment resisting connection often located in the end bays, where the end column is turned through 90° to provide increased stiffness in the longitudinal direction, as shown in Figure 9.7. This arrangement is only possible if the end frame (the gable) is constructed from a beam and column arrangement, rather than a portal frame. Gable frames are discussed in Section 10.


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2

1 1

1 Moment-resisting frames 2 Position of plan bracing

Figure 9.6 Individual, local sway frames

1 12 222

3

1 Moment connection 2 Pin connection 3 Eaves strut

Figure 9.7 Hybrid frame along the full length of the building

In design of both systems, it is suggested that:

The bending resistance of the portalised bay (not the main portal frame) is checked using an elastic frame analysis

Deflection under the equivalent horizontal forces is restricted to h/1000.

The stiffness is assured by restricting serviceability deflections to a maximum of h/360, where h is the height of the portalised bay.

In some cases, it is possible to provide conventional bracing on one elevation, and provide moment resisting frames on the other. The effects of racking action due to the difference in stiffness of the sides is generally negligible due to the diaphragm action of the roof.


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1

2

3

4

1 Vertical bracing on gable 2 Vertical bracing on elevation 3 Roof bracing 4 Portalised bracing in elevation

Figure 9.8 Portalising an opening on one side with conventional bracing on

the other side of the structure

9.2.7 Bracing to restrain columns

If side rails and column stays provide lateral or torsional restraint to the column, it is important to identify the route of the restraint force to the vertical bracing system. If there is more than one opening in the side of the building, additional intermediate bracing may be required. This bracing should be provided as close to the plane of the side rail as possible, preferably on the inside face of the outer flange (Figure 9.9).

5

2

43

1

1 Eaves beam 2 Doorways 3 Side rail restraining column stay 4 Additional bracing required in this bay on the inner face of the outer flange 5 Position of plan bracing

Figure 9.9 Typical bracing pattern in side of building with openings

It is not normally necessary for the side rail that provides restraint at column stay positions to be aligned with a node of the vertical bracing system. It can be assumed that diaphragm action in the vertical sheeting and the transverse stiffness of the column can transmit the load into the vertical bracing system.

Where a member is used to restrain the position of a plastic hinge in the column, it is essential that it is tied properly into the bracing system. This can result in the configuration shown in Figure 9.10. Where there is more than one


4 - 47

opening in the side of the building, additional intermediate bracing will be required in a similar way to that described above.

3

12

1 Member restraining plastic hinge at bottom of haunch 2 Eaves level 3 Position of plan bracing

Figure 9.10 Typical bracing pattern in building using a hot-rolled member to

restrain a plastic hinge at the base of the haunch

9.2.8 Bracing to restrain longitudinal loads from cranes

If a crane is directly supported by the frame, the longitudinal surge force will be eccentric to the column, and will tend to cause the column to twist, unless additional restraint is provided. A horizontal truss at the level of the girder top flange or, for lighter cranes, a horizontal member on the inside face of the column flange tied into the vertical bracing may be adequate to provide the necessary restraint.

For large horizontal forces, additional bracing should be provided in the plane of the crane girder (Figure 9.11 and Figure 9.12). The criteria given in Table 9.1 were given by Fisher[3] to define the bracing requirements.

3

2

1

4

1 Eaves level 2 Crane girder level 3 Position of plan bracing 4 Bracing for very large crane loads on the inside flange of the column

Figure 9.11 Elevation showing position of additional bracing in the plane of

the crane girder


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1

1 Planes of bracing

Figure 9.12 Detail showing additional bracing in the plane of the crane girder

Table 9.1 Bracing requirements for crane girders

Factored longitudinal force

Bracing requirement

Small (<15 kN) Use wind bracing

Medium (15 - 30 kN) Use horizontal bracing to transfer force from the crane to plane of bracing

Large (> 30 kN) Provide additional bracing in the plane of the longitudinal crane forces

9.3 Plan bracing 9.3.1 General

Plan bracing is placed in the horizontal plane, or in the plane of the roof. The primary functions of the plan bracing are:

To transmit horizontal wind forces from the gable posts to the vertical bracing in the walls

To transmit any drag forces form wind on the roof to the vertical bracing

To provide stability during erection

To provide a stiff anchorage for the purlins which are used to restrain the rafters.

In order to transmit the wind forces efficiently, the plan bracing should connect to the top of the gable posts.

According to EN 1993-1-1, the bracing will have to satisfy the requirement of § 5.3.1, 5.3.2 and 5.3.3 for global analysis and imperfections within the bracing system.

9.3.2 Bracing using circular hollow sections

In modern construction, circular hollow section bracing members are generally used in the roof and are designed to resist both tension and compression. Many arrangements are possible, depending on the spacing of the frames and the positions of the gable posts. Two typical arrangements are shown in


4 - 49

Figure 9.13 and Figure 9.14. The bracing is usually attached to cleats on the web of the rafter, as shown in Figure 9.15. The attachment points should be as close to the top flange as possible, allowing for the size of the member and the connection.

Location of vertical bracingPosition of gable posts

Figure 9.13 Plan view showing both end bays braced

Position of gable postsLocation of vertical bracing

Figure 9.14 Plan view showing both end bays braced where the gable posts

are closely spaced

An eaves strut may be required in the end bays, depending on the configuration of the plan bracing. In all cases, it is good practice to provide an eaves tie along the length of the building.


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Figure 9.15 Typical connection detail for circular hollow section bracing

9.3.3 Bracing using angle sections

The use of angles is not common in modern structures, but cross-braced angles have an advantage in that the diagonal members are relatively small because they may be designed to resist tension only (Figure 9.16).

Location of vertical bracingPosition of gable posts

Figure 9.16 Plan view showing both end bays braced using crossed angle

sections

9.4 Restraint to inner flanges Restraint to the inner flanges of rafters or columns is often most conveniently formed by diagonal struts from the purlins or sheeting rails to small plates welded to the inner flange and web. Pressed steel ties are commonly used. As the ties act in tension only, angles must be substituted in locations where the restraint must be provided on one side only.

The effectiveness of such restraint depends on the stiffness of the system, especially the stiffness of the purlins. The effect of purlin flexibility on the bracing is shown in Figure 9.17. Where the proportions of the members, purlins and spacings differ from proven previous practice, the effectiveness should be checked. This can be done using the formula given in Section 9.5, or other methods, such as may be found in bridge codes for U-frame action.


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Figure 9.17 Effect of purlin flexibility on bracing

9.5 Bracing at plastic hinges Section 6.3.5.2 of EN 1993-1-1 recommends that bracing should be provided to both tension and compression flanges at or within 0,5h of the calculated plastic hinges, where h is the depth of the member (see Figure 9.18).

h

2

1

0.5h 0.5h

1. Hinge position 2. Member must be braced within these limits

Figure 9.18 Bracing at plastic hinges

EN 1993-1-1 recommends that the bracing to a plastic hinge should be designed assuming that the compression flange exerts a lateral load of 2,5% of the flange force, (taken as the plastic moment resistance/depth of section) perpendicular to the web of the member.

In addition, according to § 6.3.5.2(5)B of EN 1993-1-1, the bracing system must be able to resist the effects of local forces Qm applied at each stabilised member at the plastic hinge locations, where:

1005,1 Edf,

mm

NQ

where:

Nf,Ed is the axial force in the compressed flange of the stabilised member at the plastic hinge location

αm is a coefficient to recognise the statistical benefits of restraining a group of members compared with an individual member

m

115,0m in which m is the number of members to be restrained.

Where the plastic hinge is braced by diagonals from the purlins (see Figure 6.3), the stiffness of the ‘U-frame’ formed by the purlin and diagonals is especially important. Where the proportions of the members, purlins or spacings differ from previous practice, the effectiveness should be checked. In


4 - 52

the absence of other methods, the stiffness check may be based on the work of Horne and Ajmani[4]. Thus, the support member (the purlin or sheeting rail) should have Iy,s such that:

21

223

y

fy,

sy,

10190 LL

LLLf

I

I

where:

fy is the yield strength of the frame member

Iy,s is the second moment of area of the supporting member (purlin or sheeting rail) about the axis parallel to the longitudinal axis of the frame member (i.e. the purlin major axis in normal practice)

Iy,f is the second moment of area of the frame member about the major axis

L is the span of the purlin or sheeting rail

L1 and L2 are the distances either side of the plastic hinge to the eaves (or valley) or points of contraflexure, whichever are the nearest to the hinge (see Figure 9.18).

Hinges that form, rotate then cease, or even unload and rotate in reverse, must be fully braced. However, hinges that occur in the collapse mechanism but rotate only above ULS need not be considered as plastic hinges for ULS checks. These hinges are easily identified by elastic-plastic or graphical analysis.

Analysis cannot account for all of the section tolerances, residual stresses and material tolerances. Care should be taken to restrain points where these effects could affect the hinge positions, e.g. the shallow end of the haunch instead of the top of the column. Wherever the bending moments come close to the plastic moment capacity, the possibility of a hinge should be considered.

9.6 Design summary Bracing must be provided with adequate strength and stiffness to act in conjunction with the purlins, side rails and eaves beams to resist horizontal actions, including wind, to provide overall stability to the building and to provide local stability to the columns and rafters. Bracing must be provided:

To side walls, in a vertical plane; see Section 9.2

On plan at or near the roof of the building; see Section 9.3

Stays are required to stabilise inner flanges of the columns and rafters where they are in compression and potentially unstable; see Section 9.4

At, or near, plastic hinge positions to provide torsional restraint; see Section 9.5.


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10 GABLES

10.1 Types of gable frame Gable frames are typically of two forms:

An identical portal frame to the remainder of the structure. The gable columns do not support the rafter. This form of gable is used for simplicity, or because there is the possibility of extending the structure in the future.

A gable frame comprising gable posts and simply supported rafters. The gable posts support the rafters. Gable frames of this form require bracing in the plane of the gable, as shown in Figure 10.1. The advantage of this form of gable is that the rafters and external columns are smaller than those in a portal frame.

Figure 10.1 Gable frame from columns, beams and bracing

10.2 Gable columns Gable columns are designed as vertical beams, spanning between the base and the rafter. At rafter level, the horizontal load from the gable column is transferred into the roof bracing, to the eaves, and then to the ground via the bracing in the elevations.

The gable column will be designed for pressure and suction. The maximum suction may be when the gable is on the downwind elevation, as shown in Figure 10.2(a), or more likely when the gable is parallel to the wind direction, as shown in Figure 10.2(b).


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1

2

(a)

1

2

2

(b)

1 Apex 2 Gable under suction

1 Apex 2 Gable under suction

Figure 10.2 Wind loads on gables

The internal pressure or suction contributes to the net loads on the gable. When the net loads are equivalent to an external pressure, the outside flanges of the gable columns are in compression, but are restrained out-of-plane by the side rails. When the net loads are equivalent to an external suction, the inside flanges of the gable columns are in compression. This design case may be the most onerous of the two conditions. It may be possible to reduce the length of the unrestrained inside flange of the gable columns by introducing column stays from the side rails, as illustrated in Figure 6.3.

10.3 Gable rafters If the gable is of the form shown in Figure 10.1, the gable rafters are generally simply supported I section members. In addition to carrying the vertical loads, the gable rafters often act as chord members in the roof bracing system and this design case must be verified.

If a portal frame is adopted as a gable frame, it is common to adopt an identical frame size, even though the vertical loads on the end frame are rather less. Generally, the reduced vertical loading will mean that the rafter can accommodate the axial force as part of the roof bracing system without needing to increase the section size.


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11 CONNECTIONS

The major connections in a portal frame are the eaves and apex connections, which are both moment-resisting. The eaves connection in particular must generally carry a very large bending moment. Both the eaves and apex connections are likely to experience reversal in certain combinations of actions and this can be an important design case. For economy, connections should be arranged to minimise any requirement for additional reinforcement (commonly called stiffeners). This is generally achieved by:

Making the haunch deeper (increasing the lever arms)

Extending the connection above the top flange of the rafter (an additional bolt row)

Adding bolt rows

Selecting a stronger column section.

The design of moment resisting connections is covered in detail in Single-storey Buildings. Part 11: Moment connections[5].

11.1 Eaves connections A typical eaves connection is shown in Figure 11.1. In addition to increasing the moment resistance of the rafter, the presence of the haunch increases the lever arms of the bolts in the tension zone, which is important if the connection carries a large bending moment. Generally the bolts in the tension zone (the upper bolts under conventional gravity loading) are nominally allocated to carry tension from the applied moment, whilst the lower bolts (adjacent to the compression stiffener) are nominally allocated to carry the vertical shear, which is generally modest.

Because the portal frame members are chosen for bending resistance, deep members with relatively thin webs are common in portal frames. A compression stiffener in the column is usually required. The web panel of the column may also need reinforcing, either with a diagonal stiffener, or an additions web plate (referred to as a supplementary web plate)

The end plate and column may be extended above the top of the rafter, with an additional pair of bolts. The end plate on the rafter is unlikely to require stiffening as it can simply be made thicker, but it is common to find that the column flange requires strengthening locally to the tension bolts. Stiffeners are expensive, so good connection design would minimise the need for stiffeners by judicious choice of connection geometry.

Under a reversed bending moment, it may be necessary to provide a stiffener to the column web at the top of the column, aligned with the top flange of the rafter.


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2

1

1 Haunch 2 Compression stiffener

Figure 11.1 Typical eaves connection

11.2 Apex connections A typical apex connection is shown in Figure 11.2. Under normal loading conditions the bottom of the connection is in tension. The haunch below the rafter, which in lightly loaded frames may be a simple extended end plate, serves to increase the lever arms to the tension bolts, thus increasing the moment resistance. The haunch is usually small and short, and is not accounted for in frame design.

Figure 11.2 Typical apex


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11.3 Bases, base plates and foundations 11.3.1 General

The following terminology for the components at the foundation is used in this document:

Base - the combined arrangement of base plate, holding down bolts, and concrete foundation. The terms nominally pinned and nominally rigid are usually applied to the performance of the base, in relation to its stiffness.

Base plate - the steel plate at the base of the column, connected to the column by fillet welds.

Holding down bolts - bolts through the base plate that are anchored into the concrete foundation.

Foundation - the concrete footing required to resist compression, uplift, and, where necessary, over-turning moments.

Anchor plates - plates or angles used to anchor the holding down bolts into the foundation. They should be of such a size as to provide an adequate factor of safety against bearing failure of the concrete.

In the majority of cases, a nominally pinned base is provided, because of the difficulty and expense of providing a nominally rigid base which is moment resisting. Not only is the steel base connection significantly more expensive, the foundation must also resist the moment, which increases costs significantly.

Where crane girders are supported by the column, moment resisting bases may be required to reduce deflections to acceptable limits. Typical base plate/foundation details are shown in Figure 11.3 to Figure 11.5.

In a nominally pinned base for larger columns, the bolts can be located entirely within the column profile (Figure 11.3(a)). For smaller columns (less than approximately 400 mm), the base plate is made larger so that the bolts can be moved outside the flanges (Figure 11.3(b)).

A nominally rigid, moment resisting base is achieved by providing a bigger lever arm for the bolts and a stiffer base plate by increasing the plate thickness as shown in Figure 11.4. Additional gusset plates may be required for heavy moment connections, as illustrated in Figure 11.5.


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2

3

4

1

5

6

(a) For columns greater than or equal to 400 mm deep the holding down bolts may be located

entirely within the section profile

4

2

1

5

6

3

(b) For columns less than 400 mm deep the bolts may be located outside the section profile 1 Top of concrete foundation 2 Holding down bolts in clearance holes

(bolt diameter + 6 mm) 3 Base plate, usually 15 mm thick

4 Bedding space ( 50 mm) 5 Location tube 6 Anchor plate

Figure 11.3 Typical nominally pinned bases


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2

3

1

6

5

4 1 Top of concrete foundation 2 Holding down bolts in clearance holes

(bolt diameter + 6 mm) 3 Base plate, typically > 40 mm thick

4 Bedding space ( 50 mm) 5 Location tube 6 Anchor plate

Figure 11.4 Typical nominally rigid moment resisting base

7

3

5

46

1

22

1 Top of concrete foundation 2 Holding down bolts in 6 mm clearance

holes 3 Base plate, typically > 40 mm thick 4 Bedding space ( 50 mm)

5 Location tube 6 Anchor plate 7 Gusset plate welded to column and base

plate

Figure 11.5 Nominally rigid, moment resisting base with gusset plates for high

moments


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11.3.2 Safety in erection

It is usual to provide at least four bolts in the base plate for stability during erection. The alternative is to provide temporary support immediately after the erection of the column, which on most sites would be impractical and is likely to create hazards.

11.3.3 Resistance to horizontal forces

The highest horizontal forces acting at the base of the column are generally those that act outwards as a result of bending in the column caused by vertical loading on the roof.

Horizontal reactions acting outwards can be resisted in a number of ways, by:

Passive earth pressure on the side of the foundation, as indicated in Figure 11.6(a)

A tie cast into the floor slab connected to the base of the column, as shown in Figure 11.6(b)

A tie across the full width of the frame connecting both columns beneath or within the floor slab as illustrated in Figure 11.6(c) and (d).

By far the most popular method of resisting horizontal forces is to use passive earth pressure. This has economic advantages in that the foundation size required to resist uplift is usually adequate to provide adequate passive bearing against the ground. However, the passive resistance of the surrounding ground can be less than anticipated if the ground is not compacted correctly, and drainage and service trenches alongside the frame can reduce the passive resistance considerably.

As an alternative, a bar connected to the column and cast into the floor slab, and wrapped at the end to allow vertical movement, can be relatively cheap. This detail may lead to some local cracking of the floor slab and, where a high specification floor slab is used, the warranty on the slab may be invalidated. The length of the bar should be determined by the ultimate pull out resistance required to resist the horizontal force.

A tie across the full width of the frame connected to the column at each side is the most certain way of resisting horizontal forces. It is more expensive in terms of materials and labour and can be damaged by site activities. A full width tie will generally impede the erection of the structure, which will be undertaken from within the footprint of the building.

11.3.4 Base plates and holding down bolts

The steelwork contractor will usually be responsible for detailing the base plate and holding down bolts. However, it should be made clear in the contract documentation where the responsibility lies for the design of the foundation details, as special reinforcement spacing or details may be required.

Base plates will usually be in grade S235 or S275 steel.


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H

(a) Passive earth pressure

1

1 Wrapped bar (b) Tie into floor slab, note wrapping to outer portion of bar to prevent damage to slab from

differential settlement

1

2

1 Floor slab 2 Angle wrapped in tape to prevent corrosion (c) Angle tie between columns

2

1

1 Floor slab 2 High tensile bar with threaded end and coupler, wrapped in tape to prevent corrosion (d) Tie rod between columns

Figure 11.6 Methods of providing resistance to horizontal forces at the

foundations


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The diameter of the bolt will generally be determined by consideration of the uplift and shear forces applied to the bolts, but will not normally be less than 20 mm. There is often generous over-provision, to allow for the incalculable effects of incorrect location of bolts and combined shear force and bending on the bolt where grouting is incomplete.

The length of the bolt should be determined by the properties of the concrete, the spacing of the bolts, and the tensile force. A simple method of determining the embedment length is to assume that the bolt force is resisted by a conical surface of concrete. Where greater uplift resistance is required, angles or plates may be used to join the bolts together in pairs as an alternative to individual anchor plates. Calculations should be carried out by the designer at the final design stage to check the viability of the proposed bolt spacing.

11.3.5 Foundation design at the fire limit state

If the foundation is designed to resist a moment due to rafter collapse in a fire, both the base plate and the foundation itself should be designed to resist the moment as shown in Figure 11.7(a). It may be possible to offset the base to reduce or eliminate the eccentricity generated by the moment to give a uniform pressure distribution under the base as shown in Figure 11.7(b).

M M

(a) (b) Figure 11.7 Foundation for portal frame in a fire boundary condition

11.4 Design summary Moment-resisting connections should be arranged to minimise any

additional local strengthening.

It is usually more economical to adopt nominally pinned column bases.

Experience has demonstrated that a four bolt connection with a relatively thin base plate may behave effectively as a pin, while still providing sufficient stiffness for safe erection.

Careful consideration needs to be given to resistance to shear forces, both in the column base and in the foundation.


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12 SECONDARY STRUCTURAL COMPONENTS

12.1 Eaves beam The cold-formed member that connects the individual frames at eaves level (indicated as (2) in Figure 12.1) is generally known as an eaves beam.

The primary function of the eaves beam is to support the roof cladding, side walls, and guttering along the eaves, but it may also be used to provide lateral restraint at the top of the outer flange of the column.

1 Built-up or composite cladding 2 Cold rolled eaves beam 3 Rafter stay

4 Column stiffener 5 Circular hollow section acting as eaves strut

Figure 12.1 Haunch detail with eaves beam

12.2 Eaves strut If vertical side wall bracing capable of resisting tension and compression is provided at both ends of the structure (see Section 9.2), an eaves strut is not required other than in the end bays. However, it is good practice to provide a member between the columns to act as a tie during erection and provide additional robustness to the structure.

If a circular hollow section is used to restrain the plastic hinge at the bottom of the eaves as illustrated in Figure 12.1, this can fulfil the role of a longitudinal strut as well as restraining the plastic hinge. If a member is provided as an eaves strut above this level, it is ineffective in restraining the plastic hinge at the bottom of the haunch.

1

2 3

5

4


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13 DESIGN OF MULTI-BAY PORTAL FRAMES

13.1 General Most aspects of the behaviour and design of multi-bay portal frames are similar to single bay structures. This Section describes common types of multi-bay frames and highlights key points of difference.

13.2 Types of multi-bay portals 13.2.1 Valley beams and ‘hit’ and ‘miss’ frames

In multi-span portal framed building, it is common practice to use valley beams to eliminate some internal columns. Most commonly, alternate columns are omitted and the valley of the frame is supported on a so-called valley beam spanning between the columns of adjacent frames, as shown in Figure 13.1. This arrangement is often referred to as ‘hit’ and ‘miss’ frames, the frames with columns being the ‘hit’ frames. Sometimes more than one column is omitted, though such schemes require very large valley beams and reduce the stiffness and the stability requirements of the structure, even where the remaining complete frames are used to stabilise the frames without columns.

1 1

32

1 Valley beams 2 Rafter 3 Valley beam and fabricated connection

Figure 13.1 Valley beams

Valley beams may be simply supported or continuous through the supporting columns. The choice will normally depend on the relative cost of a heavier beam for simply supported construction and the more expensive connection for continuous construction.

Valley beams often form one or more rigid frames with the internal columns along the valley to provide overall structural stability at right angles to the frames. This avoids the use of cross bracing on the internal column lines, which is often unacceptable for the intended use of the building. Alternatively, a deep truss may be provided in the plane of the rafters, which spans between the external elevations. For long trusses on multi-span structures, it would be


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common to provide a truss which is two bays deep, rather than a truss in the end bay only.

13.3 Stability The majority of multi-span portal frames have slender internal columns. When a horizontal load is applied to these frames, there is only a small bending moment induced in these slender internal columns, because the external columns are much stiffer. A typical bending moment diagram is shown in Figure 13.2.

This difference in bending moment distribution and the associated reduction in internal column stiffness has a significant impact on frame behaviour. At the Ultimate Limit State, the frame is likely to be operating at 20 to 30% of its overall elastic critical load. With the spread of plasticity from the critical hinge position, the effective critical load will reduce, increasing the effective critical load ratio further.

This effect is addressed by appropriate second order, elastic / plastic software.

H

Figure 13.2 Bending moments in a typical two-span frame under horizontal

loading

The frame in Figure 13.2 can be considered as two sub-frames, each comprising an external column and a rafter pair, as shown in Figure 13.3. For multi-span frames in general, the two external sub-frames provide the majority of the stiffness, so the same model of a pair of sub-frames could be used for hand calculations. Where the stiffness of the internal columns is to be included, it is preferable to use software for the analysis of the entire frame.

H

Figure 13.3 Sub-frames for a typical two-span frame


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Where the internal columns provide significant stiffness, it is uneconomic to ignore them and a detailed analysis of the entire frame by software would be preferable.

13.4 Snap through instability

Figure 13.4 Snap through instability

As shown in Figure 13.4, the reduced sway stiffness of frames with three or more bays may lead to snap through instability of an internal bay. Such structures may be checked with appropriate software to ensure satisfactory behaviour. Appendix B may be used to calculate an estimate of the sensitivity to snap through.

13.5 Design summary Many aspects of behaviour of multi-bay portal frames are similar to single

bay frames

Special consideration should be given to the sway stability and snap through stability of multi-bay frames.


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REFERENCES

1 EN 1993-1-1: Eurocode 3 Design of steel structures. General rules and rules for

building

2 Steel Buildings in Europe Single-storey steel buildings. Part 2: Concept design

3 FISHER, J.M. Industrial buildings Chapter 6.1 in Construction steel design: an international guide Elsevier Applied Science, London, 1992

4 HORNE, M.R. and AJMANI, J.L. Failure of columns laterally supported on one flange: Discussion The structural Engineer, Vol. 51, No. 7, July 1973

5 Steel Buildings in Europe Single-storey Buildings. Part 11: Moment connections

6 LIM, J, KING, C.M, RATHBONE, A, DAVIES, J.M and EDMONDSON, V Eurocode 3: The in-plane stability of portal frames The Structural Engineer, Vol. 83. No 21, 1st November 2005


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APPENDIX A Practical deflection limits for single-storey buildings

A.1 Horizontal deflections for portal frames

Figure A.1 Definition of horizontal deflection

Horizontal deflection limits for portal frame structures are not explicitly covered in the structural Eurocodes. Generally, limits are set nationally, either by regulation or by accepted industry practice.

Typical limiting values for horizontal deflection are given in Table A.1.


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Table A.1 Typical horizontal deflection limits

Country Structure Deflection

limits u

Comments

France Portal frames without gantry cranes Buildings with no particular requirements regarding the deflection.

Deflection at the top of the columns

H/150

Difference of deflection between two consecutive portal frames

B/150

Values are given in the French National Annex to EN 1993-1-1 and should be used if nothing else is agreed with the client. The values of the deflections calculated from the characteristic combinations should be compared to these limits.

Member supporting metal cladding

Post H/150

Rail B/150

Other single-storey buildings Buildings with particular requirements regarding the deflection (brittle walls, appearance etc..

Deflection at the top of the columns

H/250

Difference of deflection between two consecutive portal frames

B/200

Germany There are no national deflection limits. The limits should be taken from manufacturers instructions (technical approvals) or should be agreed with the client.

Spain Portal frames (without fragile elements susceptible to failure in the envelopes, façade and roof)

H/150 Values are given in the national technical document for steel structures] and in the Technical Building Code and should be used if nothing else is agreed with the client.

Single-storey buildings with horizontal roofs (without fragile elements susceptible to failure in the envelopes, façade and roof)

H/300


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A.2 Vertical deflections for portal frames

Figure A.2 Definitions of vertical deflection of apex of portal frame

Typical limiting values for vertical deflection for some countries are given in Table A.2.

Table A.2 Vertical deflection limits

Deflection limits Country Structure

wmax w3 Comments

Roofs in general L/200 L/250

Roofs frequently carrying personnel other than for maintenance

L/200 L/300

France

Roofs supporting plaster or other brittle toppings or non-flexible parts

L/250 L/350

Values are given in the National Annex to EN 1993-1-1 and should be used if nothing else is agreed with the client. The values of the deflections calculated from the characteristic combinations should be compared to these limits.

Germany There are no national deflection limits. The limits should be taken from manufacturers instructions (technical approvals) or should be agreed with the client.

A.2.1 Vertical deflections for horizontal roof members

Serviceability limit states

Guidance for deflection limits are given in Table A.3 for a selection of European countries. The definition of vertical deflection in Annex A to EN 1990 is reproduced in Figure A.3.


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wc : precamber in the unloaded structural member

w1 : Initial part of the deflection under permanent loads of the relevant combination of actions

w2 : Long-term part of the deflection under permanent loads, not to be considered for single-storey steel buildings,

w3 : Additional part of the deflection due to the variable actions of the relevant combination of actions

wtot = w1 + w2 + w3

wmax : Remaining total deflection taking into account the precamber

Figure A.3 Definition of vertical deflections

Table A.3 Recommended limiting values for vertical deflections

Deflection limitsCountry Structure

Wmax Wa

Comments

France Roofs in general L/200 L/250

Roofs frequently carrying personnel other than for maintenance

L/200 L/300

Roofs supporting plaster or other brittle toppings or non-flexible parts

L/250 L/350

Values are given in the National Annex to EN 1993-1-1 and should be used if nothing else is agreed with the client. The values of the deflections calculated from the characteristic combinations should be compared to these limits.

Germany There are no national deflection limits. The limits should be taken from manufacturers’ instructions (technical approvals) or should be agreed with the client.

Roofs in general L/300(*) -

Roofs with access only for maintenance

L/250(*)

Spain

Values are given in the national technical document for steel structures and in the Technical Building Code and should be used if nothing else is agreed with the client.

(*) This values refers to w2 + w3 but w2 = 0 for steel structures.

Ultimate limit state: Ponding

Where the roof slope is less than 5%, additional calculations should be made to check that collapse cannot occur due to the weight of water:

either collected in pools which may be formed due to the deflection of structural members or roofing material

or retained by snow.

These additional checks should be based on the combinations at the Ultimate Limit States.

Precambering of beams may reduce the likelihood of rainwater collecting in pools, provided that rainwater outlets are appropriately located.

w c

w max

w1

w2 w3

wtot


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APPENDIX B Calculation of cr,est

B.1 General EN 1993-1-1 § 5.2.1 (4) B gives:

EdH,Ed

Edcr

h

V

H

However, this can only be applied when the axial load in the rafter is not significant. Note 2B of § 5.2.1(4)B describes significant as when

Ed

y3,0N

Af , which may be rearranged to indicate that the axial load is not

significant when crEd 09,0 NN

Where:

Ncr is the elastic critical buckling load for the complete span of the rafter

pair, i.e. 2

2

crL

EIπN

L is the developed length of the rafter pair from column to column, taken as span/Cos θ (θ is the roof slope).

If the axial load in the rafter exceeds this limit, the expression in EN 1993-1-1 cannot be used.

An alternative expression, accounting for the axial force in the rafter, has been developed by J. Lim and C. King[6] and is detailed below.

For frames with pitched rafters:

cr,est = min estr,cr,ests,cr, ;

where:

cr,s,est is the estimate of cr for sway buckling mode

cr,r,est is the estimate of cr for rafter snap-through buckling mode. This mode need only be checked when there are three or more spans, or if the rafter is horizontal, or when the columns are not vertical.

B.2 Factor cr,s,est The parameters required to calculate cr,s,est for a portal frame are shown in Figure B.1. NHF is the lateral deflection at the top of each column when subjected to a notional lateral force HNHF. (The magnitude of the total lateral force is arbitrary, as it is simply used to calculate the sway stiffness). The horizontal force applied at the top of each column should be proportional to the vertical reaction.


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The practical application of this recommendation is to calculate HNHF as 1/200 of the vertical reaction at the base of the column. In combinations including wind actions, HNHF should still be calculated as 1/200 of the vertical reaction at the base.

In calculating NHF only the notional lateral forces, HNHF, are applied to the frame. Base stiffness may be included in the analysis (as described in Section 3.4).

L

h

H H NHFNHF

NHF NHF

3

1

Ed Ed

2

N N

1 Frame dimensions

2 ULS analysis, and NEd in rafter

3 Sway analysis, under HNHF alone

Figure B.1 Calculation of cr

cr can then be calculated as:

NHFcr 200

h

The lowest value of cr for any column is taken for the frame as a whole.

cr,s,est can then be calculated as:

cr

maxRcr,

Edests,cr, 18,0

NN

where:

maxRcr,

Ed

NN

is the maximum ratio in any rafter

EdN is the axial force in rafter at ULS (see Figure B.1)

2r

2

Rcr,L

EIN

is the Euler load of the rafter for the full span of the rafter

pair (assumed pinned).


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L is the developed length of the rafter pair from column to column, taken as span/Cos θ (θ is the roof slope)

Ir is the in-plane second moment of area of rafter

Factor cr,r,est

This calculation should be carried out if the frame has three or more spans, or if the rafter is horizontal.

For frames with rafter slopes not steeper than 1:2 (26°), cr,r,est may be taken as:

ryr

rcestr,cr, 2tan

2751

47,55

fIIIhL

LD

r

But where ≤ 1, cr,r,est = ∞

where:

D is cross-sectional depth of rafter, h

L is span of bay

h is mean height of column from base to eaves or valley

Ic is in-plane second moment of area of the column (taken as zero if the column is not rigidly connected to the rafter, or if the rafter is supported on a valley beam)

Ir is in-plane second moment of area of the rafter

fyr is nominal yield strength of the rafters in N/mm2

r is roof slope if roof is symmetrical, or else r = tan-1(2hr/L)

hr is height of apex of roof above a straight line between the tops of columns

is arching ratio, given by = Wr/W0

W0 is value of Wr for plastic failure of rafters as a fixed ended beam of span L

Wr is total factored vertical load on rafters of bay.

If the two columns or two rafters of a bay differ, the mean value of Ic should be used.


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APPENDIX C Determination of MCR and Ncr

C.1 Mcr for uniform members C.1.1 General expression

The method given in C.1.1 only applies to uniform straight members for which the cross-section is symmetric about the bending plane.

g2

2g2

z2

t2

z

w

2

w2

z2

1cr zCzCEI

GIkL

I

I

k

k

kL

EICM

In the case of a portal frame, k = 1 and kw = 1. The transverse load is assumed to be applied at the shear centre and therefore C2zg = 0. The expression may be simplified to:

z2

t2

z

w

2

z2

1crEI

GIL

I

I

L

EICM

E is Young modulus (E = 210000 N/mm2)

G is the shear modulus (G = 81000 N/mm2)

Iz is the second moment of area about the weak axis

It is the torsional constant

Iw is the warping constant

L is the beam length between points of lateral restraint

C1 depends on the shape of the bending moment diagram

C.1.2 C1 factor

The factor C1 may be determined from Table C.1 for a member with end moment loading, and also for members with intermediate transverse loading.


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Table C.1 C1 factor

End Moment Loading C1

M M

-1 +1

+1,00+0,75+0,50+0,250,00

–0,25–0,50–0,75–1,00

1,001,171,361,561,772,002,242,492,76

Intermediate Transverse Loading

0,94 1,17

2/3

1/3

0,62 2,60

0,86 1,35

0,77 1,69

C.2 Mcr for members with discrete restraints to the tension flange It is possible to take beneficial account of restraints to the tension flange. This may lead to a greater buckling resistance of the member.

Tension flange restraint is usually provided by elements connected to the tension flange of the member (e.g. purlins).

The spacing between tension flange restraints must satisfy the requirements for Lm as given in § BB.3.1.1 in EN 1993-1-1.

C.2.1 General expression

For the general case of a beam of varying depth but symmetrical about the minor axis, subject to a non-uniform moment:

cr0m2

cr MCcM for beams with a linearly varying moment diagram

or

cr0n2

cr MCcM for beams with a non-linearly varying moment diagram

where

Mcr0 is the critical moment for a beam subject to uniform moment. Expressions of Mcr0 is given in C.2.2

c accounts for taper (c = 1 for uniform straight member) The value of c is given by EN 1993-1-1 Annex BB.3.3.3 based on the


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depth at the shallower end of the member and limited to members where 1 ≤ hmax/hmin ≤ 3. Note that the expression for c was derived in reference 4 for elements with 1.05, which is the common case for haunches in portal frames

Cm accounts for linear moment gradients. The value is given by the Expression BB.13 of EN 1993-1-1 Annex BB. It is recommended that Cm ≤ 2,7

Cn accounts for non-linear moment gradients. The value is given by the Expression BB.14 of EN 1993-1-1 Annex BB. It is recommended that Cn ≤ 2,7

When using EN 1993-1-1 Annex BB.3.3.2, the following points need clarification:

The same definition of ‘positive’ and ‘negative’ moments applies as in BB.3.3.1: Moments that produce compression in the non-restrained flange should be taken as positive.

This is fundamental as only positive values of R should be taken.

BB.3.3.2 assumes that the loads are applied at the shear centre.

C.2.2 Calculation of Mcr0

For uniform sections, symmetric about the minor axis, restrained along the tension flange at intervals:

t2

t

w2

2t

2z

2

cr02

1GI

L

EI

L

aEI

aM

but z

2t

2

z

w2

z2

cr0π

EI

GIs

I

I

s

EIM

where:

a is the distance between the restrained longitudinal axis (e.g. the centroid of the purlins) and the shear centre of the member. This takes account of the fact that the effective restraint is provided slightly away from the flange

Lt is the length of the segment along the member between torsional restraints to both flanges

s is the distance between the restraints along the restrained longitudinal axis (e.g. the spacing of the purlins).

For tapered or haunched members, Mcr0 is calculated using the section properties of the shallow ends.

The parameters a, Lt and s are shown in Figure C.1


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1 Shear centre of the shallowest

cross-section 2 Axis where restraint is provided 3 Intermediate lateral restraints (purlins)

4 Lateral restraints to both flanges, providing torsional restraint

5 Compression flange

Figure C.1 Arrangement of tension flange restraints

C.3 Ncr for uniform members with discrete restraints to the tension flange It is possible to take beneficial account of restraints to the tension flange. This may lead to a greater buckling resistance of the member.

Tension flange restraint is usually provided by elements connected to the tension flange of the member (e.g. purlins).

C.3.1 General expression

For Class 1, 2, and 3 cross-sections, § 6.3.1.2 of EN 1993-1-1 gives

cr

y

N

Af where

2

2

crπ

L

EIN for flexural buckling

3

5

5

5

4

4

4

4

4

4

2

2

2

3

3

1

2

L

L

L

s s

s s

s s

a

t

t

t


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C.3.2 NcrT for uniform members with discrete restraints to the tension flange

The elastic critical buckling force for an I section with intermediate restraints to the tension flange is given in BB.3.3.1 as:

t2

t

w2

2t

2z

2

2crT1

GIL

EI

L

aEI

iN

s

where:

22z

2y

2s aiii

Lt is the length of the segment along the member between torsional restraints to both flanges

a is defined in C.1.

For tapered or haunched members, NcrT is calculated using the section properties of the shallow ends.


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APPENDIX D

Worked Example: Design of portal frame using elastic analysis

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APPENDIX D Worded Example: Design of portal frame using elastic analysis

1 of 44

Made by CZT Date 12/2009

Calculation sheet Checked by DGB Date 12/2009

1. Elastic analysis of a single bay portal frame

This example covers the design of a portal frame for a single-storey building, using the elastic method of global analysis. Only gravity loads are covered in this example. The frame uses hot rolled I sections for rafters and columns.

2. Frame geometry

5°

LC

30000

60

00

52

75

3020

Spacing of portal frames = 7,2 m

The cladding to the roof and walls is supported by purlins and side rails.

The purlins have been provisionally located at intervals of between 1500 mm and 1800 mm as shown. The side rails are provisionally located at intervals of no more than 2000 mm. The rafter and column verifications may require these locations to be modified.

Title APPENDIX D Worked Example: Design of portal frame using elastic

analysis 2 of 44

4 - 83

** * **

**

6000

5275

1475

1900

1900

3020

1500

0

725

800

1345

2992

1489215057

302

1647

165

LC

5°

302

1345

1198

0

7313

1700

1700

1700

1700

1700

1700

1700

13192

11492

9792

8092

6392

4692

torsional restraint to inside flange


analysis 3 of 44

4 - 84

3. Loads

3.1. Permanent loads

G = Gself-weight + Groof

Gself-weight: self-weight of the beams

Groof: roofing with purlins Groof = 0,30 kN/m2

for an internal frame: Groof = 0,30 × 7,20 = 2,16 kN/m

EN 1991-1-1

= 2,16 kN/m + self weightG

30 m

3.2. Snow loads

The characteristic value for snow loading on the roof for a specific location in a given country at certain altitude has been calculated as:

sk = 0,618 kN/m²

for an internal frame: s = 0,618 × 7,20 = 4,45 kN/m

EN 1991-1-3

30 m

= 4,45 kN/ms

3.3. Imposed load on roof

Characteristic values for loading on the roof (type H: not accessible).

qk = 0,4 kN/m2

for an internal frame: qk = 0,4 × 7,20 = 2,88 kN/m

EN 1991-1-1 Table 6.10

30 m

Qk = 2,88 kN/m


analysis 4 of 44

4 - 85

3.4. Load combinations

For simplicity, the wind actions are not considered in this example.

Therefore, the critical design combination for choosing the member size is: G G + Q Q

Where:

Q is the maximum of the snow load and the imposed load.

G = 1,35 (permanent actions)

Q = 1,50 (variable actions)

EN 1990

The snow loads are greater than the imposed loads on the roof, therefore Q = 4,45 kN/m

4. Preliminary sizing

Single-storey steel buildings. Part 2: Concept design [2] provides a table of preliminary member sizes, according to the rafter load and the height to eaves.

Rafter load = 1,35( 2,16 + self weight )+1,5 4,45 = 9,6 kN/m + self weight Say 10 kN/m to include self weight.

The section chosen for the rafter is an IPE 450, S355

The section chosen for the column is an IPE 500, S355

5. Buckling amplification factor cr

In order to evaluate the sensitivity of the frame to 2nd order effects, the buckling amplification factor, cr, has to be calculated. This calculation requires the deflections of the frame to be known under a given load combination.

EN 1993-1-1 §5.2.1

An elastic analysis is performed to calculate the reactions under vertical loads at ULS, which provides the following information:

The vertical reaction at each base: VEd = 168 kN

The horizontal reaction at each base: HEd = 116 kN

The maximum axial force in the rafters: NR,Ed = 130 kN

5.1. Axial compression in the rafter

According to the code, if the axial compression in the rafter is significant then cr is not applicable. In such situations, Appendix B of this document recommends the use of cr,est instead.

The axial compression is significant if Ed

y3,0N

Af

or if NEd 0,09 Ncr, which is an equivalent expression.

EN 1993-1-1 §5.2.1(4) Note 2B

NEd is the design axial load at ULS in the rafter, noted NR,Ed in this example.


analysis 5 of 44

4 - 86

Lcr is the developed length of the rafter pair from column to column.

Lcr = o5cos

30 = 30,1 m

Ncr = 2

cr

z2

L

EI =

3

23

42

10101,30

1033740210000

= 772 kN

0,09 Ncr = 77209,0 = 69 kN

NR,Ed = 130 kN > 69 kN

Therefore the axial compression in the rafter is significant and cr from EN 1993-1-1 is not applicable.

Following the guidance from Appendix B, frame stability is assessed based on cr,est, in Section 5.2.

5.2. Calculation of cr,est

For a pitched roof frame: cr,est = min(cr,s,est; cr,r,est)

cr,r,est only needs to be checked for portal frames of 3 or more spans. Appendix B of this document

When assessing frame stability, allowance can be made for the base stiffness. In this example, a base stiffness equal to 10% of the column stiffness has been assumed to allow for the nominally pinned bases.

To calculate cr, a notional horizontal force is applied to the frame and the horizontal deflection of the top of the columns is determined under this load.

The notional horizontal force is:

HNHF = 200

1VEd = 168

200

1 = 0,84 kN

Appendix B of this document

The horizontal deflection of the top of the column under this force is obtained from the elastic analysis as 1,6 mm.

1,6 mm 1,6 mmH HNHF NHF

cr,s,est is calculated as follows:


analysis 6 of 44

4 - 87

cr,s,est =

NHFmaxcrR,

EdR,

200

118,0

h

N

N

=

6,1

6000

200

1

772

13018,0 = 12,5

Appendix B of this document

Thus cr,est = cr,s,est = 12,5 > 10

First order elastic analysis may be used and second order effects do not need to be allowed for.

Section 2.2 of this document

6. Frame imperfections

The global initial sway imperfection may be determined from

= 0 h m

0 = 1/200

h = 82,00,6

22

h

m = 87,0)1

1(5,0 m

= )2

11(5,0 = 0,87

m = 2 (number of columns)

= 31056,387,082,0200

1

EN 1993-1-1 §5.3.2

Initial sway imperfections may be considered in two ways:

By modeling the frame out of plumb

By applying equivalent horizontal forces (EHF).

Applying equivalent horizontal forces is the preferred option and the method that is used in this worked example. The equivalent horizontal forces are calculated as:

HEHF = VEd

However sway imperfections may be disregarded where HEd 0,15 VEd. EN 1993-1-1 §5.3.2(4)

Table 1 shows the total reactions for the structure to determine HEd and VEd.

Table 1 Vertical and horizontal reactions

Left column (kN)

Right column (kN)

Total reaction (kN)

0,15 VEd (kN)

HEd VEd HEd VEd HEd VEd

Reactions 116 168 –116 168 0 336 50

HEd = 0 0,15 VEd

Therefore the initial sway imperfections have to be taken into account.


analysis 7 of 44

4 - 88

The equivalent horizontal forces:

HEHF = VEd,column = 1681056,3 3 = 0,60 kN

This force is applied at the top of each column, in combination with the permanent and variable actions.

For the ULS analysis, the bases are modeled as pinned. Otherwise the base details and foundation would need to be designed for the resulting moment.

The following figure shows the internal forces on the frame subject to the ULS loads including the equivalent horizontal forces.


analysis 8 of 44

4 - 89

5275

M=

0 k

Nm

V N M=

0 k

Nm

V N M=

693

kN

mV N M

= 2

92 k

Nm

V N M=

356

kN

m

LC V N M=

351

kN

m

V N M=

0 k

Nm

V N M=

701

kN

m

V N M=

298

kN

m

3011

5869

3011

5941

3000

0

V N M=

616

kN

m

V N M=

610

kN

m

= 1

18 k

N=

127

kN

= 1

24 k

N

= 1

50 k

N=

130

kN =

117

kN

= 1

62 k

N

= 1

0 kN

= 1

16 k

N=

0 k

N=

117

kN

= 8

6 kN

= 1

24 k

N

= 1

17 k

N=

127

kN

= 1

50 k

N=

130

kN

= 1

16 k

N=

161

kN

Ed Ed Ed

= 8

7 kN

Ed Ed

Ed

Ed

Ed

Ed

Ed Ed

Ed

Ed

Ed

Ed Ed

Ed Ed Ed

Ed Ed

Ed

Ed

Ed Ed

Ed

Ed Ed

Ed

Ed Ed


analysis 9 of 44

4 - 90

7. Summary of member verification

The cross-section resistance and the buckling resistance are verified for each member. Sections 7.1and 7.2 provide a summary of the checks carried out for each member of the frame.

7.1. Cross-section verification

The resistance of the cross-section has to be verified in accordance with Section 6.2 of EN 1993-1-1.

The cross-sectional checks carried out in this worked example are:

Shear resistance

VEd Vpl,Rd =

M0

yv 3

fA

EN 1993-1-1 §6.2.6

Compression resistance

NEd Nc,Rd = M0

y

A f

EN 1993-1-1 §6.2.4

Bending moment resistance

MEd Mpl,y,Rd = M0

yypl,

fW

EN 1993-1-1 §6.2.5

In addition, bending and shear interaction, as well as bending and axial force interaction must be verified.

EN 1993-1-1 §6.2.8 §6.2.9

7.2. Buckling verification

The rafters and the columns must be verified for out-of-plane buckling between restraints and in plane buckling.

The buckling checks due to the interaction of axial force and bending moment are carried out using Expressions 6.61 and 6.62 from EN 1993-1-1.

0,1

M1

Rkz,

Edz,Edz,yz

M1

Rky,LT

Edy,Edy,yy

M1

Rky

Ed

M

MMk

M

MMk

N

N

0,1

M1

Rkz,

Edz,Edz,zz

M1

Rky,LT

Edy,Edy,zy

M1

Rkz

Ed

M

MMk

M

MMk

N

N

EN 1993-1-1 Expressions (6.61) and (6.62)


analysis 10 of 44

4 - 91

For orthodox single-storey portal frames, these expressions can be simplified as follows:

Edy,M = 0 and Edz,M = 0 for Class 1, Class 2 and Class 3 sections.

Mz,Ed = 0

Therefore expressions (6.61) and (6.62) can be written as:

0,1Rdb,

Edy,yy

Rdy,b,

Ed M

Mk

N

N and 0,1

Rdb,

Edy,zy

Rdz,b,

Ed M

Mk

N

N

Expression (6.61) is used to verify in-plane buckling, and expression (6.62) is used to verify out-of-plane buckling.

COLUMN: IPE 500, S355

1475

6000

0 kNm

616 kNm

444 kNm

19

00

19

00

221 kNm

*V

V

= 117 kN

= 117 kN

N

N

= 162 kN

= 168 kN

Ed

Ed

Ed

Ed

Section properties:

500h mm 11600A mm2

200b mm 3ypl, 102194W mm3

2,10w t mm 4y 1048200I mm4 204y i mm

16f t mm 4z 102142I mm4 1,43z i mm

21r mm 4t 103,89 I mm4

468w h mm 9w 101249I mm6

426d mm

7.3. Cross-section classification

7.3.1. The web

wt

c =

2,10

426 = 41,8

EN 1993-1-1 Table 5.2 (Sheet 1)


analysis 11 of 44

4 - 92

dN = yw

Ed

ft

N =

3552,10

168000

= 46,4

= w

Nw

2d

dd =

4262

4,46426

= 0,55 > 0,50

The limit for Class 1 is : 113

396

= 155,013

81,0396

= 52,2

Then : wt

c = 41,8 52,2

The web is class 1.

7.3.2. The flange

ft

c =

16

9,73= 4,6

The limit for Class 1 is : 9 ε = 9 0,81 = 7,3

Then : ft

c = 4,6 8,3

The flange is Class 1

EN 1993-1-1 Table 5.2 (Sheet 2)

So the section is Class 1. The verification of the member will be based on the plastic resistance of the cross-section.

7.4. Resistance of the cross-section

7.4.1. Shear resistance

Shear area: Av = A 2btf + (tw+2r)tf but not less than hwtw

Av = 16)2122,10(16200211600 = 6035 mm2

EN 1993-1-1 §6.2.6

Conservatively = 1,0. Therefore:

Av hwtw = 2,104680,1 = 4774 mm2

Av = 6035 mm2

from EN 1993-1-1 §6.2.6(3)

Vpl,Rd =

M0

yv 3

fA

= 310

0,1

33556035 = 1237 kN

VEd = 117 kN < 1237 kN OK

Bending and shear interaction

When shear force and bending moment act simultaneously on a cross-section, the shear force can be ignored if it is smaller than 50% of the plastic shear resistance.

VEd = 117 kN < 0,5 Vpl,Rd = 0,5 1237 = 619 kN

EN 1993-1-1 §6.2.8

Therefore the effect of the shear force on the moment resistance may be neglected.


analysis 12 of 44

4 - 93

7.4.2. Compression resistance

Nc,Rd = M0

y

A f = 310

0,1

35511600

= 4118 kN

NEd = 168 kN Nc,Rd = 4118 kN OK

EN 1993-1-1 §6.2.4

Bending and axial force interaction

When axial force and bending moment act simultaneously on a cross-section, the axial force can be ignored provided the following two conditions are satisfied:

NEd 0,25 Npl,Rd and NEd M0

yww5,0

fth

0,25 Npl,Rd = 0,25 4118 = 1030 kN

3

M0

yww10

0,1

3552,104685,05,0

fth = 847 kN

168 kN < 1030 kN and 847 kN, OK

Therefore the effect of the axial force on the moment resistance may be neglected.

EN 1993-1-1 §6.2.9

Bending moment resistance EN 1993-1-1 §6.2.5

Mpl,y,Rd = M0

ypl

fW

= 63

100,1

355102194

= 779 kNm

My,Ed = 616 kNm < 779 kNm OK

7.5. Out-of-plane buckling

The out-of-plane buckling interaction is verified with expression (6.62) in EN 1993–1–1.

0,1Rdb,

Edy,zy

Rdz,b,

Ed M

Mk

N

N

This expression should be verified between torsional restraints.

If the tension flange is restrained at discreet points between the torsional restraints and the spacing between the restraints to the tension flange is small enough, advantage may be taken of this situation.

In order to determine whether or not the spacing between restraints is small enough, Annex BB of EN 1993-1-1 provides an expression to calculate the maximum spacing. If the actual spacing between restraints is smaller than this calculated value, then the methods given in Appendix C of this document may be used to calculate the elastic critical force and the critical moment of the section.


analysis 13 of 44

4 - 94

Verification of spacing between intermediate restraints

In this case the restraint to the tension flange is provided by the siderails. These siderails are spaced at 1900 mm.

The limiting spacing as given by Annex BB of EN 1993-1-1 is:

Lm = 2

y

t

2ypl,

21

Ed

z

235756

1

4,57

1

38

f

AI

W

CA

N

i

EN 1993-1-1 Annex BB §BB.3.1.1

C1 is a factor that accounts for the shape of the bending moment diagram. C1 values for different shapes of bending moment diagrams can be found in Appendix C of this document.

For a linear bending moment diagram, C1 depends on the ratio of the minimum and the maximum bending moments in the segment being considered.

The ratios of bending moments for the middle and bottom segments of the column (without considering the haunch) are as follows:

= 444

222 = 0,50 1C = 1,31

Appendix C of this document

= 222

0 = 0 1C = 1,77

1C = 1,31 is the most onerous case and therefore this is the case that will be analysed.

Lm = 2

4

23

2

3

235

355

103,8911600

102194

31,1756

1

11600

10168

4,57

1

1,4338

Lm = 1584 mm

Siderail spacing is 1900 mm > 1584 mm

Therefore the normal design procedure must be adopted and advantage may not be taken of the restraints to the tension flange.

7.5.2. Whole column (5275 mm)

Firstly the whole column is verified. If the flexural buckling, lateral torsional buckling and interaction checks are satisfied for the length of the whole column, no further restraints are required. Otherwise, intermediate torsional restraints will be introduced to the column, or the column size increased.

Flexural buckling resistance about the minor axis, Nb,z,Rd

b

h

200

500 2,5

tf 16 mm


analysis 14 of 44

4 - 95

buckling about z-z axis:

Curve b for hot rolled I sections

z 0,34

EN 1993-1-1 Table 6.2 Table 6.1

1 = yf

E = 355

210000 = 76,4 EN 1993-1-1 §6.3.1.3

z = 1z

cr 1

i

L =

4,76

1

1,43

5275 = 1,60

z = 2zzz 2,015,0

= 260,12,060,134,015,0 = 2,02

EN 1993-1-1 §6.3.1.2

z = 22

1

=

22 60,102,202,2

1

= 0,307

Nb,z,Rd = M1

yz

Af

= 3100,1

35511600307,0

= 1264 kN

NEd = 168 kN < 1264 kN OK

Lateral-torsional buckling resistance, Mb,Rd

The lateral-torsional buckling resistance of a member is calculated as a reduction factor, LT, multiplied by the section modulus and the yield strength of the section. The reduction factor is calculated as a function of the

slenderness, LT , which depends on the critical moment of the member. The expression for the critical moment, Mcr, is given below. The factor C1 accounts for the shape of bending moment diagram of the member. Appendix C of this document provides values of C1 for different shapes of bending moment diagrams. For the case of a linear bending moment diagram, C1 depends on the ratio of the bending moments at the ends of the member, given as .

For the total length of the column (without the haunch):

0616

0 77,11 C


Mcr = z

2

t2

z

w

2

z2

1EI

GIL

I

I

L

EIC

= 2

42

5275

10214221000077,1

42

42

4

9

102142210000

103,89810005275

102142

101249

Mcr = 909 106 Nmm



analysis 15 of 44

4 - 96

The non dimensional slenderness, LT , is calculated as:

LT cr

yy

M

fW =

6

3

10909

355102194

= 0,926

EN 1993-1-1 §6.3.2.2

For the calculation of the reduction factor, LT, EN 1993-1-1 provides two methods. The general method, applicable to any section, is given in §6.3.2.2. §6.3.2.3 provides a method that can only be used for rolled sections or equivalent welded sections.

In this example the second method is used, i.e. §6.3.2.3.

LT = 2LTLT,0LTLT15,0

EN 1993-1-1 recommends the following values:

LT,0 0,4

0,75

The values given in the National Annex may differ. The designer should check the National Annex of the country where the structure is to be built.

EN 1993-1-1 §6.3.2.3

b

h 2,5

Curve c for hot rolled I sections

LT 0,49

EN 1993-1-1 Table 6.3 Table 6.5

LT = 2926,075,04,0926,049,015,0 = 0,950

LT = 2

LT2

LTLT

1

LT = 22 926,075,0950,0950,0

1

= 0,685

EN 1993-1-1 §6.3.2.3

22LT 926.0

11

= 1,17

LT = 0,685

Mb,Rd = M1

yypl,LT

fW = 6

3

100,1

355102194685,0

= 534 kNm

Mb,Rd = 616 kNm 534 kNm Fails

Since the check for lateral torsional buckling resistance alone fails, the interaction of axial force and bending moment is not carried out.

It is necessary to introduce a torsional restraint between the haunch and the base, as shown in the following figure. The bending moment is greater at the top of the column and therefore the restraint is placed closer to the maximum bending moment, rather than in the middle of the column.


analysis 16 of 44

4 - 97

The restraint must be at a side rail position, since bracing from the side rail to the inner flange is used to provide the torsional restraint.

3800

1475

6000

0 kNm

616 kNm

444 kNm*

*= 117 kNVN = 162 kN

Ed

Ed

= 117 kNVN

Ed

Ed= 168 kN

7.5.3. Upper segment (1475 mm)

As previously, the flexural buckling and the lateral torsional buckling checks are carried out separately before proceeding to verify the interaction between the two.


b

h

200

500 2,5

tf 16 mm

buckling about z-z axis:


z 0,34

EN 1993-1-1 Table 6.2 Table 6.1

1 = yf

E = 355

210000 = 76,4 EN 1993-1-1 §6.3.1.3

z = 1z

cr 1

i

L =

4,76

1

1,43

1475 = 0,448

z = 2zzz 2,015,0

= 2448,02,0448,034,015,0 = 0,643

EN 1993-1-1 §6.3.1.2

z = 2

z2

zz

1

=

22 448,0643,0643,0

1

= 0,906

z = 0,906


analysis 17 of 44

4 - 98

Nb,z,Rd = M1

yz

Af

= 3100,1

35511600906,0

= 3731 kN

NEd = 168 kN < 3731 kN OK


As previously the factor C1 needs to be calculated in order to determine the critical moment of the member.

616 kNm

444 kNm

14

75

721,0616

444 16,11 C


Mcr = z

2

t2

z

w

2

z2

1EI

GIL

I

I

L

EIC

= 2

42

1475

10214221000016,1

42

42

4

9

102142210000

103,89810001475

102142

101249

Mcr = 5887 106 Nmm


LT cr

yy

M

fW =

6

3

105887

355102194

= 0,364

EN 1993-1-1 §6.3.2.2

For hot rolled sections


LT,0 0,4

0,75

EN 1993-1-1 §6.3.2.3

As previously:


LT 0,49

EN 1993-1-1 Table 6.3 Table 6.5


analysis 18 of 44

4 - 99

LT = 2364,075,04,0364,049,015,0 = 0,541

LT = 2

LT2

LTLT

1

LT = 22 364,075,0541,0541,0

1

= 1,02

EN 1993-1-1 §6.3.2.3

LT cannot be greater than 1.0, therefore:

LT = 1,0

Mb,Rd = M1

yypl,LT

fW

= 63

100,1

3551021940,1

= 779 kNm

MEd = 616 kNm < 779 kNm OK

Interaction of axial force and bending moment – out-of-plane buckling

Out-of-plane buckling due to the interaction of axial force and bending moment is verified by satisfying the following expression:

0,1Rdb,

Edy,zy

Rdz,b,

Ed M

Mk

N

N

EN 1993-1-1 §6.3.3(4)

For z 0.4, the interaction factor, kzy is calculated as:

kzy =

zRd,b,

Ed

mLTzRd,b,

Ed

mLT 25,0

1,01;

25,0

1,01max

N

N

CN

N

Cz

EN 1993-1-1 Annex B Table B.2

CmLT = 4,06,0

= 616

444 = 0,721

CmLT = 721,04,06,0 = 0,888 0,4

CmLT = 0,888


kzy =

3731

168

25,0888,0

1,01;

3731

168

25,0888,0

448,01,01max

kzy = max (0,996; 0,993) = 0,996

Rdb,

Edy,zy

Rdz,b,

Ed

M

Mk

N

N =

779

616996,0

3731

168 = 0,832 < 1,0 OK

7.5.4. Lower segment (3800 mm)

As previously the flexural buckling resistance and the lateral-torsional buckling resistance are checked individually and then the interaction between the two is verified by using interaction Expression 6.62.


analysis 19 of 44

4 - 100


As previously:


z 0,34

EN 1993-1-1 Table 6.1 Table 6.2

1 = yf

E = 355

210000 = 76,4 EN 1993-1-1 §6.3.1.3

z = 1z

cr 1

i

L =

4,76

1

1,43

3800 = 1,15

z = 2zzz 2,015,0

z = 215,12,015,134,015,0 = 1,32

EN 1993-1-1 §6.3.1.2

z = 2

z2

zz

1

=

22 15,132,132,1

1

= 0,508

Nb,z,Rd = M1

yz

Af

= 3100,1

355160010,508

= 2092 kN

NEd = 168 kN < 2092 kN OK


As previously the C1 factor needs to be calculated in order to determine the critical moment of the member.

444 kNm

38

00

0444

0 77,11 C



analysis 20 of 44

4 - 101

Mcr = z

2

t2

z

w

2

z2

1EI

GIL

I

I

L

EIC

= 2

42

3800

10214221000077,1

42

42

4

9

102142210000

103,89810003800

102142

101249

Mcr = 1556 106 Nmm


LT cr

yy

M

fW =

6

3

101556

355102194

= 0,708

EN 1993-1-1 §6.3.2.2



LT,0 0,4 and 0,75

EN 1993-1-1 §6.3.2.3

As previously:


LT 0,49

EN 1993-1-1 Table 6.3 Table 6.5

LT = 2708,075,04,0708,049,015,0 = 0,763

LT = 2

LT2

LTLT

1

LT = 22 708,075,0763,0763,0

1

= 0,822

EN 1993-1-1 §6.3.2.3

2LT

1

=

2708,0

1 = 1,99

LT = 0,822

Mb,Rd = M1

yypl,LT

fW = 6

3

100,1

355102194822,0

= 640 kNm




0,1Rdb,

Edy,zy

Rdz,b,

Ed M

Mk

N

N

EN 1993-1-1 §6.3.3(4)


analysis 21 of 44

4 - 102

For z 0.4, the interaction factor, kzy is calculated as:

kzy =

zRd,b,

Ed

mLTzRd,b,

Ed

mLT 25,0

1,01;

25,0

1,01max

N

N

CN

N

Cz

CmLT = 4,06,0

= 444

0 = 0

CmLT = 4,06,0 = 04,06,0 = 0,6 > 0,4

CmLT = 0,6


kzy =

2092

168

25,06,0

1,01;

2092

168

25,06,0

15,11,01max

kzy = max (0,974; 0,977) = 0,977


Rdb,

Edy,zy

Rdz,b,

Ed

M

Mk

N

N =

640

444977,0

2092

168 = 0,758 < 1,0 OK

7.6. In-plane buckling

The in-plane buckling interaction is verified with expression (6.61) in EN 1993-1-1.

0,1Rdb,

Edy,yy

Rdy,b,

Ed M

Mk

N

N

M

M

Ed

Ed

Ed

Ed

Ed

Ed

V

V

N

N

= 0 kNm

= 616 kNm

= 117 kN

= 162 kN

= 117 kN

= 168 kN

The maximum design values of either column occur on the right hand column (considering EHF applied from left to right) and are as follows:

MEd 616 kNm

NEd 168 kN


analysis 22 of 44

4 - 103

Firstly individual checks are carried out for flexural buckling alone and lateral-torsional buckling alone. Then the interaction expression for in-plane buckling is applied to verify that the combination of axial force and bending moment does not cause excessive buckling on the columns.

7.6.1. Flexural buckling resistance about the mayor axis, Nb,y,Rd

b

h

200

500 2,5

tf 16 mm

buckling about y-y axis:

Curve a for hot rolled I sections

y 0,21

EN 1993-1-1 Table 6.2 Table 6.1

The buckling length is the system length, which is the distance between nodes (i.e. the length of the column), L = 6000 mm.

1 = yf

E = 355

210000 = 76,4 EN 1993-1-1 §6.3.1.3

y = 1y

cr 1

i

L =

4,76

1

204

6000 = 0,385

y = 2yyy 2,015,0

= 2385,02,0385,021,015,0 = 0,594

EN 1993-1-1 §6.3.1.2

y = 22

1

=

22 385,0594,0594,0

1

= 0,956

EN 1993-1-1 §6.3.1.2

Nb,y,Rd = M1

yy

Af

= 3100,1

35511600956,0

= 3937 kN

NEd = 168 kN < 3937 kN OK

7.6.2. Lateral-torsional buckling resistance, Mb,Rd

Mb,Rd is the least buckling moment resistance of those calculated previously.

Mb,Rd = 640;779min

Mb,Rd = 640 kNm

7.6.3. Interaction of axial force and bending moment – in-plane buckling

In-plane buckling due to the interaction of axial force and bending moment is verified by satisfying the following expression:

0,1Rdb,

Edy,yy

Rdy,b,

Ed M

Mk

N

N


analysis 23 of 44

4 - 104

For Cmy, the relevant braced points are the torsional restraints at the end of the member.

The interaction factor, kyy, is calculated as follows:

kyy =

Rdy,b,

Edmy

Rdy,b,

Edymy 8,01;2,01min

N

NC

N

NC

From table B.3, Cmy is:

Cmy = 4,06,0 0,4

0

Cmy = 04,06,0 = 0,6

kyy =

3937

1688,016,0;

3937

1682,0385,016,0min

= 620,0;605,0min = 0,605

Rdb,

Edy,yy

Rdy,b,

Ed

M

Mk

N

N =

640

616605,0

3937

168 = 0,625 < 1,0 OK

Validity of column section

In Section 7.4 it has been demonstrated that the cross-sectional resistance of the section is greater than the applied forces.

The out-of-plane and in-plane buckling checks have been verified in Sections 7.5 and 7.6 for the appropriate choice of restraints along the column.

Therefore it is concluded that the IPE 500 section in S355 steel is appropriate for use as columns in this portal frame.

Rafter: IPE 450

134513451700170017001700170017001700

351 kNm354 kNm

111 kNm

298 kNm


analysis 24 of 44

4 - 105

VEd 118 kN (maximum value)

NEd 127 kN (maximum value)

MEd 356 kNm (maximum value)

Section properties

450h mm 9880A mm2

190b mm 3ypl, 101702W mm3

4,9w t mm 4y 1033740I mm4 185y i mm

6,14f t mm 4z 101676I mm4 2,41z i mm

21r mm 4t 109,66 I mm4

8,420w h mm 9w 10791I mm6

8,378d mm


7.7.1. The web

wt

c =

4,9

8,378 = 40,3

EN 1993-1-1 Table 5.2 (Sheet 1)

dN = yw

Ed

ft

N =

3554,9

127000

= 38

= w

Nw

2d

dd =

8,3782

388,378

= 0,55 > 0,50

The limit for Class 1 is : 113

396

= 155,013

81,0396

= 52,1

Then : wt

c = 40,3 < 52,1

The web is class 1.

7.7.2. The flange

ft

c =

6,14

3,69 = 4,7


Then : ft

c = 4,7 < 7,3

The flange is Class 1

EN 1993-1-1 Table 5.2 (Sheet 2)

Therefore, the section is Class 1. The verification of the member will be based on the plastic resistance of the cross-section.


analysis 25 of 44

4 - 106

7.8. Resistance of the cross-section


Shear area : Av = A - 2btf + (tw+2r)tf but not less than hwtw

Av = 6,14)2124,9(6,1419029880 = 5082 mm2

EN 1993-1-1 §6.2.6(3)

hwtw = 4,98,4200,1 = 3956 mm2

Av = 5082 mm2

from EN 1993-1-1 §6.2.6(3)

Vpl,Rd =

M0

yv 3

fA

= 310

0,1

33555082 = 1042 kN

VEd = 118 kN < 1042 kN OK

EN 1993-1-1 §6.2.6(3)

Bending and shear interaction

When shear force and bending moment act simultaneously on a cross-section, the shear force can be ignored if it is smaller than 50% of the plastic shear resistance of the cross-section.

EN 1993-1-1 §6.2.8

VEd = 118 kN < 0,5 Vpl,Rd = 521 kN OK



Nc,Rd = M0

y

A f = 310

0,1

3559880

= 3507 kN

NEd = 127 kN < 3507 kN OK

EN 1993-1-1 §6.2.4

Bending and axial force interaction

When axial force and bending moment act simultaneously on a cross-section, the axial force can be ignored provided the following two conditions are satisfied:

NEd 0,25 Npl,Rd and NEd M0

yww5,0

fth

0,25 Npl,Rd = 0,25 3507 = 877 kN

And

3

M0

yww10

0,1

3554,98,4205,05,0

fth = 702 kN

127 kN < 887 kN and 702 kN OK

EN 1993-1-1 §6.2.9

Therefore the effect of the axial force on the moment resistance may be neglected.


analysis 26 of 44

4 - 107

7.8.3. Bending moment resistance EN 1993-1-1 §6.2.5

Mpl,y,Rd = M0

yypl,

fW

= 63

100,1

355101702

= 604 kNm


7.9. Out-of-plane buckling

The out-of-plane buckling interaction is verified with expression (6.62) from EN 1993-1-1

0,1Rdb,

Edy,

Rdb,z,

Ed M

Mk

N

Nzy

The rafter should be verified between torsional restraints. If advantage is taken of intermediate restraints to the tension flange, the spacing of the intermediate restraints must also be verified.

7.9.1. Mid-span region

The purlin spacing in this region is 1700 mm.

1700 mm

1

1 Mid-span region

354 kNm351 kNm

1700

356 kNm

1 1: Bending moment

Flexural buckling resistance about minor axis bending, Nb,z,Rd

b

h

190

450 2,37

tf 14,6 mm

buckling about z-z axis


z 0,34

EN 1993-1-1 Table 6.1 Table 6.2


analysis 27 of 44

4 - 108

1 = yf

E = 355

210000 = 76,4 EN 1993-1-1 §6.3.1.3

z = 1z

cr 1

i

L =

4,76

1

2,41

1700 = 0,540

z = 2zzz 2,015,0

z = 2540,02,0540,034,015,0 = 0,704

EN 1993-1-1 §6.3.1.2

z = 2

z2

zz

1

=

22 540,0704,0704,0

1

= 0,865

Nb,z,Rd = M1

yz

Af

= 3100,1

3559880865,0

= 3034 kN

NEd = 127 kN < 3034 kN OK

Lateral-torsional buckling resistance for bending, Mb,Rd

In this zone, lateral-torsional buckling is checked between restraints, which are the purlins. For equally spaced purlins, the critical length is at the point of maximum bending moment.

In order to determine the critical moment of the rafter, the C1 factor takes account of the shape of the bending moment diagram.

In this case the bending moment diagram is nearly constant along the segment in consideration, so 1,0. Therefore:

11 C ,0


Mcr = z

2

t2

z

w

2

z2

1EI

GIL

I

I

L

EIC

= 2

42

1700

1016762100000,1

42

42

4

9

101676210000

109,66810001700

101676

10791

Mcr = 2733 106 Nmm


LT cr

yypl,

M

fW =

6

3

102733

355101702

= 0,470

EN 1993-1-1 §6.3.2.2

2LTLT,0LTLTLT 15,0

EN 1993-1-1 §6.3.2.3


analysis 28 of 44

4 - 109

LT,0 0,4 and 0,75

b

h 2,37


LT 0,49

EN 1993-1-1 Table 6.3 Table 6.5

2LT 470,075,04,0470,049,015,0 = 0,60

LT = 2

LT2

LTLT

1

LT = 22 470,075,060,060,0

1

= 0,961

EN 1993-1-1 §6.3.2.3

2LT

1

=

2470,0

1 = 4,53

LT = 0,961

Mb,Rd = M1

yypl,LT

fW

= 63

100,1

355101702961,0

= 581 kNm




0,1Rdb,

Edy,zy

Rdz,b,

Ed M

Mk

N

N

EN 1993-1-1 §6.3.3(4)

For z 0,4, the interaction factor, kzy is calculated as:

kzy =

Rdz,b,

Ed

mLTRdz,b,

Ed

mLT 25,0

1,01;

25,0

1,01max

N

N

CN

N

Cz

The bending moment is approximately linear and constant. Therefore CmLT is taken as 1.0


kzy =

3034

127

25,01

1,01;

3034

127

25,01

540,01,01max

= max (0,997; 0,994) = 0,997


Rdb,

Edy,zy

Rdz,b,

Ed

M

Mk

N

N =

581

356997,0

3034

127 = 0,653 < 1,0 OK


analysis 29 of 44

4 - 110

7.9.2. End-of-span region

In this region the bottom flange is in compression and stability must be checked between torsional restraints.

2930 mm

1 1

1 End of span region

1230 1700

298 kNm1

2

111 kNm

1 Simplified bending moment 2 Bending moment

The buckling length is taken from the torsional restraint at the sharp end of the haunch to the ‘virtual’ restraint which is the point of contraflexure of the bending moment diagram, i.e. where the bending moment is equal to zero. In some countries the assumption of a virtual restraint may not be common practice. If the practice is not allowed, the buckling length should be taken to the next purlin (i.e the first restraint to the compression flange).

From the analysis, the buckling length to the point of contraflexure is 2930 mm.

If the tension flange is restrained at discreet points between the torsional restraints and the spacing between the restraints to the tension flange is small enough, advantage may be taken of this situation.


Verification of spacing between intermediate restraints

In this case, the restraint to the tension flange is provided by the purlins. These purlins are spaced at 1700 mm.

Lm = 2

y

t

2ypl,

21

Ed

z

235756

1

4,57

1

38

f

AI

W

CA

N

i

EN 1993-1-1 Annex BB §BB.3.1.1


analysis 30 of 44

4 - 111

= 298

111 = 0,37 1C = 1,42


Lm = 2

4

23

2

3

235

355

109,669880

101702

42,1756

1

9880

10127

4,57

1

2,4138

Lm = 1669 mm

Purlin spacing is 1700 mm > 1669 mm

Therefore the normal design procedure must be adopted and advantage may not be taken of the restraints to the tension flange.


As previously:


z 0,34

EN 1993-1-1 Table 6.2 Table 6.1

1 = yf

E = 355

210000 = 76,4 EN 1993-1-1 §6.3.1.3

z = 1z

cr 1

i

L =

4,76

1

2,41

2930 = 0,931

z = 2zzz 2,015,0

z = 2931,02,0931,034,015,0 = 1,06

EN 1993-1-1 §6.3.1.2

z = 2

z2

zz

1

=

22 931,006,106,1

1

= 0,638

Nb,z,Rd = M1

yz

Af

= 3100,1

35598800,638

= 2238 kN

NEd = 127 kN < 2238 kN OK


As previously the C1 factor needs to be calculated in order to determine the critical moment of the member. For simplicity, the bending moment diagram is considered as linear, which is slightly conservative.

= 298

0 = 0 1C = 1,77



analysis 31 of 44

4 - 112

Mcr = z

2

t2

z

w

2

z2

1EI

GIL

I

I

L

EIC

= 2

42

2930

10167621000077,1

42

42

4

9

101676210000

109,66810002930

101676

10791

Mcr = 1763 106 Nmm


LT cr

yypl,

M

fW =

6

3

101763

355101702

= 0,585

EN 1993-1-1 §6.3.2.2



EN 1993-1-1 §6.3.2.3

LT,0 0,4 and 0,75

As previously:


LT 0,49

EN 1993-1-1 Table 6.3 Table 6.5

LT = 2585,075,04,0585,049,015,0 = 0,674

LT = 2

LT2

LTLT

1

LT = 22 585,075,0674,0674,0

1

= 0,894

EN 1993-1-1 §6.3.2.3

2LT

1

=

2585,0

1 = 2,92

LT = 0,894

Mb,Rd = M1

yypl,LT

fW

= 63

100,1

355101702894,0

= 540 kNm EN 1993-1-1 §6.2.5(2)



0,1Rdb,

Edy,zy

Rdz,b,

Ed M

Mk

N

N

EN 1993-1-1 §6.3.3(4)


analysis 32 of 44

4 - 113

For z 0,4, the interaction factor, kzy, is calculated as:

kzy =

Rdz,b,

Ed

mLTRdz,b,

Ed

mLT

z

25,0

1,01;

25,0

1,01max

N

N

CN

N

C

0298

0

CmLT = 4,06,0 = 04,06,0 = 0,6


kzy =

2238

127

25,06,0

1,01;

2238

127

25,06,0

931,01,01max

= max ( 0,985; 0,983 ) = 0,985


Rdb,

Edy,zy

Rdz,b,

Ed

M

Mk

N

N =

540

298985,0

2238

127 = 0,601 < 1,0 OK

7.10. In-plane buckling

The in-plane buckling interaction is verified with expression (6.61) in EN 1993-1-1.

0,1Rdb,

Edy,yy

Rdy,b,

Ed M

Mk

N

N

M

M

MM

Ed

Ed

EdEd

Ed

EdEd

Ed

EdEd

= 351 kNm

V

VV

N

NN

= 298 kNm = 701 kNm

Assumed maximum moment= 356 kNm

= 118 kN

= 127 kN

= 150 kN

= 130 kN

= 10 kN

= 116 kN

Maximum bending moment and axial force in the rafter, excluding the haunch.

MEd 356 kNm

NEd 127 kN

The haunch is analysed in Section 8.


analysis 33 of 44

4 - 114

7.10.1. Flexural buckling resistance about the major axis, Nb,y,Rd

b

h

190

450 2,37

tf 14,6 mm

buckling about y-y axis:

Curve a for hot rolled I sections

0,21

EN 1993-1-1 Table 6.1 Table 6.2

The buckling length is the system length, which is the distance between the joints (i.e. the length of the rafter, including the haunch), L = 15057 mm

1 = yf

E = 355

210000 = 76,4 EN 1993-1-1 §6.3.1.3

y = 1y

cr 1

i

L =

4,76

1

185

15057 = 1,065

y = 2yyy 2,015,0

y = 2065,12,0065,121,015,0 = 1,158

EN 1993-1-1 §6.3.1.2

y = 2

y2

yy

1

=

22 065,1158,1158,1

1

= 0,620

Nb,y,Rd = M1

yy

Af

= 3100,1

3559880620,0

= 2175 kN

NEd = 127 kN < 2175 kN OK

7.10.2. Lateral-torsional buckling resistance, Mb,Rd

Mb,Rd is the least buckling moment resistance of those calculated before.

Mb,Rd = 540;581min

Mb,Rd = 540 kNm

7.10.3. Interaction of axial force and bending moment – in-plane buckling

In-plane buckling due to the interaction of axial force and bending moment is verified by satisfying the following expression:

0,1Rdb,

Edy,yy

Rdy,b,

Ed M

Mk

N

N

The interaction factor, kyy, is calculated as follows:

kyy =

Rdy,b,

Edmy

Rdy,b,

Edymy 8,01;2,01min

N

NC

N

NC


analysis 34 of 44

4 - 115

The expression for Cmy depends on the values of h and .

= 351

298 = 0,849.

h = s

h

M

M =

356

351 = 0,986

Therefore Cmy is calculated as:

Cmy = h05,095,0 = 986,005,095,0 1,0


kyy =

2175

1278,00,11;

2175

1272,0065,110,1min

= 047,1;05,1min = 1,047


Rdb,

Edy,yy

Rdy,b,

Ed

M

Mk

N

N =

540

356047,1

2175

127 = 0,749 < 1,0 OK

The member satisfies the in-plane buckling check.

7.11. Validity of rafter section

In Section 7.8 it has been demonstrated that the cross-sectional resistance of the section is greater than the applied forces.

The out-of-plane and in-plane buckling checks have been verified in Sections 7.9 and 7.10 for the appropriate choice of restraints along the rafter.

Therefore it is concluded that the IPE500 section in S355 steel is appropriate for use as rafter in this portal frame.

8. Haunched length

The haunch is fabricated from a cutting of an IPE 550 section. Checks must be carried out at end and quarter points, as indicated in the figure below.

312

45

5°

2740

IPE 450

IPE 500

72

5

3020

685685685685


analysis 35 of 44

4 - 116

From the geometry of the haunch, the following properties can be obtained for each of the cross-sections 1 to 5, as shown in Table 2.

Table 2 Section properties of haunched member at cross-section, as per figure above

Cross-section no.

Cutting depth (mm)

Overall depth (mm)

Gross area, A (mm2)

Iy (cm4)

Wel,min (cm3)

NEd (kN)

MEd (kNm)

1 503 953 15045 200500 4055 129 661

2 378 828 13870 144031 3348 129 562

3 252 702 12686 98115 2685 128 471

4 126 576 11501 62258 2074 127 383

5 0 450 9880 33740 1500 127 298

The section properties are calculated normal to the axis of the section.

For simplicity, the section properties above have been calculated assuming a constant web thickness of 9,4 mm and neglecting the middle flange.

The actual and the equivalent cross-sections are shown in the following figure for cross-section No.1:

190 190

210210

11,1

9,4

9,4 953

503

450

14,6

14,6

17,2

Actual cross-section Equivalent cross-section

For cross-section No.1 the values of NEd and MEd are taken at the face of the column.


8.1.1. The web

The web can be divided into two webs, and classified according to the stress and geometry of each web. The upper section (i.e. the rafter) is called the upper web and the lower section (i.e. the cutting) is called the lower web.


analysis 36 of 44

4 - 117

Upper web

By inspection the upper web will be Class 3 or better, because it is mostly in tension.

Lower web

Stress in the section caused by axial load:

N = 31015045

129 = 8,57 N/mm2

Assuming an elastic stress distribution in cross-section No.1, the maximum stress available to resist bending is:

M = NM0

y

f

= 57,80,1

355 = 346 N/mm2

95

3

45

05

03

45

1,4

50

1,6

31 N/mm²

346 N/mm²

The distance from the bottom flange to the elastic neutral axis is:

z = 451,4 mm

Distance from underside of middle flange to neutral axis: 51,6 mm

Bending axial stress at the top of cutting section:

= 57,84,4516,51346 = 31 N/mm2


analysis 37 of 44

4 - 118

For Class 3 check, determine :

= 346

31 = 0,09

Considering section 1 parallel to column flange, the depth of web excluding root radius is:

cw = 242,17503 = 461,8 mm

w

w

t

c =

1,11

8,461 = 41,6

190

210

11,1

9,4

503

450

14,6

14,6

17,2

461,8

51,6E.N.A

Z = 451,4_

EN 1993-1-1 Table 5.2

For 1, the limit for Class 3 is: EN 1993-1-1 Table 5.2

33,067,0

42

= 09,033,067,0

81,042

= 53,1

wt

c = 41,6 < 53,1

The web is Class 3

8.1.2. The flanges

Top flange

ft

c =

6,14

3,69 = 4,7


Then : ft

c = 4,7 < 7,3

The top flange is Class 1

EN 1993-1-1 Table 5.2 (Sheet 2)

Bottom flange

ft

c =

2,17

45,75 = 4,4


ft

c = 4,4 < 7,3

The bottom flange is Class 1

Therefore the overall section is Class 3.


analysis 38 of 44

4 - 119

8.2. Cross-sectional resistance

IPE 450

IPE 500

312

45

5°298 kNm

383 kNm471 kNm

562 kNm661 kNm

701 kNm

72

5

3020


The shear area of cross-section No.1 can be conservatively estimated as:

Av = A (btf)topfl (btf)botfl = 2,172106,1419015045 = 8659 mm2

Vpl,Rd =

M0

yv 3

fA

= 310

0,1

33558659 = 1775 kN

VEd = 147 kN < 1775 kN OK

EN 1993-1-1 §6.2.6

Bending and shear interaction:

When shear force and bending moment act simultaneously on a cross-section, the shear force can be ignored if it is smaller than 50% of the plastic shear resistance.

VEd = 147 kN < 0,5 Vpl,Rd = 888 kN


The same calculation must be carried out for the remaining cross-sections. The table below summarizes the shear resistance verification for the haunched member:

Table 3 Shear verification for cross-sections 1 to 5

Cross- section no.

VEd

(kN) Av (mm2)

Vpl,Rd

(kN) VEd VRd 0,5VRd

(kN) Bending and shear interaction

1 147 8659 1775 Yes 888 No

2 140 7484 1534 Yes 767 No

3 132 6300 1291 Yes 646 No

4 125 5115 1048 Yes 524 No

5 118 5082 1042 Yes 521 No


analysis 39 of 44

4 - 120


The compression resistance of cross-section No.1:

Nc,Rd = M0

y

A f = 310

0,1

35515045

= 5341 kN

NEd = 129 kN < 5341 kN OK

EN 1993-1-1 §6.2.4

Bending and axial force interaction:

When axial force and bending moment act simultaneously on a cross-section, the total stress, x,Ed, must be less than the allowable stress.

x,Ed = N + M

M = y

Ed

I

zM =

4

6

10200500

6,50110661

= 165 N/mm2

x,Ed = N + M = 8,57 + 165 = 174 N/mm2

EN 1993-1-1 §6.2.9.2

The maximum allowable stress is:

max = M0

y

f

= 0,1

355 = 355 N/mm2

x,Ed = 174 N/mm2 < 355 N/mm2 OK

A similar calculation must be carried out for the remaining cross-sections. The table below summarize compression resistance verification for the haunched member:

Table 4 Compression verification for cross-sections 1 to 5

Cross-section (i)

NEd

(kN) A (mm2)

Nc,Rd

(kN) NEd Nc.Rd Bending and

axial interaction

1 129 15045 5341 Yes No

2 129 13870 4924 Yes No

3 128 12686 4504 Yes No

4 127 11501 4083 Yes No

5 127 9880 3507 Yes No

8.2.3. Bending moment resistance

The bending moment resistance of cross-section No.1 is:

Mc,y,Rd = Mel,y,Rd = M0

yminel,

fW

= 63

100,1

355104055

= 1440 kNm


EN 1993-1-1 §6.2.5(2)

A similar calculation must be carried out for the remaining cross-sections. The table below summarizes bending moment resistance verification for the haunched member.


analysis 40 of 44

4 - 121

In this case, all cross-sections have been treated as Class 3, and therefore the elastic properties have been used. This is conservative. However, from previous calculations carried out to check the rafter, it is observed that cross-section No.1 is Class 1. It may be that other sections between cross-sections No.1 and No.5 are plastic sections and therefore a greater moment resistance could be achieved.

Table 5 Bending verification for cross-sections 1 to 5

Cross-section (i)

MEd

(kNm) Wel,min

(mm3) 103

Mel,Rd

(kNm) MEd Mel,Rd

1 661 4055 1440 Yes

2 562 3348 1189 Yes

3 471 2685 953 Yes

4 383 2074 736 Yes

5 298 1500 533 Yes

8.3. Buckling resistance

There is a torsional restraint at each end of the haunched length.

298 kNm

661 kNm

471 kNm

2740 mm

Buckling length considered

When the tension flange is restrained at discreet points between the torsional restraints and the spacing between the restraints to the tension flange is small enough, advantage may be taken of this situation.


On the contrary, if the spacing between restraints is larger than the calculated value, an equivalent T-section may be used to check the stability of the haunch.


analysis 41 of 44

4 - 122

8.3.1. Verification of spacing between intermediate restraints

Lm = 2

y

t

2ypl,

21

Ed

z

235756

1

4,57

1

38

f

AI

W

CA

N

i

EN 1993-1-1 Annex BB §BB.3.2.1

For simplicity, the purlin at mid-span of the haunched member is assumed to be aligned with the cross-section No. 3.

Equally, the purlin at the end of the haunched member is assumed to be aligned with the cross-section No. 1.

= 661

471 = 0,71 1C = 1,2


According to the Eurocode, the ratio t

2pl

AI

W should be taken as the maximum

value in the segment.

In this case cross-sections No.1 and 3 have been considered, as shown in Table 6.

Table 6 t

2pl

AI

W ratio for cross-sections No.1 and 3

Cross-section (i)

A (mm2)

It (mm4) 104

Wpl

(mm3) 103

t

2pl

AI

W

1 15045 81 4888 1961

3 12686 74 3168 1069

EN 1993-1-1 Annex BB §BB.3.2.1

For simplicity, in the calculation of It and Wpl, the middle flange has been neglected.

The section properties of cross-section No.1 give the maximum ratio t

2pl

AI

W.

Therefore Lm is calculated using the section properties of cross-section No.1.

Iz = 2168 104 mm4

iz = A

I z = 15045

102168 4 = 38 mm

Lm = 2

4

23

2

3

235

355

108115045

104888

2,1756

1

15045

10129

4,57

1

3838

Lm = 700 mm

Purlin spacing is 1345 mm 700 mm

Therefore the design procedure taking advantage of the restraints to the tension flange given in Section C.2 of Appendix C cannot be used.


analysis 42 of 44

4 - 123

8.3.2. Verification of flexural buckling about minor axis

Maximum forces in the haunched member (at the face of the column) are:

NEd 129 kN

MEd 661 kNm

EN 1993-1-1 does not cover the design of tapered sections (i.e. a haunch), and the verification in this worked example is carried out by checking the forces of an equivalent T-section subject to compression and bending.

The equivalent T-section is taken from a section at mid-length of the haunched member.

The equivalent T-section is made of the bottom flange and 1/3 of the compressed part of the web area, based on §6.3.2.4 of EN 1993-1-1.

The buckling length is 2740 mm (length between the top of column and the first restraint).

Properties of cross-section No.1:

Section area A = 15045 mm2

Elastic modulus to the compression flange Wel,y = 4527 103 mm3

Properties of cross-section No.3:

Properties of the whole section

y

y

f

f

/

/

M

M

312 329

104

Elastic neutral axis (from bottom flange): z = 329 mm

Section area A = 12686 mm2

Properties of the equivalent T-section in compression:


analysis 43 of 44

4 - 124

9,4

210

104

17,2

Area of T-section:

Af = 4590 mm2

Second moment of area about the minor axis:

If,z =1328 104 mm4

Compression in the T-section

The total equivalent compression in the T-section is calculated for cross-section No.1 by adding the direct axial compression and the compression due to bending.

NEd,f = fyel,

EdfEd A

W

M

A

AN = 4590

104527

10661

15045

4590129

3

6

= 670 kN

Verification of buckling resistance about the minor axis

Buckling curve c is used for hot rolled sections

z 0,49

1 = yf

E = 355

210000 = 76,4

if,z = f

zf,

A

I =

4590

101328 4 = 53,8

zf, = 1zf,

cr 1

i

L =

4,76

1

8,53

2740 = 0,667

z = 2zf,zf,z 2,015,0

z = 2667,02,0667,049,015,0 = 0,837

EN 1993-1-1 §6.3.1.2

z = 2

zf,2

zz

1

=

22 667,0837,0837,0

1

= 0,745

EN 1993-1-1 §6.3.1.2

Nb,z,Rd = M0

yz

Af

= 3100,1

3554590745,0

= 1214 kN

NEd,f = 670 kN < 1214 kN OK


analysis 44 of 44

4 - 125

9. Deflections

The horizontal and vertical deflections of the portal frame subject to the characteristic load combination, as per Expression 6.14 of EN 1990 are as follows:

20 mm 16 mm

240 mm

Appendix A of this document provides typical deflection limits used in some European countries. These limits are only intended to be a guideline. The requirements for a given portal frame design must be agreed with the client.



Part 5: Detailed Design of Trusses



5 - ii


5 - iii

FOREWORD

This publication is part five of the design guide, Single-Storey Steel Buildings.




Part 3: Actions













5 - iv


5 - v

Contents Page No

1 INTRODUCTION 1 1.1 Definition 1 1.2 Use of trusses in single-storey buildings 1 1.3 Different shapes of trusses 4 1.4 Aspects of truss design for roof structure 7 1.5 Design of wind girders 9

2 INTRODUCTION TO DETAILED DESIGN 11 2.1 General requirements 11 2.2 Description of the worked example 12

3 GLOBAL ANALYSIS 15 3.1 General 15 3.2 Modelling 15 3.3 Modelling the worked example 16 3.4 Simplified global analysis of the worked example 18 3.5 Secondary forces 19 3.6 Effect of clearance of deflection 21 3.7 Modification of a truss for the passage of equipment 23

4 VERIFICATION OF MEMBERS 28 4.1 Verification of members under compression 28 4.2 Verification of members in tension 41

5 VERIFICATION OF CONNECTIONS 45 5.1 Characteristics of the truss post connection 45 5.2 Chord continuity 47 5.3 Connection of diagonals to chords 48

REFERENCES 51

APPENDIX A Worked Example – Design of a continuous chord connection using splice plate connections 53

APPENDIX B Worked example – Design of a truss node with gusset 79


5 - vi

SUMMARY

This publication provides guidance on the design of trusses for single-storey buildings. The use of the truss form of construction allows buildings of all sizes and shapes to be constructed. The document explains that both 2D and 3D truss forms can be used. The 2D form of truss is essentially a beam and is used to supporting a building roof, spanning up to 120 metres for large industrial buildings. The 3D form of truss can be used to cover large areas without intermediate supports; this form is often used for large exhibition halls. The detailed guidance in this document relates mainly to 2D truss structures composed of rolled profiles but the principles are generally applicable to all forms of truss structure.


5 - 1

1 INTRODUCTION

1.1 Definition A truss is essentially a triangulated system of (usually) straight interconnected structural elements; it is sometimes referred to as an open web girder. The individual elements are connected at nodes; the connections are often assumed to be nominally pinned. The external forces applied to the system and the reactions at the supports are generally applied at the nodes. When all the members and applied forces are in a same plane, the system is a plane or 2D truss.

F

1 2

1

2

1 Compression axial force 2 Tension axial force

Figure 1.1 Members under axial forces in a simple truss

The principal force in each element is axial tension or compression. When the connections at the nodes are stiff, secondary bending is introduced; this effect is discussed below.

1.2 Use of trusses in single-storey buildings In a typical single-storey industrial building, trusses are very widely used to serve two main functions:

To carry the roof load:

- Gravity loads (self-weight, roofing and equipment, either on the roof or hung to the structure, snow loads)

- Actions due to the wind (including uplift due to negative pressure).

To provide horizontal stability:

- Wind girders at roof level, or at intermediate levels if required

- Vertical bracing in the side walls and/or in the gables.

Two types of general arrangement of the structure of a typical single-storey building are shown in Figure 1.2 and in Figure 1.3.

In the first case (Figure 1.2), the lateral stability of the structure is provided by a series of portal trusses: the connections between the truss and the columns provide resistance to a global bending moment. Loads are applied to the portal structure by purlins and side rails.


5 - 2

For the longitudinal stability of the structure, a transverse roof wind girder, together with bracing in the side walls, is used. In this arrangement the forces due to longitudinal wind loads are transferred from the gables to the side walls and then to the foundations.

Lateral stability provided by portal trusses

Longitudinal stability provided by transverse wind girder and vertical cross bracings (blue)

No longitudinal wind girder

Figure 1.2 Portal frame a arrangement

In the second case, as shown in Figure 1.3, each vertical truss and the two columns on which it spans constitute a simple beam structure: the connection between the truss and a column does not resist the global bending moment, and the two column bases are pinned. Transverse restraint is necessary at the top level of the simple structure; it is achieved by means of a longitudinal wind girder carries the transverse forces due to wind on the side walls to the braced gable walls.


5 - 3

Vertical trusses are simply supported by columns

Lateral stability provided by longitudinal wind girder and vertical bracings in the gables (blue)

Longitudinal stability provided by transverse wind girder and vertical bracings (green)

Figure 1.3 Beam and column arrangement

A further arrangement is shown in Figure 1.4.The roof structure is arranged with main trusses spanning from column to column, and secondary trusses spanning from main truss to main truss.


5 - 4

A A

L

On this plan view, main trusses are drawn in blue: their span L is the long side of the column mesh.

The secondary trusses have a shorter span A (distance between main trusses).

This arrangement is currently used for “saw tooth roofs”, as shown on the vertical section:

Main beams are trusses with parallel chords

Secondary beams (green) have a triangular shape.

in red, members supporting the north oriented windows

Figure 1.4 General arrangement 3

1.3 Different shapes of trusses A large range is available for the general shapes of the trusses. Some of the commonly used shapes are shown in Table 1.1.


5 - 5

Table 1.1 Main types of trusses

Pratt truss: In a Pratt truss, diagonal members are in tension for gravity loads. This type of truss is used where gravity loads are predominant

In a truss as shown, diagonal members are in tension for uplift loads. This type of truss is used where uplift loads are predominant, such as open buildings.

Lon

g sp

ans

: ran

ge fr

om 2

0 to

100

m

Warren truss: In this type of truss, diagonal members are alternatively in tension and in compression This type of truss is also used for the horizontal truss of gantry/crane girders (see Figure 1.5)

There are two different types of X truss : if the diagonal members are designed

to resist compression, the X truss is the superposition of two Warren trusses.

if the resistance of the diagonal members in compression is ignored, the behaviour is the same as a Pratt truss.

This shape of truss is more commonly used for wind girders, where the diagonal members are very long.

It is possible to add secondary members in order to : create intermediate loading points limit the buckling length of members in

compression (without influencing the global structural behaviour).

All

thes

e ty

pes

of tr

usse

s ca

n be

use

d ei

ther

in p

orta

l tru

ss s

truc

ture

s (s

ee fi

gure

1.2

)

or in

sim

ple

tru

ss s

truc

ture

s (s

ee fi

gure

1.3

).

For any of the forms shown above, it is possible to provide either a single or a double slope to the upper chord of a roof supporting truss This example shows a duo-pitch truss

Single slope upper chord for these triangular trusses, part of a “saw tooth roof” North oriented windows

Sim

ply

supp

orte

d, s

mal

ler

spa

ns

Ran

ge fr

om 1

0 to

15

m

Fink truss: This type of truss is more commonly used for the roof of houses.


5 - 6

The horizontal truss is positioned at the level of the upper flange of the gantry girder in order to resist the horizontal forces applied by the wheels on the rail (braking of the crane trolley, crabbing)

1

3 2

1 Crane girder 2 Crane rail 3 Horizontal bracing (V truss)

Figure 1.5 Horizontal bracing for a crane girder

Figure 1.6 and Figure 1.7 illustrate some of the trusses described in Table 1.1.

Figure 1.6 N-truss – 100 m span


5 - 7

Figure 1.7 N-truss (also with N-truss purlins)

1.4 Aspects of truss design for roof structure 1.4.1 Truss or I-beam

For the same steel weight, it is possible to get better performance in terms of resistance and stiffness with a truss than an I-beam. This difference is more sensitive for long spans and/or heavy loads.

The full use of this advantage is achievable if the height of the truss is not limited by criteria other than the structural efficiency (a limit on total height of the building, for example).

However, fabrication of a truss is generally more time consuming than for an I-beam, even considering that the modernisation of fabrication equipment allows the optimisation of fabrication times.

The balance between minimum weight and minimum cost depends on many conditions: the equipment of the workshop, the local cost of manufacturing; the steel unit cost, etc. Trusses generally give an economic solution for spans over 20 or 25 m.

An advantage of the truss design for roofs is that ducts and pipes that are required for operation of the buildings services can be installed through the truss web.

1.4.2 General geometry

In order to get a good structural performance, the ratio of span to truss depth should be chosen in the range 10 to 15.

The architectural design of the building determines its external geometry and governs the slope(s) given to the top chord of the truss.


5 - 8

The intended use of the internal space can lead either to the choice of a horizontal bottom chord (e.g. where conveyors must be hung under the chord), or to an inclined internal chord, to allow maximum space to be freed up (see the final example in Table 1.1).

To get an efficient layout of the truss members between the chords, the following is advisable:

The inclination of the diagonal members in relation to the chords should be between 35° and 55°

Point loads should only be applied at nodes

The orientation of the diagonal members should be such that the longest members are subject to tension (the shorter ones being subject to compression).

1.4.3 Section of the members

Many solutions are available. The main criteria are:

Sections should be symmetrical for bending out of the vertical plane of the truss

For members in compression, the buckling resistance in the vertical plane of the truss should be similar to that out of the plane.

A very popular solution, especially for industrial buildings, is to use sections composed of two angles bolted on vertical gusset plates and intermediately battened, for both chords and internal members. It is a very simple and efficient solution.

For large member forces, it is a good solution to use:

Chords having IPE, HEA or HEB sections, or a section made up of two channels (UPE)

Diagonals formed from two battened angles.

The web of the IPE / HEA / HEB chord section is oriented either vertically or horizontally. As it is easier to increase the resistance to in-plane buckling of the chords (by adding secondary diagonal members) than to increase their to out-of-plane resistance, it is more efficient to have the web horizontal, for chords in compression. On the other hand, it is easier to connect purlins to the top chord if it has a vertical web.

It could be a good solution to have the top chord with a vertical web, and the bottom chord with a horizontal web.

Another range of solutions is given by the use of hollow sections, for chords and/or for internals.

1.4.4 Types of connections

For all the types of member sections, it is possible to design either bolted connections or welded connections. Generally, bolted connections are preferred on site. Where bolted connections are used with bolts loaded perpendicular to their shank, it is necessary to evaluate the consequences of slack in


5 - 9

connections. In order to reduce these consequences (typically, the increase of the deflections), solutions are available such as use of pre-stressed bolts, or limiting the hole size.

1.4.5 Lateral stability

It is necessary to design the chords in compression against the out-of-plane buckling. For simply supported trusses, the upper chord is in compression for gravity loading, and the bottom chord is in compression for uplift loading. For portal trusses, each chord is partly in compression and partly in tension.

Lateral restraint of the upper chord is generally given by the purlins and the transverse roof wind girder.

For the restraint of the bottom chord, additional bracing may be necessary, as shown in Figure 1.8. Such bracing allows the buckling length of the bottom chord to be limited out of the plane of the truss to the distance between points laterally restrained: they serve to transfer the restraint forces to the level of the top chord, the level at which the general roof bracing is provided. This type of bracing is also used when a horizontal load is applied to the bottom chord (for example, forces due to braking from a suspended conveyor).

A A

A A A

A

Truss

AA

Cross bracing between trusses

Thick black dots: two consecutive trusses

Blue The purlin which completes the bracing in the upper region

Green The longitudinal element which closes the bracing in the lower region

Red Vertical roof bracing

Figure 1.8 Lateral bracing

The roof purlins often serve as part of the bracing at the top chord. Introduction of longitudinal members at the lower chord allows the trusses to be stabilised by the same vertical bracing.

It is possible to create a horizontal wind girder at the level of the bottom chords, with longitudinal elements to stabilize all the trusses.

1.5 Design of wind girders 1.5.1 Transverse wind girder

In general, the form of a transverse wind girder is as follows (see Figure 1.2):

The wind girder is arranged as an X truss, parallel to the roof plane.


5 - 10

The chords of the wind girder are the upper chords of two adjacent vertical trusses. This means that the axial forces in these members due to loading on the vertical truss and those due to loads on the wind girder loading must be added together (for an appropriate combination of actions).

The posts of the wind girder are generally the roof purlins. This means that the purlins are subject to a compression, in addition to the bending due to the roof loading.

It is also possible, for large spans of the wind girder, to have separate posts (generally tubular section) that do not act as purlins.

The diagonal members are connected in the plane of the posts. If the posts are the purlins, the diagonal members are connected at the bottom level of the purlins. In a large X truss, diagonals are only considered in tension and it is possible to use single angles or cables.

It is convenient to arrange a transverse wind girder at each end of the building, but it is then important to be careful about the effects of thermal expansion which can cause significant forces if longitudinal elements are attached between the two bracing systems, especially for buildings which are longer than about 60 m.

In order to release the expansion of the longitudinal elements, the transverse wind girder can be placed in the centre of the building, but then it is necessary to ensure that wind loads are transmitted from the gables to the central wind-bracing.

Transverse wind girders are sometimes placed in the second and penultimate spans of the roof because, if the roof purlins are used as the wind girder posts, these spans are less subject to bending by roof loads.

The purlins which serve as wind girder posts and are subject to compression must sometimes be reinforced:

To reinforce IPE purlins: use welded angles or channels (UPE)

To reinforce cold formed purlins: increase of the thickness in the relevant span, or, if that is not sufficient, double the purlin sections (with fitting for the Zed, back to back for the Sigma).

1.5.2 Longitudinal wind girder

It is necessary to provide a longitudinal wind girder (between braced gable ends) in buildings where the roof trusses are not “portalized”.

The general arrangement is similar to that described for a transverse wind girder:

X truss

The chords are two lines of purlins in small buildings, or additional elements (usually tubular sections)

The posts are the upper chords of the consecutive stabilized roof trusses.


5 - 11

2 INTRODUCTION TO DETAILED DESIGN

The detailed design of trusses is illustrated in the following Sections by reference to a ‘worked example’. This Section summarizes the general requirements and introduces the example. The topics covered in subsequent Sections are:

Section 3: Global analysis

Section 4: Verification of members

Section 5: Verification of connections

Fully detailed calculations for verification of a gusset plate connection and a chord splice are given in Appendices A and B.

2.1 General requirements The parameters to be taken into account in design are:

Aesthetics

Geometry (span length, height, rise, etc)

Actions.

The following requirements have to be considered:

Regulatory requirements

Contractual requirements with regard to standards

Specific contractual requirements.

The resulting outcome of a design is the set of execution documents for the structure.

The nature of regulatory requirements varies from one country to another. Their purpose is usually to protect people. They exist in particular in the area of seismic behaviour, and for the behaviour of buildings during a fire (see Single-Storey Steel Buildings. Fire engineering Guide1).

The requirements in standards concern the determination of actions to be considered, the methods of analysis to be used, and the criteria for verification with respect to resistance and stiffness.

There is no limit to the number of specific requirements which may be imposed for any particular building but these mainly concern construction geometry; they influence determination of actions, in particular climatic actions.

Obligations and interface arrangements for detailed design might include:

Banning the use of tubes for the bottom chord of trusses to which the industry client wishes to hang equipment

Obligation to use tubes for truss chords for reasons of appearance


5 - 12

Use of the roof to stabilise certain structural elements.

The flowchart below illustrates the main steps in the design of a structural element.

DATA

CHOICE OF GLOBAL

ANALYSIS

MEMBER RESISTANCE

VERIFICATION

CONNECTIONS RESISTANCE

VERIFICATION EC3-1-8

EC3-1-1

Contractual data Geometrical data Incidence of neighbouring

construction Obligations or restrictions

in choice of sections Nature and position of

permanent loads Nature and position of

imposed loads Stabilising role of envelope

Regulatory data and Standards Climatic loads Seismic loads Exploitation loads …

SLS VERIFICATION

CRITERIA

CHAPTER 3

CHAPTER 4

CHAPTER 5

EC1 EC8

Figure 2.1 Flowchart for the design of a structural element

2.2 Description of the worked example The worked example that is the subject of subsequent Sections is a large span truss supporting the roof of an industrial building, by means of purlins in the form of trusses. This example is directly transposed from a real construction and has been simplified in order to clarify the overview.


5 - 13

1

2

1 Main truss 2 Purlin truss

Note: the horizontal bracing is not displayed in this diagram but it is designed in such a way that the purlins provide efficient lateral restraints to the main trusses.

Figure 2.2 Worked example - General layout of the roof

The roof is a symmetrical pitched roof; the slope on each side is 3%.

Each main truss has a span of 45,60 m and is simply supported at the tops of the columns (there is no moment transmission between the truss and the column).

General transverse stability of the building is provided by fixity of the columns at ground level; longitudinal stability is provided by a system of roof bracings and braced bays in the walls.

1

2 5

6

4

3

7

1

2

4

1 Upper chord IPE 330 with horizontal web 2 Lower chord IPE 330 with horizontal web 3 Post - Single angle L100x100x10 4 Top of the column (IPE 450)

5 Diagonals - Double angle 6 Secondary truss members 7 Sketch of the cross-section

Figure 2.3 Worked example – View of truss

The truss is illustrated in Figure 2.3. The truss chords are parallel and are made up of IPE 330 profiles with the webs horizontal. The diagonals are made of twinned angles: two 120 120 12 angles for diagonals in tension under gravity loads (in blue in the diagram above), two 150 150 15 angles for


5 - 14

diagonals in compression under gravity loads (in red in the diagram above); the posts are single angles 100 100 10.

Note that, in the central panels, secondary diagonals and posts are present. They would generally be installed with one or other of the following objectives:

To permit application of a point load between main nodes, without causing further bending in the upper chord

To reduce buckling, in the plane of the truss of central members of the upper chord.

In this example, the secondary trusses reduce the buckling length.

The pairs of angles which make up the section of a diagonal are joined by battens, to ensure combined action with respect to buckling between the truss nodes. To be efficient, battens must therefore prevent local slip of one angle in relation to the other. See Section 4.1.3 for more information.

Each chord is fabricated in two pieces (see Figure 3.6). The diagonals and posts are bolted at their two ends to vertical gusset plates, which are themselves welded to the horizontal webs of the IPE 330 chords. Detailed diagrams of this type of connection are given in Appendix A and in Sections 5.2 and 5.3.

The columns on which the truss is supported are IPE 450, for which the web is perpendicular to the plane of the truss beam.

In order to illustrate all of the topics here, the truss beam in the worked example is designed for two situations: a gravity load case and an uplift load case. The loads correspond to the combination of actions, determined according to EN 1990 for verification with respect to the ultimate limit state (ULS).

91 kN

136 kN 182 kN 182 kN 182 kN

136 kN 91 kN

ULS combination n°1: Gravity loading (without self-weight)

43,50 kN 65,25 kN 87 kN 87 kN 87 kN 65,25 kN 43,50 kN

ULS combination n°2: Uplift loading

Figure 2.4 Worked example – Load Combinations


5 - 15

3 GLOBAL ANALYSIS

3.1 General Section 1.1 describes the general behaviour of a truss. In reality, structures deviate from this theoretical behaviour and their global analysis involves consideration of the deviations. In particular, the deviations include the occurrence of bending in the members, in addition to the axial forces. These bending moments, known as “secondary moments”, can cause significant additional stresses in the members which make up the truss.

The deviations in design take various forms:

All the members which make up the structure are not usually articulated at their original node and their end node. Truss chords, in particular, are usually fabricated in one length only, over several truss purlins: the continuous chord members are then connected rigidly to their original and end nodes. Rotation of the nodes, resulting from general deformation of the truss beam then causes bending moments in the rigidly connected members; the more rigid the chord members, the bigger the moments (see Section 3.4).

The members are not always strictly aligned on their original and end nodes. Bending moments which result from a misalignment of axes increase in proportion to the size of the eccentricity and the stiffness of the members. This phenomenon is illustrated in Section 3.6.

Loads are not always strictly applied to the nodes and, if care is not taken to introduce secondary members to triangulate the point of application of the loads between nodes, this results in bending moments.

3.2 Modelling Several questions arise in respect of the modelling of a truss.

It is always convenient to work on restricted models. For example, for a standard building, it is common and usually justified to work with 2D models (portal, wind girder, vertical bracing) rather than a unique and global 3D model. A truss can even be modelled without its supporting columns when it is articulated to the columns.

Nonetheless, it is important to note that:

If separate models are used, it may be necessary, in order to verify the resistance of certain elements, to combine the results of several analyses; example: the upper chord of a truss also serves as chord of the wind girder.

If a global 3D model is used, “parasitic” bending can be observed, which often only creates an illusory precision of the structural behaviour process. That is why 2D models are generally preferable.

In the worked example, where the truss is simply supported on the columns, the design model chosen is that of the truss only.


5 - 16

Once the scope of the model has been decided and adapted according to use to be made of the results, it is important to consider the nature of the internal connections. In current modelling of member structures, the selection is made between “a pin-jointed member at a node” and a “member rigidly connected to a node”; the possibility offered by EN 1993 to model connections as semi-rigid is rarely used for truss structures.

For trusses, the model is commonly represented as either:

Continuous chords (and therefore chord members rigidly connected at both ends)

Truss members (diagonals and verticals) pin jointed to the chords.

3.3 Modelling the worked example In the worked example, the truss diagonals are pin jointed to the chords, although the connections are carried out using high strength bolts suitable for preloading with controlled tightening. This provides a rigid connection without slack between the diagonal and the connection gusset plates. The connection can be considered as pinned due to the fact that the vertical gusset plates are welded in the middle of the horizontal, not very stiff, IPE 330 web.

The modelling is shown in Figure 3.1, with the numbering of the members.

Left part

Right part

Figure 3.1 Computer model

It is important for the model to be representative of the eccentricities which exist in the real structure. They can have a significant effect, as illustrated in Section 3.6.1.

It is also important that modelling of the loads is representative of the real situation. In particular, the fact of applying to the truss nodes loads which, in reality, are applied between nodes, risks leading to neglect of the bending with quite significant outcomes.

The main results of the analysis are given in Figure 3.2 for the left part of the truss.


5 - 17

ULS Load combination n°1 (Gravity loading) – Axial force (N) in kN

ULS Load combination n°1 (Gravity loading) – Bending moment (M) in kNm

ULS Load combination n°2 (Uplift loading) – Axial force (N) in kN

ULS Load combination n°2 (Uplift loading) – Bending moment (M) in kNm Figure 3.2 Worked example – Axial forces and bending moments

It is interesting to note the form of the moment diagrams in the member:

In the chords and the diagonals, the self weight generates a bending moment with a parabolic shape

In the chords, continuous modelling (members rigidly connected at both ends) leads to moments at the nodes.


5 - 18

3.4 Simplified global analysis of the worked example A triangulated beam, with a constant depth, can be equated to an I-beam. This equivalence is possible and provides a good approximation, for example, for a truss with parallel chords.

The global shear force Vglobal and the global bending moment Mglobal in the equivalent beam vary very little along a panel and can be equated with the mean values in the panel. Therefore the axial load can be assessed using the following expressions (see Figure 3.3 for the notations):

Nch = ±Mglobal/h in the chords

Nd = ±Vglobal/cos θ in a diagonal

h θ

Figure 3.3 Truss with parallel chords - Notation

An estimate can also be made for the deflection of the truss beam by calculating that for an equivalent beam, for the same loading. In order to do this, the classic approach is to use elementary beam theory, giving the equivalent beam a second moment of area equal to:

22

1ch, i

iidAI

where:

Ach,i is the section area of the chord i

di is the distance from the centroid of both chords to the centroid of the chord i.

In order to take into account global shear deformations, not dealt with in elementary formulae, a reduced modulus of elasticity is used. Global shear deformations are not, in fact, negligible in the case of trusses, since they result from a variation in length of the diagonals and posts. The value of the reduced modulus of elasticity clearly varies depending on the geometry of the truss, the section of the members, etc. For a truss beam with “well proportioned” parallel chords, the reduced modulus of elasticity is about 160000 N/mm2 (instead of 210000 N/mm2).


5 - 19

4000

101 kN 158 202 202 202 158 101

7100 7200 8500 8600 7100 7100

Truss (combination n°1), including self-weight

461 (616)

303 (405)

101 (135)

-101 (-135)

-303 (-405)

-461 (-616)

562

-562

Diagram of the global shear force V (kN) In parentheses: values of Nd = V/cos

3273 (818)

5455(1364) 6320

(1580)

5455(1364)

3273 (818)

Diagram of the global bending moment M (kNm) In parentheses: values of Nch = M/h

Figure 3.4 Worked example – Approximate calculation

The values of the axial forces in the chords obtained by the simplified approach, Mglobal/h, are shown in Figure 3.4. The values are very close to the values obtained using structural analysis software (see Figure 3.2), for the sections close to the applied loads. The small difference comes from the slope (3%) of the chords of the truss in the worked example, not taken into account in the hand calculation.

The values of the axial forces in the diagonals obtained by the simplified approach, Vglobal/cos θ, are also very close to the values obtained using software.

3.5 Secondary forces 3.5.1 Influence of chord rigidity

Chord members in trusses which are used in construction are rarely pinned at the nodes and are more often rigidly connected; this means that members connected to the same node have to keep their respective angles. During deformation of the structure under load, the ends of the members all rotate at the same angle around the node. In these conditions, bending loads (bending moments and shear forces) called secondary forces are added to the axial loads in the members calculated assuming the nodes are pinned (primary forces).


5 - 20

It is routine in design to use continuous chord members and to pin the truss members.

In fact, transforming pinned connections into rigid nodes hardly leads to any modification to the axial forces in the members, because the shear transmitted by the members has little influence on the equilibrium equation of nodal forces and, on the other hand, bending of the member due to secondary bending moments only causes a slight variation in the distance between the ends of this member compared to the difference in length due to axial force.

Nevertheless, it is essential that the triangulated structures be designed properly so that the members are adequately arranged to withstand bending stresses, but not too slender so as to avoid buckling. Note that the greater the stiffness of the chords (which are usually continuous), compared to the global stiffness of the truss beam, the bigger the moments developed in the chords. For instance, for a wind girder in a roof, the stiffness of the chords is relatively small and the secondary moments remain small as well.

For a stocky truss, i.e. when the flexural stiffness of the individual chords is not significantly lower than the global stiffness of the truss, it can be necessary to take into account the secondary moments. Then the members and the connections must be designed accordingly.

This phenomenon can be illustrated in the worked example by arranging the IPE 330 sections as ‘standing up’ chord members, instead of being flat in the initial design (Figure 3.5). The chords therefore bend in the vertical plane of the truss member, mobilising their strong inertia. The calculation results demonstrate well a significant increase in the secondary moments.

Figure 3.5 Options for the orientation of the chords

In the upper chord in a standing up IPE 300 section near the half-span, the bending moment under gravity loads (ULS) is 28,5 kNm, compared to 2,7 kNm for the flat IPE 330 section.

Similarly, in the lower chord, the bending moment is 23,4 kNm, compared to 1,7 kNm.

The multiplier of the bending moments is 11 for the upper chord, and 14 for the lower chord. This is comparable with the ratio of the inertia in an IPE 330 section (about 15).

3.5.2 Assumption of rigid connections

In another evaluation of the effect of member stiffness on the value of the secondary moments, the truss in the example was recalculated by making all


5 - 21

the internal connections rigid (diagonal and verticals fixed on their original end nodes). The comparison is summarized in Table 3.1, where it can be seen that the end moments are in the same range as the moments resulting from the self-weight of the diagonals.

Table 3.1 Effect of rigid connection instead of pinned

Horizontal web Vertical web

End moment in a diagonal in tension (Double angles 120 x12)

1,03 1,17

End moment in a diagonal in compression (Double angles 150 15)

1,30 2,35

Moment resulting from the self-weight (for comparison) 1,36 1,36

Assumption of bi-hinged diagonals Acceptable Acceptable

Note: the bending moments are given in kNm.

3.6 Effect of clearance of deflection When the connections between elements which make up a truss beam are bolted connections, with bolts in shear (category A in EN 1993-1-8[2]), the clearance introduced into these connections can have a significant effect on displacement of the nodes.

In order to facilitate erection, the bolts are in fact inserted in holes which are larger than the bolts themselves. For standard bolt sizes, holes more than 2 mm bigger than the bolt are usually made (usually referred to as a 2mm clearance).

In order for a connection with clearance to transmit to the node the load required by the attached member, the bolt must come into contact with one or other of the connected parts: this is called often referred to as ‘taking up slack’. For a connected tension member, this slack can be assimilated as an additional extension that is added to the elastic elongation of the member in tension. Likewise, for a connected compression member, the slack is assimilated as a reduction in length that is added to the elastic shortening of the compressed member.

The total slack in the many different connections of a truss structure can lead to a significant increase in displacements, which can have various and more or less serious consequences. Amongst these, note:

In most of the cases, the visual effect is the worst consequence.

Increased deflection can lead to a reduction of free height under the bottom chord, which might prevent or upset the anticipated usage. For example, the additional deflection of a truss holding doors suspended in a gable of an aeroplane hangar could prevent the passage of the aeroplane.

Increase in the deflection can result in reduction in the slope of the supported roof and even, if the nominal slope were small, to a slope inversion; a risk of water accumulation is therefore associated with an inversion in pitch.

If the truss structure is not a statically determinate system, this may lead to unexpected internal forces.


5 - 22

It is therefore essential, where truss structures are concerned, to control the effect of connection slack on the displacements. In order to do this, it is often necessary:

either to limit slack in category A connections: drilling at +1 mm, even +0,5 mm and using shear bolts on a smooth bolt shank (to limit the increase in slack by deformation) of the threads and pieces; or

to use ‘fit bolts’; or

to use preloaded bolts (category C connections); or

to use welded connections instead of bolted connections.

In cases where loading in the members does not result in reversal of axial force, it is possible to calculate a value for the effect of slack in all the connections. The following calculation illustrates this phenomenon for the worked example.

Each of the chords, upper and lower, has a continuous connection with bolted splice plates around the mid-span. In addition, the diagonals are connected by bolting on gusset plates welded to the chords. Holes are 2 mm larger than the bolt diameter.

Figure 3.6 Worked example – Position of the chord connections using splice

plates

In a spliced connection of a chord, the effect of slack on the deflection can be evaluated by assuming that the bolts are initially centred on their holes. If the diameter of the holes is d + 2 mm (where d is the bolt diameter), a chord in tension is extended by 4 mm, as shown in Figure 3.7.

1 mm 1 mm d 1 mm 1 mm d

g

g + 4 mm

Figure 3.7 The effect of slack under load

In order for a diagonal to be loaded, 2 mm has to be recovered at each end: the length of a diagonal in tension is increased by 4 mm; a diagonal under compression is reduced by a further 4 mm.


5 - 23

The deflection of a truss due to the slack can be evaluated by considering the effect of a unit load applied at mid span, using the Bertrand Fontviolant equation.

-0,5 0,66 -0,68 0,66 -0,68 0,71 -0,75 0,17 -0,75 0,72 -0,68 0,66 -0,68 0,66 -0,5

2,85

Figure 3.8 Worked example – Axial forces (N1,i) under unit load

The deflection is given by:

bi

i i

iii ES

lFNv

11,

Where:

N1,i is the axial force produced in the member i by a unit force applied at the point where the deflection is required

il is the length of member i

iS is the section area of the member i

b is the number of members with bolted connection(s).

i

ii

ES

lF is the variation in length of member i due to the slack recovery

= ±4 mm according to whether the chord is in compression or tension.

Then:

v = 4 × (2,31 + 2,85 + 0,5 + 0,66 + 0,68 + 0,66 + 0,68 + 0,71 + 0,75 +…

+ 0,17 + 0,75 + 0,72 + 0,68 + 0,66 + 0,68 + 0,66 + 0,5)

v = 58,4 mm

This is a significant additional deflection, compared with the deflection due to the ULS combination (127 mm).

3.7 Modification of a truss for the passage of equipment It frequently occurs that it is necessary to modify the form of a truss in order to allow equipment to pass (a large section duct for example).

Several solutions can be provided (Figure 3.9):

Either to increase the passage area available by an eccentricity in the connection of one of the chords (case 1)

Or “break” the straight form of a diagonal, by triangulating the breakage point (case 2).


5 - 24

Case 1 Case 2

Figure 3.9 Passage of a duct – Local modification of the truss

In case 1, the secondary moments which result from the introduction of an eccentricity increase in relation to the size of the eccentricity. If there is a choice, it is always preferable to introduce an eccentricity in the least stressed chords.

In case 2, care must be taken with several phenomena:

The axial force can increase significantly in certain chords situated in the immediate proximity of the modified panel (as a result of modification to the position of the members).

“Secondary” moments appear as a result of the lack of stiffness in a broken diagonal compared with a straight diagonal, even if the breakage point is triangulated.

The breakage point must of course be triangulated in the plane of the truss; it must also be restrained out-of-plane (where three members meet) if the broken diagonal is in compression.

These two phenomena (case 1 and case 2) are illustrated using the worked example.

3.7.1 Introduction of an eccentricity axis in a diagonal (case 1)

The truss panel through which the passage of equipment is required is the second panel from the support on the right. Figure 3.10 shows a part of the truss, with the eccentricity of a diagonal.

300 mm

Figure 3.10 Passage of a duct – Eccentricity of a diagonal

Changes in axial forces in the modified area are represented on the Figure 3.11.


5 - 25

Axial force (kN)

Bending moment (kNm)

Initial structure

Modified structure

Figure 3.11 Effects of the eccentricity of diagonal under ULS gravity loading

The 300 mm eccentricity makes the triangulation imperfect.

The main consequence of this arrangement is a significant increase in the bending moments in the lower chord that receives the eccentric diagonal. A 74,15 kNm moment is calculated in the second chord member from the right hand support, a 62,72 kNm moment in the first chord member, much higher than in the initial structure without eccentricity.

The elastic moment resistance of an IPE 330 horizontal section is:

69,2 0,355 = 24,57 kNm

The bending capacity is therefore greatly exceeded, apart from any other interactions. Reinforcement of the lower chord member will therefore be required in order to support the axis eccentricity introduced.

3.7.2 “Broken” diagonal (example 2)

The panel of the penetration equipment is the same as in 3.6.1. Figure 3.12 is a diagram of the diagonal “breakage”.


5 - 26

Figure 3.12 Passage of a duct – Broken diagonal

Development of stress in the modified area is represented on the section diagrams in Figure 3.13.

Axial force (kN)


Initial structure

Axial force (kN)


Modified structure Figure 3.13 Effects of a broken diagonal under ULS gravity loading

The effects of modification on the calculated stresses are mainly:

A noticeable increase is observed in the axial force in the second lower chord member from the right hand support (in the panel with the broken diagonal): the tension calculated increases from 818 to 1350 kN.

A significant increase is also observed in the compression force in the broken diagonal compared with the rectilinear diagonal of the initial structure: compression increases from 624 to 1090 kN.

As far as the additional triangulation member is concerned, this supports a normal compression force of 755 kN.

In the lower chord, as well as an increase in the normal tension force, an increase in “secondary” moments is also observed on the three right panels


5 - 27

The modification to the structure (broken diagonal) therefore has a significant effect on the size of the members.


5 - 28

4 VERIFICATION OF MEMBERS

As seen in the preceding section, which dealt with the global analysis, the members are mainly subjected to axial forces.

It was also observed that, in many cases, members are also subject to stress by bending moments, i.e. secondary moments.

4.1 Verification of members under compression The resistance of a member to compression is evaluated by taking into account the different modes of instability:

Local buckling of the section is controlled using section classification, and when necessary, effective section properties (class 4)

Buckling of the member is controlled by applying a reduction coefficient in the calculation of resistance.

For a compression member, several buckling modes must be considered. In most truss members, only flexural buckling of the compressed members in the plane of the truss structure and out of the plane of the truss structure need be evaluated.

For each buckling mode, the buckling resistance is obtained from EN 1993-1-1[3] by applying a reduction to the resistance of the cross-section. This reduction factor is obtained from the slenderness of the member, which depends on the elastic critical force.

For the diagonals and the verticals stressed in uniform compression. the elastic critical force is determined from the buckling length of the member in accordance with EN 1993-1-1, 6.3.1.3. The following can be observed, according to Annex BB §BB.1 of EN 1993-1-1:

For buckling in the plane of the truss beam: the buckling length is taken equal to 90% of the system length (distance between nodes), when the truss member is connected at each end with at least two bolts, or by welding (EN 1993-1-1 §BB.1.1(4)).

(An exception is made by Annex BB for angle truss members, for which a different evaluation is given; it is not specified in this annex if the particular rule also concerns members made up to two pairs of angles: by way of simplification, it is recommended that a buckling length of 0,9 times the length of the axis be retained.)

For buckling out of plane of the truss beam, the buckling length is taken equal to the system length.

For buckling in the plane of the truss of the chord members in uniform compression, the buckling length may be taken as 90% of its system length (distance between nodes).


5 - 29

For buckling out of plane of the truss, it can be more difficult to determine the elastic critical force for the following reasons:

There is not necessarily a lateral support at each node of the truss

The lateral support points are not necessarily effectively rigid.

When there is no lateral support at each node along the chord, the segment located between support points is subject to variable compression between bays. In these circumstances:

A conservative approach would be to use the normal compression force at its maximum value and to take the buckling length as the distance between supports but this can lead to an under-estimate of the chord resistance.

Refined methods can be adopted by investigating an equivalent buckling length under constant compression.

In the worked example, where the truss supports a roof, with purlins at the level of the upper chord of the truss:

All the purlins connected to a roof bracing can be considered as lateral rigid support points.

Intermediate purlins can also be considered as a rigid point of support. Insofar as a diaphragm role has been attributed to the roof (class 2 construction according to EN 1993-1-3).

With regard to the lower chord, these lateral support points are provided by additional vertical bracing elements between trusses (see the braces under the truss purlins in Figure 2.2).

Another point to note, which is very common, concerning determination of the compression resistance, is the case of pairs of members. It is quite common, as was stated, to make up members from a truss structure using two angles, or two channels (UPE).

In order to ensure that such built-up members will behave as sole members in the flexural buckling mode, the two components are connected by small battens (Figure 4.1). Since the role of these members is to prevent relative slip of one component compared with the other, they must be connected without slack. The gap between the angles, and the thickness of the battens, should be the same as the thickness of the gusset to which the built-up member is connected.


5 - 30

1 1

2

A

A

A-A

1 Batten 2 Gusset

Figure 4.1 Members composed of two angles

The maximum spacing of the connections between members is limited by EN 1993-1-1 to 15 times the minimum radius of gyration of the isolated component. Otherwise a more complex verification needs to be carried out, by taking into account the shear stiffness of the composed member. This limitation is very restrictive. By way of example, in order to link two 50 × 50 × 5 angles by respecting the spacing limit, it would be necessary to provide a batten every 15 cm.

In order to illustrate the different principles stated above, justifying calculations are developed in the following sections for the different types of compressed members in the worked example truss structure. The results are taken from the basic worked example:

IPE 330 chords with horizontal web

Web members are assumed to be hinged at both ends

Chords are assumed to be continuous.

4.1.1 Upper chord in compression

The verifications set out below, concern the upper chord member adjacent to mid span (element B107 in Figure 3.1), in which the normal compression force calculated under gravity ULS loads is greatest and equal to:

NEd = −1477 kN

The checks take into account the coincident bending moments.

Note that the verification should also be carried out on the first member from the mid span, which is not restrained by the secondary truss: axial force of lesser compression, but with increased buckling length in the plane of the truss. Since the calculation is identical, it is not set out formally below. If this verification indicated a lack of resistance, the reinforcement solution would of course consist of extending the installation of the secondary truss.

The shear force and the bending moments are given in Figure 4.2.


5 - 31

2,86 kNm

-1,05 kNm

2,151

Bending moment MEd

-1,82 kN

Shear force VEd

Figure 4.2 Bending moment and shear force in the upper chord

Cross-section properties

For an IPE 330 with horizontal web (steel grade S355)

A = 62,6 cm2

Iy = 11770 cm4

Iz = 788 cm4

Wel,z = 98,5 cm3

Class of the cross-section

The material parameter is:

= 0,81

As simplification, the cross-section can be classified in uniform compression, even if it is subjected to combined axial force and bending moment.

The compressed flanges are classified as outstand flanges (EN 1993-1-1 Table 5.2, Sheet 2):

29,791,55,11

25,58

t

c

The flange is Class 1.

The web is classified as an internal compressed part (EN 1993-1-1 Table 5.2, Sheet 1):

02,34421,365,7

271

t

c

The web is Class 4.

Effective properties of the cross-section

The effective area Aeff is calculated for pure compression.

The flanges are Class 1, so fully effective.


5 - 32

The effective width of the web is evaluated according to EN 1993-1-5 (Table 4.1):

41 k

673,0782,0481,04,28

5,7271

4,28 σp

ktb

mm5,1245,0

mm249271919,0919,0)3(055,0

673,0782,0481,04,28

5,7

271

4,2841

eff2e1e

eff2p

p

σ

pσ

bbb

b

kt

b

k

beff = 0,919 × 271 = 249 mm

be1 = be2 = 0,5 beff = 124,5 mm

The effective area of the section is:

Aeff = 6260 – (271 – 249) × 7,5 = 6095 mm2

The effective elastic modulus about the weak axis (Weff,z) is calculated for pure bending.

In simple bending in the plane of the truss, about the weak axis, the flanges are inevitably Class 1, whilst the web is not stressed. Then the section is fully effective:

Weff,z = Wel,z = 98,5 cm3

Resistance of cross-section

In compression (EN 1993-1-1 §6.2.4):

0,1

355,06095

M0

yeffRdc,

fA

N = 2164 kN

1683,02164

1477

Rdc,

Ed N

N OK

In bending in the plane of the truss (EN 1993-1-1 §6.2.5):

kNm 97,340,1

355,05,98

M0

yzeff,Rdz,

fW

M

1082,097,34

86,2

Rdz,

Ed M

M OK

In shear (EN 1993-1-1 §6.2.6):

Av,y = 2×160×11,5 = 3680 mm2


5 - 33

kN7540,1

3

355,03680

3

M0

yyv,

Rdpl,

fA

V

1002,0754

82,1

Rdpl,

Ed V

V OK

Since VEd/Vpl,Rd is less than 0,5, there is no influence of the shear force on the resistance of the cross-section under bending moment and axial force.

M-N interaction (EN 1993-1-1 §6.2.93):

The M-N interaction is taken into account using the following criterion:

0,683 + 0,082 = 0,765 < 1 OK

Buckling resistance of member

Buckling resistance in the plane of the truss, i.e. about the weak axis of the cross-section (EN 1993-1-1 § 6.3.1)

The buckling length of the upper chord member is equal to 90% of the system length (EN 1993-1-1 §B.B.1.1):

Lcr,z = 0,9 × 2151 = 1936 mm

The elastic critical force is:

kN43576,193

78821000ππ2

2

2z

z2

zcr,

l

EIN

The slenderness is given by:

705,04357

355,06095

,

eff

zcr

yz

N

fA

The buckling curve to use is curve b (EN 1993-1-1 Table 6.2), and the imperfection factor is:

= 0,34

8344,0))2,0(1(5,0 2zz zΦ

781,0705,08344,08344,0

11222

z2

zz

ΦΦ

z

The design buckling resistance is then:

kN16900,1

355,06095781,0

M1

yeffzRdz,b,

fA

N

NEd / Nb,z,Rd = 1477/1690 = 0,874 OK


5 - 34

Buckling resistance out of the plane of the truss, i.e. about the strong axis of the cross-section (EN 1993-1-1 § 6.3.1)

The lateral supports of the upper chord are composed of truss purlins at 8504 mm intervals.

The normal compression force is almost constant between lateral supports (see 3.2).

There is therefore no need to use a method which allows for non-uniform force.


kN33734,850

1177021000ππ2

2

2y

y2

ycr,

l

EIN

The slenderness is given as:

8009,03373

355,06095

ycr,

yeffy

N

fA

The buckling curve is curve a (EN 1993-1-1 Table 6.2), and the imperfection factor is:

= 0,21

8838,0))2,0(1(5,0 2yy yΦ

7952,08009,08838,08838,0

11222

y2

yy

y

And so the compression resistance is therefore:

kN17200,1

355,060957952,0

M1

yeffyRdy,b,

fA

N

NEd / Nb,y,Rd = 1477/1720 = 0,859 OK

M-N interaction (EN 1993-1-1 §6.3.3):

There is no effect of lateral torsional buckling to consider for a member in bending about its weak axis (no bending about the strong axis). The criteria are:

1// M1yzeff,

Edz,yz

M1yeffy

Ed fW

Mk

fA

N (Eq. 6.61 in EN 1993-1-1)

1// M1yzeff,

Edz,zz

M1yeffz

Ed fW

Mk

fA

N (Eq. 6.62 in EN 1993-1-1)

Using resistances already calculated, these criteria can also be written as:


5 - 35

1Rdz,

Edz,yz

Rdy,b,

Ed M

Mk

N

N

1Rdz,

Edz,zz

Rdz,b,

Ed M

Mk

N

N

The interaction factors kyz and kzz are calculated according to Annex A of EN 1993-1-1, for a Class 4 section:

zcr,

Ed

ymzyz

1N

NCk

where:

zcr,

Edmz )33,0(36,021,079,0

N

NC

367,086,2

05,1

Cmz = 0,628

8624,0

3373

14777952,01

3373

14771

1

1

ycr,

Ed

ycr,

Ed

y

N

N

N

N

y

819,0

43571477

1

8624,0628,0yz

k

First interaction criterion (eq. 6.61)

1926,097,34

86,2819,0

1720

1477 OK

zcr,

Ed

zmzzz

1N

NCk

where:

Cmz = 0,628

899,0

43571477

781,01

43571477

1

1

1

zcr,

Ed

zcr,

Ed

NN

NN

z

z


5 - 36

Then, the factor kzz can be calculated:

854,0

4357

14771

899,0628,0

zzk

Second interaction criterion (eq. 6.62)

1944,097,34

86,2854,0

1690

1477 OK

Note on secondary trusses

The presence of secondary trusses in the central part of the truss (see diagram 2.3) permitted the reduction by half of the buckling length of the upper chord in the plane of the truss.

The secondary truss is sized in order to support a buckling restraint load whose value depends on the compression force in the supported chord and on its slenderness ratio (see EN 1993-3-1 on subject of design of pylons in annex H4).

4.1.2 Lower chord in compression

With respect to the complete design of the structure, it is also of course essential to check the lower chord, subject to the lower compression force, but without support from a secondary truss.

Verification of the lower chord in compression is similar to that described for the upper chord in compression, in 4.1.1.

Lateral restraint of the lower chord is provided at each purlin (Figure 2.2).

The only specific point which would be interesting to develop is an analysis of the buckling out of plane of the truss.

Buckling of the lower chord is to be considered similarly to that of the upper chord, for a length equal to the distance between truss panels, thanks to the presence of sub-panel braces (See Figure 2.3).

The difference is that the axial force in the lower chord varies along the buckling length, in two panels, whereas the force was constant along the buckling length for the upper chord.

It should also be noted here that, for the chord member with the greatest bending moment, the variation in axial force is very small; in a real design, the small reduction in buckling length due to variation of normal axial force can safely be ignored.


5 - 37

545 kN 470 kN

Axial force NEd Figure 4.3 Axial force in the lower chord

4.1.3 Diagonal in compression

The diagonal, whose resistance is calculated here, by way of example, is the second diagonal from the right support (element B40 in Figure 3.1), under ULS gravity loading.

The compression force is:

NEd = −624,4 kN

Initially, as in common practice, the bending moment due to the self weight of the member is ignored.

The effect of this moment will be evaluated later.

Cross-section properties of a single angle

For a 150 × 150 × 15 L

A = 43 cm2

zG = yG = 4,25 cm

Iy = Iz = 898,1 cm4

Iv = 369 cm4

For a pair of angles

Section area:

A = 2 × 43 = 86 cm2

Second moment of area out of plane of the truss (the section is assumed to be homogeneous), assuming the gap between the angles is 10 mm:

Iy = 2 × 898,1 + 2 × 43 × (4,25+1,0/2)2 = 3737 cm4.

Second moment of area in the plane of the truss:

Iz = 2 × 898,1 = 1796 cm4

Class of section in uniform compression

Material parameter for fy = 355 N/mm2: = 0,81

For an angle (EN 1993-1-1 Table 5.2 (Sheet 3)):

31,95,11 10152

1502

2

15,1215 1015

150

t

bht

h


5 - 38

The section is a Class 4 and it is therefore not fully effective in uniform compression. The effective area of the cross-section should be calculated with reference to EN 1993-1-5. Such a calculation leads to a fully effective area:

Aeff = A = 86 cm2

Resistance of the cross-section

The resistance of the section in uniform compression is therefore given by:

kN30530,1

355,08600

M0

yRdc,

Af

N

Buckling resistance of member

Buckling resistance in the plane of the truss

The buckling length is equal to:

0,9 × 5,464 = 4,918 m


kN15398,491

179621000ππ2

2

2y

z2

zcr,

l

EIN


408,11539

355,08600

zcr,

yz

N

Af

The buckling curve is curve b (EN 1993-1-1 Table 6.2), and the imperfection factor is:

34,0

697,1))2,0(1(5,0 2zz zΦ

378,0408,1697,1697,1

112222

zzz

z

And the buckling resistance is then:

kN11540,1

355,08600378,0

M1

yzRdz,b,

Af

N

Buckling resistance out of plane of the truss

The buckling length is equal to the system length: Lcr,y = 5,464m.

The critical axial force is:

kN25945,546

373721000ππ2

2

2y

y2

ycr,

l

EIN


5 - 39


085,12594

355,08600

,

x

N

Af

ycr

yy

The buckling curve to use is curve b (see EN 1993-1-1, table 6.2), and the imperfection factor is:

34,0

239,1))2,0(1(5,0 2zyy Φ

544,0085,1239,1239,1

112222

yyy

y

The design buckling resistance is:

kNAf

NM

yyRdyb 1661

0,1

355,08600544,0

1,,

The buckling resistance in the plane of the truss is less and the verification is:

0,1541,01154

4,624

Rdb,

Ed N

N OK

The resistance of the diagonal is adequate; its section could be optimised.

Connection battens

The diagonal is composed of two angles linked by battens. The calculation of the resistance previously undertaken assumed the section is homogenous (for the buckling out of plane of the truss).

In order to support this hypothesis, EN 1993-1-1 requires the placing of connection bars spread out at no more than 15 times the minimum radius of gyration of the isolated angle;, for an angle 150 × 150 × 15 that is a distance of 15 × 29,3 = 440 mm.

In view of the resistance reserves, it is recommended that the connection bars be spaced further apart (the costs of fabrication and installation are not negligible). Instead of the 12 connection battens per diagonal which the above condition lead to, consider only 3 bars be placed, 1366 mm apart.

L 150x150x15

Plate 150x150x10 and 2 pre-tensioned bolts with controlled tightening

Figure 4.4 Connection batten

In order for the battens to be effective, they must be arranged as illustrated here. This results in a buckling length about the principal axis equal to 0,7 × 1366 = 956 mm.


5 - 40

For this type of buckling the elastic critical force is:

kN836810956

10369210000ππ 32

42

2v

v2

vcr,

l

EIN

The slenderness for a single angle is:

427,08368000

3554300

,

vcr

yv

N

Af

The buckling curve to use is curve b and the imperfection factor is: = 0,34

630,0))2,0(34,01(5,0 2 vvvΦ

915,0427,0630,0630,0

11222

v2

vv

v

ΦΦ

Conservatively, the resistance to the compression may be evaluated calculating the reduction factor as the product of that for the whole member and that for an individual angle between battens:

= Min(y ; z) × v = 0,378 × 0,915 = 0,346

The design buckling resistance of the diagonal is:

kN 1056100,1

3558600346,0 3

M1

yRdb,

Af

N

0,1591,01056

4,624

Rdb,

Ed N

N

The compression resistance is adequate.

Local verification of the section to the right of the gusset plate connection

This verification carried out in Appendix B

Effect of bending moment due to self weight of the diagonal

The bending moment is:

My,Ed = 2,20 kNm (see 3.2 above).

The elastic modulus of the cross-section for bending in the plane of the truss is: Wel,z = 167 cm3.

Interaction criteria are given in EN 1993-1-1 §6.3.3:

1// M1yzel,

Edz,yz

M1yy

Ed fW

Mk

Af

N

1// 1,

,

1

Myzel

Edzzz

Myz

Ed

fW

Mk

fA

N


5 - 41

where:

The kyz factor is:

zcr,

Ed

ymzyz

1NN

Ck

863,0

25944,624

544,0915,01

25944,624

1

1

1

ycr,

Edyv

ycr,

Ed

y

N

N

NN

012,11539

4,62403,0103,01

zcr,

Edmz

N

NC

47,1

15394,624

1

863,0012,1yz

k

The kzz factor is:

zcr,

Ed

zmz

1N

NCkzz

691,0

15394,624

378,0915,01

15394,624

1

1

1

zcr,

Edzv

zcr,

Ed

z

N

N

N

N

18,1

15394,624

1

691,0012,1zz

k

From which:

1465,00,1/355167000

1020,247,1

0,1/3558600544,0915,0

624400 6

1635,00,1/355167000

1020,218,1

0,1/3558600378,0915,0

624400 6

When the bending moment due to self weight of the diagonal is taken into account, the resistance criterion increases from 0,591 to 0,635: that is an increase of 7%.

4.2 Verification of members in tension A particular feature when checking the resistance of tension members is the existence of criteria which bring into play the net section of the member. This is explored for the worked example.


5 - 42

4.2.1 Lower chord in tension (flat IPE 330)

The lower chord in tension is verified for calculated forces near the mid-span. Given the results shown in 3.2 above:

NEd = 1582 kN

MEd = 1,69 kNm

The tension resistance of the section is determined by two conditions, one in a “gross” section and the other in a “net” section :

Gross section

A = 6260 mm2

kN22220,1

355,06260

M0

yRdpl,

xAfN

Net section

2net mm4661)5,7223()5,11244(6260 A

kN171125,1

51,046619,09,0

M0

unetRdu,

fA

N

Tension resistance is given by:

kN1711),min( Rdu,Rdpl,Rdt, NNN

In simple bending, in the truss plane (EN 1993-1-1 (6.2.5)), class 1 of the section allows the plastic modulus to be mobilised:

32

pl cm2,1474

1615,12

W

kNm3,520,1

355,02,147

M0

yplRdpl,

fW

M

The verification is:

03,03,52

69,1

93,01711

1582

Rd

Ed

Rdt,

Ed

M

M

N

N

N-M Interaction: 0,93 + 0,03 = 0,96 < 1

4.2.2 Diagonal in tension (double angles L120 120 12)

Checking is done for the diagonal at the left hand support, under gravity loads. Given the results shown in 3.2 above:

NEd = 616,3 kN


5 - 43

MEd = 1,36 kNm

Tension resistance

The tension resistance of the section is determined by two conditions, on in gross section and the other in net section:

Gross section

kN19560,1

355,05510

M0

yRdpl,

xAfN

Net section (See arrangements described in Annex 2)

2net mm4886)12262(5510 A

For angles connected by a single leg, EN 1993-1-8 gives an additional requirement for the effect of eccentricity of the tension force in the angle (distance between the neutral axis and the gauge marking) on the forces (appearance of secondary moments).

This method involves the application of an ultimate resistance reduction factor for the angle (EN 1993-1-8 Clause 3.10.3(2))

M2

unet3Rdu, γ

fAβN

The reduction factor β3 depends on the distance between axes p1.

For, p1= 2,5 d0 = 65 mm: 3 = 0,5 (EN 1993-1-8 Table 3.8)

N.B.: The reduction factors β are only provided for a simple angle; the method is conservative for a “double angle”. It is recommended that, within the connection, the behaviour of the two simple diagonals is considered with respect to these local phenomena.

kN99725,1

51,048865,05,0

M0

unetRdu,

fA

N

Then:

kN997),min( Rdu,Rdpl,Rdt, NNN

Bending resistance

In simple bending in the truss plane (EN 1993-1-1 (6.2.5)):

3el cm46,85W

kNm3,300,1

355,046,85

M0

yelRdel,

fW

M

Verification:


5 - 44

05,03,30

36,1

162,0997

3,616

Rd

Ed

Rdt,

Ed

M

M

N

N

And the M-N interaction criterion is: 0,62 + 0,05 = 0,67 < 1


5 - 45

5 VERIFICATION OF CONNECTIONS

5.1 Characteristics of the truss post connection 5.1.1 General

It is essential to connect the truss and post according to the assumptions in the modelling.

In particular, the choice between a fixed connection and a pinned connection must be respected. The difference between these two types of connection is that the pinned connection allows a rotation independent deflection of the truss and the post. The outcome in terms of loading is that the hinge does not transmit any bending moment from the truss to the post, whereas a fixed connection does.

The rotation at the support of a truss is manifested by a differential horizontal displacement between the original node of the upper chord and the original node of the lower chord.

In order to permit global rotation, it is therefore necessary to allow the horizontal displacement of the end of one of the chords in relation to the post: usually, the displacement of the chord which does not receive the diagonal on support is released.

A

Figure 5.1 Elongated hole on the bottom chord of the truss

With such an arrangement, the axial force is zero in the lower chord in the first panel. The lower chord of the first truss node could therefore be stopped short (A in the diagram); nevertheless it is preferable to lengthen the lower chord and to connect it to the post in order to provide lateral stability of the truss at the level of the lower chord.

An application of this type of hinge action in the worked example is given in 5.1.2 below.

By contrast, in order to carry out a rigid truss-column connection, it is necessary to make a connection without slack from each of the chords of the truss to the column.


5 - 46

5.1.2 Convergence of the axes at the truss-column connection

Another question to be asked when carrying out the connection of a truss on a post is that of convergence of the axes of the connected members and of its effect on the modelling. The choices are illustrated in Figure 5.2.

Convergence of the axes

column/chord/diagonal: solution to avoid

Axis convergence of the axes chord/diagonal at the internal

face of the column: recommended solution

1

1 : Rigid links

Figure 5.2 Rigid truss-column connection

In the first example, the actual physical connection and the model are not consistent: there is a risk of causing significant secondary moments in the diagonal and the chord. In the second example, the consistency is much greater; the eccentric moment is clearly supported by the post, which has a higher bending resistance than the chord or the diagonal, particularly when the truss is hinged at the post.

Note that this not the case in the worked example in which the posts have their web perpendicular to the plane of the truss: the convergence of the three axes happens then without causing secondary moments.

5.1.3 Worked example: detailing a pinned joint

The Figure 5.3 represents horizontal displacements of the lower and upper nodes of the two support sections, for cases of ULS gravity load combinations and for cases of ULS uplift load combinations. We can observe that, when the structure is symmetric or symmetrically loaded, each load case produces equal global rotations in the two support sections.


5 - 47

35,6 mm 8,6 mm

44,2 mm

(44,2 – 8,6 = 35,6 mm) Gravity loading

12,2 mm 3,1 mm

15,2 mm

(15,3 – 3,1 = 12,2 mm) Uplift loading

Figure 5.3 Rotations at truss supports

In order for the global rotations at the supports to be free (assumption for truss with pinned connections to the column), the elongated holes introduced into the column on lower chord connection must allow a 35,6 mm movement towards the outside and 12,2 mm towards the inside. It is of course prudent to allow for a certain safety margin on the sizing of the elongated holes (say 50 mm), and to check after erection that, under self weight, the freedom of movement remains adequate in both directions.

5.2 Chord continuity It is often necessary to deliver large span truss beams to site in several sections; it is therefore necessary to provide continuous chord joints between these sections. Generally, the preferred method is to make such connections on site by bolting rather than by welding.

The design of these bolted connections depends on the type of chord section to be connected. However, we can distinguish between two types of such connections:

Those in which the bolts are mainly loaded in tension : these use end plates

Those in which bolts are loaded perpendicular to their shank: these use splice plates.

When the chords are made of a single profile/section in I or H, either of the connections can be used.

When the chords are made of two double angle or channel sections, splice connections are generally used.


5 - 48

When the chords are made of hollow sections end plate connections are generally used (use of hollow sections is outside the scope of this guide).

Continuity using end plate connections

Continuity using splice plate connections

Figure 5.4 Chord continuity

The splice plate connection shown Figure 5.4 has double cover splice plates on the web and flanges (giving two interfaces for shear forces). If the force in the splice is low, single external spliced plates can be used, although double plates are normally used on the web, to preserve symmetry in the transmission of the axial force.

The resistance of the splice connections of truss chords must be verified under dominant load with secondary bending moment in the truss plane, according to EN 1993-1-8, by adapting the components method developed for beam-post connections. Software is freely available for this verification (see the SteelBizFrance.com website developed by CTICM). Verification of this type of connection, for the worked example, is given in Appendix A.

As well as verifying the resistance, it is essential to ensure the stiffness of the continuous chord connections. Generally, when the resistance of a beam-beam connection using end plates is selected, it can be considered as rigid.

Spliced plate connections are only effectively rigid when the slack is controlled (see Section 3.6 for evaluation example of the effect of slack in the bolted connections of the truss in the worked example). For splice connections, it is therefore recommended that one of the following options is selected:

Use preloaded bolts with controlled tightening, allowing transmission of loads by friction (non-slip)

Use fit bolts, preferably loaded on the shank in order to avoid slip under load by distortion of the thread of the connected pieces.

5.3 Connection of diagonals to chords Connection of diagonals and posts to chords can be made in different ways, according to the type of sections to be connected.

When the chords are made of double members (two angles or two UPE sections), common practice is to insert gusset plates between the two


5 - 49

component members of the chord. The gussets are, therefore, either welded or bolted on the chords. The diagonals and posts are connected to the gussets, usually by bolting.

When the chords are made of IPE or HEA/HEB sections, the most common connection method is also to use a welded gusset plate on the chord. The gusset plate is attached to the flange when the section is upright (vertical web), and to the web when the section is flat (horizontal web).

(a) Bolted gusset in the space between double angle chords, truss members in bolted double angles onto gusset

(b) Welded gusset on HEA chord flange, double angle truss members bolted to gusset

(c) Gusset welded to web of flat IPE chord

Figure 5.5 Truss connections on chord

When the chord sections are flat, it is also common to use IPE or HEA truss members with the same depth as the chords and to connect them by double gussets, one on each flange. An alternative solution is to design a welded connection without gussets, as shown in Figure 5.6.


5 - 50

1

2

1

2

1

3

4

5

1 Truss members

2 Chord

3 Fillet weld

4 Half-V fillet weld

5 K-fillet weld Figure 5.6 Welded connection between truss members and chord

When the chords are hollow sections (outside the scope of this guide), the connection using a gusset welded on the chord is also used. Direct welding of the diagonals and posts to the chords is also used; this requires profiling for connections to circular section chords.

In the gusset connections described above, verification of the resistance of the bolted or welded connection clearly defined in EN 1993-1-8. However, verification of the resistance of the gusset plate is not. Verification of a gusset plate connection for the worked example is given in Appendix B.

Special attention must be given to checking of the gussets, particularly those which have a large non stiffened part: many truss problems have been caused local buckling of the gusset plate. For example, in the connections in Figure 5.5(c), if the height of the flat chord web is insufficient for the angles making up the truss members to be connected near the web, the unstiffened part of the gusset and its stability must be examined carefully.

Although hollow section trusses are not the subject of the present guide, note that EN 1993-1-8 devotes a Section to the design of welded connections of hollow sections.

In the connections to the chords, slip must also be controlled (as indicated for continuous chords), in order to control displacements of the structural components, and, as a result, the distribution of forces if the structure is hyperstatic.


5 - 51

REFERENCES 1 Single-Storey Steel Buildings. Part 7: Fire engineering.

2 EN 1993-1-8:2005 Eurocode 3: Design of steel structures. Part 1.8 Design of joints.

3 EN 1993-1-1: 2005, Eurocode 3: Design of steel structures. Part 1.1 General rules and rules for buildings.


5 - 52


5 - 53

APPENDIX A Worked Example – Design of a continuous chord

connection using splice plate connections

5 - 54

Appendix A Worked Example: Design of a continuous chord connection using splice plate connections

1 of 24

Made by PM Date 02/2010

Calculation sheet Checked by IR Date 02/2010

1. Splice joint using bolted cover plates

This calculation sheet refers to the splice plate connection located on the Figure A.1. This connection has double spliced plates on the web and single external spliced plate on the flanges (see Figure A.2).

1

1 Splice plate connection studied Figure A.1 Location of the splice plate connections

2

3

2

3 1

3

1 Longitudinal axis 2 Lower chords to assembly (IPE 330) 3 Splice plate connection

Figure A.2 Chord continuity by splice plate connections

The resistance of this connection must be verified under tension axial force with secondary moment in the plane of the truss.

Four bolted cover plates must be verified (See Figure A.3)

It is also essential to ensure the stiffness of the continuous chord connection. A slip resistant connection is required.

Title APPENDIX A Worked Example: Design of a continuous chord

connection using splice plate connections 2 of 24

5 - 55

2 1 3

Z

Y

X

Y

1 cover plates of web chord 2 cover plate of flange 1 (on the right-hand side) 3 cover plate of flange 2 (on the left-hand side)

Figure A.3 Cover plates

The global coordinates system is such as:

The XOZ plane is that of the truss plane The XOY plane is that of the web chord

2. Basic data

The sizes of the cover-plates and the positioning of holes are shown on the Figure A.4.



5 - 56

35

70

70

140

70

70

35

35

70

70

35

100

40 95 95 40

14 11,5

7 / 7,5 / 7

165 165

5

50

50

30

30

Figure A.4 Sizes (in mm) and positioning

Material data (except bolts)

The I-profile and the cover-plates are grade S355 to EN 10025-2.

Steel grade S355

Yield strength fy = 355 N/mm2

Ultimate tensile strength fu = 510 N/mm2

EN 1993-1-1 Table 3.1

I Beam data

Depth h = 330 mm

Flange width b = 160 mm

Web thickness tw = 7,5 mm

Flange thickness tf = 11,5 mm

Radius of root fillet r = 18 mm

Cross-section area A = 62,61 cm2

Second moment of area Iy = 788,1 cm4

Plastic modulus Wpl,y = 153,7 cm3



5 - 57

Bolted connections data

Category of bolted connections Category C

Bolt Class Class 10.9

Yield strength fyb = 900 N/mm2

Ultimate tensile strength fub = 1000 N/mm2

For flanges cover plates

Nominal bolt diameter df = 22 mm

Hole diameter d0,f = 24 mm

For web cover plates

Nominal bolt diameter dw = 18 mm

Hole diameter d0,w = 20 mm

EN 1993-1-8

Table 3.1

Partial Factors (Recommended values)

Structural steel M0 = 1,00


Bolts M2 = 1,25

Bolts M3 = 1,25

EN 1993-1-1 6.1 NOTE 2B EN 1993-1-8 2.2 NOTE

Internal forces

For the direction of the internal forces see Figure A.5

MEd = 1,71 kNm (about y-y axis)

VEd = 1,7 kN

NEd = 1567,4 kN (tension force)

Note: the bending moment and the shear force can be ignored. For all that in some phases we take them into account so as to show the concept of the calculation in the presence in such internal forces.



5 - 58

Y

X

Y

Z

VEd

NEd MEd

MEd

Figure A.5 Internal forces and moment

3. Classification of cross-section chord

For the classification of the cross-section, it’s necessary to know the distribution of the normal stresses.

EN 1993-1-1 Table 5.2 Sheet 2 of 3

For the web we consider a uniform stress equal to:

A

N Edw = -250,34 N/mm2

For the flanges we have:

iyy

EdEdi

vI

M

A

N

Where vi is the position of the considered fibre.

And for the upper part (Z > 0) of the flange:

2f1 /bv and rtv 2w2

1 = 180,91 N/mm2, 2 = 245,62 N/mm2

And for the inner part (Z < 0) of the flange:

2f1 /bv and rtv 2w2

1 = 319,78 N/mm2, 2 = 255,06 N/mm2

In view of these results, the cross-section being all over in tension is considered of class 1.



5 - 59

4. Global checking of the cross-section chord

4.1. Effect of the shear force EN 1993-1-1 6.2.10

Determination of Rdpl,

Ed

V

V

With: wv thAA w = 3959 mm2

M0

yvRdpl,

3

fA

V = 811,3 kN

EN 1993-1-1 6.2.6(2)

From where Rdpl,

Ed

V

V = 0,002< 0,5

So, no reduction due to the shear force needs to be taken into account.

EN 1993-1-1 6.2.10 (2)

4.2. Combination M + N – Effect of the axial force EN 1993-1-1 6.2.9.1

kN4,8174,1567M0

ywwEd

fth

N

Allowance has to be made for the effect of the axial force.

EN 1993-1-1 6.2.9.1 (5)

4.3. Combination M + N – Consideration of fastener holes

Axial force

Under tension axial force, the fastener holes should be considered.

Category C connection the design tension resistance is:

M0

ynetRdnet,Rdt,

fANN

EN 1993-1-1 6.2.3(4)

For the net cross-section, we consider 7 holes for fastener (2 by flange and 3 for the web).

The net area is: netA = 4707 mm2

Therefore: Rdnet,N = 1671 kN

Bending moment

With ff tbA and ff0,fnetf, 2 tdAA

For each flange in tension, one checks:

kN2,6534739,0

M0

yf

M2

unetf,

fAfA

So, the holes for fasteners in the flange should be considered.

EN 1993-1-1 6.2.5 (4)



5 - 60

With ww0,ff0,net 34 tdtdAA

For the full tension area, one checks:

kN7,22224,17289,0

M0

y

M2

unet AffA

So, the holes for fasteners in the web should be considered.

EN 1993-1-1 6.2.5 (5)

Design resistance for bending

With for a IPE 330: yplW , = 153,7 cm3

dz = 50 mm = distance from centre of holes of flange to z-z axis

zff0,holesy,pl, 4 dtdW = 55,2 cm3

The design plastic moment resistance of the net section is:

M0

yholesy,pl,ypl,Rdpl,

fWWM

= 34,967 kNm

EN 1993-1-1 6.2.5(2)

4.4. Combination M + N – Verification

The following criterion should be verified:

RdN,Ed MM

EN 1993-1-1 6.2.9.1(1)

With: Rdnet,

Ed

N

Nn = 0,938

5,0;/)2(min AtbAa f = 0,412

EN 1993-1-1 6.2.9.1(3)

We obtain :

2

Rdpl,RdN,1

1a

anMM = 6,99 kNm

MEd = 1,71 < MN,Rd = 6,99 kNm OK

5. Distribution of the internal forces EN 1993-1-8 2.5

Note that the web is in the horizontal plane.

5.1. Axial force

The axial force is distributed between the web and the flanges. This distribution is based on the ratio of the gross cross-section of the web and the flanges. The fillets are appointed to the flange.

So, with: wfw )2( tthA 2302,5 mm2

2/)( wf AAA 3958,5 mm2 (per flange)

Then: AANN /wEdwN, = 576,4 kN

2/wN,EdfN, NNN = 495,5 kN



5 - 61

5.2. Shear force

The shear force is fully transferred by the flanges.

So: 2/EdfV, VV (per flange)

5.3. Bending moment

The bending moment about the weak axis is fully transferred by the flanges:

fM,M 0,855 kNm for each flanges

6. Internal forces in each connected parts

6.1. Connection of the webs

The cover plate of webs (and its bolts) is only subjected to an axial force:

NN,w = 576,4 kN

6.2. Connection of the flanges

Each of cover plates of flanges (and its bolts) is subjected to:

An axial force NN,f = 495,49 kN,

A shear force VV,f = 0,85 kN

A bending moment MM,f = 0,855 kNm

The moment due to the eccentricity of the shear force against the centroid of the joint (see Figure A.6):

VfV,fV, eVM

With: eV= 140 mm MV,f = 0,119 kNm

VV,f G

ev

MV,f

Figure A.6 Moment due to the eccentricity of the shear force



5 - 62

6.3. Summary of the internal forces and moments

In the web: Nw = 576,42 kN

In one flange: Nf = 495,49 kN

Vf = 0,85 kN

Mf = 0,97 kN

7. Verification of the web connection

The connection of the webs is a double lap joint.

The web component will be verified and by symmetry only one plate component.

7.1. Design details EN 1993-1-8 Table 3.3

It is assumed that the structure is not exposed to the weather or other corrosive influences.

The design details are verified for the web component and for the plate component in the tables below

Table A.1 Connection of the webs – Web component – Design details

Distance or spacing Min. value Design value Max. value

e1 24 47,5

e2 24 1)

p1 44 70 105

p2 48 95 105 1) Not applicable because of the proximity of the flange

Table A.2 Connection of the webs – Plate component – Design details


e1 24 35

e2 24 40

p1 44 70 98

p2 48 95 98

7.2. Design shear force FV,Ed for each bolt

6w

wEd,V,N

F = 96,07 kN for the component web EN 1993-1-8 3.12 (3)

6

2/wpEd,V,

NF = 48,03 kN for each component plate

7.3. Design slip resistance FS,Rd

By considering: Bolts in normal holes 0,1s k



5 - 63

Class friction surfaces = Class A 5,0

And with: ws,A 192 mm2 tensile stress area of the bolt

ws,ubcp, 7,0 AfF 134,4 kN pretension force

n number of the friction surfaces

2wn relatively to the web component

1pn relatively to the plate component

Then: cp,M3

wswRd,s, F

nkF

107,52 kN

cp,M3

pspRd,s, F

nkF

53,76 kN

EN 1993-1-8 3.9.1 (1)

7.4. Design bearing resistance Fb,Rd for each bolt

Table 3.4 of EN 1993-1-8 gives the expressions of the design bearing resistance. In these expressions, the coefficients b and 1k depend on the orientation of the loading, the position compared with the ends of the component and also the position of the other bolts.

EN 1993-1-8 Table 3.4

The general expression for the design bearing resistance is:

M2

ub1Rdb,

tdfkF

EN 1993-1-8 Table 3.4

According to Table 3.4 of the Eurocode 1993-1-8, the coefficients b and k1 are determined from:

For end bolts

0,1;;3

minu

ub

0

1endb,

f

f

d

e

5,2;7,18,2;7,14,1min0

2

0

2end1,

d

e

d

pk

For inner bolts

0,1;;4

1

3min

u

ub

0

1b,inner

f

f

d

p

5,2;7,14,1min0

21,inner

d

pk

Web component

Figure A.7 shows how it is processed for the determination of the coefficients

b and 1k .



5 - 64

Nw

FV,Ed,w

b b

k1 k1

b,inner k1,end

b,inner k1,inner

b,inner k1,end

b,end k1,end

b,end k1,inner

b,end k1,end

b4 b5 b6

b1 b2 b3

Figure A.7 Connection of the webs – Web component – Determination of

type of bolts

The determination of coefficients k1 is carried out perpendicularly to the direction of load transfer. But two directions are conceivable for this perpendicular and it is difficult for some bolts (b1, b4, b3, and b6) to determine if they are end or inner bolts.

In these cases we consider the minimum value of k1,inner and k1,end. And by noticing that end1,end1,1,inner ;min kkk , these bolts are considered as end

bolts.

In addition, for the web component, it is reminded that the edge distance e2 is not applicable because of the proximity of the flange. So, the expressions of k1,inner and k1,end are identical.

As the design shear force is identical for each bolt and furthermore:

k1,inner = k1,end = 2,50

So only one row of bolts is considered, for example the bolts b1 and b4.

Then, for the bolt b1:

79,0endb1,b,b1b,

kN01,109wRd,b1,b, F

And for the bolt b4:

92,0innerb4,b,b4b,

kN23,126wRd,b4,b, F



5 - 65

Therefore, in the end for the web component,

kN01,109wRd,b, F

Plate component

Compared with the web component, for the plate it can be noticed that the bolts b1, b2, b3 become inner bolts and the bolts b4, b5, b6 become end bolts (see Figure A.8).

Then, for the bolt b1:

92,0innerb1,b,b1b,

kN81,117pRd,b1,b, F

And for the bolt b4:

58,0endb4,b,b4b,

kN97,74pRd,b4,b, F

In the end, for the plate component, it should retained:

kN97,74pRd,b, F

Figure A.8 Connection of the webs – Plate component – Determination of

type of bolts

b b

k1 k1

b,end k1,end

b,end k1,inner

b,end k1,end

b,inner k1,end

b,inner k1,inner

b,inner k1,end

FV,Ed,w

b4 b5 b6

b1 b2 b3

Nw/2



5 - 66

7.5. Checking bolts

7.5.1. With regard to the web component

Individual checking

Design bearing resistance kN01,10907,96 wRd,b,wEd,V, FF

Design slip resistance kN52,10707,96 wRd,s,wEd,V, FF

EN 1993-1-8 Table 3.2

Group of fasteners

The shear resistance per shear plane Rdv,F is taken as:

M2

ubvRdv,

AfF

EN 1993-1-8 Table 3.4

By considering that the shear plane does not pass through the threaded portion of the bolt in normal holes:

v = 0,6

A = 254,47 mm2 (gross cross-section of the bolt)

Then: Rdv,F = 122,15 kN

Since wRd,b,Rdv, FF for only three bolts as a result the design of our group

of fasteners:

kN06,65401,1096min wRd,bi,b,biwRd,b,r, FnFg

EN 1993-1-8 3.7

Then: kN06,65442,576 wRd,b,r,w gFN

7.5.2. With regard to the plate component

Individual checking

Design bearing resistance kN97,7403,48 pRd,b,pEd,V, FF

Design slip resistance kN76,5303,48 pRd,s,pEd,V, FF

EN 1993-1-8 Table 3.2

Group of fasteners

The shear resistance per shear plane Error! Objects cannot be created from editing field codes. is equal to:

Rdv,F = 122,15 kN

Since Error! Objects cannot be created from editing field codes. for each of the bolts as a result the design of our group of fasteners:

kN34,57897,74381,11731

Rdh,bi,b,Rdh,b,gr, bin

FF

EN 1993-1-8 3.7

Then: kN34,57821,2282/ Rdb,r,w gFN



5 - 67

7.6. Design of net cross-section

For a connection in tension, the design plastic resistance of the net cross-section at bolt holes should be verified:

b

1Rdnet,EdV,

n

NF

where nb is the number of bolts located in the considered net cross-section.

EN 1993-1-8 Table 3.2

7.6.1. Web component

The net cross-section is taken as 2ww0,wnetw, mm5,18523 tdAA

The design resistance is: kN64,657M0

ynetw,Rdnet,w,

fA

N

Then: kN21,28807,96364,6573

1wEd,V,Rdnet,w, FN

7.6.2. Plate component

The net cross-section is taken as 2pw0,pnetp, mm14703 tdAA

The design resistance is: kN85,521M0

ynetp,Rdnet,p,

fA

N

Then: kN10,14403,48385,5213

1wEd,V,Rdnet,w, FN

7.7. Design for block tearing

The Figure A.9 shows the block tearing for the web and for the plate. EN 1993-1-8 3.10.2 (1)


The bolt group is subjected to concentric loading.

And with: 2w02nt mm1125)22( tdpA

2w011nv mm5,1312)5,1(2 tdpeA

EN 1993-1-8 3.10.2 (2)

Then: kN01,728Rdeff,1, V

576,42kN01,728 wRdeff,1, NV


Two block tearing are defined. For the both, the shear area is the same, so the case giving the minimum area subjected in tension is considered. The bolt group is subjected to concentric loading.

EN 1993-1-8 3.10.2 (2)

And with: 2p02nt mm420)2( tdeA

2p011nv mm1050)5,1(2 tdpeA



5 - 68

kN57,386Rdeff,1, V

So: kN21,8822/57,386 wRdeff,1, NV

Nw/2

Ant

Anv Nw

Ant

Anv Anv

Nw/2

Ant

Anv Anv

1

2

3

1 Block tearing for web component (concentric loading) 2 First block tearing for plate component (concentric loading) 3 Second block tearing for plate component (concentric loading)

Figure A.9 Block tearing for connection of the webs

8. Checking of connection of the flanges

The connection of the flanges is a single lap joint.

The flange component and the plate component will be verified.

In general rule in the presence of a combination of loads, we obtain for each bolt a design shear force not parallel to the edge of the components. In this case, the Eurocode states that the bearing resistance can be verified separately for the bolt load components parallel and normal to the end of components.

EN 1993-1-8 Table 3.4 3)

Rdh,bi,b,Edh,bi,V, FF

Rdv,bi,b,Edv,bi,V, FF

In the ECCS publication P126 (European recommendations for the Design of Simple Joints in Steel Structures – 2009), an additional check is proposed, based on an interaction expression:

1

2

Rdv,bi,b,

Edv,bi,V,2

Rdh,bi,b,

Edh,bi,V,

F

F

F

F

The load components will be performed in a basis vh , located at the centre of gravity of the joint and oriented with the principal directions of the flange (See Figure A.10).



5 - 69

8.1. Design details EN 1993-1-8 Table 3.3

It is assumed that the truss is not exposed to weather or other corrosive influences.

The design details should be verified in both directions of loading. By taking into consideration the limits specified in Table 3.3 of EN 1993-1-8, the following requirement have to be fulfilled:

021 2,1;min dee

021 2,2;min dpp

mm200;14min;max 21 tpp

The tables below check the design details for each component.

Table A.3 Connection of the flanges – Plate component – Design details


21 ee ;min 28,8 30

21 pp ;min 52,8 70

21 pp ;max 100 161

Table A.4 Connection of the flanges – Plate component – Design details


21 ee ;min 28,8 30

21 pp ;min 52,8 70

21 pp ;max 100 196

8.2. Design shear force FV,Ed for each bolt

With regard to the flange component

The components of the design shear force are calculated in the basis vh ,

(see Figure A.10). The group of bolts is subjected to a axial force fN , a shear

force fV and a bending moment fM (see 6.2)

The axial force fN generates a horizontal shear force:

kN58,826

fhbi,N,

NF for each bolt

The shear force fV generates a vertical shear force:

kN14,06f

vbi,V, V

F for each bolt



5 - 70

The moment fM is divided out the bolts according to the distance ir between the centre of bolts bi and the centre of gravity of the group of bolts

6

1

2i

ifbiM,

r

rMF

This shear force biM,F resolved in the basis vh , gives:

6

1

2i

ifhbi,M,

r

vMF a horizontal component for the bolt bi.

6

1

2i

ifv'bi,M,

r

hMF a vertical component for the bolt bi.

With ih and iv coordinates of centre of bolt bi.

In the end, for each bolt:

hbi,M,hbi,N,Edh,bi,V, FFF Horizontal design shear force

vbi,M,vbi,V,Edv,bi,V, FFF Vertical design shear force

2,,,

2,,,Edbi,V, EdvbiVEdhbiV FFF Resulting design shear force

The Figure A.10 shows the distribution of the internal forces.

Vf

G Mf Nf

FV,bi,v

FN,bi,h FM,bi

h

v

b1 b2 b3

b6 b5 b4

Figure A.10 Distribution of the internal forces for the flange component.

The Figure A.11 shows the directions of the resulting force and its components.



5 - 71

FV,v,Ed

FV,h,Ed FV,Ed

h

v

Figure A.11 Directions of the design shear force

Table A.5 sums up the determination of the design shear forces.

The vertical component of the load can be neglected. We will confine to the horizontal direction for the design bearing resistance checking.

In addition, if we had not considered the shear force EdV and the moment

EdM , the unique horizontal design shear force would be:

hbi,N,Edh,bi,V, FF = -82,58 kN

That is a difference of 2%

So the value of 84,02 kN can be retained (= maximum value obtained for

Edbi,V,F ) for the design shear force: kN02,84EdV, F .



5 - 72

Table A.5 Connection of the flanges – Flange component – Design shear

forces in kN in the basis vh , .

Bolt b1 b2 b3 b4 b5 b6

ih -70 0 70 -70 0 70

iv 50 50 50 -50 -50 -50

ir 86,02 50 86,02 86,02 50 76,02

biM,F 2,42 1,41 2,42 2,42 1,41 2,42

hbi,M,F 1,41 1,41 1,41 -1,41 -1,41 -1,41

vbi,M,F 1,97 0 -1,97 1,97 0 -1,97

hbi,N,F -82,58 -82,58 -82,58 -82,58 -82,58 -82,58

vbi,V,F 0,14 0,14 0,14 0,14 0,14 0,14

Edbi,V,F 81,20 81,17 81,20 84,02 83,99 84,01

Edh,bi,V,F -81,17 -81,17 -81,77 -83,99 -83,99 -83,99

Edv,bi,V,F 2,11 0,14 -1,83 2,11 0,14 -1,83

With regard to the plate component

The connection of the flanges is a single lap joint so the design shear forces for each bolt with regard to the plate component are directly deduced from the previous results.

The value of 84,02 kN can be retained.

8.3. Design slip resistance FS,Rd

By considering: Bolts in normal holes 0,1s k

Class friction surfaces = Class A 5,0

And with: fs,A 303 mm2 tensile stress area of the bolt

fs,ubcp, 7,0 AfF 212,1 kN pretension force

n number of the friction surfaces

Single lap joint 1n for each component

Then: cp,M3

spRd,s,fRd,s, F

nkFF

84,54 kN EN 1993-1-8 3.9.1

8.4. Design bearing resistance Fb,Rd for each bolt EN 1993-1-8 Table 3.4

We confine to the horizontal direction for the determination of the design bearing resistance (see 8.2).



5 - 73

Flange component

Figure A.12 shows for each bolt how the factors b and 1k are determined.

b

k1 k1

k1k1

b,end

k1,end

b,inner

k1,end

b,inner

k1,end

b,end

k1,end

b,inner

k1,end

b,inner

k1,end

FV,h,Ed

b1 b2 b3

b4 b5 b6

Figure A.12 Connection of the flanges – Flange component – Determination of

type of bolts

For all the bolts: k1,end = 1,80.

For the bolt b1 and b4: 94,0endb,

kN19,174fRd,b, F

For the other bolts: 72,0b,inner

kN19,134fRd,b, F

In the end for the flange component, the minimum value is retained:

kN19,134fRd,b, F

Plate component

For all the bolts, k1,end = 1,80.

For the bolt b3 and b6: 49,0endb,

kN32,90pRd,b, F



5 - 74

For the other bolts: 72,0b,inner

kN19,134pRd,b, F

In the end for the plate component, the minimum value is retained:

kN32,90pRd,b, F

8.5. Verification of the bolts

8.5.1. With regard to the flange component

Individual checking

Design bearing resistance kN19,13402,84 wRd,b,wEd,V, FF

Design slip resistance kN54,8402,84 wRd,s,wEd,V, FF

EN 1993-1-8 Table 3.2

Group of fasteners

The design shear resistance per shear plane Rdv,F is taken as:

M2

ubvRdv,

AfF

EN 1993-1-8 Table 3.4

By considering that the shear plane does not pass through the threaded portion of the bolt in normal holes:

v = 0,6

A = 380,13 mm2 (gross cross-section of the bolt)


Since wRd,b,Rdv, FF for all the bolts, the design resistance of our group of

fasteners is equal to:

kN15,88519,134419,1742bi

1fRd,bi,b,wRd,b,r,

n

g FF

EN 1993-1-8 3.7

Then: kN15,88549,495 fRd,b,r,f gFN

8.5.2. With regard to the plate component

Individual checking

Design bearing resistance: kN32,9002,84 pRd,b,pEd,V, FF

Design slip resistance: kN54,8402,84 pRd,s,pEd,V, FF

EN 1993-1-8 Table 3.4

Group of fasteners

The shear resistance per shear plane Rdv,F is equal to:

Rdv,F = 182,46 kN



5 - 75

Since wRd,b,Rdv, FF for all the bolts, the design of our group of fasteners is

equal to:

kN40,71719,134432,902bi

1pRd,bi,b,pRd,b,r,

n

g FF

EN 1993-1-8 3.7

Then: kN40,71749,495 pRd,b,r,fp gFNN

8.6. Design of net cross-section

For a connection in tension, the design plastic resistance of the net cross-section at bolt holes should be verified:

b

1Rdnet,EdV,

n

NF

Where nb is the number of bolts located in the considered net cross-section.

EN 1993-1-8 Table 3.2

8.6.1. Flange component

The net section area is: 2ff0,netf, mm25,14272 tdAA f

And: kN67,506M0

ynetf,Rdnet,f,

fA

N

Then: kN04,16802,84267,5062

1fEd,V,Rdnet,f, FN


The net cross-section is taken as 2pw0,pnetp, mm15682 tdAA

From where kN64,556M0

ynetp,Rdnet,p,

fA

N

Then: kN0416802842645562

1pEd,V,Rdnet,p, ,,, FN

Note: The global cross-section of the beam has been verified accounting for the holes for fastener and the combination of the internal forces (see 4).

The net cross-section of the plate component should also be verified under this combination of internal forces.

Assuming a uniform distribution of the load in the section, it is proposed that:

y22

max 3 f

Where: vI

M

A

N

tnep,

p

netp,

p and

netp,

p

A

V



5 - 76

Assuming a uniform distribution of the shear stresses, this leads to a conservative situation.

With 2netp, mm1568A

4holesp,grossp,netp, cm643062317187477 ,,, III

Then: 2N/mm316 and 2N/mm3125,

Finally: 2y

2 N/mm355N/mm31341 f,max

8.7. Design for block tearing EN 1993-1-8 3.10.2


The bolt group is subjected to a concentric loading Nf and an eccentric loading Vf but considering the presence of the web we only consider the case with a concentric loading.

The Figure A.13 shows the block tearing for the flange component

Ant Anv Nf

Figure A.13 Connection of the flanges – Block tearing for flange

component

With: 2f02nt mm414)5,0(2 tdeA

2f011nv mm5,3392)5,22(2 tdpeA


And: kN49,95424,826 wRdeff,1, NV


The bolt group is subjected to a concentric loading Np and an eccentric loading Vp.

The Figure A.14 shows the block tearing for the plate component



5 - 77

For the cases with a concentric loading, only the case giving the minimum area in tension is considered:

With : 2p0202nt mm504)5,0(2);(min tdedpA

2p011nv mm3220)5,22(2 tdpeA


And: kN49,49560,865 fRdeff,1, NV

Ant

Anv

Anv

Ant Anv

Ant

Anv Vp

Np Np

1

3

2

1 First block tearing with concentric loading 2 Second block tearing with concentric loading 3 Block tearing with eccentric loading

Figure A.14 Connection of the flanges - Block tearing for plate component

For the case with an eccentric loading, with:

2p011nt mm1610)5,22( tdpeA

2p0nv mm1316)5,122( tdpeA


And: kN85,017,598 pRdeff,2, VV

So we have just verified successively the bolt group according to the two loadings. An additional requirement based on an interactive expression should be fulfilled:

0,1;min 3,,2,2,,1,1,,1,

blockRdeff

p

blocRdeffblockRdeff

p

V

V

VV

N

Then: 0,157,017,598

85,0

60,865

49,495 OK


5 - 78


5 - 79

APPENDIX B Worked example – Design of a truss node with gusset

5 - 80

Appendix B Worked Example: Design of a truss node with gusset

1 of 44

Made by CZT Date 12/2009

Calculation sheet Checked by DGB Date 12/2009

The truss includes several types of joints: splice joints by bolted cover plates, T joints and KT joints. This Appendix gives the detailed design of a KT joint located on the upper chord, as shown in Figure B.1.

7100 7200 8500 8600 7100 7100

4000

91 kN 136 182 182 136 136 91 kN

1

1 KT joint

Figure B.1 Location of the KT joint

The values of the internal forces in the truss members (see Table B.1) result from a gravity load case. This load case corresponds to a ULS combination of actions, determined according to EN 1990.

Table B.1 KT joint – Internal forces in the truss members

Member N (kN) V (kN) M (kNm)

Diagonal 35 -609,4 -1,27 0

Diagonal 24 406,9 1,03 0

Post 36 2,6 0 0

Chord 101 -413,8 1,25 -0,46

102 101

24

36 35

136 kN

Chord 102 -1084 1,26 -0,09

1. General presentation of KT joint

The KT joint studied consists of the following connections: the gusset to web chord welded connection and the angles to gusset bolted connection (see Figure B.2 and Figure B.3). Both connections should be verified according to the rules from EN 1993-1-1 and EN 1993-1-8.

The gusset to web chord welded connection is a plate welded perpendicular to the web of the chord by two fillets welds (See Figure B.7).

The angles to gusset bolted connection is composed of two back-to-back double-angle diagonal members (See Figure B.4) and a single angle post member (See Figure B.5).

There are three shear connections to be designed as Category C.

Title Appendix B Worked Example: Design of a truss node with gusset 2 of 44

5 - 81

136 kN

1 2 3 1 Chord (IPE 330) 2 Gusset plate 3 Axes of the web members

Figure B.2 General presentation of KT joint

1

2

3

4

5 6

A

A

B B

1 Web of the chord (IPE 330) 2 Gusset plate 58026015 3 Angles L15015015 4 Angle L10010010 5 Fillet weld 6 Axes of the web members

Figure B.3 KT joint


5 - 82

Figure B.4 KT Joint – Section AA Figure B.5 KT Joint- Section BB

2. Gusset plate to web chord welded connection

This connection is a welded plate perpendicular to the web of the chord, see Figure B.6. The two fillet welds are identical. The design of the gusset plate and its weld to the chord takes into account the axial forces in all three angle members connected to it.

O

α3 α1

Y

Z

260 320

30

260

Og

N1,Ed

N2,Ed N3,Ed

Figure B.6 Gusset plate to web chord welded connection

The longitudinal axes of all three angle members intersect on the chord axis at the point O in the web.


5 - 83

The gusset plane is not positioned symmetrically about the normal OY to the web plane (see Figure B.6 and Figure B.7). The moment resulting from the eccentricity eZ should be taken into account.

The moment resulting from the eccentricity eY = tw/2 can be neglected.

Y

Z O

eZ=30

eY=7,5/2 Og

Y

X O

Og tw=7,5

tg=15

Figure B.7 Gusset plate to web chord – Details

The basic assumption is that gusset plate transfers axial forces acting in its plane and in the direction of the member axes.

2.1. Data

Global coordinates system (see Figure B.6 and Figure B.7)

The YOZ Plane is that of the gusset plate

The XOZ Plane is that of the chord web

Geometric data

Gusset plate thickness tg = 15 mm

Web thickness tw = 7,5 mm

Angle between gusset and web a = 90°

Number of fillet welds na = 2

Effective throat thickness a = Value to be defined

Length of welds Lw = 560 mm

Material data

Steel grade: S355

Yield strength: fy = 355 N/mm2

Ultimate tensile strength: fu = 510 N/mm2

EN 1993-1-1 Table 3.1

Note: The specified yield strength and ultimate tensile strength of the filler metal are required to be at least equivalent to those specified for the parent material.

EN 1993-1-8 4.2(2)


5 - 84

Partial Factor

Resistance of weld: M2 = 1,25 (recommended value)

EN 1993-1-8 Table 2.1 NOTE

Internal forces in the truss members (see Figure B.6)

All axial forces are applied in the gusset plate XOZ plane:

Tension axial force at an angle to normal OY of 1 = 42°:

N1,Ed = 406,9 kN

Tension axial force on the normal OY so 2 = 0°

N2,Ed = 2,6 kN

Compression axial force at an angle to normal OY of 3 = -41,3°

N3,Ed = -609,4 kN

2.2. Stresses in the gusset cross-section in front of welds

The approach is based on a linear-elastic analysis that leads to a safe estimation of the resistance of the welded joint.

EN 1993-1-8 2.4(2)

2.2.1. Design forces in the gusset plate at the chord web face

The effects of the small eccentricity eY from the chord axis will be neglected. The gusset plate section is verified for the following forces:

Ng,Ed Axial force at an eccentricity of eZ = 30 mm to the centreline of the gusset plate

Vg,Ed shear force

With:

3

1iiiEdg, )cos(NN

3

1iiiEdg, )sin(NV

and Edg,M , the moment resulting from the eccentricity, Edg,ZEdg, NeM

Then: Ng,Ed = -152,83 kN

Vg,Ed = 674,47 kN

Mg,Ed = 4,585 kNm

Note: the high axial force component Ng,Ed is due to the local point load at the joint and the self weight of the truss.

2.2.2. Normal stress

Assuming a uniform distribution of the load in the section, the normal stress is:

vI

M

A

N

g

Edg,

g

Edg,maxg,


5 - 85

Where: Ag is the cross-section area

Ig is the second moment of cross-section

v is the position of the end fibre

With: 58015wgg LtA = 8700 mm2

12

3wg

g

LtI = 243,89.106 mm4

v = 290 mm

Then: maxg, = -23,02 N/mm2

2.2.3. Shear stress

The shear mean stress is:

g

Edg,g

A

V

Then: g = 77,53 N/mm2

One usually checks the combination of axial and shear stresses in the gusset plate section using the Von Mises criterion.

2.3. Design resistance of the fillet weld

The design resistance of a fillet weld should be determined using either the directional method or the simplified method.

EN 1993-1-8 4.5.3.1(1)

The directional method is based on the comparison between the design tensile strength and the applied stress in the most severely loaded part of the weld throat. The applied stress, being determined from a Von Mises formulation, accounts for the influence on the weld strength of the inclination of the resultant force per unit length to the weld axis and plane.

The simplified method is based on the design shear strength of the weld to which is compared directly to an applied weld throat shear stress obtained by dividing the resultant force per unit of length b the weld throat size. The simplified method is always safe compared to the directional method.

Here, the directional method is applied. EN 1993-1-8 4.5.3.2

2.3.1. Directional method

Note: a uniform distribution of stress is assumed in the throat section of the weld.

EN 1993-1-8 4.5.3.2(4)

With: the normal stress to the throat plane

the shear stress (in the plane of throat) perpendicular to the axis of the weld

the shear stress (in the plane of throat) parallel to the axis of the weld


5 - 86

Note: the normal stress in the weld needs not to be considered. EN 1993-1-8 4.5.3.2(5)

On the throat section of the weld, the force per unit length are:

a = )2/sin( aa

gmaxg,

n

e = -122,08 N/mm.mm

a = )2/cos( aa

gmaxg,

n

e= -122,08 N/mm.mm

a = a

gg

n

e = 581,44 N/mm.mm

The design resistance of the fillet weld will be sufficient if the following conditions are both fulfilled:

w = [2+3 (2+2) ]0,5 ≤ fu / (w M2)

≤ 0,9 fu / M2

EN 1993-1-8 4.5.3.2(6)

Where: w is the correlation factor for fillet weld

w = 0,8

EN 1993-1-8 Table 4.1

These conditions can be rewritten in the following forms:

(a w) / a ≤ fu / (w M2)

(a ) / a ≤ 0,9 fu / M2

From these conditions, a minimum value for the effective throat thickness is derived.

a1,min = a w / [ fu / (w M2)] = 2,03 mm

a2,min = a / (0,9 .fu / M2) = 0,33 mm

amin = max(a1,min ; a2,min) = 2,03 mm

The following requirements must be satisfied:

a 3 mm

leff max(30 mm ; 6 a) with leff = Lw – 2 a

EN 1993-1-8 4.5.2(2) 4.5.2(1)

An effective throat thickness of 4 mm is then sufficient.


5 - 87

3. Angles to gusset bolted connection

Three shear connections are designed as Category C. These connections are shown in Figure B.8.

320 260

260

16

41.3° 42°

15

N1

N2 N3

Figure B.8 Angles to gusset bolted connections

This connection is composed of two back-to-back double-angle diagonal members (N1 and N3) and a single angle post member (N2).

The internal forces in the truss members are:

N1,Ed = 406,9 kN tension axial force

N2,Ed = 2,6 kN tension axial force

N3,Ed = -609,4 kN compression axial force

3.1. Basic Data

Material data (except bolts)

Steel grade S355

Yield strength fy = 355 N/mm2

Ultimate tensile strength fu = 510 N/mm2

EN 1993-1-1 Table 3.1

Gusset plate

Thickness tg = 15 mm

Length Lg = 580 mm

Width Hg = 260 mm

Angle members

N1 two equal-leg angles L15015015

N2 one equal-leg angle L10010010

N3 two equal-leg angles L15015015


5 - 88

Bolted connections data

Category of bolted connections Category C

Bolt Class Class 10.9

Yield strength fyb = 900 N/mm2

Ultimate tensile strength fub = 1000 N/mm2

Nominal bolt diameter d = 24 mm

Hole diameter d0 = 26 mm

EN 1993-1-8 Table 3.1

Partial Factors (Recommended values)




Bolts M2 = 1,25

Bolts M3 = 1,25

EN 1993-1-1 6.1 NOTE 2B EN 1993-1-8 2.2 NOTE

3.2. Global checking of gross cross-sections of the gusset plate

The gross cross-sections of the gusset plates to check are located on the Figure B.9.

Note: The gross cross-sections of the angles are verified afterward.

320 260

260

2

1

N3,Ed

N2,Ed

N1,Ed

1 = 42° 3 = 41.3°

Figure B.9 Location of the gross cross-sections of the gusset plate

Checking of gross cross-section 1

With Ag1 cross-sectional area 1 Ag1 = Hg tg = 3900 mm2


5 - 89

Shear resistance

2Ed2,1Ed1,Edg1, cos;cosmax NNV = 457,82 kN

3M0yg1Rdpl,g1, fAV = 799,34 kN

Rdpl,g1,Edg1, VV OK

Axial force resistance

3

1iiEdi,Edg1, )sin(NN = 674,47 kN

M0yg1Rdpl,g1, fAN = 1384,50 kN

Rdpl,g1,Edg1, NN OK

Checking of gross cross-section 2

With Ag2 cross-sectional area 2 Ag2 = Lg tg = 8700 mm2

Shear resistance

3

1iiEdi,Edg2, )sin(NV = 674,47 kN

3M0yg2Rdpl,g2, fAV = 1783,15 kN

Rdpl,g2,Edg2, VV OK

Axial force resistance

3

1iiEdi,Edg2, )cos(NN = 152,83 kN

M0yg2Rdpl,g2, fAN = 3088,5 kN

Rdpl,g2,Edg2, NN OK

3.3. Connection N3 – Back-to-back double-angle diagonal member N3 to gusset bolted connection

The shear connection in compression is designed as Category C.

The sizes of the components and the positioning of the holes are shown on the Figure B.10 and Figure B.11.


5 - 90

172

124

76

90

57

99

141

33

60

57

67,5

65

67 65

65

35

C

C

G

Figure B.10 Connection N3 – Sizes (in mm) and positioning

60 33 57

42.5

15

1

1 Angles neutral axis

Figure B.11 Connection N3 – Section CC

3.3.1. Connection N3 – Design forces

With: N3,Ed Axial compression force at an eccentricity of eN3 to the centre of gravity of the joint

M3,N,Ed Bending moment resulting from the eccentricity, M3,N,Ed = eN3 N3,Ed.

For the gusset:

N3,g,Ed = 609,4 kN

eN3 = 44,5 mm

M3,g,Ed = eN3 N3,g,Ed = 27,12 kNm


5 - 91

For each angle:

N3,a,Ed = 304,7 kN

M3,a,Ed = 13,56 kNm

3.3.2. Connection N3 – Checking of angle

Resistance of gross cross-section

Longitudinal stress

Assuming a uniform distribution of the load in the section, the longitudinal stress is:

vI

M

A

N

a3,

Eda,3,

a3,

Eda,3,i

Where: A3,a is the section area of the angle

A3,a = 4302 mm2

I3,a is the second moment of area of angle

I3,a = 8,981.106 mm4

v position of considered end fibre (see Figure B.12)

v1 = 87 mm

v2 = 63 mm

Then the normal stresses are:

1 = 202,18 N/mm2 (compression)

2 = -24,29 N/mm2 (tension)

2

1

eN3

N3,a,Ed

Compression Tension

M3,a,Ed = eN3 N3,a,Ed

υ2 υ1

Figure B.12 Stresses in the angle N3


5 - 92

Class of section

20,121510 th

36,95,11102 thb

class 4

14,81/10/1093,7 tc

class 2

Class of angle = class 4

EN 1993-1-1 Table 5.2 Sheet 3 of 3 Table 5.2 Sheet 2 of 3

Combination M + N

Criterion to satisfy: M0

y

effa,3,

Eda,3,

effa,3,

Eda,3,Edx,

f

W

M

A

N

with: A3,a,eff effective area of cross-section

leg2eff,a,3,leg1eff,a,3,effa,3, AAA

where A3,a,eff,leg1 effective area relative to the “free” leg

A3,a,eff,leg2 effective area relative to the “connected” leg

EN 1993-1-1 6.2.9.3

determination of the effective area of cross-section A3,a,eff,leg1

11 = 1,0

buckling factor k = 0,43

p = 0,660 = 1 no reduction

EN 1993-1-5 Table 4.2 EN 1993-1-5 4.4 (2)


12 = -0,120



EN 1993-1-5 Table 4.2 EN 1993-1-5 4.4 (2)

Verification

a3,effa,3, AA (no reduction)

35518,202);max(M0

y21Edx,

f N/mm2

criterion satisfied

Resistance of net cross-section

From 6.2.5 (5) of EN 1993-1-1, the fastener holes in tension zone need not be allowed for, provided that the following limit is satisfied for the complete tension zone:

M0

yt

M2

unett, 9,0

fAfA

EN 1993-1-1 6.2.5 (5)


5 - 93

Here, the holes are in the tension zone (see Figure B.12).

Accounting for a3,effa,3, AA , the following criterion should be fulfilled:

M0

ya3,Rdc,a,3,Eda,3,

fANN

With 2a3, mm4302A :

kN2,15277,304 Rdc,a,3,Eda,3, NN

Buckling resistance

A compression member should be verified against buckling.

This condition has been verified in the section dealt with the verification of the members (see § 4 of this document).

3.3.3. Connection N3 – Checking of gusset plate


For the determination of the gross cross-section of gusset plate, a diffusion of 45° of the axial force Ng,Ed is assumed (see Figure B.13).

286,5

45° 45°

112

Figure B.13 Connection N3 – Diffusion by 45° of the axial force

The following criteria must be satisfied:

M0

y

g3,

Edg,3,

g3,

Edg,3,Edx, /

f

vI

M

A

N

with: 2gg3, mm5,42975,286 tA

43g3, mm2939570612/5,286 gtI

mm2/325v

Then: 2

M0

yEdx, N/mm35572,29192,14980,141

f


5 - 94

Buckling resistance

The gusset is made similar to an embedded column of characteristics:

Area 2,3 mm5,4297gA

Height hc = 112 mm (see Figure B.13)

Second moment of area Ic,zz = 80578 mm2

We should satisfy:

M1

yg3,Rdb,g,3,Edg,3,

fANN

Where is the reduction factor for the relevant buckling curve

EN 1993-1-1 6.3.1.1

With a buckling length of 2hc, the slenderness is given by:

c2

yc2c4

EI

fAh

= 0,677

The buckling curve to use is curve c and the imperfection is:

= 0,49

2)2,015,0 = 0,846

22

1

= 0,739

Table 6.1 EN 1993-1-1 6.3.1.2

Then: kN11274609 Rdb,g,3,Edg,3, NN ,

3.3.4. Connection N3 – Checking of bolts with regard to the gusset component

Design shear force FV,Ed for each bolt

Due to the orientation of the axial force N3,Ed, the load on each bolt is not parallel to the edge of gusset. Also, the components of the design shear load will be performed in a suitable basis.

EN 1993-1-8 Table 3.4 3)

In first the components are calculated in the basis vh , located at the centre of gravity of the joint and oriented in agreement with the principal directions of the fasteners which are also the principal directions of the angles (See Figure B.14).

Then a change of basis is performed from the initial vh , to the basis

vh , (see Figure B.15).

In the basis vh , the normal force N3,g,Ed causes a horizontal shear load for each bolt bi:

5

Edg,3,hbi,N,

NF = 101,57 kN


5 - 95

The moment due to eccentricity is divided out according to the distance ir between the centre of bolts bi and the centre of gravity of the joint:

5

1

2i

iEda,1,biM,

r

rMF

FM,b6,h’ FM,b6,v’

FM,b6

FN,b6

N3,g,Ed

M3,g,Ed

G

h’ v’

b4

b5

b6

b2

b3

b1

Figure B.14 Connection N3 – Gusset component – Locations

FV,b1,Ed

G h

v

FV,b1,h,Ed

FV,b1,v,Ed

b3

b2

b1 b4

b5

b6

Figure B.15 Connection N3 – Gusset component – Loadings


5 - 96

This shear load FM,bi is resolved in the basis vh , :

5

1

2i

iEda,1,hbi,M,

r

vMF horizontal component

5

1

2i

iEda,1,v'bi,M,

r

hMF vertical component

With ih and iv coordinates of centre of bolt bi.

And we obtain (see Table B.2):

hbi,M,hbi,N,Ed,hbi,V, FFF Horizontal shear force,

vbi,M,Ed,vbi,V, FF Transverse shear force,

2Ed,vbi,V,

2Ed,hbi,V,Edbi,V, FFF Resulting shear force

Table B.2 Connection N3 – Gusset component – Design shear forces in kN

in the basis vh , .


ih 81,25 16,25 -48,75 48,75 -16,25 -81,25

iv -30 -30 -30 30 30 30

ir 86,61 34,12 57,24 57,24 34,12 86,61

biM,F -98,34 -38,74 -64,99 -64,99 -38,74 -98,34

hbi,M, F 34,06 34,06 34,06 -34,06 -34,06 -34,06

vbi,M, F 92,25 18,45 -55,35 55,35 -18,45 -92,25

biN,F 101,57 101,57 101,57 101,57 101,57 101,57

Edbi,V,F 164,03 136,88 146,49 87,30 69,98 114,31

Ed,hbi,V, F 135,63 135,63 135,63 67,50 67,50 67,50

Ed,vbi,V, F 92,25 18,45 -55,35 55,35 -18,45 -92,25

The change of basis is performed with:

)cos()sin( 3Ed,vbi,V,3Ed,hbi,V,Edh,bi,V, FFF

)sin()cos( 3Ed,vbi,V,3Ed,hbi,V,Edv,bi,V, FFF

Where 3 = 41,3° (See Figure B.6)

Table B.3gives the results.


5 - 97

Table B.3 Connection N3 – Gusset component – Design shear loads in kN in

the vh , reference system


Edbi,V,F 164,03 136,88 146,49 87,30 69,98 114,31

Edh,bi,V,F -20,21 -75,65 -131,10 -2,97 -58,41 -113,86

Edv,bi,V,F 162,78 114,07 65,36 87,25 38,54 -10,17

Design details

The structure is not exposed to the weather or other corrosive influences.

We have to verify the design details in the two directions of the components of loading. By considering the limits specified in Table 3.3 of EN 1993-1-8, we have to satisfy the following checks:

EN 1993-1-8 3.5 (1) and Table 3.3

021 2,1;min dee

021 2,2;min dpp or 021 2,1;min dpp if 04,2 dL

mm200;14min;max 21 tpp

EN 1993-1-8 Table 3.3 5)

For e1 and e2 observe the minimum end and edge distances according to the directions Gh and Gv. And For p1 and p2 consider the spacing according to the directions Gh’ and Gv’.

The design details are verified in the table below.

Table B.4 Connection N3 – Gusset component – Design details

Distance or spacing Minimum value Design value Maximum value

21 ee ;min 31,2 57

21 pp ;min 31,2 60

21 pp ;max 65 200

Design bearing resistance Fb,Rd for each bolt

Table 3.4 of EN 1993-1-8 gives the expressions for the determination of the design bearing resistance. These expressions bring into play two coefficients

b and 1k .

EN 1993-1-8 Table 3.4

For each bolt the value of these coefficients depend on the orientation of its loading, its location compared with the ends of the gusset but also with the location of the other bolts.

So we are considering successively the horizontal loading (loads in the direction Gh) and the vertical loading (loads in the direction Gv).


5 - 98

Horizontal loading

The horizontal loading coming from the results of Table 3 is shown on the Figure B.16.

On this figure we indicate for each bolt how we are processing for the determination of its coefficients b and 1k . So, we can specify for each bolt:

the end and edge distances (e1 and e2) and the spacing (p1, p2 and L) to consider

the type; end or inner, or end and inner

b3

b2

b1

b4

b5

b6

b

b

b

k1 k1 k1 k1

Figure B.16 Connection N3 – Gusset component – Horizontal loading

The general expression for the design bearing resistance is:

M2

ub1Rdb,

tdfkF

EN 1993-1-8 Table 3.4

According to Table 3.4 of the Eurocode 1993-1-8, the coefficients b and k1 are determined from:

For end bolts

0,1;;3

minu

ub

0

1endb,

f

f

d

e

5,2;7,18,2;7,14,1min0

2

0

2end1,

d

e

d

pk

For inner bolts

0,1;;4

1

3min

u

ub

0

1b,inner

f

f

d

p

5,2;7,14,1min0

21,inner

d

pk

Table B.6 gives the value of the horizontal component of the design bearing resistances Fb,bi,h,Rd.


5 - 99

Table B.5 Connection N3 – Gusset component – Horizontal component of the design bearing resistances in kN


e1

e2 172 124 76 90

p1 1) 68,24 68,24 68,24 68,24 68,24 68,24

p2 65 65 2) 65 2) 65 2) 65 2) 65

b,inner b,inner b,inner b,inner b,inner b,inner

b 0,62 0,62 0,62 0,62 0,62 0,62

min1,k 3) min1,k 3) min1,k 3) 1,innerk 1,innerk min1,k 3)

1k 1,80 1,80 1,80 1,80 1,80 1,80

RdhbibF ,,,

165,19 165,19 165,19 165,19 165,19 165,19

1) the distance L have been retained

2) L;65min

3) end1,;inner1,minmin,1 kkk

Vertical loading

The vertical loading coming from the results of Table 3 is shown on the Figure B.17

b3

b2

b1

b4

b5

b6

k1

b b b b

k1

k1

Figure B.17 Connection N3 – Gusset component – Vertical loading

Table B.6 gives the value of the vertical component of the design bearing resistances Fb,bi,v,Rd.


5 - 100

Table B.6 Connection N3 – Gusset component – Vertical component of the design bearing resistances in kN


e1 90

e2 141 99 57

p1 65 65 1) 65 1) 65 1) 65 1)

p2 2) 68,24 68,24 68,24 68,24 68,24 68,24

b,inner b,inner b,inner b,inner b,inner endb,

b 0,58 0,58 0,58 0,58 0,58 1,00

1,innerk 1,innerk 1,innerk min1,k 3) min1,k 3)

min1,k 3)

1k 1,97 1,97 1,97 1,97 1,97 1,97

RdvbibF ,,, 169,16 169,16 169,16 169,16 169,16 289,98

1) L;65min



Design slip resistance Fs,Rd

With: As = 353 mm2 tensile stress area of the bolt

subCp, 7,0 AfF = 247,1 kN pretension force

n = 2 number of the friction surfaces relatively to the gusset

EN 1993-1-8 3.9 EN 1993-1-8 3.9.1 (2)

And by considering:

Bolts in normal holes ks = 1,0

Class of friction surfaces = Class A = 0,5

EN 1993-1-8 Table 3.6 Table 3.7

Then: Cp,M3

sRdS, F

nkF

= 197,68 kN EN 1993-1-8 3.9.1 (1)

Checking bolts – Individual checking

The criteria to satisfy are:

In relation to the design slip resistance

RdS,Edbi,V, FF

EN 1993-1-8 Table 3.2

In relation to the design bearing resistance

Rdh,bi,b,Edh,bi,V, FF

Rdv,bi,b,Edv,bi,V, FF

EN 1993-1-8 Table 3.2 and Table 3.4 3)

Note: an additional check based on an interactive expression is proposed:

1

2

Rdv,bi,b,

Edv,bi,V,2

Rdh,bi,b,

Edh,bi,V,

F

F

F

F


5 - 101

Each bolt has to be verified. The highest values of resistance do not necessary correspond with the bolt the most loaded.

Table B.7 summarizes only the checks for the bolt b1.

Table B.7 Connection N3 – Gusset component – Checking bolt b1

Design values Resistance values

Edb1,V,F 164,03 197,68 RdS,F

Edh,b1,V,F 20,21 165,19 Rdh,b1,b,F

Edv,b1,V,F 162,78 169,16 Rdv,b1,b,F

2

Rdv,b1,b,

Edv,b1,V,2

Rdh,b1,b,

Edh,b1,V,

F

F

F

F 0,94 1

Checking bolts – Group of fasteners

From the Eurocode, the design resistance of a group of fasteners may be taken as:

bin

FF1

Rdbi,b,Rdb,gr, if for each bolt bi we have Rdbi,b,Rdv, FF

else Rdbi,b,biRdb,r, min FnFg

EN 1993-1-8 3.7

Where RdvF , , the shear resistance per shear plane, is taken as:

M2

ubvRdv,

AfF

By considering that the shear plane passes through the threaded portion of the bolt in normal holes:

v = 0,5

A = As= 353 mm2 (tensile stress area)


Finally for the design resistance we obtain:

Rdh,b,r,gF = 991,17 kN for the horizontal components

Rdv,b,r,gF = 1014,94 kN for the vertical components

And we verify that:

21,402)sin( 3,,3 EdgN < kN17,991Rdh,b,r, gF

82,457)cos( 3,,3 EdgN < kN94,1014Rdh,b,r, gF


5 - 102

3.3.5. Connection N3 – Checking bolts with regard to the angle component

Determination of the design ultimate shear load FV,Ed for each bolts

Table B.8 gives the results of the design ultimate shear load FV,bi,Ed and its components FV,bi,h,Ed and FV,bi,v,Ed (See Figure B.18).

These results are deduced from the results obtained for the gusset in the basis vh , .

FV,b6,Ed

N3,a,Ed

M3,a,Ed

G

h v

b4

b5

b6

b2

b3

b1

FV,b6,v,Ed

FV,b6,h,Ed

Figure B.18 Connection N3 – Angle component – Loading

Table B.8 Connection N3 – Angle component – Design shear loads in kN


Edbi,V,F 82,01 68,44 73,24 43,65 34,99 57,16

Edh,bi,V,F -67,81 -67,81 -67,81 -33,75 -33,75 -33,75

Edv,bi,V,F -46,13 -9,23 27,68 -27,68 9,23 46,13

Design details


Table B.9 Connection N3 – Angle component – Design details


21;min ee 31,2 33

21;min pp 31,2 60

21;max pp 65 200

Determination of the design bearing resistance Fb,Rd for each bolts

Horizontal loading

The horizontal loading coming from the results of Table B.8 is shown on the Figure B.19


5 - 103

b4

b5

b6

b2

b3

b1

k1

k1

k1

b

b

Figure B.19 Connection N3 – Angle component – Horizontal loadings


Table B.10 Connection N3 – Angle component – Horizontal component of the design bearing resistances in kN


e1

e2 33 33 33

p1 65 65 65 65 65 65

p2 1) 68,24 68,24 68,24 68,24 68,24 68,24

b,inner b,inner b,inner b,inner b,inner b,inner

b 0,58 0,58 0,58 0,58 0,58 0,58

1,innerk 1,innerk 1,innerk min1,k 2) min1,k 2) min1,k 2)

1k 1,97 1,97 1,97 1,85 1,85 1,85

RdhbibF ,,, 169,16 169,16 169,16 158,84 158,84 158,84



Vertical loading

The vertical loading coming from the results of Table B.8 is shown on the Figure B.20


5 - 104

b4

b5

b6

b2

b3

b1

b

b

b

k1

k1

Figure B.20 Connection N3 – Angle component – Vertical loading


Table B.11 Connection N3 – Angle component – Vertical component of the design bearing resistances in kN


e1 33 33

e2 35 67,5

p1 1) 68,24 68,24 68,24 68,24 68,24 68,24

p2 65 65 65 65 65 65

b,inner b,inner b,inner b,inner endb, endb,

b 0,62 0,62 0,62 0,62 0,42 0,42

min1,k 2) 1,innerk 1,innerk min1,k 2)

1,innerk 1,innerk

1k 1,80 1,80 1,80 1,80 1,80 1,80

RdvbibF ,,, 165,19 165,19 165,19 165,19 111,85 111,85


2) end1,inner1,min,1 ;min kkk

Determination of the design slip resistance Fs,Rd

For the angle component, the number of the friction surfaces is equal to 1.

So with n = 1 we obtain:

Cp,M3

sRdS, F

nkF

= 98,84 kN

EN 1993-1-8 3.9 EN 1993-1-8 3.9.1 (2)


Each bolt has to be verified.

Table B.12 summarizes only the checks for the bolt b1.


5 - 105



Edb1,V,F 82,01 98,84 RdS,F

Edh,b1,V,F 67,81 169,16 Rdh,b1,b,F

Edv,b1,V,F 46,13 165,19 Rdv,b1,b,F

2

Rdv,b1,b,

Edv,b1,V,2

Rdh,b1,b,

Edh,b1,V,

F

F

F

F 0,24 1

Checking bolts - Group of fasteners

For the angle we can consider only the horizontal component. In this case:

Rdh,b,r,gF = 991,17 kN

And we verify that:

70,304,,3 EdaN < kN03,953Rdh,b,r, gF

3.3.6. Connection N3 – Design of net cross-section

For a connection in tension, the design plastic resistance of the net cross-section at bolt holes should be verified only for a connection in tension.

EN 1993-1-8 3.4.1 (1) c)

3.3.7. Connection N3 – Design of block tearing

Given that this connection is in compression it is not necessary to execute the design for block tearing.

3.4. Connection N1 – Back-to-back double-angle diagonal member N1 to gusset bolted connection

We have a shear connection in tension to be designed as Category C.

The sizes of the components of this connection and the positioning of the holes are shown on the Figure B.21. The section DD is identical to the section CC of the connection N3 (See Figure B.11).


5 - 106

35

65

65

33

60

57

54

D

D

G

76 124

80

67,5

Figure B.21 Connection N1 – Sizes (in mm) and positioning

3.4.1. Connection N1 – Design forces

With: N1,Ed the normal tension force at an eccentricity of eN1, to the centre of gravity of the joint

M1,N,Ed the moment resulting from the eccentricity, M1,N,Ed = eN1

N1,Ed.

We have for the gusset:

N1,g,Ed = 406,9 kN

eN1 = 44,5 mm

M1,g,Ed = eN1 N1,g,Ed = 18,11 kNm

And for each angle:

N1,a,Ed = 203,45 kN

M1,a,Ed = 9,05 kNm

3.4.2. Connection N1 – Checking of angle

Resistance of gross cross-section

Longitudinal stress

Assuming an uniform distribution of the load on the section, the longitudinal stress is:

vI

M

A

N

a1,

Eda,1,

a1,

Eda,1,i


5 - 107

Where: A1,a cross-sectional area of angle

I1,a second moment of cross-section of angle

v position of considered end fibre

With: A1,a = 4302 mm2

I1,a = 8,981.106 mm4

v1 = 87 mm and v2 = 63 mm (see Figure B.22)

We obtain (with compression positive):

1 = -134,99 N/mm2

2 = 16,22 N/mm2

Class of section

20,121510 th

36,95,11102 thb

class 4

14,81/10/1093,7 tc

class 2

Class of angle = class 4

EN 1993-1-1 Table 5.2 Sheet 3 of 3 Table 5.2 Sheet 2 of 3

1

2

eN1

N1,a,Ed

Compression

Traction

M1,a,Ed = eN1 N1,a,Ed

G

Figure B.22 Stresses in the angle N1


5 - 108

Combination M + N

Criterion to satisfy: M0

y

effa,1,

Eda,1,

effa,1,

Eda,1,Edx,

f

W

M

A

N

with: A1,a,eff effective area of cross-section

leg2eff,a,1,leg1eff,a,1,effa,1, AAA

where A1,a,eff,leg1 effective area relative to the “free” leg

A1,a,eff,leg2 effective area relative to the “connected” leg

EN 1993-1-1 6.2.9.3


No reduction because “free” leg in traction


12 = -0,120



EN 1993-1-5 Table 4.2 EN 1993-1-5 4.4 (2)

Verification

a1,effa,1, AA (no reduction)

35599,134);max(M0

y21Edx,

f

criterion satisfied

Resistance of net cross-section

We should satisfy:

M0

yneta,1,Rdnet,a,1,Eda,1,

fANN

EN 1993-1-1 6.2.3. (1) and (4)

The net cross-sections considered are shown on the Figure B.23

1 1

2

2 2

Figure B.23 Net cross-sections of angle N1


5 - 109

With: 22,,11,,1neta,1, mm3588)3588;3912min();min( netaneta AAA

we satisfy:

kN52,131745,203 Rdnet,a,1,Eda,1, NN

3.4.3. Checking of gusset


For the determination of the gross cross-section of gusset, we use an approach based on a diffusion of 45° of the internal force Ng,Ed (see Figure B.24).

45°

45°

195

Figure B.24 Connection N1 – Diffusion by 45° of the internal force

The following criteria must be satisfied:

M0

y

g1,

Edg,1,

g1,

Edg,1,Edx,

/

f

vI

M

A

N

with: 2gg1, mm2925195 tA

43g3, mm926859412/195 gtI

mm2/195v

We obtain: 2

M0

yEdx, N/mm35562,32951,19011,139

f

3.4.4. Connection N1 – Checking of bolts with regard to the gusset component


Due to the orientation of the normal force N1,Ed, the load on each bolt is not parallel to the edge of gusset. By consequent the components of the design shear load parallel and normal to the end will be performed.

EN 1993-1-8 Table 3.4 3)


5 - 110

The calculation of the components is performed in the same way as for connection N3 (see 3.3.4). We calculate the components in the basis vh ,

(see Figure B.25).) then in the basis vh , (see Figure B.26).

N1,g,Ed

M1,g,Ed

b1

b2

b3

b4

FN,b2

FM,b2

FM,b2,h’

G

FM,b2,v’

h’

v’

Figure B.25 Connection N1 – Gusset component – Locations

Table B.13 gives the calculations and the results of the design ultimate shear load FV,bi,Ed and its two components FV,bi,h’,Ed and FV,bi,v’,Ed for each bolt bi in the vh , reference system.


the vh , reference system.

Bolt b1 b2 b3 b4

ih -16,25 48,75 -48,75 16,25

iv -30 -30 30 30

ir 34,12 57,24 57,24 34,12

biM,F 69,56 116,70 116,70 69,56

hbi,M, F 61,16 61,16 -61,16 -61,16

vbi,M, F -33,13 99,39 -99,39 33,13

biN,F 101,73 101,73 101,73 101,73

Edbi,V,F 166,22 190,82 107,35 52,37

Ed,hbi,V, F 162,89 162,89 40,56 40,56

Ed,vbi,V, F -33,13 99,39 -99,39 33,13


5 - 111

b1

b2

b3

b4

h

v

G

FV,b3,Ed

FV,b2,Ed

FV,b1,Ed

FV,b4,Ed

Figure B.26 Connection N1 – Gusset component – Loadings

The change of basis is performed with:

)sin()cos( 3Ed,vbi,V,3Ed,hbi,V,Edh,bi,V, FFF

)cos()sin( 1Ed,vbi,V,1Ed,hbi,V,Edv,bi,V, FFF

Where 1 = 42° (See Figure B.6)

Table B.14 gives the results.


the vh , reference system.

Bolt b1 b2 b3 b4

Edbi,V,F 166,22 190,82 107,35 52,37

Edh,bi,V,F 84,37 182,86 -46,72 51,76

Edv,bi,V,F -143,22 -54,54 -96,65 -7,97

Design details


For e1 and e2 we observe the minimums end and edge distances according to the appropriate direction (Gh or Gv). For p1 and p2 we consider the spacing according to the principal direction of the joint (Gh’ or Gv’).

Table B.15 Connection N1 – Gusset component – Design details


21 ;min ee 31,2 54

21 ;min pp 31,2 60

21 ;max pp 65 200


5 - 112


Horizontal loading


b1

b2

b3

b4

b

b

b

k1 k1

Figure B.27 Connection N1 – Gusset component – Horizontal loading


Table B.16 Connection N1 – Gusset component – Horizontal component of the design bearing resistances in kN

Bolt b1 b2 b3 b4

e1 80 54

e2 124 76

p1 65 1) 65

p2 65 1) 65 1) 65 1) 65 1)

b,inner endb, b,inner endb, b

0,58 1,00 0,58 0,69

min1,k 3) min1,k 3) 1,innerk 1,innerk 1k

1,80 1,80 1,80 1,80

Rdh,bi,b,F 154,22 264,38 154,22 183,04

1) L;65min



5 - 113

Vertical loading

The vertical loading coming from the results of Table B.14 is shown on the Figure B.28.

b1

b2

b3

b4

b b

k1

k1

k1

Figure B.28 Connection N1 – Gusset component – Vertical loading


Table B.17 Connection N1 – Gusset component – Vertical component of the design bearing resistances in kN

Bolt b1 b2 b3 b4

e1 124 76

e2 80 98 54

p1 65 1) 65 1)

p2 65 1) 65 65 65 1)

endb, endb, b,inner b,inner b

1,00 0,97 0,58 0,58

1,innerk min1,k 2) min1,k 2)

min1,k 2)

1k 1,80 1,80 1,80 1,80

RdvbibF ,,, 264,38 257,60 154,22 154,22

1) L;65min

2) end1,1,innermin,1 ;min kkk


5 - 114


With n = 2, the number of the friction surfaces relatively to the gusset, we obtain:

Cp,M3

sRdS, F

nkF

= 197,68 kN

EN 1993-1-8 3.9 EN 1993-1-8 3.9.1 (1)


Each bolt has to be verified.

Table B.18 and Table B.19 summarize only the checks for the bolt b1 and b2.



Edb1,V,F 166,22 197,68 RdS,F

Edh,b1,V,F 84,37 154,22 Rdh,b1,b,F

Edv,b1,V,F 143,22 264,38 Rdv,b1,b,F

2

Rdv,b1,b,

Edv,b1,V,2

Rdh,b1,b,

Edh,b1,V,

F

F

F

F 0,59 1



Edb1,V,F 190,82 197,68 RdS,F

Edh,b1,V,F 182,86 264,38 Rdh,b1,b,F

Edv,b1,V,F 54,54 257,60 Rdv,b1,b,F

2

Rdv,b1,b,

Edv,b1,V,2

Rdh,b1,b,

Edh,b1,V,

F

F

F

F 0,52 1


By considering that the shear plane passes through the threaded portion of the bolt in normal holes:

v = 0,5

A = As= 353 mm2 (tensile stress area)

We obtain:

Rdv,F = 141,12 kN


5 - 115

And for the design resistance:

Rdh,b,r,gF = 616,90 kN for the horizontal components

Rdv,b,r,gF = 616,90 kN for the vertical components

And we verify that:

27,272)sin( 1,,1 EdgN < kN90,616Rdh,b,r, gF

39,302)cos( 1,,1 EdgN < kN90,616Rdh,b,r, gF

3.4.5. Connection N1 – Checking bolts with regard to the angle component


Table B.20 gives the results of the design ultimate shear load FV,bi,Ed and its components FV,bi,h,Ed and FV,bi,v,Ed (See Figure B.29).

These results are deduced from the results obtained for the gusset in the basis vh , .

N1,a,Ed

M1,a,Ed

b1

b2

b3

b4

h v

G

FV,b1,Ed

FV,b2,Ed

FV,b3,Ed

FV,b4,Ed

Figure B.29 Connection N1 – Angle component – Loading

Table B.20 Connection N1 – Angle component – Design shear loads in kN

Bolt b1 b2 b3 b4

Edbi,V,F 83,11 95,41 53,67 26,19

Edh,bi,V,F 81,44 81,44 20,28 20,28

Edv,bi,V,F 16,57 -49,70 49,70 -16,57

Design details



5 - 116

Table B.21 Connection N1 – Angle component – Horizontal loading – Design details


21 ;min ee 31,2 33

21 ;min pp 57,2 60 200

21 ;max pp 65 200


Horizontal loading


b1

b2

b3

b4

b

b

k1

k1

Figure B.30 Connection N1 – Angle component – Horizontal loadings



5 - 117

Table B.22 Connection N1 – Angle component – Horizontal component of the design bearing resistances in kN

Bolt b1 b2 b3 b4

e1 67,5 35

e2 33 33

p1 65 65

p2 1) 68,24 68,24 68,24 68,24

endb, b,inner endb, b,inner b

0,87 0,58 0,45 0,58

1,innerk 1,innerk min1,k 2) min1,k 2) 1k

1,97 1,97 1,85 1,85

Rdh,bi,b,F 250,95 169,16 122,18 158,84


2) end1,inner1,min,1 ;min kkk

Vertical loading

The vertical loading coming from the results of Table 20 is shown on the Figure B.31

b1

b2

b3

b4

k1

k1

Figure B.31 Connection N1 – Angle component – Vertical loading



5 - 118

Table B.23 Connection N1 – Angle component – Vertical component of the design bearing resistances in kN

Bolt b1 b2 b3 b4

e1 33

e2 67,5 35

p1 1) 68,24 68,24 68,24

p2 65 65 65 65

b,inner b,inner endb, b,inner b

0,62 0,62 0,42 0,62

min1,k 2) 1,innerk min1,k 2)

1,innerk 1k

1,80 1,80 1,80 1,80

Rdh,bi,b,F 165,19 165,19 111,85 165,19




For the angle component, the number of the friction surfaces is equal to 1.

So with n = 1 we obtain:

Cp,M3

sRdS, F

nkF

= 98,84 kN

EN 1993-1-8 3.9 EN 1993-1-8 3.9.1 (2)


Each bolt has to be verified. Table B.24 summarizes only the checks for the bolt b2.

Table B.24 Connection N1 – Angle component – Checking bolt b2


Edb1,V,F 95,41 98,84 RdS,F

Edh,b1,V,F 81,44 169,16 Rdh,b1,b,F

Edv,b1,V,F 49,70 165,19 Rdv,b1,b,F

2

Rdv,b1,b,

Edv,b1,V,2

Rdh,b1,b,

Edh,b1,V,

F

F

F

F 0,32 1


For the angle we can consider only the horizontal component:

Rdh,b,r,gF = 488,73 kN

And we verify that:

45,203,,1 EdaN < kN73,488Rdh,b,r, gF


5 - 119

3.4.6. Connection N1 – Design of net cross-section

Gusset component

For a connection in tension, the design of the net cross-sections have to be verified.

Verify on the net cross-section marked 1 on the Figure B.32. For this section, we have to satisfy:

M0

ynet1

b

Edg,1,b

fA

n

Nn

t

EN 1993-1-8 3.4.1 (1) c) and Table 3.2

Where 2b n number of bolts relative to the cross-section

4bt n total number of the connection

With 1netA 2194 mm2

We satisfy: kN7784,203M0

ynet1

b

Edg,1,b

fA

n

Nn

t

Angle component

We have been already verified the net cross-section (see 3.4.2).

Moreover these checking have been realised with NEd in loco nb FV,Ed.

3.4.7. Connection N1 – Design for block tearing

Gusset component

EN 1993-1-8 3.10.2

The Figure B.32 shows the block tearing for the gusset.

N1,g,Ed

1

1

1

Ant

Anv

Anv

Anv

Anv

Figure B.32 Connection N1 – Block tearing for gusset

Our bolt group is subjected to eccentric loading and we have to satisfy:

Rdeff,2,Edg,1, VN

EN 1993-1-8 3.10.2 (3)


5 - 120

Where M0

nv

M2

ntuRdeff,2,

3

15,0

AfAf

Vy

With Ant = 633,6 mm2

Anv = 3533,1 mm2

We satisfy:

kN4,8539,406 Rdeff,2,Edg,1, VN

Angle component

The Figure B.33 shows the block tearing for the gusset.

N1,a,Ed

Anv

Anv

Ant

Ant

Figure B.33 Connection N1 – Block tearing for angle

Our bolt group is subjected to eccentric loading and we have to satisfy:

Rdeff,2,Eda,1, VN

EN 1993-1-8 3.10.2 (3)

With Ant = 933,6 mm2

Anv = 1402,5 mm2

We satisfy:

kN91,40745,203 Rdeff,2,Edg,1, VN

3.5. Connection N2 – Single angle post member N2 to gusset bolted connection

We have a shear connection in tension to be designed as Category C.

Given that the loading is low, the checking of this connection is not carry out. Otherwise the procedure stays the same with in addition the following point.


5 - 121

We are dealing with a single angle in tension by a single row of bolts in one leg. During the checking of the net cross-section of this angle, the design ultimate resistance should be determined as follows:

M2

unet2Rdu,

fAN

With 4,02 ( 01 5,265 dp )

EN 1993-1-8 3.10.3 (2) and Table 3.8

3.6. Influences of the eccentricity and other parameters

We consider only the bolts with regard to the gusset component.

3.6.1. Connection N3 – Moment due to eccentricity

The effects of the eccentricity depend of the locations of the bolts comparatively with the neutral axis but also to each other.

Lets the moment due to the eccentricity equal to 0. In this case and whatever the bolt we obtain in the basis vh , :

kN57,101Edb,V, F (value without moment due to eccentricity)

kN03,67Edh,b,V, F (value without moment due to eccentricity)

kN30,76Edv,b,V, F (value without moment due to eccentricity)

Values to compare at the results obtained for the bolt b1:

kN03,164Edb,V, F (value with moment due to eccentricity)

kN21,20Edh,b,V, F (value with moment due to eccentricity)

kN78,162Edv,b,V, F (value with moment due to eccentricity)

3.6.2. Connection N3 – Influence of number of bolts and spacing p1

Reduce the number of bolts from 6 to 5 by suppression of bolt marked b6 (see Figure B.14). This modification modifies the location of the centre of gravity of the bolt group. Even if the moment due to eccentricity decrease, the design shear loads per bolt increase. And two bolts (b1 and b3) do not again satisfy to the criteria relative to the design bearing resistances (see tables below).


5 - 122

Table B.25 Connection N3 – Gusset component – Bolt b1 – Reduction of total number of bolts


Total number of bolts

6 5

Edb1,V,F 164,03 189,76 197,68 RdS,F

Edh,b1,V,F 20,21 28,43 165,19 Rdh,b1,b,F

Edv,b1,V,F 162,78 187,62 169,16 Rdv,b1,b,F




6 5

Edb1,V,F 146,49 189,76 197,68 RdS,F

Edh,b1,V,F 131,10 182,40 165,19 Rdh,b1,b,F

Edv,b1,V,F 65,36 52,36 169,16 Rdv,b1,b,F

At this stage, increase the value of the spacing p1 from 65 to 75 mm. So all the bolts satisfy the criteria. Look for example the results for bolt b1.

Table B.27 Connection N3 – Gusset component – Bolt b1 – Increasing of spacing p1 to 75 mm


Edb1,V,F 180,06 197,68 RdS,F

Edh,b1,V,F 28,74 225,70 Rdh,b1,b,F

Edv,b1,V,F 177,75 220,50 Rdv,b1,b,F

3.6.3. Connection N1 – Influence of number of bolts

Reduce the number of bolts from 4 to 3 by suppression of bolt marked b3 (see Figure B.25). The moment due to eccentricity decrease whereas the design shear loads per bolt increase. And two bolts (b1 and b2) do not again satisfy to the criteria relative to the design bearing resistances (see tables below).


5 - 123




4 3

Edb1,V,F 166,22 222,19 197,68 RdS,F

Edh,b1,V,F 84,37 57,25 154,22 Rdh,b1,b,F

Edv,b1,V,F 143,22 214,69 264,38 Rdv,b1,b,F




4 3

Edb1,V,F 190,82 222,19 197,68 RdS,F

Edh,b1,V,F 182,86 207,52 264,38 Rdh,b1,b,F

Edv,b1,V,F 54,54 79,38 257,60 Rdv,b1,b,F

In order to satisfy the criteria we need to increase the value of the spacing p1 from 65 to a minimum of 101 mm. Look for example the results for bolt b1.

Table B.30 Connection N3 – Gusset component – Bolt b1 – Increasing of spacing p1 to 101 mm


Edb1,V,F 197,33 197,68 RdS,F



Part 6: Detailed Design of

Built-up Columns


Part 6: Detailed Design of

Built-up Columns

6 - ii

Part 6: Detailed Design of Built-up Columns

6 - iii

FOREWORD

This publication is part six of the design guide, Single-Storey Steel Buildings.




Part 3: Actions



Part 6: Detailed design of built-up columns










6 - iv


6 - v

Contents Page No

FOREWORD iii

SUMMARY vi

1 INTRODUCTION 1

2 TYPES OF BUILT-UP MEMBERS AND THEIR APPLICATION 2 2.1 General 2 2.2 Laced built-up columns 5 2.3 Battened built-up columns 7

3 DETAILED CALCULATIONS 9 3.1 General 9 3.2 Design methodology for laced built-up columns 9 3.3 Design methodology for battened built-up columns 14 3.4 Buckling length 17

REFERENCES 19

APPENDIX A Worked Example: Design of a laced built-up column 21


6 - vi

SUMMARY

This guide covers the structural arrangements and the calculations for built-up columns fabricated from hot rolled sections.

The calculations refer to the European Standard EN 1993-1-1, with complementary information where necessary.

The design procedures of EN 1993-1-1 are presented to verify a built-up column with lacing or battening using simplified equations and formulas.

A worked example is given in Appendix A.


6 - 1

1 INTRODUCTION

Built-up columns are used in steel construction when the column buckling lengths are large and the compression forces are relatively low. This guide covers two types of built-up columns:

Built-up columns with lacing

Built-up columns with battens.

This document includes an overview of common details for such members. It describes the design method according to EN 1993-1-1[1] for the determination of the internal forces and the buckling resistance of each member (chords, diagonals, etc) of built-up columns made of hot rolled profiles.

It should be noted that due to the shear deformation, battened built-up columns are more flexible than solid columns with the same inertia; this must be taken into account in the design.

In order to derive the axial resistance of a steel built-up column, the following must be addressed:

Analysis of the built-up column to determine the internal forces by taking into account an equivalent initial imperfection and the second order effects

Verification of the chords and bracing members (diagonals and battens)

Verification of the connections.

A fully worked example of a built-up column with an N-shape arrangement of lacings is given in Appendix A, which illustrates the design principles.


6 - 2

2 TYPES OF BUILT-UP MEMBERS AND THEIR APPLICATION

2.1 General In general, built-up columns are used in industrial buildings, either as posts for cladding when their buckling length is very long, or as columns supporting a crane girder.

When used as a post for cladding with pinned ends, the column is designed to support the horizontal forces, mainly due to wind. Hence the bending moment in such a built-up column is predominant compared to the compression force.

Figure 2.1 Post for cladding with pinned ends

A typical built-up column that supports a crane girder is shown in Figure 2.2. They usually have a fixed base and a pinned end at the top, and are designed to resist:

The compression forces that result either from the frame or from the crane rail

The horizontal forces that result from the effects of the crane applied on the internal chord and the wind loads applied to the external one.

In this case, the compression forces are predominant compared to the bending moment.


6 - 3

1 Crane girder

Figure 2.2 Built-up column supporting a crane girder

The built-up columns are composed of two parallel chords interconnected by lacings or battens – see Figure 2.1. In general, the truss system concentrates material at the structurally most efficient locations for force transfer.

In an industrial building and for a given height, built up columns theoretically have the least steel weight of any steel framing system.

Any hot rolled section can be used for the chords and the web members of built-up columns. However, channels or I-sections are most commonly used as chords. Their combination with angles presents a convenient technical solution for built-up columns with lacing or battens. Flat bars are also used in built-up column as battens.

This guide covers two types of built-up columns with pinned ends that are assumed to be laterally supported:

Laced columns

Battened columns.

1 NEd = 900 kN MEd = 450 kNm


6 - 4

Laced column Battened column

Figure 2.3 Built-up columns

The difference between these two types of built-up columns comes from the mode of connection of the web members (lacings and battens) to the chords. The first type contains diagonals (and possibly struts) designed with pinned ends. The second type involves battens with fixed ends to the chords and functioning as a rectangular panel.

The inertia of the built-up column increases with the distance between the chord axes. The increase in stiffness is counterbalanced by the weight and cost increase of the connection between members.

Built-up columns provide relatively light structures with a large inertia. Indeed, the position of the chords, far from the centroid of the built-up section, is very beneficial in producing a great inertia. These members are generally intended for tall structures for which the horizontal displacements are limited to low values (e.g. columns supporting crane girders).

The axial resistance of built-up columns is largely affected by the shear deformations. The initial bow imperfection is significantly amplified because of the shear strains.

It is possible to study the behaviour of built-up columns using a simple elastic model.


6 - 5

2.2 Laced built-up columns 2.2.1 General

There is a large number of laced column configurations that may be considered. However, the N-shape and the V-shape arrangements of lacings are commonly used.

Figure 2.4 Built-up column with lacings in an industrial building

The selection of either channels or I-sections for chord members provides different advantages. I-sections are more structurally efficient and therefore are potentially shallower than channels. For built-up columns with a large compressive axial force (for example, columns supporting cranes), I or H sections will be more appropriate than channels. Channels may be adequate in order to provide two flat sides.

Tee sections cut from European Column sections are also used for the chord members. The web of the Tee sections should be sufficiently deep to permit easy welding of the bracing members.

The angle web members of the laced column allow use of gusset-less welded connections, which minimises fabrication costs. Other member types require either gussets or more complex welding.

The centroidal axes of the compression and tension web members are not necessarily required to meet at the same point on the chord axes. In fact, laced columns with an eccentricity at the joints can be as efficient as those without eccentricity. The chord-web joint can be separated without an increase in steel weight. Although eccentric joints require that local moments be designed for, there are several advantages in doing so. Eccentric joints provide additional


6 - 6

space for welding, hence reducing fabrication complexity. In addition, the reduced length of the compression chord provides enhanced buckling and bending resistance which partly compensates for the additional moments generated by the joint eccentricity. For single angles, it is recommended that joint eccentricity is minimised.

2.2.2 Various lacing geometries

The N-shape arrangement of lacings, as shown in Figure 2.5(a), can be considered as the most efficient truss configuration, for typical frames in industrial buildings. The web of the N-shape arrangement comprises diagonals and posts that meet at the same point on the chord axes.

This arrangement reduces the length of the compression chords and diagonals. It is usually used in frames with a significant uniform compressive force.

The V-shape arrangement of lacings increases the length of the compression chords and diagonals and provides a reduction of buckling resistance of the members. This arrangement is used in frames with a low compressive force.

The X-shape configurations are not generally used in buildings because of the cost and the complexity of fabrication.

(a) N-Shape

(b) V-shape

(c) X-shape

Figure 2.5 Different shape arrangements of lacing


6 - 7

2.2.3 Construction details

Single lacing systems on opposite faces of the built-up member with two parallel laced planes should be corresponding systems as shown in Figure 2.6(a) (EN 1993-1-1 § 6.4.2.2(1)).

When the single lacing systems on opposite faces of a built-up member with two parallel laced planes are mutually opposed in direction, as shown in Figure 2.6(b), the resulting torsional effects in the member should be taken into account. The chords must be designed for the additional eccentricity caused by the transverse bending effect, which can have a significant influence on the member size.

Tie panels should be provided at the ends of lacing systems, at points where the lacing is interrupted and at joints with other members.

1 2 2 1

1 1

2 2

A B

Lacing on face A Lacing on face B

(a) Corresponding lacing system (Recommended system)

1 2 2 1

1 1

2 2

A B

Lacing on face A Lacing on face B (b) Mutually opposed lacing system

(Not recommended)

Figure 2.6 Single lacing system on opposite faces of a built-up member with

two parallel laced planes

2.3 Battened built-up columns Battened built-up columns are not appropriate for frames in industrial buildings. They are sometimes used as isolated frame members in specific conditions, where the horizontal forces are not significant.

Channels or I-sections are mostly used as chords and flat bars are used as battens. The battens must have fixed ends on the chords.


6 - 8

Battened built-up columns are composed of two parallel planes of battens which are connected to the flanges of the chords. The position of the battens should be the same for both planes. Battens should be provided at each end of the built-up member.

Battens should also be provided at intermediate points where loads are applied, and at points of lateral restraint.

a) Chords made of channels

b) Chords made of I sections

Figure 2.7 Battened compression members with two types of chords


6 - 9

3 DETAILED CALCULATIONS

3.1 General The design methodology described hereafter can be applied to verify the resistance of the various components of a built-up member with pinned ends, for the most critical ULS combination. The design axial force, NEd, and the design bending moment, MEd, about the strong axis of the built-up member are assumed to have been determined from analysis in accordance with EN 1993-1-1[1].

This methodology is applicable to built-up columns where the lacing or battening consists of equal modules with parallel chords. The minimum number of modules in a member is three.

The methodology is summarized in the flowchart in Figure 3.2 for laced built-up columns, and in Figure 3.4 for battened built-up columns. It is illustrated by the worked example given in Appendix A.

3.2 Design methodology for laced built-up columns 3.2.1 Step 1: Maximum compression axial force in the chords

Effective second moment of area

The effective second moment of area is calculated using the following expression (EN 1993-1-1 § 6.4.2.1(4)):

ch20eff 5,0 AhI

where:

h0 is the distance between the centroids of chords.

Ach is the cross-sectional area of one chord.

Shear stiffness

For the stability verification of a laced built-up column, the elastic elongations of the diagonals and the posts must be considered in order to derive the shear stiffness Sv. Formulae for the shear stiffness Sv are given in Table 3.1 for different arrangements of lacing.

Initial bow imperfection

The built-up column is considered as a column with an initial bow imperfection of e0, as shown in Figure 3.1:

e0 =L/500

where:

L is the length of the built-up member


6 - 10

Table 3.1 Shear stiffness Sv of built-up columns

N-shape V-shape K-shape X-shape

Ad

Av

h0

a

d Ad

Ad

h0

a

d

Ad

Av

h0

a

d

Ad

Av

h0

a

d

3d

30d3

30d

1dA

hAd

ahnEASV

3

20d

2d

ahnEAS V 3

20d

d

ahnEAS V 3

20d2

d

ahnEAS V

n is the number of planes of lacing Ad is the section area of a diagonal Av is the section area of a post d is the length of the diagonal

Figure 3.1 Initial bow imperfection

Maximum axial compression force in the chords

Verifications should be performed for chords using the design forces Nch,Ed

resulting from the applied compression force NEd and the bending moment MEd at mid-height of the built-up column.

For a member with two identical chords, the design force Nch,Ed is determined from the following expression (EN 1993-1-1 § 6.4):

Nch,Ed = eff

ch0EdEd

22 I

AhMN

NEd

e0 = L/500

L/2

L/2


6 - 11

where:

MEd is the maximum bending moment at mid-height of the built-up column including the equivalent imperfection e0 and the second order effects:

MEd =

v

Ed

cr

Ed

IEd0Ed

1S

N

N

NMeN

Ncr is the effective critical force of the built-up column:

2

effcr

²π

L

EIN

NEd is the design compression axial force applied to the built-up column.

IEdM is the design value of the maximum moment at mid-height of the

built-up column without second order effects.

3.2.2 Step 2: In-plane buckling resistance of the chord

Classification of the cross-section of the chord

The cross-section of the chord must be classified according to EN 1993-1-1 Table 5.2.

Buckling resistance of a chord about z-z axis

The resistance of the chord has to be verified for flexural buckling in the plane of the built-up member, i.e. about the weak axis of the cross-section of the chord (z-z axis). The buckling verification is given by (EN 1993-1-1 § 6.4.2):

1Rdz,b,

Edch, N

N

where:

Nb,z,Rd is the design buckling resistance of the chord about the weak axis of the cross-section, calculated according to EN 1993-1-1 § 6.3.1.

Information on the buckling length Lch of the chord is given in Section 3.4 of this guide.

3.2.3 Step 3: Out-of-plane buckling resistance of the chords

Out-of-plane buckling of the member, i.e. buckling about the strong axis of the cross-section of the chords (y-y axis), has to be considered. The buckling verification is given by:

1Rdy,b,

Edch, N

N

where:

Nb,y,Rd is the design buckling resistance of the chord about the strong axis of the cross-section, calculated according to EN 1993-1-1 § 6.3.1.

The buckling length depends on the support conditions of the built-up member for out-of-plane buckling. At the ends of the member, the supports are


6 - 12

generally considered as pinned. However intermediate lateral restraints may be provided.

3.2.4 Step 4: Maximum shear force

The verification of the web members of a built-up column with pinned ends is performed for the end panel by taking into account the shear force as described below.

For a built-up member subject to a compressive axial force only, the expression for the shear force is:

L

MV Ed

Ed

where:

MEd is the bending moment as calculated in Step 2, with: 0IEd M

For a built-up member subject to a uniformly distributed load, the expression for the shear force is:

L

MV Ed

Ed 4

where:

MEd is the maximum bending moment due to the distributed load.

Built-up columns are often subjected to a combination of a compressive axial force NEd and a uniformly distributed load. Thus the coefficient varies between π/L and 4/L. As a simplification, the shear force may be calculated by linear interpolation:

EdEdEd

EdEd )4(4

1M

MNe

Ne

LV

Io

o

where:

MEd is the maximum bending moment as calculated in Step 2. The bending moment I

EdM is the maximum moment due to the distributed load.

3.2.5 Step 5: Buckling resistance of the web members in compression

Maximum compressive axial force

The maximum axial force NEd in the web members adjacent to the ends is derived from the shear force VEd.

Classification of the web members in compression

The cross-section of the web member is classified according to EN 1993-1-1 Table 5.2.

Buckling resistance

The buckling verification of the web members should be performed for buckling about the weak axis of the cross-section, using the following criterion:


6 - 13

1Rdb,

Edch, N

N

where, Nb,Rd is the design buckling resistance of the web member about the weak axis of the cross-section, calculated according to EN 1993-1-1 § 6.3.1.

Information about the buckling length of web members is given in Section 3.4.

3.2.6 Step 6: Resistance of the web members in tension The resistance of the cross-section of the web members should be verified according to EN 1993-1-1 § 6.2.3 for the tensile axial force which is derived from the maximum shear force VEd as described in Step 3.

3.2.7 Step 7: Resistance of the diagonal-to-chord connections The resistance of the connections between the web members and the chords has to be verified according to EN 1993-1-8[2]. This verification depends on the details of the connection: bolted connection or welded connection. This verification should be performed using the internal forces calculated in the previous steps.

The worked example in Appendix A includes the detailed verification of a welded connection.

3.2.8 Flowchart

Step 2: In-plane buckling resistance of the chords

Effective second moment of area Ieff

Loads ULS load combination

Maximum compression force in the chord Nch

Section properties of the chords

Section properties of the web members

Global dimensions Of the built-up member

Start

End

Shear stiffness Sv

Initial bow imperfection e0

Step 3: Out-of-plane buckling resistance of the chords

Step 4: Maximum shear force VEd

Step 5: Buckling resistance of the web members in compression

Step 7: Design of the web members-to-chord connections

Step 6: Resistance of the web members In tension

Step 1: Maximum compression axial force in the chords

EN 1993-1-1 §6.4.1(6)

EN 1993-1-1 §6.4.1(1)

EN 1993-1-1 Figure 6.9

EN 1993-1-1 6.4.2.1(4)

EN 1993-1-1 §6.4.2.1(2)and §6.3.1

EN 1993-1-1 §6.3.1

EN 1993-1-1 §6.4.1(7)

EN 1993-1-1 §6.3.1

EN 1993-1-1 §6.2.3

EN 1993-1-8

Figure 3.2 Flowchart of the design methodology for laced built-up columns


6 - 14

3.3 Design methodology for battened built-up columns

3.3.1 Step 1: Maximum compressive axial force in the chords

Effective second moment of area

The effective second moment of area is calculated using the following expression (EN 1993-1-1 § 6.4.3.1(3)):

chch20eff 2 5,0 IAhI

where:

h0 is the distance between the centroids of chords

Ach is the cross-sectional area of one chord

Ich is the in-plane second moment of area of one chord

is the efficiency factor according to Table 3.2.

Table 3.2 Efficiency factor (EN 1993-1-1 Table 6.8)

Criterion Efficiency factor

≥ 150 0

75 < < 150 2 – /75

≤ 75 1,0

where: 0i

L

ch

10 2A

Ii chch

20 25,0 IAhIt

Shear stiffness

For the stability verification of a battened built-up column, the elastic deformations of the battens and the chords must be considered in order to derive the shear stiffness Sv using the following expression (EN 1993-1-1 § 6.4.3.1(2)):

²

²π2

21²

24 ch

0

b

ch

ch

a

EI

a

h

nI

Ia

EISv

But Sv should not be taken greater than ²

²π2 ch

a

EI

where:

a is the distance between the battens

n is the number of planes of battens

Ib is the in-plane second moment of area of one batten.


6 - 15

VEd a/2

a/2

h0

a/2

VEd a/2

VEd a/4 VEd a/4

Bending moment diagram

VEd a/h0

a/2

h0

a/2

VEd/2

VEd/2 VEd/2

VEd/2

VEd a/h0

Shear forces

Figure 3.3 Bending moments and shear forces in a panel of a battened

built-up column

Initial bow imperfection

The initial bow imperfection e0 is:

e0 =L/500

where:

L is the length of the built-up member

Maximum axial compressive force in the chords

The maximum axial compression Nch,Ed in the chords is calculated from the expression given in 3.2.1.

3.3.2 Step 2: In-plane buckling resistance of a chord

Classification of the cross-section of the chord

The cross-section of the chord is classified according to EN 1993-1-1 Table 5.2.

Buckling resistance of a chord about z-z axis

The resistance of the chord has to be verified for bending and axial compression and for buckling in the plane of the built-up member, i.e. about the weak axis of the cross-section of the chord (z-z axis), according to


6 - 16

EN 1993-1-1 § 6.3.3. Depending on the geometry of the battened built-up member, the verifications should be performed for different segments of the chord:

For an end panel with the maximum shear force and thus the maximum local bending moment

For a panel located at mid-height where the compression axial force may be maximum in the chord.

3.3.3 Step 3: Out-of-plane buckling resistance of the chords

The out-of-plane buckling resistance is verified using the following criterion:

1Rdy,b,

Edch, N

N

where:

Nb,y,Rd is the design buckling resistance of the chord about the strong axis of the cross-section, calculated according to EN 1993-1-1 § 6.3.1.

The buckling length depends on the support conditions of the built-up member for out-of-plane buckling. At the ends of the member, the supports are generally considered as pinned. However intermediate lateral restraints may be provided.

3.3.4 Step 4: Shear force

The shear force VEd is calculated from the maximum bending moment as for a laced built-up member, according to § 3.2.4 of this guide.

3.3.5 Step 5: Resistance of the battens

As shown in Figure 3.3, the battens should be designed to resist the shear force:

0Ed h

aV

And the bending moment:

2Ed

Ed

aVM

The cross-section classification should be determined according to EN 1993-1-1 Table 5.2, for pure bending. The section resistance should be verified using the appropriate criteria given EN 1993-1-1 § 6.2.

3.3.6 Step 5: Resistance of the batten-to-chord connections

The resistance of the connections between the battens and the chords has to be verified according to EN 1993-1-8. This verification depends on the details of the connection: bolted connection or welded connection. This verification is performed using the internal forces calculated in the previous steps.


6 - 17

3.3.7 Flowchart

Step 2: In-plane buckling resistance of the chords (M-N interaction)

Effective second moment of area Ieff

Loads ULS load combination

Maximum compression force in the chord Nch

Section properties of the chords

Section properties of the battens

Global dimensions Of the built-up member

Start

End

Shear stiffness Sv

Initial bow imperfection e0

Step 3: Out-of-plane buckling resistance of the chords

Step 4: Maximum shear force VEd

Step 5: Section resistance of the battens

Step 6: Design of the batten-to-chord connections

Step 1: Maximum compression axial force in the chords

EN 1993-1-1 §6.4.1(6)

EN 1993-1-1 §6.4.1(1)

EN 1993-1-1 §6.4.3.1(2)

EN 1993-1-1 §6.4.3.1(3)

EN 1993-1-1 §6.3.3

EN 1993-1-1 §6.3.1

EN 1993-1-1 §6.4.1(7)

EN 1993-1-1 §6.2

EN 1993-1-8

Figure 3.4 Flowchart of the design methodology for battened built-up

columns

3.4 Buckling length 3.4.1 Laced compression members

Chords

According to EN 1993-1-1 Annex BB, the buckling length Lcr of a rolled I or H section chord member of built-up columns is taken as 0,9L for in-plane buckling and 1,0L for out-of-plane buckling. These values may be reduced if it is justified through detailed analysis.

L is the distance in a given plane between two adjacent points at which a member is braced against displacement in this plane, or between one such point and the end of the member.

Web members

Angles are mostly used as web members.

Provided that the chords supply appropriate end restraint to web members in compression made of angles and the end connections supply appropriate fixity (at least 2 bolts if bolted), the buckling length Lcr for in-plane buckling is taken as 0,9L, where L is the system length between joints.


6 - 18

When only one bolt is used for end connections of angle web members, the eccentricity should be taken into account and the buckling length Lcr is taken equal to the system length L.

The effective slenderness ratio eff of angle web members is given in EN 1993-1-1 § BB.1.2 as follows:

7,035,0eff

where:

is the non-dimensional slenderness defined in EN 1993-1-1 § 6.3.

For sections other than angles, the web members may be designed for in-plane buckling using a buckling length smaller than the system length and using the non-dimensional slenderness as defined in EN 1993-1-1 § 6.3, provided that the chords provide appropriate end restraint and the end connections provide appropriate fixity (at least 2 bolts if bolted). In practice, the buckling length Lcr of a rolled profile is equal to the distance between joints for in-plane buckling and for out-of-plane buckling.

3.4.2 Battened compression members

For simplicity, any potential restraint at the ends of the columns is neglected and the buckling length of the chords may be taken as the system length.


6 - 19

REFERENCES

1 EN 1993-1-1:2005 Eurocode 3 Design of Steel structures. General rules and rules for

buildings

2 EN 1993-1-8:2005 Eurocode 3 Design of Steel structures. Design of joints


6 - 20


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APPENDIX A Worked Example: Design of a laced built-up column

6 - 22

APPENDIX A. Worked Example: Design of a laced built-up column

1 of 12



1. Introduction

This worked example deals with the verification of a typical built-up column under compressive axial force and bending moment. The calculations are carried out according to EN 1993-1-1. No National Annex is considered and the recommended values of EN 1993-1-1 are used in the calculations.

The calculations are performed according to the design methodology given in Section 3.2 of this guide.

2. Description

The geometry of the built-up column is described in Figure A.1 and in Figure A.2. For the most unfavourable ULS combination of actions, an axial force and a bending moment about the strong axis of the compound section are applied at the top of the column.

1 Lateral restraints

Figure A.1 Design model

The built-up column is restrained against out-of-plane buckling at both ends and at mid-height.

Title APPENDIX A. Worked Example: Design of a laced built-up column 2 of 12

6 - 23

1 Chords HEA 200

2 Posts Angles 90 9

3 Diagonals Angles 80 8

y y

z

z

Figure A.2 Geometry of the built-up column

Section properties

Note that the y-y axis and the z-z axis refer to the strong axis and the weak axis respectively, of the cross-section of each component.

Chords: HEA 220 – S355

ch = 64,3 cm2

iy = 9,17 cm iz = 5,51 cm

Diagonals: Equal angles L 90 × 90 × 9 – S355

Ad = 15,52 cm2

iy = iz = 2,73 cm iu = 3,44 cm iv = 1,75 cm

Posts: Equal angles L 80 × 80 × 8 – S355

Av = 12,27 cm2

iy = iz = 2,43 cm iu = 3,06 cm iv = 1,56 cm


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3. Step 1: Maximum compressive axial force in the chords

3.1. Effective second moment of area

The effective second moment of area of the built-up section about the strong axis is calculated using the following expression:

Ieff = 0,5 h02

Ach

where:

Ach is the section area of a chord

h0 is the distance between the centroids of the chords

EN 1993-1-1 § 6.4.2.1

The value of the effective second moment of area is:

Ieff = 0,5 × 802 × 64,3 = 205800 cm4

3.2. Shear stiffness

For N-shaped arrangement of lacings, the expression of shear stiffness is:

3v

30d3

20d

v

1dAhA

d

ahnEAS

where:

d = 22220 25,18,0 ah = 1,48 m

EN 1993-1-1 Figure 6.9

n is the number of planes of lacings (n = 2)

Ad is the section area of the diagonals

Av is the section area of the posts.

Therefore:

3

3

33

2

v 10

14801227

800155211480

800125015522100002

S

Sv = 134100 kN

3.3. Initial bow imperfection

The initial bow imperfection is taken equal to:

e0 = L/500 = 10000/500 = 20 mm

EN 1993-1-1 § 6.4.1(1)


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3.4. Maximum axial compressive force in the chords

The maximum compressive axial force in the chords, Nch,Ed, is determined at mid height of the built-up column as follows:

Nch,Ed =eff

ch0EdEd

22 I

AhMN

EN 1993-1-1 § 6.4.1(6)

where:

MEd =

v

Ed

cr

Ed

IEd0Ed

1S

N

N

NMeN

Ncr is the effective critical axial force of the built up member:

kN 426501010000

10205800210000²

²

² 32

4eff

cr

L

EIN

The maximum bending moment, including the bow imperfection and the second order effects is:

MEd = kNm 4,481

134100

900

42650

9001

45002,0900

In the most compressed chord, the axial force is:

Nch,Ed = kN 1052102058002

1034,648,04,481

2

9008

4

4. Step 2: In-plane buckling resistance of the chord

4.1. Classification of the cross-section of the chord

= 0,81 for steel grade S355

Flange slenderness: c/tf = 88,5 / 11 = 8,05 < 10 = 8,10 Class 2

Web slenderness: c/tw = 152 / 7 = 21,7 < 33 = 26,73 Class 1

Therefore the cross-section is Class 2 for pure compression.

4.2. Buckling resistance of a chord

The buckling resistance of the most compressed chord is verifed according to EN 1993-1-1 § 6.3.1 for buckling about the weak axis of the cross-section, i.e. about the z-z axis.

The buckling length of a hot-rolled H-section member can be taken equal to 0,9 a for in-plane buckling, where a is the system length between two nodes of the built-up column.


6 - 26

Buckling length of chords:

Lcr,z = 0,9 a = 0,9 × 1,25 = 1,125 m

EN 1993-1-1 BB.1.1(2)B

The slenderness is:

z

zcr,z i

L

where

iz is the radius of gyration of the gross cross-section, about the weak axis.

therefore: 42,201,55

1125z

9,93y

1 f

E With: = 0,81 for steel grade S355

06,7681,09,931

The non-dimensional slenderness is:

268,006,76

42,20

1

zz

Buckling curve c for buckling about the weak axis, since:

Steel grade S355

h/b < 1,2

tf < 100 mm

The imperfection factor is: z = 0,49

EN 1993-1-1 Table 6.2

The reduction factorz can be calculated from the following expressions:

553,0268,02,0268,049,015,02,015,0 22zzzz

965,0268,0553,0553,0

11222

z2

zz

z

EN 1993-1-1 § 6.3.1.2(1)

The design buckling resistance is equal to:

kN 2203100,1

3556430965,0 3

1M

ychzRdz,b,

fA

N

The resistance criterion is:

1477,02203

1052

Rdz,b,

Edch, N

N OK


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5. Step 3: Out-of-plane buckling resistance of the chords

The built-up column is pinned at both ends and is laterally supported at mid-height. Therefore the buckling length for buckling about the strong axis of the chords is taken equal to:

Lcr,y = L/2 =10000/2 = 5000 mm

The slenderness is:

y

ycr,y i

L

where

iy is the radius of gyration of the gross cross-section, about the strong axis.

Therefore:

53,547,91

5000

y

ycr,y

i

L

06,76 9,931

The non-dimensional slenderness is:

717,006,76

53,54

1

yy

Buckling curve b for buckling about the strong axis, since:

Steel grade S355

h/b < 1,2

tf < 100 mm

The imperfection factor is: y = 0,34

The reduction factor y can be calculated from the following expressions:

845,0717,02,0717,034,015,02,015,0 22yyyy

774,0717,0845,0845,0

11222

y2

yy

y

EN 1993-1-1 § 6.3.1.2(1)

The design buckling resistance is equal to:

kN 1767100,1

3556430774,0 3

1M

ychyRdy,b,

fA

N


1595,01767

1052

Rdy,b,

Edch, N

N OK


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6. Step 4: Maximum shear force

The maximum compressive axial force is obtained in the diagonals of the end panels of the built-up column. It depends on the shear force in this panel. The shear force can be assessed by the following expression:

III

MMNe

Ne

LV Ed

EdEdo

EdoEd )4(4

1

where:

L = 10 m

e0 = 0,02 m

NEd = 900 kN IEdM = 450 kNm

IIEdM = 482 kNm

Therefore:

VEd =

45090002,0

90002,0)4(4

10

1 482 = 191,2 kN

7. Step 5: Buckling resistance of the web members in compressive

7.1. Diagonals

7.1.1. Maximum compression axial force

The expression of the compression axial force Nd,Ed in a diagonal is derived from the shear force as follows:

0

EdEdEdd,

cos

nh

dV

n

VN

where:

h0 = 800 mm

d = 1480 mm

n is the number of plans of lacings: n = 2

then:

kN 86,1768002

14802,191Edd,

N


6 - 29

7.1.2. Classification of a diagonal in compression

h/t = 90 / 9 = 10 < 15 = 12,15

(b+h) / (2t) = (90+90) / (2 × 9) = 10 > 11,5 = 9,31 Class 4

Although the cross-section is Class 4, according to EN 1993-1-1 Table 5.2 Sheet 3, the calculation of the effective section area leads to no reduction. The section area is therefore fully effective and the calculation is the same as for a Class 3 Section.

EN 1993-1-1 Table 5.2 Sheet 3

7.1.3. Buckling resistance of a diagonal

The non dimensional slenderness can be calculated according to EN 1993-1-1 § BB.1.2 in so far as the diagonals are welded at both ends and the chords are stiff enough to ensure that the ends are clamped.

Slenderness about the weakest axis:

57,845,17

1480

vv

i

d

Non dimensional slenderness

112,181,09,93

57,84

9,93v

Effective non dimensional slenderness

128,1112,17,035,07,035,0 vveff,

EN 1993-1-1 § BB.1.2

Buckling curve b is used for the determination of the reduction factor:

v = 0,34

Therefore:

294,1128,12,0128,134,015,02,015,0 22veff,veff,v

EN 1993-1-1 § 6.3.1

519,0128,1294,1294,1

11222

veff,2

vv

v

The design buckling resistance of a compression member is equal to:

kN 9,285100,1

3551552519,0 3

1M

ydvRdd,-b

fA

N


162,09,285

8,1761

Rdd,-b

Edd, N

N OK


6 - 30

7.2. Posts

7.2.1. Maximum compressive axial force

The maximum compressive axial force is:

Nh,Ed = VEd = 191,2 kN

7.2.2. Classification of the cross-section

h/t = 80 / 8 = 10 < 15 = 12,15

(b+h) / (2t) = (80+80) / (2 × 8) = 10 > 11,5 = 9,31 Class 4

Although the cross-section is Class 4, according to EN 1993-1-1 Table 5.2 Sheet 3, the calculation of the effective section area leads to no reduction. The section area is therefore fully effective and the calculation is the same as for a Class 3 section.

EN 1993-1-1 Table 5.2 Sheet 3

7.2.3. Buckling resistance

The buckling length is equal to:

Lcr = h0 = 800 mm

Slenderness about the weakest axis:

28,516,15

800

v

yh,v

i

L

Non dimensional slenderness:

674,081,09,93

28,51

9,93v

v

Effective non dimensional slenderness:

822,0674,07,035,07,035,0 vveff,

EN 1993-1-1

§ BB.1.2

The buckling curve b is used for the determination of the reduction factor:

= 0,34

Therefore:

943,0²822,02,0822,034,015,02,015,02

veff,veff, v

712,0822,0943,0943,0

11222

veff,2

vv

v

The design buckling resistance of a compression member is equal to:

kN 310100,1

3551227712,0 3

1M

yhvRdb,

fA

N


6 - 31


162,0310

2,191

Rdb,

Edh, N

N OK

8. Step 6: Resistance of the web members in tension

It is necessary to verify the resistance of the diagonals in tension, even if this situation is generally less critical than compression.

The verification of these members includes the verification of the resistance of the cross-section and the verification of the resistance of the net section for bolted connections.

Maximum design value of the tensile axial force:

Nt,Ed = 176,8 kN


0,1 Rdt,

Edt, N

N

EN 1993-1-1 §6.2.3

The design tension resistance Nt,Rd is taken as the design plastic resistance of the gross cross-section:

kN 551100,1

3551552 3

M

y dRdpl,Rdt,

0

fA

NN


0,132,00,551

8,176

Rdt,

Ed N

N OK


6 - 32

9. Step 7: Resistance of the diagonal-to-chord welded connection

The diagonals (L90 90 9) are welded to the chord (HEA 220) by fillet welds, see Figure A.3.

L90x90x9

26

64

3

150

HEA 220

NEd

Figure A.3 Welded connection of a diagonal to the chord

Throat thickness: a = 3 mm

Effective longitudinal length of the fillet weld: leff-L = 150 mm

Effective transverse length of the fillet weld: leff-T = 90 mm

Axial force in the diagonal: Nd,Ed = 176,8 kN

The design resistance of a fillet weld is determined using the simplified method given in EN 1993-1-8 § 4.5.3.3.

At every point along the length of the fillet weld, the resultant of all the forces per unit length transmitted by the weld should satisfy the following criterion:

Rdw,Edw, FF

where:

Fw,Ed is the design value of the force per unit length

Fw,Rd is the design weld resistance per unit length

The design resistance is independent of the orientation of the weld throat plane and it is determined from:

Fw,Rd = fvw,d a

where:

fvw,d is the design shear strength of the weld

2M

udvw,

3/

w

ff

EN1993-1-8

§ 4.5.3.3


6 - 33

fu is the ultimate tensile strength of the weaker part:

fu = 510 N/mm2

w is the appropriate correlation factor:

w = 0,9 for steel grade S355

M2 = 1,25

EN 1993-1-1

Table 3.1

EN1993-1-8

Table 4.1

therefore:

N/mm 3,453901502

176800

N/mm 2,78557,261

N/mm 7,26125,19,0

3/5103/

eff

Edd,Edw,

dvw,Rdw,

2

2Mw

udvw,

l

NF

afF

ff

Therefore:

Fw,Ed = 453,3 N/mm2 < Fw,Rd =785,2 N/mm2 OK

The minimum throat thickness amin = 3 mm is acceptable.

To prevent corrosion, the diagonal may be welded all around in one pass (a = 3 mm).

To account for eccentricity a 5 mm (2 passes) throat fillet weld is recommended on the unconnected leg side, as shown in Figure A.4.

a = 5 mm

a = 3 mm

Figure A.4 Throat thickness of the weld fillets



Part 7: Fire Engineering



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7 - iii

FOREWORD

This publication is the seventh part of the design guide, Single-Storey Steel Buildings.




Part 3: Actions













7 - iv


7 - v

Contents Page No

FOREWORD iii

SUMMARY vi

1 INTRODUCTION 1

2 FIRE RISKS IN SINGLE-STOREY BUILDINGS 2 2.1 Fire safety objectives 2 2.2 Fire risk analysis 2 2.3 Main requirements of current fire regulations 3

3 PRACTICAL FIRE ENGINEERING OPTIONS IN THE EUROCODES 6 3.1 Current design approaches 6 3.2 Fire analysis 7 3.3 Heat transfer analysis 8 3.4 Structural analysis 8

4 GUIDANCE ON APPROPRIATE FIRE ENGINEERING SOLUTIONS 10 4.1 Field of application of different design methods 10 4.2 Choice of optimum design approach 11

5 DIRECT USE OF SIMPLE ENGINEERING OPTIONS FOR USE BY NON SPECIALISTS 12 5.1 Fire models 12 5.2 Thermal Models 16 5.3 Structural Models 21 5.4 Specific design rules for single-storey buildings 31 5.5 Simplified design methods 33 5.6 Design recommendations 37

6 GUIDANCE ON THE USE OF MORE ADVANCED SOLUTIONS 47 6.1 Fire models 47 6.2 Thermal Models 50 6.3 Structural models 51

REFERENCES 56

APPENDIX A German fire safety procedure for single-storey industrial and commercial buildings 57


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SUMMARY

This document provides guidance for the fire design of single-storey steel building structures. It contains detailed information to allow engineers and designers to be more familiar with the current design approaches and calculation models, which can be applied not only to meet the prescriptive requirements but also to develop the performance-based fire safety design. The design methods introduced in the guide, ranging from simple design rules to more sophisticated calculation models, are derived from EN 1993-1-2 and 1994-1-2. They cover both steel and composite structures (unprotected or protected). In addition, some specific design rules are given, allowing simple verification of whether the behaviour of the steel structure of single-storey industrial buildings in fire situation fulfils the safety objectives on the basis of performance-based requirement.


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1 INTRODUCTION

Due to the particularities of single-storey buildings, the life safety objective in case of fire can be met easily without onerous fire resistance requirement for the structure. However, other safety objectives have to be taken into account if the collapse of these buildings or a part of them may be accepted. In consequence, many European fire safety building regulations are moving toward acceptance of alternative fire safety engineering designs. Prescriptive rules can then be replaced with performance based requirements, such as adequate fire behaviour of the structure, aimed at satisfying fire safety objectives that include life safety of people (occupants and fire-fighters), protection of environment, property protection and business continuity. Benefits and successful application of the performance-based approach to building fire safety designs have already been well demonstrated for single-storey buildings, especially where fire resistance was required, allowing in some cases more innovative, cost effective and safer solutions to be adopted.

To help the structural fire design of buildings, a new set of European Standards has been developed, the Eurocodes. The Parts of the Eurocodes that are relevant to the fire design of single-storey building consist of EN 1991-1-2[1] (which includes principal concepts and rules necessary for describing thermal and mechanical actions on structures exposed to fire) and Parts of material –specific Eurocodes dealing with the fire design of structures, such as EN 1993-1-2,[2], related to steel structures and EN 1994-1-2[3] related to composite steel and concrete structures.

The fire parts of Eurocodes provide at present a wide range of calculation methods. They allow engineers to follow either a prescriptive approach to meet the fire safety requirements, as specified in national building regulations, or to carry out on the basis of performance-based rules, a fire safety engineering design that involves in general more complex computational analysis and provides more accurate answers to fire safety objectives.

The present guide provides an overview of the current design methods available for evaluating the fire performance of single-storey buildings composed of either steel or composite structure as well as their application fields. Simple calculations methods, easy to use, and more advanced calculations models are dealt with separately. Moreover, to allow quick assessment, simple design rules are given to assess quickly whether the structural behaviour of steel structures of storage and industrial buildings fulfils the fire safety objectives required by the fire safety regulations for industrial buildings.

This guide aims also to help the engineer to understand more clearly the different calculation methodologies and to carry out the structural fire design of single-storey building according to the Eurocodes, from a relatively simple analysis of single members under standard fire conditions to a more complex analysis under real fire conditions.


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2 FIRE RISKS IN SINGLE-STOREY BUILDINGS

2.1 Fire safety objectives The primary objective of most fire safety regulations is to ensure the protection of life (building occupants and fire fighters), environment and to some extent property (building contents and building itself). Through a lot of measures including a combination of active and passive fire protection systems, the objectives are:

To reduce and prevent the incidence of fire by controlling fire hazards in the building.

To provide safe escape routes for evacuation of building occupants.

To prevent fire spread from the fire compartment to others parts of the building and to neighbouring buildings.

To ensure that the building remains structurally stable for a period of time sufficient to evacuate the occupants and for the fire-fighters to rescue occupants, if necessary.

2.2 Fire risk analysis Single-storey buildings used as factories, warehouses or commercial centres constitute a very common type of steel construction today. In the specific case of warehouses, according to the storage arrangement (including free standing storage, palletised rack storage, post-pallet storage or storage with solid or slatted shelves) and the combustibility of materials being stored, fire may develop very quickly and then might endanger occupants long enough before the structural collapse of the building. Indeed, fire growth may be extremely important, as the upward flame propagation is usually very rapid. Vertical and horizontal shafts formed between adjacent pallets and racking behave as chimneys, which increase the spread of flames up to the roof. The smoke quickly forms a hot layer under the roof and then descends progressively with fire development. Obviously, the rate at which this occurs varies according to the combustible contents and the building arrangement. In unventilated conditions, single-storey buildings can become smoke-logged in few minutes. Although the smoke is largely made up of ‘entrained’ air, it contains enough toxic substances and asphyxiates to incapacitate or kill within minutes people exposed to them. Moreover, the hot smoke layer will also radiate high heat flux to people escaping from fire area. A hot gas layer at 500°C leads to a heat flux of about 20 kW/m² (corresponding to the radiant energy emitted by a blackbody at the temperature of 500°C) and, under such thermal conditions, skin burn will occur after only a few seconds4. Generally, it is agreed that the tenability threshold is 2.5 kW/m2, which is much lower than heat flux needed to lead to the failure of structural members. Consequently, buildings will survive longer than occupants and the structural collapse of steel structures of single-storey buildings generally does not provide additional threat to people escaping from the fire area.


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Regarding fire service operations, it is commonly accepted that fire-fighters should not enter a single-storey building because of fast fire growth. Usually they are forced to fight the fire from outside, covering neighbouring walls with water. Hazard in this case for fire-fighters is then reduced to zero in the event of structural collapse since it occurs at a level of temperature at which fire-fighters can not withstand (provided that the progressive collapse, in the case of compartmented buildings, and the collapse of the structure toward outside do not occur[5,6]). In the event of, at the beginning of fire, they need to enter within the building to rescue people, they cannot last within the building after the heat flux is more than 7 kW/m², which is also very far for the risk of collapse of the structure.

For these reasons, an increase of the intrinsic fire resistance of single-storey buildings is unnecessary. However, the overall stability of the structure and the stability of fire walls need to be accurately considered, to avoid any progressive collapse. A single-storey building undergoes progressive collapse when local failure of the heated part of the structure leads for the failure of adjoining cold structures. In addition, to provide a safe situation to fire-fighters located around the building, the structure of single-storey building (including façade elements) must collapse towards the inside of the building.

Many National Regulations have taken into account previous remarks for industrial single-storey buildings as well as for public buildings by not requiring any fire resistance rating for such works but introducing specific safety requirements in terms of overall structural behaviour and concentrating requirements on egress facilities and early fire detection and/or suppression.

With regards to other single-storey buildings with relatively low fire loads, the risk of life in the event of fire is reduced as egress of occupants and fire-ground operations are straightforward.

2.3 Main requirements of current fire regulations 2.3.1 Fire resistance of structural members

Despite the comments above, fire resistance ratings are sometimes required for the structure of single-storey buildings[7].

The fire resistance is expressed as the time during which a building element can withstand exposure to fire without losing its function (load-bearing elements or separating element). Usually, building elements are classified using three performance criterion:

The load bearing capacity, R, which is the ability for a load-bearing element to resist a fire without losing its structural stability

The integrity, E, which is the ability of a separating element, when exposed to fire on one side, to prevent the passage through it of flames and hot gases

The insulation, I, is the ability of a separating element, when exposed to fire on one side, to restrict the temperature rise on the unexposed face below specified levels (in general a average value of 140°C).


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In prescriptive fire regulations, required fire resistance for a building element is expressed in terms of the minimum period of time during which the building element would function satisfactorily while subject to the standard fire.

When fire stability requirements are given for single-storey buildings, they usually range from 15 minutes (R15) to 60 minutes (R60), depending on the occupancy class of the building, the provision of sprinklers, the building height and the compartment size.

2.3.2 Compartmentation and building separation

Single-storey building must be subdivided into compartments separated by fire walls when the floor area of the building exceeds the allowed maximum compartment size. Limits on the compartment size may be removed by fitting the building with sprinklers.

The effects providing compartmentation on property loss is that direct damage is confined to the content of the compartment in which the fire starts, reducing the chances of the fire growing large. As regards the life safety, people in other parts of the building can use escape routes to get out safely without being exposed to the smoke or gases from the fire.

When considering fire walls between compartments, fire resistance is generally in the range of REI 60 to REI 120.

Fire spread to neighbouring buildings also needs to be prevented. This is achieved traditionally by sufficient separating distances or façade elements with adequate fire resistance. In the French research project Flumilog, a design method has been recently developed to assess the thermal radiant effects of fires in single-storey storage buildings. The method allows calculation of the safe separating distances, taking into account the main characteristics of the building, such as the building content, the type of façade elements and roof, etc.

2.3.3 Fire suppression

Sprinklers may be required by national fire regulations. In addition to their obvious effect in the reduction of the fire growth, their use leads usually to a reduction of the fire resistance rating required for the structure. They allow also larger fire compartment sizes.

2.3.4 Smoke control systems

National fire regulations may require that smoke control systems are implemented in public buildings, storage building and industrial buildings in order to facilitate escape, by minimising risks of smoke inhalation and injury and to some extend to enable fire-fighters to better see the fire and therefore to extinguish it more speedily and effectively. Smoke control systems help in removing smoke from the fire area, and in limiting the spread of hot gas beneath the roof, which increases the time for the compartment to become smoke-logged, giving people more time to escape safely from the building. This can be achieved by a combination of smoke exhaust systems (mechanical or natural) and screens (which contain the smoke in specific areas).


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2.3.5 Fire detection and fire alarms

Adequate measures are necessary for detecting any outbreak of fire and for alerting the building occupants and the fire department of the occurrence of fire. In small single-storey buildings where all exits are visible, it is likely that any fire will be quickly detected by the occupants and a shout of ‘Fire!’ may be sufficient. In larger single-storey buildings, a simple sounder such as a battery powered alarm or rotary bell may be adequate. In an industrial building, the ambient noise has to be considered, to ensure that the alarm will be heard by the occupants.

2.3.6 Egress facilities

For safe evacuation, appropriate means of escape are needed, such as a proper number and width of emergency exits and proper length, width and height of passages and evacuation accesses. Escape routes in small single-storey buildings generally lead directly to a safe location outside the building; they do not normally require any special treatment. In larger buildings, where travel distances are greater and where the fire is likely to make a single escape routes unusable, an alternative means of escape may be necessary. Consideration of disabled people must also be made


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3 PRACTICAL FIRE ENGINEERING OPTIONS IN THE EUROCODES

3.1 Current design approaches Using the fire parts of Eurocodes[8,9], single-storey buildings can be designed using either the prescriptive approach or the performance-based approach applying fire safety engineering principles[10].

The prescriptive approach is mostly applied to fulfil standard fire resistance requirements usually prescribed in national fire regulations. It gives a safety level that is relatively easy to achieve and implement. However it may be conservative, in requiring the use of important passive fire protection to fulfil the required fire resistance rating. This approach is usually carried out for the design of relatively simple buildings and structures.

As an alternative or when allowed by national regulation, the performance-based approach can allow to assess adequate measures to satisfy a set-out of defined fire safety objectives, such as stated in paragraph 2.1, and the corresponding performance criteria. Using structural fire engineering, engineers can assess the necessary fire resistance to structure in order to avoid the spread of fire and/or to prevent a premature structural collapse. As regards the single-storey buildings, the main structure could be designed to remain stable under fire exposure conditions long enough for the occupants to escape. Such an approach takes into account the severity of fire exposure by appropriate estimations of actual fire loads and fire development parameters, which may be calculated from the building activity.

The performance-based approach provides flexibility when selecting technical solutions to meet the fire safety objectives, but usually requires the use of sophisticated design tools. Engineers and designers using advanced calculations models need to be properly educated in their use and in their limitations. As fire safety engineering allows for highly efficient designs, with little unassigned reserve capacity, an experienced user is required to ensure that appropriate models are used.

Where national fire regulations authorise the performance-based approach, regulatory bodies may require that the fire design is checked by a third party.

The fire performance of a whole structure, or a part of it, is carried out by following, for a given design fire scenario, three successive steps of structural fire engineering[1].

Fire Analysis. To calculate the thermal actions/exposure - Fire models.

Thermal analysis. To determinate the heating rate and temperatures on structural members - Thermal models.

Structural analysis. To calculate the mechanical response of structural members- Structural models.


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Available design methods to evaluate the fire performance of structure are briefly described below. These methods range from simple hand calculations to the use of sophisticated computer models. The overall complexity of the fire safety design will depend on the assumptions and methods adopted to predict each of the three design steps.

3.2 Fire analysis The main objective of the fire modelling is the simulation of the fire development and the prediction of thermal actions (gas temperature, heat flux) on the structural members (in order to determinate, in a following step, the temperature in the structural members).

Although common practice is to represent a fire by a standard fire curve, structural fire design may be based on a design fire that provides more realistic conditions in fire compartment. In this way, parameters such as the magnitude of the fire load, the rate of heat release and the ventilation factor, which play an important role in fire severity, are taken into account. Moreover, the identification of relevant and realistic design fire scenarios is a crucial aspect of the fire safety design. The design fire scenarios used for the analysis of a building fire have to be deduced from all the possible fire scenarios. In most buildings, the number of possible fire scenarios is infinite and need to be reduced. Only ‘credible worst case’ fire scenarios will need to be studied. When the design fire scenarios are chosen, a number of fire models are available to assess the fire severity and calculate the corresponding thermal actions

Different levels of fire models are relevant to the various stages of fire development. When a fire is initiated, it is localised within a compartment and, according to the characteristics of the compartment and of the fire load, it can remain localised or becomes generalised to the whole compartment. In the case of small compartments or compartments with small ventilation openings relative to the size of the compartment, the fire develops into to a fully engulfed fire.

Three levels of modelling are available to describe both localised and fully generalised fires, as shown in Table 3.1.

Table 3.1 Levels of fire models

Levels of the model Localised fire Generalised fire

Simplified model Hasemi model Heskestad model

Parametrical fires

Zone models 2 zone model 1-zone model

Field model CFD CFD

The simplified models are generally empirical models based on conventional assumptions. The zone models take into account the main parameters controlling the fire, but introduce simplified assumptions that limit the domain of application. They would be used in simple easily defined compartment geometries. The field models are more accurate but are rather complex for use


7 - 8

as a general design tool; they would be required in compartments with complex geometries or with high and irregular ceilings.

Conditions of use will be briefly detailed in Chapter 6.

3.3 Heat transfer analysis Once the thermal actions are calculated, the thermal transfer to the structural elements has to be calculated. Thermal models, which will be used, should be based on the acknowledged principles and assumptions of the theory of heat transfer.

Different modelling can be used according to the assumptions and needs. In the thermal models, there are the analytical rules allowing obtaining an estimation of uniform temperature across-section, mainly for steel elements. There are also advanced calculation methods based on either finite elements or the finite difference method, allowing determination of the 2D or 3D temperature distribution in structural members (through the cross-section and along the length). Advanced models can be applied for any type of structural member analysis in fire design.

Thermal models will be briefly detailed in following chapters.

3.4 Structural analysis From the temperature fields previously obtained in the structural members and from the combination of the mechanical actions loads in case of fire the structural behaviour can be assessed following one of the three possible approaches:

Member analysis, in which each member of the structure will be assessed by considering it fully separated from other members. The connection condition with other members will be replaced by appropriate boundary conditions.

Analysis of parts of the structure, in which a part of the structure will be directly taken into account in the assessment by using appropriate boundary conditions to reflect its links with other parts of the structure

Global structural analysis, in which the whole structure will be used in the assessment


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Member analysis

Analysis of part of the structure Global structural

analysis Figure 3.1 Different design approaches for mechanical response of

structures in fire

Member analysis is easy to use particularly with simplified calculation methods and therefore largely used under standard fire condition. The analysis of the whole structure or its subassemblies considers at least several structural members together, so that the interaction effect between them will be directly dealt with. In this way, load redistribution from heated parts (weakened parts inside fire compartment) to cold parts (stronger parts outside fire compartment) can be taken into account in accurate way and global analysis provides therefore a much better understanding of overall behaviour of structure under fire condition.

According to the Eurocodes, three types of design methods can be used to assess the mechanical behaviour of structures under fire situation in the different design approaches explained above. Fire design can be carried out by means of:

A simple calculation method, based on predefined tabulated data, as given in EN 1994-1-2[3]. This method is only applicable to steel and concrete composite structures. The tables were evaluated by numerical models and experiments for basic types of structures, such as slabs, beams and columns, for certain time of fire resistance, for heating according to the nominal fire curve and for defined level of loading. The tables are easy to use and safe but cover only a limited range of section types.

Simple calculation models. This type of design method can be divided into two different families. The first one is the critical temperature method widely applied to steel structural member analysis. The second is the use of simple mechanical models (verification in strength domain) developed for both steel and composite structural member analysis. Models have been developed for standard structural elements, e.g. slabs, beams, and columns.

Advanced calculation models. This kind of design method can be applied to all types of structures and the models are, in general, based on either finite element method or finite difference method. They should provide a realistic analysis of structures. The results of the analysis are generally obtained in terms of deformation of structure during the whole fire period.

Structural models will be briefly detailed in following chapters.


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4 GUIDANCE ON APPROPRIATE FIRE ENGINEERING SOLUTIONS

4.1 Field of application of different design methods The following table shows the field of application of the available fire design methods, considering either design according to prescriptive requirements based on the standard fire or a performance-based fire design[11]. Table 4.1 Field of application of different design methods

Approach Tools Thermal actions

Thermal modelling

Structural modelling

Pre-engineered data from standard fire tests (Data from manufacturers)

Tabulated data from EN 1994-1-2

EN 1994-1-2, §4.2

Steel EN 1993-1-2 §4.2.5

Steel EN 1993-1-2 §4.2.3 §4.2.4

Simplified calculation models given in Eurocodes

Composite EN 1994-1-2 §4.3

Steel and composite

Pre

scrip

tive

appr

oach

(S

tand

ard

fire

desi

gn)

Advanced calculation models

Standard ISO curve

EN 1991-1-2

FEA* or FDA** FEA*

Simplified calculation models

Fully engulfed fire (Parametric fire, standard ISO curve***)

Localized fire

Steel EN 1993-1-2 §4.2.5

Steel EN 1993-1-2 §4.2.3 §4.2.4

Specific rules based on fully engulfed fire §5.4

Steel and composite

Per

form

ance

bas

ed a

ppro

ach

(n

atur

al f

ire d

esi

gn)

Advanced calculation models

Zone models

Field models FEA* or FDA** FEA*

*FEA : Finite element Analysis **FDA : Finite Difference analysis

*** Collapse of single-storey buildings usually occurs when the building structure (a part of it or the whole structure) is fully engulfed in fire. In such fire condition, because the gas temperature rise has no significant effect on the failure mode of the building structure, a performance-based approach referring to thermal actions based on standard fire curve is appropriate to investigate the fire behaviour of single-storey buildings. This approach can be used to demonstrate the non-progressive collapse and the failure inwards of the building structure.


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4.2 Choice of optimum design approach The choice of the design approach depends on the type of building (storage building, industrial building, commercial building, etc.), the requirements specified in the corresponding national fire regulation and the acceptance or not by the regulatory authorities of applying a performance-based approach as an alternative to prescriptive rules.

Some suggestions on the choice of fire design approach are given below.

With the diversity of requirement, the most important first step is to answer the following:

What is the required fire resistance rating, if any?

Is it possible to carry-out a performance-based approach?

When a prescriptive approach is to be used (with reference to standard fire design):

It may be appropriate to use simplified calculation models where low fire resistance ratings (R15 or R30) are required for structural members

Advanced calculation models must be used where structural members are not covered by the simplified calculation models. They can also be employed with some economic benefits for steel structure where high fire resistance ratings (higher than R60) are required, reducing the thickness of fire protection on steel members.

Where the performance-based approach is accepted by the regulatory authorities and structural stability is needed:

A performance-based approach is most likely to be beneficial where the structure is unusual and may not be well covered by traditional prescriptive methods

Localised fire protection may be needed, considering the overall behaviour of the whole structure in a real fire, to ensure adequate life safety for the building occupants and firemen.

National fire regulations may require the use of the performance based approach for single-storey buildings with significant fire risks (high fire loads).

National fire regulations may allow a performance-based fire safety design to refer to simple rules and design recommendations for single-storey buildings. Such approaches are given in §5.4 and Appendix A. Other design guidance and recommendations can be found in reference[12].

Active fire protection measures (installation of sprinklers, fire detectors, fire alarms, smoke exhaust systems) and passive fire protection measures (compartmentation, egress facilities, etc.) are usually implemented in buildings in accordance with the requirements in fire national regulations.


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5 DIRECT USE OF SIMPLE ENGINEERING OPTIONS FOR USE BY NON SPECIALISTS

This chapter gives an overview of current easy-to-use ‘simple’ calculation design rules, for assessing the fire resistance of steel and composite steel and concrete structural members.

Specific simple design rules and design recommendations to satisfy specific safety requirements in terms of structural behaviour introduced recently in fire safety regulations of many European countries for single-storey storage and industrial buildings are given. It is noted that these methods are also applicable to other type of single-storey buildings.

5.1 Fire models 5.1.1 Nominal temperature-time curves

EN 1991-1-2[1] provides three standard fire curves, defining arbitrary hot gas temperature-time relationships in which no physical parameters of the fire load or fire compartment are taken into account. The most commonly used relationships in building design and in regulation prescriptions is the standard temperature-time curve (standard ISO fire) which represents a fully developed compartment fire. The second curve, the external fire curve, is intended for façade elements and the third curve is the hydrocarbon fire curve, representing a fire with hydrocarbon or liquid type fuel.

The nominal temperature-time curves are defined as follows:

For standard temperature-time curve (standard ISO fire ):

)18(log34520 10 tg (1)

For the external fire curve:

20)313,0687,01(660 8,332,0g tt ee (2)

For the hydrocarbon fire curve:

20)675,0325,01(1080 5,2167,0g tt ee (3)

where:

θg is the gas temperature in the fire compartment [°C]

t is the time [min]

It is important to note that the previous curves are reference curves. They do not represent the real thermal effect of a fire. The temperatures given by these curves always increase with time, without considering the limited fire load. The standard fire resistance rating required for structural members (expressed in terms of time) does not therefore indicate the actual time for which they will survive in a building fire.


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5.1.2 Parametric fires

Parametric fire models provide a rather simple design method to estimate gas temperature in fire compartment, taking into account in a simplified way the main parameters that influence the fire development, such as the fire compartment size, the fire load (corresponding to the mass of combustible materials in the fire compartment), ventilation conditions (openings) and thermal properties (such as thermal conductivity and specific heat) of the compartment walls and ceilings.

Like nominal temperature-time curves, parametric temperature-time curves provide gas temperature-time relationships for design. They are based on the hypothesis that the temperature is uniform in the compartment, which limits their field of application to post-flashover fires (fires generalised to the whole compartment) in compartments of reasonable dimensions. The predicted fire curve comprises a heating phase represented by an exponential curve up to a maximum temperature, followed by a linearly decreasing cooling phase to a residual temperature that is usually the ambient temperature. The maximum temperature and the corresponding fire duration are the two main parameters affecting the fire behaviour of structural members. Consequently, they were adopted as the governing parameters in the design formulae for the parametric fires.

Such a model is given in Annex A of EN 1991-1-2. It is valid for compartments up to 500 m² of floor area, without openings in the roof, and a maximum compartment height of 4 m, for compartment linings with thermal inertia between 100 and 2200 J/m2s1/2K, for an opening factor in the range 0,02 to 0.20 and for compartments with mainly cellulosic type fire loads. Due to these limitations, the model is mainly used for the office part of single-storey buildings.


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Time

g

max

t*max

heating phase

cooling phase

g=20+1325(1-0,324e-0,2t*-0,2e-1,7t*-0,427e-19t*)

with t*= t.C where t is the time (hours) and )²1160/04.0/(]²b/O[R

Main parameters:

- Wall characteristics : thermal inertia cb

- Opening characteristics: opening factor tv A/hAO

max= g (t*max) = g (tmax . ) (°C)

with tmax = max{ (0.2.10-3 qt,d / O). / O, tlim } (hours)

where tlim is a function of fire growth rate (according to building type):

- tlim =25 min if slow fire growth rate

- tlim =20 min if medium fire growth rate,

- tlim =15 min if fast fire growth rate,

- qt,d is the design value of the load density [MJ/m²]

g = g (t*, t*max, x) (°C)

= max – 625.(t* - t*max.x) if t*max 0,5

= max – 250.(3- t*max).(t* - t*max.x) if 0,5 < t*max 2

= max – 250.(t* - t*max) if t*max > 2

with t*= t. t*max = (0.2.10-3 qt,d / O).

and x is a function of tmax as follows:

x = 1 if tmax > tlim

x = tlim. / t*max if tmax = tlim

Figure 5.1 Parametric Fire (Annex A of EN 1991-1-2)

The inputs for the parametric fire curves are the design fire load density, the fire growth rate, the ventilation conditions (described by the size and the position of the openings) and the thermal properties (heat capacity, the density and the conductivity) of walls to evaluate the heat losses which occur by convection and radiation at the compartment boundaries. For the fire load density, it is common practice in design to refer to the characteristic values given in EN 1991-1-2.

Even though these parametric fire curves offer a significant improvement compared to the standard “ISO-fire”, the parametric fires are not yet able to provide a very accurate evaluation of the fire severity. Consequently, some European countries recommend their use only for pre-design calculation.

5.1.3 Localised fire

EN 1991-1-2 provides simple approaches for determining thermal actions of localised fires in Annex C. Two situations are distinguished according to the height of the fire flame relative to the ceiling of the compartment: where the flame is not impacting the ceiling (based on Heskestad’s method); and where the flame is impacting the ceiling (based on Hasemi’s method).


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Flame axis

L

z D

f

H

Z0 = 1,02 D + 0,00524 Q2/5

z0

Flame axis

L

z D

f

H

Z0 = 1,02 D + 0,00524 Q2/5

z0

Flame axis Lh

D

H

r

Flame axis Lh

D

H

r

The flame is not impacting the ceiling The flame is impacting the ceiling

Required data: - Rate of heat realase: Q (W) - Distance fire Source-ceiling: H (m) - Diameter of the fire: D (m)

Results:

- Flame length Lf (m) :

Lf = -1,02 D + 0,0148 Q2/5

-Temperature (z) in the plume along the symmetrical vertical axis:

(z) = 20 + 0,25 (0.8Q)2/3 (z-z0)-5/3

(z) 900°C

Results:

- Horizontal flame length Lh

- heat flux received by the fire exposed unit surface area at the level of the ceiling at the distance r from the flame axis: h = 100000 if y 0,30

h = 136300-121000 y if 0,30 < y < 1,0

h = 15000 y-3,7 if y 1,0

with

'

'

h zHL

zHry

where

r: is the distance from the flame axis to the point where the thermal flux is calculated (m)

z: is the vertical position of the virtual heat source (m)

D: is the diameter of the fire (m)

Figure 5.2 Localised Fires (Annex C of EN 1991-1-2)

For situations where the fire is not impacting the ceiling, a design formula is given to calculate the temperature in the plume at heights along the vertical flame axis. For situations where the fire is impacting the ceiling, some simple steps are given to calculate the heat flux received by the fire-exposed surfaces at the level of the ceiling.

These models are most often used to calculate thermal actions (expressed in terms of heat flux resulting from a radiation part and a convection part) on horizontal structural members, such as beams. At the present time, no method is available for vertical steel members affected by a localised fire.

The input data are the rate of heat release (RHR), the distance between the fire source and the ceiling, and the diameter of fire. The RHR is usually determined by using EN 1991-1-2 section E.4.

These approaches are limited to cases where the diameter of fire D is less than 10 m and the rate of heat release of fire Q is less than 50 MW.


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5.2 Thermal Models Considering the high thermal conductivity of steel and the small thickness of steel profiles commonly used in the construction, it is sufficiently accurate to ignore thermal gradients within the cross-section of structural members and assume a uniform temperature when uniformly heated.

Consequently, simple design equations can be used to predict the temperatures of steel members that are fully exposed to fire or steel members that support a concrete slab and are exposed on three sides. Similar rules exist for fire-protected steel sections, although the thermal properties of the proposed protection material are needed, which can be difficult to obtain.

For the composite steel-concrete members, strictly speaking, there are no simplified models to estimate the evolution, as a function of time, of temperature distribution through members. To simplify the design, information on temperature distribution at current time of standard fire exposure (i.e. 30, 60, 90 and 120 minutes) is given in EN 1994-1-2.

5.2.1 Unprotected steel member

Heating of the unprotected steel members can be determined by means of the simple analytical approach given in EN 1993-1-2. In this method, the temperature rise depends on the thermal actions (expressed in terms of net heat fluxes), the thermal properties of the steel and the section factor of the element Am/V defined as the ratio between the surface area exposed to the heat flux Am [m²/m] and the volume of the element by unit length V [m3/m]. The section factors for some unprotected steel members are shown in Figure 5.3.

b

h

t t

t

Am/V=Perimeter exposed to fire /Cross-section area Am/V=1 / t Am/V=2 / t

Figure 5.3 Example of section factor for unprotected steel members

Assuming an equivalent uniform temperature distribution in a cross-section, the increase of temperature a,t in an unprotected steel member during a time interval t may be determined from:

thc

/VAk dnet,aa

mshta,

with t 5 s (4)

where:

shk is the correction factor for the shadow effect caused by local

shielding of radiant heat transfer due to shape of steel profile

aC is the specific heat of steel [J/kgK]


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a is the unit mass of steel [kg/m3]

h dnet, is the net heat flux per unit area [W/m²]

Solving the incremental equation step by step gives the temperature development of the steel element during the fire. In order to assure the numerical convergence of the solution, some upper limit must be taken for the time increment t. In EN 1993-1-2, it is suggested that the value of t should not be taken as more than 5 seconds.

The thermal actions are determined by the net heat flux rnet,h absorbed by the

steel member during the fire exposure. It is expressed in terms of the hot gas

temperature as the sum of two distinct fluxes: a convective component cnet,h

and a radiant component rhnet, .

Convective heat flux is expressed as:

)( mgccnet, h (5)

where:

c is the coefficient of heat transfer by convection [W/m²K]

g is the gas temperature [°C]

m is the surface temperature of the member [°C]

Radiant heat flux is given by:

)273)()273(( 4m

4rm0rnet, h (6)

where:

is the configuration factor, including position and shape effect (<1)

m is the surface emissivity of the member

r is the radiation temperature of the fire environment [°C] (r ≈ g)

m is the surface temperature of the member [°C]

0 is the Stephan Boltzmann constant [= 5,67 10-8 W/m2 K4]

According to EN 1991-1-2, for many practical cases the configuration factor may be taken equal to unity. The coefficient of convection ( c ) varies from

25 W/m²K (standard fire conditions) to 50 W/m²K (hydrocarbon fire conditions). The emissivity of carbon steel and composite steel and concrete members may be taken as 7,0m .


7 - 18

For cross-section with a convex shape, such as hollow steel sections, fully embedded in fire, the shadow effect does not play a role and it can be taken that ksh = 1. Otherwise, the correction factor for the shadow effects ksh is given by:

casesothersfor

actions fire nominalunder sections-Ifor

/

]/[/

]/[9,0

m

bm

m

bm

sh

VA

VAVA

VA

k (7)

where:

bm ]/[ VA is the box value of the section factor [m-1].

Application of the EN 1993-1-2 calculation method with standard ISO fire exposures of 15 and 30 minutes leads to the temperature curves illustrated in Figure 5.4 and given in Table 5.1 as function of the section factor including shadow effect (Am/V)sh = ksh Am/V.

Figure 5.4 Temperature of unprotected steel members after 15 and

30 minutes of standard ISO fire exposure

0

100

200

300

400

500

600

700

800

900

0 50 100 150 200 250 300 350 400 450 500(Am/V) sh= k sh (Am /V) (m -1)

Temperature (°C)

15 minutes

30 minutes

10


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Table 5.1 Temperature of unprotected steel members after 15 and 30 minutes of standard ISO fire exposure

Steel temperature (°C) Steel temperature (°C) Section factor

(Am/V)sh 15 min 30 min

Section factor

(Am/V)sh 15 min 30 min

10 113 257 130 621 802

20 194 431 140 634 809

30 265 554 150 646 815

40 328 636 160 655 819

50 383 690 170 664 822

60 432 721 180 671 825

70 473 734 190 677 827

80 509 741 200 682 828

90 539 753 250 699 833

100 565 767 300 708 835

110 586 781 400 716 837

120 605 792 500 720 838

5.2.2 Protected steel member

EN 1993-1-2 also provides a simple design approach for insulated members with passive fire protection materials. In such cases, the temperature rise depends on the section factor Ap/V for the steel member insulated by fire protection material (Ap is the appropriate area of fire protection material per unit length and V is volume of the steel member per unit length) and the insulation characteristics. The insulating materials can be in form of profiled or boxed systems, but this simple approach does not cover intumescent coatings. Assuming uniform temperature distribution, the temperature increase a,t in an insulated steel member during a time interval t may be determined from:

tg,10/

ta,tg,p

aa

ppta, 1e

3/1

1/

tV

A

c

d (8)

with

V

Ad

c

c pp

aa

pp

(9)

where:

pd is the thickness of fire protection material [m]

pC is the specific heat of fire protection material [J/kgK]

p is the thermal conductivity of the fire protection material [W/mK]

p is the unit mass of the fire protection material [kg/m3]


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g is the gas temperature [°C]

Figure 5.5 gives expressions to calculate the section factor of protected steel members.

Am/V= (P-b) / As

b

Am/V= (2h+b) / As Am/V= 2(2+b) / As Am/V= P / As

h

b b

h

P : perimeter ; As : cross-section area

Figure 5.5 Example of section factor for insulated steel members

It is important to note that thermal characteristics of fire protection materials are usually determined from fire tests performed under standard fire conditions. Consequently, referring to thermal actions based on natural fires, the use of Equation (8) for the fire design situation of protected steel members should be handled with some caution. The calculation should be performed only if appropriate data are available or if it can be shown that fire conditions have no significant effects on thermal characteristics and integrity of fire protection materials. Nevertheless, it is commonly assumed that thermal properties of an insulation material can be used under natural fire conditions when the temperatures of hot gases remain lower than the maximum temperature reached during the standard fire test for the insulation material (For example, about 1100°C for 4 hours of the standard temperature-time curve).

The material properties given in Table 5.2 may be used as a first approximation to calculate heating of protected steel members. These average values are derived from fire tests by material manufacturers.


7 - 21

Table 5.2 Average materials properties of main fire protection materials

Material Density

p [(kg/m3]

Conductivity

p [W/mK]

Specific heat

pC [J/kgK])

Mineral fibre 300 0,12 1200

Vermiculite and cement

350 0,12 1200 Sprays

perlite 350 0,12 1200

vermiculite (or perlite) and cement

550 0,12 1100 High density

sprays vermiculite (or

perlite) and gypsum 650 0,12 1100

vermiculite (or perlite) and cement

800 0,2 1200

fibre-silicate or fibre calcium-silicate

600 0,15 1200

fibre-cement 800 0,15 1200

Boards

gypsum board 800 0,2 1700

Compressed fibre boards

fibre-silicate, mineral, stone-wool

150 0,2 1200

5.3 Structural Models According to the Eurocodes, several simple design methods can be used to assess the fire resistance of structures under fire conditions. The first one is the critical temperature method widely applied to steel structural member analysis and the second one is the simple mechanical models developed for both steel and composite steel and concrete structural members.

It is important to remember that the design methods available for composite members are only valid for the standard fire exposure. Moreover, design methods given for columns should be only applied to members of braced frames (where the column ends have no horizontal displacement).

5.3.1 Critical temperature method

The critical temperature is calculated by using applied mechanical actions, design resistance in the normal temperature condition and the strength loss of steel at elevated temperature. This critical temperature generally varies between 500°C and 800°C. It can be obtained by calculation according to the simple rules given in the EN 1993-1-2 or by referring to default values.

According to the critical temperature method, the fire resistance of a steel member without instability effect is satisfied after a time t if the steel temperature t,a does not exceed the critical temperature cr of the element:

crt,a (10)


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The critical temperature of the member can be calculated from the degree of utilization 0 as follows:

48219674.0

1ln19,39 833.3

0

cr (11)

The degree of utilization 0 is obtained from:

d,0fi,

dfi,0 R

E (12)

where:

dfi,E is the design effect of actions for the fire design situation, according

to EN 1991-1-2

d,0fi,R is the corresponding design resistance of the steel member, for the

fire design situation, at time t = 0 (at normal temperature) but with safety factor fi,M in fire situation

The expression for θcr can be used for all classes of section except the very slender Class 4 sections, for which a single conservative critical temperature of 350°C should be used.

In principle, Expression (11) applies for members in pure bending, short columns without buckling and members in tension, heated uniformly or with slight temperature gradient. However, in situations of instability (slender columns, unrestrained beams), the method becomes applicable by calculating the design resistance for the fire design situation at time t = 0 with a value of the slenderness that takes into account temperature effects on the slenderness of structural members. As a simplification, the slenderness in fire situations can be taken as 3.1 (where is the non dimensional slenderness at

normal temperature).

As an alternative, to relation (11) nationally determined critical temperatures can be given in the National Annex to EN 1993-1-2.

A simple conservative expression for 0 can also be used for tension members and restrained beams (where lateral-torsional buckling is not a potential failure mode):

21M

fi,Mt,fi0

(13)

where:

t,fi is the load level at time t

fi,M is the relevant partial safety factor for fire situation ( 1fi,M )

0M is the partial safety factor at normal temperature ( 10M )


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κ1, κ2 are the adaptation factors to take account a non-uniform temperature distribution on steel member.

The load level at time t is defined as:

d

dfi,tfi, R

E (14)

where:


to EN 1991-1-2

dR is the ultimate resistance in room temperature

For a given fire duration t, assuming that crt,a , the maximum value of

utilization level 0 of unprotected steel members to satisfy the required fire

resistance may be easily calculated from (11), as function of section factor including the shadow effect (Am/V)sh. In this way, it may be assumed that fire resistance of unprotected steel members is satisfied after a time t if:

max0 (15)

Maximum degrees of utilisation max calculated for standard fire resistance

R15 and R30 are given in Figure 5.6. It should be noted that for a fire resistance R30, unprotected members with a section factor (Am/V)sh higher than 50 m-1 can only achieve very low values of the degree of utilisation.

Figure 5.6 Maximum utilization level as a function of section factor (Am/V)sh

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300 350 400 450 500(Am/V) sh = ksh (A m/V)(m-1)

max

10

15 minutes

30 minutes

practical field of 0


7 - 24

5.3.2 Simple design method for steel members

According to EN 1993-1-2, the load-bearing function of a steel member should be assumed to be maintained at a time t if:

tfi,d,dfi, RE (16)

where:


to EN 1991-1-2

tfi,d,R is the corresponding design resistance of the steel member, for the

fire design situation, at time t

The following simplified calculation methods allow the designer to assess the design fire resistance (buckling resistance, resistance moment) of steel members. They are mainly based on the assumption of constant temperature within the section.

Steel columns under compression only

The design resistance for the fire design situation at time t of a compression member with a Class 1, 2 or 3 cross-sections at a uniform temperature θa should be determined from:

Rdθy,fM,

M0fRdt,fi, NkN

ii

(17)

where:

θy,k is the reduction factor for the yield strength of steel at the steel

temperature θ reached at time t

fi,M is the partial safety factor for fire situation ( 1fi,M )

0M is the partial safety factor at normal temperature ( 10M )

RdN is the design resistance of the cross-section Npl,Rd for the normal

temperature design according to EN 1993-1-1

fi is the reduction factor for flexural buckling in the fire design situation

The reduction factor fi for flexural buckling is obtained from the non-

dimensional slenderness at temperature θ using:

2θ

2θθ

f1

i but fi 1.0 (18)

with

2θθθ 1

2

1


7 - 25

where:

is the imperfection factor for the appropriate buckling curve given

by y/23565.0 f with fy is characteristic yield strength of steel.

The non dimensional slenderness at temperature θ is given by:

θE,θy,θ / kk (19)

where:

θy,k is the reduction factor for the yield strength of steel at the

temperature

θE,k is the reduction factor for the slope of the linear elastic range at the

temperature

The non dimensional slenderness at normal temperature, according to EN 1993-1-1

The non dimensional slenderness at normal temperature is given by:

E

f

iycr

π

1 (20)

where:

cr is the buckling length in the buckling plane considered

i is the radius of gyration about the relevant axis, determined using the properties of the gross cross-section

For a practical use, the reduction factor if for flexural buckling can be directly

calculated from values given in Table 5.3, according to the steel grade and the non dimensional slenderness of steel member at normal temperature . Values of reduction factor fi in Table 5.3 were calculated assuming a slenderness in

the fire situation equal to 3.1θ . For intermediate value of non-

dimensional relative slenderness, linear interpolation may be used.


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Table 5.3 Values of reduction factor fi as function of non dimensional slenderness at normal temperature and the steel grade

Steel grade Steel grade S235 S275 S355

S235 S275 S355

0,2 0,8480 0,8577 0,8725 1,7 0,1520 0,1549 0,1594

0,3 0,7767 0,7897 0,8096 1,8 0,1381 0,1406 0,1445

0,4 0,7054 0,7204 0,7439 1,9 0,1260 0,1282 0,1315

0,5 0,6341 0,6500 0,6752 2 0,1153 0,1172 0,1202

0,6 0,5643 0,5800 0,6050 2,1 0,1060 0,1076 0,1102

0,7 0,4983 0,5127 0,5361 2,2 0,0977 0,0991 0,1014

0,8 0,4378 0,4506 0,4713 2,3 0,0903 0,0916 0,0936

0,9 0,3841 0,3951 0,4128 2,4 0,0837 0,0849 0,0866

1 0,3373 0,3466 0,3614 2,5 0,0778 0,0788 0,0804

1,1 0,2970 0,3048 0,3172 2,6 0,0725 0,0734 0,0749

1,2 0,2626 0,2691 0,2794 2,7 0,0677 0,0686 0,0699

1,3 0,2332 0,2387 0,2473 2,8 0,0634 0,0642 0,0653

1,4 0,2081 0,2127 0,2200 2,9 0,0595 0,0602 0,0612

1,5 0,1865 0,1905 0,1966 3 0,0559 0,0565 0,0575

1,6 0,1680 0,1714 0,1766

Steel beams

The design moment resistance for the fire design situation of a laterally unrestrained beam with a Class 1, 2 or 3 cross-section, at a uniform temperature a is given by:

Rdθy,fiM,

M0fLT,Rdt,fi, MkM i

(21)

where:

θy,k is the reduction factor for the yield strength of steel at the steel

temperature θ reached at time t

RdM is the moment resistant of the gross cross-section (plastic moment

resistant Rdpl,M or elastic plastic moment resistant Rdel,M for the

normal temperature design calculated using EN 1993-1-1

fiLT, is the reduction factor for lateral-torsional buckling in the fire

design situation. It may be calculated in the same way as the reduction factor for flexural buckling but using the appropriate non-dimensional slenderness

For laterally restrained beams, the same design method can be used, adopting 1fiLT, .

Often structural members will not have a uniform temperature. An adaptation factor κ1 can be introduced to take account a non-uniform temperature distribution over the height of the steel section. A further adaptation factor κ2 can be also introduced to account for variations in member temperature along the length of the structural member when the beam is statically indeterminate.


7 - 27

The value of the adaptation factors κ1 and κ2 should be taken according to EN 1993-1-2.

Members subject to combined bending and axial compression

A simplified design method is also available to verify the fire resistance of steel members subjected to combined bending and axial compression, such as slender columns under eccentric load and long beams with lateral buckling. For this situation, the simple calculation model takes into account the combination effect of bending and compression by combining above two models for the simple loading condition. Detailed information is given in EN 1993-1-2.

5.3.3 Determination of fire protection material thickness

In situations where requirements with respect to fire resistance are high (generally more than R30), the application of prescriptive rules usually leads to the fire protection of steel structures. When passive fire protection is necessary, the knowledge of the critical temperature, the section factor and the fire resistance time required, allow for a given fire protection system (spray, board, intumescent coating), determination of the thickness to apply. Only products which were tested and assessed in standard fire tests according to the European standard EN 13881 may be used in practice.

The required thickness can usually be determined from manufacturer’s published data. Such manufacturer’s data can be given in form of table or diagram as illustrated in Figure 5.7. The data generally relates the thickness of fire protection material to the section factor of the steel member (Ap/V), the critical temperature and the fire resistance time required. For typical building construction using standard I and H steel profiles, the value of Am/V is usually in the range 30 – 450 m-1.

Fire resistance rating R60

Section factor Ap/V (m-1)

Ste

el

tem

pe

ratu

re (

°C)

Figure 5.7 Example of French diagram for boarded fire protection

In practical design, for a given fire protection material, the thickness may be determined according to following steps:

Choose the data related to the fire resistance time required

Calculate the section factor according to the shape of the steel profile, the presence of any shading of the structural member against heat transfer from


7 - 28

the fire during the fire duration (for example a concrete slab put on the upper flange of the profile), the type of fire protection (according to the outline of the steel profile or in box)

Determine the thickness from the manufacturer’s data using the critical temperature and the section factor. Linear interpolation is permissible to determine thickness.

The European Convention for Constructional Steelwork (ECCS) has developed so-called Euro-nomograms[13], which relate for a given time of standard fire exposure, the temperature reached by insulated steel members to the factor (λp/dp) (Ap/V) depending on the fire protection characteristics (λp and dp) and the section factor Ap/V. Note that these Euro-nomograms are determined on the basis of the ENV version of the fire part of Eurocode 3. Also for this reason they should be used with some caution. Other nomograms based on EN 1993-1-2 have been recently developed[14].

5.3.4 Design tables for composite members

Design tables for composite members are given in EN 1994-1-2. They are applicable only to steel and concrete composite members (composite beams with partially or fully concrete encasement of steel beam, composite columns with partially or fully concrete encased profiles, composite columns with concrete filled rectangular or circular steel hollow sections). They use predefined values, based mainly on standard fire test results, improved with analytical investigation. The tables allow the designer to quickly obtain the member size (minimum dimensions of cross-section, the necessary reinforcing steel area and its minimum concrete cover) as a function of the load level for common standard fire resistances. The most important advantage of this method is the ease of application. However it is limited by a very strict set of geometrical rules and it gives more conservative results compared to other simple calculation models or advanced calculation models. As a consequence, it should only be applied for the pre-design of a building.

Detailed information is given in EN 1994-1-2.

5.3.5 Simplified calculations models for composite members

The following design methods have been developed to predict the resistance of individual members when exposed to a standard fire curve. Therefore they are not applicable to “natural” fires.

Only the design methods for the most commonly used composite members in single-storey building (composite columns and partially encased concrete beams) are described here.

Composite columns

The simple design methods for columns allow the designer to assess the fire resistance of a composite column by calculating its buckling resistance using the temperature distribution through the cross-section and the corresponding reduced material strength defined at the required fire resistance time. This method is based on the buckling curve concept: the plastic resistance to axial compression Nfi,pl,Rd and the effective flexural stiffness (EI)fi,eff, are used to derive a reduction factor for buckling. The method is applicable to all types of


7 - 29

composite column provide that an appropriate buckling curve is used. Checking the column consists of proving that the axial compression (for the combination of actions considered in fire situation according to EN 1991-1-2) is less than the buckling resistance of the column.

For a given temperature distribution across the cross-section, the design resistance of a composite column Nfi,Rd can be determined from the appropriate buckling column curve relating the load capacity Nfi,Rd to the plastic load Nfi,pl,Rd and the elastic critical load Nfi,cr as follows:

Rdpl,fi,θRdfi, .NN (22)

is the reduction factor for flexural buckling depending on the slenderness in

fire situation θ .For composite columns, θ may be defined as:

crfi,Rpl,fi,θ / NN (23)

where:

crfi,N is the Euler buckling load

Rpl,fi,N is the value of Nfi,pl,Rd according to (24) when the partial security

factors M,fi,a, M,fi,s, and M,fi,c,of the materials are taken as 1.0

The reduction factor is determined as for normal temperature design but using an appropriate buckling curve defined as function of column type (partially encased steel section, filled hollow steel section).

The ultimate plastic load, Nfi,pl,Rd of the cross-section is determined by summing the strengths of every part of the cross-section (yield stress for steel parts, compressive strength for concrete parts) multiplied by the corresponding areas, taking into account the effect of temperature on these elements, without considering their interaction (due to differential thermal stresses), i.e.:

m

ck

sj

fA

fA

fAN )()().(

cfi,M,

θc,

sfi,M,

θs,

afi,M,

θay,aRdpl,fi,

(24)

Nfi,cr is the Euler buckling load calculated as a function of the effective flexural

stiffness of the cross-section efffi,)(EI and the buckling length of the

column in fire situation, i.e.:

2θ

efffi,2crfi,

)(π

EIN (25)

The effective rigidity (EI)fi,eff is determined from:

mkj

IEIEIEEI )()()()( θc,θsec,c,θc,θs,θs,θs,θa,θa,θa,efffi, (26)

where:

θ,iE is the characteristic modulus of material i at the temperature . For

steel, it is the modulus of elasticity. For concrete: 2/3 secc,c, EE


7 - 30

where θsec,c,E is the characteristic value for the secant modulus of

concrete in the fire situation, given by the ration between fc,θ and cu,

Ii is the second moment of area of material i related to the central axis (y or z) of the composite cross-section

a, (for steel profile), s, (for reinforcements) and c, (for concrete) are reduction coefficients due to the differential effects of thermal stresses.

Detailed information is given in EN 1994-1-2 §4.3.5.

Partially encased steel beams

The simple design method for partially encased steel beams allows the designer to assess the fire resistance by calculating its bending resistance at the required fire resistance time. It is based on the simple plastic moment theory. The method requires the calculation of the neutral axis and corresponding bending resistance, taking into account temperature distribution through the cross-section and corresponding reduced material strength. Distinction is made between sagging moment capacity (usually at mid-span) and the hogging moment capacity (at the support, if appropriate). If the applied moment is less than the bending resistance of the beam, the member is deemed to have adequate fire resistance.

The plastic neutral axis of the beam is determined such that the tensile and compressive forces acting in the section are in equilibrium:

01 cfi,M,

c,,θc,

1 afi,M,

,y,y,

m

j

jjj

n

i

iii

fkA

fkA

(27)

where:

fy,i is the nominal yield strength for the elemental steel area Ai taken as positive on the compression side of the plastic neutral axis and negative on the tension side

fc,j is the nominal compressive strength for the elemental concrete area Aj taken as positive on the compression side of the plastic neutral axis and negative on the tension side

The design moment resistance Rdt,fi,M may be determined from:

m

1j c,fi,M

jc,j,c,jj

n

1i a,fi,M

i,yi,y,iiRd,t,fi

fkzA

fkzAM

(28)

where:

zi, zj are the distances from the plastic neutral axis to the centroid of the elemental area Ai and Aj


7 - 31

For the calculation of the design value of the moment resistance, the cross-section of the beam is divided into various components, namely:

the flanges of the steel profile

the web (lower and upper parts) of the steel profile

the reinforcing bars

the encased concrete.

To each of these parts of the cross-section, simple rules are given which define the effect of temperatures and allow calculation of the reduced characteristic strength in function of the standard fire resistance R30, R60, R90 or R120.

Detailed information is given in EN 1994-1-2 §4.3.4.

5.4 Specific design rules for single-storey buildings National fire regulations of many European countries have been changed recently to introduce, for single-storey storage and industrial buildings with significant fire risks (high fire loads), specific safety requirements in terms of structural behaviour as an alternative to standard prescriptive requirements. The following criteria relating to the structural behaviour of storage and industrial buildings (load-bearing structure, façade elements, roofing and fire walls) must be satisfied to ensure adequate life safety for building occupants and firemen:

In case of fire occurring in one of the cells of the building, its structure (including façade elements) must not collapse towards the outside.

In case of fire occurring in one of the cells of the building, the localized failure of the cell in fire must not lead to the collapse of the neighbouring cells.

To help the design of storage and industrial buildings with a steel structure, several simple design methods can be used5,6. These design methods allow the designer to easily prove that the behaviour of the steel structure of these buildings in fire situations fulfils the above criteria. The methods are implemented in the LUCA software[15].

The design methods enable the designer to:

Evaluate forces induced by the collapse of the heated part of the structure. These forces should be used as additional horizontal load for the stability check of the part of the frame that remains cold during the fire. That part can be assessed using normal conditions design tools for structure analysis.

Provide maximum horizontal displacements developed at the ends of the compartment affected by the fire. These displacements are used to ensure that movements of the structure in the event of fire do not adversely affect the stability of fire walls or building façades. Design methods used for this verification depend on the type of the wall (such as in lightweight concrete, reinforced concrete, hollow block, steel sheeting with insulator, plasterboard, bricks, etc.) and connection to the steel frame.


7 - 32

The following buildings can de designed by these methods:

Storage and industrial buildings with steel structure. Either steel portal frames with standard H or I hot rolled profiles or equivalent welded plate girders, or steel frames based on lattice beams with columns in standard H or I hot rolled profiles or equivalent welded plate girders

Storage and industrial buildings of portal frame construction divided in several cells, separated one from each other by fire walls. These walls can be either perpendicular to the steel portal frames or parallel to the steel portal frames (see Figure 5.8).

These methods were specifically developed for storage and industrial buildings but they can also be applied to other type of single-storey buildings.

fire wall perpendicular to the steel frame

fire wall parallel to the steel frame

Figure 5.8 Location of fire wall compared to steel frames

Calculation methods (see Section 5.5) are only required when fire walls are perpendicular to steel frames of the building and the building height exceeds 20 m5. When fire walls are parallel to steel frames, the risks of collapse towards the outside and progressive collapse (between different fire compartments) can be simply avoided by following the recommendations in Section 5.5.3.


7 - 33

5.5 Simplified design methods A flowchart showing simplified calculation methods is given in Figure 5.9.

yes

No

No

yes

(*) For all the possible fire scenarios according to the building arrangement

Industrial hall

Checking of failure modes

Choice of fire scenario(*)

(see Figure 5-14)

Calculation of displacements of the steel structure δi (see expression (30))

Calculation of tensile force Fi (see expression (29))

Checking of the compatibility of displacements Steel structure and partition elements Steel structure and facade elements

Checking of the stability at the ultimate limit states of the cold

parts of the steel structure

End of checking

yes

Change in the steel structure

Change in the design of partition or facade elements to ensure the compatibility of displacements

No

Is it a simple isolated portal frame?

Design recommendations at the bottom of columns

(see end of §5.6.2)

yes

Figure 5.9 Application flowchart of calculation methods

The calculations of tensile force and lateral displacements at compartment ends must be performed for all possible fire scenarios. Examples of scenarios are given in Section 5.5.3. Calculation methods are given in Sections 5.5.1 and 5.5.2.

5.5.1 Tensile force at compartment ends

m1 = 1 m2 = 2 n = 1

K2 F F

K1

Figure 5.10 Horizontal tensile force at the fire compartment ends

When a fire occurs in a compartment of the building, the horizontal tensile force F at the compartment ends resulting from the collapse of the roof structure (see Figure 5.10), which is needed to verify the stability of the cold part of the structure can be obtained from:

qncF effp (29)


7 - 34

where:

pc is an empirical coefficient (depending on the slope of the roof and

the type of steel structure)

Frames Latticefor

Frames Portalfor

45,1

slope10%for10,1

slope5%for16,1

slope0%for19,1

pc

neff is a coefficient related to the total number of heated bays n in the fire compartment (see Table 5.4)

q is the linear load on roof [N/m] (equal to the load density multiplied by the spacing between frames) applied on the beam and calculated in fire situation (q = G + 1 Sn), where G is the permanent load including self-weight of the steel frame and service overloads, Sn is the snow load and 1 is the load factor according to load combination coefficients defined in EN 1990 and corresponding national annexes.

is the span of on heated bay connected to the column [m]

Table 5.4 Values of coefficient neff

Portal frame Lattice Frame

Setting of compartment in fire Setting of compartment in fire

Number of bay in fire

end middle end middle

n = 1 neff=0,5 neff=1,0 neff=0,6 neff=1,0

n 2 neff=1,0 neff=2,0 neff=1,0 neff=1,0

Where columns of the steel frame support a boundary fire wall, columns should be designed (providing adequate robust base to columns) to resist a horizontal force calculated according to equation (29) but using neff = 1,0.

5.5.2 Lateral displacements at the fire compartment ends

In the event of fire, movements of steel single-storey buildings can be of the order of several tens of centimetres and therefore could lead to the failure of façade or the partition element if it is not sufficiently ductile or not accurately fixed. So it is important to check that façade elements and fire walls in contact with the steel structure are compatible with the lateral displacements developed at the ends of fire compartments and that they keep their integrity to avoid the collapse towards outside and the progressive collapse between different fire compartments


7 - 35

Maximum lateral displacements δi (i = 1, 2) induced at the top of columns located at the compartment ends can be obtained using the following expression (see Figure 5.11):

building theof middle in the is fire when the;Max

building theof end at the is fire when the

tht

tht

ii

ii

K

Fnlc

K

K

nlcK

K

(30)

where:

n is the number of heated bays

Ki is the equivalent lateral stiffness of the considered part i of the structure [N/m]

Kt is the equivalent stiffness (depending on equivalent stiffnesses

1K and 2K ) given by:

21

21t KK

KKK

is the span of one heated bay connected to the column [m]

F is the tensile force [N]

cth is an empirical coefficient (dependent on the slope of the roof and the type of steel structure)

Frames Lattice for

Frames Portal for

009,0

slope10%for015,0

slope5%for011,0

slope0%for01,0

thc

Lateral stiffness K for fire in the middle of a frame

If the fire compartment is in the middle of the frame as illustrated in Figure 5.11 , K1 and K2 should be calculated by an elastic method.

1 2

m1 = 1 m2 = 2 n = 1

K2

K1

Figure 5.11 Fire located in a cell at the middle of the building

However, for usual steel frames (constant range, even standard steel profiles from one span to another), the equivalent lateral stiffness iK on either side of

the fire can be calculated approximately according to the number of cold spans on that side (mi) using the following relationships:


7 - 36

2for

1for

i

ii mck

mkK (31)

)6,0

1(

21

12

22

1

)(

12

21

with

c

b

3c

h

f

l

fh

I

I

j

im

j

jc

fh

EIk

(32)

where, for each side in turn (i = 1, 2):

h is the height of the columns

f is the ridgepole

l is the length of the span

Ib is the second moment of area of the beam

Ic is the second moment of area of the column

E is the modulus of elasticity of steel for normal temperature

f

h

mi=2

Ib

Ic

Figure 5.12 Definition of parameters of cold parts on side i of the frame

Lateral stiffness K for fire at the end of a frame

If fire compartment is at the end of the frame, K2 should be calculated as for fire in the middle compartment. K1, which is defined as the lateral stiffness of the steel frame of the heated fire compartment, should be calculated as follows:

frames latticefor 2for3,0

1for2,0

framesportalfor

2for13,0

2for13,0

1for065,0

2

2

1

nK

nK

nkc

nk

nk

K (33)

where k and c are calculated from equation (32) with m1 = n − 1, where n is the number of heated bays, as shown in Figure 5.13.


7 - 37

K1 1 2

n = 1 m2 = 3

K2

Figure 5.13 Fire in a compartment at the end of the building

5.5.3 Example of fire scenarios

The above calculations must be performed for all possible fire scenarios. These scenarios are defined in accordance with the arrangement of the storage building (structure and partitioning) as illustrated in the example in Figure 5.14.

Configuration of storage building: 5 spans and 3 cells

Cell 1 Cell 2 Cell 3

Fire wall Fire wall

Scenario 1: fire in cell 1



3 fire scenarios need to be considered

Figure 5.14 Fire scenarios according to the arrangement of the building

5.6 Design recommendations Additional design recommendations for fire walls, façade elements and bracing systems must be put into practice to avoid the collapse toward the outside of the building and the progressive collapse of the steel structure. Obviously, recommendations allow also the collapse of the steel structure under fire condition on either side of fire wall without causing any damage to this wall.


7 - 38

5.6.1 Fire walls

To limit the fire spread to a neighbouring compartment from the fire compartment, a solution that requires the building to be subdivided into independent compartments can be achieved by implementing one of the following construction details:

Two independent fire walls (such as sandwich panels, prefabricated panels, etc.) each fixed to an independent structural frame (see Figure 5.15 (a)). In this case, when one structure and its fire wall collapse during a fire, the fire cannot spread to the neighbouring structure, which remains stable and fire protected by the second fire wall

A single fire wall inserted between both structures. This fire wall can be a self-stabilized wall and fully independent. The fire wall can be also fixed at its top to both structures by means of “fusible” ties (see Figure 5.15 (b)) which, in case of fire near the wall, releases the connection to the ‘hot’ structure (usually when a temperature from 100 to 200°C is reached in bolts) without causing any damage to the wall (it one remains attached to the steel structure located on the ‘cold’ side) and the stability of the neighbouring cold structure.

Self-stabilized walls are commonly used in practice. However during a fire, this solution can be dangerous for people (occupants and firemen) because they collapse away from the fire as a consequence of thermal bowing effect. So, they should be used only if their behaviour has been evaluated by advanced calculation model taking into account second order effects. Moreover, where spacing from the self-stable wall to the neighbouring steel structure is not sufficient, it is important to make sure that the fire wall can bear the force which may be induced by the movements of the building due to the thermal elongation of the roof structure (beams and purlins) due to the increase of temperature in the cell with the fire.

As an alternative to the previous solutions, it is possible to insert the fire wall into the steel structure of the single-storey building as illustrated in Figure 5.15(c). Such wall can be either perpendicular to the steel frame or parallel to the steel frame. Several solutions can be then considered: fire wall inserted into a line of columns, fire wall attached to columns or fire wall moved from a line of columns. For these solutions, adequate measures must be implemented to avoid the collapse of the wall as a result of significant lateral displacements of the steel structure. These measures concern:

The attachment of fire walls to the steel structure

The fire protection of the steel structure near fire walls,

The roof system above fire walls

The bracing system.


7 - 39

a) Doubling of the structure as well as fire walls

b) Doubling of structure with fire wall fixed by “fusible” ties

c) Example of fire wall inserted into the steel structure

Figure 5.15 Some solutions of fire walls

Attachment of façade elements and fire walls to steel structure

Fire walls and façade elements fixed to steel structure of single-storey-buildings have to remain solidly attached in order to prevent any failure of these elements due to significant lateral displacements of structure in the event of fire, and so to avoid risks of progressive collapse and collapse towards the outside of the building.

3m

3m

3m

3m

Fire wallFacade element

Figure 5.16 Design detail for façade elements and fire walls

One solution consists of fixing these elements to the columns of the load-bearing structure by means of suitable attachment systems uniformly distributed over the building height. The maximum spacing of these attachments will be fixed by the manufacturer of the walls; it is recommended that the spacing should not exceed 3 m for walls constructed on-site walls (concrete, masonry, etc.).

In addition, fastenings used to connect fire walls and façade elements on the columns must be designed to resist the forces produced due to wind and self-weight of partition elements under the effect of the lateral displacement induced by the steel frame of the building. If these fastenings are in steel and unprotected against fire, each of them must be designed at ambient temperature to resist the following force:

ndpWF i /5 (34)

where:

W is the characteristic wind load used for the design at ambient temperature and applied to each fastening [N]

p is the self-weight of the wall [N/m²]

d is the spacing between frames [m]


7 - 40

n is the total number of fastenings (uniformly distributed along the height)

i is the maximum lateral displacement obtained from relation (26) [m]

Fire protection of steel elements near to fire walls

The requirement that there should be no fire propagation between different compartments and no progressive collapse (i.e. the integrity condition of fire walls must be preserved and the cold parts of the structure must remain stable), leads to the requirement that that columns used as supports of fire walls must achieve the same fire resistance as required for fire walls. In common cases, these fire requirements lead to the application of fire protection to the columns. On the other hand, columns which do not support fire walls will not require fire protection.

Additionally, structural members that could damage fire walls (such as beams and purlins near or crossing the walls) will also have to be fire protected.

5.6.2 Recommendations for steel portal frames

Fire wall perpendicular to steel frame

Figure 5.17 illustrates the situation where the fire wall is perpendicular to the steel frame. For this situation:

Columns that are built into or near a wall must be fire protected.

Where fire wall is inserted between the flanges of the columns, no additional fire protection is needed for the roof beams (Figure 5.17 (a)).

Where portal frames do not have haunches and fire wall is fixed to one flange of columns, fire protection must be applied to any beam crossing the fire wall (on the side of the wall) over a minimum length of 200 mm beyond the wall limit. This protection allows a shift of the plastic hinges away from the walls and thus prevents damage to the wall as a result of the collapse of the beam (see Figure 5.17 (b)). Where portal frames have haunches, no fire protection is needed for the beams.

Purlins do not cross the fire wall in this situation and no special considerations are required.

The thickness of fire protection material applied to columns may be calculated assuming a critical temperature of 500°C and the same required fire resistance as the fire walls. Fire protection should be provided over the full height of columns.

If beams are partially protected, the thickness of fire protection material may be calculated assuming a steel section exposed on four faces for the section factor, a standard fire exposure of one hour and a critical temperature of 500°C.


7 - 41

beam purlin

fire wall

protected column

purlin

fire wall

protected column

fire protection

d 200 mm

beam

a) Wall inserted between the flanges of

columns b) Wall fixed to one flange of columns

Figure 5.17 Design detail near fire walls perpendicular to portal steel frame

Fire wall parallel to steel frame

Figure 5.18 illustrates the situation where the fire wall is parallel to the steel frame.

For this situation:

The fire wall either be located between two frames or in the plane of the frame, between faces of the columns and beams.

Columns and beams that within the fire wall or near a fire wall must be fire protected.

Purlins will cross the fire walls. It is therefore necessary to fire protect continuous purlins (over a distance of 200 mm from the wall) or to design a non-continuous purlin system. For example, where fire wall is in the plane of a frame, steel elements fixed to the beams should be inserted through the wall to support the purlins.

The thickness of fire protection material applied to columns and beams may be calculated assuming a critical temperature of 500°C and the same required fire resistance as the fire walls. Fire protection should be provided over the full height of columns.


7 - 42

fire wall

protected beam

purlin

protected column

purlin

flexible fire protection material

continuous purlin

protected beam

d 200 mm

protected column fire wall

fire protection

purlin

Rigid support

fire wall

purlin

protected beam

protected column

a) Fire wall inserted between the flanges of columns

b) Fire wall fixed to one flange of columns

Figure 5.18 Design detail near fire walls parallel to portal steel frame

If purlins are partially protected, the thickness of fire protection material may be calculated assuming a steel section exposed on four faces for the section factor, a standard fire exposure of one hour and a critical temperature of 500°C.

Additional design recommendations for simple portal steel frames

In the case of single-storey buildings with simple portal steel frame where the column height/beam span ratio of the frame (h/l) is greater than 0,4, the failure mode towards the outside can be avoided by designing the connections between columns and foundation, and the foundation itself, to have sufficient resistance to sustain the vertical loads in the fire situation together with an additional bending moment equal to 20% of the ultimate plastic moment of the column at normal temperature.

Fire wall

simple portal steel frame

simple portal steel frame

h

L

Figure 5.19 Single-storey buildings with simple portal steel frame

Examples of fire walls

Illustrations of fire walls adopting some of the above recommendations are shown in Figure 5.20. They show clearly that the fire walls were not damaged, despite the collapse of the steel structure.


7 - 43

a) Self-stable fire wall inserted between two

independent steel framework b) Partially fire protected steel beam crossing

a fire wall fixed to steel columns Figure 5.20: Views of fire walls after fire disaster in steel single-storey building

5.6.3 Recommendations for steel frames based on lattice beams

Fire wall perpendicular to steel frame

Figure 5.21 illustrates the situation where the fire wall is perpendicular to the steel frame. For this situation:

Columns that are built into or near a wall must be always fire protected.

Where fire wall is inserted between the flanges, the lattice beams should be fire protected on both side of the wall (see Figure 5.21 (a)).

Were the fire wall is fixed to one flange, only the lattice beams on the wall side have to be protected. Fire protection must be applied to the beams over a minimum length equal to the distance separating the wall with the first vertical member of lattice frame (see Figure 5.21 (b)).

Purlins do not cross the fire wall in this situation and no special considerations are required.

The thickness of fire protection material applied to columns may be simply calculated assuming a critical temperature of 500°C and the same fire resistance as required for fire walls. Fire protection should be provided over the full height of the columns.

If lattice beams are partially protected, the thickness of fire protection material may be calculated assuming for the section factor: a steel section exposed on four faces for bottom chords, vertical members and diagonals; and on three faces for top chords. A standard fire exposure of one hour and a critical temperature of 500°C may be used.


7 - 44

first vertical member

fire wall

protected column

fire protection lattice beam

fire Wall

protected column

fire protection

first vertical member

lattice beam

a) Fire wall inserted between the flanges

of columns


Figure 5.21 Design detail near fire walls perpendicular to steel frame with

lattice beam

Where fire wall is parallel to steel frame

Figure 5.22 illustrates the situation where the fire wall is parallel to the steel frame. For this situation:

It is not practical to provide a wall in the plane of a frame, because it is difficult to make it continuous through the depth of the lattice beam. roof, Fire walls parallel to a frame are therefore usually either beside and in contact with the steel frame or between two independent steel structures.

Where the fire wall is attached to a steel frame, the columns and beams must be fire protected (see Figure 5.22 (b)). Moreover purlins and beam stays near the wall must be fire protected over a minimum length corresponding to the distance from the wall to the joint purlin/beam stay when the roof structure is made of purlins.

Where the fire wall is inserted between two independent steel structures, no fire protection is needed (see Figure 5.22 (a)).

If columns are protected, the thickness of fire protection material may be calculated assuming a critical temperature of 500°C and the same fire resistance as required for fire walls. Fire protection should be provided over the full height of the columns.

If lattice beams are protected, the thickness of fire protection material may be calculated assuming for the section factor: a steel section exposed on four faces for bottom chords, vertical members and diagonals; and three faces for top chords. A standard fire exposure of one hour and a critical temperature of 500°C may be assumed. Fire protection should be provided over the full length of the lattice beams.

The thickness of fire protection material applied to purlins and beam stays may be simply calculated assuming a steel section exposed on four faces for the section factor, a standard fire exposure of one hour and a critical temperature of 500°C.


7 - 45

purlin fire wall

beam stay

column

protected column

purlin

fire wall

protected lattice beam

beam stay

a) Fire wall inserted between two independent

steel framework


Figure 5.22 Design detail near fire walls parallel to steel frame with lattice

beam

5.6.4 Recommendations for bracing system

The requirement for no collapse towards the outside of the building in the the longitudinal direction (perpendicular to steel frames) can be satisfied using appropriate bracing systems. Specifically, each compartment must have its own bracing system.

Fire wall perpendicular to the steel frame

Figure 5.23 (a) illustrates the situation where the fire wall is perpendicular to the steel frame. For this situation:

Use additional vertical bracing systems at both ends of fire wall, to ensure integrity of wall. These bracing systems should be designed to support a lateral load taken as 20% of that due to normal wind actions (according to the combination of actions for the fire situation), calculated for a gable area that is limited to the width between gable posts.

Provide double bracing systems (i.e. have bracing systems on both sides of fire walls) or protect the bracing system.

The bracing systems must be arranged in a way that they will not cause problems for normal temperature design, for example by compromising movement of an expansion joint.

Fire wall parallel to the steel frame

Figure 5.23 (b) illustrates the situation where the fire wall is parallel to the steel frame. For this situation:

Install bracing systems (vertical bracing and horizontal bracing on roof) in each compartment. This solution may lead to additional bracing systems for normal conditions.

Design each bracing system to provide adequate stability in normal condition and to support in fire condition a horizontal uniform load [N/m] taken as F = 1,19 (G + ψ1 Sn)lf, where lf is the spacing between steel frames, G is the permanent action, including service overloads, Sn is the


7 - 46

snow load and ψ1 is the frequent combination factor according given in the relevant National Annex to EN 1990.

Where the fire wall is fixed to one flange of the columns, the elements of bracing systems must be fixed to rigid steel elements supporting the purlins on the side of the wall.

Fire wall

Building end

Doubling of additional bracing system put at the end of fire wall

Bracing system for normal temperature

Building end

Wall perpendicular to steel frame

Fire wall

Bracing system

Wall parallel to steel frame

Figure 5.23 Recommendations for bracing system

5.6.5 Recommendations for roof systems above the separation elements

The roof should be independent from one compartment to the next, adopting the following recommendations (see Figure 5.24 (a)):

Purlins should be provided either side of the fire wall.

The roof should be stopped on both sides of the fire wall

The roof should be provided with fire protection over a width of 2,50 m either side of the wall.

Alternatively, the wall may be extended above the roof, up to a specific distance d (see Figure 5.24 (b)).

National regulations may specify other special requirements for roof covering adjacent to fire walls.

protected column

Fire wall

beam

purlin

roof with fireproof material 2x2,50m

roof

part of roof between purlins

fire protection

Protected column

fire wall beam

purlin

roof

d

fire protection

a) Roof with fireproof material b) wall above the roof

Figure 5.24 Roof system above the separation elements


7 - 47

6 GUIDANCE ON THE USE OF MORE ADVANCED SOLUTIONS

This chapter gives an overview of advanced calculation models available for fire modelling, thermal modelling, and structural modelling that can be used in fire engineering design [9,16].

6.1 Fire models Two kind of numerical models are available to model the development of real fires: zone models and field models. These models and allow temperatures, smoke descent, flame spread, time to flashover and many other effects to be calculated.

6.1.1 Zone models

The simplest model is a one-zone model for fully developed fires (post-flashover fires), in which the conditions within the compartment are assumed to be uniform and represented by a single temperature.

Two-zone models may be used for pre-flashover situations, mainly in the growth phase of a fire. The model is based on the hypothesis of smoke stratification, separating the fire compartment into two distinct layers: a hot upper layer (containing most of the fire’s heat and smoke), and a cool lower layer (which remains relatively uncontaminated by smoke). A fire plume feeds the hot zone just above the fire. The temperature of each layer is calculated from conservation of energy; the amount of toxic combustion products in each layer is calculated from conservation of chemical species; and the size of each zone is calculated from conservation of mass. Simple rules govern plume entrainment, heat exchange between zones and mass flow through openings to adjoining compartments. As a result of the simulation the evolution of gas temperature in each of the two layers, the evolution of wall temperatures, evolution of flux through the openings and the evolution of the thickness of each layer are given as a function of time. The thickness of the lower layer, which remains at rather cold temperature and contains no combustion products, is very important to assess the tenability of the compartment for the occupants. Often, the local effect near the fire may be studied using a simple model such as Hasemi methodology with the two-zone models. The combination of both models then allows the determination of the gas temperature field near and far from the fire (see Figure 6.1).

When the thickness of the lower layer is too small compared to the height of the compartment, the two-zone assumption becomes inapplicable and a one zone model becomes more appropriate. Moreover if the fire area is big compared to the floor area, the one-zone model assumption is usually better than the two-zone one.

Some zone models include the possibility of a switch from a two-zone model to a one-zone model when some conditions for temperatures, fire area and smoke layer thickness corresponding to flashover) are encountered.


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It is also still possible to choose to follow a two-zone or a one-zone strategy for the entire duration of a fire. With these strategies, the whole simulation is made considering two or one zones, from the initial time to the end of the calculation. No modification of the rate of heat release is made, except via the combustion models.

Localised fire 2 zone model

roof

g

Beam

Hasemi method’s

20°C

z

g

2-zone model

at beam level

x

Figure 6.1 Combination of two-zone model with Hasemi method’s

Some of the more complex zone models allow radiation calculations between the upper layer and room objects. They may also allow multiple fire plumes and multiple compartment analysis with mass exchange between each compartment (see Figure 6.2).

The input data are usually the room geometry, room construction (including all walls, floors and ceilings), number of vents (or holes) and their sizes, room furnishing characteristics, and fire data (such as RHR curve, pyrolisis rate, combustion heat of fuel). The output data are usually the prediction of sprinkler and fire detector activation time, time to flashover, upper and lower layer temperature, smoke layer height, and species yield.

The fire load can be considered to be uniformly distributed if the combustible material is present more or less over the whole floor surface of the fire compartment and when the fire load density (quantity of fuel per floor area) is more or less uniform. By contrast, the fire load should be “localised” if the combustible material is concentrated on quite a small surface compared to the floor area with the rest of the floor area being free of fuel.

An essential parameter in advanced fire models is the rate of heat release. For design it is common practice to refer to the values given in EN 1991-1-2.

For irregular or complex building geometry, complex ventilation systems, or where more detail is required on convective or radiant heat exposure levels at specific targets, the use of a field model should be considered.


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A712.5m*9m

A1325m*54m

A312.5m*9m

A412.5m*9m

A812.5m*9m

A225m*18m

A125m*18m

A1225m*18m

A912.5m*9m

A1425m*54m

A1012.5m*9m

A512.5m*9m

A612.5m*9m

A1125m*18m

Fire source

Figure 6.2 Example of fire modelling using zone models for an industrial

building

6.1.2 Field models

Field models (computational fluid dynamics models) are the most sophisticated deterministic models for simulating enclosure fires. They incorporate sub-models for turbulence, heat transfer and combustion.

The CFD modelling technique is based on a complete, time-dependent, three-dimensional solution of the fundamental conservation laws (conservation of mass, momentum, and energy). The volume under consideration, usually a fire compartment, is divided into a very large number (sometimes hundreds of thousands or even millions) of cells. The approximate number of cells appropriate for the studied compartment will depend on the compartment geometry, the accuracy required, and from a practical standpoint, the computer speed and memory.

Three cases of field models, according to the turbulence method implemented in model, exist:

Direct numerical simulations (DNS): The basic equations are directly solved but need very short time and spatial steps in order to simulate all time and spatial scales coming from the turbulent and the chemical processes. DNS require particularly powerful computers and are used for academic studies or are confined to simple applications.

Large Eddy Simulation (LES): Large scale motions of the flow are calculated while the effect of smaller scales is modelled using sub-grid scale model. The most commonly used sub-grid model is the Smazorinsky model.


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Reynolds-averaged Navier Stokes (RANS): The basic equations are averaged and all turbulent scales are modelled. The most frequently model used is k model.

The input data are the same as those required for a zone model but they have to be supplied with a higher degree of detail. They are the detailed room geometry, room construction (including all walls, floors and ceilings), number of vents (or holes) and their sizes, room furnishing characteristics, fuel/combustion characteristics, turbulence parameters, and radiation parameters.

The output data are the smoke and heat movements, prediction of sprinkler and fire detector activation time, time to flashover, temperatures in the domain, velocities, smoke layer height, and species yield.

Due to their complexity and the CPU time needed, field models are very little used for evaluating fire resistance of structures, particularly for fully developed fire. In the fire domain, the use of a field model is often reduced to specific cases with sophisticated geometry.

6.2 Thermal Models Advanced heat transfer models can be used to calculate temperature distribution in a structure in a fire. They are mostly based on either finite difference methods or finite element methods. They are often used to estimate temperature gradients through structural members primarily made of materials with a low thermal conductivity and/or high moisture content, such as concrete. Moreover, they can be applied to structural members under nominal fire conditions or natural fire conditions.

Such methods have to take into account non-linearity due to temperature dependence of material properties and boundary conditions. As commonly assumed in fire design, heat transfer from fire to exposed surfaces is essentially by convection and radiation. Inside homogeneous materials such as steel, heat is only transferred by conduction. On the other hand, for porous materials such as concrete or where internal cavities exist, heat transfers are more complex. The three processes: conduction, convection and radiation can occur together, to which may be added mass exchange. However, by way of simplification, only the dominating process is explicitly introduced in thermal analysis, taking into account secondary processes through adequate adjustment. In fire design, it is usually assumed that concrete is a homogeneous material and that heat transfer occur mainly by conduction. Heat transfer by convection and radiation occurring in pores are considered as secondary processes and are implicitly taken into account in thermal properties available for concrete (conductivity, specific heat). Moreover, mass-exchange is generally neglected and only moisture evaporation in concrete is taken into account. The effects of moisture (assumed uniformly distributed in the concrete) is treated in a simplified way, assuming that when the temperature in a concrete part reaches 120°C, all of the heat transferred to that part is used to evaporate water. Moisture movements are rarely modelled. For composite members, contact between steel parts and concrete parts can be assumed to be perfect (no gap). Radiation in internal


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voids (such as hollow steel section) should be considered in the thermal analysis.

In principle, where the effects of a fire remain localised to a part of the structure, temperature distributions along structural members can be strongly non-uniform. So a precise calculation of temperatures should be determined by a full 3D thermal analysis. However, due to the prohibitive computing time of such analysis, it is often considered an acceptable simplification to perform a succession of 2D thermal analyses through the cross-sections of the structural members. Calculations are then performed at relevant location along the length of each structural member and the temperature gradients are obtained, assuming linear variation between adjacent temperature profiles. This approach gives usually a reasonable approximation to the actual temperature profile through members and allows significant reduction of the modelling and numerical effort. In 2D thermal analysis, cross-sections of members are commonly discretised by means of triangular or quadrilateral plane elements with thermal conduction capability. All sections encountered in civil engineering can thus be modelled. Each plane element describing the cross-section can have its own temperature-dependent material such as steel, concrete or insulation materials.

Boundary conditions can be either prescribed temperatures or prescribed impinging heat flux to simulate heat transfer by convection and radiation from fire to the exposed faces of structural members. Effects of non-uniform thermal exposure may be introduced in modelling with appropriate boundary conditions.

Effects of mechanical deformations (such as buckling of steel element, cracking and crushing of concrete, etc.) on the temperature rise of structural members is neglected, which is the standard practice. Consequently geometry of structural members does not vary during the analysis

As for simple models, the use of advanced models require knowledge of the geometry of structural members, thermal properties of the materials (thermal conductivity, specific heat, density, moisture...) and heat transfer coefficients at the member’s boundaries (emissivity, coefficient of heat transfer by convection).

Usually for fire design, temperature-dependent thermal material properties of concrete and steel are taken from EN 1992-1-2 and EN 1993-1-2 and heat transfer coefficients are those given in EN 1991-1-2 respectively.

6.3 Structural models Advanced numerical models for the mechanical response should be based on the acknowledged principles and assumptions of the theory of structural mechanics. They are usually finite element models. They can simulate a partial or a whole structure in static or dynamic modes, providing information on displacements, stress and strain states in structural members and the collapse time of whole building if collapse occurs within the period of the fire. The changes of mechanical properties with temperature, as well as non-linear geometrical and non-linear material properties, can be taken into account in the structural fire behaviour. The transient heating regime of structures during fire


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is modelled by use of step-by-step iterative solution procedures, rather than a steady state analysis.

This Section outlines some of the primary considerations in modelling the behaviour of single-storey buildings with steel or composite frames in the fire situation, notably features related to material models, computation procedure, structural modelling, etc.

Advanced calculation models can be used in association with any heating curve, provided that the material properties are known for the relevant temperature range and that material models are representative of real behaviour. At elevated temperature, the stress-strain curve of steel is based on a linear-elliptic-plastic model, in contrast to the elasto-plastic model adopted for normal temperature design. The steel and concrete stress-strain relationships given in EN 1993-1-2 and EN 1994-1-2 are commonly used.

In the fire situation, the temperature field of structural members varies with time. As stress-strain relationships of materials are non-linear and temperature dependant, an appropriate material model has to be adopted in advanced numerical modelling to allow the shift from one behaviour curve to another, at each step of time (and thus of temperature). The so-called kinematical material model is usually used for steel structures, assuming that the shift from one stress-strain curve to another one due to the change of temperature is made by staying at a constant plastic strain value (see Figure 6.3). This model can be used at any stress state of steel (tension or compression). For concrete, it is much more complicated, since the material has a different behaviour in tension and in compression. Therefore, different shift rules are needed for when the material is in tension or in compression. Generally, this kinematic model is used in most advanced calculation models for fire safety engineering applications.

Behaviour of steel is often modelled with a Von Mises yield contour including hardening. Behaviour of concrete in compression is modelled with a Drucker-Prager yield contour, including hardening.

),ε(θdε

dσ01

θ(t)θ 1

Δt)θ(tθ 2

a) Behaviour law of structural steel

Parallel to

)02

, ε(θdε

dσParallel to

Compression

b) Behaviour law of concrete

θ(t)θ 1

Δt)θ(tθ 2

tensile

Figure 6.3 Kinematic material models for steel and concrete

Another aspect to be noted in the application of advanced calculation models for steel and composite structures under natural fire conditions is the material behaviour during cooling phase. It is well known that for commonly used steel grades, the variation of mechanical properties with temperature are considered


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as reversible, which means that once they cool down they will recover their initial mechanical properties. However, this phenomenon is not true with concrete, whose composition will be totally modified when heated to an elevated temperature. After cooling down, it cannot recover its initial strength. Indeed, its strength might even be less after cooling than at maximum temperature.

The effects of thermal expansion should be taken into account. This is done by assuming that the total deformation of structural members is described by the sum of independent terms:

rtrcσtht )( (30)

where th , σ , r and c are the strains due to thermal expansion, stress, residual

stress and creep, respectively. tr is the strain due to transient and non uniform

heating regime for concrete (usually neglected).

In Eurocodes, the creep strain is considered to be included implicitly in stress-strain relationships of steel and concrete. The residual stress is usually neglected except for some special structural analysis. The thermal strain is the thermal expansion (L/L) that occurs when most materials are heated. Thermal strains are not important for fire design of simply supported steel members, but they must be considered for composite members, frames and complex structural systems, especially where members are restrained by other parts of the structure (as for single-storey building divided into cells separated from one another by fire walls) since thermally induced strains, both due to temperature rise and temperature differential, can generate significant additional internal forces.

Distribution of temperaturefor z = cte

Unit strain Cross-section(x = cte)

z

y

G c

th

t

r

Figure 6.4 Strain composition of material in advanced numerical modelling

In general, the structural analysis in the fire situation is based on ultimate limit state analysis, at which there is equilibrium of the structure between its resistance and its applied loading. However, significant displacement of the structure will inevitably occur, due to both material softening and thermal expansion, leading to large material plastification. Therefore, advanced fire analysis is a non-linear elasto-plastic calculation in which both strength and stiffness vary non-linearly. From a mathematical point of view, the solution of such analysis cannot be obtained directly and has to be achieved using an iterative procedure:

A step-by-step analysis is carried out in order to find the equilibrium state of the structure at various instants (at different temperature fields).

Within each time step, an iterative solution procedure is carried out to find the equilibrium state of the structure behaving in elasto-plastic way.


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Different types of convergence procedure are usually employed, such as the pure Newton-Raphson procedure and the modified Newton-Raphson procedure. The pure Newton-Raphson procedure is recommended for structures made of beam elements, and the modified Newton-Raphson procedure is recommended for structures made of shell elements.

Static analysis is normally sufficient for modelling the behaviour of a structure in fire. However, local failure or instability of a structural member (such as lateral buckling of purlin) does not lead to overall structural failure. Consequently, analysis should be performed by a succession of subsequent static and dynamic analyses to pass instabilities and to obtain the complete failure mechanism to predict the influence of a local failure on the global behaviour of the structure and to follow eventually progressive collapse. It has to be kept in mind that here the aim is not the precise modelling of dynamic effects. So, default values of the main parameters fixed in models to determinate acceleration and damping effects can be used.

Existing boundary conditions should be rightly represented. It is common to design structure by assuming pinned support conditions at the column bases. However, as fully pinned bases of columns are never achieved in reality, it is also possible, when data are available, to introduce semi-rigid connections. Where only a part of the structure is modelled, some restrained conditions from unmodelled part of the structure should be taken into consideration in appropriate way. The choices of restrained conditions that have to be applied at the boundaries between the modelled substructure and the rest of the structure have to be chosen by the designer. For example, in case of symmetry boundary, restraints to translation across the symmetry boundary and rotational restraint about the two major axes on the plane of symmetry are introduced in modelling.

Usually, beam-to-column joints are assumed to be fully rigid in the fire design of steel and steel-concrete composite frames. However, in the case of steel frames based on lattice beams, joints between members of lattice beams and connections between top and bottom chords of lattice beams and columns can be assumed pinned or fully rigid according to the type of truss.

Two types of action need to be applied to heated structures. The first type is static loading. It must correspond to that for fire situation. The second type consists of the temperature increase (above ambient) of the structural members obtained, from previous thermal analysis. Boundary conditions at supports as well as applied gravity loads are assumed to remain unchanged throughout the fire exposure

It is important to choose an appropriate structural modelling strategy. Simulation of the mechanical behaviour of single-storey building in fire conditions can be performed either by a 2D or a 3D analysis.

In a 2D analysis, simulation are performed in the plane of each portal frame, assuming a three dimensional behaviour of the frame to take into account the lateral instability of the members (columns, beams). In such modelling, adequate restraint conditions should be introduced to stabilize the frame laterally. In reality, these out-of-plane restraints are provided by roof structure


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(as purlins) as well as façades elements fixed on columns (concrete walls, sandwich panels, steel sheeting), so that out-of-plane collapse does not occur.

In a 3D analysis, several parallel portal frames, the roof structure (purlins) and eventually bracing system are explicitly modelled (see Figure 6.5). The main difference in this 3D analysis is that the interaction effects between members will be directly dealt with; load redistribution from heated parts (weakened parts inside fire compartment) to cold parts (stronger parts outside fire compartment) can be taken into account in an accurate way and the global behaviour of structures will be analysed, providing a more realistic situation of mechanical response of structures in fire. Computation cost with a three-dimensional analysis is high because of significant number of elements used in the modelling.

The choice between 2D and 3D analysis will depend on several parameters, such as the type of structure (steel or composite frame), the dimensions of the single-storey building, the fire scenario and objectives of structural fire design (to fulfil a prescriptive requirement, or to verify a failure mode).

Fire wall

Figure 6.5 Example of 3D mechanical modelling

The basic finite element set-ups used to represent the structural members of frame are given below. Solid elements are omitted. as they are numerically too expensive.


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REFERENCES

1 EN 1991-1-2:2002 Eurocode 1: Actions on structures - Part 1-2: General rules - Actions on structures exposed to fire

2 EN 1993-1-2:2003 Eurocode 3: Design of steel structures - Part 1-2: General rules – Structural fire design

3 EN 1994-1-2:2003 Eurocode 4: Design of composite steel and concrete structures – Part 1-2: General rules - Actions on structures exposed to fire

4 HOCKEY, S.M., and REW, P.J. Human response to thermal radiation HSE Books, UK, 1996.

5 VASSART, O., CAJOT, L-G., ZHAO, B., DE LA QUINTA, J.MARTINEZ DE ARAGON, J. and GRIFFIN, A. Fire Safety of industrial halls and low-rise buildings: Realistic fire design, active safety measures, post-local failure simulation and performance based requirements ECSC research project 7210-PR-378.

6 RFCS Research: Fire safety of industrial hall, Design Guide, Arcelor Mittal, CTICM, Labein tecnalia, ULG, Directorate-General for research, Research Fund for Coal and Steel Unit, RFS2-CR-2007-00032, Luxembourg, 2007.

7 Report to ECCS: Fire building regulations for single-storey buildings in 9 European countries. Document RT915. Version 02 June 2002.

8 LENNON, T., MOORE,D., WANG, B. Y. C. and BAILEY, G. Designers’ Guide to EN 1991-1-2, EN 1992- 1-2, EN 1993-1-2 and EN 1994-1-2 Actions on Structures Exposed to Fire and Structural Fire Design Thomas Telford, 2007.

9 DIFISEK - Dissemination of Structural Fire Safety Engineering Knowledge ECSC research project RFS-C2-03048.

10 PURKISS, J.A. Fire safety design of structures Butterworth-Heinemann, Oxford, UK

11 Risk Based Fire Resistance Requirements Competitive (RISK -REI), ECSC research project 7210-PR-378.

12 SIMMS, W.I., and NEWMAN, G.M. Single-storey steel framed building in fire boundary conditions (P313) The Steel Construction Institute, 2002.

13 ECCS TC3: Euro-monograms for fire exposed steelwork.

14 SD005a-EN-EU, Data: Nomogram for protected members, www.steel-access.com

15 RFCS Research: Fire safety of industrial hall, Design Guide, Arcelor Mittal, CTICM, Labein tecnalia, ULG, Directorate-General for research, Research Fund for Coal and Steel Unit, RFS2-CR-2007-00032, Luxembourg, 2007.

16 FRANSSEN J. M., KODUR V. and ZAHARIA R. Designing steel structures for fire safety Balkema Book, 2009.


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APPENDIX A German fire safety procedure for single-storey industrial and commercial buildings In Germany, buildings for commercial and industrial use must conform to the “Musterbauordnung” (MBO) and to all federal state building regulations “Bauliche Anlagen und Räume besonderer Art und Nutzung” (“Structural facilities and spaces with special requirements and uses”). In such cases, and in order to meet essential requirements (concerning human safety, public security, and protection of the natural environment), it is possible to adopt alternative solutions to the prescriptive federal state building regulations.

This general statement has to be considered in the context of physical and technical fire protection requirements for a building with reference to of “Wohngebäude und vergleichbare Nutzungen” (“residential and similar uses”) according to the federal state building regulations. For commercial and industrial uses, it is neither necessary nor appropriate to apply the requirements of the federal state building regulations. When it comes to meeting general structural fire protection objectives, it is more important to consider each building on an individual basis.

A standard procedure for assessing requirements, using scientifically based methods, is recommended.

Since industrial buildings are considered “Sonderbauten” (“special buildings”) within the definition of §51 Abs.1 MBO and cannot usually be exempt from the applicable regulations, the goal of MIndBauRl (the technical construction regulation) is to determine the minimum requirements for structural fire prevention. The MIndBauRl also uses design procedures according DIN 18230-1: Structural fire protection in industrial buildings –fire resistance design.

Regarding §3 Abs. 3, Satz 3 MBO, which permits variations from technical construction standards, the procedure limits this to accepted methods for fire protection engineering and requires that these are listed in accordance with Annex 1.

The aim of the procedure is to regulate the minimum requirements for fire protection of industrial buildings, in particular regarding:

the fire resistance of components and the flammability of building materials

the size of fire compartments and fire-fighting areas

the availability, location and length of emergency escape routes.

The procedure will facilitate design for building owners, designers, draftsmen and specialists; for the authorities it will provide justification for relaxation or deviation from the alternatively applicable rules of the MBO. It offers building control and approval bodies a benchmark for equivalent risks. A design method that requires no detailed engineering analyses and no particular calculation has been established. This responds to legal responsibilities and offers a straightforward form of approval.


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MIndBauRl applies to all industrial buildings regardless of their size. It does not apply to:

industrial buildings which are only used for storing technical equipment or facilities and where only access is temporarily needed for maintenance and inspection purposes

industrial buildings that are mostly open, such as covered outdoor areas or open warehouses

buildings which can be assimilated due to their behaviour in fire.

In addition, the procedure does not apply to storage shelves more than 9.0 m high (to the top of stored material).

This procedure may also be used for allowing and justifying relaxation of the regulations according to §51 MBO for buildings and structural facilities, which are not directly covered by the scope of MIndBauRl, although they are comparable to industrial structures in respect to fire risk.

Justification for relaxation of conditions under §51 Abs. 1 MBO may be provided with one of the following procedures.

Simplified procedure

In the procedure according to Abs. 6, the maximum fire compartment surface for a fire section area will depend on the fire-resistance classification of the supporting and stiffening components as well as the structure’s fire technical protection infrastructure.

Complete verification procedure

In the procedure according to Abs. 7, the maximum surface area and the requirements for the components in accordance with the fire safety classes for a fire compartment will be based on the calculation procedure according to DIN 18230-1.

Engineering methods

Instead of proceeding according to Abs. 6 and 7, standard fire protection engineering design methods may also be used.

The initiator of a fire protection concept has the choice which method (Abs. 6 or 7) will be implemented when using the MIndBauRl. However it is not permissible to combine procedures.

Concerning the fire engineering methods, the MIndBauRl identifies the principles and conditions for the hypotheses of such designs. It regulates the verification and checking as well as documentation.

The MIndBauRl, which has been introduced as a standard in the Building Regulations in all German states, is legally applicable. As part of the application of IndBauRl, there are several procedural methods. The same general requirements apply for all verifications; these are identical for all procedures and must be respected. These include fire-fighting water requirements, smoke evacuation, location and accessibility, emergency exits and fire spread.


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Fire-fighting water requirements must be agreed with the responsible fire department taking into account the surface areas and fire loads. These requirements should be assumed to last for a period of two hours.

minimum 96 m³/h for a surface area up to 2500 m²

minimum 192 m³/h for a surface area greater than 4000 m².

Intermediate values can be linearly interpolated.

For industrial buildings with automatic fire extinguishing systems, a water quantity of at least 96 m³/h over a period of one hour is sufficient to extinguish the fire.

Any factory or warehouse with an area of more than 200 m² must have wall or ceiling openings to allow smoke evacuation.

Individual spaces which are bigger than 1600 m² must have a smoke evacuator, so that fire fighting operations are possible. This is because a smoke layer of 2,5 m height has been mathematically proven.

In addition to the location and accessibility of each fire compartment, at least one side has to be located at one outside wall and be accessible from there for the fire department. This is not applicable for fire compartments which have an automatic fire extinguishing system.

Stand-alone and linked industrial structures with foundations of greater than 5,000 m² have to be accessible from all sides by fire fighting vehicles. These access routes must meet the requirements for fire brigade usage.

The fire service access roads, operating areas and other routes should be kept continuously free. They have to be permanently and easily recognizable.

Included in the emergency exits in industrial buildings are the main production corridors and storage areas, the exits from these areas, staircases and exits to the outside. Each room with an area of more than 200 m² must have at least two exits.

Regarding the maximum allowable length for emergency escape routes, equipment and structural fire protection both influence each other.

The maximum length of emergency escape routes is limited as a rule to 35 m for a clear height up to 5 m. However, if a fire alarm system is installed, then this increases to 50 m.

The maximum increase in length in relation to free height up to 50 is 70 m.

The distances are measured as distances in space, but not through construction elements or components. The real length should not be more than 1.5 times the distance that was measured in space. Attention should be paid to the fact that from any point in a room, a main gangway must be reachable within a maximum of 15 minutes.


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In case of fire, roofs often contribute significantly to fire spread; damage will depend on which structural fire prevention measures were implemented for the roof.

Regarding fire propagation in case of a fire from below, then the following failure mechanisms are typical:

The “Durchbrand” burn- through. This is the worst case, with fire spreading on top of the roof, followed by the spread of fire down into other areas through existing roof openings.

Failure of the load-bearing roof shell by slipping from the supports, for example with large spans.

Fire propagation below the roof.

Fire propagation within the roof shell. This is very dangerous because it will not be seen from below. It becomes very critical when the fire services are fighting at the fire source and suddenly it begins to burn behind them.

Table A.1 Fire compartment sizes

Maximum fire compartment size (m²)

Safety category Without fire resistance requirement

“R0”

With fire resistance requirement

R30

K1 Without requirements

1800* 3000

K2 Fire detection

2700* 4500

K3 Rescue service

3200 - 4500* 5400-7500

K4 Fire suppression

(Sprinkler system) 10000 10000

* heat extraction area 5% and building width 40m

The simplified method is based on the relationship between the permitted surface area of the fire compartment and the safety category, the number of storey and the fire rating classification of the components.

The surface area is given in Table A.1 and is well within extreme safety measures.

For industrial buildings with an existing sprinkler system (safety category K4), a maximum fire compartment surface area of 10000 m² can be realized without requirements for the fire resistance of structural components.

Without any fire protection requirements, surface areas up to 1800 m² can be left unprotected.

For industrial buildings which cannot be evaluated using the simplified procedure, the entire verification procedure will be based in accordance with DIN 18230-1.


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First, the equivalent fire duration is determined using this method. With the equivalent fire duration, a relationship between the incendiary effect of a natural fire and the “Einheitstemperaturzeitkurve” (ETK standard temperature time curve) is generated. The equivalence refers to the maximum temperature of structural components under a natural fire.

Once the equivalent fire duration has been determined, two different methods are available.

The first method is to determine the maximum floor surfaces using Table A.2. No requirements for fire resistance of structural components are needed when using this table.

The second method requires somewhat more effort. First, the maximum floor surface is calculated using a formula. In this procedure, the fire resistance rating of the structural components has to be proven. This is done with the necessary fire resistance.

Table A.2 Maximum floor area (m2) according to safety category and equivalent fire duration

Equivalent fire duration Safety category

15 30 60 90

K1 Without requirements

9000* 5500* 2700* 1800*

K2 Fire detection

13500* 800* 4000* 2700*

K3 Rescue service

1600-22500* 10000-13500* 5000-6800* 3200-4500*

K4 Fire suppression

(Sprinkler system)

30000 20000 10000 10000

Minimum heat extraction area

1 1 3 4

Maximum building width 80 60 50 40

In Table A.2, the maximum admissible floor surface can be defined with reference to its safety category and the equivalent fire duration. In addition, the corresponding heat extraction surface can be identified, indicated as a % of the floor surface and the corresponding maximum width of the building.

Using the second method for the entire verification procedure, the maximum floor area (m²) is calculated using the base value for the surface area of 3000 m² and factors F1 to F5.

A = 3000 F1 F2 F3 F4 F5

where:

F1 the equivalent fire duration

F2 the safety category

F3 : the height of the lowest floors


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F4 : the number of storey

F5 : the type of floor openings

The sum of the total surface area shall not exceed 60000 m².

According to the Table A.2, when the simplified procedure is used for structural components without requirements, the result is a maximum possible surface area of 10 000 m².

When using the full verification procedure according to this table, a maximum surface of 30000 m² is possible. When using the full verification procedure in addition to the fire resistance calculation, then a 60000 m² surface area is possible.

Under very special conditions, even larger surfaces, up to 120000 m² can be achieved.

Example:

The procedure and possibilities associated with MIndBauRl can best be shown and explained by an example:

Building parameters

Length: 100 m

Width: 50 m

Average height: 6 m

Size: 5000 m²

Number of storey: 1

Openings in the roof: 135 m²

Doors, windows: 132 m²

Fire load: qR = 126 kWh/m²

Automatic fire alarm systems: Safety category K2

No internal fire walls

The first possibility is the simplified method according to Table A.1. The industrial building must be equipped with an automatic sprinkler in order to meet the above conditions.

In order to apply fully the full verification method, the equivalent fire duration must first be determined. In this case, the heat extraction factor w is needed. The heat extraction factor is determined by taking into account the related opening surfaces. The related opening surfaces are auxiliary values. This is simply a question of dividing the roof openings by the ground surface and then the wall openings by the ground surface.

Determination of the related horizontal opening surface ah:

ah = Ah / A = 135 m² / 5000 m² = 0,027


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Determination of the related vertical opening surface av:

av = Av / A = 132 m² / 5000 m² = 0,026

The values of the related opening surfaces are introduced in Figure A.1 and the value w0 can be defined. In Figure A.2, the height of the hall is considered.

vertical opening area av

horizontal opening area ah

Figure A.1 Factor w0 according to opening areas

height of the hall (m)

Figure A.2 Factor w according to height of the hall

The heat extraction value of the buildings is:

w = w0 = 1,70 1,0 = 1,70

The equivalent fire duration (tä) is based on the following factors: the fire load density, the heat extraction factor and a factor c which takes into account the


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heat extraction surface of the peripheral construction elements. In this example c is given, for simplicity, the worst value.

tä = qR c w = 126 0,25 1,70 = 54,0 min

Through interpolation in Table A.2, in the safety category K2 for an equivalent fire duration of 54 minutes, a maximum surface area of 4800 m² can be defined. At this point, some additional work by the designer could be useful in reviewing the input data. Is the fire load case too high? What will happen when the opening surfaces are modified and the ground floor is also modified at the same time? Alternatively, what about the surfaces? Can the surface be reduced by 200m²? The onus is on the designer to present and explain the different opportunities to the client and to list the comparison costs.

The second possibility using the full verification method is more precise. The maximum floor surface is calculated using the basic value for the surface of 3000 m² times factors F1 to F5. The factor values are taken from tables of DIN 18230-1 and do not need to be determined.

According to table 3 of DIN 18230-1 the factor F1 is: 1,9




According to table 7 of DIN 18230-1the factor F5 is: 0,7.

Inserted into the formula:

A = 3000F1F2F3F4F5 = 3000 1,9 1.5 1,0 1,0 0,7

A = 5989 m².

In this method, the fire resistance classification of the structural components has to be calculated with the following equation:

Required fire resistance duration tf = täL

The design of the fire resistance duration includes the following factors:

the equivalent fire duration of 54 minutes

the safety factor of 0,6 according to Table 2 of DIN 18230-1, and

the factor alpha L takes into account the fire related infrastructure of 0,9 according to Table 4 of DIN.

Hence: tf = 54 0,6 0,9 = 29,16 min => R30


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Table A.3 Summary of maximum compartment sizes

Area given by simplified method (m2) Safety

category Without fire resistance requirement

With fire resistance requirement

K1

K2 2700 4500

K3 5400-7500

K4 10000

R0 R30

A comparison of these methods, the options available and responsibilities of the designer, can be seen in table A.3. In order to contain the industrial building in one single fire compartment without requirements for the load-bearing structure, it is necessary to install an automatic sprinkler system when using the simplified method. When using the full verification method and respecting the given conditions, a fire compartment of 4800 m² is possible. To achieve one fire compartment of 5000 m², at least one plant fire service must be present.

With a fire resistance requirement of R30 for the load bearing structure, at least one plant fire service is required for the simplified method (according to the table). With a fire detector system, however, only one fire compartment area of 4500 m² is possible. With the full verification method, a fire compartment surface of 5989 m² is possible.

Based on the results of the different methods, the designer’s task is clearly defined. He should not only develop one fire protection concept, but has to demonstrate alternative and more economical procedures to the client in relation to the various production processes.



Part 8: Building Envelope



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FOREWORD

This publication is part eight of the design guide, Single-Storey Steel Buildings.




Part 3: Actions













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Contents Page No

FOREWORD iii

SUMMARY vii

1 INTRODUCTION 1 1.1 The building envelope 1 1.2 The functions of building envelope 3

2 TYPES OF METAL CLADDING SYSTEMS 4 2.1 Single-skin trapezoidal sheeting 4 2.2 Built-up double skin cladding 5 2.3 Insulated (composite or sandwich) panels 8 2.4 Standing seam systems 9 2.5 Structural liner trays 10 2.6 Structural deck and membrane roof systems 10

3 SPECIFICATION OF THE CLADDING 12 3.1 Weathertightness 13 3.2 Building appearance 14 3.3 Thermal performance 15 3.4 Interstitial condensation 18 3.5 Acoustics 18 3.6 Fire performance 20 3.7 Durability 21 3.8 Structural performance 21

4 COLD ROLLED SECONDARY STEELWORK 24 4.1 Purlin and side rail options 24 4.2 Loading 30 4.3 Deflections 31 4.4 Purlin and side rail selection 31 4.5 Restraint provided to the rafters and columns 32 4.6 Restraint of purlins and cladding rails 33

5 HOT-ROLLED SECONDARY STEELWORK 35

REFERENCES 37


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SUMMARY

This publication provides guidance on selection of the building envelope for single-storey buildings. The building envelope is generally formed of secondary steelwork (often cold-rolled steel members) and some form of cladding. In addition to providing a weathertight barrier, the envelope may also have to meet thermal, acoustic and fire performance requirements. In some arrangements, the building envelope may have an important structural role in restraining the primary steel frames.

The document describes the common forms of cladding for single storey buildings, and offers advice on how an appropriate system is specified. The document also describes the systems of secondary steelwork that support the cladding.


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1 INTRODUCTION

Metal cladding systems provide an efficient, attractive and reliable solution to the building envelope needs of single storey buildings (steel, concrete or wood framed structures). Over the years, these systems have evolved from the single skin metal cladding often associated with agricultural buildings to highly developed systems used in industrial, retail and leisure applications. However, as with all construction components, the ability of the cladding to satisfy its functional requirements is dependent on its correct specification and installation and, equally as important, on its interaction with the other elements of the building envelope and structure.

This publication provides guidance relating to the secondary structures and building envelope types used in single storey buildings. Description is given of the common types of profiled metal cladding systems currently used in Europe. These systems include insulated panels, built-up systems, deck and membrane, and liner trays. Guidance is also given on key issues that should be considered when specifying either the building envelope or its supporting structure.

Reference is made to a selection of technical documents published by The Metal Cladding and Roofing Manufacturers Association (MCRMA). These technical documents provide comprehensive guidance on various associated topics, which are applicable throughout Europe and can be readily downloaded from www.mcrma.co.uk. Additional information can also be found on the French language website Acier Construction at http://www.acierconstruction.com

Guidance has been included in this document which considers the restraining action of the secondary steelwork to primary steelwork and the restraint provided by cladding sheeting to secondary steelwork. However, in certain countries within Europe (e.g. in France), this restraining behaviour cannot be utilised, and a footnote has been added highlighting where this is the case.

1.1 The building envelope The principal components of a modern metal-clad industrial type building are shown in Figure 1.1.


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2

1

34

5

1 Profiled steel roof cladding 2 Wall cladding 3 Purlins

4 Side rails 5 Primary steel frame

Figure 1.1 Principal building components

There are essentially three layers to the structure:

1. The primary steel frame, consisting of columns, rafters and bracing. The example shown in Figure 1.1 is a portal frame, but the guidance given in this publication is also applicable to other types of structure.

2. The secondary steelwork, consisting of side rails for the walls and purlins for the roof. These members serve three purposes:

- To support the cladding

- To transfer load from the cladding to the primary steel frame

- To restrain the primary steel frame members (see Section 4.5 on limitations on such use) .

3. The roof and wall cladding, whose functions include some or all of the following:

- Separating the enclosed space from the external environment

- Transferring load to the secondary steelwork

- Restraining the secondary steelwork

- Providing thermal insulation

- Providing acoustic insulation

- Preventing fire spread

- Providing an airtight envelope


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- Providing ventilation to a building (ventilated or unventilated roofs and walls).

The cladding will also normally include ancillary components such as windows, rooflights, vents and gutters.

As an alternative to the layout shown in Figure 1.1, some types of cladding may be installed directly to the primary steelwork without the need for purlins or cladding rails. Examples of this type of construction are deck and membrane for roofs and liner trays for walls. Where such solutions are chosen, the cladding must be designed to:

- Span directly between the rafters, roof beams or trusses. This is usually achieved by the use of deep profiled decks or trays, but where these are insufficient for the required span, intermediate supports in the form of secondary beams or hot-rolled purlins will need to be installed.

- Restrain the primary steel members. Structural decks and liner trays, if fastened correctly, should be able to provide sufficient lateral restraint to the outer flange of the supporting rafter or column. This should allow the columns and rafters to be designed as fully restrained under gravity loads or positive wind pressure. However, additional restraining members will need to be included in the structure in order to provide intermediate restraint against wind suction (uplift on the roof).

1.2 The functions of building envelope All buildings, whatever their use, must provide a controlled internal environment that is protected from the variable and uncontrollable external climate. The nature of the internal environment will depend on the intended use of the building and this will naturally determine the requirements for the building envelope.

Generating and maintaining a controlled internal environment is a complex process, requiring a combination of mechanical and electrical services to heat and/or cool the building and a well-designed building envelope to regulate the heat gain and loss. The design of the building envelope is an important factor in specifying the Mechanical and Electrical (M&E) plant and in determining the energy performance of the building. With pressure to reduce energy consumption now being placed on the construction industry across Europe, the building envelope has never before been under such close scrutiny.

In addition to forming the building envelope, the roof and wall cladding may also have an important role to play in the structural performance of the building, by providing restraint to the secondary steelwork against lateral-torsional instability. Where such restraint is assumed (as is often the case in the purlin and side-rail manufacturers’ load/span tables), it is essential that the cladding is capable of providing this restraint in practice.


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2 TYPES OF METAL CLADDING SYSTEMS

There are a number of proprietary types of cladding that may be used in industrial buildings. These tend to fall into a few broad categories as described in this Section.

The steel sheet is generally coated with a zinc or zinc-aluminium alloy in a hot-dip process. The top coating is an organic coating to provide an attractive finish, typically based on Polyvinyl–chloride (PVC or Plastisol), Polyvinylidene–fluoride (PVDF or PVF2), Polyester or Polyurethane formulations. Aluminium cladding sheets are also available.

For hot-dip galvanised sheeting, typical design lives are shown in Table 2.1.

Table 2.1 Typical design life for coated steel sheet

Coating Design life (years)

PVC – 200 microns 10 – 30

PVC – 120 microns 10 – 25

PVDF or PVF2 – 25 microns 10 – 15

Polyester – 25 microns 5 – 10

Polyurethane – 50 microns 10 – 15

2.1 Single-skin trapezoidal sheeting Single-skin sheeting is widely used in agricultural and industrial structures where no insulation is required. The sheeting is fixed directly to the purlins and side rails as shown in Figure 2.1. The cladding is generally made from 0,7 mm gauge pre-coated steel with a 32 mm to 35 mm trapezoidal profile depth.

1

1 Slope

Figure 2.1 Single-skin trapezoidal sheeting


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2.2 Built-up double skin cladding This common type of cladding consists of a metal liner, a layer of insulation material, a spacer system and an outer metal sheet, as illustrated in Figure 2.2. The span of such systems is limited by the spanning capability of the cladding sheets, which is typically in the order of 2 m to 2,5 m depending on the applied loading. Built-up cladding systems must, therefore, be supported by secondary steelwork (purlins or side rails). As the name suggests, these systems are built up from their constituent parts on site.

21

6

54

3

1 Weather sheet 2 Slope 3 Bar

4 Liner sheet 5 Bracket 6 Insulation

Figure 2.2 Built-up roof cladding

2.2.1 Liner sheet

The liner sheet serves several purposes:

It supports the thermal insulation

It provides an airtight layer

It provides restraint to the purlins.

Liner sheets are usually manufactured from cold formed pre-coated steel or aluminium and possess a shallow trapezoidal profile (i.e. height 18 mm to 20 mm is illustrated in Figure 2.3). For steel liners, the sheet thickness is usually either 0,4 mm or 0,7 mm, while aluminium liner sheets are slightly thicker at 0,5 mm or 0,9 mm. The choice of liner will depend on the required spanning capability, the cladding installation method and the acoustic requirements of the cladding. Where required, the acoustic performance of the cladding, in particular its ability to absorb sound and minimise reverberation, may be enhanced by the use of a perforated liner sheet.


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1

2

1 Thickness (0,4 – 0,7 mm) 2 Profile height (18 – 20 mm)

Figure 2.3 Liner sheet profile

The shallow liner sheets are not strong enough to walk on, so it is essential that the insulation, spacer system and weather sheet are installed from boards or access platforms, as illustrated in Figure 2.4. However, they do provide a non-fragile barrier against falling once they have been fully fastened. Where walking access is required, it is common practice to replace the shallow liner profile with a more substantial sheet (i.e. 32 mm to 35 mm trapezoidal profile in 0,7 mm gauge steel).

Figure 2.4 Liner sheet installation progressing into the span of the purlins.

2.2.2 Insulation

The primary function of the insulation layer is to provide a barrier to the flow of heat between the interior of the building and the external environment. The thickness of the insulation layer in roof and wall assemblies has increased significantly in recent years from approximately 80 mm in the 1980s to values approaching 200 mm in 2009. Further increases in thickness are expected over the next few years as the regulations on energy use in buildings become more onerous.

The most common form of insulation in built-up cladding systems is mineral wool quilt, which is favoured due to its light weight, low thermal conductivity, ease of handling and relatively low cost. Rigid mineral wool slabs are available, but are less deformable than mineral wool quilts, giving rise to the


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potential for air gaps between the insulation and the profiled metal sheets. Rigid mineral wool slabs are also much heavier than mineral wool quilts, with consequences for the loading on the supporting steelwork and manual handling on site.

2.2.3 Spacer system

The primary function of the spacer system is to support the weather sheet at the required spacing from the liner sheet. The components of the system must, therefore, possess sufficient strength and stiffness to safely transmit the required loading through to the purlins, without excessive deformation. A common form of spacer is a bar and bracket system, as shown in Figure 2.5. The system consists of cold formed steel bars, which provide continuous support to the weather sheet, supported at intervals by steel brackets firmly attached to the purlins through the liner. Many bar and bracket systems also incorporate plastic pads (which act as thermal breaks) in order to minimise thermal bridging. Other types of spacer systems are also available, for example Z spacers supported on thermally insulating plastic blocks.

1

2

3

4

1 Bar 2 Bracket 3 Sway bracket 4 Purlin

Figure 2.5 Bar and bracket spacer system

2.2.4 Weather sheet

The outer sheet of a double skin built-up cladding system is known as the weather sheet. As the name suggests, its primary function is to protect the building from the exterior climate by forming a weather-tight envelope. However, the weather sheet should also be regarded as a structural element, as it plays an important role in transferring externally applied loads (e.g. from wind, snow and foot traffic) through to the other cladding components, secondary steelwork and the primary load-bearing frame.

The weather sheets are usually made from either steel or aluminium and are available in a wide variety of finishes and colours. Steel weather sheets are manufactured from pre-coated steel coil. Aluminium weather sheets are available in a mill finish or in a range of painted finishes. Detailed requirements for the weather sheets for roof and wall cladding applications are given in EN 14782[1].


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2.2.5 Fasteners

A wide variety of proprietary fasteners are available, which where required, can be watertight. Most fasteners used for metal cladding applications are both self-tapping and self-drilling, although screws which are only self-tapping are also available for use in pre-drilled holes. Fasteners can be used to connect sheeting to supporting steelwork (or other materials) or to connect adjacent sheets. For most fastener applications, a choice between plated carbon steel and stainless steel (typically grade 304 austenitic stainless steel is used) is made. Visible fasteners have the option of factory coloured plastic heads to suit the weather sheet. Further information describing these and other fasteners (e.g. secret fix fasteners) is available from MCRMA Technical Paper No 12 Fasteners for Metal Roof and Wall Cladding: Design, Detailing and Installation Guide[2].

2.3 Insulated (composite or sandwich) panels Insulated roof and wall cladding panels consist of a rigid layer of insulation sandwiched between two metal skins, as shown in Figure 2.6. The result is a strong, stiff, lightweight panel with good spanning capabilities due to composite action in bending. These panels are commonly used on industrial buildings and retail ‘sheds’ in place of the built-up cladding described in Section 2.2. In this case, the panels span between cold formed purlins or side rails, which in turn span between the primary frame members. However, for commercial buildings, where the secondary steelwork is not needed for restraint purposes, it is quite common for composite wall cladding panels to span directly between the columns.

Standing seam and through-fixed systems are available, with either a trapezoidal weather sheet and shallow profiled liner, as shown in Figure 2.6, or two flat / micro-ribbed sheets. Profiled composite panels are used for roofs to allow rainwater to run off without penetrating the fastener holes, while flat panels are favoured for walls due to their better appearance.

1

2 1 Insulation 2 Metal sheets

Figure 2.6 Insulated panel

Unlike built-up systems, there is no need for a spacer system, as the rigid insulation is strong and stiff enough to maintain the correct spacing of the sheets. Any loads applied in the plane of the cladding (e.g. down-slope loads


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on a pitched roof) are transferred from the external sheet through the two adhesive bonds and the layer of insulation to the internal sheet and the supporting structure.

Polyisocyanurate (PIR) is the most common insulation material used in foam-insulated panels. PIR expands rapidly when sprayed onto the metal profile and bonds to it without the need for an adhesive. This property makes it ideally suited to the type of continuous manufacturing process employed by the larger manufacturers of foam-filled panels. Alternatively, rigid slabs of mineral wool or other insulating materials may be bonded to the metal sheets using an adhesive. This method is commonly used for flat-faced wall panels.

2.4 Standing seam systems ‘Standing seam’ or ‘secret fix’ systems use a specially designed profile for the weather sheet, which incorporates a clipped joint between adjacent sheets. This eliminates the need for exposed fasteners and improves the weather tightness of the cladding system. Consequently, standing seam systems may be used on very low roof slopes (down to 1º compared to 4º for systems with exposed fasteners). Insulated panel systems are also available with a standing seam joint in the weather sheet. Standing seam sheeting can be manufactured from steel or aluminium.

A typical standing seam system is shown in Figure 2.7.

5

3

4

1 2

1 Outer sheeting 2 Slope 3 Standing seam clip

4 Inner sheeting 5 Insulation

Figure 2.7 Standing seam roof cladding

The disadvantage of this system is that significantly less restraint is provided to the purlins than with a conventionally fixed system. Nevertheless, a correctly fixed liner will provide adequate restraint.

Further information on standing seam cladding systems may be obtained from MCRMA Technical Paper 3 Secret fix roofing design guide[3] and also from ECCS-TC7 Publication 41 Good practice in steel cladding and roofing[6].


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2.5 Structural liner trays Structural liner trays are a popular alternative to composite wall panels. They comprise a deep structural profile into which a slab of insulation is inserted on site. The assembly is completed with the addition of an external profiled metal sheet, as shown in Figure 2.8. Unlike built-up systems, liner trays span directly between the main structural columns, thereby removing the requirement for secondary cladding rails. This is possible because of the depth of the liner tray profile and its resulting bending stiffness. The lack of secondary steelwork therefore can have clear advantages in terms of the speed and cost of the construction process and installation tolerances.

However, consideration, should be given to thermal bridging that can exist with liner trays. This issue may be partially overcome by placing an additional layer of rigid insulation on the outside of the tray.

Where plastic design of portal frames is a common design approach, the absence of side rails can create issues when attempting to provide restraint to the inside flange of the columns (e.g. in the hogging region of a portal frame), since traditional knee bracing cannot easily be attached to the liner tray profile.

Structural liner trays can also be specified with perforations where improved acoustic performance is required.

1

2

3

1 External profile sheeting 2 Insulation 3 Liner tray

Figure 2.8 Structural liner tray cladding systems

2.6 Structural deck and membrane roof systems Structural deck and membrane systems provide a long spanning alternative to built-up cladding on cold formed purlins and are especially popular on ‘flat’ or very low pitch roofs on which a waterproof membrane is required. The roof construction comprises a trapezoidal profiled metal deck of sufficient depth and gauge to span directly between the rafters, roof beams or trusses. A common metal deck typically has a profile height of 100 mm and a steel


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thickness between 0,75 mm and 1,0 mm. The deck supports a layer of rigid insulation on top of which the waterproof membrane is placed, as shown in Figure 2.9. The use of a high density rigid membrane permits the loads from foot traffic and snow to be carried through the insulation layer to the structural deck without the need for an external metal sheet or spacer system. The deck is capable of restraining the top of the beam or truss, making it ideal for building designs that have simply supported roof structures. However, structural decks are not suitable for plastically designed portal frames due to the need to restrain the inner flange of the rafter in the hogging region.

1

2

3

4

5

6

1 Structural deck 2 External membrane 3 Rigid gypsum roof

boards 4 Insulation 5 Vapour retarder 6 Supporting steelwork

Figure 2.9 Structural deck and membrane cladding system


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3 SPECIFICATION OF THE CLADDING

The specification of roof and wall cladding has implications well beyond the aesthetics and weathertightness of the building. The choice of cladding can affect many aspects of the building’s performance, from its construction right through to its eventual demolition and disposal. Indeed, the fitness for purpose of the whole building could be compromised if sufficient care is not taken when specifying the cladding. Listed below are the factors that should be taken into consideration when specifying profiled metal cladding systems. Further details on the principal technical considerations are given in Sections 3.1 to 3.8.

Weathertightness

Strength and rigidity

Thermal insulation

Control of condensation

Control of thermal movement

Sound insulation

Fire resistance

Appearance

Durability

Cost

Daylighting

External attachments

Lightning protection

Design detailing

Maintenance, remedial work and renewal.

Control of air leakage.

Minimum performance requirements for a number of these factors are laid down by legislation in Europe. Other factors, such as appearance and day lighting, may not seem to be as critical from an engineering viewpoint, but might be crucial to the success of the building in terms of the well-being of the occupants and the acceptance of the building by the local community. It should not be forgotten that the cost of the insulated cladding in a typical commercial or industrial building is usually a significant proportion of the overall construction cost, so decisions related to the cladding could influence the economic success or failure of the project. The cladding also has a significant impact on the operational energy requirements and, therefore, the operating costs of the building in service, specifically heating, cooling and lighting.


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3.1 Weathertightness The primary function of the cladding system is to provide a weathertight building envelope, suitable for the intended use of the building. With this in mind, the cladding specifier must give careful consideration to the selection of the cladding components and the detailed design of the system. The location of the building, its orientation and the external climate should all be considered when specifying the cladding. The satisfactory performance of the system also depends on the correct assembly of the components in the factory and/or on site.

In general, roofs are at greater risk of leakage than walls, and this risk increases as the roof pitch decreases. This is an important factor in the design of modern non-domestic buildings, since many have low pitch or flat roofs in order to minimise the volume of empty roof space. Not all types of roof cladding are suitable for use on low pitch roofs. Specifiers must, therefore, pay careful attention to the minimum pitch recommended by the manufacturers, together with the published guidance on detailing and installation.

Trapezoidal metal roof sheets with through fix fasteners are generally suitable for slopes of 4º (7%) or steeper. This 4º limit is critical to the performance of the cladding and should take into account deflections in the supporting steelwork and localised cladding deformations that may lead to ponding. Where the primary steelwork is precambered to off-set the deflections due to permanent actions, great care must be taken to ensure that excessive precamber does not result in local high points, as these could also cause ponding. For shallower pitches, down to 1,5º (1,5%), a secret fix system with no exposed through fasteners, special side laps and preferably no end laps should be used. Secret fix systems may also be used on steeper roofs where increased reliability is desired.

For low pitch roofs, ponding is a potential problem that must be considered at the design stage in order to avoid the deleterious effects of prolonged soaking and the increased loading due to the weight of the water. Where ponding occurs on rooflights, there is also the additional problem of the water leaving dirt deposits as it evaporates.

Side and end laps in profiled sheeting are weak points in the building envelope, where the wind and rain could potentially penetrate the cladding. The design and construction of the laps is therefore critical to the weathertightness of the cladding system. End laps typically consist of two continuous butyl sealant strips, which are compressed to form a weathertight seal by the clamping action of the fasteners. The pitch of fasteners required to achieve a proper seal will depend on the profile geometry, but one fastener per trough is common. A typical side lap between trapezoidal sheets is formed by overlapping the profiles with a strip of butyl sealant positioned on the weather side of the fastener to provide a weather-resistant seal. The side laps should be stitched at 500 mm centres or closer using steel stitcher fasteners. Further information on side and end lap details is given in MCRMA Technical Paper No. 6 Profiled metal roofing design guide[4] and Technical Paper No. 16 Guidance for the effective sealing of end lap details in metal roofing constructions[5]. Reference can also be made to ECCS-TC7 Publication 41 Good practice in steel cladding and roofing[6].


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3.2 Building appearance The choice of wall and roof cladding can have a significant impact on the appearance of a building. The following factors are particularly important:

Profile shape

Colour

Fasteners.

The profile shape can have a significant impact on the appearance of a building due to its effect on the perceived colour and texture of the cladding (caused by the reflection of light). The orientation of the cladding (ribs horizontal or ribs vertical) will also influence the appearance of the building, due to the effects of shadow and reflection. A potential disadvantage of horizontal ribs is that they tend to suffer from an accumulation of dirt over time, unless the cladding is cleaned regularly. Where the location and function of the building demand a smooth flat exterior, insulated wall panels with flat facing sheets may be used, however, it should be noted that any defect on the surface will be readily noticeable.

The steel from which profiled cladding sheets are made is available pre-coated in a wide range of colours and textures, allowing architects to choose a finish that best suits the location and function of the building. In choosing the finish, the architect should bear in mind the influence of the profile shape on the overall appearance by making an allowance for the effects of reflection and shadow on the perceived shade of colour.


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Figure 3.1 Typical wall cladding with a mix of flat panels and profiled

sheeting

The overall appearance of the building can also be affected by the choice of fasteners, especially on wall cladding or on steeply pitched roofs. Cladding specifiers should, therefore, give careful consideration to the size, shape, colour and locations of the fasteners and washers. Fasteners with factory coloured plastic heads are available to match the colour of the weather sheet. Where exposed fasteners are considered detrimental to the appearance of the building, the architect may consider the use of secret fix insulated panels or standing seam systems in which all fasteners are hidden from view. Further information on fasteners is available from MCRMA Technical Paper No 12 Fasteners for Metal Roof and Wall Cladding: Design, Detailing and Installation Guide[2].

3.3 Thermal performance 3.3.1 Energy consumption

The increase in public awareness of global climate change and the association with human activity has placed energy consumption and carbon dioxide emissions high on the political agenda. Under the terms of the Kyoto Protocol, European countries are now legally bound to reduce their carbon dioxide


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emissions and meeting this obligation will require significant changes in many sectors of industry, especially construction.

A significant proportion of carbon dioxide emissions in Europe is related to the operational energy requirements of buildings (heating, lighting, ventilation etc.). This issue is addressed by European Directive 2002/91/EC: Energy performance of buildings[7]. Although many factors influence a building’s energy efficiency, the thermal performance of the building envelope is significant. Consequently, it has been sought to reduce energy consumption by improving the thermal performance of the cladding and associated components.

The main sources of heat loss through the building envelope are shown in Figure 3.2.

1 2 3 1 Thermal bridge (metal spacer) 2 Thermal transmittance through insulation 3 Air leakage through joints

Figure 3.2 Main sources of heat loss through the building envelope

3.3.2 Thermal transmittance

Thermal transmittance through the building envelope can be a significant source of energy loss within a building, especially if there is insufficient insulation. One measure of thermal transmittance is the “U-value”, which is defined as the rate of heat transfer through an element of the building envelope (e.g. a wall, window, section of roof or rooflight) per square metre. The SI unit for the U-value is W/m2K. For an individual component such as a cladding panel, the elemental U-value depends on the conductivity and thickness of the insulation, the profile shape and the presence of thermal bridges. Cladding and insulation manufacturers usually quote U-value for their products for a range of insulation thicknesses. Alternatively, the U-value of a given built-up of envelope may be calculated using software.

National regulations generally specify maximum U-values. These are often the weighted average (or similar “overall” figure) for the whole of the roof or wall, with maximum values for individual elements such as doors. The individual elements tend to have much higher U-values than the cladding.

Typical limiting U-values are shown in Table 3.1.


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Table 3.1 Limiting U-values

Element Area weighted average

(Wm-2K-1)

Wall 0,35

Roof 0,25

Window 2,2

Pedestrian door 2,2

Roof ventilator 6

Over recent years, the drive to improve the energy performance of buildings has resulted in a significant reduction in the U-values for building envelope elements, resulting in a considerable increase in insulation thickness. This has had important implications for the structural performance of the cladding system and its relationship with other structural elements. Of particular concern to the structural engineer are the increased depth and weight of the cladding and its ability to adequately restrain the purlins or side rails. Inevitably the trend will continue towards improved thermal efficiency. However, the diminishing returns obtained from further reductions in U-values means that in future more emphasis is likely to be placed on airtightness and the performance of mechanical services, rather than ever increasing insulation thicknesses.

While some countries have adopted the U-value as the preferred means of quantifying the performance of the envelope, elsewhere the chosen parameter is the R-value or thermal resistance. The R-value is simply the reciprocal of the U-value and the points noted in the preceding paragraphs are equally applicable in these countries.

Typical U-values for different cladding systems are shown in Table 3.2.

Table 3.2 Typical U-values for cladding

Element U-value (Wm-2K-1)

Built-up system, 180 mm insulation 0,25

Built-up system, 210 mm insulation 0,2

Composite panel, mineral fibre, 120 mm 0,34

Composite panel, mineral fibre, 150 mm 0,27

Composite panel, PIR, 60 mm 0,33

Composite panel, PIR, 100 mm 0,20

3.3.3 Thermal bridges

Thermal bridges are areas or components within the roof or wall cladding assembly whose thermal insulation properties are lower (often much lower) than those of the surrounding material, thereby permitting local high heat flows through the building envelope. A common example of a thermal bridge would be an all-metal spacer in a built-up cladding system. In general, all metal components will act as thermal bridges, because of their high thermal conductivity, unless specific measures are taken to interrupt the heat flow by introducing a layer of thermal insulation. Thermal bridging increases the heat


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loss from a building, thereby increasing the operational energy requirement. It can also lead to a reduction in the internal surface temperature of the cladding, causing condensation to form under certain conditions.

3.3.4 Airtightness

The airtightness of a building is central to the requirements of the building regulations and is likely to become even more important as architects strive to improve the thermal performance of the building envelope without significant increases in insulation thickness. The airtightness of a building is quantified in terms of its air permeability, which is defined as the volume flow rate of air per square metre of building envelope and floor area at a given pressure. The maximum permissible air permeability for a given building will depend on a number of factors including the requirements of the building regulations, the specified CO2 rating for the building and the means by which this rating is to be achieved (e.g. the architect may specify a very low level of air permeability as an alternative to increasing the thickness of insulation). In many countries, achievement of the specified air permeability must be demonstrated by post-construction testing.

3.4 Interstitial condensation Interstitial condensation occurs within the layers of the cladding construction and is due to warm moist air from within the building penetrating the liner and condensing on the cold outer sheet and other components. The severity of the problem will depend on the relative humidity of the air within the building, the external air temperature and humidity, and on how well the liner is sealed. Buildings in cold climates and those containing swimming pools, laundries or other similar applications are most at risk, as are cladding systems that incorporate a perforated liner and separate vapour control barrier. In extreme cases, the condensation could result in corrosion of steel components within the roof assembly or in wetting of the insulation.

Recommendations for avoiding interstitial condensation are usually given in National Standards.

3.5 Acoustics Depending on the application, acoustic performance can be an important consideration when specifying roof and wall cladding. There are three categories of acoustic performance to consider, as illustrated in Figure 3.3.

3.5.1 Airborne sound transmission

Where there is a need to limit the passage of sound through the building envelope, the cladding specifier needs to consider the Sound Reduction Index (SRI) of the cladding. The SRI is a measure of the reduction in sound energy (in decibels) as sound passes through a construction at a given frequency. The acoustic performance of a particular cladding system will depend on the insulation material, the weather sheet and liner sheet profiles and the method of assembly. Of these, the insulation is the dominant factor, with soft mineral wool insulation giving better sound insulation than rigid board (dependent upon density).


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3

1

2

1 Impact noise from rain 2 Reverberation 3 Airborne sound transmission

Figure 3.3 Categories of acoustic performance

3.5.2 Reverberation

In certain applications, such as offices or residential accommodation, internal acoustic performance might be critical to the functionality of the building. Of particular interest is the reverberation caused by sound waves reflecting off hard internal surfaces, including elements of the building envelope. Typically, the internal finishes of the building will be used to limit reverberation, but architects may also take advantage of the sound absorbing properties of the cladding insulation layer by replacing the standard liner sheet with a perforated liner. Where the envelope consists of insulated sandwich panels, it is not uncommon to install a perforated liner and a layer of mineral wool insulation on the inside of the envelope in order to reduce reverberation.

3.5.3 Impact noise

The noise created by the impact of rain or hail on metal roof sheeting can sometimes create a nuisance for the building occupants. Where impact noise is considered to be important, it can sometimes be reduced by placing a flexible insulation layer directly below the outer sheet to act as a damper.

3.5.4 Noise associated with building services equipment

Consideration should also be given to attenuating noise emanating from services equipment. These include providing sound enclosures for noise prone machinery and/or including equipment supports with dampers. Reduction of noise from services is particularly appropriate in industrial buildings.

National regulations may specify acoustic performance standards in terms of reducing noise coming into a building – but these are often for residential buildings. 65 dB is generally considered a suitable indoor noise level in industrial buildings, whereas 50 to 55 dB is considered a suitable indoor ambient noise level for commercial, retail and leisure buildings. For industrial buildings, noise break-out is usually a greater concern. Local regulations may


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specify acoustic requirements to reduce noise break-out from within a building (for example if the building is sited adjacent to a residential area).

Cladding system manufacturers will be able to provide acoustic performance data for different constructions, and be able to recommend a system to meet the specification.

A built-up system comprising an inner and outer sheet of pre-finished steel with mineral wool insulation generally achieves over 40 dB of sound reduction. Rock mineral wool has a greater density than glass mineral wool, and generally improves the sound insulation. Sound insulation can be improved by including a layer of dense acoustic mineral wool slab, in addition to the insulation quilt.

In general, factory insulated foam filled composite systems are not as effective as built up systems, because of the low mass of the foam core and the direct coupling of the inner and outer skins.

The sound reduction index Rw for various systems is shown in Table 3.3. A higher index indicates higher sound reduction.

Table 3.3 Sound reduction index for typical cladding systems

Cladding type Sound reduction index Rw

Built-up system – with rock wool and acoustic insulation

47

built-up system with rock wool 45

built-up system with glass mineral wool 41

composite panel with mineral wool 31

composite panel with foam 25

single skin 24

3.5.5 Further information

Further guidance is available in MCRMA Technical paper No. 8 Acoustic design guide for metal roof and wall cladding[8] and also from ECCS-TC7 Publication 41 Good practice in steel cladding and roofing[6].

3.6 Fire performance In general, any concerns about the reaction of cladding to fire are far outweighed by concerns about the smoke and gas generated by the contents of the building, not the envelope.

Single sheet cladding is considered to contribute significantly to any fire. Single sheet cladding is generally assumed not to make any contribution to fire resistance, although in practice some integrity and resistance will be provided. Single skin sheeting is generally not used on boundaries, when prevention of fire spread to neighbouring structures is important.

Built-up systems that use mineral wool or glass wool insulation are not considered to contribute significantly to any fire. Built-up systems may also be


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specified to meet the requirements for external envelope applications. Composite panels that use mineral wool fall in the same category.

Factory insulated composite panels may use polyurethane (PUR) or polyisocyanurate (PIR). It is generally considered that PIR panels have improved performance in fire compared to PUR panels. The core of either type of panel is difficult to ignite. Panels with appropriate joint designs with either PUR or PIR filling do not present an undue fire risk, and PUR panels are the standard core in many European countries.

Polystyrene filled panels present a fire risk, and their use is diminishing.

3.7 Durability All cladding systems suffer a certain degree of degradation over time due to moisture, atmospheric pollution and UV radiation. However, the cladding specifier can have a considerable influence on the long term performance of the cladding through careful selection of materials and good detailing. Once in service, regular maintenance will prolong the life of the building envelope.

The metal from which the weather sheet is made is available with several types of coating with a wide variety of colours and finishes. Guidance on the expected design lives of these coatings is available from MCRMA Technical paper No. 6 Profiled metal roofing design guide[4] and also from ECCS-TC7 Publication 41 Good practice in steel cladding and roofing[6]. It is worth noting that the colour of the coating has a very significant impact on its design life. Light colours reflect thermal radiation more efficiently than dark colours, resulting in lower surface temperatures and a reduction in the degradation experienced by the coating.

When detailing the building envelope, particular attention should be given to the avoidance of water and dirt traps by specifying suitable slopes and end laps. Careful detailing is needed at the external interfaces to avoid the ingress of water and at the internal interfaces to prevent water vapour from within the building entering the cladding assembly (resulting in interstitial condensation).

In order to ensure that the building envelope remains fully functional throughout its design life, it is important that it receives regular maintenance, including inspection, removal of debris, cleaning and repair of damage. Since maintenance usually involves access by workmen, often carrying equipment, it is essential that this is allowed for in the design of the building envelope and the supporting structure. The need for maintenance may be greatly reduced by specifying a coating for the weathersheet with a ‘maintenance free’ guarantee for the expected design life of the cladding (typically 20 to 30 years). Such coatings can provide significant benefits to the client in terms of whole life costs and improved safety.

3.8 Structural performance Metal cladding systems are required to carry externally applied loads, such as snow and wind loading without deflecting excessively or compromising the other performance requirements. The individual characteristic loads (actions)


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should be obtained from the appropriate part of EN 1991[9], taking into account the building geometry and location as applicable. These individual actions should then be combined using the appropriate safety factors from EN 1990[10] to obtain the load cases used in design.

3.8.1 Actions

Permanent actions

For most industrial and commercial applications of metal cladding technology, the only permanent action for which the roof cladding needs to be designed is its own self-weight, including the weight of the insulation. Typical weights of insulated panels and built-up cladding systems are given in Table 3.4. For information on specific cladding products, designers should consult the technical literature available from manufacturers or suppliers. For wall cladding, it is not normally necessary to consider permanent actions, since the self-weight acts in the plane of the cladding. However, where a rainscreen system is attached to the outer face of the cladding panel or assembly, it will be necessary to consider the impact of the rainscreen system weight when specifying the fasteners.

Table 3.4 Typical cladding system weights

Sheet thickness System Insulation Depth*

Inner Outer

Weight kN/m2

Built-up Mineral wool 180 mm 0,4 mm 0,7 mm 0,16

Built-up Mineral wool 180 mm 0,7 mm 0,7 mm 0,20

Insulated Panels

PIR 80 mm 0,4 mm 0,5 mm 0,12

* The depths chosen in Table 3.1 correspond to a U-value of 0,25 W/m2K for typical cladding systems using the insulation shown.

Variable actions

In addition to its self-weight, the roof cladding must also be designed for the following variable actions as specified in the appropriate parts of EN 1991:

Access for cleaning and maintenance

A uniformly distributed load due to snow over the complete roof area. The value of this load will depend on the building’s location

Asymmetric snow load and loading due to snow drifts

Wind pressure and suction.

Care should be taken when ‘green’ roofs are specified, as they tend to be considerably heavier than traditional metal roofs and, in the case of roof gardens, must be designed for the presence of garden furniture and people.

Wall cladding should be designed for wind loading according to EN 1991-1-4[9]. Positive wind pressure and wind suction will need to be considered, with special attention paid to the areas of high wind suction close to the corners of the building. The wind suction design case is often governed by the resistance of the fasteners connecting the cladding panels or sheets to the supporting steelwork.


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3.8.2 Deflections

The cladding must be capable of carrying the specified design loads without deflecting excessively, if the other performance requirements such as weathertightness, airtightness and durability are to be achieved. The predicted deflections are normally calculated for the unfactored variable actions only. Loading at the construction stage is not normally included in the serviceability load cases and is not normally considered when specifying cladding systems. However, care must be taken on site to avoid excessive local deflections, especially those caused by concentrated loads such as foot traffic or stacked materials on roof liner sheets, as these could result in permanent damage to the cladding. Typical deflection limits imposed on the cladding are dependent on the loading regime considered (imposed load only or permanent plus imposed loading), the location (wall or roof) of the structural component and whether a brittle material is present. Deflection limits may be specified by National regulations. Common deflection limits are:

Span/150 for wall cladding, spanning between secondary steelwork

Span/200 for roof cladding, spanning between purlins

Span/180 for purlins or side rails.

3.8.3 Use of safe load tables

The manufacturers of profiled metal sheeting and insulated panels provide safe load tables for their products, which may be used either to select a suitable profile or, where the profile has already been chosen, to determine the maximum permissible purlin spacing. It is important to note that the load tables often assume that the loading is uniformly distributed and that safe working loads are usually specified. If in doubt, specifiers should seek guidance from the cladding manufacturers.


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4 COLD ROLLED SECONDARY STEELWORK

For steel portal framed industrial type buildings with low pitch roofs (5 to 10 degrees), the cladding panels or sheets are normally supported by a system of light steel purlins and side rails spanning between the rafters and columns respectively. See Figure 4.1 showing secondary steelwork in the roof where the purlins span between the rafters of the main frame. The primary function of these secondary members is to transfer load from the cladding to the primary steel frame, including cladding self-weight, wind loads and, for roofs, imposed loads due to snow and maintenance access. The purlins and side rails may also be used to provide restraint to the rafters and columns and to transfer horizontal loads into the bracing system.

Figure 4.1 Purlins spanning between rafters in the roof

This Section presents guidance on some of the key issues relating to the use of cold formed purlins and cladding rails.

4.1 Purlin and side rail options Purlins and side rails are generally cold formed light gauge galvanized steel members, supplied as part of a proprietary cladding support system, together with fittings, fasteners and other associated components.

4.1.1 Section options

Purlins and side rails are available in a variety of shapes and a wide range of sizes. The depth of the section typically lies between 120 mm and 340 mm, with the profile thickness varying between 1,2 mm and 3,2 mm. Some of the more common section shapes are shown in Figure 4.2. Purlins and side rails, because of their high length/thickness values, are typically classed as Class 4


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sections as defined in EN 1993-1-3[11], hence section properties will be need to be based on effective values (reduced gross properties).

Further information on these sections may be obtained from the manufacturers’ technical literature.

1 2 3 4

1 Zed 2 Ultrazed 3 Zeta 4 Sigma

Figure 4.2 Common types of purlin

4.1.2 Purlin and side rail layout options

Most manufacturers produce guidance on typical purlin layouts that are efficient for various situations. These layouts are governed by such aspects as maximum purlin length (generally not more than 16 m for transport and site access reasons) and the ability to provide semi continuity by the use of sleeves or overlaps for maximum efficiency. The most commonly used layouts are shown in Figure 4.3 to Figure 4.7. Specifiers seeking further information on when and how to use a particular layout should consult the purlin manufacturers for detailed information relating to their specific systems. In any event, the purlin manufacturer should be consulted before the layout is finalised.

Single-span lengths - sleeved system

In sleeved systems, each purlin is the length of a single span but sleeves are provided at alternate supports so that each purlin is effectively continuous across two spans (Figure 4.3). At the penultimate support, sleeves are provided at each purlin, to provide semi continuity and additional strength in the end bay. This system is considered to be the most efficient for buildings with bay centres between 5 m and 7 m. Heavier sections can be provided in the end bay if necessary.

1 23

4

1 Sleeved purlin 2 Penultimate

support 3 Rafter 4 Sleeve

Figure 4.3 Single-span lengths – sleeved system


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Single-span lengths - butted system

Single-span butted systems have a lower capacity than the other systems, but are simpler to fix either over the rafters or between rafter webs (Figure 4.4). This layout may be used for small buildings with close frame centres, such as agricultural applications.

1 Single-span purlin

2 Rafter

Figure 4.4 Single-span lengths - butted system

Single-span lengths - overlapping system

An overlapping system provides greater continuity and can be used for heavy loads and long spans (Figure 4.5). It is best suited to buildings with a large number of bays.

1 Purlin 2 Rafter

Figure 4.5 Single-span lengths - overlapping system

Double-span lengths – non sleeved system

In this system, the double-span lengths are staggered (Figure 4.6). Sleeves are provided at the penultimate supports to ensure semi continuity. The capacity will generally be less than for the equivalent double span sleeved system, but double-span purlins use fewer components and lead to faster erection. This system is limited to bay sizes less than 8 m, for reasons of transport and erection of the purlins.


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1 Double-span purlin

2 Penultimate support

3 Rafter 4 Sleeve

Figure 4.6 Double-span lengths – non sleeved system

Double-span lengths - sleeved system

In double-span sleeved systems, the double-span lengths are staggered and sleeves are provided at alternate supports (Figure 4.7). Sleeves are provided to every purlin at the penultimate support to ensure semi continuity. A double span sleeved system has a slightly higher capacity than the double-span non-sleeved system and has the advantages of semi continuity at all sleeve positions. This system is limited to bay sizes less than 8 m, for reasons of transport and erection. Heavier purlins can be provided in the end bays, if necessary.

1 Sleeved double-span purlin

2 Sleeve

Figure 4.7 Double span lengths - sleeved system

4.1.3 The use of anti-sag rods for purlins

Anti-sag rods are small rods or angles that are bolted or clipped between the purlins. A typical arrangement is shown in Figure 4.8; other systems are also available. When used, they are commonly placed either at mid-span or at third points along the purlin and serve the following functions:

They provide restraint to the purlins against lateral-torsional buckling under wind uplift conditions


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They provide restraint to the purlins in the construction condition (before the installation of the cladding)

They provide additional support to the down-slope component of the applied loads

They help to maintain the alignment of the purlins.

The anti-sag rods are assisted in these functions by eaves beam struts and apex ties, both of which are also illustrated in Figure 4.8.

6

108

117

9

1

2

3

4

5

1 Purlin 2 Eaves beam 3 Column 4 Eaves beam 5 Column 6 Eaves beam strut

7 Purlin 8 Anti-sag ties (at 1/2 or 1/3 span) 9 Rafter 10 Apex tie 11 Rafter

Figure 4.8 Typical anti-sag ties and eaves beam strut layout

The need for anti-sag rods is dependent on a number of factors, including the chosen purlin section, the spacing between the purlins, the span of the purlins and the magnitude of the applied loads. Advice on this issue may be obtained from the purlin manufacturers’ technical literature. In some instances, the specifier may have a choice between the use of anti-sag rods or the selection of a heavier purlin that does not require intermediate restraint or support. There is clearly a trade-off between the cost of a heavier purlin section and the time (and corresponding cost) associated with the installation of additional components.

Anti-sag rods only provide restraint at discrete locations along the span of the purlin. The purlins should only be considered to be ‘fully’ restrained under


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gravity loading in the finished condition, when continuous restraint is provided to the compression flange of the purlin by the cladding.

4.1.4 The use of side rail supports for wall cladding

Support for wall cladding is provided by a framework of horizontal cladding side rails that span between the columns of the building’s primary steelwork. Vertical restraints are connected to the side rails at discrete locations (similar to the anti-sag rods in roofs). These restraints prevent the occurrence of lateral-torsional buckling (due to bending of the side rails under wind suction loading) and also prevent the side rails from sagging under the weight of the cladding and its supporting steelwork. These vertical restraints are typically light gauge steel sections (tubes, angles or channels) or steel bars/rods.

In order to channel the forces generated in the side rail supports efficiently to the primary structure (columns) and to prevent the side rails from sagging prior to the installation of the cladding, it is customary to provide a vertical braced bay arrangement between the lowest two side rails, as shown in Figure 4.10. These bracing members operate in tension, so it is common to use steel wires rather than cold formed light gauge steel sections. To restrict the forces in the tie wires, it is common practice to restrict the angle of the tie wire to the cladding rail to a minimum of 25° or 30° (refer to the manufacturers’ recommendations). With this restriction imposed on the diagonal tie wires, the number of side rail supports is predetermined, based on the spacing of the side rails and the spacing of the columns.

For column spacings up to 6 m with a typical side rail spacing of 1,8 m, a single central vertical restraint will normally be sufficient (see Figure 4.10). However, for greater column spacings, two or even three vertical restraints may be required. In many cases, the uppermost side rail is connected to the eaves beam. This arrangement will reduce the forces in the tie wires, but the additional force in the eaves beam will need to be considered when this member is sized. It is also worth noting that, once installed, the cladding will stiffen up the wall substructure and transfer a significant proportion of the vertical load to the columns by diaphragm action. The cladding will also fully restrain the side rails against lateral-torsional buckling in the sagging case and will provide partial restraint in the hogging case.

4.1.5 Cleats

Purlins are attached to rafters using cleats that are usually welded to the rafter in the shop before delivery to site. However, the use of bolted cleats (see Figure 4.9) is becoming popular due to savings in transportation (as the rafters stack more compactly) and the opportunity they present to adjust the alignment of the purlins on site (with beneficial consequences for the installation of the cladding). The cleats are often provided by the purlin manufacturer, in which case it is likely that they will have been designed specifically for that design of purlin. However, generic bolted cleats made from an angle section or simple flat plates welded to the rafter may also be used in many cases, either unstiffened or stiffened.


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1

2

3

4

5

1 Eaves beam 2 Main column 3 Tension wire 4 Anti sag bar

(section or tube)5 Side rail

Figure 4.9 Cleat supporting a purlin using a bolted connection

1

2

1 Purlin 2 Cleat

Figure 4.10 Side rail support for wall cladding

4.2 Loading The purlins and cladding rails need to be designed to carry all of the loads applied to them from the cladding and to transfer these loads into the structural frame. These loads will include the permanent actions due to the weight of the cladding and secondary steelwork together with the variable actions described in Section 3.7.1. It will usually be acceptable to consider these actions as acting uniformly over the purlins, but account must be taken of high local forces such as the wind suction forces close to the edges of the building. In addition to the cladding loads, the purlins may also be required to support the weight of


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services or suspended ceilings. The structural engineer responsible for specifying the purlins will frequently play little or no part in the specification of the services or ceilings. Nevertheless, it is important that an accurate estimate of these loads is obtained together with the nature of the loading (whether concentrated or distributed), since they could form a significant proportion of the overall gravity loading on the purlins. Particular care should be taken where the purlins are required to support concentrated loads. Gutters and their supporting structure require special attention, as the loads associated with them are often very high. Designers need to consider the weight of the gutters plus that of their contents (water or snow). Specific information on the specified gutter system should be sought from the gutter manufacturers.

During the construction stage, the purlins may still be required to carry significant gravity loads, but without the benefit of any restraint provided by the cladding. The magnitude of the construction load will depend largely on the cladding installation procedure and the materials, plant and labour used. The cladding installation sequence, in particular, can have a significant effect on the buckling resistance of a purlin, due to its influence on the unrestrained length of the purlin and the location of the load within the span. It is therefore essential that the designer takes account of the proposed method of working when specifying the purlins. Preferably, this should be achieved by dialogue between the roofing contractor and the designer at the time of the purlin specification.

4.3 Deflections The deflection limits for the purlins and side rails are generally governed by the choice of roof and wall cladding, since the governing factor is the ability of the cladding to deflect without compromising weathertightness, airtightness, non-fragility or any other performance requirement. In general, the greater the flexibility of the cladding, the larger the allowable purlin or side-rail deflection. In this respect, profiled metal cladding systems are far more tolerant of deflections than brittle materials such as masonry. By contrast, windows are often critical and further guidance should be sought from the glazing manufacturers.

Excessive deflection under purlin or rail self-weight, or under the action of construction loads prior to the fixing of the cladding, can lead to difficulties for the cladding installation. This should be addressed by careful consideration of the likely construction loading and by specifying a method of cladding installation that avoids overloading the unrestrained purlins. Gutters are especially sensitive to deflections, due to the need to avoid backfalls.

4.4 Purlin and side rail selection The major purlin and cladding rail suppliers have invested heavily over many years in the development and testing of their systems and all publish design guidance and load/span tables for their products. In many cases, design software is also available. Thanks to these design tools, the structural engineer is spared the complexities of the design of light steel members and can simply select the most suitable section from the available range. However, specifiers


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should note that in using the load/span tables they are automatically accepting the assumptions made by the purlin and cladding rail manufacturers, including assumptions regarding the level of restraint provided by the cladding to the supporting steelwork. If in doubt, the secondary steelwork specifiers should contact the manufacturers for advice on the suitability of the chosen section for the application in question, taking into account the proposed cladding type and any other circumstances likely to invalidate the manufacturer’s assumptions, e.g. heavy point loads.

4.5 Restraint provided to the rafters and columns The structural efficiency of any steel framed building depends not only on the selection of light and efficient sections, but also on the interaction between the frame members, the secondary steelwork and the cladding system. For this reason, it is common practice to use the secondary steelwork (the purlins and rails) to restrain the primary steelwork.

It is generally accepted that purlins and rails need not be checked for forces arising from the lateral restraint of rafters in either roof trusses or portal frames provided that the following conditions are met:

The purlins are adequately restrained by sheeting

There is bracing of adequate stiffness in the plane of the rafters or alternatively the roof sheeting is capable of acting as a stressed-skin diaphragm

The rafters carry predominantly roof loads.

In certain European countries, the assumption that the secondary members can restrain the primary frame is acceptable as long as the secondary member providing the restraint is connected to a node point of the bracing system. In other countries, it is presumed that the roof system supplies a sufficiently stiff diaphragm to relax the requirement. In this case, roof bracing is still required, but need not intersect with every secondary member providing restraint. If a purlin or side rail cannot be used with stays (as shown in Figure 4.11) as a torsional restraint, a hot rolled member may be provided to meet this requirement.

Ideally, the compression flange of the rafter or column should be laterally restrained by direct attachment of the purlins or cladding rails. However, under the action of wind uplift, or close to the haunches of a portal frame under gravity loading, the inner flange of the member (i.e. the one to which the cladding is not attached) will be in compression and cannot be restrained directly by the purlins or cladding rails. In this situation, the frame designer can either introduce an additional hot-rolled steel member (often a structural hollow section) to laterally restrain the compression flange or, alternatively, the compression flange can be effectively held in position by a combination of lateral restraint to the tension flange (provided by the purlins or rails) and torsional restraint provided by rafter or column stays. Recommendations for the provision and design of restraints are given in EN 1993-1-1[12], § 6.3.5.2 and Annex BB.3.


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Rafter or column stays, as shown in Figure 4.11, may be used to provide torsional restraint to the rafter or column provided that they are connected to a suitably stiff purlin or cladding rail. Thin cold formed steel straps (working as ties) are often used, although angles may be used if the stay must work in compression (for example, if a stay can only be provided on one side of a member).

2

1

3

4

1 Built up or composite cladding

2 Cold-rolled eaves beam

3 Rafter stay 4 Column stay

Figure 4.11 Details of column and rafter stay and connection

In order to provide the required level of torsional restraint to the rafters or columns, the purlins or cladding rails must possess sufficient flexural stiffness. Otherwise, there is a risk that the restraining member will bend and allow the restrained members to rotate, as shown in Figure 4.12. As a rule of thumb, it is normally adequate to provide a purlin or cladding rail of at least 25% of the depth of the member being restrained. In practice, this generally means that the purlins and side rails will be sufficiently stiff for portal frames with spans up to 40 m and frame spacings of 6 to 8 m. However, as the span increases relative to the frame spacing (and the rafter size increases relative to that of the purlins), the purlin stiffness may become insufficient to provide adequate torsional restraint and should, therefore, be checked.

Figure 4.12 The importance of adequate purlin stiffness

4.6 Restraint of purlins and cladding rails Cold formed steel purlins and cladding rails are extremely efficient at carrying loads by bending action, but they are susceptible to failure through lateral-torsional buckling unless they are adequately restrained. The economic


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and safe design of the cladding and its supporting steelwork relies on the interaction between the individual components that make up the whole system.

Purlins and cladding rails are normally selected from manufacturer’s load/span tables, which are derived from analytical models supported by test data. In producing their design data, all purlin manufacturers have to make a judgement regarding the degree of restraint that is available from the cladding system under gravity and wind uplift conditions. These assumptions are central to the design model and can have a significant effect on the design resistance of the purlin or rail. It is therefore essential that an equal or greater level of restraint is achieved in practice. This will depend on the choice of sheeting and the spacing of the fasteners.

In the gravity load case (or positive wind pressure in the case of a wall), restraint is provided directly to the top flange of the purlin (or side rail) by the liner sheet or insulated panel, as shown in Figure 4.13(a). Built-up cladding and insulated panels are generally capable of providing sufficient lateral restraint for the gravity loading case. In general, perforated liners are not considered to be restraining and the supporting purlins should, therefore, be designed as unrestrained members.

C

T

(a)

(b)

T

C

1

2

1 Lateral restraint provided to compression flange by cladding

2 Cladding provides lateral restraint to tension flange and partial torsional restraint

Figure 4.13 Purlin restraint

For wind uplift (or negative pressure on a wall), the cladding cannot provide lateral restraint directly to the compression flange. In this case, the purlin (or cladding rail) is restrained by a combination of lateral restraint to the tension flange and torsional restraint, as shown in Figure 4.13(b). The ability of the cladding to provide restraint is dependent not only on its in-plane shear stiffness (including the fasteners), but also its flexural stiffness. EN 1993-1-3 includes a method in Section 10 for assessing the degree of restraint provided by the cladding in this case. Unlike the gravity load case, the cladding only provides partial restraint to the purlin or rail. Consequently, the purlin manufacturers’ technical literature should always give a lower capacity for purlins subjected to wind uplift loading (or suction on cladding rails).

EN 1993-1-3[11] covers the design of purlins, liner trays and sheeting in Section 10.


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5 HOT-ROLLED SECONDARY STEELWORK

As an alternative to cold formed steel, purlins and cladding rails may also be made from hot-rolled steel sections. At one time, this type of purlin was common in industrial buildings, often used in conjunction with steel roof trusses. The development of cold formed purlins (which are considerably lighter and cheaper) and the trend towards plastically designed portal frames with their onerous restraint requirements meant that the use of hot-rolled purlins became unusual in the UK and Ireland. However, hot-rolled purlins continue to be used in Continental Europe, often with long spanning cladding solutions such as deck and membrane or composite panels. They are particularly useful for providing an intermediate support to structural decking, where the decking by itself is incapable of spanning rafter to rafter.

Hot-rolled purlins have a higher load-carrying capacity than all but the largest cold formed purlins. This means that they are generally used at much greater spacings than their cold formed counterparts, typically 3 m or more. This wide spacing makes them unsuitable for plastically designed portal frames, which commonly require restraint to the rafters at approximately 1,8 m intervals. However, they are suitable for elastic frames and also for spans beyond the range of standard cold formed purlins (above 8 m). Hot-rolled purlins could of course be used at closer centres, but this would be uneconomic in most circumstances.

A considerable advantage of hot-rolled purlins over their cold formed rivals is their resistance to lateral-torsional bucking, especially where rectangular hollow sections are used. This property is essential if the cladding is unable to provide adequate restraint against lateral-torsional buckling. By contrast, cold formed purlins are only able to span as far as they do (typically 6 m to 8 m) because of the continuous restraint provided by the cladding. Similarly, where the local building regulations forbid using the cladding to restrain the structure, hot-rolled purlins are the only viable alternative to long spanning decks running rafter to rafter. Of course, apart from square hollow sections, hot-rolled purlins are not immune to lateral-torsional buckling and must, therefore, be designed with this mode of failure in mind.

Unlike cold formed purlins, it is not common for the manufacturers to produce safe load tables for hot-rolled beams. Their capacities must, therefore, be calculated by a structural engineer according to the recommendations of EN 1993-1-1[12], taking account of the cross section resistance, lateral-torsional buckling and deflections. This process must be repeated for gravity and uplift load cases. If lateral-torsional buckling is the critical design criterion, the resistance of the member could be enhanced by the introduction of tubular restraints either at the mid-span or third points of the purlin. However, this will add cost to the structure in terms of additional steelwork and erection time.

Hot-rolled purlins can be designed as single or double-span beams. The latter option will significantly increase the bending stiffness of the purlin and should be used where deflection is the governing criterion. However, the high reaction at the intermediate support (1,25 load in one span) can cause web crushing at this location. Sleeves are not generally used with hot-rolled purlins.


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Hot rolled purlins have the added advantage of better fire resistance than light gauge cold formed purlins. This is shown by the noticeably higher inherent Massivity factor (cross section area/perimeter) which is used as a measure to define the fire resistance of a structural section.


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REFERENCES

1 EN 14782:2006 Self-supporting metal sheet for roofing, external cladding

and internal lining. Product specification and requirements

2 MCRMA Technical Paper No 12: Fasteners for metal roof and wall cladding: Design, detailing and installation guide The Metal Cladding and Roofing Manufacturers Association, 2000

3 MCRMA Technical Paper No. 3: Secret fix roofing design guide. The Metal Cladding and Roofing Manufacturers Association, 1999

4 MCRMA Technical Paper No. 6: Profiled metal roofing design guide The Metal Cladding and Roofing Manufacturers Association, 2004

5 MCRMA Technical paper No. 16: Guidance for the effective sealing of end lap details in metal roofing constructions The Metal Cladding and Roofing Manufacturers Association, 2004

6 ECCS Publication 41 European recommendations for steel construction: Good practice in steel cladding and roofing European Convention for Constructional Steelwork – Recommendations for steel construction Technical Committee TC7, 1983.

7 European Directive 2002/91/EC: Energy Performance of Buildings The European Commission, 2002

8 MCRMA Technical paper No. 8: Acoustic design guide for metal roof and wall cladding. The Metal Cladding and Roofing Manufacturers Association, 1994

9 EN 1991:2002: Eurocode 1 Actions on structures

10 EN 1990: 2002: Eurocode Basis of structural design

11 EN 1993-1-3:2006: Eurocode 3 Design of steel structures. General rules. Supplementary rules for cold-formed members and sheeting

12 EN 1993-1-1:2005: Eurocode 3 Design of steel structures. General rules and rules for buildings



Part 9: Introduction to Computer

Software


Part 9: Introduction to Computer

Software

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Part 9: Introduction to Computer Software

9 - iii

FOREWORD

This publication is part nine of the design guide, Single-Storey Steel Buildings.




Part 3: Actions













9 - iv


9 - v

Contents Page No

FOREWORD iii

SUMMARY vi

1 INTRODUCTION 1 1.1 Software listing 1 1.2 Use of software 2

2 AVAILABLE FREE SOFTWARE 3 2.1 Member design, such as beams and columns 3 2.2 Composite construction 4 2.3 Cellular beam design 6 2.4 Portal frames 6 2.5 Simple connections 7 2.6 Moment resisting connections 8 2.7 Fire 8 2.8 Seismic 10


9 - vi

SUMMARY

This document contains details of freely available software to assist in design of single-storey steel buildings according to the Eurocodes.


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1 INTRODUCTION

Design in accordance with the Eurocodes may be facilitated by the use of software. In many cases, the verifications required by the Standard can be readily programmed into simple spreadsheets or into more complex programmes, which minimise the manual effort and reduce the risk of numerical errors.

In many countries, software has been written for the purpose of facilitating design to the Eurocodes and has been made freely available. This publication presents a summary of software that is available, at March 2010. All the software listed in this document is freely available.

No endorsement of any of the software programmes listed in this document should be presumed. Equally, the omission of existing software from the listing does not imply that it is inappropriate, inaccurate or non-endorsed. More software will undoubtedly become available as design to the Eurocodes becomes more widespread.

Apart from the list of freely available software presented here, there are numerous software houses that provide comprehensive analysis and design packages, covering all aspects of steel building design, as described in this guide.

1.1 Software listing In Section 2, software is listed under the following headings:

Member design, such as beams and columns

Composite construction

Cellular beam design

Analysis of frames

Portal frames

Simple connections

Moment resisting connections

Fire

Seismic

For each item of software, the following details are listed:

Scope. A general description of the software

Design Standard. The design standard may be the published Eurocode, but may be early versions of the Standard. Users must ensure that the version of the Eurocode is appropriate.

National Annex. Which National Annex is covered in the software, if any

Source. Where the software can be obtained (web site)

Language. The language used in the software


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1.2 Use of software No systematic review of the software listed in this document has been undertaken, so the user must verify that the software is appropriate for the design situation.


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2 AVAILABLE FREE SOFTWARE

2.1 Member design, such as beams and columns

Software Verifica di profili sottili piegati a freddo

Scope Design and analysis of cold formed sections

Design Standard EN 1993-1-3, EN10162

National Annex Italian NTC2008

Source http://www.promozioneacciaio.it/costruttori_schede.php

Language Italian

Software Corus sections interactive "blue book"

Scope The Corus sections interactive "blue book" comprises design data for the Advance®, Celsius® and Hybox® ranges of sections. All design data is generated from the root software functions used to populate SCI P363: Steel Building Design: Design Data, in accordance with Eurocodes and the UK National Annexes and SCI P202: Steelwork Design Guide to BS 5950-1: 2000. Volume 1 - Section Properties - Member Capacities.

Design Standard BS 5950 and BS EN 1993-1-1

National Annex UK only

Source http://www.corusconstruction.com/en/design_guidance/the_blue_book/

Language English

Software A3C (ArcelorMittal CTICM Columns Calculator)

Scope A3C is a new software that allows a structural designer to check the resistance of a member under bending moment and axial force according to EN 1993-1-1.

The field of application covers rolled profiles.

The ULS verifications include classification of the cross-sections, section resistance, flexural buckling, lateral torsional buckling, shear buckling and all interactions (M+N, M+V, M+N+V). Various design options are available (for example: Annex A or Annex B for interaction factors in EN 1993-1-1).

A detailed calculation sheet can be edited and printed.

Design Standard EN 1993-1-1

National Annex French National Annex as option

Source http://www.arcelormittal.com/sections http://www.cticm.com

Language English, French


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Software LTBeam

Scope LTBeam software has been designed to calculate the critical moment for Lateral Torsional Buckling (LTB), in simple or complex situations.

Even for simple cases, the critical moment is often a complex step in the process of verification of the LTB resistance. Moreover usual formulae do not allow the designer to take into account the specific restraint conditions of real cases. So they lead the designer to choose conservative assumptions. That is why LTBeam can be used to determine a more realistic value of the critical moment.

LTBeam software is based on a modelling by beam elements that permits to take into account specific aspects like warping stiffness, position of the transverse loads from the shear centre, position of the lateral restraints, etc.

LTBeam aims at facilitating the application of Eurocode 3, but it can be used with other codes, for a LTB verification based on the concept of critical moment.

Even though the calculations are complex, LTBeam is very simple to use and it does not require special training provided that the phenomenon is well known by the user.

Design Standard n/a

National Annex n/a

Source http://www.cticm.com/spip.php?rubrique6

Language French, English

2.2 Composite construction Software ABC V2.11

Scope ABC Software allows a structural designer to check the resistance of beams according to the European standards EN 1993-1-1 and EN 1994-1-1.

The field of application covers simply supported beams, composite or non composite, made from a I-rolled profile.

For composite beams, the connection can be ensured by either welded studs or HILTI connectors. Partial connection is allowed. At the construction stage, the composite beam can be fully propped or a propping can be defined. Appropriate verifications at the construction stage are carried out when necessary.

The ULS calculations include the verification of the section resistance under bending moment and shear force, the resistance to lateral torsional buckling, the shear buckling resistance where necessary. The resistance to lateral torsional buckling is based on the critical moment calculated by a modal analysis performed by the LTBeam engine.

A detailed calculation sheet can be edited and printed.

Design Standard EN 1993-1-1 and EN1994-1-1

National Annex n/a

Source http://www.arcelormittal.com/sections/index.php?id=119

Language French, English


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Software ACP V1.02

Scope Construction phase for composite solution. To check the LTB behaviour of composite and/or partially encased beams during erection

Design Standard EN 1993-1-1 and EN1994-1-1

National Annex n/a


Language English, French, German, Spanish, Portuguese

Software ACD V3.06

Scope ArcelorMittal composite column design according to Eurocode 4. Replaces CDD

Design Standard ENV 1994-1-1

National Annex n/a


Language English, French, German, Spanish

Software Software compendium for steel and composite structures

Scope This new software (currently a Beta version) for the analysis, calculation and design of steel and composite structures, has been developed by Consulting Engineers FHECOR with funding from the Association for the Advancement of Steel Technology (APTA) and ArcelorMittal. It is meant as a tool for use in design offices to facilitate the pre-design of structures or verification of existing projects and designs. It is not intended to compete with commercial software and can be used as a teaching tool for steel structures (levels of deformation, stresses, effective widths, section grade, etc.). as well as the development of checking examples.

Design Standard It complies with Spanish CTE code and Eurocode 3, according to user’s selection.

National Annex n/a

Source http://piem.fhecorconocimiento.es/

Language Spanish


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2.3 Cellular beam design Software ACB+ V2.01

Scope Cellular beams design

ACB+ is a piece of software dedicated to the design of cellular beams made up from rolled profiles. It covers composite and non composite cellular beams, including curved beams.

ACB+ includes practical tools for selecting the diameter and the spacing of the openings in accordance with fabrication requirements.

ULS verifications are performed according to the principles of the Eurocodes (EN 1993-1-1 and EN 1994-1-1), with specific verifications for cellular beams (Vierendeel effect, web post buckling, etc).

For SLS verifications, the deflections are calculated by taking into account the local bending due to the Vierendeel effect.

ACB+ allows the designer to assess the fire resistance according to the principles of EN 1993-1-2 and EN 1994-1-2.

Design Standard EN 1993-1-1, EN 1994-1-1, EN 1993-1-2, EN 1994-1-2

National Annex n/a


Language English, German, French, Italian

Software AngelinaTM

Scope Angelina software has been especially designed for the calculation of a special type of beams with sinusoidal web openings, called Angelina beams, fabricated from hot rolled I-profiles. This new software covers both composite and non composite beams.

ULS verifications are carried out according to the principles of the Eurocodes. They take into account the specific aspects of such beams, like local bending by Vierendeel effect. The deflections are also calculated by appropriate methods, in view to SLS verifications.

Design Standard EN 1993-1-1, EN 1994-1-1

National Annex



2.4 Portal frames Software PORTAL Version 1.1

Scope PORTAL is a pre-design software for portal frames with single span, made of rolled sections. It includes an automatic calculation of the snow load and the wind action, elastic global analysis of the frame, verifications of the members, calculations of the deflections. The calculations are carried out according to Eurocodes (ENV 1993-1-1).

The automatic pre-design is based on the weight criterion for a given steel grade, but sections can be defined by the user for performing verifications.


National Annex Not suitable for National Annex application. Only partial safety factors may be user defined.




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Software Pre-design of one span of a portal frame

Scope Pre-design of one span of a portal frame


National Annex EN 1993-1-1 ANB 2008

Source Online calculation on www.infosteel.be

Language Dutch and French

Software Pre-deSsign of a roof structure for residential buildings

Scope Pre-design of a roof structure for residential buildings


National Annex EN 1993-1-1 ANB 2008

Source Online calculation on www.infosteel.be

Language Dutch and French

2.5 Simple connections Software ACOP V1.02

Scope Connection programme to design joints in steel building structures.


National Annex n/a


Language English, French, German

Software Unioni bullonate

Scope Bolted joints. Scheda di calcolo (ZIP – 4 Mb)



Source http://www.promozioneacciaio.it/costruttori_schede.php

Language Italian

Software Unioni saldate

Scope Welded joints.



Source http://www.promozioneacciaio.it/costruttori_schede.php Scheda di calcolo (ZIP 500 kb).

Language Italian


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Software Verifica collegamenti a squadretta

Scope Joint design.

Design Standard EN 1993-1-1 and EN 1993-1-8


Source http://www.promozioneacciaio.it/costruttori_schede.php Scheda di calcolo (ZIP – 600 Kb).

Language Italian

Software Dimensionamiento unioni travature reticolari

Scope Joint verification of the trusses, bolted and welded



Source http://www.promozioneacciaio.it/costruttori_schede.php Scheda di calcolo (ZIP – 650 Kb)

Language Italian

2.6 Moment resisting connections Software PlatineX

Scope PlatineX is an on-line software that covers the design of moment connections made of rolled profiles (European I and H sections), according to EN 1993-1-8. Various geometries are possible for beam-to-beam connections (apex connections) and beam-to-column connections. This piece of software checks the validity of the dimensions defined by the user (edge distances, distance between bolts, etc). If the geometry is valid, it calculates the moment resistance, the shear resistance, the axial resistance and the flexural stiffness. A detailed calculation sheet can be edited and saved as PDF file.


National Annex French NA

Source http://www.steelbizfrance.com/prog/platinex/

Language French

2.7 Fire Software ArcelorMittal Ozone 2.2.6

Scope Gas temperature in the event of fire according to EN 1991-1-2, corresponding steel temperature according to EN 1993-1-2 and simplified resistance check.


National Annex n/a


Language English


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Software Software LUCA

Scope LUCA is software accompanying a design guide for industrial halls in fire conditions. This tool calculates displacements and additional horizontal forces that appear in industrial halls during fire enabling the engineers to consider their effect in the design in order to avoid collapse or risk of human life. Software was developed within RFCS project RFS2-CR-2007-00032.

Design Standard EN 1991-1, EN 1993-1-2

National Annex n/a


Language English, French, Spanish

Software AFCB V3.08

Scope Composite beam design in case of fire


National Annex n/a



Software AFCC V3.06

Scope Composite column design in case of fire


National Annex n/a



Software Fracof

Scope Composite floor slabs This software designs composite floor slabs at elevated temperatures by taking into account the enhancing effects of the membrane action in slab. FRACOF also checks perimeter beams and provides a critical temperature for each of them.

Design Standard EN 1994-1-1, EN 1990, EN1991-1

National Annex n/a


Language English and French


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2.8 Seismic Software INERD 1.0.0

Scope Innovation for earthquake design. INERD concept is a composite constructive system to improve the robustness and the safety of reinforced concrete frame structure

Design Standard

National Annex


Language English



Part 10: Model Construction

Specification


Part 10: Model Construction

Specification

10 - ii

Part 10: Model Construction Specification

10 - iii

FOREWORD

This publication is the tenth part of the design guide, Single-Storey Steel Buildings.




Part 3: Actions













10 - iv


10 - v

Contents Page No

FOREWORD iii

SUMMARY vii

1 INTRODUCTION 1 1.1 Scope 2

2 NORMATIVE REFERENCES 4

3 BASIS OF STRUCTURAL DESIGN 9 3.1 General assumptions according to EN 1990 9

4 ACTIONS ON STRUCTURES 10 4.1 Self-weight and imposed loads for buildings 10 4.2 Snow loads 10 4.3 Wind loads 11 4.4 Thermal actions 11 4.5 Actions during execution 11 4.6 Accidental actions 13 4.7 Actions induced by cranes 14 4.8 Seismic actions 15

5 DESIGN OF STEEL STRUCTURES 17 5.1 Rules for single-storey buildings – EN 1993-1-1 17 5.2 Supplementary rules for sheeting – EN 1993-1-3 18 5.3 Design of plated structural elements – EN 1993-1-5 18 5.4 Design of joints – EN 1993-1-8 18 5.5 Fatigue – EN 1993-1-9 19 5.6 Material toughness and through-thickness properties – EN 1993-1-10 19 5.7 Crane supporting structures – EN 1993-6 20

6 EXECUTION SPECIFICATION 21 6.1 General 21 6.2 Execution classes 21 6.3 Preparation grades 21 6.4 Geometrical tolerances 21

7 CONSTITUENT PRODUCTS 23 7.1 Identification, inspection documents and traceability 23 7.2 Structural steel products 23 7.3 Welding consumables 23 7.4 Mechanical fasteners 23 7.5 Grouting materials 24

8 PREPARATION AND ASSEMBLY 25 8.1 Identification 25 8.2 Handling and storage 25 8.3 Cutting 25 8.4 Shaping 25 8.5 Holing 25 8.6 Assembly 26

9 WELDING 27 9.1 General 27 9.2 Qualification of welding procedures 27


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9.3 Welders and welding operators 27 9.4 Welding coordination 27 9.5 Preparation and execution of welding 27 9.6 Acceptance criteria 29

10 MECHANICAL FASTENING 30

11 ERECTION 31

12 CONSTRUCTOR’S DOCUMENTATION 34

13 INTERFACES OF THE STEEL STRUCTURE 35 13.1 Interface to concrete surfaces 35 13.2 Interface to neighbouring constructions 36

Appendix A MODEL PROJECT SPECIFICATION 37


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SUMMARY

This guide is a Model Construction Specification to be used in contract documents for a typical construction project of a single-storey building. Its main objectives are to achieve greater uniformity in steelwork contract specifications in Europe and to provide a guide to specification of appropriate standards for the design, fabrication and erection of steelwork structures for buildings.

It deals with structural steelwork designed in accordance with applicable parts of the Eurocode Standards, to be executed in accordance with applicable parts of EN 1090. All the relevant Sections of the model specification are included in an appendix that can be directly copied and used in contracts, with any additional project-specific information that may be required.


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1 INTRODUCTION

This guide is a Model Construction Specification to be used in contract documents for a typical construction project of a single-storey building. Its main objectives are:

To achieve greater uniformity in steelwork contract specifications in Europe.

To provide a guide to specification of appropriate standards for the design, fabrication and erection of steelwork structures for buildings.

It is essential that the designer and the steelwork contractor receive, on time, all information necessary for them to carry out the contract. This Model Construction Specification gives guidance on the items and information that should be included in the Project Specification.

The Member States of the EU and EFTA recognise that Eurocodes serve as reference documents for the following purposes:

As a means to prove compliance of building and civil engineering works with the essential requirements of Construction Products Directive 89/106/EEC of 21 December 1988 (amended by Directive 93/68/EEC of 22 July 1993), particularly Essential Requirement No. 1 – Mechanical resistance and stability – and Essential Requirement No. 2 – Safety in case of fire.

As a basis for specifying contracts for construction works and related engineering services.

As a framework for drawing up harmonised technical specifications for construction products (ENs and ETAs).

The Eurocodes, as far as they concern the construction works themselves, have a direct relationship with the Interpretative Documents referred to in Article 12 of the Construction Products Directive, although they are of a different nature from harmonised product standards. There is a need for consistency between the harmonised technical specifications for construction products and the technical rules for works.

The steel construction industry in Europe will have to use CE marked products. The performances of these products can be declared by reference to requirements given in:

The harmonised European Standards such as the standards EN 10025 and EN 1090. Parts 1 of these Standards (i.e. EN 10025-1 and EN 1090-1 respectively) include a special Annex ZA relating to CE marking.

A European Technical Approval (ETA).

CE Marking of steel products to EN 10025 has been mandatory since 2006. The use of CE marked products according to EN 1090 will be mandatory from the first semester 2011 for most of the European countries. Once it appears in the European Official Journal, the standard will be in the application phase.


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In EN 1090-1, for some special types of construction products (modular construction for example), reference is made to the Eurocodes. In this case, it shall be mentioned which Nationally Determined Parameters have been taken into account.

Much of the information noted in this Model Construction Specification is based upon that given in these Standards, but it must not be inferred that the full details of the standards are not relevant.

References to applicable parts of European Standards have been made throughout this Model Construction Specification.

1.1 Scope This Model Construction Specification deals with structural steelwork designed in accordance with applicable parts of the Eurocode Standards and executed in accordance with applicable parts of EN 1090.

It can be used for all types of single- storey building construction designed for static loading, including cases where the dynamic effects are assessed using equivalent quasi-static loads and dynamic amplification factors, including wind actions and actions induced by hoists and cranes and cranes on runway beams.

It is not intended to be used for steelwork in dynamically loaded structures.

This Model Construction Specification covers structural steelwork produced from hot rolled structural steel products only. It does not cover structural steelwork produced from cold formed structural steel (only cold formed profiled steel sheeting and cold formed stressed-skin sheeting used as a structural diaphragm are herein covered), structural hollow sections, channels and tubes, and stainless steel products.

This Model Construction Specification should be introduced into a steelwork contract by a Project Specification, the contents of which are detailed in Appendix A of this document and completed with project-specific information. The Project Specification should also include any additions or modifications that may be required by the National Structural Steelwork Specification by the Client for a particular contract if the form of behaviour or other aspects of the structure are unorthodox.

Contract documents (which include architectural and/or structural design drawings, specifications and addenda) vary considerably in intricacy and completeness. Nonetheless, the designer, the fabricator and the erector must be able to rely upon the accuracy of the contract documents, in order to allow them to provide the Client with bids that are adequate and complete. It also enables the preparation of the general arrangement drawings and the shop and erection drawings, the ordering of materials and the timely fabrication and erection of construction components.

Critical requirements that are necessary to protect the Client’s interest, that affect the integrity of the structure or that are necessary for the designer, the


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fabricator and the erector to proceed with their work, must be included in the contract documents. Non-exhaustive examples of critical information include:

Standard specifications and codes that govern structural steel design and construction, including bolting and welding

Material specifications

Welded-joint configuration and weld-procedure qualification

Surface preparation and shop painting requirements

Shop and field inspection requirements

If any, non-destructive testing (NDT) requirements, including acceptance criteria

Special requirements on delivery and special erection limitations.


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2 NORMATIVE REFERENCES

The European Standards incorporate, by dated or undated reference, provisions from other publications. These normative references are cited at the appropriate places in the text and the publications are listed in Tables 2.1 to 2.3.

Table 2.1 Design and structural engineering

Title

EN 1990:2002 Basis of structural design

EN 1991-1-1:2003 Actions on structures – Part 1-1: General actions – Densities, self- weight, imposed loads for buildings

EN 1991-1-2:2002 Actions on structures – Part 1-2: General actions – Actions on structures exposed to fire

EN 1991-1-3:2003 Actions on structures – Part 1-3: General actions – Snow loads

EN 1991-1-4:2005 Actions on structures – Part 1-4: General actions – Wind loads

EN 1991-1-5:2003 Actions on structures – Part 1-5: General actions – Thermal actions

EN 1991-1-6:2005 Actions on structures – Part 1-6: General actions – Actions during execution

EN 1991-1-7:2006 Actions on structures – Part 1-7: General actions – Accidental actions

EN 1991-3:2006 Actions on structures – Part 3 : Actions induced by cranes and machinery

EN 1993-1-1:2005 Design of steel structures – Part 1-1: General rules and rules for buildings

EN 1993-1-2:2005 Design of steel structures – Part 1-2: General rules – Structural fire design

EN 1993-1-3:2006 Design of steel structures – Part 1-3: General rules – Supplementary rules for cold-formed members and sheeting

EN 1993-1-4:2006 Design of steel structures – Part 1-4: General rules – Supplementary rules for stainless steels

EN 1993-1-5:2005 Design of steel structures – Part 1-5: Plated structural elements

EN 1993-1-8:2005 Design of steel structures – Part 1-8: Design of joints

EN 1993-1-9:2005 Design of steel structures – Part 1-9: Fatigue

EN 1993-1-10:2005 Design of steel structures – Part 1-10: Material toughness and through-thickness properties

EN 1993-6:2007 Design of steel structures – Part 6: Crane supporting structures

EN 1998-1:2004 Design of structures for earthquake resistance – Part 1: General rules, seismic actions and rules for buildings


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For each European country, each part of the Eurocode applies with its National Annex when the latter is available.

Table 2.2 Execution, fabrication and erection

Title

EN 1090-1:2009 Execution of steel structures and aluminium structures. Part 1: Requirements for conformity assessment of structural components

EN 1090-2:2008 Execution of steel structures and aluminium structures. Part 2: Technical requirements for steel structures

EN ISO 12944 Paints and varnishes – Corrosion protection of steel structures by protective paint systems

EN 1461 Hot dip galvanized coatings on fabricated iron and steel articles – specifications and test methods

EN ISO 17659:2004 Welding - Multilingual terms for welded joints with illustrations

EN ISO 14555:1998 Welding - Arc stud welding of metallic materials

EN ISO 13918:1998 Welding - Studs for arc stud welding

EN ISO 15609-1:2004

Specification and qualification of welding procedures for metallic materials - Part 1: Welding procedure specification for arc welding of steels

EN ISO 15614-1:2004

Specification and qualification of welding procedures for metallic materials – Welding procedure test - Part 1: Arc and gas welding of steels and arc welding of nickel and nickel alloys

EN 1011-1:1998 Welding – Recommendations for welding of metallic materials Part 1: General guidance for arc welding

EN 1011-2:2001 Welding – Recommendations for welding of metallic materials Part 2: Arc welding of ferritic steels

EN ISO 25817:2003 Arc-welded joints in steel - Guidance for quality levels for imperfections

ISO 286-2:1988 ISO system of limits and fits - Part 2: Tables of standard tolerance grades and limit deviations for hole and shafts


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Table 2.3 Products

Title

EN 10025-1:2004 Hot-rolled products of structural steels - Part 1: General delivery conditions.

EN 10025-2:2004 Hot-rolled products of structural steels - Part 2: Technical delivery conditions for non-alloy structural steels.

EN 10025-3:2004 Hot-rolled products of structural steels - Part 3: Technical delivery conditions for normalized rolled weldable fine grain structural steels.

EN 10025-4:2004 Hot-rolled products of structural steels - Part 4: Technical delivery conditions for thermo-mechanical rolled weldable fine grain structural steels.

EN 10025-5:2004 Hot-rolled products of structural steels - Part 5: Technical delivery conditions for structural steels with improved atmospheric corrosion resistance.

EN 10025-6:2004 Hot-rolled products of structural steels - Part 6: Technical delivery conditions for flat products of high yield strength structural steels in the quenched and tempered condition.

EN 10164:2004 Steel products with improved deformation properties perpendicular to the surface of the product - Technical delivery conditions.

EN 10210-1:2006 Hot finished structural hollow sections of non-alloy and fine grain structural steels – Part 1: Technical delivery requirements.

EN 10219-1:2006 Cold formed hollow sections of structural steel Part 1: Technical delivery requirements.

EN 10029:1991 Hot rolled steel plates 3 mm thick or above - Tolerances on dimensions, shape and mass

EN 10034:1993 Structural steel I- and H-sections - Tolerances on shape and dimensions

EN 10051:1991 Continuously hot-rolled uncoated plate, sheet and strip of non-alloy and alloy steels - Tolerances on dimensions and shape

EN 10055:1995 Hot rolled steel equal flange tees with radiused root and toes - Dimensions and tolerances on shape and dimensions

EN 10056-1:1995 Structural steel equal and unequal leg angles Part 1: Dimensions

EN 10056-2:1993 Structural steel equal and unequal leg angles Part 2: Tolerances on shape and dimensions

EN 13001-1:2004 Cranes – General design – Part 1 : General principles and requirements

EN 13001-2:2004 Crane safety – General design – Part 2 : Load effects

EN 14399-1:2002 High strength structural bolting for preloading Part 1 : General Requirements

EN 14399-2:2002 High strength structural bolting for preloading Part 2 : Suitability Test for preloading

EN 14399-3:2002 High strength structural bolting for preloading Part 3 : System HR - Hexagon bolt and nut assemblies


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Table 2.3 Continued…

Title

EN 14399-4:2002 High strength structural bolting for preloading Part 4 : System HV - Hexagon bolt and nut assemblies

EN 14399-5:2002 High strength structural bolting for preloading Part 5 : Plain washers for system HR

EN 14399-6:2002 High strength structural bolting for preloading Part 6 : Plain chamfered washers for systems HR and HV

EN ISO 898-1:1999 Mechanical properties of fasteners made of carbon steel and alloy steel - Part 1: Bolts, screws and studs (ISO 898-1:1999)

EN 20898-2:1993 Mechanical properties of fasteners Part 2: Nuts with special proof load values - Coarse thread (ISO 898-2:1992)

EN ISO 2320:1997 Prevailing torque type steel hexagon nuts - Mechanical and performance requirements (ISO 2320:1997)

EN ISO 4014:2000 Hexagon head bolts - Product grades A and B (ISO 4014:1999)

EN ISO 4016:2000 Hexagon head bolts - Product grade C (ISO 4016:1999)

EN ISO 4017:2000 Hexagon head screws - Product grades A and B (ISO 4017:1999)

EN ISO 4018:2000 Hexagon head screws - Product grade C (ISO 4018:1999)

EN ISO 4032:2000 Hexagon nuts, style 1 - Product grades A and B (ISO 4032:1999)

EN ISO 4033:2000 Hexagon nuts, style 2 - Product grades A and B (ISO 4033:1999)

EN ISO 4034:2000 Hexagon nuts - Product grade C (ISO 4034:1999)

EN ISO 7040:1997 Prevailing torque hexagon nuts (with non-metallic insert), style 1 - Property classes 5, 8 and 10

EN ISO 7042:1997 Prevailing torque all-metal hexagon nuts, style 2 - Property classes 5, 8, 10 and 12

EN ISO 7719:1997 Prevailing torque type all-metal hexagon nuts, style 1 - Property classes 5, 8 and 10

ISO 1891:1979 Bolts, screws, nuts and accessories - Terminology and nomenclature – Trilingual edition

EN ISO 7089:2000 Plain washers- Nominal series- Product grade A

EN ISO 7090:2000 Plain washers, chamfered - Normal series - Product grade A

EN ISO 7091:2000 Plain washers - Normal series - Product grade C

EN ISO 10511:1997 Prevailing torque type hexagon thin nuts (with non-metallic insert)

EN ISO 10512:1997 Prevailing torque type hexagon nuts thin nuts, style 1, with metric fine pitch thread - Property classes 6, 8 and 10

EN ISO 10513:1997 Prevailing torque type all-metal hexagon nuts, style 2, with metric fine pitch thread - Property classes 8, 10 and 12

When manufactured construction products, with Harmonised Standards (i.e. EN 10025, EN 1090), are to be used, CE marking shall be placed on the products according to the relevant European Harmonised Standards. Harmonised Standards are European Standards adopted by the European


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Committee for Standardisation (CEN), following a mandate issued by the European Commission (mandate M/120 for structural metallic products). Not all European Standards (ENs) are harmonised - only those which have been listed in the Official Journal.

When manufactured construction products, without Harmonized Standards, are to be used (i.e. metal anchors, fire protective products, metal frame building kits, fire stopping and fire sealing products, prefabricated building units, etc.), European Technical Approval Guidelines (ETAG) require manufacturers to place CE marking on their products in accordance with the relevant European Technical Approval (ETA).

The relevant ETAs shall be specified in the contract documents.

An full list of valid ETAs is available on the official website of the European Organisation for Technical Approvals (EOTA): www.eota.be.

The latest edition of the publication referred to applies.

National Standards Bodies publish up-to-date versions on their official websites.

Table 2.4 National Standards Bodies

Country Standards body Web site

Belgium NBN www.nbn.be

France AFNOR www.afnor.org

Germany DIN www.din.de

Italy UNI www.uni.com

Netherlands NEN www.nen.nl

Poland PKN www.pkn.pl

Spain AENOR www.aenor.es

Switzerland SNV www.snv.ch

Luxembourg ILNAS www.ilnas.lu

Austria ASI www.as-institute.at


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3 BASIS OF STRUCTURAL DESIGN

EN 1990 establishes the Principles and Requirements for safety, serviceability and durability of structures, describes the basis for their design and verification and gives guidelines for related aspects of structural reliability.

For the design of new structures, EN 1990 is intended to be used, for direct application, together with Eurocodes EN 1991 to 1999.

EN 1990 is applicable for the structural appraisal of existing construction, in developing the design of repairs and alterations or in assessing changes of use.

Design of steel structures shall conform to the basic requirements of § 2.1 of EN 1990.

Reliability, durability and quality management shall conform to § 2.2, § 2.4 and § 2.5 of EN 1990.

National choice is allowed through clauses listed in the Foreword to EN 1990.

3.1 General assumptions according to EN 1990 The choice of structural system and the design of the structure is made by

appropriately qualified and experienced personnel

Execution is carried out by personnel having the appropriate skill and experience

Adequate supervision and quality control is provided during the execution of the work, i.e. in design offices, factories, plants and on site

The construction materials and products are used as specified in EN 1990 or in the relevant execution standards or reference material or product specifications

The structure will be adequately maintained

The structure will be used in accordance with the design assumptions.

Additional contract document requirements

According to § 2.1(4)P of EN 1990, relevant additional specific events (impact, explosion, etc.), defined by the Client and the relevant authority, must be taken into account in the design and the execution of a structure.

According to § 2.3 of EN 1990, the contract documents should specify the design working life of the structure.

According to § 3.3(2) of EN 1990, the contract documents should state any relevant additional specific circumstances where the limit states that concern the protection of the contents are to classified as ultimate limit states.

According to § 3.4(1) of EN 1990, the contract documents shall specify the serviceability requirements of the project.


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4 ACTIONS ON STRUCTURES

4.1 Self-weight and imposed loads for buildings EN 1991-1-1 gives design guidance and actions for the structural design of buildings, including the following aspects:

Densities of construction materials and stored materials

Self-weight of construction elements

Imposed loads for buildings.

National choice is allowed through clauses listed in the Foreword to EN 1991-1-1.


According to § 3.3.2(4) of EN 1991-1-1, the contract documents shall specify the imposed loads to be considered for serviceability limit state verifications, in accordance with the service conditions and the requirements concerning the performance of the structure.

According to § 4.1(1) and 4.1(2) of EN 1991-1-1, characteristic values of densities of construction and stored materials shall be specified in the contract documents, especially for materials which are not covered by the Tables in Appendix A.

According to § 6.1(4) of EN 1991-1-1, loads for heavy equipment (e.g. in communal kitchens, radiology rooms, boiler rooms, etc.) shall be agreed between the Client and the relevant authority and specified in the contract documents.

4.2 Snow loads EN 1991-1-3 gives guidance to determine the values of loads due to snow, to be used for the structural design of buildings.



According to § 1.5 of EN 1991-1-3, in some circumstances tests and proven and/or properly validated numerical methods may be used to obtain snow loads on the construction works. These circumstances are those agreed with the Client and the relevant authority, and specified in the contract documents.

According to § 4.1(1) of EN 1991-1-3, to cover unusual local conditions, the National Annex may additionally allow the Client and the relevant authority to agree upon different characteristic values of snow load which have to be specified in the contract documents.


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4.3 Wind loads EN 1991-1-4 gives guidance on the determination of natural wind actions for the structural design of buildings (with heights up to 200 m) for each of the loaded areas under consideration.



According to § 7.2.2 of EN 1991-1-4, the rules for the velocity pressure distribution for leeward wall and sidewalls may be given in the National Annex or be defined for the individual project and specified in the contract documents.

4.4 Thermal actions EN 1991-1-5 gives design guidance, principles and rules for calculating thermal actions arising from climatic and operational conditions for the structural design of buildings. Principles needed for cladding and other appendages of buildings are also provided.

EN 1991-1-5 describes the changes in the temperature of structural elements. Characteristic values of thermal actions are presented for use in the design of structures which are exposed to daily and seasonal climatic changes. For structures not exposed to climatic conditions, thermal actions may not need to be considered.

National choice is allowed through clauses listed in the foreword to EN 1991-1-5.


According to § 5.2(2)P of EN 1991-1-5, operational effects (due to heating, technological or industrial processes) shall be considered in accordance with the particular project, and thus specified in the contract documents.

According to § 5.2(3)P of EN 1991-1-5, values of TM and Tp may be provided for the particular project, and thus specified in the contract documents.

4.5 Actions during execution EN 1991-1-6 gives principles and general rules for the determination of actions to be taken into account during the execution of buildings. EN 1991-1-6 can be used as guidance for the determination of actions to be taken into account during structural alterations, reconstruction, partial or full demolition, and for the determination of actions to be used for the design of auxiliary construction works (false-work, scaffolding, propping system, etc.) needed for the execution phases. Rules and additional information are given in Annexes A1 and B, and can also be defined in the National Annex or in the contract documents for the individual project.


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National choice is allowed through clauses listed in the foreword to EN 1991-1-6.


The rules concerning the safety of persons, on and around the construction site, shall be specified in the contract documents for the individual project, and are outside the scope of EN 1991-1-6.

EN 1991-1-6 also provides rules for determining the actions that can be used for the calculation of auxiliary construction works needed for the execution phases.

The contract documents shall classify construction loads in accordance with Tables 2.2 and 4.1 of EN 1991-1-6.

Loads due to construction equipments, cranes and/or auxiliary structures can be classified as fixed or free loads, depending on their possible spatial variation; contract documents shall specify the loads and their classification.

If construction loads are classified as fixed, then the contract documents shall define tolerances for the possible deviations to the theoretical position.

If construction loads are classified as free, then the contract documents shall define the limits of the potential area of spatial variation.

In the absence of any specific requirement in the National Annex, the contract documents shall specify:

Return periods for the assessment of the characteristic values of variable (climatic, seismic, etc.) actions during execution phases (see § 3.1(5) of EN 1991-1-6)

A minimum wind velocity during execution phases (see § 3.1(5) of EN 1991-1-6)

Rules of combination of snow loads and wind action with the construction loads (see § 3.1(7) of EN 1991-1-6)

Geometric imperfections of the structure and the structural elements, for the selected design situations during execution (see § 3.1(8) of EN 1991-1-6)

Criteria associated with serviceability limit states during execution (see § 3.3(2) of EN 1991-1-6)

When appropriate, frequent values of particular loads to be taken into account (see § 3.3(5) of EN 1991-1-6)

Requirements of suitability for service of auxiliary structures in order to avoid excessive deformation and/or deflection that affect the durability, fitness for use or aesthetic appearance in the final stage (see § 3.3(6) of EN 1991-1-6).

Concerning the wind actions, the contract documents shall specify whether or not a procedure is needed for calculating dynamic response of the structure during the various stages of execution, taking into account the degree of


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completion and stability of the structure and its components (see § 4.7(1) of EN 1991-1-6).

The contract documents shall specify the maximum allowable wind velocity during crane operations or other short term execution stages (see § 4.7(1) of EN 1991-1-6).

The contract documents shall specify, when relevant, accidental design situations due to cranes or exceptional conditions applicable to the structure or its exposure, such as impact, local failure and subsequent progressive collapse, fall of structural or non-structural parts, and abnormal concentrations of building equipment and/or building materials, water accumulation on steel roofs, fire, etc. (see § 4.12(1) and (3) of EN 1991-1-6).

The contract documents shall specify, when relevant, the design values of the ground acceleration as well as the importance factor I to be taken into account for the assessment of seismic actions, given the reference period of the considered transient situation (see § 4.13 of EN 1991-1-6).

The contract documents shall specify the characteristic values of horizontal actions due to imperfections or deformations related to horizontal displacements to be taken into account during execution phases (see § A1.3(1) of EN 1991-1-6).

4.6 Accidental actions EN 1991-1-7 describes Principles and Application rules for the assessment of accidental actions on buildings and bridges. The following actions are included:

Impact forces from vehicles, rail traffic, ships and helicopters

Actions due to internal explosions

Actions due to local failure from an unspecified cause.

EN 1991-1-7 does not specifically deal with accidental actions caused by external explosions, warfare and terrorist activities, or the residual stability of buildings damaged by seismic action or fire.



According to § 2(2)P of EN 1991-1-7, the contract documents may specify the treatment of accidental actions which are not classified as free actions.

According to § 3.1(2) of EN 1991-1-7, the contract documents shall specify the strategies and rules to be considered for accidental design situations.

According to § 3.1(2) of EN 1991-1-7, notional values for identified accidental actions may be specified in the contract documents.


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According to § 3.4(1) of EN 1991-1-7, the strategies for accidental design situations may be based on the Consequence Classes as set out in EN 1990. Thus, these Consequence Classes shall be specified in the contract documents.

According to § 4.3.1(2) of EN 1991-1-7, the contract documents shall specify whether or not the equivalent static design forces due to vehicular impact on members supporting structures over or adjacent to roadways, Fdx and Fdy, act simultaneously.

According to § 4.5.1.2 of EN 1991-1-7, if the building may be subject to impact from derailed railway traffic, the contract documents shall define whether it is a Class A or Class B structure.

According to § 4.5.2(1) of EN 1991-1-7, frontal and lateral dynamic design forces due to impact from river and canal traffic, as well as the height of application of the impact force and the impact area shall be specified in the contract documents.

4.7 Actions induced by cranes EN 1991-3 gives design guidance and specifies imposed loads (models and representative values) induced by hoists and cranes on runway beams, which include dynamic effects and braking, acceleration and accidental forces.

National choice is allowed through clauses listed in the Foreword to EN 1991-3.


Unless more accurate data (concerning the crane characteristics) is specified in the contract documents (the crane supplier shall therefore be known at the time of writing the contract documents), provisions of Section 2 of EN 1991-3 apply.

According to § 2.3(6) of EN 1991-3, the contract documents shall specify whether or not tests are performed with cranes on the supporting structures for the serviceability limit state verification.

According to § 2.5.2.2(2) of EN 1991-3, the contract documents shall specify whether one or several forces of the five horizontal types (a) to (e) listed in 2.5.2.2(1) shall be included in the same group of simultaneous crane load components.

According to § 2.5.2.2(4) of EN 1991-3, the contract documents shall specify the way the longitudinal horizontal forces HL,i and the transverse horizontal wheel forces HT,i, caused by acceleration and deceleration of masses of the crane or the crab, shall be applied. Otherwise, provisions given in Figure 2.3 of EN 1991-3 shall apply.

According to § 2.5.3(2) of EN 1991-3, the contract documents shall define the maximum number of cranes to be taken into account as acting simultaneously.


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The Hoisting Class (HC1 to HC4) of the crane shall be specified in the contract documents, unless it is specified in the crane supplier specification. Reference can be made to Annex B (informative) of EN 1991-3.

According to § 2.9.1(1) of EN 1991-3, the contract documents shall specify the vertical load to be applied to access walkways, stairs and platform. Otherwise, provisions given in § 2.9.1(2), 2.9.1(3) or 2.9.1(4) shall apply.

According to § 2.9.2(1) of EN 1991-3, the contract documents shall specify the horizontal load to be applied to the guard rail. Otherwise, provisions given in § 2.9.2(1) or 2.9.2(2) shall apply.

To make allowance of relevant accidental actions, the contract documents shall specify:

Whether buffers are used or not

Whether or not a crane with horizontally restrained loads can tilt when its load or lifting attachment collides with an obstacle.

To make allowance for fatigue effects, the contract documents shall provide sufficient information on the operational conditions; the fatigue loads can then be determined according to EN 13001 and Annex A of EN 1993-1-9. Otherwise, provisions of § 2.12 of EN 1991-3 apply.

Where a simplified approach for determining the fatigue loads is favoured in the contract documents, the latter shall specify:

the class of load spectrum (Q0 to Q5) for all tasks of the crane

the class of total number of working cycles (U0 to U9) during the design life of the crane

the crane classification (S0 to S9). If the crane classification is not included in the crane supplier specification, reference can be made to Annex B (informative) of EN 1991-3.

According to § A.3.2(1) of the normative Annex A of EN 1991-3, the contract documents shall specify the partial factor for actions on crane supporting structures to be used in serviceability limit states. Otherwise, this partial factor shall be taken as 1,0.

4.8 Seismic actions EN 1998-1 applies to the design and construction of buildings and civil engineering works in seismic regions. Its purpose is to ensure that in the event of earthquakes:

Human lives are protected

Damage is limited

Structures important for civil protection remain operational (special structures such as nuclear power plants, offshore structures and large dams, are beyond the scope of EN 1998-1).


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One fundamental issue in EN 1998-1 is the definition of the seismic action. Given the wide difference of seismic hazard and seismo-genetic characteristics in the various member countries, the seismic action is herein defined in general terms. The definition allows various Nationally Determined Parameters which shall be confirmed or modified in the National Annexes.



According to § 2.1(2) and (3) of EN 1998-1, target reliabilities for the no-collapse requirement and for the damage limitation requirement are established by the National Authorities for different types of buildings on the basis of the consequences of failure. Contract documents shall specify the Importance Class of the individual project (see 4.2.5 of EN 1998-1).

Depending on the Importance Class of the structure and the particular conditions of the project, contract documents shall specify whether or not ground investigations and/or geological studies shall be performed to identify the ground type (A, B, C, D, E, S1 or S2), according to Table 3.1 of EN 1998-1.

Contract documents shall specify the seismic zone of the individual project (according to the zonation map, decided by the National Authority, and found in the National Annex to EN 1998-1).

Contract documents shall specify according to which concept earthquake resistant steel buildings shall be designed to (DCL, DCM or DCH).

According to 6.2(8) of EN 1998-1, the required toughness of steel and welds and the lowest service temperature adopted in combination with the seismic action shall be defined in the contract documents.


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5 DESIGN OF STEEL STRUCTURES

Eurocode 3 is intended to be used in conjunction with:

EN 1990 Basis of structural design

EN 1991 Actions on structures

ENs, ETAGs and ETAs for construction products relevant for steel structures

EN 1090 Execution of Steel Structures – Technical requirements

EN 1992 to EN 1999 when steel structures or steel components are referred to.

Eurocode 3 is concerned only with requirements for resistance, serviceability, durability and fire resistance of steel structures. Other requirements, e.g. concerning thermal or sound insulation, are not covered.

5.1 Rules for single-storey buildings – EN 1993-1-1 EN 1993-1-1 gives basic design rules for steel structures with material thicknesses t > 3 mm. It also gives supplementary provisions for the structural design of single-storey steel buildings.

Material properties for steels and other construction products and the geometrical data to be used for design shall be those specified in the relevant ENs, ETAGs or ETAs unless otherwise indicated.



The design working life shall be taken as the period for which a building structure is expected to be used for its intended purpose. For the specification of the intended design working life of a permanent building see Table 2.1 of EN 1990.

The effects of deterioration of material, corrosion or fatigue where relevant shall be taken into account by appropriate choice of material, see EN 1993-1-4 and EN 1993-1-10, and details, see EN 1993-1-9, or by structural redundancy and by the choice of an appropriate corrosion protection system.

The dimensional and mass tolerances of rolled steel sections and plates shall comply with the relevant product standard, ETAG or ETA unless more severe tolerances are specified.

Any semi-finished or finished structural product used in the structural design of buildings shall comply with the relevant EN Product Standard or ETAG or ETA.


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With reference to Annex A1.4 of EN 1990, limits for vertical deflections according to Figure A1.1, for horizontal deflections according to Figure A1.2 and for vibrations of structures on which the public can walk, shall be specified in the contract documents and agreed with the Client.

5.2 Supplementary rules for sheeting – EN 1993-1-3 EN 1993-1-3 gives, among other, design requirements for profiled steel sheeting. Methods are also given, in this part of Eurocode 3, for stressed-skin design using steel sheeting as a structural diaphragm.



According to § 2(6) of EN 1993-1-3, contract documents shall define the Structural Class (I to III) of the construction, associated with failure consequences according to Annex B of EN 1990:

Structural Class I: construction where sheeting is designed to contribute to the overall strength and stability of a structure

Structural Class II: construction where sheeting is designed to contribute to the strength and stability of individual structural elements

Structural Class III: construction where sheeting is used as an element that only transfers loads to the structure.

5.3 Design of plated structural elements – EN 1993-1-5 EN 1993-1-5 gives design requirements of stiffened and unstiffened plates which are subject to in-plane forces.


5.4 Design of joints – EN 1993-1-8 EN 1993-1-8 gives design methods for the design of joints subject to predominantly static loading using steel grades S235, S275, S355 and S460.



According to § 3.4.1 of EN 1993-1-8, the category of bolted connections (Category A, B or C for joints loaded in shear, and Category D or E for joints loaded in tension) shall be specified in the contract documents.


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According to § 3.9 of EN 1993-1-8, the contract documents shall specify the class of friction surfaces for slip-resistant connections using pre-loaded 8.8 or 10.9 bolts.

According to § 4.1 of EN 1993-1-8, the contract documents shall specify the quality level of welds according to EN ISO 25817. The frequency of inspection of welds shall be specified in the contract documents and shall conform to the requirements of EN 1090-2.

5.5 Fatigue – EN 1993-1-9 EN 1993-1-9 gives methods for the assessment of fatigue resistance of members, connections and joints subjected to fatigue loading.

According to § 2(1) of EN 1993-1-9, structures designed using fatigue actions from EN 1991 (i.e., EN 1991-3) and fatigue resistance according to EN 1993-1-9 are deemed to satisfy an acceptable level of probability that their performance will be satisfactory throughout their design life.



According to § 3(1) of EN 1993-1-9, contract documents shall specify whether fatigue assessment shall be undertaken using either ‘damage tolerant method’ or ‘safe life method’. If the ‘damage tolerant method’ is specified, a prescribed inspection and maintenance regime for detecting and correcting fatigue damage shall be implemented throughout the design life of the structure. The ‘safe life method’ shall be specified in cases where local formation of cracks in one component could rapidly lead to failure of the structural element or structure.

According to § 3(7) of EN 1993-1-9, contract documents shall specify the Failure Consequence classification (Low Consequence or High Consequence) in order to determine the partial factor for fatigue strength, in conjunction with the specified fatigue assessment method.

5.6 Material toughness and through-thickness properties – EN 1993-1-10 EN 1993-1-10 contains design guidance for the selection of steel for fracture toughness and for through-thickness properties of welded elements where there is a significant risk of lamellar tearing during fabrication, for constructions executed in accordance with EN 1090.

The guidance given in Section 2 of EN 1993-1-10 shall be used for the selection of material for new construction. The rules shall be used to select a suitable steel grade from the European Standards for steel products listed in EN 1993-1-1.

The choice of Quality Class shall be selected from Table 3.1 EN 1993-1-10 depending on the consequences of lamellar tearing.


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Depending on the Quality Class selected from Table 3.1, either:

through thickness properties for the steel material shall be specified from EN 10164, or

post-fabrication inspection shall be used to identify whether lamellar tearing has occurred.

Guidance on the avoidance of lamellar tearing during welding is given in EN 1011-2.


5.7 Crane supporting structures – EN 1993-6 EN 1993-6 provides design rules for the structural design of runway beams and other crane supporting structures. It covers overhead crane runways inside buildings and outdoor crane runways for:

Overhead travelling cranes, either:

- supported on top of the runway beams or

- underslung below the runway beams

Monorail hoist blocks.



According to § 2.1.3.2(2) of EN 1993-6, the design working life of temporary crane supporting structures shall be agreed with the Client and the Public Authority, taking account of possible re-use.

According to § 4(3) of EN 1993-6, where crane rails are assumed to contribute to the strength or stiffness of a runway beam, contract documents shall specify the appropriate allowances for wear to be made in determining the properties of the combined cross-section.

According to § 4(4) of EN 1993-6, where actions from soil subsidence or seismic actions are expected, tolerances for vertical and horizontal imposed deformations shall be specified in the contract documents, agreed with the crane supplier, and included in the inspection and maintenance plans.

According to § 7.3(1) of EN 1993-6, the specific limits for deformations and displacements, together with the serviceability load combinations under which they apply, shall be specified in the contract documents for each project.


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6 EXECUTION SPECIFICATION

6.1 General The necessary information and technical requirements for execution of each part of the works shall be agreed and complete before commencement of execution of that part of the works. Execution of works shall comply with the requirements of EN 1090-2.

6.2 Execution classes Execution Classes (EXC1 to EXC4) may apply to the whole structure or to a part of the structure or to specific details. A structure can include several Execution Classes. A detail or group of details will normally be ascribed one Execution Class. However, the choice of an Execution Class does not necessarily have to be the same for all requirements.

If no Execution Class is specified EXC2 shall apply.

The list of requirements related to Execution Classes is given in Annex A.3 of EN 1090-2.

Guidance for the choice of Execution Classes is given in Annex B of EN 1090-2.

The choice of Execution Classes is related to Production Categories and Service Categories, with links to Consequence Classes as defined in Annex B of EN 1990.

6.3 Preparation grades Preparation grades (P1 to P3 according to ISO 8501-3) are related to the expected life of the corrosion protection and corrosivity category as defined in § 10 of EN 1090-2.

Preparation grades may apply to the whole structure or to a part of the structure or to specific details. A structure can include several preparation grades. A detail or group of details will normally be ascribed one preparation grade.

6.4 Geometrical tolerances Two types of geometrical tolerances are defined in § 11 of EN 1090-2:

a) Essential tolerances shall be in accordance with Annex D.1 of EN 1090-2. The values specified are permitted deviations.

- Manufacturing tolerances are described in § 11.2.2 of EN 1090-2;

- Erection tolerances are described in § 11.2.3 of EN 1090-2.


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b) Functional tolerances in terms of accepted geometrical deviations shall be in accordance with one of the following two options:

- The tabulated values described in § 11.3.2 and Annex D.2 of EN 1090-2;

- The alternative criteria defined in § 11.3.3 of EN 1090-2.

If no option is specified the tabulated values shall apply.

Tolerances on products are defined in the standards:

- EN 10034 for structural steel I and H sections,

- EN 10056-2 for angles,

- EN 10210-2 for hot-finished structural hollow sections,

- EN 10219-2 for cold formed hollow sections.


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7 CONSTITUENT PRODUCTS

7.1 Identification, inspection documents and traceability If constituent products that are not covered by the European Standards listed in Table 2 of EN 1090-2, are to be used, their properties shall be specified in the contract documents.

The properties of supplied constituent products shall be documented in a way that enables them to be compared to the specified properties. Their conformity with the relevant product standard shall be checked in accordance with § 12.2 of EN 1090-2.

For metallic products, the inspection documents according to EN 10204 shall be as listed in Table 1 of EN 1090-2.

For Execution Classes EXC3 and EXC4, constituent products shall be traceable at all stages from receipt to hand over after incorporation in the works.

For Execution Classes EXC2, EXC3 and EXC4, if differing grades and/or qualities of constituent products are in circulation together, each item shall be designated with a mark that identifies its grade.

Methods of marking shall be in accordance with that for components given in § 6.2 of EN 1090-2.

7.2 Structural steel products Structural steel products shall conform to the requirements of the relevant European product standards as listed in Table 2 of EN 1090-2, unless otherwise specified. Grades, qualities and, if appropriate, coating weights and finishes, shall be specified together with any required options permitted by the product standard, including those related to suitability for hot dip zinc-coating, if relevant.

7.3 Welding consumables All welding consumables shall conform to the requirements of EN 13479 and the appropriate product standard, as listed in Table 5 of EN 1090-2. The type of welding consumables shall be appropriate to the welding process (defined in § 7.3 of EN 1090-2), the material to be welded and the welding procedure.

7.4 Mechanical fasteners All mechanical fasteners (connectors, bolts, fasteners) shall conform to the requirements of § 5.6 of EN 1090-2.


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7.5 Grouting materials The grouting materials to be used shall conform to the requirements of § 5.7 of EN 1090-2.


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8 PREPARATION AND ASSEMBLY

This Section specifies the requirements for cutting, shaping, holing and assembly of constituent steel components.

Structural steelwork shall be fabricated considering the surface treatment requirements in § 10 of EN 1090-2, and within the geometrical tolerances specified in § 11 of EN 1090-2.

8.1 Identification At all stages of manufacturing, each piece or package of similar pieces of steel components shall be identifiable by a suitable system, according to the requirements of § 6.2 of EN 1090-2.

8.2 Handling and storage Constituent products shall be handled and stored in conditions that are in accordance with product manufacturer's recommendations. Structural steel components shall be packed, handled and transported in a safe manner, so that permanent deformation does not occur and surface damage is minimized.

Handling and storage preventive measures specified in Table 8 of EN 1090-2 shall be applied as appropriate.

8.3 Cutting Known and recognized cutting methods are sawing, shearing, disc cutting, water jet techniques and thermal cutting. Hand thermal cutting shall be used only if it is not practical to use machine thermal cutting. Cutting shall be carried out in such a way that the requirements for geometrical tolerances, maximum hardness and smoothness of free edges as specified in § 6.4 of EN 1090-2 are met.

8.4 Shaping Steel may be bent, pressed or forged to the required shape either by the hot or by the cold forming processes, provided the properties are not reduced below those specified for the worked material.

Requirements of § 6.5 of EN 1090-2 shall be applied as appropriate.

8.5 Holing Dimensions of holes, tolerances on hole-diameters and execution of holing shall comply with the requirements of § 6.6 of EN 1090-2.


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8.6 Assembly Assembly of components shall be carried out so as to fulfil the specified tolerances. Precautions shall be taken so as to prevent galvanic corrosion produced by contact between different metallic materials.

Requirements of § 6.9 and § 6.10 of EN 1090-2 shall be applied as appropriate.


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9 WELDING

9.1 General Welding shall be undertaken in accordance with the requirements of the relevant part of EN ISO 3834 or EN ISO 14554 as applicable.

A welding plan shall be provided as part of the production planning required by the relevant part of EN ISO 3834. The content of a welding plan is described in § 7.2.2 of EN 1090-2.

Welding may be performed by the welding processes defined in EN ISO 4063, and listed in § 7.3 of EN 1090-2.

9.2 Qualification of welding procedures Welding shall be carried out with qualified procedures using a Welding Procedure Specification (WPS) in accordance with the relevant part of EN ISO 15609 or EN ISO 14555 or EN ISO 15620. If specified, special deposition conditions for tack welds shall be included in the WPS.

Qualifications of welding procedures, depending on welding processes, are described in § 7.4.1.2 and § 7.4.1.3 of EN 1090-2.

9.3 Welders and welding operators Welders shall be qualified in accordance with EN 287-1 and welding operators in accordance with EN 1418. Records of all welder and welding operator qualification tests shall be kept available.

9.4 Welding coordination For Execution Class EXC2, EXC3 and EXC4, welding coordination shall be maintained during the execution of welding by welding coordination personnel suitably qualified for, and experienced in the welding operations they supervise as specified in EN ISO 14731.

With respect to the welding operations being supervised, and for structural carbon steels, welding coordination personnel shall have a technical knowledge according to Table 14 of EN 1090-2.

9.5 Preparation and execution of welding Precautions shall be taken to avoid stray arcing, and if stray arcing does occur the surface of the steel shall be lightly ground and checked. Visual checking shall be supplemented by penetrant or magnetic particle testing.

Precautions shall be taken to avoid weld spatter. For Execution Class EXC3 and EXC4, it shall be removed.


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Visible imperfections such as cracks, cavities and other not permitted imperfections shall be removed from each run before deposition of further runs.

All slag shall be removed from the surface of each run before each subsequent run is added and from the surface of the finished weld.

Particular attention shall be paid to the junctions between the weld and the parent metal.

Any requirements for grinding and dressing of the surface of completed welds shall be specified.

Joint preparation shall be appropriate for the welding process. If qualification of welding procedures is performed in accordance with EN ISO 15614-1, EN ISO 15612 or EN ISO 15613, joint preparation shall comply with the type of preparation used in the welding procedure test. Tolerances for joints preparations and fit-up shall be given in the WPS.

Joint preparation shall be free from visible cracks. Visible cracks shall be removed by grinding and the joint geometry corrected as necessary.

If large notches or other errors in joint geometry are corrected by welding, a qualified procedure shall be used, and the area shall be subsequently ground smooth and feathered into the adjacent surface.

All surfaces to be welded shall be dry and free from material that would adversely affect the quality of the welds or impede the process of welding (rust, organic material or galvanizing).

Prefabrication primers (shop primers) may be left on the fusion faces only if they do not adversely affect the welding process. For Execution Class EXC3 and EXC4, prefabrication primers shall not be left on the fusion faces, unless welding procedure tests in accordance with EN ISO 15614-1 or EN ISO 15613 have been completed using such prefabrication primers.

Other special requirements are described in EN 1090-2, as indicated in Table 9.1:


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Table 9.1 Special requirements

Clause

Storage and handling of welding consumables 7.5.2

Weather protection 7.5.3

Assembly for welding 7.5.4

Preheating 7.5.5

Temporary attachments 7.5.6

Tack welds 7.5.7

Fillet welds 7.5.8

Butt welds 7.5.9

Stud welding 7.5.12

Slot and plug welds 7.5.13

9.6 Acceptance criteria Welded components shall comply with the requirements specified in § 10 and § 11 of EN 1090-2.

The acceptance criteria for weld imperfections shall conform to the requirements of § 7.6 of EN 1090-2.


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10 MECHANICAL FASTENING

Section 8 of EN 1090-2 covers requirements for shop and site fastening, including the fixing of profiled sheeting; it refers to bolting assemblies consisting of matching bolts, nuts and washers (as necessary).

Contract documents shall specify if, in addition to tightening, other measures or means are to be used to secure the nuts.

Minimum nominal fastener diameter, bolt length, length of protrusion, length of the unthreaded bolt shaft and clamp length shall comply with the requirements of § 8.2.2 of EN 1090-2.

Requirements given in § 8.2.3 of EN 1090-2 for washers shall apply.

Tightening of non-preloaded bolts shall comply with the requirements of § 8.3 of EN 1090-2.

Precautions and preparation of contact surfaces in slip resistant connections shall comply with the requirements of § 8.4 and Table 18 of EN 1090-2. Slip factor shall be determined by test as specified in Annex G of EN 1090-2.

Tightening methods of preloaded bolts shall comply with the requirements of § 8.5 of EN 1090-2, and shall be specified in the contract documents.


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11 ERECTION

Section 9 of EN 1090-2 gives requirements for erection and other work undertaken on site including grouting of bases as well as those relevant to the suitability of the site for safe erection and for accurately prepared supports.

Erection shall not commence until the site for the construction works complies with the technical requirements with respect to the safety of the works. Safety items related to site conditions are listed in § 9.2 of EN 1090-2.

If the structural stability in the part-erected condition is not evident, a safe method of erection, on which the design was based, shall be provided. Items related to the design basis method of erection are listed in § 9.3.1 of EN 1090-2.

A method statement describing the steelwork contractor's erection method shall be prepared and checked in accordance with design rules. The erection method statement shall describe procedures to be used to safely erect the steelwork and shall take into account the technical requirements regarding the safety of the works. The erection method statement shall address all relevant items in § 9.3.1 of EN 1090-2; additional items are listed in § 9.3.2 of EN 1090-2.

Erection drawings or equivalent instructions, in accordance with the requirements of § 9.6.1 of EN 1090-2, shall be provided and form part of the erection method statement.

Site measurements for the works shall be in accordance with the survey requirements of § 9.4 of EN 1090-2.

The condition and location of the supports shall be checked visually and by appropriate measurement before the commencement of erection. If supports are unsuited to erection, they shall be corrected prior to the commencement of erection. Nonconformities shall be documented.

All foundations, foundation bolts and other supports for the steelwork shall be suitably prepared to receive the steel structure. Installation of structural bearings shall comply with the requirements of EN 1337-11. Erection shall not commence until the location and levels of the supports, anchors or bearings comply with the acceptance criteria in § 11.2 of EN 1090-2, or an appropriate amendment to the specified requirements.

If foundation bolts are to be pre-stressed, arrangements shall be made that the upper 100 mm of the bolt, as a minimum, has no adhesion to the concrete. Foundation bolts intended to move in sleeves shall be provided with sleeves three times the diameter of the bolt with a minimum diameter of 75 mm.

Whilst erection is proceeding, the supports for the steelwork shall be maintained in an equivalent condition to their condition at the commencement of erection.


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Areas of supports that require protection against rust staining shall be identified and appropriate protection provided.

Compensation for settlement of supports is acceptable, unless otherwise specified in the contract documents. This shall be done by grouting or packing between steelwork and support. The compensation will generally be placed beneath the bearing.

Shims and other supporting devices used as temporary supports under base plates shall be placed in accordance with the requirements of § 8.3, 8.5.1, § 9.5.4 and § 9.6.5.3 of EN 1090-2.

Grouting, sealing and anchoring shall be set in accordance with their specification and the requirements of § 5.8, 9.5.5 and § 9.5.6 of EN 1090-2.

Components that are individually assembled or erected at the site shall be allocated an erection mark, in accordance with the requirements of § 6.2 and § 9.6.2 of EN 1090-2.

Handling and storage on site shall comply with the requirements of § 6.3 and § 9.6.3 of EN 1090-2.

Any site trial erection shall be performed in accordance with the requirements of § 6.10 and § 9.6.10 of EN 1090-2.

The erection of the steelwork shall be carried out in conformity with the erection method statement and in such a way as to ensure stability at all times.

Foundation bolts shall not be used to secure unguyed columns against overturning unless they have been checked for this design situation.

Throughout the erection of the structure, the steelwork shall be made safe against temporary erection loads, including those due to erection equipment or its operation and against the effects of wind loads on the unfinished structure.

At least one third of the permanent bolts in each connection should be installed before that connection can be considered to contribute to stability of the part completed structure.

All temporary bracing and temporary restraints shall be left in position until erection is sufficiently advanced to allow its safe removal.

All connections for temporary components provided for erection purposes shall be made in accordance with the requirements of EN 1090-2 and in such a way that they do not weaken the permanent structure or impair its serviceability.

If backing bars and draw cleats are used to support the structure during welding, it shall be ensured that they are sufficiently strong and that their retaining welds are appropriate for the erection load conditions.

If the erection procedure involves rolling or otherwise moving the structure, or part of the structure, into its final position after assembly, provision shall be


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made for controlled braking of the moving mass. Provision for reversing the direction of movement may need to be considered.

All temporary anchoring devices shall be made secure against unintentional release.

Only jacks that can be locked in any position under load shall be used unless other safety provisions are made.

Care shall be taken that no part of the structure is permanently distorted or over-stressed by stacking of steelwork components or by erection loads during the erection process.

Each part of the structure shall be aligned as soon as practicable after it has been erected and final assembly completed as soon as possible thereafter.

Permanent connections shall not be made between components until sufficient of the structure has been aligned, levelled, plumbed and temporarily connected to ensure that components will not be displaced during subsequent erection or alignment of the remainder of the structure.

Alignment of the structure and lack-of-fit in connections may be adjusted by the use of shims (see above). If lack-of-fit between erected components cannot be corrected by the use of shims, components of the structure shall be locally modified in accordance with the methods specified in EN 1090-2. The modifications shall not compromise the performance of the structure in the temporary or permanent state. This work may be executed on site. Care shall be taken with structures built of welded latticed components and space structures to ensure that they are not subjected to excessive forces in an attempt to force a fit against their inherent rigidity.

Unless otherwise prohibited in the contract documents, drifts may be used to align connections. Elongation of holes for bolts used for transmission of loads shall not be more than the values given in § 6.9 of EN 1090-2.

In case of misalignment of holes for bolts, the method of correction shall be checked for consistency with the requirements of § 12 of EN 1090-2.

Realigned holes may be proven to comply with the oversize or slotted hole requirements specified in 8.1 of EN 1090-2, provided the load path has been checked.

Correction of misalignment by reaming or using a hollow milling cutter is preferred, but if the use of other cutting methods is unavoidable, the internal finish of all holes formed by these other methods shall be specifically checked for consistency with the requirements of § 6 of EN 1090-2.

Completed site connections shall be checked in accordance with 12.5 of EN 1090-2.

Erection tolerances are detailed in § 11.2.3 and Tables D.1.11 to D.1.15 and Tables D.2.19 to D.2.28 of Annex D of EN 1090-2.


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12 CONSTRUCTOR’S DOCUMENTATION

Quality documentation, mandatory for Execution Classes EXC2 to EXC4, is defined in § 4.2.1 of EN 1090-2.

If required, a quality plan (defined in EN ISO 9000) for the execution of the works is described in § 4.2.2 of EN 1090-2. Annex C of EN 1090-2 gives a check-list for the content of a quality plan recommended for the execution of structural steelwork with reference to the general guidelines in ISO 10005.

Method statements giving detailed work instructions shall comply with the technical requirements relating to the safety of the erection works as given in § 9.2 and § 9.3 of EN 1090-2.

Sufficient documentation shall be prepared during execution and as a record of the as-built structure to demonstrate that the works have been carried out according to the execution specification.

Design and structural engineering documentation shall be prepared before execution of the works, and approved by any approval body designated by the Owner. The documentation should contain:

Design assumptions

Software used (if any)

Member and joint design verification

General Arrangement drawings and joint details.


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13 INTERFACES OF THE STEEL STRUCTURE

13.1 Interface to concrete surfaces Information showing holding-down bolts and the interface of steelwork components to foundations shall include a Foundation Plan showing the base location, position and orientation of columns, the marks of all columns, any other components in direct contact with the foundations, their base location and level, and the datum level.

Similar information shall also be provided for components connecting to walls and other concrete surfaces.

Complete details of fixing steel and bolts to the foundations or walls, method of adjustment and packing space shall be provided.

Before erection of steelwork starts, the steelwork contractor shall inspect the prepared foundations and holding-down bolts for position and level; if he finds any discrepancies which are outside the deviations specified in § D.2.20 of EN 1090-2, he shall request that remedial work be carried out before erection commences.

Shims and other supporting devices used as temporary supports under base plates shall present a flat surface to the steel and be of adequate size, strength and rigidity to avoid local crushing of the substructure concrete or masonry.

If packings are subsequently to be grouted, they shall be placed so that the grout totally encloses them with a minimum cover of 25 mm unless otherwise specified.

If packings are left in position after grouting, they shall be made from materials with the same durability as the structure.

If adjustment to the position of the base is achieved using levelling nuts on the foundation bolts under the base plate, these may be left in position unless otherwise specified. The nuts shall be selected to ensure that they are suitable to maintain the stability of the part-erected structure but not to jeopardize the performance of the foundation bolt in service.

If spaces under base plates are to be grouted, fresh material shall be used in accordance with § 5.8 of EN 1090-2.

Grouting shall not be carried out under column base plates until a sufficient portion of the structure has been aligned, levelled, plumbed and adequately braced.

Grouting material shall be used as follows:

The material shall be mixed and used in accordance with product manufacturer's recommendations notably regarding its consistency when used. Material shall not be mixed or used below 0°C unless the manufacturer's recommendations permit it.


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The material shall be poured under a suitable head so that the space is completely filled.

Tamping and ramming against properly fixed supports shall be used if specified and/or recommended by the grout manufacturer.

Vent holes shall be provided as necessary.

Immediately before grouting, the space under the steel base plate shall be free from liquids, ice, debris and contaminants.

If treatment of steelwork, bearings and concrete surfaces is required before grouting, it shall be specified in the contract documents.

Care shall be taken that the external profile of grouting allows water to be drained away from structural steel components. If there is a danger of water or corrosive liquid becoming entrapped during service, the grout around base plates shall not be surcharged such that it rises above the lowest surface of the base plate and the geometry of the concrete grout shall form an angle from the base plate.

If no grouting is needed, and the edges of the base plate are to be sealed, the method shall be specified.

Anchoring devices in concrete parts of the structure or adjacent structures shall be set in accordance with their specification. Suitable measures shall be taken to avoid damage to concrete in order to achieve the necessary anchoring resistance.

Foundations shall be adequately designed by a qualified foundation engineer to support the building reactions and other loads which may be imposed by the building use. The design shall be based on the specific soil conditions of the building site.

13.2 Interface to neighbouring constructions The mutual influence of neighbouring constructions for wind or snow actions must be carefully considered. Design wind and snow loads may vary considerably regarding the site and the construction environment, hence, precise indications shall be given, in the contract documents, concerning the surrounding constructions.


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APPENDIX A MODEL PROJECT SPECIFICATION

The execution of steelwork for single-storey buildings in Europe will generally be specified to be in accordance with EN 1090-2, and the design to be in accordance with applicable parts of the Eurocode Standards. These Standards, which cover technical requirements for a wide range of steel structures, include clauses where the execution/design specification for the works is required to give additional information or where it has the option to specify other requirements.

Appendix A offers a set of clauses that may be used for single-storey steel building projects to supplement and quantify the rules of the European Standards.

The clauses are arranged in a two-column format. The left column contains the proposed clauses. The right column gives a commentary to several clauses, for the information of the person drawing up project documents; those commentaries are not intended to be included within the execution specification. The model specification must be made specific to the construction project by completing the relevant clauses with appropriate information.

The model project specification proposed in this Appendix covers structural steelwork produced from hot rolled structural steel products only. It does not cover structural steelwork produced from cold formed structural steel (only cold formed profiled steel sheeting and cold formed stressed-skin sheeting used as a structural diaphragm are herein covered), structural hollow sections, channels and tubes and stainless steel products. This model project specification relates principally to conventional construction using constituent products to the standards referenced in EN 1090-2. If more complex forms of construction are involved or other products are used, designers need to consider any modifications that might be needed to the execution specification to ensure that the desired quality and/or functionality are achieved.

For consistency, in Appendix A, those clause headings that are numbered and in bold, correspond to the Section headings of this document.


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Proposed Clauses Commentary

3 BASIS OF STRUCTURAL DESIGN

3.1 Design of steel structures shall conform to the basic requirements of § 2.1 of EN 1990.

3.2 Reliability, durability and quality management shall conform to § 2.2, 2.4 and 2.5 of EN 1990.

3.3 The following additional specific events shall be taken into account for the design and the execution of the structure: (insert list)

§ 2.1(4) of EN 1990.

3.4 The design working life of the structure shall be equal to ... years.

§ 2.3 of EN 1990. For the specification of the intended design working life of a permanent building, see Table 2.1 of EN 1990. A working life of 50 years will provide adequate durability for common single-storey buildings.

3.5 For the following additional specific circumstances, the limit states that concern the protection of the contents shall be classified as ultimate limit states: (insert list)

§ 3.3(2) of EN 1990.

3.6 The serviceability requirements of the project shall be as follows: (insert requirements)

§ 3.4(1) of EN 1990.

4. ACTIONS ON STRUCTURES

4.1 Self-weight and imposed loads

4.1.1 The following imposed loads shall be considered for serviceability limit state verifications: (insert list)

§ 3.3.2(4) of EN 1991-1-1. In accordance with the service conditions and the requirements concerning the performance of the structure.

4.1.2 The characteristic values of densities of construction and stored materials shall be taken as follows: (insert list)

§ 4.1(1) and 4.1(2) of EN 1991-1-1. Especially for materials which are not covered by the Tables in Annex A of EN 1991-1-1.

4.1.3 Loads of heavy equipments shall be as specified on the relevant drawings.

§ 6.1(4) of EN 1991-1-1. e.g. in communal kitchens, radiology rooms, boiler rooms, etc.

4.2 Snow loads

4.2.1 In the following circumstances, tests and proven and/or properly validated numerical methods may be used to obtain snow loads on the construction works: (insert particular circumstances, if any)

§ 1.5 of EN 1991-1-3. These circumstances should be agreed upon with the Client and the relevant authority.

4.2.2 Particular snow loads shall comply with the following requirements: (insert special requirements, if any)

§ 4.1(1) of EN 1991-1-3. To cover unusual local conditions, the National Annex may additionally allow the Client and the relevant authority to agree upon different characteristic values of snow load.


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4.3 Wind loads

4.3.1 (Optional) The following rules for the velocity pressure distribution for leeward wall and sidewalls shall apply: (insert rules)

§ 7.2.2 of EN 1991-1-4. Certain rules may also be given in the National Annex.

4.4 Thermal actions

4.4.1 The following specific operational thermal effects shall apply: (insert list of specific thermal actions)

§ 5.2(2)P of EN 1991-1-5. due to heating, technological or industrial processes.

4.4.2 The following specific values of TM and TP shall apply: (insert values)

§ 5.2(3)P of EN 1991-1-5. TM : linear temperature difference component; TP : temperature difference between different parts of a structure given by the difference of average temperatures of these parts.

4.5 Actions during execution

4.5.1 The following rules concerning the safety of persons, on and around the construction site, shall apply: (insert rules)

These rules are outside the scope of EN 1991-1-6.

4.5.2 Construction loads shall be as specified on the relevant drawings

See Tables 2.2 and 4.1 of EN 1991-1-6.

4.5.3 Tolerances for the possible deviations to the theoretical position of construction loads shall be as specified on the relevant drawings

If construction loads are classified as fixed loads.

4.5.4 The limits of the potential area of spatial variation of construction loads shall be as specified on the relevant drawings

If construction loads are classified as free loads.

4.5.5 The following minimum wind velocity during execution phases shall apply: ...

§ 3.1(5) of EN 1991-1-6. In the absence of any choice in the National Annex.

4.5.6 The following rules of combination of snow loads and wind action with the construction loads shall apply: (insert rules)


4.5.7 The geometric imperfections of the structure and the structural elements during execution shall be as follows: (insert values)


4.5.8 Criteria associated with serviceability limit states during execution shall be as follows: (insert criteria)


4.5.9 The maximum allowable wind velocity during crane operations shall be ...

§ 4.7(1) of EN 1991-1-6.

4.6 Accidental actions

4.6.1 The following notional accidental loads shall apply: (insert accidental actions)

Equivalent static design forces due to vehicular impact; Frontal and lateral dynamic design forces due to impact from river and canal traffic, as well as the height of application of the impact force and the impact area; Classification of structures subject to impact from derailed railway traffic (§ 4.5.1.2 of EN 1991-1-7);


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4.7 Actions induced by cranes

4.7.1 For the serviceability limit state verification, tests shall (or may not) be performed with the cranes on the supporting structures (specify the alternative to be recommended)

§ 2.3(6) of EN 1991-3

4.7.2 The following forces shall be included in the same group of simultaneous crane load components: (insert list of forces)

§ 2.5.2.2(2) of EN 1991-3 Insert one or several forces among the five horizontal types (a) to (e) listed in § 2.5.2.2(1) of EN 1991-3.

4.7.3 The longitudinal horizontal forces HL,i and the transverse horizontal wheel forces HT,i, caused by acceleration and deceleration of masses of the crane or the crab, shall be applied according to the following provisions: (insert provisions)

§ 2.5.2.2(4) of EN 1991-3 Otherwise, provisions given in Figure 2.3 of EN 1991-3 should apply.

4.7.4 The maximum number of cranes to be taken into account as acting simultaneously shall be: (insert number)

§ 2.5.3(2) of EN 1991-3

4.7.5 The Hoisting Class of the crane shall be: (specify class from HC1 to HC4)

Hoisting class to be specified unless it is specified in the crane supplier specification. Reference can be made to Annex B (informative) of EN 1991-3

4.7.6 The vertical load to be applied to access walkways, stairs and platform shall be equal to: (insert provisions)

§ 2.9.1(1) of EN 1991-3 Otherwise, provisions given in § 2.9.1(2), 2.9.1(3) or 2.9.1(4) should apply.

4.7.7 The horizontal load to be applied to the guard rail shall be equal to: (insert provisions)

2.9.2(1) of EN 1991-3 Otherwise, provisions given in § 2.9.2(1) or 2.9.2(2) should apply.

4.7.8 To make allowance of relevant accidental actions: - Buffers are (or are not) used; - A crane with horizontally restrained loads can (or cannot) tilt when its load or lifting attachment collides with an obstacle.

(specify construction conditions)

4.7.9 To make allowance for fatigue effects, the following operational conditions shall apply: (insert information)

If sufficient information is provided, the fatigue loads can then be determined according to EN 13001 and Annex A of EN 1993-1-9. Otherwise, provisions of § 2.12 of EN 1991-3 should apply.


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(Optional clause in case a simplified approach for determining the fatigue loads is favoured)

4.7.10 - The class of load spectrum for all tasks

of the crane shall be: (specify class from Q0 to Q5);

- The class of total number of working cycles (U0 to U9) during the design life of the crane shall be: (specify class from U0 to U9);

- The crane classification shall be: (specify class from S0 to S9)

If the crane classification is not included in the crane supplier specification, reference can be made to Annex B (informative) of EN 1991-3.

4.7.11 The partial factor for actions on crane supporting structures to be taken in serviceability limit states shall be equal to: (specify factor value)

Clause A.3.2(1) of normative Annex A of EN 1991-3 Otherwise, this partial factor should be taken as 1,0.

4.8 Seismic actions

4.8.1 The Importance Class of the project shall be ...

Table 4.3 of EN 1998-1. Ordinary buildings (other than schools, fire stations, power plants, hospitals, etc.) correspond to Importance Class II;

4.8.2 The Ground Type shall be as specified on the relevant documents.

Table 3.1 of EN 1998-1. Depending on the particular conditions of the project, contract documents should specify whether ground investigations and/or geological studies should be performed to identify the ground type;

4.8.3 The seismic zone of the project shall be....

According to the zonation map, decided by the National Authority, and found in the National Annex of EN 1998-1

4.8.4 Earthquake resistant steel building shall be designed according to ... concept

DCL, DCM or DCH.

5. DESIGN OF STEEL STRUCTURES

5.1 General rules

5.1.1 To ensure durability, the building and its components shall either be designed for environmental actions (and fatigue if relevant) or else protected from them.

§ 2.1.3.3(1)B of EN 1993-1-1.

5.1.2 The effects of deterioration of material and corrosion (and fatigue where relevant) shall be taken into account by appropriate choice of material (see EN 1993-1-4 and EN 1993-1-10), and details (see EN 1993-1-9), or by structural redundancy and by the choice of an appropriate protection system.

§ 2.1.3.3(2)B of EN 1993-1-1.

5.1.3 For the following components, the possibility of their safe replacement shall be verified as a transient design situation (insert list of the components of the building that need to be replaceable)

§ 2.1.3.3(3)B of EN 1993-1-1.


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5.1.4 With reference to Annex A1.4 of EN 1990, vertical deflections (according to Figure A1.1), horizontal deflections (according to Figure A1.2) and vibrations of structures on which the public can walk shall comply with the following limits: (insert serviceability limits states)

§ 7 of EN 1993-1-1.

5.2 Rules for sheeting

5.2.1 The Structural Class of the construction (Class I to III), associated with failure consequences according to Annex B of EN 1990, shall be as specified on the relevant documents.

§ 2(6) of EN 1993-1-3 Structural Class I: construction where sheeting is designed to contribute to the overall strength and stability of a structure; Structural Class II: construction where sheeting is designed to contribute to the strength and stability of individual structural elements; Structural Class III: construction where sheeting is used as an element that only transfers loads to the structure.

5.4 Design of joints

5.4.1 Bolted connections Category shall be as specified on the relevant documents.

§ 3.4.1 of EN 1993-1-8.

5.4.2 Friction surfaces for slip-resistant connections using pre-loaded 8.8 or 10.9 bolts shall be as specified on the relevant documents.

§ 3.9 of EN 1993-1-8.

5.4.3 According to EN ISO 25817, the quality level of welds shall be as specified on the relevant documents.

§ 4.1 of EN 1993-1-8.

5.4.4 The frequency of inspection of welds shall conform to the requirements of EN 1090-2 and shall be as specified on the relevant documents.

§ 4.1 of EN 1993-1-8.

5.5 Fatigue

5.5.1 Fatigue assessment shall be undertaken using ‘damage tolerant method’ or ‘safe life method’ (specify assessment method to be used).

§ 3(1) of EN 1993-1-9 If the ‘damage tolerant method’ is specified, a prescribed inspection and maintenance regime for detecting and correcting fatigue damage should be implemented throughout the design life of the structure. The ‘safe life method’ should be specified in cases where local formation of cracks in one component could rapidly lead to failure of the structural element or structure.

5.5.2 In order to determine the partial factor for fatigue strength, in conjunction with the specified fatigue assessment method, the failure Consequence classification shall be taken as ‘Low Consequence’ or ‘High Consequence’ (specify the consequence class).

§ 3(7) of EN 1993-1-9

5.6 Material toughness and through-thickness properties

5.6.1 The guidance given in section 2 of EN 1993-1-10 shall be used for the selection of materials for fracture toughness.


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5.6.2 The guidance given in section 3 of EN 1993-1-10 shall be used for the selection of materials for through-thickness properties.

5.7 Crane supporting structures

5.7.1 Where crane rails are assumed to contribute to the strength or stiffness of a runway beam, the properties of the combined cross-section shall be determined as follows:

(Specify the appropriate allowances for wear to be made).

§ 4(3) of EN 1993-6

5.7.2 Where actions from soil subsidence or seismic actions are expected, tolerances for vertical and horizontal imposed deformations shall be taken as follows:

(Specify the appropriate allowances).

§ 4(4) of EN 1993-6 These allowances should be agreed with the crane supplier, and included in the inspection and maintenance plans.

5.7.3 The limits for deformations and displacements shall be taken as follows: (specify the specific limits together with the serviceability load combinations under which they apply).

§ 7.3(1) of EN 1993-6

6. EXECUTION SPECIFICATION

6.1 General

6.1.1 The requirements for the execution of structural steelwork for the project are given in the following documents: (Insert list)

Insert a list of the relevant drawings and other documents, including reference to EN 1090-2.

6.2 Execution Class

6.2.1 For building structures, EXC2 shall generally apply, except where specified otherwise on the drawings.

The use of EXC2 as the default class will provide adequate reliability for most elements of ordinary buildings. For some structures, a greater scope of inspection and testing and/or higher quality level acceptance criteria may be required, either generally or for particular details. Particular details where this is required, such as where special inspection and testing is required, should be indicated on the drawings. Table A.3 of EN 1090-2 gives a list of requirements related to execution classes; Annex B of EN 1090-2 gives guidance for the choice of execution classes; The choice of execution classes is related to production categories and service categories, with links to consequence classes as defined in Annex B of EN 1990.

6.3 Preparation grades

6.3.1 The preparation grade of all surfaces to which paints and related products are to be applied shall be ... Otherwise, The expected life of the corrosion protection shall be ... years or corrosivity category shall be ...

Preparation grades (P1 to P3 according to ISO 8501-3) are related to the expected life of the corrosion protection and corrosivity category as defined in § 10 of EN 1090-2.


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6.4 Geometrical tolerances

6.4.1 For essential tolerances, the tabulated values in Annex D.1 of EN 1090-2 shall apply. If the steelwork is not within tolerance, it shall be reported to the designer of the permanent works and shall be adjusted, if necessary, to maintain the structural adequacy in accordance with the design rules.

Manufacturing tolerances are described in § 11.2.2 of EN 1090-2; Erection tolerances are described in § 11.2.3 of EN 1090-2;

6.4.2 For functional tolerances (in terms of accepted geometrical deviations), either the tabulated values in § 11.3.2 and Annex D.2 of EN 1090-2 shall apply, or, the alternative criteria defined in § 11.3.3 of EN 1090-2 shall apply.

7. CONSTITUENT STEEL PRODUCTS

7.1 Identification, inspection documents and traceability

7.1.1 Properties for (...) shall comply with the requirements given in (...).

§ 5.1 of EN 1090-2 Insert details for any constituent product not covered by the European Standards listed in Table 2 of EN 1090-2.

7.1.2 The inspection documents (according to EN 10204) shall be as listed in Table 1 of EN 1090-2.

§ 5.2 of EN 1090-2.

(Optional clause) 7.1.3 For Execution Classes EXC3 and

EXC4, constituent products shall be traceable at all stages from receipt to hand over after incorporation in the works.

§ 5.2 of EN 1090-2.

7.1.4 For Execution Classes EXC2, EXC3 and EXC4, if different grades and/or qualities of constituent products are in circulation together, each item shall be designated with a mark that identifies its grade.

§ 5.2 of EN 1090-2. Methods of marking should be in accordance with that for components given in § 6.2 of EN 1090-2. If marking is required, unmarked constituent products should be treated as non conforming product.

7.2 Structural steel products

7.2.1 The grade and quality of structural steel shall be as specified on the drawings.

7.2.2 For structural steel plates, thickness tolerances class A, in accordance with EN 10029, shall be used.

§ 5.3.2 of EN 1090-2. Class A is usually sufficient, even where EXC4 is specified, but if class C is required by the technical authority or for other reasons, that class should be specified instead.


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7.2.3 Structural carbon steels shall conform to the requirements of the relevant European product standards as listed in Table 2 of EN 1090-2, unless otherwise specified on the drawings. Grades, qualities and, if appropriate, coating weights and finishes, together with any required options permitted by the product standard, including those related to suitability for hot dip zinc-coating, if relevant, shall be as specified on the drawings.

§ 5.3.1 of EN 1090-2.

7.2.4 For carbon steels, surface condition shall be as follows: Class A2, for plates in accordance with the requirements of EN 10163-2; Class C1, for sections in accordance with the requirements of EN 10163-3. If relevant, surface imperfections (such as cracks, shell or seams) or repair of surface defects by grinding in accordance with EN 10163, shall comply with the following restrictions : (insert list of special restrictions)

§ 5.3.3 of EN 1090-2.

(Optional clause) 7.2.5 For EXC3 and EXC4, the locations (and

width) where internal discontinuity quality class S1 of EN 10160 is required, are specified on the relevant drawings.

§ 5.3.4 of EN 1090-2. Especially for welded cruciform joints transmitting primary tensile stresses through the plate thickness, and for areas close to bearing diaphragms or stiffeners.

7.2.6 Areas where material shall comply with requirements for improved deformation properties perpendicular to the surface (according to EN 10164) are specified on the drawings.

§ 5.3.4 of EN 1090-2. Consideration should be given to specifying such material for cruciform, T and corner joints. Should only be invoked where necessary; specify only those parts of the structure which need these properties.

7.3 Welding consumables

7.3.1 All welding consumables shall conform to the requirements of EN 13479 and the appropriate product standard, as listed in Table 5 of EN 1090-2. The type of welding consumables shall be appropriate to the welding process (defined in § 7.3 of EN 1090-2), the material to be welded and the welding procedure.

§ 5.5 of EN 1090-2.

7.4 Mechanical fasteners

7.4.1 All mechanical fasteners (connectors, bolts, fasteners) shall conform to the requirements of § 5.6 of EN 1090-2. Studs for arc stud welding including shear connectors for steel/concrete composite construction shall comply with the requirements of EN ISO 13918.

7.4.2 The property classes of non-preloaded bolts and nuts, and surface finishes, shall be as specified on the drawings.

7.4.3 The property classes of preloaded bolts and nuts, and surface finishes, shall be as specified on the drawings.

HV bolts are sensitive to over-tightening, so they require a greater level of site control. It is not advisable to use both HR and HV assemblies on the same project.


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7.4.4 The chemical composition of weather resistant assemblies shall comply with the requirements for Type 3 Grade A fasteners to ASTM standard A325, or equivalent.

7.4.5 Reinforcing steels may be used for foundation bolts. In this case, they shall conform to EN 10080 and the steel grade shall be as specified on the drawings.

(Optional clause) 7.4.6 Where locking devices are specified on

the drawings, they shall comply with the relevant standards listed in § 5.6.8 of EN 1090-2, and additionally ... (Insert any particular requirements for locking devices).

7.5 Grouting materials

7.5.1 Grouting materials to be used shall be as specified on the relevant drawings.

8. PREPARATION AND ASSEMBLY

8.1 Identification

8.1.1 Soft or low stress stamps may be used, except in any areas specified on the drawings.

Soft or low stress stamp marks can easily be obliterated by the protective system. The fabricator will usually mask the stamped area after application of primer and complete the coating locally after erection.

8.1.2 Areas where identification marks are not permitted or shall not be visible after completion are specified on the drawings.

8.2 Handling and storage

8.2.1 Structural steel components shall be packed, handled and transported in a safe manner, so that permanent deformation does not occur and surface damage is minimized. Handling and storage preventive measures specified in Table 8 of EN 1090-2 shall be applied as appropriate.

8.3 Cutting

8.3.1 Hand thermal cutting shall be used only if it is not practical to use machine thermal cutting. Cutting shall be carried out in such a way that the requirements for geometrical tolerances, maximum hardness and smoothness of free edges, as specified in § 6.4 of EN 1090-2, are met.

8.4 Shaping

8.4.1 Requirements of § 6.5 of EN 1090-2 shall be applied as appropriate.


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8.5 Holing

8.5.1 Dimensions of holes, tolerances on hole-diameters and execution of holing shall comply with the requirements of § 6.6 of EN 1090-2.

8.5.2 Where specified on the drawings, holes with special dimensions shall be provided for connections of movement joints.

8.5.3 Special tolerances on hole diameters shall be as specified on the drawings.

Special tolerances would only be needed in exceptional conditions. If pins are used, tolerances should be specified for both holes and pins.

8.5.4 Holes for fasteners shall be formed by drilling or by punching followed by reaming.

8.5.5 Long slotted holes shall be executed as specified on the drawings.

This option is only needed for special cases, such as slotted holes for pins in movement joints. Details must then be given on the drawings.

8.6 Assembly

8.6.1 Requirements of § 6.9 and 6.10 of EN 1090-2 shall be applied as appropriate.

8.6.2 Holes for which elongation is not permitted are shown on the relevant drawings.

This option is needed for fit bolts for instance.

8.6.3 The acceptability of the addition of any welded temporary attachments and the making of any butt welds additional to those specified on the drawings shall be verified according to the design rules. A record of the details of such attachments and butt welds shall be provided as part of the constructor’s execution documentation. Areas where temporary attachments have been made shall be made good. If weld repairs are necessary these shall be carried out in accordance with the requirements of the appropriate Standard.

If there are any restrictions on positioning of temporary attachments, they should be specified, either in this clause or on the drawings. In general, temporary welded attachments are not acceptable within 25 mm of the edges of flange plates.

9. WELDING

9.1 General

9.1.1 Welding shall be undertaken in accordance with the requirements of the relevant part of EN ISO 3834 or EN ISO 14554 as applicable.

9.1.2 A welding plan shall be provided as part of the production planning required by the relevant part of EN ISO 3834.

The content of a welding plan is described in § 7.2.2 of EN 1090-2.

9.1.3 Welding may be performed by the welding processes defined in EN ISO 4063.

Welding processes are listed in § 7.3 of EN 1090-2.


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9.2 Qualification of welding procedures

9.2.1 Welding shall be carried out with qualified procedures using a Welding Procedure Specification (WPS) in accordance with the relevant part of EN ISO 15609 or EN ISO 14555 or EN ISO 15620.

Qualifications of welding procedures, depending on welding processes, are described in § 7.4.1.2 and 7.4.1.3 of EN 1090-2.

9.3 Welders and welding operators

9.3.1 Welders shall be qualified in accordance with EN 287-1 and welding operators in accordance with EN 1418. Records of all welder and welding operator qualification tests shall be kept available.

9.4 Welding coordination

9.4.1 Welding coordination shall be maintained during the execution of welding by welding coordination personnel suitably qualified for, and experienced in the welding operations they supervise as specified in EN ISO 14731.

This option is needed for Execution Class EXC2, EXC3 and EXC4. With respect to the welding operations being supervised, and for structural carbon steels, welding coordination personnel should have a technical knowledge according to Table 14 of EN 1090-2.

9.5 Preparation and execution of welding

9.5.1 Precautions shall be taken to avoid stray arcing, and if stray arcing does occur the surface of the steel shall be lightly ground and checked. Visual checking shall be supplemented by penetrating or magnetic particle testing.

9.5.2 Precautions shall be taken to avoid weld spatter.

For Execution Class EXC3 and EXC4, weld spatter should be removed.

9.5.3 Visible imperfections such as cracks, cavities and other not permitted imperfections shall be removed from each run before deposition of further runs.

9.5.4 All slag shall be removed from the surface of each run before each subsequent run is added and from the surface of the finished weld.

9.5.5 Particular attention shall be paid to the junctions between the weld and the parent metal.

9.5.6 Special requirements for grinding and dressing of the surface of completed welds are shown on the relevant drawings.

9.5.7 Joint preparation shall be free from visible cracks. Visible cracks shall be removed by grinding and the joint geometry corrected as necessary.

9.5.8 If large notches or other errors in joint geometry are corrected by welding, a qualified procedure shall be used, and the area shall be subsequently ground smooth and feathered into the adjacent surface.


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9.5.9 All surfaces to be welded shall be dry and free from material that would adversely affect the quality of the welds or impede the process of welding.

Such as rust, organic material or galvanizing.

9.5.10 Requirements of § 7.5.1 to 7.5.16 of EN 1090-2 shall be applied as appropriate.

9.6 Acceptance criteria

9.6.1 Welded components shall comply with the requirements specified in § 10 and 11 of EN 1090-2.

9.6.2 The acceptance criteria for weld imperfections shall conform to the requirements of § 7.6 of EN 1090-2.

10. MECHANICAL FASTENING

10.1 General

10.1.1 Minimum nominal fastener diameter, bolt length, length of protrusion, length of the unthreaded bolt shaft and clamp length shall comply with the requirements of § 8.2.2 of EN 1090-2.

10.1.2 Requirements given in § 8.2.3 of EN 1090-2 for washers shall apply.

10.1.3 Tightening of non-preloaded bolts shall comply with the requirements of § 8.3 of EN 1090-2. The bolt shall protrude from the face of the nut, after tightening, not less than one full thread pitch.

10.1.4 Precautions and preparation of contact surfaces in slip resistant connections shall comply with the requirements of § 8.4 and Table 18 of EN 1090-2. Slip factor shall be determined by test as specified in Annex G of EN 1090-2.

10.1.5 Tightening methods of preloaded bolts shall comply with the requirements of § 8.5 of EN 1090-2; special requirements are specified on the relevant documents.

10.2 Bolts

10.2.1 Bolt sizes for structural bolting shall be as specified on the drawings.

10.2.2 Where the structure has been designed to utilise the shear resistance of the unthreaded shank of bolts, this is specified on the drawings and the dimensions of the bolts are given.

The locations and dimensions must be given on the drawings. Reliance on the resistance of the unthreaded shank, rather than the threaded part, is inadvisable because it requires a higher level of control on bolt supply and installation to ensure that only unthreaded parts exist in the part of the connection where the resistance to shear is required.

10.3 Nuts

10.3.1 Nuts shall be assembled so that their designation markings are visible for inspection after assembly.


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10.3.2 Nuts shall run freely on their partnering bolt, which is easily checked during hand assembly.

Any nut and bolt assembly where the nut does not run freely should be discarded.

10.4 Washers

10.4.1 Washers shall be provided under the nut or the bolt head of non-preloaded bolts, whichever is to be rotated.

10.4.2 For preloaded bolts : - for 8.8 bolts, a washer shall be used under the bolt head or the nut, whichever is to be rotated; - for 10.9 bolts, washers shall be used under both the bolt head and the nut.

10.5 Preparation of contact surfaces in slip-resistant connections.

10.5.1 The area of contact surfaces in preloaded connections shall be as specified on the drawings. For contact surfaces in slip-resistant connections shown on the relevant drawings, the following particular treatment shall apply: ... (Insert requirements). The treated surfaces shall be adequately protected until they are brought together.

10.5.2 Preparation of contact surfaces in slip-resistant connections shall comply with the requirements of § 8.4 of EN 1090-2; special requirements are specified on the relevant documents.

10.6 Tightening of preloaded bolts

10.6.1 The nominal minimum preloading force Fp,C shall be taken as indicated on the relevant drawings.

Usually, Fp,C = 0,7.fub.As.

10.6.2 The following tightening method(s) shall be used: ... (insert specific tightening methods)

The different tightening methods are described in Table 20 of EN 1090-2.

10.6.3 As an alternative to Table 20 of EN 1090-2, calibration to Annex H of EN 1090-2 may be used: - for all tightening methods; - for all tightening methods, except for the torque method.

(choose one of the above options)

10.6.4 When bolts are tightened by rotation of the bolt head, the following special precautions shall be taken: ... (insert special precautions depending on the tightening method adopted).

10.6.5 For thick surface coatings shown on the relevant drawings, the following measures shall be taken to offset possible subsequent loss of preloading force: ... (insert specific measures, depending on the tightening method adopted).

If torque method is used, this may be by retightening after a delay of some days.


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10.6.6 For the combined method, when using the value Mr,1 for the first tightening step, the simplified expression of Mr,1 (in § 8.5.4 of EN 1090-2) may (or may not) be used. (choose one of the above options)

10.6.7 For the combined method, values other than those given in Table 21 of EN 1090-2 shall not be used unless calibrated in accordance with Annex H of EN 1090-2.

10.6.8 For the HRC method, the first tightening step shall be repeated as necessary if the pre-tightening is relaxed by the subsequent tightening of the remainder of the bolts in the connection.

This first step should be completed for all bolts in one connection prior to commencement of the second step. Guidance of the equipment manufacturer may give additional information on how to identify if pre-tightening has occurred, e.g. sound of shear wrench changing, or if other methods of pre-tightening are suitable.

10.7 Fit bolts

10.7.1 Where permitted on the drawings, the length of the threaded portion of the shank of a fit bolt may exceed 1/3 of the thickness of the plate, subject to the following requirements: ... (Insert details)

Insert this clause if such permission is to be given and specify on the drawings for which bolts the longer thread length is permitted.

11. ERECTION

11.1 The design is based on the construction method and/or sequences given in the following documents: (Insert list).

11.2 Requirements for temporary bracing compatible with the construction method and/or sequences are specified on the following drawings: (Insert list)

Insert list of relevant drawings and other documents. Information should include, amongst other things, allowances for permanent deformations (pre-camber), settlement of supports, assumptions for temporary stability and assumptions about propped/un-propped conditions in staged construction. The designer has the duty to ensure that the permanent works can be built safely. The drawings will show a construction method and/or sequences and will show either in detail or indicatively the nature and positions of temporary bracings compatible with those sequences. These temporary bracings will normally be those required to provide stability in the ‘bare steel’ and ‘wet concrete’ conditions. The elements of the temporary bracing would normally be designed by the permanent works designer; if that is not the case, it should be stated in the contract documents (preferably on the drawings) that their design is the constructor’s responsibility.


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11.3 The allowances for permanent deformation and other associated dimensions specified on the relevant drawings allow for the quasi-permanent effects of the following actions, using the design basis method of erection: i) after steelwork erection: - Self weight of structural steelwork; ii) after completion of structure: - Self weight of structural steelwork; - Self weight of structural concrete; - Self weight of non-structural parts; - The effects of shrinkage modified

by creep.

It is the designer’s responsibility to determine the allowances (i.e. the addition to the nominal profile) required to offset the effects of permanent actions, including shrinkage effects. These allowances have often been termed, somewhat loosely, ‘pre-camber’.

11.4 If the constructor proposes to adopt an alternative construction method and/or sequences to that referred to 11.1, the constructor shall verify, in accordance with the design rules, that the alternative method and/or sequences can be used without detriment to the permanent works. The constructor shall allow a period of at least ... (insert number) weeks for the verification of the erection method in accordance with the design rules, to the satisfaction of the permanent works designer.

For major single-storey structures, the design basis method of erection will normally be produced through a close working between the designer and the constructor because the method of erection will often dictate aspects of the design. Even for lesser or minor structures, the fundamental issue is that the constructor's erection method must be compatible with the design basis method of erection or, if it is different, for whatever reason, the design of the permanent works must be re-verified, for that erection method.

11.5 The steelwork dimensions on the drawings are specified for a reference temperature of ... °C (Insert reference temperature)

The steelwork contractor will make adjustments to suit the calibration temperature of his measuring equipment.

11.6 Compensation for settlement of supports shall be made by the constructor if such settlement differs from the design assumptions.

The designer should state the range of settlement of the supports (including temporary supports) that was considered in the design.

11.7 The finished cover to steel packings (comprising a total thickness of grout and any concrete) shall comply with the cover requirements of EN 1992.

It is normal practice to remove steel packings. Softer packings may be left in place.

11.8 Packings and levelling nuts may be left in position, provided that it can be verified, in accordance with the design rules, that there is no detriment to the permanent works.

The implications of introducing a hard spot into the bearing area should be checked with respect to both steel and concrete elements.

11.9 The treatment of steelwork, bearings and concrete surfaces before grouting shall be as specified on the drawings.

11.10 Areas where the edges of the base plate are to be sealed, without grouting, are specified on the drawings.

If grouting is not specified in bearing areas, the perimeter of base plates should be sealed. The locations for sealing must be shown on the drawings.

11.11 Surfaces that are to be in contact with concrete, including the undersides of baseplates, shall be coated with protective treatment applied to the steelwork, excluding any cosmetic finishing coat, for the first ...mm (insert length, minimum 50 mm) of the embedded length, and the remaining surfaces need not be coated (or shall be coated, choose one option).

Additional requirements are given in § 10.7 of EN 1090-2.



Part 11: Moment Connections



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FOREWORD

This publication is part eleven of the design guide, Single-Storey Steel Buildings.




Part 3: Actions













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Contents Page No

FOREWORD iii

SUMMARY vi

1 INTRODUCTION 1 1.1 Design approach 1 1.2 Tension zone 1 1.3 Plastic distribution 4 1.4 Resistance of the compression zone 5 1.5 Resistance of the column web panel 6 1.6 Calculation of moment resistance 6 1.7 Weld design 7 1.8 Vertical shear 8 1.9 Stiffeners 9

2 JOINT STIFFNESS 10 2.1 Classification by calculation 10 2.2 Classification boundaries 11

3 BEST PRACTICE GUIDELINES FOR MOMENT CONNECTIONS 12 3.1 Eaves haunch 12 3.2 End plate 12 3.3 Stiffeners 13 3.4 Bolts 13 3.5 Apex connections 14 3.6 Welds 14

4 JOINT DESIGN TABLES 16 4.1 General 16 4.2 Main design assumptions 17 4.3 Notes to the tables 18 4.4 Apex connections 21 4.5 Eaves connections 37

REFERENCES 53


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SUMMARY

This publication provides an introduction to the design process for moment-resisting bolted connections in single storey steel framed buildings. It explains that the design process is complex, involving many steps to determine the resistance of individual bolt rows in the tension zone, checking whether the resistance of the bolt group has to be reduced on account of the performance of the connected elements, and evaluating the bending resistance from the tensile resistances of the rows. To simplify design, a series of design tables for standard connections are given, for eaves and apex connections in portal frames, with haunched and un-haunched rafters.


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1 INTRODUCTION

Manual design of moment-resisting bolted connections is laborious, particularly when there are several bolt rows acting in tension. Any iteration of connection geometry or connection component (such as changing the bolt setting out or bolt size) necessitates a full re-design. For these reasons, the design of moment-resisting bolted connections is generally carried out by using appropriate software.

This Section aims to provide an introduction to the verification process described in EN 1993-1-8[1].

1.1 Design approach The verification of a bolted moment resisting connection involves three distinct steps:

1. Determine the potential resistance of the bolt rows in the tension zone, in isolation.

2. Check whether the total tension resistance can be realised, as it may be limited by the web panel shear resistance of the column, or the resistance of the connection in the compression zone.

3. Calculate the moment resistance as the sum of the tension forces multiplied by their respective lever arms.

The key features of the approach are firstly that a plastic distribution of bolt row forces is allowed, as long as either the end plate or the column flange is sufficiently thin. The second key feature is that the complex yield line patterns in the tension zone are replaced by an equivalent, simple T-stub model which is more amenable to calculation.

1.2 Tension zone According to EN 1993-1-8 § 6.2.7.2(6), the effective design tension resistance Ftr,Rd at each bolt row in the tension zone is the least of the following resistances:

Column flange bending and bolt strength (Ft,fc,Rd)

Column web in transverse tension (Ft,wc,Rd)

End plate bending and bolt strength (Ft,ep,Rd)

Rafter beam web in tension (Ft,wb,Rd).

For each bolt row, the effective design tension resistance may thus be expressed as:

Ftr,Rd = min(Ft,fc,Rd; Ft,wc,Rd; Ft,ep,Rd; Ft,wb,Rd)

The relevant clauses of EN 1993-1-8 for the above components are given in Table 1.1.


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Table 1.1 Components of the joint to determine the potential design resistance of a bolt row

Component EN 1993-1-8 clause number

Column flange in bending Rdfc,t,F 6.2.6.4 and Table 6.2

Column web in transverse tension

Rdwc,t,F 6.2.6.3

End-plate in bending Rdt,ep,F 6.2.6.5 and Table 6.6

Rafter web in tension Rdwb,t,F 6.2.6.8

The resistance for each row is calculated in isolation. The connection resistance may be limited by:

The design resistance of a group of bolts

The stiffness of the column flange or end plate, which may preclude a plastic distribution of tension forces

The shear resistance of the column web panel

The resistance in the compression zone.

Because the tension resistance of a row may be limited by the effects of forces in other rows in the bolt group, the effective design tension resistances are considered to be potential resistances – their full realisation may be limited by other aspects of the design.

The potential design tension resistance Ftr,Rd for each bolt row should be determined in sequence, starting from the furthest bolt row from the centre of compression (with the maximum lever arm). In accordance with § 6.2.7.2(4), the resistance of any bolt rows closer to the centre of compression are ignored when calculating the resistance of a specific bolt row, or group of rows.

Subsequent rows are verified both in isolation and also as part of a group in combination with rows above. The resistance of row 2 is therefore taken as the lesser of:

the resistance of row 2 acting alone, and

the resistance of rows 1 and 2 acting as a group minus the resistance already allocated to row 1.

Row 1 is furthest from the centre of compression, and rows are numbered sequentially.

A stiffener in the column, or in the rafter, disrupts any common yield line pattern, which means that groups containing a stiffener need not be verified on that side. In a detail with an extended end plate, such as in Figure 1.1, the flange of the rafter means that there cannot be a common yield line pattern around the top two bolt rows in the end plate. On the column side, however, a common yield line pattern around the top two rows is possible, and must be verified.


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r =1

r =2

r =3

r =4

Figure 1.1 Extended end plate in a haunched eaves connection

1.2.1 End plate and column flange in bending

When determining the potential tension resistance of the end plate in bending, Ft,ep,Rd and the column flange in bending, Ft,fc,Rd, EN 1993-1-8 converts the real yield line patterns into an equivalent T-stub. Generally, a number of yield line patterns are possible – each with a length of equivalent T-stub. The shortest equivalent T-stub is taken. When bolts are located adjacent to a stiffener, or adjacent to the rafter flange, the increased resistance of the flange or end plate is reflected in a longer length of equivalent T-stub. Bolts adjacent to an unstiffened free edge will result in a shorter length of equivalent T-stub..

Effective lengths of equivalent T-stubs eff are given in Table 6.4 of EN 1993-1-8 for unstiffened flanges, in Table 6.6 for unstiffened end plates and in Table 6.5 for stiffened flanges (or end plates)..

In all cases, effective lengths of equivalent T-stubs are given for individual bolt rows and for bolt rows as part of a group – the length of the equivalent T-stub for a group of bolts is assembled from the contributions of the rows within the group.

The beneficial effect of stiffeners depends on the geometry of the stiffener, the location of the bolt and the proximity to the web. This is addressed in Figure 6.11 of EN 1993-1-8, which provides an factor used in determining the effective length of equivalent T-stub. When the bolt is sufficiently far from both web and stiffener, the stiffener has no effect – the effective length is the same as that in an unstiffened zone.

Once the effective length of T-stub has been determined, the resistance of the T-stub is calculated. Three modes, as illustrated in Figure 1.2, are examined:

Mode 1, in which the flange of the T-stub is the critical feature, and yields in double curvature bending

Mode 2, in which the flange and the bolts yield at the same load

Mode 3, in which the bolts are the critical component and the resistance is the tension resistance of the bolts.


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Mode 1 Mode 2 Mode 3

Figure 1.2 Behaviour modes of an equivalent T-stub

The expressions to calculate the resistance in the different modes are given in Table 6.2 of EN 1993-1-8.

1.2.2 Column web in transverse tension

The design resistance of an unstiffened column web in transverse tension is given by expression 6.15 in EN 1993-1-8, and is simply the resistance of a length of web, with a reduction factor for the interaction with shear in the column web panel. For bolted connections, § 6.2.6.3(3) states that the length of web to be assumed at each row, or for each group of rows, is equal to the length of the equivalent T-stub determined for that row (or group of rows).

1.2.3 Beam web in tension

The design resistance for a beam web in tension is given by § 6.2.6.8 and is the same as that for the column web in transverse tension, (see Section 1.2.2), but without an allowance for shear. The length of the beam web in tension is taken to be equal to the length of the equivalent T-stub determined for that pair (or group) of bolts.

1.3 Plastic distribution A plastic distribution of forces in bolt rows is permitted, but this is only possible if the deformation of the column flange or end plate can take place. This is ensured by placing a limit on the distribution of bolt row forces if the critical mode is mode 3, because this failure mode is not ductile.

According to § 6.2.7.2(9) of EN 1993-1-8, this limit is applied if the resistance of one of the previous bolt rows is greater than 1,9 Ft,Rd, where:

Ft,Rd is the tensile resistance of a single bolt

The limit is applied by reducing the resistance of the row under consideration, to a value Ftr,Rd , such that:

xRdtx,Rd,t / hhFF rr , where:

Ftx,Rd is the design tension of the furthest row from the centre of compression that has a design tension resistance greater than 1,9 Ft,Rd

hx is the lever arm from the centre of compression to the row with resistance Ftx,Rd

hr is the lever arm from the centre of compression to the row under consideration.


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The effect of this limitation is to apply a triangular distribution of bolt row forces.

1.4 Resistance of the compression zone 1.4.1 General

The design resistance in the compression zone may be limited by:

The resistance of the column web (Fc,wc,Rd), or

The resistance of the beam (rafter) flange and web in compression (Fc,fb,Rd).

The relevant clauses of EN 1993-1-8 are given in Table 1.2.

Table 1.2 Joint Components in compression

Component EN 1993-1-8 clause number

Resistance of column web Fc,wc,Rd 6.2.6.2

Resistance of the beam (rafter) flange and web

Fc,fb,Rd 6.2.6.7

1.4.2 Column web without a compression stiffener

Ideally, stiffeners in the column should be avoided, as they are expensive and can be disruptive when making connections in the minor axis. However, stiffeners in the compression zone of a column are usually required, especially in a portal frame eaves connection. In a portal frame, the bending moment is large, producing a large compression force, and the column is usually an I-section with a relatively thin web.

The design resistance of an unstiffened column web subject to transverse compression is given by EN 1993-1-8, § 6.2.6.2. The design resistance is based on an effective width of web in compression, with the web verified as a strut, and with a reduction factor ω for shear and a reduction factor ρ for longitudinal compressive stress in the column.

1.4.3 Column web with a compression stiffener

The design resistance of a stiffened column subject to transverse compression may be calculated in accordance with § 9.4 of EN 1993-1-5.

1.4.4 Beam (rafter) flange and web in compression

The compression resistance of the beam flange and adjacent web in compression is given in § 6.2.6.7 of EN 1993-1-8 by:

fb

Rdc,Rd,fb,c, th

MF

where:

h is the depth of the connected beam


11 - 6

Mc,Rd is the design moment resistance of the beam cross-section, reduced if necessary to allow for shear, see EN 1993-1-1 § 6.2.5. For a haunched beam, such as a rafter, Mc,Rd may be calculated neglecting the intermediate flange

tfb is the flange thickness of the connected beam.

For haunched beams, such as those commonly used for rafters in portal frames, the depth h, should be taken as the depth of the fabricated section, and the thickness tfb should be that of the haunch flange.

If the height of the beam (rafter + haunch) exceeds 600 mm the contribution of the rafter web to the design compression resistance should be limited to 20%. This means that if the resistance of the flange is fby,fbfb fbt then:

8,0fby,fbfb

Rdfb,c,

fbtF

1.5 Resistance of the column web panel The resistance of the column web panel is given by § 6.2.6.1 of EN 1993-1-8, which is valid for 69wtd .

The resistance of an unstiffened column web panel in shear, Vwp,Rd is given by:

M0

vcwcy,Rdwp,

3

9,0

Af

V

where:

Avc is the shear area of the column, see EN 1993-1-1 § 6.2.6(3).

1.6 Calculation of moment resistance Having calculated potential resistances in the tension zone (Section 1.2), the design resistance in the compression zone (Section 1.4) and the resistance of the column web panel in shear (Section 1.5), the effective design resistances in the tension zone may be determined.

According to EN 1993-1-8 § 6.2.7.2(7), the total design resistance in the tension zone must not exceed the design resistance in the compression zone.

Similarly, the total design resistance in the tension zone must not exceed the design resistance of the column web panel, modified by a transformation parameter, . This is expressed as:

Rdwp,Rdt, VF

The transformation parameter, is taken from § 5.3(7), and may be taken from Table 5.4 as 1.0 for one-sided connections.

If either the resistance in the column web panel or in the compression zone is less than the total design resistance in the tension zone, the resistances in the tension zone must be reduced.


11 - 7

The resistance of the bolt row nearest the centre of compression is reduced as a first step, and then the next row, until the total design resistance in the tension zone is no more than the compression resistance, or the web panel shear resistance. Reducing the bolt row resistance in this way is satisfactory, as the design approach presumes a plastic distribution of bolt forces.

As an alternative to reducing the resistance in the tension zone, stiffeners can be provided to increase the design resistance of the web panel in shear, and the web in compression.

Once the effective design tension resistances have been calculated, by reducing the potential resistances if necessary, the design moment resistance of the connection can be calculated, as the summation of each bolt row tension resistance multiplied by its lever arm from the centre of compression, i.e.:

r

rr FhM Rd,tRdj, (as given in § 6.2.7.2 of EN 1993-1-8)

The centre of compression is assumed to be in line with the centre of the compression flange.

1.7 Weld design EN 1993-1-8 § 6.2.3(4) requires that the design moment resistance of the joint is always limited by the design resistance of its other basic components, and not by the design resistance of the welds. A convenient conservative solution is therefore to provide full-strength welds to components in tension. When components are in compression, such as the bottom flange of a haunch, it is normally assumed that the components are in direct bearing, and therefore only a nominal weld is required. If the joint experiences a reversed bending moment, the weld will be required to carry some tension force, and this should be considered.

1.7.1 Tension flange welds

The welds between the tension flange and the end plate may be full strength.

Alternatively, common practice is to design the welds to the tension flange for a force which is the lesser of:

(a) The tension resistance of the flange, which is equal to bf tf fy

(b) The total tension force in the top three bolt rows for an extended end plate or the total tension force in the top two bolt rows for a flush end plate.

The approach given above may appear conservative, but at the ultimate limit state, there can be a tendency for the end plate to span vertically between the beam flanges. As a consequence, more load is attracted to the tension flange than from the adjacent bolts alone.

A full strength weld to the tension flange can be achieved by:

a pair of symmetrically disposed fillet welds, with the sum of the throat thickness equal to the flange thickness, or

a pair of symmetrically disposed partial penetration butt welds with superimposed fillet welds, or


11 - 8

a full penetration butt weld.

For most small and medium sized beams, the tension flange welds will be symmetrical, full strength fillet welds. Once the leg length of the required fillet weld exceeds 12 mm, a full strength detail with partial penetration butt welds and superimposed fillets may be a more economical solution.

1.7.2 Compression flange welds

Where the compression flange has a sawn end, a bearing fit can be assumed between the flange and end plate and nominal fillet welds will suffice. If a bearing fit cannot be assumed, then the weld must be designed to carry the full compression force.

1.7.3 Web welds

It is recommended that web welds in the tension zone should be full strength. For beam webs up to 11,3 mm thick, a full strength weld can be achieved with 8 mm leg length (5.6 mm throat) fillet welds. It is therefore sensible to consider using full strength welds for the full web depth, in which case no calculations are needed for tension or shear. For thicker webs, the welds to the web may be treated in two distinct parts, with a tension zone around the bolts that have been dedicated to take tension, and with the rest of the web acting as a shear zone.

Tension zone

Full strength welds are recommended. The full strength welds to the web tension zone should extend below the bottom bolt row resisting tension by a distance of 1,73g/2, where g is the gauge (cross-centres) of the bolts. This allows an effective distribution at 60° from the bolt row to the end plate.

Shear zone

The resistance of the beam web welds for vertical shear forces should be taken as:

Psw = 2 a fvw,d Lws

where:

a is the fillet weld throat thickness

fvw,d is the design strength of fillet welds (from EN 1993-1-8, § 4.5.3.3(2))

Lws is the vertical length of the shear zone welds (the remainder of the web not identified as the tension zone).

1.8 Vertical shear Design for vertical shear is straightforward. Generally, the bolts at the bottom of the connection are not assumed to be carrying any significant tension, and are allocated to carry the vertical shear. The bolts must be verified in shear and bearing in accordance with EN 1993-1-8 Table 3.4.


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1.9 Stiffeners Components of the joint may be strengthened by providing additional material, although this means additional expense. Table 1.3 summarises the opportunities to strengthen moment resisting joints. Types of stiffeners are illustrated in Figure 1.3.

Table 1.3 Stiffeners

Stiffener type Effect Comments

Compression stiffener Increases the resistance to compression

Generally required in portal frame connections.

Flange stiffener in the tension zone

Increases the bending resistance of the column flange

Diagonal shear stiffener

Improves the column web panel resistance and also strengthens the tension flange

A common solution – connections on the minor axis may be more complicated.

Supplementary web plate

Increases the column web resistance to shear and compression

Minor axis connections are simplified. Detail involves much welding. See §6.2.6.1 of EN 1993-1-8.

End plate stiffener Increases the bending resistance of the end plate

Should not be used – a thicker end plate should be chosen.

Cap plate Increases the bending resistance of the flange, and the compression resistance (in reversed moment situations)

Usually provided in the column, aligned with the top flange of the rafter. Generally provided for the reversal load combination, but effective as a tension stiffener to the column flange.

Flange backing plate Increases the bending resistance of the flange

Only effective to increase mode 1 behaviour. See EN 1993-1-8, §6.2.4.3

1 1

2

3

4

5

6

1 Compression stiffener 2 Column flange stiffener 3 Cap plate

4 Shear stiffener 5 Supplementary web plate 6 End plate stiffener

Figure 1.3 Types of stiffeners


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2 JOINT STIFFNESS

EN 1993-1-8 § 5.2 requires that all joints are classified, by strength or by stiffness. Classification by strength is appropriate for plastic global analysis.

According to § 5.2.2.1(1), a joint may be classified according to its rotational stiffness, which should be calculated in accordance with the method described in Section 6.3 of EN 1993-1-8. It is recommended that software is used to calculate the initial joint stiffness. An introduction to the approach is given in Section 2.1.

In § 5.2.2.1(2) it is noted that joints may be classified on the basis of experimental evidence, experience of previous satisfactory performance in similar cases or by calculations based on test evidence. Some countries will accept classification on the basis of satisfactory performance – this may even be confirmed in the National Annex, which may point to nationally accepted design methods or joint details, and allow these to be classified without calculation.

2.1 Classification by calculation In § 6.3.1(4) the initial stiffness, Sj is given as:

ii

2

j 1k

EzS

where:

E is the modulus of elasticity

is a stiffness ratio that depends on the ratio of the applied moment to the moment resistance of the joint

z is the lever arm, given by § 6.2.7

ki is the stiffness of the basic joint component

2.1.1 Stiffness of basic joint components

Table 6.10 of EN 1993-1-8 identifies the basic joint components to be considered. For a one-sided bolted end plate connection, such as in a portal eaves frame, the basic joint components to be considered are given in Table 2.1.


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Table 2.1 Basic joint components in a portal frame eaves connection

Stiffness coefficient Joint component

k1 column web panel in shear

k2 column web in compression

k3 column web in tension

k4 column flange in bending

k5 end plate in bending

k10 bolts in tension

For a joint with two or more rows of bolts, the basic components for each row should be represented by a single equivalent stiffness, keq. For a beam-to-column joint with an end plate connection, this equivalent stiffness is determined using k3, k4, k5 and k10 for each individual bolt row, and an equivalent lever arm. (see EN 1993-1-8, § 6.3.3.1(4)).

Table 6.11 of EN 1993-1-1 indicates how the individual stiffness coefficients should be determined.

2.2 Classification boundaries Classification boundaries are given in EN 1993-1-8 § 5.2.2.5. They depend on the initial stiffness, Sj,ini, the second moment of area of the beam, Ib, the length of the beam, lb and a factor, kb that depends on the stiffness of the frame.

Joints are classified as rigid when bbbinij, lEIkS

Thus, for a given initial stiffness Sj,ini, a minimum beam length, lb, may be calculated such that the joint is classified as rigid. This is the basis for the minimum lengths given in Section 4.


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3 BEST PRACTICE GUIDELINES FOR MOMENT CONNECTIONS

Any moment-resisting connection will involve additional expense compared to simple (shear only) details. Connections should be detailed to carry the applied forces and moments in the most economical way. This may involve providing larger member sizes, or changing the geometry of the connection, to reduce the fabrication effort involved in fitting stiffeners.

The following Sections offer guidance on appropriate detailing.

3.1 Eaves haunch The ‘haunch’ in a portal frame is usually taken to mean an additional triangular cutting that is welded below the rafter beam at the connection to the column. The length of the cutting will generally be around 10% of the span, or up to 15% of the span in the most efficient elastic designs. The haunch is generally cut from the same section as the rafter, or a deeper and heavier section.

Pairs of haunch cuttings are fabricated from one length of member, as shown in Figure 3.1. If the haunch is cut from the rafter section, the maximum depth of the haunched section is therefore just less than twice the depth of the rafter section. Deeper haunches require larger sections, or fabrication from plate.

Figure 3.1 Fabrication of haunch cuttings

3.2 End plate End plates are generally fabricated from S275 or S235 steel. For class 8.8 bolts and S275 steel, the end plate thickness should be approximately equal to the bolt diameter. Common thicknesses are:

20 mm thick when using M20 class 8.8 bolts

25 mm thick when using M24 class 8.8 bolts

The end plate should be wider than the rafter section, to allow a weld all around the flanges. The end plate should extend above and below the haunched section, to allow for the fillet welds. In the compression zone, the end plate should extend below the fillet weld for a distance at least equal to the thickness of the plate, as shown in Figure 3.2, to maximise the stiff bearing length when verifying the column in compression.


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tp

> tp

tp

> tp

Figure 3.2 End plate – compression zone

3.3 Stiffeners The various types of stiffener used in an eaves connection are shown in Figure 1.3. A compression stiffener is usually provided. Other stiffeners should be avoided if possible. Stiffeners to the end plate are never needed – a thicker end plate can be chosen to increase the resistance. Column flange stiffeners are used to increase the resistance of the connection. In preference to providing stiffeners, increased resistance can also be achieved by:

Providing more bolt rows

Extending the end plate above the top of the rafter, as shown in Figure 3.3

Increasing the depth of the haunch

Increasing the weight of the column section.

21

1 Extended column – may require skew cut 2 End plate stiffener – not preferred

Figure 3.3 Extended end plate connection

3.4 Bolts Bolts in moment connections are generally M20 or M24, class 8.8 or 10.9. In some countries, class 8.8 is standard. Bolts should be fully threaded, which means that the same bolts may be used throughout a building.

Bolts are generally set out at cross-centres (gauge) of 90 or 100 mm. The vertical pitch is generally 70 to 90 mm. In some countries, common practice is to have bolts regularly spaced over the complete depth of the connection. In other countries there may be a significant distance between the ‘tension’ bolts and the ‘shear’ bolts. EN 1991-1-8 does not preclude either detail. Maximum bolt spacings are given in the Standard to ensure components do not buckle


11 - 14

between connectors, but this behaviour does not occur in end plate connections.

Preloaded bolts are not required in portal frame connections.

3.5 Apex connections A typical apex connection is shown in Figure 3.4. Under gravity loads the bottom of the haunch is in tension. The haunch may be fabricated from the same section as the rafter, or may be fabricated from plate.

Figure 3.4 Typical apex connection

For modest structures and small bending moments, the apex detail may simply have a stiffening plate, as shown in Figure 3.5, rather than a flanged haunch.

Figure 3.5 Alternative apex detail

3.6 Welds As described in Section 1.7, full strength welds are generally required to the tension flange and adjacent to the tension bolts, as shown in Figure 3.6 for the eaves connection. The remainder of the weld to the web is designed to carry shear. Although the ‘shear’ web welds may be smaller than those in the tension zone, it is common practice to continue the same size weld for the full depth of the web.

In the compression zone, assuming that the ends of the member have been sawn, the components are in direct bearing and only a nominal weld is required. For the reversed moment design situation (with uplift due to wind), the welds at the bottom of the eaves haunch and at the top of the apex connection are in tension, and the welds should be verified for adequacy under this combination of actions.


11 - 15

1 nominal weld (but verified for tension when moment is reversed) 2 continuous fillet weld 3 full strength weld

Figure 3.6 Haunch welds

The weld between the haunch cutting and the underside of the rafter is generally a continuous fillet weld. Although an intermittent weld would be perfectly adequate structurally, it is usually more convenient to provide a continuous weld.

1

2

3


11 - 16

4 JOINT DESIGN TABLES

4.1 General This Section gives design tables for several typical configurations of moment connections in portal frames. It covers both eaves and apex connections.

Three basic profiles are covered: IPE 300, IPE 400 and IPE 500, in steel grades S235, S275 and S355. The profile sizes are generally those appropriate to span lengths of 20, 25 and 30 m respectively.

For each profile, three configurations of apex connections are tabulated for a typical bolt size and end plate thickness, and three configurations of eaves connections are tabulated for the same typical bolt size and end plate thickness. For each profile there are two additional tables, one for a different bolt class and the other for a different end plate thickness. These two additional tables are only given for apex connections without external bolts and for eaves connections with half haunch. Tables 4.1 and 4.2 give the table numbers of all the configurations.

Table 4.1 Apex connections

Profile End platetp (mm)

Bolt size

Bolt class

Without external bolts

With external bolts

With external bolts and stiffener

IPE 300 15 M16 8.8 Table 4.10 Table 4.13 Table 4.14

15 10.9 Table 4.11

20 8.8 Table 4.12


20 10.9 Table 4.16

25 8.8 Table 4.17


25 10.9 Table 4.21

20 8.8 Table 4.22

Table 4.2 Eaves connections


Bolt size

Bolt class

Haunch (a)

½ haunch (b)

No haunch


15 10.9 Table 4.26

20 8.8 Table 4.27


20 10.9 Table 4.31

25 8.8 Table 4.32


25 10.9 Table 4.36

20 8.8 Table 4.37

(a) The depth of the haunched beam is twice the depth of the basic profile

(b) The depth of the haunch beam is 1,5 times the depth of the basic profile


11 - 17

In Tables 4.10 to 4.39, the following information is given:

A detailed sketch of the connection

The basic parameters (profile, bolt size, bolt class, end plate thickness)

The main design resistances (moment resistance, axial resistance, shear resistance).

The tables provide the following results:

The design moment resistance Mj,Rd+ for positive moment

The minimum span length Lb,min for the connection to be considered as ‘rigid’, for positive moment

The design moment resistance Mj,Rd– for negative moment

The minimum span length Lb,min for the connection to be considered as ‘rigid’, for negative moment

The design axial resistance Nt,j,Rd for tension

The design axial resistance Nc,j,Rd for compression

The maximum shear resistance Vj,Rd for which no interaction with bending moment needs to be considered.

When a connection is subjected to a bending moment MEd and an axial force NEd, a linear interaction criterion should be applied from the above mentioned resistances:

NEd/Nj,Rd + MEd/Mj,Rd ≤ 1,0

The interaction should use the appropriate design resistances, in the same direction as the internal forces:

Nt,j,Rd or Nc,j,Rd for the axial force (tension or compression)

Mj,Rd+ or Mj,Rd

– for the bending moment (positive or negative)

4.2 Main design assumptions The tables have been prepared using the PlatineX software available on the web site www.steelbizfrance.com. This software can be freely used online and allows the designer to deal with any configuration of connections – apex or eaves connection.

The tables are based on the following design assumptions:

Calculations according to EN 1993-1-8

S235 end plate and stiffeners with S235 members, S275 otherwise

Bolt classes 8.8 and 10.9

Partial factors M as recommended (not to any particular National Annex).


11 - 18

Sign convention:

The bending moment is positive when it generates compression stresses in the lower flange and tension stresses in the upper flanges (Figure 4.1).

IPE 300 M > 0 IPE 300IPE 300 M > 0

Figure 4.1: Sign convention for bending moment

4.3 Notes to the tables 4.3.1 Apex connections

Tables 4.4 to 4.6 summarize the design moment resistances for the apex connections subject to positive moments. They can be compared with the plastic moment resistance of the cross-section (Table 4.3).

Table 4.3 Plastic moment resistance of the cross section (kNm)

Profile S235 S275 S355

IPE 300 148 173 223

IPE 400 307 359 464

IPE 500 516 603 779

Bolts outside the profile have a major influence on the moment resistance when they are in tension. The stiffener welded to the tension flange always increases the moment resistance, but not to the same degree.

The moment resistance is lower than the plastic moment of the cross-section. However this is not a problem since the member resistance is usually reduced by the buckling effects, including lateral-torsional buckling.

The minimum span length to consider the apex connection as fully rigid is relatively low. In practice, these connections will always be used for portal frames with a span length greater than this minimum value, and so can be considered rigid.

At the apex, the shear force is small and this verification will never be critical in common practice.


11 - 19

Table 4.4 Apex connections with S235 beams – Moment resistance (kNm)


Bolt size

Bolt class


With external bolts


IPE 300 15 M16 8.8 75,4 118 123

15 10.9 86,3

20 8.8 78,4

IPE 400 20 M20 8.8 189 258 269

20 10.9 210

25 8.8 197

IPE 500 25 M24 8.8 358 449 472

25 10.9 363

20 8.8 340



Bolt size

Bolt class


With external bolts


IPE 300 15 M16 8.8 78,4 123,5 132,8

15 10.9 91,7

20 8.8 78,4

IPE 400 20 M20 8.8 199,7 284,3 301,2

20 10.9 231,0

25 8.8 199,7

IPE 500 25 M24 8.8 407,3 504,8 533,6

25 10.9 421,5

20 8.8 360,0



Bolt size

Bolt class


With external bolts


IPE 300 15 M16 8.8 78,4 123,5 132,8

15 10.9 91,7

20 8.8 78,4

IPE 400 20 M20 8.8 199,7 293,9 318,4

20 10.9 231,3

25 8.8 199,7

IPE 500 25 M24 8.8 426,3 577,1 620,4

25 10.9 479,4

20 8.8 360,0


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4.3.2 Eaves connections

The minimum span length to consider the eaves connection as fully rigid is relatively low when a haunch is provided, and in practice these connections will always be used for portal frames with a span length greater than this minimum value. The connections may therefore be considered as rigid.

Without a haunch, the bending resistance is lower and the connection might be classified as semi-rigid. Therefore it is good practice to design the eaves connections with a haunch, so that the overall depth is at least 1,5 times the depth of the rafter.

The shear resistance of the column web is often the critical criterion.

For the eaves connections, the shear force is significant but the verification is generally not critical for the design.

Table 4.7 Eaves connections (S235 members) – Moment resistances (kNm)


Bolt size

Bolt class

Haunch ½ haunch No haunch

IPE 300 15 M16 8.8 177,2 134,7 87,4

15 10.9 136,4

20 8.8 134,7

IPE 400 20 M20 8.8 388,0 291,2 186,6

20 10.9 293,9

25 8.8 291,2

IPE 500 25 M24 8.8 683,3 511,0 327,8

25 10.9 514,9

20 8.8 500,2



Bolt size

Bolt class


IPE 300 15 M16 8.8 204,1 154,3 98,9

15 10.9 158,2

20 8.8 154,3

IPE 400 20 M20 8.8 451,8 338,3 214,8

20 10.9 341,6

25 8.8 338,3

IPE 500 25 M24 8.8 795,8 593,9 379,0

25 10.9 599,2

20 8.8 580,9


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Bolt size

Bolt class


IPE 300 15 M16 8.8 251,9 187,4 113,6

15 10.9 197,2

20 8.8 189,1

IPE 400 20 M20 8.8 564,0 417,5 258,2

20 10.9 435,2

25 8.8 420,8

IPE 500 25 M24 8.8 1000 739,7 462,3

25 10.9 763,7

20 8.8 716,4

4.4 Apex connections

IPE 300 M > 0

Figure 4.2 Sign convention for bending moment in apex connections


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Table 4.10 Apex connection – IPE 300

60

M16

60

75

150

300 IPE 3008.8

4

3303x70

15

15

6

8.5

15

Bolts M16 8.8

Hole diameter 18 mm

End plate tp = 15 mm

Beam IPE 300 S235 S275 S355

Positive moment

Design moment resistance Mj,Rd (kNm) 75,4 78,4 78,4

Minimum span length for ‘rigid’ Lb,min (m) 6,37

Negative moment



Design axial resistance

Tension Nt,j,Rd (kN) 567 595 595

Compression Nc,j,Rd (kN) 1264 1480 1710

Design shear resistance Vj,Rd (kN) 135


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60

M16

60

75

150

300 IPE 300

4

3303x70

15

15

6

8.5

10.9

15

Bolts M16 10.9

Hole diameter 18 mm


Beam IPE 300 S235 S275 S355

Positive moment



Negative moment








11 - 24


4

6

8.5

20

60

60

3x70 300 IPE 3008.8

M16

75

15015

15

330

Bolts M16 8.8

Hole diameter 18 mm


Beam IPE 300 S235 S275 S355

Positive moment



Negative moment








11 - 25


4

15

6

8.5

60

35

80

15

300 IPE 300

150

75

8.8

3x70

M16

70

385

Bolts M16 8.8

Hole diameter 18 mm


Beam IPE 300 S235 S275 S355

Positive moment



Negative moment








11 - 26


4

15

6

8.5

60

35

80

300 IPE 300

150

75

8.8

3x70

M16

70

385

158

Min = 140

70

7.15

Bolts M16 8.8

Hole diameter 18 mm


Stiffeners tp = 8 mm

Beam IPE 300 S235 S275 S355

Positive moment



Negative moment








11 - 27


5

15

7

9.9

8.8400

75

75

4x70 430

15 20

180

90

M20 IPE 400

Bolts M20 8.8

Hole diameter 22 mm


Beam IPE 400 S235 S275 S355

Positive moment



Negative moment








11 - 28


5

15

7

9.9

400

75

75

4x70 430

15 20

180

90

M20 IPE 40010.9

Bolts M20 10.9

Hole diameter 22 mm


Beam IPE 400 S235 S275 S355

Positive moment



Negative moment








11 - 29


5

15

7

9.9

8.8400

75

75

4x70 430

15180

90

M20 IPE 400

25

Bolts M20 8.8

Hole diameter 22 mm


Beam IPE 400 S235 S275 S355

Positive moment



Negative moment








11 - 30


5

15

7

9.9

75

4x70

20

180

90

M20 IPE 400

105

8.8

45

505

90

400

Bolts M20 8.8

Hole diameter 22 mm


Beam IPE 400 S235 S275 S355

Positive moment



Negative moment








11 - 31


5

15

7

75

4x70

20

180

90

M20 IPE 400

105

8.8

45

505

90 90

400

Min = 180

9.9

10

68.5

Bolts M20 8.8

Hole diameter 22 mm



Beam IPE 400 S235 S275 S355

Positive moment



Negative moment








11 - 32


6

15

8.8

15

500

90

90

5x70M24

100

200

530

25

IPE 500

4

10.3

Bolts M24 8.8

Hole diameter 26 mm


Beam IPE 500 S235 S275 S355

Positive moment



Negative moment








11 - 33


6

15

15

500

90

90

5x70M24

100

200

530

25

IPE 500

4

10.3

10.9

Bolts M24 10.9

Hole diameter 26 mm


Beam IPE 500 S235 S275 S355

Positive moment



Negative moment








11 - 34


6

15

8.8

15

500

90

90

5x70M24

100

200

530 IPE 500

4

10.3

20

Bolts M24 8.8

Hole diameter 26 mm


Beam IPE 500 S235 S275 S355

Positive moment



Negative moment








11 - 35


6

15

8.8500

90

5x70M24

100

20025

IPE 500

4

10.3

625

110

130

55

Bolts M24 8.8

Hole diameter 26 mm


Beam IPE 500 S235 S275 S355

Positive moment



Negative moment








11 - 36


6

15

8.8500

90

5x70M24

100

200

25

IPE 500

4

10.3

625

110

130

55

12

110

68.5

Min = 220

Bolts M24 8.8

Hole diameter 26 mm



Beam IPE 500 S235 S275 S355

Positive moment



Negative moment








11 - 37

4.5 Eaves connections

IPE 300IPE 300 M > 0

Figure 4.3 Sign convention for bending moment in eaves connections


11 - 38

Table 4.25 Eaves connection – IPE 300

4

56

8.5

3

4.2

300

70

60

IPE 300

IPE 300M16

7.1

80

35

80

10

10450

150

70

75

150

3x70

535

15

15

8.8

Bolts M16 8.8

Hole diameter 18 mm

Column stiffeners tp = 10 mm


Column IPE 300 Beam IPE 300 S235 S275 S355

Positive moment



Negative moment








11 - 39


4

56

8.5

3

4.2

300

70

60

IPE 300

IPE 300M16

7.1

80

35

80

10

10450

150

70

75

150

3x70

10.9 535

15

15

Bolts M16 10.9

Hole diameter 18 mm




Positive moment



Negative moment








11 - 40


4

56

8.5

3

4.2

300

70

60

IPE 300

IPE 300M16

7.1

80

35

80

10

10450

150

70

75

150

3x70

535

15

8.8

20

Bolts M16 8.8

Hole diameter 18 mm




Positive moment



Negative moment








11 - 41


4

56

8.5

300 IPE 300IPE 300

7.1

80

35

10

10

70

75

150

3x70

15

8.8

60

M16

15

385

Bolts M16 8.8

Hole diameter 18 mm




Positive moment



Negative moment








11 - 42


4

56

8.5

3

4.2

300

IPE 300

IPE 300

7.1

80

35

80

10

10855

70

75

150

3x70

3x70

15

15

55

285

670M168.8

Bolts M16 8.8

Hole diameter 18 mm




Positive moment



Negative moment








11 - 43


5

67

9.9

3

4.2

8.5

12

12

600

15

8.8

4590

4x70

105

400

70200

705

18090

105

100

M16

IPE 400

IPE 400

20

Bolts M20 8.8

Hole diameter 22 mm




Positive moment



Negative moment








11 - 44


5

67

9.9

3

4.2

8.5

12

12

600

15

4590

4x70

105

400

70200

705

18090

105

100

M20

IPE 400

IPE 400

20

10.9

Bolts M20 10.9

Hole diameter 22 mm




Positive moment



Negative moment








11 - 45


5

67

9.9

3

4.2

8.5

12

12

600

15

8.8

4590

4x70

105

400

70200

705

18090

105

100

M20

IPE 400

IPE 400

25

Bolts M20 8.8

Hole diameter 22 mm




Positive moment



Negative moment








11 - 46


5

67

9.9

8.5

12

12

15

8.8

4590

4x70

105

400

18090

IPE 400IPE 400

75

505M20

20

Bolts M20 8.8

Hole diameter 22 mm




Positive moment



Negative moment








11 - 47


5

7

9.9

3

4.2

12

121155

8.8

20

IPE 400

IPE 400

90

180

4590

105

4x70

4x70

105

15

890

385

400

75

M20

6

8.5

Bolts M20 8.8

Hole diameter 22 mm




Positive moment



Negative moment








11 - 48


6

7

3

4.2

8.8

15

875M24

5x70

2x70

70

500

110

250

130

100

200

14

14

IPE 500

IPE 500

4

10.3

9.9

750

25

55

130

Bolts M24 8.8

Hole diameter 26 mm




Positive moment



Negative moment








11 - 49


6

7

3

4.2

15

875M24

5x70

2x70

70

500

110

250

130

100

200

14

14

IPE 500

IPE 500

4

10.3

9.9

750

25

10.9

55

130

Bolts M24 10.9

Hole diameter 26 mm




Positive moment



Negative moment








11 - 50


6

7

3

4.2

15

875M24

5x70

2x70

70

500

110

250

130

100

200

14

14

IPE 500

IPE 500

4

10.3

9.9

750

55

130

8.8

20

Bolts M24 8.8

Hole diameter 26 mm




Positive moment



Negative moment








11 - 51


6

7

15

5x70 500

110

100

200

14

14

IPE 500 IPE 500

4

10.3

9.9

25

55

130

8.8

90

625M24

Bolts M24 8.8

Hole diameter 26 mm




Positive moment



Negative moment








11 - 52


6

7

3

4.2

15

5x70 500

110

100

200

14

14

IPE 500

IPE 500

4

10.3

9.9

1455

25

55

130

8.81110M24

5x70

130

485

95

Bolts M24 8.8

Hole diameter 26 mm




Positive moment

Design moment resistance Mj,Rd (kNm) 683,3 795,8 1000


Negative moment








11 - 53

REFERENCES

1 EN 1993-1-8: Eurocode 3 Design of steel structures. Joint design