shell structures

ADVANCE BUILDING CONSTRUCTION - I Unit II - Shell & folded plate structures

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Introduction

The word shell is an old one and is commonly used to describe the hard covering of eggs, crustacea, tortoises, etc. The dictionary says that the word shell is derived from the Latin scalus, as in fish scale.The shell structure is typically found in nature as well as in classical architecture. Its efficiency is based on its curvature (single or double), which allows a multiplicity of alternative stress paths and gives the optimum form for transmission of many different load types. Various different types of steel shell structures have been used for industrial purposes; singly curved shells, for example, can be found in oil storage tanks, the central part of some pressure vessels, in storage structures such as silos, in industrial chimneys and even in small structures like lighting columns.

Application of shell structure in various fields

Architecture and building

Power and chemical engineering

Structural engineering

Vehicle body structures

Composite construction

Thin-shell structures are light weight constructions using shell elements. These elements are typically curved and are assembled to large structures. Typical applications are fuselages of aero planes, boat hulls and roof structures in some buildings.

A thin shell is defined as a shell with a thickness which is small compared to its other dimensions and in which deformations are not large compared to thickness. A primary difference between a shell structure and a plate structure is that, in the unstressed state, the shell structure has curvature as opposed to plate’s structures which are flat. Membrane action in a shell is primarily caused by in-plane forces (plane stress), though there may be secondary forces resulting from flexural deformations. Where a flat plate acts similar to a beam with bending and shear stresses, shells are analogous to a cable which resists loads through tensile stresses. Though the ideal thin shell must be capable of developing both tension and compression.

http://en.wikipedia.org/wiki/Plane_stress

http://en.wikipedia.org/wiki/Tensile_structure


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A shell is a 3 d structure considered with a curved membrane acting as a stretched skin. Capable of transferring loads in more than two directions to supports without bending or twisting. thin membrane is made structurally possible by providing restraint at edges against bending stresses

Single curvature shells

Double curvature shells

single curvature shells are curved on one linear axis and are part of a cylinder or cone eg.1) barrel vaults 2) conoid shells.

Double curvature shells are either part of a dome or a hyperboloid or revolution.

Types of shell structures

Folded plate Barrel vaults Short shells Domes Intersection shells Warped surfaces Shell arches

Advantages:

Attraction of elegant simplicity of curved shell forms that utilize the natural strength and stiffness of shell form with great economy in the use of material. Continuity and Curvature- The essential ingredients of a shell structure

Disadvantages:

More expensive than a part framed structure, cost of labor, the

construction of centering of shell is very high. While rigidity and strength are in many cases desirable attributes of shell structures, there are some important difficulties that can occur precisely on account of unavoidable rigidity.Materials:

Most suited: concrete, highly plastic with small section, reinforcement bars to follow curvature of shells


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Translation shell:

It is a type of shell obtained by moving a vertical curve parallel to itself along another vertical in a plane at right angles to the plane of a sliding curve.

Hyperbolic parabolic shell:

Is obtained by sliding a vertical parabola with upward curvature in a plane at right angles. The plane of the first here and the curvature of the two sections will be in opposite directions, up in one and down in other.

The hyperbolic paraboloid shells designed by Felix candela of Mexico demonstrated the dramatic shapes and structural possibility of doubly curved shells. This shape is formed when a parabolic directix with the plane of the generator remaining vertical as it moves along the directrix. Resulting surface is described because horizontal sections through the surface are hyperbolas and vertical sections are parabolas.

The structural significance of this shape is that at every point on the surface , straight lines which lie in the surface is made up of a network of interesting straight lines

Therefore, centering for RCC hyperbolic paraboliod consists of thin straight sections of timber which are simple to fix and support.

Folded plates:

The distinguishing feature of the folded plate is the ease in forming plane surfaces. Therefore, they are more adaptable to smaller areas than curved surfaces which require multiple uses of forms for maximum economy. A folded plate may be formed for about the same cost as a horizontal slab and has much less steel and concrete for the same spans. Folded plates are not adapted to as wide bay spacing as barrel vaults. For widths of plate over, say, 12 feet, the thickness of the folded plate must be thicker than for a barrel vault. Some advantage may be gained by increasing the thickness of the slab just at the valleys so it will act as a haunched beam and as an I section plate girder.


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THREE SEGMENT FOLDED PLATE

This sketch shows a folded plate structure with three segments for each barrel. The end stiffeners are rigid frames rather than deep girders as in the last example. The forces from the reactions of the sloping plates on these rigid frames will be quite large and at an outside column they will not be balanced by thrusts from the adjacent plates. The size of the frames may be reduced by using a steel tie between the tops of the columns which can be concealed in the fenestration.

The dimensions of the plates are dependent on both the width of the barrel and on the span. The depth of the shell should be about 0.10 times the span and the maximum slope of a plate should not be greater than 40 degrees. For example, assume for the above structure that the span is 60 feet and the bay width is 24 feet. The depth of the shell should be about 6 feet and the horizontal width of each plate with a three segment plate should be about 8 feet. The slope of the plates is 6/8, which is about 37 degrees and is satisfactory. The thickness of the plates could be about 3 ½ inches.

Z SHELL

Each of the units in sketch has one large sloping plate and two edge plates arranged with space between the units for windows. This form has been called a Z shell and is similar to the louver used for window ventilation. The architectural effect is very dramatic if the structure can be shown by a cantilever projected out beyond the support. The windows are normally open to the north but most of the light is actually reflected south light. To increase this effect, the roof surface can be painted with aluminum so light from the sun is reflected through the windows to the ceiling and the windows need not be very large. Adjacent units should be tied together by structural window mullions. In constructing the Z shell, movable forms need only be lowered a short vertical distance if construction is started on the right and proceeds to the left.

The Z shell is not an efficient structural shape since it is discontinuous and its effective depth is much less than the actual vertical depth. Therefore, the spans are limited in comparison to the plates having a large number of units side by side.


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CANOPIESA folded plate structure for a small canopy at the entrance of a building is shown. This folded plate has four segments. A two segment structure is not desirable because it has very little torsional resistance. This instability can be demonstrated by a paper model having the ends of the model glued to vertical pieces of cardboard, acting as stiffening members. If it is absolutely necessary to have a two element system, a torsion member can be placed in the valley which will carry the unbalanced loads.

Stiffeners can often be hidden on the top surface so they are not in evidence and the shell will appear to spring from the vertical column. At the wall of the building there should also be a stiffener hidden in the wall construction. Provision should be made for drainage of the center valley.

TAPERED FOLDED PLATESFolded plate structures may be built with tapered elements and only one of the many possible combinations is shown here. Another possibility is to place the smaller depths all at one end so that the entire structure forms a circular ring. The height of the shells at the center of the span is the critical dimension for bending strength. Therefore, the structure is not very efficient and not suitable for long spans because of the excess height required for the large ends. Another weak element in this design is the transfer of shear from the small end of the triangular plate to the large end. If a large number of units are used in each span, the transfer of loads may be difficult.

A folded plate may be used for walls as a thin structural element by casting each plate flat on the floor and grouting the joints full of concrete. A wall of this type can be made much thinner than a flat wall.

EDGE SUPPORTED FOLDED PLATES

The usual upturned edge plate can be eliminated and the roof structure can be made to appear very thin if the edge plate is replaced by a series of columns. The slab between columns must be designed as a beam and it may be convenient to extend the main roof slab as a cantilever canopy. The beam element that carries the load of the roof between columns will then be wider. Wind loads are taken by rigid frame action in the columns and stiffeners.


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FOLDED PLATE TRUSSThe term "folded plate truss" is intended to indicate the structural action of this structure. There are horizontal ties across the width only at the ends of the building and the structure acts as an edge supported shell as shown in the previous example. The thrusts from the triangular crossed arches are carried lengthwise to the ends. The top chord of the inclined truss is formed by the ridge member. The bottom chords are the ties at the base of the side gables and the diagonals are formed by the sloping valleys at the intersection of the gables and the triangular plates. The top longitudinal compression member may require some additional thickness to form a compression member of sufficient size to carry the compression force.

FOLDED PLATE RIGID FRAMEAn arch with straight segments is sometimes called a rigid frame. It is not as efficient as the curved arch because the bending moments are greater. Ties across the plates are required at the knees and at the crown in order to distribute the forces at the ends of each segment.

BARREL VAULTS

Elements of barrel vaultsThe structure above is a single barrel vault with edge beams. The shell has been allowed to project beyond the edge of the stiffener in order to show the shape of the shell. Stiffeners are required at columns. They do not necessarily have to be complete diaphragms, as shown here, but may be arches with a horizontal tie.

In contrast to folded plates where the thickness is based on the design of a slab element, the thickness of the barrel shell is usually based on the minimum thickness required for covering the steel for fireproofing, plus the space required for three layers of bars, plus some space for tolerance. If these bars are all half inch rounds, a practical minimum would be 3 1/4 inches. Near the supports the thickness may be greater for containing the larger longitudinal bars.

If more than one barrel is placed side by side, the structure is a multiple barrel structure and if more than one span, it is called a multiple span structure. Any numbers of continuous barrels or continuous spans are possible except that eventually provision should be made for expansion joints in a large structure.


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BASIC ELEMENTS OF SHORT SHELLSThis sketch illustrates some of the principle parts of a short shell structure: 1) the shell spanning between arches, and 2) the arch structure. In this structure, the edge beams are provided at the lowest point of the shell and the arch is placed on top of the shell so that forms may be moved through the barrel. In small structures, the edge beam can be omitted if the shell is thickened. The curve of the shell is determined by the proper shape of the arch and may be a circle for small structures or may conform to the thrust line of the arch for long span structures.

The minimum shell thickness should be at the top in the center of the span. At the arch, the shell thickness is increased slightly for local stresses. The thickness increases toward the springing line of the arch and if not supported by an edge beam, the thickness here should be based on the thickness for a slab spanning the same distance. The edge beams act like the folded plate structures described in the first chapter.

DOME

A dome is a space structure covering a more or less square or circular area. The best known example is the dome of revolution, and it is one of the earliest of the shell structures. Excellent examples are still in existence that was built in Roman times. They are formed by a surface generated by a curve of any form revolving about a vertical line. This surface has double curvature and the resulting structure is much stiffer and stronger than a single curved surface, such as a cylindrical shell. The simple dome of revolution is a portion of a sphere. However, other curves are also satisfactory, such as the ellipse, the parabola, other conic sections, or random curves.

TYPES -

Domes - square in plan

Multiple domes

Translation domes

Folded plate domes

Multi facet dome


SQUARE IN PLAN

MULTIPLE DOMES

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SHELL ARCHES

Folded plates and cylindrical barrel shells are essentially beams. The same cross sectional shapes can be used for arches and a new set of forms, having different structural properties, is obtained.

Shell arches are somewhat in the same category as short shells in that the shell action is subservient to the arch action. All the thicknesses can be made quite small of an arch is used because the stresses will be principally compression. The curve of the arch has to be generally a funicular form, that is, it should fit the thrust line of the applied loads. Shells are not very efficient structures if the bending moments are high, as in the folded plate rigid frame.

There are types of shells that fit in several categories. The hyperbolic paraboloidal dome is really a shell arch.

FOLDED PLATE ARCHThis structure is suitable for quite long spans and forms for the concrete can be used many times because each unit can be made self-supporting.

All of the different section shapes of folded plates are possible with this type of structure. The Z shape can be used to provide north light.

As in the folded plate shapes, an edge plate is required for the outside member. Placing of concrete on the steep slope at the springing of the arches may be a problem unless blown-on concrete is used or the lower portion of the shell may be precast on the ground and lifted into place.

BARREL ARCH

This shape is similar to the folded plate shell arch except that cross sectional elements are curved instead of being made with plane surfaces. The surface is more difficult to form but the widths of the individual elements may be made greater than for the folded plate shape. Arches of very long span are possible because the bending moments in an arch are much less than in a beam of comparable span. Any number of different shapes may be used, such as the

corrugated shape or the north light Lazy S shape. Lighting may be obtained by using skylights. The shearing forces are not very large

in an arch so larger holes may be used than for a barrel shell.


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SHELL vs. FOLDED PLATE STRUCTURES

A shell is a three dimensional body with■ One of the shell dimensions is much smaller than the other two■ the curvature of the shell mid-surface in the current configuration is non-zero

A plate is a three dimensional body with■ One of the plate dimensions much smaller than the other two■ the curvature of the plate mid-surface in the reference configuration is zero

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shell structures