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Wind-moment Design ofUnbraced Composite Frames

Specialist Design Guides I

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SCI PUBLICATION 264

Wind-moment Design of

Unbraced Composite

Frames

J S HENSMAN BEng, MPhiIAGJWAY MEng

Published by:

The Steel Construction InstituteSilwood ParkAscotBerkshire SL5 7QN

Tel: 01344623345Fax: 01344622944

© 2000 The Steel Construction Institute

Apart from any fair dealing for the purposes of research or private study or criticism or review, aspermitted under the Copyright Designs and Patents Act, 1 988, this publication may not bereproduced, stored or transmitted, in any form or by any means, without the prior permission inwriting of the publishers, or in the case of reprographic reproduction only in accordance with theterms of the licences issued by the UK Copyright Licensing Agency, or in accordance with the termsof licences issued by the appropriate Reproduction Rights Organisation outside the UK.

Enquiries concerning reproduction outside the terms stated here should be sent to the publishers, TheSteel Construction Institute, at the address given on the title page.

Although care has been taken to ensure, to the best of our knowledge, that all data and informationcontained herein are accurate to the extent that they relate to either matters of fact or acceptedpractice or matters of opinion at the time of publication, The Steel Construction Institute, the authorsand the reviewers assume no responsibility for any errors in or misinterpretations of such data and/orinformation or any loss or damage arising from or related to their use.

Publications supplied to the Members of the Institute at a discount are not for resale by them.

Publication Number: SCI-P264

ISBN 1 85942 1148

British Library Cataloguing-in-Publication Data.A catalogue record for this book is available from the British Library.

FOREWORD

This publication has been prepared by Mr Jason Hensman of Caunton Engineering and MrAndrew Way of The Steel Construction Institute. The background analytical work leadingto the publication was carried out by Mr J Hensman whilst studying at the University ofNottingham. The assistance of Dr Graham H Couchman (The Steel Construction Institute)in developing the publication is acknowledged.

SCI publications related to the wind-moment method are:

Wind-moment design for unbraced frames (SCI P082, 1991, superseded by SCI P263)

Wind-moment design of low rise frames (SCI P263, 2000, replacement for SCI P082)

Joints in steel construction: Moment connections (SCI P207, 1995, SCI/BCSA)

Funding for the project was gratefully received from the Department of the Environment,Transport and the Regions (DETR) and Corns (formerly British Steel).

III

Page blankin original

CONTENTSPage No.

SUMMARY vii

1 INTRODUCTION 1

1 .1 Benefits of the wind-moment method 1

1 .2 Benefits of composite construction 1

1.3 Scope 2

2 PRINCIPLES OF WIND-MOMENT DESIGN 62.1 Design method 6

3 CONNECTIONS 103.1 Connection classification 103.2 Beam-to-column connections 103.3 Standard connections 123.4 Column bases 13

4 DESIGN FOR THE ULTIMATE LIMIT STATE 144.1 Global analysis 144.2 Design of beams 154.3 Design of columns 1 6

4.4 Design of connections 1 7

5 DESIGN FOR SERVICEABILITY LIMIT STATE 195.1 General 19

5.2 Sway prediction 19

6 REFERENCES 23

APPENDIX A: Portal method of analysis 27

APPENDIX B: Connection detailing 31

APPENDIX C: Capacity Tables 37

APPENDIX D: Worked Example 51

51

V

Page blankin original

SUMMARY

This publication presents procedures for the design of wind-moment compositeframes in accordance with BS 5950-1 and BS 59550-3. In this method of design,the frame is made statically determinate by treating the connections as pinnedunder vertical loads and fixed under horizontal loads (with certain assumed pointsof zero moment). The publication gives design procedures for frames (withcomposite beams, slabs and connections) that are braced in the minor axisdirection. The limitations of the method are explained. In particular, it shouldbe noted that the method is only recommended for low-rise frames up to fourstoreys high.

In addition to design procedures for the ultimate and serviceability limit states,fully worked design example is presented. The publication also reproduces theresistance tables for standard wind-moment composite connections taken fromSCI/BCSA publication Joints in steel construction: Composite connections. Theseconnections use steel reinforcement, flush end plates and grade 8.8 M20 or M24bolts, and achieve sufficient rotation capacity by ensuring that the momentresistance is not governed by local concrete crushing or bolt or weld failure.

Dimensionnement sous moments dus au vent de cadres composites noncontreventes

Resumé

Cette publication présente des procedures de dimensionnement de cadrescomposites sous moments dus au vent qui suivent les normes BS 5950-1 etBS 59550-3. Dans cette méthode de dimensionnement, le cadre est rendustatiquement déterminé en considérant les assemblages comme articulés sous lescharges verticales et encastrés sous les sollicitations horizontales (avec certainspoints oà on suppose les moments nuls). La publication donne des procedures dedimensionnement pour les cadres (avecpoutres, dalles et assemblages composites)contreventés seulement dans Ia direction de I 'axe faible d 'inertie. Les limites dela méthode sont expliquées. En particulier, on doit noter que la méthode estseulement recommandée pour les cadres ne presentant pas plus de quatre étages.

En plus des procedures de dimensionnement pour les états limites ultimes et deservice, des exemples complets de dimensionnement sont presentes. La publicationreproduit egalement les tables de résistance pour des assemblages compositesstandardisés repris de la publication SCI/BCSA "Joints in steel constructioncomposite connections ".

Ces assemblages utilisent des plaques d 'about ou non débordantes avec boulonsde type 8.8 M20 ou M24 et assurent une capacite de rotation suffisante enimposant que la résistance en flexion ne soit pas conditionnée par 1 'écrasementlocal du béton ou par une rupture d 'un boulon ou d 'une soudure.

VII

'WindMomentBerechniiiig" verschieblicher Rahmen aus Verbundbauteilen

Zusammenfassung

These Publikation prasentiert Vorgehensweisen für die Berechnung von Rahmenaus Verbundbauteilen unter Einwirkung von Momenten info/ge Windlasten("wind-moment composite frames ") nach BS 5950-1 und BS 5950-3. Bei dieserMethode wird das Tragwerk statisch bestimmt gemacht durch Annahme vongelenkigen Verbindungen unter vertikalen Lasten und biegesteifer Verbindungenunter horizontalen Lasten (mit gewissen angenommenen Momenten-Nulipunkien).Die Publikation zeigt Berechnungsweisen auf für Rahmen (mit Verbundtragern,-decken und Verbindungen) die bezuglich der schwachen Achse unverschieblichsind. Die Grenzen der Methode werden erläutert. Besonders solite beachtetwerden, daft die Methode nur für Rahmen geringer Höhe mit bis zu vierGeschossen empfohlen wird.

Zusätzlich zu den Berechnungsmethoden im Grenzzustand der Tragfahigkeit undGebrauchstauglichkeit werden Berechnungsbeispiele vorgestelit. DieVeraffentlichung reproduziert auch die Tabellen für Standard- Verbindungen imVerbundbau unter Einwirkung von Momenten info/ge Windlasten aus derSCI/BCSA-Publikation Verbindugen im Stahlbau: Verbindungen im Verbundbau.Diese Verbindungen berucksichtigen die Bewehrung, bundige Stirnplatten mitSchrauben M20 oder M24 der Güte 8.8 und weisen ausreichendeRot ationskapazität auf, ohne /okales Betonversagen, Schrauben- oderSchwezj3nahtversagen.

Dimensionamiento de porticos sin arriostramientos frente a momentos deviento

Resumen

Esta publicación presenta métodos para el dimensionamiento a carga de viento depOrticos mixtos de acuerdo con BS5950-1 y BS59550-3. En este método de ca/cubel portico se convierte en isostático considerando las uniones como articu/adasante cargas vertica/es y fijas para cargas horizontales (con ciertos puntos dondese supone momento nub). La obra da métodos para porticos (con vigas mixtas,p/acas y uniones) arriostradas en direcciOn del eje menor, explicOndose suslimitaciones. En particular debe hacerse notar que Ia aplicaciOn del método se/imita a edificios de menos de 4 alturas.

Ademds de métodos de proyecto para los estados /Imites de servicio y áltimo, sepresentan ejemplos desarrollados. También se reproducen tablas con resistenciasde uniones mixtas tipo, tomadas de Ia publicación. "Uniones en estructuras deacero. Uniones mixtas" de SCI/BCSA.

Estas uniones usan armaduras de acero, platabandas y tornillos de calidad 8.8M20 o M24 y consiguen una capacidad de rotación suficiente al garantizar quee/ momento resistente no estO controlado por aplastamiento local del hormigOn opor roturas de soldaduras o tornilbos

VIII

Progettazione alle azioni orizzontali di tetai non controventati composti

Sommario

Questa pubblicazione presenta gli approcci per la progettazione alle azioniorizzontali di telai composti secondo le normative BS5950-1 e BS5950-3. Inaccordo a questo metodo progettuale, ii sistema intelaiato viene consideratoisostatico, schematizzando i collegamenti come cerniere in presenza di carichiverticali e come nodi rigidi in presenza delle azioni orizzontali (con prefissate zonein cui I 'azione fiettente viene ipotizzata nulla). La pubblicazione propone leprocedure progettuali specifiche per i sistemi intelaiati (con travi composte, solettee collegamenti) che sono controventati nella direzione di minore rigidezza dellacolonna.

Sono descritte le limitazioni del metodo e, in particolare, viene precisato chequesto è applicabile soltanto ad edfici di altezza modesta, fino a un numeromassimo di quattro piani.

A corredo della trattazione progettuale proposta e riferita agli stan limite, sia diservizio sia ultimi, vengono presentati anche quattro esempi progettuali completi.La pubblicazione riporta anche le tabelle di resistenza per le piO tradizionalitipologie di collegamenti per sistemi composti, già proposte nella pubblicazioneSCI/B GSA 'I giunti in strutture metallliche:i collegamenti composti'. Questicollegamenti, che vengono realizzati mediante barre di armatura in acciaio, giuntifiangiati con piatti in spessore di trave o estesi oltre 1 'altezza di trave e bulloni didiametro 20mm o 24mm e classe di resistenza 8,8, consentono di ottenereun 'adeguata capacitO rotazionale garantendo che la resistenzafiessionale del nodonon sia condizionata dalla fessurazione locale del calcestruzzo o dalla crisi neibulloni o nelle saldature.

Vindmoment dimensionermg av ofOrstarkta sammansatta ramar

Samnianfattning

Denna publikation presenterar ett metod for dimensionering av vindmoment isammansatta ramar i enlighet med brittiska standarderna 5950-1 och 59550-3. Idenna metod är ramen Or gjord statiski bestämbar genom att be hand/a allaknutpunkter som fritt upplagda for vertikala laster och alla knutpunkter som fastinspOnda for horisontella laster. ('där vissa punkter antas ha noll moment). Ipublikationen finns dimensioneringsmetoder for ramar (med sammansatta balkar,plattor och knutpunkler,.) som är forankrade i den mindre axeins riktning.BegrOnsningarna med denna metod arfOrklarade. Det Or värt att notera att dennametod enbart rekommenderas for ramverk pa upp till 4 vdningar.

Som tillagg till dimensioneringsmetoden presenteras hell genomarbetade exempelfor att underlätta användbarheten. Publikationen redovisar även tabeller forstandard vindmoment for sammansatta knutpunkter tagna fran SGI/BGSAspublikation "Joints in steel construction: Gomposite connections ". Dessa

knutpunkter innehOller stalforstarkningar med glatta ellerforlangda andplOtar ochk/ass 8.8 M20 eller M24 bultar. Knutpunkterna erhOller tillrackligrotationskapacitet genom att det Or sakerstOllt att bOjmotstOndet inte begransas avlokala tiyckbrott, bultbrott el/er svetsbrott.

ix

1 INTRODUCTION

When a steel frame is unbraced, an established technique to provide resistanceagainst wind loading is to rely on the rotational stiffness of the beam-to-columnconnections; under vertical load the connections are assumed to be nominallypinned. This design philosophy has become known as the wind-moment methodor wind-connection method and is used extensively in the UK and North America.

The wind-moment method is described in the SCI publication Wind-moment designof low rise frames'1 for bare steel frames, and this publication is an extension ofthat guidance for composite frames.

The frames covered by this publication comprise composite steel and concretebeams, composite beam-to-column connections, and steel columns. Theprocedures given in this publication are consistent with the design rules given inBS 5950-1 [2] and BS 5950-3, Section 3.1 [31•

1.1 Benefits of the wind-moment methodOne of the main advantages of the wind-moment method from the designer's pointof view is its simplicity, as is explained in Reference 111]. The internal momentsand forces are not dependent on the relative stiffnesses of the frame membersbecause the frame is treated as statically determinate (see Section 2). The needfor an iterative analysis and design procedure, which usually makes the use ofsoftware virtually essential, is therefore avoided.

From a construction viewpoint, the major advantage of wind-moment frames is therelative simplicity of the steelwork when compared with fully rigid construction.Much of the work carried out by steelwork contractors is concerned with makingthe connections, and it has been estimated that the fabrication and workshophandling costs associated with the connections can be as high as 50% of the totalcost of the erected steelwork.

1.2 Benefits of composite constructionThe general benefits of composite construction, as given in the SCI publicationDesign of composite slabs and beams with steel decking141, are:• Reduction in weight of the steel beams by 30 to 50% when compared with

non-composite construction, leading to a significant reduction in frame cost.• Increased stiffness of the floor construction giving better serviceability

performance.• Longer spans for a given beam depth or, alternatively, shallower construction

for the same span.• Good load resistance and robustness.• Diaphragm action through the floor slab, eliminating plan bracing and

providing direct load transfer to vertical bracing or core walls.• Rapid construction of both the steel framework and concrete slabs is possible

by using the decking as both a working platform and permanent formwork.

1

The procedures given in this guide enable designers to combine the benefits of thewind-moment method and composite construction.

1.3 ScopeThe recommendations given in this design guide have been formulated usingknowledge gained from an extensive background study151. The limits ofapplication have, where appropriate, been based on the existing wind-momentmethod limits defined in Reference 1 and Wind-moment design of unbracedframes161. It should also be recognised that the scope is dependent on the rangesconsidered in the background study, and hence the method has only been validatedwithin the given limits.

1.3.1 Frame proportionsFor composite wind-moment design, the geometry of the frames should be withinthe limits defined in Table 1.1. Frames may have more than four bays, but anyadditional bays (over and above four) should not be considered to participate inresisting the applied wind load. When adding non-active bays, the designer shouldensure that the notional horizontal loads do not become critical.

Table 1 .1 Frame geometry limits

Minimum Maximum

Number of storeys 2 4

Number of bays 2 4

Bay width (m) 6.0 12.0

Bottom storey height (m) 4.5 6.0

Storey height elsewhere (m) 3.5 5.0

Bay width: storey height (bottom storey) 1 .33 2.67

Bay width: storey height (above bottom storey) 1 .33 3.43

Greatest bay width: Smallest bay width 1 1 .5

Frames designed using this design guide must also display the following features:• The frame must consist primarily of horizontal beams and vertical columns

(Figure 1.1).• The width of each bay must be constant over the height of the frame, except

that the columns may terminate at the top floor to allow an open-plan topstorey (Figure 1.2).

• Frames must be effectively braced against out-of-plane sway at each floorlevel and at the roof level (i.e. major axis sway frames only).

• Beam grids must be consistent with one of the layouts shown in Figure 1.3.

• Composite slabs should span in directions as shown in Figure 1.3.

• Sections should be orientated in such a way that loads in the plane of theframe tend to cause bending about the major axis (i.e. major axis swayframes only).

2

Figure 1.1 Uneven bay widths Figure 1.2 Open plan top storey

H H. - Floor span-

—.

H—.-

-H

-S

H H(a)

Figure 1.3 Grid of primary and secondary beams with deck spanning(a) parallel and (b) perpendicular to the beam

1.3.2 Individual ComponentsFor the design procedure to be applicable, the individual components need tocomply with the following requirements:• Frames must have composite beams, in-situ slabs (based on steel decking; see

Figure 1.4), and connections. Slabs formed from precast concrete units areexcluded because suitable composite connection details for use with this typeof construction have not yet been developed, therefore this type ofconstruction was not considered in the background studies.

• Internal connections must be composite flush end plate (non-composite detailsmay not possess sufficient stiffness to ensure frame stability).

• External connections must be either composite flush end plate, bare steelflush end plate or bare steel extended end plate.

• All sections within the frame must be the same steel grade (S275 or S355).• Universal beams must be used as the steel component of composite beams.

• Universal columns must be used for the columns.

• Universal columns must be at least section size 203 x 203 X 60.

3

(b)

1.3.3 LoadingLoading should be within the limits defined in Table 1.2.

The wind loads may be calculated by using either CP3 Chapt.V71 or BS 63992[8].The wind loads are taken as concentrated point loads applied at each floor level.

Table 1 .2 Frame loading limits

Minimum Maximum

Dead load on floors (kN/m2) 3.50 5.00

Imposed load on floors (kN/m2) 4.00 7.50

Dead load on roof (kN/m2) 3.75 3.75

Imposed load on roof (kN/m2) 1 .50 1 .50

Wind loads (kN) 10 40

1.3.4 Choice of wind-moment methodThe designer can rapidly determine whether the wind-moment method will beappropriate for a given frame by using the flowchart provided in Figure 1.5. Ifthe frame is likely to be controlled by SLS sway deflections an alternative designmethod should be used.

4

Figure 1.4 Composite beam sections

NOTE: This flow chart is not a designprocedure. It should be used only asa 'first-check, to determine if thewind-moment method outlined in thisdocument is a suitable method forthe frame in question

Define frame geometry

Define load types andmagnitude(1) Gravity(2) Wind

Design composite beamsas simply supported with

capacity of 0.9 Mp

PUsing the wind-momentmethod to design this

frame for ULS is likely toresult in unsatisfactory

inter-storey swaybehaviour.

Design frame as rigid atthe 1st storey level, orinclude vertical bracing.

The bottom storey SLSsway is likely to control

the frame design.Increasing the column

section sizes mayresolve this problem; if

not then it may beappropriate to

use an altemativemethod.

Predict the SLS swayusing the method in

Section 5

Design the frame usingthe wind-moment

method, as detailed inthis document.

1 Increase

sizes

4Yes

Nthetota1frame

NoI,

Using the wind-momentmethod to design this

frame for ULS is likely toresult in unsatisfactorySLS sway behaviour.

Figure 1.5 Flow chart to determine the suitability of the wind-momentmethod for a given frame

5

Estimate required columnsections

The frame design islikely to be controlled

by SLS sway.However, a suitable

frame design may stillbe achieved using thewind-moment method.Consider increasingthe member sizes.

Yes

Design the frame asrigid, or include vertical

bracing

2 PRINCIPLES OF WIND-MOMENT DESIGN

The distinguishing features of the wind-moment method are the basic assumptionsthat are made at the design stage. These assumptions are that:

• under vertical loads the connections are assumed to act as pins (Figure2.1(a)),

• under wind loads the connections are assumed to behave as rigid joints, withpoints of contraflexure occurring at the mid-height of the columns and at themid-span of the beams (Figure 2.1(b)).

flI4U________________

7(a) (b)

Figure 2.1 Frame assumptions for the wind-moment method

2.1 Design methodThe first step in the design sequence is to design the composite beams for theultimate limit state (ULS) fully factored vertical loads, assuming a nominal endfixity moment of 10%. The frame is then analysed under wind loads, with theassumption that the beam-to-column connections behave in a rigid manner. Theinternal forces and moments are then combined using the principle ofsuperposition, and adopting appropriate load factors for each combination. Designfor the ULS is completed by, when necessary, amending the initial section sizesand connection details so that they can withstand the combined effects(Figure 2.2).

Second order, or P-i, effects are accounted for by designing the columns usingeffective lengths that are greater than the true column lengths. The need forcomplicated second order calculations is therefore avoided.

The serviceability sway displacements are calculated assuming the beam-to-columnconnections are rigid. To account for the true flexibility of the connections, asway amplification factor is used.

6

r

33 + 3333333333+

7

(a)

Figure 2.2 Internalmoments and forces according to the wind-momentmethod

2.1.1 BeamsBeams designed using the wind-moment method tend to be overdesigned becausefull account of the true moment resisting nature of the connections is not takenwhen determining the applied mid-span sagging moments due to vertical loading.Only a nominal 10% reduction in mid-span sagging moment is considered. Inreality, substantial hogging moments (up to 40% of the beam sagging momentcapacity) may occur at the beam ends, and the subsequent reduction in the saggingmoment is not fully exploited in the beam design.

2.1.2 ColumnsColumns designed using the wind-moment method tend to be underdesigned dueto the adverse effect of the hogging moments developed at the beam ends undervertical loading. This effect is not fully accounted for in the design procedure asonly a nominal 10% hogging moment is considered. These hogging moments canbe as high as 40% of the composite beam sagging moment capacity, and areparticularly significant for external columns or internal columns that are subjectto unbalanced loading from adjacent beam spans.

2.1.3 Connections

Unlike bare steel wind-moment connections, composite connections will tend tohave excess moment resistance. This is because the area of reinforcement neededto provide the connection with sufficient rotation capacity will often exceed thearea needed to provide sufficient moment resistance. The addition of a reinforcedconcrete slab to a bare steel connection significantly increases the moment capacityof the connection, at the expense of some rotation capacity. However, the mostimportant change to the bare steel connection behaviour, with regard to thewind-moment method, is the increase in connection stiffness; it is thischaracteristic that provides stability to the frame. The addition of reinforcementsubstantially increases the bare steel connection stiffness.

7

I(b)

2.1.4 Sway displacementThe sway displacements will be larger than those predicted assuming rigidbeam-to-column connections. The flexibility of the connections is taken intoaccount using sway amplification factors, as discussed later.

2.1.5 Frame stabilityThe wind-moment method is, in part, a plastic design method91. Accordingly, thefollowing conditions must be satisfied at collapse:

• a mechanism of plastic hinges must have formed

• the internal moments and forces must be in equilibrium with the externalloads

• nowhere may the internal moment exceed the plastic moment of resistance.

If the last two conditions are satisfied, the lower-bound theorem states that theapplied loads are either less than or equal to the loads that will cause the frame tocollapse. These conditions are met by a design using the wind-moment method,which will therefore result in a safe design, provided that the following twocriteria are also satisfied:

• the effect of deflections on equilibrium is negligible

• premature collapse does not occur as a result of any form of buckling.

These aspects of the design are satisfied implicitly when plastic or compactsections and ductile connections are used, and the design method given in thispublication is adopted (for example with regard to the effective lengths ofcolumns).

Adhering to the recommendations presented in this document will result in aframing system that is capable of resisting the applied loads when the concretefloor slabs are in place, and the concrete has reached the appropriatestrength. When the frame is in the bare steel state, the beams and connectionswill not provide the same level of stability to the frame (because neither the beamnor the connection stiffness is achieved until the slab is structurally effective).However, studies have shown that wind loads on unclad framed structures can besignificant during the construction stage of a project'°1. It is important, therefore,that the designer is aware of this, and takes adequate measures to ensure that thestructure is stable at all times during the construction phase, as well as when thebuilding is complete. It may therefore be necessary to provide temporary bracingduring erection to ensure frame stability.

2.1.6 FoundationsOne of the principal frame requirements is the provision of adequate lateralstiffness, so that second order effects remain within acceptable limits. The framemust also conform with acceptable sway displacement limitations under workingload conditions. Studies have shown that the degree of rotational restraintprovided at the column bases plays a significant part in the overall frame responseunder lateral loads. Indeed, background studies have shown that the overall swayresponse varies substantially depending on whether fully encastré bases ornominally rigid bases (based on approximations of base stiffness111'211131) areassumed in the frame analysis. Nominally-pinned bases do not generally provide

8

adequate stability and cannot therefore be used.

Section 3.4 outlines the minimum requirements for base plate details that can bepresumed acceptable for frames designed using the wind-moment method.

9

3 CONNECTIONS

3.1 Connection classificationConnections are classified according to their moment-rotation (M-5)characteristics, with particular regard to strength (moment resistance), stiffness(rigidity), and ductility (rotation capacity).

According to publication Composite steel-concrete joints in braced frames forbuildings1141, the transition from rigid to semi-rigid connection behaviour for anunbraced frame should be taken as 25E1/L; where 1 is the second moment of areaof the uncracked composite beam. A connection possessing a greater stiffnessthan this may therefore be classified as 'rigid', even though it does not exhibitinfinite stiffness (see Figure 3.1) and will therefore undergo some rotation asmoment is applied.

Connections are described as being full strength, or partial strength, with respectto the adjacent beam. This means that in a composite frame the strength of theconnections is defined relative to the negative (hogging) moment resistance of thecomposite beam.

Curve 1 in Figure 3.1 represents a typical rigid, full strength connection. Curve 2represents a rigid partial strength connection, and Curve 3 represents a semi-rigidpartial strength connection. Composite connections are typically rigid and partialstrength (Curve 2) in their final, composite state.

3.2 Beam-to-column connectionsThe scope of this publication covers only major axis sway frames. Thus, allconnections discussed here are to the column flange face.

Only flush end-plate steelwork details should be used as the basis for compositeconnections. Various forms of stiffening may be necessary to increase theperformance of the connections, although it should be noted that increasing thecolumn section size may be a more economical way of improving resistance thanadding stiffeners. The need to balance large tensile forces in the reinforcement,across the column, means that it is not unusual to require column webcompression stiffeners. Transverse beams that frame into the column web may

10

Figure 3.1 Moment-rotation characteristic

provide beneficial stiffening to the column web'51.

Design of composite connections is covered by the SCI/BCSA publication Jointsin steel construction: Composite connections116. Included in that publication aredesign procedures, standard connection details and standard connection capacitytables. Standard connections are described briefly below and Appendix C of thispublications presents tables from Reference 16.

3.2.1 Internal connections

Figure 3.2 shows a typical internal connection detail that behaves in a way that iscompatible with the wind-moment method of frame design. As explained inReference 16, the end-plate should be of S275 steel (design grade 43), and notthicker than 20 mm. All bolts should be Grade 8.8 or similar, with one or moretension rows. Standard connection details for this type of connection are given inAppendix C.

3.2.2 External connectionsThe frame design is dependent on the type of external connections that areadopted. Figure 3.3 shows the two types of external connection detail that can beused. The detail shown in Figure 3.3(a) includes a small cantilever concrete slabbeyond the external column flange. This detailing enables the longitudinalreinforcement to be properly anchored around the column, so that an effectivecomposite connection can be achieved.

The detail shown in Figure 3.3(b) does not allow sufficient anchorage of thelongitudinal reinforcement, and connections of this type should be designed as baresteel connections in accordance with the SCIIBCSA publication Joints in steelconstruction: Moment connections'71. Any contribution to moment resistancefrom the reinforcement is ignored.

Reference 16 recommends the use of non-composite edge connections in bracedframes for practical reasons, given that connection rotation stiffness is not requiredfor frame stability. However, for unbraced frames, connection rotation stiffnessis required, and hence composite external connections are beneficial.

Regardless of the slab detailing, the steelwork should comply with therecommended bolt and endplate arrangements given in Reference 17. Thiscondition is satisfied by the standard composite connections given in Appendix C.

11

Universal beam

IN Universal column

Figure 3.2 Typical internal connection

Longitudinal

Concrete slabs

Figure 3.3 External connection details (a) Composite (b) EffectivelyNon-composite

The influence of the external connection detailing on the frame sway displacementsis accounted for using the 'sway factors' given in Table 5.1 (Section 5); details asshown in Figure 3.3(b) result in greater sway than when full composite action canbe achieved.

When there is insufficient anchorage for the longitudinal reinforcement theexternal bay may only be considered as actively resisting lateral loading if a baresteel connection of sufficient strength can be adopted.

Connections similar to that shown in Figure 3.3(a) should use end-plates that areno thicker than 20 mm, and bolt locations should be in accordance with thestandard layouts presented in Reference 17 and reproduced in Appendix C.

3.2.3 Reinforcement detailing at the connectionsThe nature of unbraced frames can result in substantial unbalanced moments beinggenerated across internal columns. These moments must be resisted by tension inthe longitudinal reinforcement in the slab (at the connection), with the unbalancedtensile forces being resisted by bearing of the concrete slab against the column.The amount of longitudinal reinforcement that can be adopted in the connectionsmust therefore be limited to prevent local crushing of the concrete against thecolumn flange. Transverse reinforcement is also required to prevent splitting ofthe slab on the low moment side of the connection41.

Appendix B provides specific details about reinforcement requirements andpractical detailing rules. Reinforcing mesh is not considered to act structurally aspart of the composite connections, because its limited ductility may lead to failureat relatively low values of connection rotation.

3.3 Standard connectionsMoment and shear capacities, as well as detailing guidance, are given for a rangeof standard composite wind-moment connections in Appendix C. When standardconnections are used the designer can be sure that the connection will have thelevel of rotation capacity and stiffness required by connections for use inwind-moment composite frames designed in accordance with this guide.

12

Longitudinal rebar(no anchorage)

Structuralmetal decking

Structuralmetal decking

beam

(a) (b)

The standard connections have the following attributes:

• 12 mm thick flush end plates when M20 bolts are used,

• 15 mm thick flush end plates when M24 bolts are used,• end plates fabricated from S275 steel,

• full strength flange welds, with a minimum visible fillet of 10 mm,• continuous 8 mm fillet web welds,

• 1St shear connector at least 100 mm from the column face,

• longitudinal reinforcing bars situated approximately 20 mm above the decking(ie as near to the top of the decking as possible, whilst maintaining sufficientconcrete cover).

3.4 Column basesColumns should be rigidly connected to the foundations in accordance with usualpractice for this type of construction. A minimum of four Grade 8.8 bolts shouldbe used, with a minimum base-plate thickness of 25 mm. The centre line of thebolt rows should be at least 50 mm outside of the column flange (measured fromthe outside face of the column flange), as shown in Figure 3.4. Base plateconnections should be checked using the usual design procedures for axial loadand moment. More detailed guidance on column bases is given in Reference 17.

50mm

0

Figure 3.4

13

Plan Elevation

J

Universal column

I I Base plate25mm

GroutJ. packing

-I--)0

Concrete foundation

Typical column base-plate connection

4 DESIGN FOR THE ULTIMATE LIMITSTATE

4.1 Global analysis4.1.1 Load combinationsThe following load combinations should be considered in the design:

1.4 x Dead load + 1.6 x Imposed load + 1.0 x Notional horizontal forces1.2 x Dead load + 1.2 x Imposed load + 1.2 x Wind load1.4 x Dead load + 1.4 X Wind load

The notional horizontal forces should be taken as 0.5% of the factored dead plusimposed loads (BS 5950-1:1990 Clauses 5.6.3, 5.1.2.3)12]

Pattern loading should be considered, in addition to full vertical load applied toall beams.

4.1.2 Internal moments and forces due to vertical loadsAllowance should be made for the end restraint provided by the compositeconnections at the beam-ends. An end restraint moment equal to 10% of the freebending moment (i.e. the maximum sagging moment for the beam, assuming it tobe simply supported) should be considered at the connections (see Figure 4.1).

0.1 Mmax restraint

MmLFigure 4.1 Assumed end restraint moments

As a result of the vertical loading, each column should be designed to resist thealgebraic sum of the restraint moments from opposing beams, plus the momentsdue to an assumed eccentricity of the beam reactions. The beam reactions areassumed to be applied 100 mm from the column faces (BS 5950-1:1990 Clause4.7.6). The net moment applied to a column at any given level should be dividedbetween the column lengths above and below that level in accordance withBS 5950-1:1990 Clause 4.7.7. It is assumed that this moment has no effect atother levels.

4.1.3 Internal moments and forces due to horizontal loads

Analysis should be by the 'portal method', and based on the followingassumptions:• horizontal loads are applied at floor levels

• there is a point of contraflexure at the mid-height of each column• there is a point of contraflexure at the mid-span of each beam

14

• each bay acts as a simple portal, and the total horizontal load applied to theframe is divided between the bays in proportion to their spans.

Algebraic formulae based on these assumptions are given in Appendix A.

4.2 Design of beams4.2.1 Construction stageThe bare steel beam sections must be capable of resisting the construction stageloading (BS 5950-3: Section 3.1 Clause The construction loads shouldbe treated as imposed loads, using appropriate load factors from BS 59501[21.

The lateral restraint offered to the steel beams, and therefore their momentcapacity will depend on the direction in which the steel decking spans. When theribs of the decking run parallel to the beam (Figure 1.3(a)) no lateral restraint isprovided, and the effective length of the beam should be taken as equal to thedistance between any secondary (transverse) beams. Conversely, decking spanningperpendicularly to the beam (Figure 1.3(b)) does provide lateral restraint when itis appropriately fixed to the beam.

4.2.2 Moment resistance (sagging)

Composite beams should be Class 1, plastic, or Class 2, compact, and within thescope detailed in Section 1.2.2. The plastic moment resistance of the compositebeam can be determined from the formulae presented in BS 5950-3: Section 3.1:Appendix B131 or in Reference 4.

Beams should be designed as simply supported, with the sagging momentresistance limited to 90% of the plastic moment resistance.

4.2.3 Moment resistance (hogging)The hogging resistance of the composite beam may be determined using formulaepresented in BS 5950-3:Section 3.1 Appendix B.2.4. Only the bare steel sectionand the longitudinal reinforcing bars (not mesh) are considered when determiningthe hogging resistance of the composite beam; cracked concrete is assumed to havezero strength.

Detailing must be such that the hogging resistance of the composite beam isgreater than the moment resistance of the adjacent (partial strength) connection.

4.2.4 Shear connectionThe degree of shear connection provided should be consistent with the limits givenin BS 5950-3:Section 3.1 Clause 5.4.5.5 and Clause 5.5.2. Full shear connectionshould be provided in hogging moment regions.

When determining the required number of shear studs (which are 25% weaker inhogging regions than in sagging), the hogging length at each end of the beamshould be taken as span/5.

15

4.3 Design of columns4.3.1 Effective lengthsWhen determining the compression resistance for a major axis sway frame wherethe minor axis is braced, the values of and P, should be based on thefollowing effective lengths:

• For in-plane behaviour (bending about the major axis):

LEX = 1.5L

• For out-of-plane behaviour (bending about the minor axis):

LEY = 1.OL

Values of P and P, are tabulated in the SCI publication Steelwork design guideto BS 5950: Part 1: 1990- Volume 1 Section properties and member capacities' 8}

4.3.2 Equivalent slenderness for buckling resistancemoment

When determining the buckling resistance moment (BS 5950-1:1990 Clauses4.3.7.3 and 4.3.7.4), the slenderness kT should be taken as 2LT = 0.5 (L/r).Values of MbS are tabulated in Reference 18.

4.3.3 Design momentsFor each load combination (Section 4.1.1) the colunm moments should be takenas the sum of:

• the net (i.e. out of balance) moments due to the assumed eccentricity of thebeam reactions arising from vertical load (BS 5950-1: 1990 Clause 4.7.6),

• the net moments due to the assumed '10%' restraint moments at the beamends arising from vertical loads (BS 5950-1:1990 Clause 2.1.2.4),

• the moments due to horizontal loads (i.e. wind or notional forces).

Because the horizontal loads may reverse, the design moments should bedetermined by addition of the numerical magnitudes of each of the componentmoments.

4.3.4 Class of sectionSections should be Class 1 (plastic) or Class 2 (compact), so that they can attaintheir plastic moment resistance M.

4.3.5 Overall buckling checkThe following relationship (BS 5950-1:1990, Clause 4.8.3.3) should be satisfied:

F M M— -1- —- + � 1.0 (1)

MbS PY Zy

16

where:

F is the applied compression load in the member

P is the compression resistance (taken as the lesser of P, and calculated forLEY and LEX respectively)

M is the applied moment about the major axis

MbS is the buckling resistance moment for simple design

M is the applied moment about the minor axis

is the design strength of the steel

Z, is the elastic section modulus about the minor axis.

4.4 Design of connections4.4.1 Applied moments and forcesFor each load combination (refer to Section 4.1.1), the moments at theconnections should be taken as the sum of:• the '10%' restraint moments due to partial fixity at the beam ends under

vertical load (refer to Section 4.1.2)• the moments due to horizontal loads (i.e. wind or notional forces).

The vertical shear forces at the connections should be taken as the sum of:• the beam end shears due to vertical load• the shear forces in the beams due to horizontal loading on the frame.

The connections should be designed for both maximum (hogging) and minimum(potentially sagging) moments because the direction of the horizontal loads mayreverse. However, if sagging does occur it is acceptable for the connections tobe understrength in sagging, provided that this understrength is compensated bya corresponding overstrength in hogging. The design criterion is not then that thehogging strength of the connection exceeds the maximum applied hoggingmoment, and that the sagging strength exceeds the maximum applied saggingmoment, but rather that the sum of the hogging and sagging resistances exceedsthe absolute sum of the applied hogging and sagging moments. The resistance ofa composite connection in sagging may be conservatively taken as that of the baresteel detail (with the lower bolts in tension). For a more typical case wheresagging does not occur (there is simply a reduction in hogging as the winddirection reverses) the connection should be designed for the larger hoggingmoment, and nominal resistance to sagging will suffice.

4.4.2 Design procedureAs mentioned in Section 3.3, it is strongly recommended that standard connectionsare used. The connection design procedure then requires only a simplecomparison of the maximum absolute sum of the applied hogging and saggingmoments with the tabulated connection strengths in order to identify a suitablestandard detail. Resistances and detailing guidance for standard connection detailsare tabulated in Appendix C. Additional guidance on reinforcement detailing is

17

given in Appendix B.

Reference should be made to Joints in steel construction - Compositeconnections1161 for full design procedures and principles relating to compositeconnections. Although the connection design procedures given in that publicationare for simplicity described as being applicable to braced frames only, they areappropriate for use in wind-moment frames which comply with the scope specifiedin Section 1.2 of this publication. This 'relaxation' is possible because for suchframes the connections will not in practice be subject to significant saggingmoments.

In addition to possessing adequate strength, the connections must possess sufficientrotation capacity to behave as a plastic hinge. This can be achieved by appropriatedetailing. The standard connections presented in this guide satisfy this criterionfor both propped and unpropped construction.

18

5 DESIGN FOR SERVICEABILITY LIMITSTATE

5.1 General

Sway behaviour, and in particular the prediction of sway displacements, is verycomplex. The magnitude of sway displacements is influenced by a number offactors: relative member stiffnesses, connection characteristics, the ratio ofhorizontal to vertical loading, and colunm base behaviour. All these factors havea significant influence on the sway response of an unbraced frame.

It has been found that composite frames designed using the ULS procedures givenin this guide will, in most practical cases, conform to the common sway limit ofh/300. Indeed, for frames with two or more 9 m or 12 m span bays, the swaydisplacement is likely to be well below this limit even under high wind loads.However, for some frames that are subjected to relatively severe wind loading, thesway displacements within the first storey may be critical. This is particularlytrue for 'slender' two bay frames. Conversely, numerical studies5 havedemonstrated that if the first storey sway of a frame is less than about h/200, thenthe frame will generally prove adequate under ultimate limit state conditions.

It should be remembered that the common sway limit of h/30021191 is not a strictperformance criterion; rather the limit is intended to be compared with calculateddeflections for unclad frames, recognising that the beneficial influence of claddingand other components is not accounted for in such calculations. Although thelimit of h/300 appears to have proved successful in preventing damage to claddingand glazing systems in existing buildings by preventing excessive displacements,its justification rests solely on this 'track record'. Alternative limits may beacceptable in some cases.

It has been found that accounting for the true flexibility of the beam-to-columnconnections in a composite wind-moment frame increases the sway displacementsby about 30% compared with a similar frame analysed assuming fully rigidconnections51. This increase is allowed for in wind-moment design by using thesway amplification factors that are presented below.

5.2 Sway prediction5.2.1 Initial analysisA frame which has been designed for the ultimate limit state should, as a firststep, be analysed as an elastic rigidly-jointed frame to determine the swaydisplacements. Unfortunately this procedure is complicated by the fact that, unlikebare steel beams, the cross-sectional properties of composite beams are notconstant along their length. Composite beam properties vary significantlydepending on the type and magnitude of loading applied, and the strength andstiffness of the restraining end connections because these factors effect the lengthof beam in hogging. It is not sufficiently accurate to consider the composite beamto have a constant flexural stiffness (equal to that of the uncracked cross-section)along its entire length when attempting to calculate sway displacements of acomposite frame. However, using an equivalent beam model (as described in

19

5.2.2 Equivalent beam model

= Bending moment diagram for vertical load only= Bending moment diagram for vertical load and wind load

Figure 5.1 Schematic bending moment diagram for a beam in a swayframe

5.2.3 Graphical method of sway predictionStudies5' have shown that sway predictions, based on the graphical proceduredetailed in a paper by Wood and Roberts20, and modified using the swayamplification factors given in Table 5.1, are in excellent agreement with theresults obtained using more sophisticated analysis. The sway amplification factorsare used to allow for the 'wind-moment connections' being more flexible than'rigid' details.

Table 5.1 Sway amplification factors

External connection type Frame sway amplification factor

Composite (Figure 3.3(a)) 1 .4

Non-composite (Figure 3.3(b)) 1 .6

20

Section 5.2.2) with a simple graphical method of sway prediction (as described inSection 5.2.3) excellent results can be obtained.

An expression for equivalent beam stiffness has been developed51 based on theexpected moment distribution along the length of the beam (see Figure 5.1). Theequivalent beam stiffness is given as:

7.5 ,'eq

=2

g (2)9 I + 2 'g

where:

is the second moment of area of the uncracked 'sagging' composite beam

I is the second moment of area of the cracked 'hogging' composite beam.

Procedures for calculating 'g and I are given in BS 5950-3:Section 3. 1:1990Clause B.3.

Leewardconnection

Windwa>\connection

5.2.4 Sway limitsIn addition to checking that the overall frame sway deflection is less than h/300,it is important to check that the sway within each storey is less than h/300 (whereh is the storey height)21. The bottom storey sway is likely to be the most critical;its magnitude can be estimated from the total frame sway using the values givenin Table 5.2.

Table 5.2 Bottom storey sway percentages

Total number of storeys Bottom storey sway as apercentage of total frame sway

2 storeys 80%

3 storeys 65%

4 storeys 55%

5.2.5 Redesign for stiffnessIf sway deflections are unacceptable, the frame may be modified to increase itsstiffness as an alternative to redesigning as a braced frame. Member sizes couldbe increased, remembering that increases in the beam depth, or the column flangethickness, will also increase the connection stiffness (although they may notnecessarily increase its moment resistance).

21

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6 REFERENCES

1. SALTER, P.R., COUCHMAN, G.H. and ANDERSON, D.Wind-moment design of low rise frames (P263)The Steel Construction Institute, 2000

2. BRITISH STANDARDS INSTITUTIONBS 5950: Structural use of steelwork in buildingBS 5950-1:1990: Code of practice for design in simple and continuousconstruction

3. BRITISH STANDARDS INSTITUTIONBS 5950: Structural use of steelwork in buildingBS 5950-3: Design in composite constructionSection 3.1:1990: Code of practice for design of simple and continuouscomposite beams

4. LAWSON, R.M.Design of composite slabs and beams with steel decking (P055)The Steel Construction Institute, 1989

5. HENSMAN,J.S.Investigation of the wind-moment method for unbraced compositeframes.M.Phil thesis, University of Nottingham, 1998

6. ANDERSON, D., READING, S.J. and KAVIANPOUR, K.Wind-moment design for unbraced frames (P082)The Steel Construction Institute, 1991

7. BRITISH STANDARDS INSTITUTIONCP 3: Basic data for the design of buildingsChapter V: LoadingPart 2: Wind loadBSI, 1972

8. BRITISH STANDARDS INSTITUTIONBS 6399: Loading for buildingsBS 6399-2:1997: Code of practice for wind loads

9. NEAL, B.G.Plastic Methods of Structural AnalysisChapman & Hall Ltd and Science Paperbacks, 1970

10. WILLFORD, M.R. and ALSOP, A.C.Design guide for wind loads on unclad building structures duringconstructionBuilding Research Establishment, 1990

23

11. GUISSE, S., VANDEGANS, D. and JASPART, J-P.Application of the component method to column bases -experimentation and development of a mechanical model forcharacterization. Report No. MT 195Research Centre of the Belgian Metalworking Industry, SteelConstruction Dept., Dec. 1996

12. CIMsteel: EUREKA PROJECT 130Modelling of steel structures for computer analysis (P 148)The Steel Construction Institute, 1995

13. WALD, F., BAUDUFFE, N., SOKOL, Z. and MUZEAU J-P.Pre-design model of the column-base stiffnessIABSE Colloquium, Istanbul, 1996

14. COST, C.!.Composite steel-concrete joints in braced frames for buildingsed. Anderson, D.European Commission, Brussels, 1996

15. LI, T.Q., NETHERCOT, D.A. and CHOO, B.S.Behaviour of flush end-plate composite connections with unbalancedmoment and variable shear/moment ratios - I Experimental behaviourJournal of Constructional Steel Research, pp 125-164, Vol. 38 (2),1996

16. THE STEEL CONSTRUCTION INSTITUTE and THE BRITISHCONSTRUCTIONAL STEELWORK ASSOCIATIONJoints in Steel Construction: Composite Connections (P213)SCI/BCSA, 1998

17. THE STEEL CONSTRUCTION INSTITUTE and THE BRITISHCONSTRUCTIONAL STEELWORK ASSOCIATIONJoints in Steel Construction: Moment Connections (P207)SCI/BCSA, 1995

18. THE STEEL CONSTRUCTION INSTITUTESteelwork Design Guide to BS 5950: Part 1: 1990Volume 1: Section properties and member capacities (P202)SC!, 1997

19. BRITISH STANDARDS INSTITUTIONEurocode 3: Design of Steel StructuresDD ENV 1993-1-1:1992: General rules and rules for buildings(including UK NAD)

20. WOOD, R.H. and ROBERTS, E.H.A graphical method of predicting sidesway in multistorey buildingsProceedings of the Institution of Civil Engineers, Part 2, Vol. 59,pp 353-272, June 1975

21. BRITISH STANDARDS INSTITUTIONBS 8110: Structural use of concreteBS 8110-1:1985: Code of practice for design and construction

24

22. BRITISH STANDARDS INSTITUTIONBS 4449:1988: Specification for carbon steel bars for the reinforcementof concrete

23. BRITISH STANDARDS INSTITUTEDD ENV 10080:1996: Steel for the reinforcement of concrete weldableribbed reinforcing steel B500. Technical delivery conditions for bars,coils and welded fabric (including UK NAD)

24. BRITISH STANDARDS INSTITUTIONBS 4466:1989: Specification for scheduling, dimensioning, bending andcutting of reinforcement for concrete

25. LI, T.Q., NETHERCOT, D.A. and CHOO, B.S.Behaviour of flush end plate composite connections with unbalancedmoment and variable shear/moment ratios - II prediction of momentcapacity.Journal of Constructional Steel Research, Vol 38 (2), 1996

26. LEON, R.T.Composite connectionsProgress in Structural Engineering and Materials Vol 1(2): pp159-1691998

25

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APPENDIX A: Portal method of analysis

The following guidance is reproduced from the publication Wind-moment designof low rise frames111.

A. '1 IntroductionThe forces and moments in a multi-storey, multi-bay wind-moment frame can bedetermined by simple manual calculation using the so-called portal method. Thewind and notional horizontal forces are shared between the bays according to therelative bay widths, and the forces in the beams and columns are calculated forthis distribution of loading. A detailed explanation is given below for part of amulti-storey two-bay frame.

A.2 Distribution of horizontal loadEach bay is assumed to act as a single portal and the total horizontal load isdivided between the bays in proportion to their spans. For a two bay frame, theloads in the two separate bays (as shown in Figure A. ib) are given by:

H11

H12

= L1 W1 /(L1 + L2); H21 =

= L1 W2 /(L1 + L2); 1122 =

L2 W1 I(L1 + L2)

L2 W2 /(L1 + L2)(A.1)

Wi

w2

w3 Li

(a) Two bay frame (b) Two single portals

Figure A. 1 Distribution of horizontal load

A.3 Calculation of internal forces in columnsThe forces acting on a part of one bay and the pin locations assumed in wind-moment design are shown in Figure A.2a.

The forces acting on the portion of the bay above the points of contraflexure at Aand D are shown in Figure A.2b. The horizontal force H1 is assumed to bedivided equally between the two columns. Thus

hj

H21.

I-i

112 j

Si = H/2 (A.2)

27

The vertical forces F1 can be found by taking moments about the point ofcontraflexure at either A or D:

F1L = H1h1/2

which gives:

F1 = H1 h1 / (2 L) (A. 3)

Hj

D h1(a) H2 1B E

4 h2H3

L

Hi —(b)

J

S1.4—ÔA S1.4—ÔD

F1 tFi

F.S1—- A S1—*- D

h1/2(C)H2 1B E

h2/2

S2-4—— c S2-4--— G

F

Figure A.2 Internal forces in columns

The forces acting on the portion ABCDEG of the bay are shown in Figure A.2c.It follows from the assumption above that:

S2 (H1 + H2)/2 (A.4)

Taking moments about the point of contraflexure at either C or G:

F2L = H2 h2 /2 + 2 S1 (h1 + h2)/2 + F1 L

Substituting for S and F1 and re-arranging:

F2 = H1 h1 IL + (H1 + 112) h2 /(2L) (A.5)

28

A.4 Calculation of internal momentsIt is clear from Figure A.2b that the internal moment at the head of each columnis given by:

M1 = S1h1/2

Substituting for S1:

M1 = H1h1/4 (A.6)

For equilibrium, the moment at each end of the roof beam is also equal to M1.The bending moment diagram is shown in Figure A.3a.

Shear force V

M

(a) M1

Referring to Figure A.2c, the internal moment in each upper column at B and Eis also M1. The corresponding moment in the lower columns is given by:

M2 = S2h2/2

Substituting for S2:

M2 = (H1 + H2) h2 /4 (A.7)

For equilibrium at B and E, the internal moment at each end of the beam BEequals (M1 + M2), as shown in Figure A.3b.

A.5 Calculation of shear forces in beamsAs a point of contraflexure is assumed at the mid-length of each beam(Figure A.3), the shear force in the roof beam is given by:

V1 = M1/(L/2)

Substituting for M1:

V1 = H h1 /(2 L) (A.8)

(b)

M1

1 2

M2

Figure A.3 Internal moments

29

Similarly, the shear force V2 in beam BE is given by:

V2 = (M + M2)/(L/2)

Substituting for M1 and M2:

V2 = H (h1 + h2)I (2 L) + H2 h2 1(2 L) (A.9)

A.6 Forces and moments in an internal columnThese are obtained by summing the values calculated for adjacent bays on eitherside of the column.

It is found that the vertical forces in an internal column due to horizontal loadingare zero.

30

APPENDIX B: Connection detailing

The following information is based on that found in Joints in steel construction:Composite connections161, Sections 5 and 4.2. References to compact sectioncapacity have been omitted because plastic hinge analysis is invoked in wind-moment frame design.

B. 1 IntroductionAppropriate connection detailing is necessary in order to:

• prevent premature failure of the tension bolts or reinforcement

• ensure sufficient deformation takes place to generate the tension bolt andreinforcement forces assumed in the design

• prevent concrete crushing against the column under unbalanced loading.

• ensure that the connections have sufficient rotation capacity to form a plastichinge.

The detailing rules that follow should be used in conjunction with the minimumreinforcement area requirements given in Table B. 1, and the maximum arealimitations presented in Section B2.2.

B. 1.1 Reinforcement and shear connectionConventional reinforcement detailing according to BS 81 10L2h1 should be adopted.Bar diameters should not be less than 16 mm, since smaller diameter bars aregenerally less ductile. Effective anchorage of the reinforcement is achieved bycurtailing the bars in the compression zone of the slab. This zone normally startsat about 0.2 times the beam span on either side of the support, and sufficientanchorage length should be provided beyond this point, as in conventionalreinforced concrete practicet2fl (for example 40 times the bar diameter for a 'Type2 deformed' bar in concrete with a cube strength of 30 N/mm2). To ensureadequate bar anchorage for composite connections to perimeter columns, thelongitudinal bars should be 'wrapped' around the columns as shown schematicallyin Figure B. 1 b). The cantilever dimension, c, for perimeter connections willdepend on the reinforcement detailing to ensure adequate cover and anchorage.Although reinforcing mesh may also be present in the slab to control cracking, itscontribution to moment capacity should be ignored.

The following detailing rules are shown schematically in Figure B. 1. Limitationson the positions of reinforcing bars ensure that they can work effectively ascomponents in a truss to resist unbalanced loads.

1. Longitudinal reinforcing bars should be uniformly spaced either side of thecolumn, with the nearest bars approximately 20 mm from the column edge,to achieve adequate cover. The furthest bars to be included in the effectivearea should not be more than approximately 2b from the column centreline(dimension e1).NOTE: eL is a function of the column width, rather than the beam span.

2. Transverse reinforcing bars (which are necessary to resist forces in theconcrete 'behind' the column when unbalanced loading is applied) should not

31

extend more than the required anchorage length211 beyond points 2b eitherside of the colunm centre line. This should ensure that the orthogonalconnection behaviour is not significantly influenced by these bars.

C,

.0N-J

CD

CD.00-oCCD

0-cC)CDC

Figure B.1 Geometrical detailing rulesconnections

beam-to-column composite

3. Transverse reinforcing bars should be uniformly spaced either side of thecolumn (Figure B. 1), with the nearest bars approximately 20 mm from thecolunm edge. The furthest bars included in the effective area should not bemore than approximately 3b from the column face (dimension e1).

4. Longitudinal reinforcing bars should be placed approximately 20 mm abovethe top of the decking, to ensure adequate concrete cover. The position ofthe transverse bars above or below the longitudinal bars will depend on theorientation of the decking and the depth of slab above the decking. All thebars must be positioned so that they have adequate cover to the decking andthe top of slabt2 1I)

Keeping the longitudinal bars close to the top of the decking minimises thestrain they must undergo to achieve a given rotation.

5. The first shear connector should be at least 100 mm from the face of thecolumn.

This limitation ensures that reinforcing bars are strained over a substantiallength, so that sufficient rotation can take place.

32

eT_3bC eT_3bC

.0N-J

CD

/ Longitudinalreinforcement

— Transversereinforcementct

mm

a)C)CD

0-CuCCD

+EE0CC)

.0N-J

a)

.0N-J

a,

I C I

Plan (decking and mesh omitted for clarity)

Approx.60mm

f

Elevation

a) Internal column

Elevation

b) Perimeter column

B.1.2 Steelwork1. The end plate thickness should be not more than 60% of the bolt diameter;

12 mm for M20 bolts and 15 mm for M24 bolts. End plates should be madefrom S275 steel.

2. Horizontal spacing of the bolts (gauge) should be not less than 90 mm.

These steelwork restrictions ensure that, as the connection rotates, end platedeformation is the 'weak link'. Steelwork details complying with these rules havebeen shown in tests to possess sufficient rotation capacity.

B.2 Reinforcement area limitsB.2.1 Minimum area of reinforcementIn general, the rotation capacity of a connection increases as the area ofreinforcement increases1161. A minimum area is therefore needed to ensuresufficient rotation capacity for a plastic connection. Minimum areas that shouldbe provided are given in Table B. 1 as a function of:

• beam size

• beam steel grade• reinforcement properties

Table B.1 Minimum area of reinforcement - 'plastic' connections

Steel Rebarelongationlimit

Beam depth (mm)

203 254 305 356 406 457 533 610

S275 5% 500 500 500 650 1100 1450 1800 3000

10% 500 500 500 500 500 600 750 1150

S355 5% 500 500 600 1400 2100 3100 - -

10% 500 500 500 500 650 900 2000 2850

Note: A dash (-) in the table indicates that excessive reinforcement is required.

The minimum values in Table B. 1 marked '5%' should normally be used. Thesevalues are appropriate for connections using high yield bars, grade 460Bcomplying with British Standard BS 4449[22]• This grade of reinforcement has amandatory requirement of 14% minimum elongation at fracture, and a non-mandatory requirement of 5% minimum elongation at maximum force. GradeB500B bars complying with BS EN 100801231 are required to have similarproperties; they must be able to achieve 5% total elongation at maximum force.Elongation at fracture and elongation at maximum force are illustrated inFigure B.2.

Minimum reinforcement areas are also given in Table B. 1 for connections that usereinforcement which is capable of achieving 10% total elongation at maximumforce. The increased reinforcement ductility offers considerable advantages insome cases because it permits the use of less reinforcement.

33

It is essential that when a design is based on the use of 10% elongation bars, thisis made clear in the project specification. This can be done by giving the bars an'X' designation, rather than the 'T' generally used for high tensile bars241. The'X' informs the contractor that the bars need specific, non-standard properties.It is recommended that, if possible, the reinforcement supplier uses coloured labelsto clearly distinguish the high elongation 'X' bars on site. In case of doubtconcerning the elongation capacity of bars, approximately half the UKmanufacturers provide reinforcement suppliers with appropriate test information.It should therefore be relatively easy for the contractor to confirm suitability withhis reinforcement supplier.

Cl,Cl,

StrainsElongation at Minimum elongation

maximum force at fracture(�5% for B500B to ( 14% according to

DD ENV 10080) BS 4449)

Figure B.2 Elongation limits for reinforcement

Bars that are currently produced using a hot forming process may be assumed tobe appropriate for use with the '10%' limits. All 20 mm diameter bars producedby major manufacturers in the UK currently are hot formed, as are, often, 16 mmbars.

B.2.2 Maximum area of reinforcement

The reinforcement area must also be limited to a maximum value in order to:

• prevent local concrete crushing failure under unbalanced loading

• keep the compression zone in the lower half of the steel beam.

The reasons for these limits are discussed below.

In order to consider the potential concrete crushing failure, a truss model has beendeveloped to represent how double sided composite connections behave when theapplied moments on either side are unequalL'41. Figure B.3 illustrates thecomponents in the truss, showing that the connection resistance relies on theability of the concrete to bear against the column on the low moment side. Thenet force in the reinforcement is therefore limited by the strength and area ofconcrete in bearing. An enhancement factor may be applied to the concretestrength because of its confinement11511251.

34

slab

Effective truss members formed by:Slongitudinal reinforcement•transverse reinforcement•concrete

Figure B.3 Truss model for connection behaviour under unbalancedmoment

According to the truss model, the area of longitudinal reinforcement must notexceed:

1.5 bAL � (B.1)Lfwhere:

1.5 is a factor that includes allowances for the enhanced concrete strength dueto confinement1151125, the total area of concrete in bearing1261 and thematerial partial safety factor

Note: This factor has been modified from the value given in Reference 16as a result of the application of more recent research115t2511261.

b is the width of column

d is the depth of slab above decking

fcu is the cube strength of concrete

4 is the yield strength of the rebar

j. is a function of the difference in applied moments, and beam depths, eitherside of the node, given by:

35

Fright > Fleft

M10 h1/= An (B.2)high r2

where:

M10 is the smaller applied moment (may be taken as the larger connectionmoment resistance less the vector addition of the applied moments. Thevector addition is the difference in the applied moments if both are hogging,and the sum if one is sagging)

Mhigh is the larger applied moment (may be taken as the larger connection momentresistance)

hr1 is the reinforcement lever arm on the high moment side

hr2 is the reinforcement lever arm on the low moment side.

Transverse reinforcement acts as a tension member in the truss model (seeFigure B.3). The area of transverse reinforcement must satisfy the followinglimit:

0.35 /.L ALAT �

.J. - 0.3 (B.3)

eL

where:

eL (this is the outer limit of the longitudinal reinforcement from thecolunm centre line)

eT 3.0b

eL and eT are identified in Figure B. 1.

It is assumed that the longitudinal and transverse reinforcing bars have the samenominal yield strength.

In theory, the length of transverse reinforcement must be limited so that, whilstsufficient anchorage is provided for the bars to act in the truss, they do not affectthe behaviour of the 'transverse beam connections'. In practice, this should notbe critical. Detailing rules are given in Section Bi .1.

Additional reasons for imposing an upper limit on the reinforcement area are:

• to ensure adequate strain in the reinforcement, compression must be restrictedto the lower half of the steel beam (i.e. the plastic neutral axis must not behigher than the mid-depth of the web)

• to avoid the need for colunm compression stiffeners. The standard connectioncapacity tables, in Appendix C, indicate whether or not a compression stiffeneris required in the colunm.

36

APPENDIX C: Capacity Tables

The information given in this appendix is a representation of the data fromAppendix B of Joints in steel construction: composite connectionsL'6]. A fullexplanation of the calculation of the moment capacity is given in that publication.

37

Composite Connections

1 ROW M20 8.8 BOLTS200 x 12 S275 END PLATE

BEAM SIDE

BEAMSerial

Size

Effective reinforcement (option, number and size of bars, Areinf, Freinf)

A4No.416804 mm2351 kN

B

6No.4161210 mm2529kN

C8No.161610 mm2704kN

D10No.162010 mm2878kN

E4No.4201260 mm2551 kN

F

6No.4201890 mm2826kN

G8No.4202510 mm21097kN

H10No.4203140 mm21372kN

'A'

mmMkNm

'A'

mmMkNm

'A'

mmMckNm

'A'

mmMkNm

'A'

mmMkNm

'A'

mmMkNm

'A'

mmMkNJm

'A'

mmMkNm

457x191x9889827467

3983952390387

268*266*265*264*262*

398395392390387

362*359*358*356*354*

398395392390387

454451

449447444

398

395392384387

546*543540*531*535*

398395392390387

373*371*369*367*365

3983953923,90

387

518*515*513*57Q*508*

398395392390

661

648*

654*

651*

398395

807

802

457x152x82746760

52

396

391

388

384

267*

264*263*

261

396

394391

388

384

361*359*356*355*

352*

396394385388

453450*443*445*

396

382

391

—

545*

529*

538*——

396394391

388

384

372*370*368*366*

363*

396386391

517*506*511*

396387

660*648*

406x178x74676054

345342340337

239*237*236*234*

345342340337

323*321*319*317*

345342340

337

406*4Q3*401*

399*

345

336

489

486

345

342

34Q

333

333*

331*

33Q*

324*

345

342

340

464*461*459*

345 593

406x140x46

39

338

334

235*

232*

338 317* — — 338 328*

356x171x67

57

51

45

296

292

289

287

211*

209*

207*

206*

296

292

289

287

286*

284*

282*

280*

296

292

289

361

357

355

289——

—

428——

—

296

292

289

287

296*

293*

291*

289*

296

292

413

409

296—

528—

—

—

—

—

356x127x39

33

281

280

203*

202*

305x165x54

46

40

244

241

238

182

180

179

244

241

238

248

246

244

244—

—

313—

—

—

—

—

—

—

—

244238238

256254252

244—

—

359——

—

—

—

—

—

—

—

—

—

—

—

—

305x127x48

42

37

244

241

232

182

181

171

237

224

231

239

221

233

239——

308——

—

—

—

—

—

—

235

222

229

244

225

238

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

305x102x33

28

25

230

211—

163

143—

—

—

—

—

—

—

—

-—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

254x146x43

37

31

193

191

177

151

149

128

188

175

—

195

176

—

—

—

—

—

—

—

—

—

—

—

—

—

187

172

—

199

179

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

254x102x2825

172

—121

——

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

398 Beam may be either grade S275 or grade S355369 Beam must be grade S355 to satisfy neutral axis position requirements264 Beam must be grade S275 to satisfy minimum reinforcement requirements (see Table B.1)* Reinforcement requires a guaranteed strain at maximum load of at least 10% for S355 beams, and possibly for S275

beams (check using Table B. 1)256 Connection capacity exceeds 0.8 M of composite beam in hogging (see ref. 16 Section 3.2.1 for significance of this(The value of Fri is based on the assumption that the NA is at least 200 mm below the bolt row. It should be reduced inaccordance with ref. 16 Section 4.2 Step 1D when necessary.

38

Composite Connections

1 ROW M20 8.8 BOLTS200 x 12 S275 END PLATE COLUMN SIDE

S275

ColumnSerialSize

S355

Compression ZoneTension

ZoneWeb

Compn.Cap.

PanelShearCap.

PanelShearCap.

WebCompn.

TensionZone Compression Zone

Cap. F1 Reinforcement option

A B C D E F G HReinforcement option

A B C D E F G HF

(kN) (kN) (kN) (kN) (kN) (kN)

1000849725605

1141935766605

/111

I111

I11S

I1SS

1SSS

/IIS

/SSS

SSSS

SSSS

356x368x202x177x153x129

IIIII1II

11IS

11SS

11II

11SS

1SSS

SSSS

1111

14861217974788

13021105944787

1037816703595503

14321051

858692553

11111

1111S

111SS

11SSS

1SSSS

1IISS

1ISSS

1SSSS

SSSSS

305x305

x198x158x137x118x97

IIIII

III1S

1IISS

1IISS

1IIIS

1IISS

1ISSS

1SSSS

11111

186513681116909713

13501062915774649

882685551

434360

1384992744557436

11111

111SS

111SS

11SSS

1SSSS

1ISSS

1SSSS

1SSSS

SSSSS

254x254

x167x132x107x89x73

IIII/

IIISS

IIISS

IISSS

IIISS

IISSS

ISSSS

1SSSS

11111

18021292969725563

1149892717566465

459353322

701512440

I11

ISS

SSS

SSS

SSS

SSS

SSS

SSS

SSS

203x203

x86x71

x60

I/1

ISS

ISS

SSS

ISS

SSS

SSS

SSS

I11

913666568

598460415

Tension Zone:

/ Column satisfactory for bolt row tension values shown for the beam side.195 Recalculate moment capacity based on reduced bolt row force (195 kN) using dimension 'A' to derive appropriate

lever arm - or provide tension stiffener at the appropriate bolt row level.Compression Zone:/ Column capacity exceeds JF = F&flf+FlS Provide compression stiffener.

Vertical Shear Capacity258 kN without shear row442 kN with shear row

.•. • L..

I 604

,, Optional" shear row

39

Composite Connections

2 ROWS M20 8.8 BOLTS200 x 12 S275 END PLATE

BEAM SIDE

BEAMSerial

Size

Effective reinforcement (option, number and size of bars, Arejflf, Freinf)

A4No.416804 mm2351 kN

B6No.4161210 mm2529kN

C8No.4161610 mm2704kN

D10No.162010 mm2878kN

E4No.4201260mm2551 kN

F6No.4201890 mm2826kN

G8No.202510 mm21097kN

HlONo.4203140 mm21372kN

'A'mm

MkNm

'A'mm

MckNm

'A'mm

MckNm

'A'mm

MkNm

'A'mm

MkNm

'A'mm

MckNm

'A'mm

MkNm

'A'mm

MkNm

533x210x122

109

101

92

82

384380

378375

372

363*360*358*357

354

384380

378375

372

470*466*465*462*

459*

384

380

378

375372

575*

571*

569*566*563

384380

378375372

681*676

674*670666*

384380

378375372

483*480*478*475w

472*

384380

378

375361

649*645642*

639*623

384380

378375

813*807*791

800*

377380378

967*973*969*

457x191x98

89

82

74

67

308

305

302

300

297

310*

307*

306*

304

302*

308

305

302

300

297

403*

401*

398*

396*

394*

308

305

302

300

297

495*

492*

490*

487*

484*

308

305

302300

588

584

572*578*

308

305

302

300297

415*

412*

410*

408*405*

308

305

302

300297

560*

556*

553

551*548*

301

305302

693*699*695*

308 848

457x152x82

67

6052

306

301

287

309*

305*

295*

306

304301

288289

402*400*397*386387*

306

295285292

494*482*472*479*

294304293

—

571*583*570

—

—

306

304

296286287

414

411*404*395397*

297285295

548*531546*

301 693*

406x178x74

67

6054

255

252

250247

273

271*

270*268*

255

252

250233

357*

355*

353*337*

255

244

250

440*

425*

435*

243252

—

502520

—

—

255

252245247

368*365*357361*

247

252485495*

250 618 — —

406x140x46

39

237235

255*255*

398 Beam may be either grade S275 or grade S355369 Beam must be grade S355 to satisfy neutral axis position requirements264 Beam must be grade S275 to satisfy minimum reinforcement requirements (see Table B.1)* Reinforcement requires a guaranteed strain at maximum load of at least 10% for S355 beams, and possibly for S275

beams (check using Table B. 1)256 Connection capacity exceeds 0.8 M of composite beam in hogging (see ref. 16 Section 3.2.1 for significance of this)The value of F, is based on the assumption that the NA is at least 200 mm below the bolt row. It should be reduced inaccordance with ref. 16 Section 4.2 Step 1D when necessary.

40

Composite Connections

2 ROWS M20 8.8 BOLTS200x12S275ENDPLATE co N SILUM DE

S275

ColumnSerialSize

S355

Compression ZoneTension

ZoneWeb

Compn.PanelShearCap.

PanelShearCap.

WebCompn.

Cap.

TensionZone Compression Zone

,2 Reinforcement option

A B C D E F G HReinforcement option

A B C D E F G H'2 Cap.

(kN) (kN) (kNI (kN) (kN) (kN)

1000849725605

1141935766605

/ // /1 // /

/1IS

/1SS

ISSS

SSSS

IISS

SSSS

SSSS

SSSS

356x368x202x177x153x129

I1III1IS

I1SS

ISSS

IIIS

IISS

ISSS

SSSS

/ // /V // /14861217974788

13021105944787

1037816703595503

14321051

858692553

/ // // 1/ // /

II1SS

IISSS

1ISSS

1SSSS

1ISSS

1SSSS

SSSSS

SSSSS

305x305

x198x158x137x118x97

IIIII

II1IS

II1SS

I1SSS

I1IIS

I1SSS

1SSSS

1SSSS

/ // // // // /

186513681116909713

13501062915774649

882685551434360

1384992744557436

1 1/ // I/ // /

11ISS

11SSS

1SSSS

1SSSS

1ISSS

1SSSS

5SSSS

SSSSS

254x254

x167x132x107x89x73

II1IS

II1SS

1ISSS

1ISSS

1IISS

1ISSS

1SSSS

1SSSS

/ 1/ // // 1/ /

18021292696725563

1149892717566465

459353322

701512440

/ // // /

/SS

SSS

SSS

SSS

SSS

SSS

SSS

SSS

203x203x86x71

x60

ISS

1SS

SSS

SSS

1SS

SSS

SSS

SSS

/ // // /

913666568

598460415

Tension Zone:/ Column satisfactory for bolt row tension values shown for the beam side.195 Recalculate moment capacity based on reduced bolt row force (195 kN) using dimension 'A' to derive appropriate

lever arm - or provide tension stiffener at the appropriate bolt row level.Compression Zone:I Column capacity exceeds >F = F01f+FS Provide compression stiffener.

41

Vertical Shear Capacity331 kN without shear row515 kN with shear row

Composite Connections

2 ROWS M20 8.8 BOLTS250 x 12 S275 END PLATE BEAM SI ED

BEAMSerial

Effective reinforcement (option, number and size of bars, Areinf, Freinf)

A4N0.d?16804 mm2

B6No.d,161210 mm2

C8No.4161610 mm2

D10No.4162010 mm2

E

4No.4201260 mm2

F

6No.201890 mm2

G8No.202510mm2

H10No.203140 mm2

Size 351 kN 529kN 704kN 878kN 551 kN 826kN 1097kN 1372kN

'A'

mmMckNm

'A'

mmMkNm

'A'

mmfl

kNm'A'

mmMkNm

'A'

mmMkNm

'A'

mmMkNm

'A'

mmMkNm

'A'

mmMkNm

533x210x122 384 375 384 482* 384 588* 384 693* 384 495* 384 662* 384 825* 375 976*

109 380 372* 380 479 380 583* 380 688* 380 492* 380 657* 375 811* 380 985*101 378 371* 378 477 378 581* 378 686* 378 490* 378 654* 367 800* 378 981*92 375 369* 375 474* 375 578* 375 682 375 487* 375 651* 375 812*

82 372 366 372 471* 366 569* 372 678* 372 484* 359 631*

457x191x98 308 319 308 413* 308 505* 308 597* 308 425* 308 570* 299 7QQ* 308 858

89 305 317* 305 410* 305 502* 305 5,94* 305 422* 305 566 305 708*82 305 315* 302 408* 302 499* 293 579* 302 419* 296 556* 302 705*

74 QQ j 300 406* 294 497k 300 588* 300 417 300 560*67 297 404* 297 494* — 297 4/5* 293 552*

457x152x82 306 319* 306 412* 306 504* 292 578* 306 423* 295 555* 300 701*

74 304 409* 293 489* 304 592* 304 421* 283 534*

67 301 314* 296 402* 283 475 291 577* 294 412* 294 553*

60 298 312* 285 393* — — 298 416*52 284 303* 287 394* — — 285 404*

398 Beam may be either grade S275 or grade S355369 Beam must be grade S355 to satisfy neutral axis position requirements264 Beam must be grade S275 to satisfy minimum reinforcement requirements (see Table B.1)

Reinforcement requires a guaranteed strain at maximum load of at least 10% for S355 beams, and possibly for S275

beams (check using Table 8.1)256 Connection capacity exceeds 0.8 M of composite beam in hogging (see ref. 16 Section 3.2.1 for significance of this)The value of Fri is based on the assumption that the NA is at least 200 mm below the bolt row. It should be reduced inaccordance with ref. 16 Section 4.2 Step 1D when necessary.

42

Composite Connections

2 ROWS M20 8.8 BOLTS25Ox12S275ENDPLATE

L IDECO UMNS

S275

ColumnSerialSize

S355

Compression ZoneTension

ZoneWeb

Compn.Cap.

PanelShearCap.

PanelShearCap.

WebCompn.

Cap.

TensionZone Compression Zone

F Reinforcement option

A B C D E F G HReinforcement option

A B C D E F G HF 2

(kN) {kN) (kN)lkN) (kN) (kN)

1000849725605

1141935766605

/ // // // /

/IIS

/ISS

/SSS

SSSS

/ISS

SSSS

SSSS

SSSS

356x368

x202x177x153x129

IIIIIIIS

IISS

ISSS

IIIS

IISS

ISSS

SSSS

/ // // // /14861217974788

13021105944787

1037816703595503

14321051

858692553

/ // // 1/ // I

II1SS

IISSS

ISSSS

ISSSS

IISSS

ISSSS

SSSSS

SSSSS

305x305

x198x158x137x118x97

IIIIS

IIIIS

1IISS

IISSS

IIISS

IISSS

ISSSS

ISSSS

/ // // // // /

186513681116909713

13501062915774649

882685551

434360

1384992744557436

/ // 1/ // // /

111S5

11SSS

1SSSS

1SSSS

1ISSS

1SSSS

SSSSS

SSSSS

254x254

x167x132x107x89x73

IIISS

IIISS

IISSS

IISSS

IIISS

IISSS

ISSSS

ISSSS

/ // // // /1 /

18021292969725563

1149892717566465

459353322

701

512440

/ // // /

SSS

SSS

SSS

SSS

SSS

SSS

SSS

SSS

203x203

x86x71

x60

ISS

ISS

SSS

SSS

SSS

SSS

SSS

SSS

/ // // /

913666568

598460415

Tension Zone:I Column satisfactory for bolt row tension values shown for the beam side.

195 Recalculate moment capacity based on reduced bolt row force 195 kN) using dimension A' to derive appropriate

lever arm - or provide tension stiffener at the appropriate bolt row level.

Compression Zone:/ Column capacity exceeds >F =

S Provide compression stiffener.

43

Optionalshear row

9o---60t

Vertical Shear Capacity331 kN without shear row515 kN with shear row

Composite Connections

1 ROW M24 8.8 BOLTS200x15S275ENDPLATE EA SIDEB M

BEAMSerial

Size

Effective reinforcement (option, number and size of bars,Areinf, Freinf)

A4No.416804 mm2351 kN

B6No.161210 mm2529 kN

C8No.4161610 mm2

704 kN

DlONo.4162010 mm2

878 kN

E

4No,4201260 mm2

551 kN

F6No.4201890 mm2

826 kN

G8No.202510 mm21097 kN

H

lONo,4203140 mm21372 kN

'A'

mmMkNm

'A'

mmMkNm

'A'

mmMkNm

'A'

mmMckNm

'A'

mmMkNm

'A'

mmMkNm

'A'

mmMkNm

'A'

mmMckNm

457x191x9889827467

398

392390

307*

303*

300*

398395392390387

401*398*396*394*392*

398395392390387

493*490*487485*482*

398395387390

585*581*572576*—

398395392390387

412*410*407*405*403*

398395

392390

387

557*554551

549*

545*

392

395

392

693*

696*

693*

398 846

457x152x8274676052

396

j.388

380

306*

QLQZ.301*295*

396394391

381

381

400*397395*

386386*

396387378

388

492*482*473*

483*

386

394

385

572

580*

570*—

396394391

379379

411*409*406396*397*

389

378

397

548*

536*

549*

396 699

406x178x74

67

60

54

345

342

340

337

272*

271*

269*

267*

345

342

340

337

357*

354

353

350*

345

336

340

440*

431*

435*

—

336

342

—

512

520—

345

342

340

337

367*

365*

363

360*

339

342

4,97w

495*345 626 — —

—

406x140x46

39

331

327

263*

261*

356x171x67

57

51

45

296

292

289282

240*

237*

236*231*

296

292

289

315*

312*

310*

296

292

390

386

296—

—

464—

—

296292289

325*327*319*

296 442 — — — —

356x127x39

33

273—

235*— — — — — — — — — — — — — — —

305x165x54

46

40

244

241

234

206

204

193

244

241—

272

270—

244—

—

337——

—

—

—

—

—

—

244

241—

280

278—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

305x127x48

42

37

244

232

221

206

189

170

229

213—

242

216—

—

—

—

—

—

—

—

—

—

—

—

—

227

210—

246

219—

—

—

—

—

—

—

—

—

—

—

—

—

305x102x33

28

25

215

——

157

——

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

254x146x43

37

31

193

183—

169

144

—

180——

190

——

—

—

—

—

—

—

—

—

—

—

—

—

177

——

193

——

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

398 Beam may be either grade S275 or grade S355369 Beam must be grade S355 to satisfy neutral axis position requirements264 Beam must be grade S275 to satisfy minimum reinforcement requirements (see Table B.1)

Reinforcement requires a guaranteed strain at maximum load of at least 10% for S355 beams, and possibly for S275beams (check using Table B. 1)

256 Connection capacity exceeds 0.8 M of composite beam in hogging (see ref. 16 Section 3.2.1 for significance of thislThe value of Fri is based on the assumption that the NA is at least 200 mm below the bolt row. It should be reduced in

accordance with ref. 16 Section 4.2 Step 10 when necessary.

44

Composite Connections

1 ROW M24 8.8 BOLTS200 x 12 S275 END PLATE

COLU S

S275

ColumnSerialSize

S355

PanelShearCap.

WebCompn.

Cap.

TensionZone Compression Zone Compression Zone

TensionZone

WebCompn.

Cap.

PanelShearCap.1 Reinforcement option

A B C D E F G HReinforcement option

A B C D E F G HF

(kN) (kN) (kN) (kN) (kN) (kN)

1000849725605

1141935766605

/111

/11S

/1SS

/SSS

SSSS

/ISS

VSSS

SSSS

SSSS

356x368x202x177x153x129

/III

/IIS

VISS

IISS

VIIS

IISS

ISSS

SSSS

I111

14861217974788

13021105944787

1037816703595503

14321051858692553

11111

1111S

111SS

1

1SSS

/SSSS

/IISS

/SSSS

ISSSS

SSSSS

305x305

x198x158x137x118x97

IIIII

IIIIS

IIISS

IISSS

IIIIS

IISSS

ISSSS

ISSSS

11111

186513681116909713

13501062915774

649

882685551

434360

1384992744557436

1111

297

111SS

11SSS

1SSSS

1SSSS

1ISSS

1SSSS

SSSSS

SSSSS

254x254

x167x132x107x89x73

IIIIS

IIISS

IISSS

IISSS

IIISS

IISSS

1SSSS

1SSSS

11111

18021292696725563

1149892717566465

459353322

701512440

11

297

1SS

SSS

SSS

SSS

SSS

SSS

SSS

SSS

203x203

x86x71x60

IIS

ISS

SSS

SSS

ISS

SSS

SSS

SSS

I11

913666568

598460415

Tension Zone:I Column satisfactory for bolt row tension values shown for the beam side.

195 Recalculate moment capacity based on reduced bolt row force (195 kNI using dimension A' to derive appropriatelever arm - or provide tension stiffener at the appropriate bolt row level.

Compression Zone:I Column capacity exceeds XF =S Provide compression stiffener. - -- - - — —__________________________________________________________

45

Composite Connections

2 ROWS M24 8.8 BOLTS200x15S275ENDPLATE

AM DEBE SI

BEAMSerial

Size

Effective reinforcement (option, number and size of bars, Areinf, Freinf)

A4No.16804 mm2351 kN

B6No.4161210 mm2529 kN

C8No.4161610 mm2704 kN

DlONo.4fl62010 mm2878 kN

E

4No.4201260 mm2551 kN

F6No.4201890 mm2826 kN

G

8No,4202510 mm21097 kN

HlONo.4203140 mm21372 kN

'A'

mmMckNm

'A'

mmMkNm

'A'

mmMkNm

'A'

mmMkNm

'A'

mmMkNm

'A'

mmMkNm

'A'

mmMkNm

'A'

mmMckNm

533x210x122109

101

9282

384

380

378

375

372

445*

442*

440*437*434*

384

380378

375367

552*548*546

543534

384

380378

375372

658*653*651*647643*

384

380370362

366

763*758*744*732

738*

384

380378

375

366

566*561*559*556*546*

384380

373

365372

732*727*716*706775*

384366378

370

895*867886*

873*

367

380

1029

1054*

457x191x98

89

82

74

67

308

305

302

297

377*

375*

373*

LJ.368*

308

305

302

295

283

471*

468

465*

458*

444k

308

305

294

3ØØ

291

563

560*

547

554*

543*

302

291

282

293

647

631*

610

635*—

308

305

302

294

282

483*

479*

477*

468*

450

308

294

286

300

628*

610*

594*

617*

289

305

734

766

299 900

457x152x82

74

67

60

52

306

304

301

287267

376*

374*

371*359*327*

306

294

284

291

470*

456*

443k

454*

293

279

292

545

516

544*

.

279

292

—

600

634——

306

292

282

290—

481*

466*

450

464*—

283

267—

—

585*

549*—

—

292

—

—

745

—

—

—

—

—

—

406x178x74

6]

60

54

255

252

245

232

331

328*

320*

296*

255

243

231

212

415

394*

369*

322*

242

228

469

447*

228

——

510——

—

255

241

228

209

425*

400*

374

323k

232

244

503533 — — — —

406x140x46

39

213—

251*— — — — — — — — — — — — — — —

398 Beam may be either grade S2]5 or grade S355369 Beam must be grade S355 to satisfy neutral axis position requirements264 Beam must be grade S275 to satisfy minimum reinforcement requirements (see Table B.1)* Reinforcement requires a guaranteed strain at maximum load of at least 10% for S355 beams, and possibly for S275

beams (check using Table B.1)256 Connection capacity exceeds 0.8 M, of composite beam in hogging (see ref. 16 Section 3.2.1 for significance of this)The value of Fri is based on the assumption that the NA is at least 200 mm below the bolt row. It should be reduced in

accordance with ref. 16 Section 4.2 Step 1D when necessary.

46

Composite Connections

2 ROWS M24 8.8 BOLTS200 x 15 S275 END PLATE COLUMN SIDE

S275

ColumnSerialSize

S355

PanelShearCap.

WebCompn.

Cap.

TensionZone Compression Zone Compression Zone

TensionZone

WebCompn.

Cap.

PanelShearCap.F F,2 Reinforcement option

ABCDEFGHReinforcement option

ABCDEFGHF, F,2

(kN) (kN) (kN) (kN) (kN) (kN)

1000849725605

1141

935766

605

/ // // // /

I/SS

I5SS

S5SS

SSSS

/ SS SS SS S

SSSS

SSSS

356x368

x202x177x153x129

IIIS

IISS

ISSS

/SSS

/SSS

SSSS

SSSS

/ // // // /

14861217974788

13021105944787

1037816703595503

14321051

858692553

/ // // /1 // /

/ISSS

I5SSS

ISSSS

/SSSS

11S SS SS SSS

SSSSS

SSSSS

305x305

x198x158x137x118x97

1IIIS

1IISS

1ISSS

11S /S /S SSS

//SSS

1SSSS

SSSSS

1 // // // // /

186513681116909713

13501062915774649

882685551434360

1384992744557436

/ // // // /297/

1ISSS

1S5SS

1S5SS

5SSSSSSS

/S S

5SS

SS5SS

SS5SS

254x254

x167x132x107x89x73

III5S

IIS5S

IIS5S

/ /S /SSSSSS

/SSSS

ISSSS

SS5SS

/ // // // // /

18021292969725563

1149892717566465

459353322

701512440

/ // /297204

5SS

5SS

5SS

SSSSSS

SSS

SSS

SSS

203x203

x86x71x60

I5S

SSS

5SS

SSSSSS

5SS

5SS

SSS

/ // // /

913666568

598460415

Tension Zone:/ Column satisfactory for bolt row tension values shown for the beam side.195 Recalculate moment capacity based on reduced bolt row force (195 kN) using dimension 'A' to derive appropriate

lever arm - or provide tension stiffener at the appropriate bolt row level.Compression Zone:/ Column capacity exceeds F =S Provide compression stiffener.

47

Vertical Shear Capacity476 kN without shear row739 kN with shear row

Composite Connections

2 ROWS250 x 15

M24S275

8.8 BOLTSEND PLATE

BEAM SIDE

BEAMSerial

Size

Effective reinforcement (option, number and size of bars, Arejflf, Freinf)

A4No.416804 mm2351 kN

B6No.161210 mm2529 kN

C8No.4161610 mm2704 kN

D1ONo.162010 mm2878 kN

E4No.4201260 mm2551 kN

F6No.4201890 mm2826 kN

G8No.4202510mm21097 kN

HlONo.4203140 mm21372 kN

'A'

mmMkNm

'A'

mmMkNm

'A'

mmMkNm

'A'

mmMkNm

'A'

mmMkNm

'A'

mmMckNm

'A'

mmMkNm

'A'

mmMkNm

533x210x122

109

101

9282

384

380

378375372

459'

455'

453'451'447'

384

380

378

375365

566'

562'

559'556'545'

384

380

378

370353

671'

666'

664'

653'

632'

384

380

368

359

364

777'

771'

754'

741'

748*

384

380

378

375364

579'

575'

572'

569'557'

384

380

371

363

343

745'

740'

727*716'

721'

384

364

378

369

909'

876*

899*

884*

365

374

1038'

1055'

457x191x98

89

82

74

67

308305302

300

297

388'385'383'

381'

379'

308305302

293280

482'478'476'

466'

446'

308299292

280

289

574*

563'

554*

529*

551'

300

288

279

292—

655'

633'

610'

643*—

308

305302

292278

493'490'487'

476*451'

308

292

283

294

639*

617'

596'

620*

287

299

736'

766'

298—

908—

457x152x827467

60

52

306 387'304 384'

295 376'

283 365'

301

291281

289

475'464'445'

462'

290 550'

276 516'

290 552'— —- I -

276

290——

599'

641'——

300

289279

288

485'473*451'

472'

280

263——j

585*

546*——

—

—

—

—

—

—_-—

—

398 Beam may be either grade S275 or grade S355369 Beam must be grade S355 to satisfy neutral axis position requirements264 Beam must be grade S275 to satisfy minimum reinforcement requirements (see Table B. 1)' Reinforcement requires a guaranteed strain at maximum load of at least 10% for S355 beams, and possibly for S275

beams (check using Table B. 11

256 Connection capacity exceeds 0.8 M, of composite beam in hogging (see ref. 16 Section 3.2.1 for significance of this)The value of Fri is based on the assumption that the NA is at least 200 mm below the bolt row. It should be reduced in

accordance with ref. 18 Section 4.2 Step 1D when necessary.

48

Composite Connections

2 ROWS M24 8.8 BOLTS250 x 15S275 END PLATE

COLUMN SIDE

S275

ColumnSerialSize

S355

PanelShearCap.

WebCompn.

Cap.

TensionZone Compression Zone Compression Zone

TensionZone

WebCompn.

Cap.

PanelShearCap.F,1 F,2 Reinforcement option

A B C D E F G HReinforcement option

A B C D E F G HF,1 F,2

(kN) (kN) (kN) (kN) (kN) (kN)

1000849725605

1141935766605

/ // // // /

/ISS

1SSS

SSSS

SSSS

SS SSS

S

SSSS

SSSS

356x368x202x177x153x129

1IIS

1ISS

1SSS

/ /S /SSS S

/SSS

SSSS

SSSS

/ /I // // /

14861217974788

13021105944787

1037816703595503

14321051858692553

/ // // // /1 /

I1SSS

ISSSS

ISSSS

S /SSSSS

/SSSS

SSSSS

SSSSS

305x305

x198x158x137x118x97

IIISS

IIISS

IISSS

/ /S /S SS SSS

ISSSS

ISSSS

SSSSS

/ // // 1I // /

186513681116909713

13501062915774649

882685551

434360

1384992744557436

/ // I/ I/ /297/

1ISS5

1SSS5

1SSS5

5 /S SS SSSSS

SSSSS

SSSSS

SSSSS

254x254

x167x132x107x89x73

IIISS

IISSS

IISSS

/ /S /S SSSSS

/SSSS

ISSSS

SSSSS

/ // // // 1/ /

18021292969725563

1149892717566465

459353322

701

512440

/ // /297204

SS5

SS5

SSS

SSSSSS

SSS

SSS

SSS

203x203

x86x71x60

SS5

SS5

SS5

SSSSSS

SSS

SSS

SSS

/ 1/ // /

913666568

598460415

Tension Zone:/ Column satisfactory for bolt row tension values shown for the beam side.195 Recalculate moment capacity based on reduced bolt row force (195 kN) using dimension 'A' to derive appropriate

lever arm - or provide tension stiffener at the appropriate bolt row level.Compression Zone:/ Column capacity exceeds >F = F + FS Provide comoression stiffener.

80 90 80

_______________________ 250Vertical Shear Capacity476 kN without shear row739 kN with shear row

49

Composite Connections

DIMENSIONS FOR DETAILING

Beam Dimension Dimension End plateserial size a

mma2

mmoverall depth

DF mm

Lf

533x210x122109101

9282

425420415415410

245240235235230

600

457x191x9889827467

350345340340335

170165160160155

520

457x152x8274676052

345340340335330

165160160155150

520

406x178x74676054

295290285285

115110105105

0

406x140x4639

280275

10095 450

356x171x675751

45

245240235230

—

—

—

—

420

356x127x3933

235230

—

— 410

305x165x544640

190185185

—

——

360

305x127x484237

190185185

———

360

305x102x332825

195190185

—

——

370

254x146x4337

31

140135135

——

—310

25 _______60

a D1 F

,r25(see appropriate capacity tab'e)

25 _____60

• ___--4--

90

a

9c _(see a0Dropriate caracitv table)

254x102x282522

140135135

310

See capacity table diagram for plate thickness and other dimensions appropriate to the moment capacities.All plates to be S275. ______________________________

50

APPENDIX D: Worked Example

D. 1 Introduction

The design example given in this Appendix is for a frame that is braced out of plane inorder to prevent sway about the minor axis of the columns.

Calculations are given to demonstrate the following aspects of the design rules:

• compliance with the scope• framing and loads

• wind analysis• notional horizontal forces and analysis

• beam design• column loads

• internal column design

• external column design

• connections design• serviceability limit state.

D. 1.1 ComplianceThe frame in this example forms part of a steel structure that conforms to the framelayout specified in Section 1.2. In particular:• The floor layout comprises primary and secondary beams as shown in Figure 1.3

• The frame is braced against sway about the minor axis

• The bay width is constant over the frame height

D.1.2 Frame dimensions

The frame dimensions conform to the limitations given in Section 1.2.1:

No. of storeys = 4 OK

No. of bays = 5 Therefore consider only 4 to resist wind loads

Bay width = 9 m OK

Bottom storey height = 4.5 m OK

Storey height = 3.5 m OK(above bottom storey)

Bay width / storey height 9 / 4.5 = 2 OK

(bottom)

Bay width / storey height 9 / 3.5 = 2.57 OK(above bottom storey)

Greatest bay width / smallest bay width 9 / 9 = 1 OK

51

D.1.3 LoadingThe following unfactored loading conforms to the range given in Section 1.3.3, Table 2:

Dead load on floors = 5 kN/m2 OK

Imposed load on floors = 7.5 kN/m OK

Dead load on roof = 3.75 kN/m OK

Imposed load on roof = 1.5 kN/m2 OK

Wind loads see Figure D.2

D.1.4 DesignThe members were designed using rules given in BS 5950-1: 1990121 and BS 5950-3:199O, with additional requirements as specified in this publication.

Member capacities were either obtained directly from tables given in Steelwork designguide to BS 5950: Part 1:1990 - Volume j[181 or calculated using the method given inBS 5950-3.

52

The SteelConstructionInstitute

Job No: P264fra9e

1 of 25 A

Job Title Wind-moment Composite Frames

Subject Framing and LoadsSilwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Client SCI

Made

by JSH

Checked by AW

Date

Date

Nov.

Dec.

99

99

D.2 FRAMING AND LOADS

1 m parapet

3.5 m

3.5 m

3.5 m

4.5 m

Frame spacing is at 6m centres

Figure D.1 Frame elevation

In accordance with Section 1.3.1, the number of active bays in thewind-moment frame must not exceed four. Therefore, consider only four of thefive bays to be active when carlying out the wind analysis using the portalmethod, see below.

-- iJ 1f !' 1( J I( 1I—

I I I I I I I—

Beams are loaded by transverse beams at Vs span points

Figure D.2 Frame loading arrangement

RQ(Dead loadImposed load

FloorDead loadImposed load

3. 75kN/m2 equivalent to two point loads of1.5OkN/m2 equivalent to two point loads of

5.00kN/m equivalent to two point loads of7.SOkN/m2 equivalent to two point loads of

53

67.5 kN/m227 kN/m2

90 kN/m2

135 kNIm2

9m 9m 9m , 9m m—I —I

10 kN

1 5 kN

1 5 kN

17 kN

I I I I

4 x 9 m bays are considered to resist wind loading

The SteelConstructionInstitute

Job No: P264IPage

2 of 25 A

Job Title Wind-moment Composite Frames

Subject Wind AnalysisSilwood Park, Ascot, Berks SL5 JONTelephone: (01344) 623345Fax: (01344) 62944

CALCULATION SHEET

Client SCI by JSH Date Nov. 99

by AW Date Dec. 99

D.3 WIND ANALYSIS

10 kN ___. 2.2 kNm _____________ 4.4 kNm _____________1.75

15 kN 5.5 kNm ______________ 10.9 kNm ______________ F4 1.751.75

F 1.7515 kN _ 8.8 kNm I I 17.5 kNm _______________ c3

7 i.is

17 kN ••_ 16.0 kNm / / 32.1 kNm / _____________ F 1.75____ ____ ____ ____ c2/ / / /

Figure D.3 Frame analysis under wind loads (columns)

Table D. 1 Shear forces and bending moments in columns due to wind load

StoreyTotal windshear (kN)

Shear force incolumn (kN)

Bending moment in column (kNm)

External Internal External Internal

4 10 1.25 2.5 1.25x1.75 = 2.2 2.5x1.75 = 4.4

3 25 3.13 6.25 3.13 xl.75 = 5.5 6.25x1.75 = 10.9

2 40 5 10 5.Oxl.75 = 8.8 1O.Oxl.75 17.5

1 57 7.13 14.25 7.13 x2.25 = 16 14.25x2.25 = 32.1

Table D.2 Moments and axial loads due to wind loads

Storey Moments about point of contraflexure at mid-height

4 36 F,4 = lOxl.75 0.5

3 36F= 10x5.25+15x1.75 2.2

2 36F2 = 10x8.75 + 15x5.25 + 15x1.75 5.3

1 36F1 = 10x12.75 + 15x9.25 + 15x5.75 + 17x2.25 10.9

N.B. Values are UNFACTORED

Axial forces in the beams due to wind loads are small and may be neglected.

54

lOkN —.

15 kN —-

15 kN —.

17 kN —.

Figure D.4 Frame analysis under wind loads (beams)

Table D.3 Bending moments in beams due to wind load

Floorlevel

Bending moment in external Column(kNm) Bending moment in beam

(kNm)Upper column Lower column

4 0 2.2 0.0 + 2.2 = 2.2

3 2.2 5.5 2.2 + 5.5 = 7.7

2 5.5 8.8 5.5 + 8.8 = 14.3

1 8.8 16 8.8 + 16.0 = 24.8

N.B. Values are UNFACTORED

55

The SteelConstructionInstitute

Job No: P264IPage

3 of 25 A

Job Title Wind-moment Composite FramesSubject Wind Analysis

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 62944

CALCULATION SHEET

Client SCI Made by JSH Date Nov. 99

Checked by AW Date Dec. 99

— - —-

The Steel L7ConstructionInstitute

Job No: P264 Page4 of 25 A

Job Title Wind-moment Composite Frames.

Subject•

Notional ForcesSilwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Client SCI Made by JSH Date Nov. 99

Checked by AW Date Dec. 99

D.4 NOTIONAL HORIZONTAL FORCES

— - —-—7 - —---

36m>1

Figure D.5 Frame analysis under notional horizontal loads

Notional horizontal force = 0.005 (1.4 dead + 1.6 imposed)

Roof H=0.005(1.4x3.75+1.6X1.5)X36X6

Floor H=0.005(1.4X5.0+1.6X7.5)X36X6 =

Table D.4 Shear force and bending moment in the columnshorizontal forces

8.3 kN —..

20.5 kN —.

20.5 kN —*-

20.5 kN

/ / / 'I

8.3 kN

20.5 kN

due to notional

Storey Totalshear(kN)

Shear force in column(kN)

Bending moment in column (kNm)

External Internal External Internal

4 8.3 1 2.1 1.OxI.75 = 1.8 2.lxl.75 = 3.6

3 28.8 3.6 7.2 3.6x1.75 = 6.3 7.2x1.75 = 12.6

2 49.3 6.2 12.3 6.2x1.75 = 10.9 12.3 xl.75 = 21.5

1 69.8 8.7 17.5 8.7x2.25 = 19.6 17.5x2.25 = 39.4

Table D.5 Bending moments in beams due to notional horizontal forces

Floorlevel

Bending moment in external column (kNm) Bending moment in beam(kNm)Upper column Lower column

Roof 0 1.8 0.0 + 1.8 = 1.8

3 1.8 6.3 1.8 + 6.3 = 8.1

2 6.3 10.9 6.3 + 10.9 = 17.2

1 10.9 19.6 10.9 + 19.6 = 30.5

N.B Values are UNFACTORED

56

D.5 BEAM DESIGN

D. 5.1 Roof beam design

Slab depth

Metal decking

Shear studs

Longitudinal rebar

The SteelConstructionInstitute

Job No: BCB478 JPae 5 of 25 JRev A

Job Title Wind-moment Composite Frames

Subject Roof Beam DesignSilwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Client SCI

Made

by JSH

Checked by AW

Date

Date

Nov.

Dec.

99

99

<3m

>k3m

4<3m

>L L

>1

Figure D. 6 Roof beam

Ultimate Limit State

Dead and Imposed Loading

(T=point loads from transverse beams)

Design load for ULS: T = 1.4 x 67.5 + 1.6 x 27 = 137.7kN

Moment:Take end restraint moment due to gravity load equal to 10% of the maximumsagging moment of a simply-supported beam

Sagging moment:0.9TL 0.9 x 137.7 x 9M =

3=

3= 372 kNm

Hogging moment:0.1TL 0.1 x 137.7 x 9M =

3=

3= 41.3 kNm

Shear:

F,, = (1.4x3.75+1.6x1.50)x6x9/2 = 207kN

Try 356 x 171 UB 57 Grade S355

D.2, Sheet 1

Section 4.1.2

Sheet 1

= 140mm

= 1 mm gauge, 50 mm deep, trapezoidal profile

= 19 mm g5, 95 mm high @ 150 mm c/c

= T16@l5Omm

57

The SteelConstructionInstitute

Job No: BCB478 frae 6 of 25 A

Job Title Wind-moment Composite Frames

Subject Roof Beam DesignSilwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: 101344) 622944

CALCULATION SHEET

Client SCI

Made

by JSH

Checked by AW

Date

Date

Nov.

Dec.

99

99

Transverse rebar = T12 @ 200 mm

Concrete = C30 lightweight concrete

The composite beam is designed using BS 5950-3: Section 3.1: 1990, and is Ref. 3classified as a Class 1 plastic section. Ref. 18

Section sagging bending capacity, M = 680 kNm Ref. 3

Reduced composite beam sagging capacity:

0.9 M = 612 kNm> 372 kNm OK

Beam hogging moment capacity, based on steel section alone:

Mhog = 359 kNm >41. 3kNm OK Ref. 18

Shear check: P,, = 0.6 p A,, = 618 kN > 207 kN OK Ref. 18

Dead load plus wind loadinR

Maximum roof beam end moments due to wind = 2.2 kNm Sheet 3

Maximum hogging moment = 1.4 (0.1 x 67.5 x 9

+

2.2)= 31.4 kNm

Sheet 1

Hence, wind load does not cause sagging moments at beam ends

and Mhog > 31.4 kNm OK

Dead load plus imposed load plus wind loading

Maximum roof beam end moments due to wind = 2.2 kNm

(0.lx(67.5+27)x9Maximum hogging moment = 1.23

+ 2.2

= 36.7 kNm

Hence, wind load does not cause sagging moments at beam end

and Mhog > 36.7 kNm OK

58

Job No: BCB478 Jpae 7 of 25 A

Job Title Wind-moment Composite Frames

Roof Beam Design

The SteelConstructionInstitute LSilwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944 Client

CALCULATION SHEET

SCI Made by JSH Date Nov. 99

Checked by AW Dote Dec. 99

Serviceability limit state

Design load for SLS: T = 27 kN Sheet 1

Deflection of simply supported beam:

2Ta (3L2 - 4a2) Lômid

=48 El where a =

for unpropped construction with partial shear connection

o = O+0.3(1-NJN)(O5-O) Ref.3Cl. 6.1.4

where: 4 deflection of uncracked composite section4 = deflection of steel section acting alone

E = 205 kN/mm2 Ref. 2'steel = 1604 x lit mm4 Ref. 18tcompo = 5238 x 10 mm4 Ref. 3

— 2x27x3x1113[3(9xllt)2-4(3xHJ3)21—

48x205x5238xHt

6.5mm

— 2x27x3xli'J3[3(9x1&3)2—4(3xHJ)2]—

48x205x1604xHfr

= 21.25mm

Deflection at mid-span:

0 = ô +(i _) (21.25 -6.5) 7.36mm

= span span OK1223 360

Use 356 x 171 x 57 UB composite beam

59

The SteelConstructionInstitute

Job No: BCB478 Page8 of 25 A

Job Title Wind-moment Composite Frames

Subject Floor Beam DesignSilwood Park, Ascot, Berks SL5 7QNTelephone: 101344) 623345Fax: (01344) 622944

CALCULATION SHEET

Client SCI

Made

by

Checked by

JSH

AW

Date

Date

Nov.

Dec.

99

99

D.5.2 Floor beam design

T

k 3m+<

3m>k

3m

k L

0.9TL 0.9x342x9M = = ______3 3

Hogging moment:

M

Shear:

Slab depth

Metal decking

= 140mm

60

= 103 kNm

= 513kN Sheet 1

Figure D. 7 Floor beam

Ultimate Limit State

Dead and Imposed Loading

(T = point loads from transverse beam)

Design load for ULS: T = 1.4 x 90 + 1.6 x 135 = 342 kN

Moment:Take end restraint moments due to gravity load equal to 10% of the maximumsagging moment of a simply supported beam

Sagging moment:

923 kNm

Sheet 1

Section 4.1.2

—0.1 TL

— 0.1 x 342 x 9—

3—

3

F, = (1.4 x 5.00 + 1.6 x 7.50) x 6 x 9/2

Try 457 x 191 UB 98 Grade S355

= 1 mm gauge, 50 mm deep, trapezoidal profile

The SteelConstructionInstitute

Job No: BCB478 9 of 25 JRev A

Job Title Wind-moment Composite Frames

Subject Floor Beam DesignSilwood Park, Ascot, Berks SL5Telephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

7QN

Client SCI by JSH Date Nov. 99

MadeChecked by AW Date Dec. 99

Shear studs = 19 mm qS, 95 mm high 150 mm c/c

Longitudinal rebar = T16@ 150 mm

Transverse rebar = T12 200 mm

Concrete = C30 lightweight concrete

The composite beam is designed using BS 5950-3: Section 3.1: 1990, and is Ref. 3classified as a Class 1 plastic section. Ref. 18

Section sagging moment capacity, M = 1211 kNm Ref. 3

Reduced composite beam sagging capacity:

0.9 M = 1090 kNm > 923 kNm OK

Beam hogging moment capacity, based on steel section alone:

Mhog= 770 kNm > 103 kNm OK Ref. 18

Shear check: P,, = 0.6p,, A = 1100 kN> 513 kN OK Ref. 18

Dead load vlus wind loadin

Maximum floor beam end moments due to wind = 24.8 kNm Sheet 3

Maximum hogging moment = 1.4(

0.1 x ;o x 9+

24.8)= 72.5 kNm

Sheet 1

Hence, wind load does not cause sagging moments at beam ends

and Mhog > 72.5 kNm OK

Dead load plus imposed load plus wind loadinR

Maximum floor beam end moments due to wind = 24.8 kNm Sheet 3

(0.1 x (90 + 135) x 9 Sheet 1Maximum hogging moment = 1.2,, 3

+

24.8)

= 111 kNm

Hence, wind load does not cause sagging moments at beam end

61

Sheet 1

Table D.4

Table D. 1

The SteelConstructionInstitute

Job No: BCB478IPage

10 of 25 A

Job Title Wind-moment Composite Frames

Subject Floor Beam DesignSilwood Park, Ascot, Berks SL5Telephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

7QN

Client SCI Made by JSH Date Nov. 99

Checked by AW Date Dec. 99

and Mhog > 111 kNm

Serviceability limit state

Design load for SLS: T 135 kN

Deflection checked for unfactored imposed load (similar to Sheet 7)

Use 457 x 191 x 98 UB composite beam

D. 6 COLUMN LOADS

Data for calculation of column moments are given in Table D. 6.

Table D. 6 Data for calculation of column moments

OK

OK

Sheet 1

Storey

Beam reactions(kN)

10% restraintMoment (kNin)

Moments due to horizontal loads (kNm)

Dead(kN)

imposed(kN)

Dead(kNm)

imposed(kNm)

Notional loads Wind loads

External(kNm)

internal(kNm)

External(kNm)

internal(kNm)

3 90 135 27 40.5 6.3 12.6 5.5 10.9

1 90 135 27 40.5 19.6 39.4 16 32.1

N.B. All values are UNFACTORED, except for moments due to notionalhorizontal loads

The values for the 10% restraint moment are calculated from the unfactoredfloor loads

Dead 0.1 x 90 x 9 /3 = 27.0 kNm

Imposed = 0.1 x 135 x 9 /3 = 40.5 kNm

62

The SteelConstructionInstitute

Job No: BCB478 Pae 11 of 25 A

Job Title Wind-moment Composite Frames

Subject Internal ColumnsSilwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Client SCI lM by JSH Date Nov. 99

by AW Date Dec. 99

D. 7 INTERNAL COLUMNS

The columns will be spliced above the second storey floor beams, where achange in section size may take place. Therefore, design calculations will berequired for storeys 3 and 1.

Table D. 7 Loading on internal columns

Storey

Loading (kN) S ofcol.(kN)

Total load (kN) Reductionin imposedload (kN)

Reducedimposed

load (kN)Dead ImposedDea L.......J DeadImposed I I Imposed

101.3-- II 40.53 206

81

10%

081

135.0I—H 202.5 486

Ib0°'

49437

2 135.0°F—I 202.5

7's'

891

120%

178713

135.0202.5 I—H 202.5

6 1030

1296

130%

389

907

N.B. Values are UNFACTORED

The reduction in imposed load for the number of storeys carried is given byBS 6399-1: Table 2.

D. 7.1 Storey 3

Dead load plus imposed load plus notional horizontal forces

Design load at ULS: F = 1.4 x 479 + 1.6 x 437 = 1370 kN

Design moment at ULS: M = 12.6 kNm Table D. 6

Moments due to eccentric reactions and the 10% restraint moment balance andproduce no net moment about the major axis.

Storey height = 3.5 m

LEY= 1.OL = 3.5 m, LEX = 1.5L = 5.25 m Section 4.3.1

Try 203 x 203 UC 60 S355 (Grade 50)

63

The SteelConstructionInstitute

y' Job No: BCB478IPage

12 of 25 A

Job Title Wind-moment Composite Frames.

Subject Internal ColumnsSilwood Park, Ascot, Berks SL5Telephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

7QN

Client SCI Made by JSH Date Nov. 99

Checked by AW Date Dec. 99

Section is Class 1 plastic Ref. 18

At LEY= 3.5 m, P = 1720 kN> 1370 kN OK Ref. 18

At Lex = 5.25m, P = 2105 kN> 1370 kN OK Ref. 18

At L = 3.5m, MbS = 226 kNm > 12.6 kNm OK Ref. 18

Overall buckling stability check:

F M 1370 12.6 Section 4.3.5+

M,=

1720= 0.85 < 1.0 OK

Dead load plus imposed load plus wind loadinif

Design load at ULS: F = 1.2 x (479 + 437) = 1099 kN Table D. 7

Design moment at ULS: M = 1.2 x 10.9 = 13 kNm Table D.6

1099 13 Section 4.3.5Overall buckling check:

1720+ = 0.70 < 1.0 OK

Dead load plus wind loadin'

Design load at ULS: F = 1.4 x 479 = 671 kN Table D. 7

Design moment at ULS: M = 1.4 x 10.9 = 15 kNm Table D.6

671 15 Section 4.3.5Overall buckling check:

1720+ = 0.46 < 1.0 OK

Pattern Loadinv Dead load plus imposed load plus notional horizontal forces

Design loada.t ULS: F = 1.4 x 479 + 1.6 (0.5 x 437) = 1021 kN Table D. 7

Design moment for ULS: M = 12.6 + 1.6 x 40.5 = 77kNm Table D.6

1021 77 Section 4.3.5Overall buckling check:

1720= 0.93 < 1.0 OK

Use 203 x 203 UC 60 S355 (Grade 50) for internal 3rd and 4" store y columns

64

Design load at ULS:

Design moment at ULS: M1

Storey height = 4.5 m

L = 1. OL = 4.5 m, LEX

Try 254 x 254 UC 132 S355 (Grade

FOverall buckling check: -

Design load at ULS:

Design moment for ULS:

Overall buckling check:

Dead load plus wind loadinf

Design load at ULS:

Design moment at ULS:

Overall buckling check:

= 1.5L = 6.75m

50)

Table D. 7

Table D. 6

Section 4.3.1

Ref. 18

Ref. 18

Ref. 18

Ref. 18

Section 4.3.5

Table D. 7

Table D. 6

Section 4.3.5

Table D. 7

Table D. 6

Section 4.3.5

The SteelConstructionInstitute

Job No: BCB478IPage

13 of 25 A

Job Title Wind-moment Composite Frames

Subject Internal ColumnsSilwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Client SCI IM by JSH

by AW

Date

Date

Nov.

Dec.

99

99

D.7.2 Storey 1

Dead load plus imposed load plus notional horizontal forces

= 1.4x1030+L6x907= 2893kN

= 39.3 kNm

Section is Class

At LEY =

At LEX =

At L =

1 Plastic

4. Sm,

6. 75m,

4. Sm,

'cy

PCI

MbS

M+

= 3715 kN> 2893 kN OK

= 4540 kN> 2893 kN OK

= 627 kNm > 39.3 kNm OK

2893 39.3= ____ + -- = 0.84 < 1.0 OK

Dead load plus imposed load olus wind loadinR

M1=

23243715

= 1.2(1030+907)

1.2 x 32.1

38.5+— =0.69<1.0627

= 2324 kN

= 38.5 kNm

= 1442 kN

= 44.9kNm

= 1.4 x 1030

M1 = 1.4 x 32.1

1442 44.9+— =0.46<1.03715 627

OK

OK

By inspection, pattern loading is not critical

Use 254 x 254 UC 132 (S355) for internal jSI and 2nd storey columns

65

The SteelConstructionInstitute

Job No: BCB478 Page14 of 25 A

Job Title Wind-moment Composite Frame

Subject External Column DesignSilwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Client SCI

Made

by

Checked by

JSH

AW

Date

Date

Nov.

Dec.

99

99

Storey

Loading (kN)S ofCol.(kN)

Total load (kN)

Dead Imposed

Reduction inimposed load

(kN)

Reducedimposed

load (kN)Dead

IjI Imposed

4I

l—l 13I

3 104

41

0%

041

3I

l—II

3 242

243

10%

24219

2I

I

5 382

446

20%

89"'

'1 F—H135.0202.5

I

6 523

648

30%

194

454

N.B. Values are UNFACTORED

D.8.1 Storey 3

Dead load plus imposed load plus notional horizontal forces

= 689 kNDesign load for ULS: F = 1.4 x 242 + 1.6 x 219

Design moment for ULS: M

Assume section is 200 mm deep

Eccentricity moment (1.4 x 90 + 1.6 x 135) (0.1 + 0.1) = 68.4 kNm

10% restraint moment (1.4 x 27) + (1.6 x 40.5) 102. 6kNm

Sum of moments = 171 kNm

Divide moments equally between upper & lower column lengths = 85.5 kNm

Notional horizontal load induced moment = 6.3 kNm

D. 8 EXTERNAL COLUMN DESIGN

Table D.8 Loading on external columns

Table D.8

Table D.6

Table D.6

Section 4.3.3

Table D.6

66

Total design moment, M

Column length = 3.5 m

LEY= 1. OL = 3.5 m, LEX = 1. 5L = 5.25 m

Try 203 x 203 UC 60 S355 (Grade 50)

Section is Class 1 Plastic

At Ley = 3.5m,

At Lex = 5.25 m, P

At L = 3.5m, MbS

Overall buckling check:

F M 689 91.8+

M,,=

1720 226= 0.81 < 1.0 OK

Dead load plus imposed load plus wind loadin'

Design load at ULS: F = 1.2 (242 + 219 + 2.2)

Design moment for ULS: M

Eccentricity moment 1.2 (90 + 135) (0.1 + 0.1)

10% restraint moment 1.2 (27 + 40.5)

Sum of moments

Divide equally between upper and lower columns

Wind induced moment 1.2 x 5.5

Total design moment, M

Overall stability check 556 Z1 = 0.65 < 1.01720 226

= 54kNm

=8lkNm

= 135 kNm

= 67.5kNm

= 6.6kNm

= 74.1 kNm

The SteelConstructionInstitute

Job No: BCB478 fre 15 of 25 A

Job Title Wind-moment Composite FrameSubject External Column Design

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Client SCI

Made

by

Checked by

JSH

AW

Date

Date

Nov.

Dec.

99

99

= 91.8 kNm

= 1720kN> 689kN

= 2105 kN> 689 kN

= 226 kNm > 91.8 kNm

OK

OK

OK

= 556 kN

Section 4.3.1

Ref. 18

Ref. 18

Ref. 18

Section 4.3.5

Table D.8Table D.2

Table D. 6

Table D. 6

Table D.6

Section 4.3.5OK

67

Dead load plus wind loadinci

By inspection, not critical (stability factor = 0.37)

Use 203 x 203 UC 60 S355 for external 3Mand 4" store y columns

D.8.2 Storey 1

Dead load plus imposed load plus notional horizontal forces

Design load for ULS: F = 1.4 x 523 + 1.6 x 454 = 1459 kN

Design moment for ULS: M

Assume section is 200 mm deep

Eccentricity moment (1.4 x

10% restraint moment (1.4 x

Sum of moments

Conservatively consider moment to be divided equallybetween upper and lower column lengths

Notional horizontal load induced moment

Total design moment, M

Column length = 4.5 m

LEY= 1. OL = 4.5 m, Lex = 1.5 L

Try 254 x 254 UC 89 S355 (Grade 50)

Section is Class 1 Plastic

At LEY= 4.5 m, = 2455 kN > 1459 kN OK

At LEX= 6.75 m, P = 3005 kN > 1459 kN OK

At L = 4.5 m, MbS = 408 kNm > 105 kNm OK

The SteelConstructionInstitute

Job No: BCB478 frae 16 of 25 A

Job Title Wind-moment Composite Frame

Subject External Column DesignSilwood Park, Ascot, Berks SL5Telephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

7QN

Client SCI

Made

by JSH

Checked by AW

Date

Date

Nov.

Dec.

99

99

90 + 1.6 x 135) (0.1 + 0.1)

27) + (1.6 x 40.5)

Table D.8

Table D. 6

Table D.6

Section 4.3.3

Table D. 6

= 68.4 kNm

= 102.6kNm

= 171 kNm

= 85.5 kNm

= 19.6 kNm

= 105 kNm

= 6.75m

68

= 1185 kN

= 54 kNm Table D. 6

= 81 kNm Table D. 6

= 135 kNm

= 67.5 kNm

= l9kNm

= 86.5 kNm

OK

Dead load plus wind loadin

By inspection, not critical (stability factor = 0.44)

Use 254 x 254 UC 89 S355 for external Pt and 2ndstorey columns

69

The SteelConstructionInstitute

Job No: BCB478 Pae 17 of 25 A

Job Title Wind-moment Composite Frame

Subject External Column DesignSllwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Client SCI IMade by JSH

Checked by AW

Date

Date

Nov.

Dec.

99

99

= 0.85 < 1.0 OK Section 4.3.5

Overall buckling check:

F M 1459 105

—p:

=2455

Dead load vius imposed load plus wind loadinR

Design load for ULS: F = 1.2 (523 + 454 + 10.9)

Design moment for ULS: M

Eccentricity moment

10% restraint moment

Sum of moments

Divide equally between

Wind induced moment

Total design moment

1.2 (90 + 135) (0.1 + 0.1)

1.2 (2.7 + 40.5)

upper and lower columns

1.2 x 16

1185 86.5Overall stability check = 0.69 < 1.0

2455 408

Table D. 6

Section 4.3.5

The SteelConstructionInstitute L

b No: BCB478 fr 18 of 25 Rev A

Job Title Wind-moment Composite Frame

Connection LoadsSilwood Park, Ascot, Berks SL5 7QNJTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Client SCI Made by JSH Date Nov. 99

Checked by AW Date Dec. 99

D.9 CONNECTION

D.9.1 Connection loading

Calculations are given for connections at l floor level only, as an example ofhow the design should be carried out.

Dead load plus imposed load plus notional horizontal forces

Maximum hogging moment: Table D.5(moment from 10% beam restraint Table D.6and notional horizontal forces)

Minimum hogging moment: Table D.5(moment from 10% beam restraint Table D. 6and notional horizontal forces)

Table D. 6Design shear at ULS: Table D.5

(Shear from beam reactionsand notional horizontal forces)

Dead load plus imposed load plus wind loading

Maximum hogging moment: Table D. 6(moment from 10% beam restraint Table D.3and wind loading)

Minimum hogging moment: Table D. 6(moment from 10% beam restraint Table D.3and wind loading)

Table D.6Design shear for ULS: Table D.3

(shear from beam reactionsand wind loading)

Dead load plus wind loading

Maximum hogging moment:(moment from 10% beam restraintand wind loading)

Minimum hogging moment:(moment from 10% beam restraintand wind loading)

= (1.4x27)+(1.6x40.5)+30.4

= 133 kNm

= (1.4 x 27) + (1.6 x 40.5) - 30.4

= 72kNm

30.4F =(1.4x90)+(1.6x135)+—j—5--

= 349kN

= 1.2 (27 + 40.5 + 24.8)

= 111 kNm

= 1.2 (27 + 40.5 - 24.8)

= 51 kNm

24.8F = 1.2 (90 + 135 +

= 277kN

= 1.4 (27 + 24.8)

= 73kNm

= 1.4 (27-24.8)

= 3.1 kNm

Table D. 6Table D.3

Table D.6Table D.3

70

The SteelConstructionInstitute

Job No: BCB478 frae 19 of 25 A

Job Title Wind-moment Composite Frame.

Subject .Connection Loads

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Client SCI Made by JSH Date Nov. 99

Checked by AW Date Dec. 99

The connection does not go into sagging when wind direction reverses.Therefore, the connection should be designed for the largest hogging momentof 133 kNm, nominal sagging resistance will suffice (see Section 4.4.1).

Design 1st floor connections for M = 133 kNm

and F = 349 kN

Check rebar area for greatest difference between maximum and minimumhogging moment = 73 - 3.1 69 kNm

D.9.2 Connection design

Internal Connection

Beam size 457 x 191 UB 98 Sheet 10

Try connection with rebar Option A (4 No 160 bars) and 1 row of M20 8.8 Appendix Cbolts, 200 x 12 S275 end plate from page C2.

Connection is not acceptable with S355 beam.

Therefore, try rebar Option B (6 No 16b bars)

Moment capacity (beam side) = 362 kNm > 133 kNm OK Appendix C

Vertical shear capacity (with shear row) = 442 kN> 349 kN OK Appendix C

Note that from page C2 bars will need to be X16, specified to be able to achievea strain at maximum load of at least 10%.

Check that rebar area satisfies upper limit:

Area = 1210 mm2

Limit AL = 1.5bdJ'4if, Section B.2.2

With = 1 -Mlow/Mhigh

= 1 - (362 - 69)1362 = 0.19

So AL =1.5x256x90x30/0.19x460 =11863mm2 OK

Column = 254 x 254 UC 132 (S355) Sheet 13

From tables: Column does not require compression stiffening OK

Panel shear capacity = 892 kN — Appendix C

71

The SteelConstructionInstitute

Job No: BCB478 Pae 20 of 25 A

Job Title Wind-moment Composite Frame

Subject Connection LoadsSilwood Park, Ascot, Berks SL5Telephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

7QN

Client SCI

Made

by

Checked by

JSH

AW

Date

Date

Nov.

Dec.

99

99

As there are no sagging moments at the connections, conservatively assume that

Panel shear = + Fi,,je = 529 + 208 = 737 kN < 892 kN OK Appendix C

Use rebar Option B and 1 row of M20 8.8 bolts and 200 x 12 S275 end plate

External connection

Column = 254 x 254 UC 89 (S355) Sheet 17

There is no rebar anchorage around column therefore the connection must bedesigned as a bare steel wind-moment connection

Try connection with 2 rows of M20 8.8 bolts, 200 x 12 (S275) extended endplate

Moment capacity (beam side) = 141 kNm > 133 kNm OK Ref. 1

Vertical shear capacity (no shear row) = 515 kN> 349 kN OK Ref. 1

Column does not require compression stiffening

Panel shear capacity = 566 kN

Panel shear = )' F,,011 = 124 + 208 = 332 kN < 566 kN OK

Use 2 rows of M20 8.8 bolts, 200 x 12 (S275) extended end plate

(3rd floor and roof connections should be designed in the same manner.)

72

The SteelConstructionInstitute

Job No: BCB478 Pae 21 of 25 A

Job Title Wind-moment Composite Frames

Subject Serviceability Limit StateSilwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Client SCJ IMade by

Checked by

JSH

AW

Date

Date

Nov.

Dec.

99

99

D. 10 SERVICEABILITY LIMIT STATE - SWAY DUE TO WIND

Sway deflections can be calculated using any recognised method. The methodused in the design example is a simplified procedure developed by Wood andRoberts (201

The actual frame is replaced by a substitute beam-column frame. The basis ofthe substitute frame is that:

(i) For horizontal loading on the actual frame, the rotations of alljoints atany one level are approximately equal, and

(ii) Each beam restrains a column at both ends.

The total stiffness K,, of a beam in the substitute frame is obtained from asummation over oil the beams in the actual frame at the level being considered.

The total stiffness K of a column in the substitute frame is obtained by asummation over all the columns in the actual frame at the level beingconsidered.

In the simplified method of Wood and Roberts, the sway of a storey is dependentpartly on stiffness distribution coefficients calculated for the substitute frame.

To allow for continuity of columns in a multi-storey structure, it is recognisedthat each floor beam restrains column lengths above and below its own level.This is reflected in the form of the distribution coefficients.

The stiffness distribution coefficients enable a non-dimensional sway index q'to be determined from the chart given below (Figure B.11). By definition:

Nh=Fh/(12EK)

whereNh is the sway angle of the storey being consideredF is the total wind shear on the column of the substitute frameE is Young's modulus of elasticity (205 kN/mm2)

Values of k and k,, for use with Figure D.8 are defined and calculated inTable D.11.

73

The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Hinged 1.0

1 .0Hinged

Figure D. 8 Sway index qS

Figure D.9

Members:

Frame model for serviceability limit state calculations

356 x 171 UB 57 + 140 slab457 x 191 UB 98 + 140 slab

203 x 203 UC 60

Job No: BCB478

Job Title

Subject

Pae 22 of 25

Wind-moment Composite Frames

Serviceability Limit State

Date Nov. 99

Date Dec. 99

0.8

k0.6

0.4

0.2

Fixed 00

Fixed0.2 0.4 0.6 0.8

kb

Bi Bi Bi

B2

B2

B2 C2

Bi

C3

C3

C4

C4

B2

B2

B2 C2

B2

B2

82 C2

B2 C3

B2 C3

B2 C4

C2 C2

-*-K04 3•5-*- -Kc3 3•5

-Kc2 3•5- ___4.5

Substitute frame

C2 C4

BiB2

Cl

74

The SteelConstructionInstitute

C2 = 254 x 254 UC 132C3 = 203x203UC60C4 = 254x254UC89

Equivalent beam stiffness

________ ==9Ij+2IgI

7•5IgI, ='eq

=9I+2IgI

Stiffness calculations for substitute frame

Table D.9 Beam stiffness

Storey 4 (cm4) Lfr (cm) Kb = 3 L' I1/Lfr Kb(cmi)

4 30669 900 3 x 4 x 30669/900 408.9

3 68310 900 3 x 4 x 68310/900 910.8

2 68310 900 3 x 4 x 68310/900 910.8

1 68310 900 3 x 4 x 68310/900 910.8

Table D.10 Column stiffness

Storey 'b (cm4) Lb (cm) h (cm) Kb = 3 )JIb/Lb Kb(cm3)

4 6125 6125 350 5 x 6125/350 87.5

3 6125 6125 350 5 x 6125/350 87.5

2 14270 22530 350 (2 x 14270+3 x 22530)/350 274.7

1 14270 22530 450 (2 x 14270 + 3 x 22530) /450 213.6

75

No: BCB478 IPage 23 of 25 IR A

Job Title Wind-moment Composite Frames)Ject Serviceability Limit State

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Client SCI Made by JSH Date Nov. 99

Checked by AW Date Dec. 99

Roof Beam: I = 49927 cm4 I = 31113 cm4(values calculated using method give in Ref. 3, Appendix B, B.3)

7.5x49927x311132

Floor Beam:

9 x31113 +2(49927x31113)

110424 cm4

7.5x110424x706972

Ref 3

Section 5.2.2

Ref 3

Section 5.2.2

= 30669 cm4

I = 70697 cm4

68310 cm49 x 706972+2(110424x 70697)

The SteelConstructionInstitute

Job No: BCB478 frae 24 of 25 Rev A

Job Title Wind-moment Composite Frames

Subject Serviceability Limit StateSilwood Park, Ascot, Berks SL5Telephone: 101344) 623345Fax: 101344) 622944

CALCULATION SHEET

7QN

Client SC!

Made

by

Checked by

JSH

AW

Date

Date

Nov.

Dec.

99

99

Stiffness distribution coefficients

Table D.11 Joint stiffness coefficients

Sway defiections

Table D.12 Sway deflections for a rigid frame

TOTAL

76

1/2142 7

Where: K,,K1

Ic,Kbb

is the stiffness of the column above the storeyis the stiffness of the column below the storeyis the stiffness of the beam above the storeyis the stiffness of the beam below the storey

Storey K, Kb F(kN)1 Fhb— =h I2EK,

i—h

j(mm)

4 0.18 0.16 1.31 10(lOx 350 x 1.31)

(12 x 20500 x 87.5)1/4694 0.7

3 0.16 0.28 1.44 25(25x350x1.44)

(12x20500x87.5)1/1 708 2

2 0.28 0.35 1.71 40 (40x350x1.71)(12x20500x274.7)

35800 1.2

1 0.35 0 1.35 57(57x450x 1.35)

(12 x20500x213.6)1/1517 3

Job No: BCB478 frae 25 of 25 A

ConstructionInstitute

Job Title Wind-moment Composite Frames

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Serviceabilily Limit State

Client SCI Made by JSH Date Nov. 99

Checked by AW Date Dec. 99

The Steel

Allowance for connection flexibility

The deflections calculated treating the frame as rigid-jointed are increased thesway amplification factor to make an appropriate allowance for connectionflexibility (see Section 5.2.3)

Sway amplification factor for frame with non-composite external connections=1.6

Storey Rigid framezi (mm)

Wind-moment frame1.6 (mm)

Wind-rn oment frame1. 6J/h (mm)

LIMIT Check

4 0.7 1.1 1/3182 1/300 OK

3 2 3.2 1/1 094 1/300 OK

2 1.2 1.9 1/1 842 1/300 OK

1 3 4.8 1/938 1/300 OK

Total 7 [ 11 1/1364[ 1/300 OK

Table D. 13 Sway deflections allowing for connection flexibility

Section 5.2.3Table 3

Table D.12

Section 5.2.4

Frame design is acceptable for wind deflections under SLS loading.

77

Typeset and page make-up by The Steel Construction Institute, Ascot, Berks. SL5 7QNPrinted and bound by Alden Press, Osney Mead, Oxford, 0X2 OEF1 500 - 6/00 (BCB478)

Sd P264

Wind-moment Designof Unbraced Composite Frames