Steel–concrete compositebridges

David Collings

Published by Thomas Telford Publishing, Thomas Telford Ltd,1 Heron Quay, London E14 4JD.www.thomastelford.com

Distributors for Thomas Telford books areUSA: ASCE Press, 1801 Alexander Bell Drive, Reston, VA 20191-4400, USAJapan: Maruzen Co. Ltd, Book Department, 3–10 Nihonbashi 2-chome,Chuo-ku, Tokyo 103Australia: DA Books and Journals, 648 Whitehorse Road, Mitcham 3132,Victoria

First published 2005

Figures 5.2, 10.10, 11.2 courtesy of BenaimFigure 10.9 courtesy of T HamblyFigures 5.4, 5.5 courtesy of Amec Group LtdFigure 10.12 courtesy of Arup.

A catalogue record for this book is available from the British Library

ISBN: 0 7277 3342 7

# Thomas Telford Limited 2005

All rights, including translation, reserved. Except as permitted by the Copyright, Designs andPatents Act 1988, no part of this publication may be reproduced, stored in a retrieval systemor transmitted in any form or by any means, electronic, mechanical, photocopying or otherwise,without the prior written permission of the Publishing Director, Thomas Telford Publishing,Thomas Telford Ltd, 1 Heron Quay, London E14 4JD.

This book is published on the understanding that the author is solely responsible for the state-ments made and opinions expressed in it and that its publication does not necessarily implythat such statements and/or opinions are or reflect the views or opinions of the publishers.While every effort has been made to ensure that the statements made and the opinions expressedin this publication provide a safe and accurate guide, no liability or responsibility can be acceptedin this respect by the author or publishers.

Typeset by Academic þ Technical, BristolPrinted and bound in Great Britain by MPG Books, Bodmin

Dedication

For my father

iii

Contents

Foreword ix

Acknowledgements x

Notation xi

1. General concepts 1

Introduction 1Structural forms 1Materials 2Codes 2Concrete 3Steel 6Composite action 11Shear connectors 13

2. Simple beam bridges 16

Introduction 16Initial sizing 16Example 2.1 16Initial design of girder 20Bracing of the steelwork 20Initial design of the concrete slab 25Initial shear connector design 26Safety through design 26Environmental issues 27

3. Integral bridges 29

Introduction 29Soil–structure interaction 30Example 3.1 31Weathering steel 34Compact sections 38Portal frame structures 38Example 3.2 38Effects of skew 40Example 3.3 41

v

Painting 42Shrinkage 44Differential temperature 44

4. Continuous bridges 46

Introduction 46Motorway widening 47Moment–shear interaction 49Example 4.1 50Moment rounding 51Cracking of concrete 53Bearing stiffeners 55Precamber 55Natural frequency 57Through-girder bridges 58Example 4.2 60Shear lag 61Fatigue 63

5. Viaducts 66

Introduction 66Concept design 66Example 5.1 68Articulation 69Construction methods 71Deck slab 74

6. Haunches and double composite action 78

Introduction 78Haunches 78Longitudinal shear at changes of section 79Double composite action 80Example 6.1 80Slender webs 81Lightweight concrete 83

7. Box girders 85

Introduction 85Behaviour of boxes 85Diaphragms 87Example 7.1 88Example 7.2 92Noise from bridges 93Shear connectors for composite boxes 94Composite plates 95Example 7.3 97

vi

8. Trusses 98

Introduction 98Example 8.1 99Member type 101Steel sections under axial load 101Joints in steelwork 102Example 8.2 103Enclosure 104Local loading of webs 107Continuous trusses 109High-strength steel 110

9. Arches 111

Introduction 111Example 9.1 112Composite compression members 114Example 9.2 117Fabrication of curved sections 118Nodes in tubular structures 118Aesthetics 120Tied arches 122Example 9.3 123Arch buckling 124

10. Cable-stayed bridges 129

Introduction 129Deck–stay connection 130Example 10.1 131High-strength concrete 131Buckling interaction 137Shear connection 138Towers 139Tower top 140Example 10.2 141Stainless steel 142Strain-limited composite section 143

11. Prestressed steel–concrete composite bridges 145

Introduction 145Displacement of supports 145Prestress using tendons 146Design of prestressed composite structures 147Prestress losses 148Example 11.1 149Durability 151Prestressed composite box girders 151Corrugated webs 151Example 11.2 152Extra-dosed bridges 153

vii

12. Assessment of composite bridges 155

Introduction 155History 155Structure types 157Inspection 157Loads 157Materials 159Testing of the shear connection 160Analysis 160Incidental and partial composite action 161Cased beams 161Strengthening 162Life-cycle considerations 162

Appendix A: Approximate methods 164

Appendix B: Calculation of section properties 165

Section properties for steel sections 165Section properties for steel–concrete composite sections 165Section properties for cracked steel–concrete composite sections withreinforcement 166

Appendix C: Section properties for examples 167

Appendix D: Plastic section properties for steel–concrete composite

sections 168

Appendix E: Torsional properties for steel–concrete composite

sections 170

Appendix F: Moment–axial load interaction for compact

steel–concrete composite sections 171

References 172

Index 177

viii

Foreword

The bridge crossing it, with its numberless short spans and lack of bigness, beauty andromance he gazed upon in instant distain. It appeared to creep, cringing and apologetic,across the wide waters which felt the humiliation of its presence . . . Yet he received ashock of elation as the train had moved slowly along the bridge, carrying him with it, andhe gazed downward upon flowing waters, again he marvelled at what men could do; at thepower of men to build; to build a bridge so strong . . . [1].

I see this book as a journey. A journey of experience from the first simple rivercrossing to the more complex suspended spans of the early twenty-first century.A journey across the world from the bleak post-industrial landscapes that are stillscattered across Britain, around the broad untamed rivers of Bengal and into theracing development of South East Asia. But it is also a subjective journey, overand under the numberless spans of motorway bridges that are the ‘bread andbutter’ of many bridge designers, through to the countless bridges that performtheir task with pride, and always marvelling at how we build so strong, alwaysquestioning.This book has its origins in the composite bridge chapter of the Manual of Bridge

Engineering [139]. This book expands upon that chapter and provides details of moresteel–concrete composite bridges. It is intended to show how composite bridgesmay be designed simply from basic concepts without the need for a clause-by-clause checking of codes and standards. All chapters use examples of variousbridges to illustrate the design and construction methods. The book looks impar-tially at this construction form and compares composite bridges with other types,and often places limits on their use. The book is intended for a number ofreaders, first those who use the Manual of Bridge Engineering and wish to find moredetail on steel–concrete composite bridges. Second, it is for those engaged indesign who require a deeper understanding of the methods used as well as howthey are verified against design codes. The book aims to show how to choose thebridge form, and design element sizes to enable drawings to be produced. Thebook covers a wide range of examples, in all of which the author has had aninvolvement or interest.

ix

Acknowledgements

Many of the examples and photographs are derived from work carried out atBenaim, and the support of the staff and directors is gratefully acknowledged.Particular thanks go to Rup Shandu for his help with drafting some of the morecomplex figures and to Robert Henderson for patiently reading the drafts of eachchapter.I would like to thank John Bowes and Phil Girling for the aerial views of the

Doncaster Viaduct and Brian Bell for the photographs of the Irish bridges, notall of which were used in the final version. I am also indebted to Naeem Hussainand Steve Kite of Arup for the information on the Stonecutters Bridge tower,and to Sally Sunderland for the information on Brunel’s Paddington Bridge.

x

Notation

A areaAa steel areaAac composite sectionAc concrete areaAs reinforcing steel areaB widthD depth of girder, rigidityE Young’s modulusEa steel modulus of elasticityEc concrete modulus of elasticityEc0 long-term concrete modulusF force or loadFF force on fixed bearingsG permanent load, shear modulusH heightI second moment of areaJ torsional constantJm mass moment of inertiaK stiffness of member, soil pressure coefficientL length of beam or slabLe effective lengthM momentMD design resistance momentMf design resistance moment of flangesMu ultimate momentM0 reduction of momentN axial loadND design resistance loadNo number of connectorsNpk chord plastification-k jointNpx chord plastification-x jointNu ultimate axial resistanceNul squash loadP load on single connector, bolt capacity, wind susceptibility factorPi initial prestressPo prestress force after lossesPu resistance of a connectorPUL resistance of a connector in lightweight concrete

xi

Q variable loadQl longitudinal shearR reactionS Strouhal numberT torsion, tension, periodV shear force, wind speedVarch punching shear resistanceVcf critical wind speed-flutterVcv critical wind speed-vortex sheddingVD design shear resistanceVw design shear resistance of web onlyW loadZ section modulusZb bottom flange modulusZc modulus of concrete elementZt top flange modulus

a web panel lengthb width of sectiond depthe eccentricityf stress, frequencyfck concrete cylinder strengthfcu concrete cube strengthfu ultimate tensile strengthfy yield strengthg gaph height of sectioni integerk coefficient, constantm mass per length unitmf relative flange stiffnessn modular ratior radius of gyration, radiussb spacing of reinforcing barstf flange thicknesstw web thicknessv shear stressx distance along membery distancez lever arm

� axial contribution factor, prestress loss�fl partial load factor�fm partial material factor�f3 partial factor (BS 5400)� deflection, settlement" strain� angle� slenderness parameter

xii

� creep function’ dynamic increment

Subscriptsa steela–c steel–concrete compositeb bottomc concretecr critical bucklingc–s steel–concrete composite, cracked sectiondes destabilisingf flangei integerm momentmax maximummin minimums reinforcing steelt topu ultimateua ultimate strength of steel shear connectorv shearw weby yieldC compressionDW distortional warpingN axial effectsT tensionTW torsional warping0,1,2 general number, construction stage

xiii

Steel–concrete compositebridges

David Collings

Published by Thomas Telford Publishing, Thomas Telford Ltd,1 Heron Quay, London E14 4JD.www.thomastelford.com

Distributors for Thomas Telford books areUSA: ASCE Press, 1801 Alexander Bell Drive, Reston, VA 20191-4400, USAJapan: Maruzen Co. Ltd, Book Department, 3–10 Nihonbashi 2-chome,Chuo-ku, Tokyo 103Australia: DA Books and Journals, 648 Whitehorse Road, Mitcham 3132,Victoria

First published 2005

Figures 5.2, 10.10, 11.2 courtesy of BenaimFigure 10.9 courtesy of T HamblyFigures 5.4, 5.5 courtesy of Amec Group LtdFigure 10.12 courtesy of Arup.

A catalogue record for this book is available from the British Library

ISBN: 0 7277 3342 7

# Thomas Telford Limited 2005

All rights, including translation, reserved. Except as permitted by the Copyright, Designs andPatents Act 1988, no part of this publication may be reproduced, stored in a retrieval systemor transmitted in any form or by any means, electronic, mechanical, photocopying or otherwise,without the prior written permission of the Publishing Director, Thomas Telford Publishing,Thomas Telford Ltd, 1 Heron Quay, London E14 4JD.

This book is published on the understanding that the author is solely responsible for the state-ments made and opinions expressed in it and that its publication does not necessarily implythat such statements and/or opinions are or reflect the views or opinions of the publishers.While every effort has been made to ensure that the statements made and the opinions expressedin this publication provide a safe and accurate guide, no liability or responsibility can be acceptedin this respect by the author or publishers.

Typeset by Academic þ Technical, BristolPrinted and bound in Great Britain by MPG Books, Bodmin

Dedication

For my father

iii

Index

Page numbers for figures and illustrations are shown in italics. Bridges cited are in theUK unless otherwise stated.

A13 London bridge 152�153aesthetics

colours 43�44detail 122fashion 121political influences 120proportion 122scale 121�122visual unity 121

Ah Kai Sha Bridge (China) 149�150, 149analysis

cable-stayed bridges 142�143continuous bridges 50�51, 51grillagebeam and slab bridges 19, 19integral bridges 33�34, 33, 35through girder bridges 61, 61

approximation methods 164arched bridges

bucklinganalysis 125�127, 125loadings 124�125, 124

composite bowstring 123�124composite interaction curves 116,

116composite tubular arches 117compression members 114�116,

116constructionfalsework 113, 114sequences 113, 114

curved sections, fabrication 118forms 111, 111geometric ratios 112loadingsabnormal 112�113analysis 112�113, 117�118

stiffening 113, 113thrust 111�112tied 122�124, 123construction sequences 126intersections 127�128, 127

tubular nodesjoint capacities 119�120, 119, 120K joints 119, 119profiling 120X joints 119, 119

atmospheric corrosion, steel 42

bar connectors, capacity 14beam and slab bridges

analysis, grillage 19, 19construction, non-composite stage 20,

20girdersbracing 20�24, 21, 22, 24design 20, 22�23, 22flange stability 23maximum loading 20vertical stiffeners 24, 24web thickness 23�24

loadingsdead 18, 18, 19HA vehicular 18, 19HB vehicular 18, 19

risk mitigation 26�27shear connectors, numbers 26slabsdepths 18design parameters 25�26, 26HB vehicular loadings 25, 25

span–depth ratios 16, 17beams see girdersbearing stresses, truss bridges 108

177

bearingscontinuous bridges, stiffeners 55viaducts, expansion joints 69�71, 70

boltsHSFG, properties 103truss joints 102�103, 102, 105�106

box girder bridgesbracing, torsional analysis 97composite, shear connectors 94�95, 95composite plates

compression 95failure 95, 96longitudinal shear 95

curved interchange 96, 97connectors 97, 97effective shear 97loadings 97

history 85intermediate diaphragms 86

elimination of 91, 91stiffness requirements 87, 88types 87�88

longitudinal distortional warping86�87, 87

prestressed concrete 151, 152�153corrugated webs 151�152, 152

railway bridgesbending stresses 90deflection limits 92�93details 89finite element analysis 90�91high speed lines 92�93, 92loadings 88shear stresses 88�90skew crossings 92, 92weld details 90, 91

steel 85torsional distortion 85�86, 86uses 85

bridge designcodes of practice 2�3environmental issues

concrete substitutes 28energy use 27recycled steel 27�28

British Standards see codes of practicebuckling interaction coefficients, cable-

stayed bridges 137�138, 137

cable-stayed bridgesanalysis 142�143anchorages, forces 129�130, 129axial loadings 139back spans, concrete 130, 130

buckling interaction coefficients137�138, 137

cable load analysis 136cable-out scenarios 136construction, cantilever phase 138extra-dosed 153�154, 153loadings

dead 132highway 132wind 132�136, 133, 134, 142

stay-deck connections 130�131, 130towers

analysis 143�144, 144forms 139�140, 141, 141inclination 140, 140top anchorages 140�141, 141

channel connectors, capacity 14codes of practicebridge design 2�3, 16�17European 17

colours, aesthetics of 43�44composite actionscurves 116, 116interface connections 12modular ratio 11�12

composite bowstring arched bridges123�124

composite bridgesassessments 155

cased beams 161�162shear connections 160�161, 160, 161

definitions 1embedded joists 156�157, 156history 155�156inspections 157life cycles 162�163loadings

highway 157�158, 158railway 158�159, 159

slab formation 157span ranges 1�2, 2

composite structureseffective lengths 8, 8moment–axial load interaction 171plastic modulus 38plastic section properties 168�169,

168section properties 165�166torsional properties 170, 170

composites, definitions 1concretebending moments 5�6, 5corrosion, chloride contaminated water

151, 162

178

Index

crackingcauses 53�54hogging limits 54�55, 54

creep 5heat, reinforcement control 3�5high-strength 131�132tensile strength 131

lightweight 83�84modulus 3, 4propertiescompressive strength 2, 3tensile strength 3

shrinkage 44, 44strain curve 4, 5

strength, assessments 159strengthening 162stress–strain curves 3, 4substitutes 28

concrete boxes, prestressed, viaducts68�69, 68

concrete structures, moment rounding51�53, 52

connectorsbox girder bridges 97, 97capacity 14continuous bridges, fatigue stresses

64�65, 64number of 12shearflexible 13, 13rigid 14

shear planes 15, 15construction

beam and slab bridges 20, 20continuous bridges 55, 55tied arched bridges 126viaductsconnectors 82�83, 83crane erection 71�73, 72and piers 82slab launching 73�74

continuous bridgesanalysis 50�51, 51deflectionsconstruction phase 55, 56long-term 57predicting 56�57railway limits 55�56vibration frequency effects 58

fatigue stress, assessments 63�64frequencies, natural 57�58, 57hogging, limiting 54�55, 54loadings 50moment rounding 51�53, 52

motorway widening 47�49, 48piersbearing stiffeners 55steelwork bracing 52�53, 52

shear lag 61�63, 62slabs, pour sequences 56span–depth ratios 46through girder types 58�61, 59uses 46�47

continuous truss bridges 109, 109corrosion

concrete, chloride contaminated water151, 162

stainless steel 142steelatmospheric 42blast cleaning 43cladding resistance 104rates of 42submergence 42weathering 34

deflectionscontinuous bridgesconstruction phase 55, 56long-term 57predicting 56�57railway limits 55�56vibration frequency effects 58

limits, high-speed railway lines 92�93Doncaster North Viaduct 68�69, 68

bearing layout 70�71, 70construction 71�72, 72slab design 74

double composite piersflanges 81, 81loadings 80�81, 81stress build-up 82

environmental issuesaestheticscolour 43�44detail 122fashion 121proportion 122scale 121�122surroundings 120�121visual unity 121

bridge constructionconcrete substitutes 28energy use 27recycled steel 27�28

noise emissions 93�94, 94European codes of practice 17

179

Index

expansion jointsviaducts

bearings 69�71, 70uses 69

fatiguerailway bridges 11steel 11

fatigue stresscontinuous bridges

assessments 63�64connectors 64�65

flexible connectors, types 13, 13floods, steel, corrosion 42frequencies, continuous bridges, natural

57�58, 57

girdersbottom flange, stresses 34�35bracing

cross 21, 21ineffective 21, 21piers 52�53, 52plan 21, 21U-frame 21, 21

cased, assessments 161�162fabrication 9�10, 10

welding 10flange stability 23longitudinal-shear flow 35, 37, 37moment–shear interaction 49, 49vertical stiffeners 24, 24webs

shear capacity 49slenderness effect 81�82thickness 23�24

haunchingforms of 79, 79longitudinal shear 79�80viaducts, moments 78�79, 78

high-strength concrete 131�132tensile strength 131

high-strength steel 110welding 110

highway bridgescontinuous motorway 47, 47fatigue, assessments 64motorway widening 47�49, 48noise emissions 93�94, 94vehicular loadings

abnormal 112�113HA 18, 19, 132, 132, 158HB 18, 19, 25�26, 25

Himi Bridge (Japan) 153hogging, limiting 54�55, 54hoop connectors, capacity 14HSFG bolts, properties 103

inspections, composite bridges 157integral bridgessee also semi-integral bridgesanalysis, grillage 33�34, 33, 35deck slabs, shrinkage 44, 44definitions 29girders

bottom flange stresses 34�35longitudinal-shear flow 35, 37,

37portal structures

design 29, 29, 38, 38skew effects 40, 40, 41�42, 41soil loadings 39, 39

reinforcement, details 37, 37soil pressure coefficients 30�31,

30soil–structure interactions 30�31uses of 29

jointsbolted 102�103, 102, 105�106tubular nodes

capacities 119�120, 119, 120K 119, 119profiling 120X 119, 119

welded 102

Kuala Lumpur highway intersection 96,97

launch sequencestruss bridges 106, 107

patch loadings 107�108, 108viaducts, slabs 73�74, 74

limit statesserviceablity 3, 11�12ultimate 3

longitudinal shear, haunching 79�80low temperatures, steel, brittle 11

Maupre Bridge (France) 91, 91metal arc welding (MAW) 10moment rounding 51�53, 52moment–axial load interaction, composite

structures 171moment–bending interaction, girders 49,

49

180

Index

motorwayswideningcosts 47highway bridges 47�49, 48

Nanny Bridge 41�42, 41Nantenbach Bridge 109noise emissions

railway bridges 93�94vehicular 93viaducts 93�94, 94vibration frequencies 93�94

Øresund Bridge (Denmark–Sweden) 109

paintingsteel 43�44costs 34

pierscontinuous bridges, bearing stiffeners 55double composite 80�81, 81steelwork, bracing 52�53, 52

plastic modulus, composite structures 38plastic section properties, composite

structures 168�169, 168political influences, aesthetics 120portal structures

integral bridgesdesign 29, 29, 38, 38skew effects 40, 40, 41�42, 41soil loadings 39, 39

prestressed composite box girders 151,152�153

corrugated webs 151�152, 152prestressed composite bridges

construction stresses 149, 150extra-dosed 153�154, 153limiting stresses 147�148stress analysis 147�148, 147support displacement 145�146

prestressingdefinitions 145lossesconcrete creep 149concrete shrinkage 148misalignment 148relaxation 148slip 148

tendonsbonded 146, 147deviators 146unbonded 146�147

Quakers Yard Bridge 16�18, 17

railway bridgesbox girder bridges, steel 88�93, 89, 91,

92deflection limits 55�56, 61�62expansion joints 69fatigueassessments 64steel 11

loading assessments 158�159, 159noise emissions 93�94, 94through deck 59�60, 59trusses, span–depth ratios 99

reinforcing steel 6permanent formwork 37, 37

rigid connectorsbehaviour 13�14static strengths 14

Rittoh Bridge (Japan) 153River Blyth Bridge 31�34, 31, 34, 35

steelwork details 36road bridges see highway bridgesRunnymede Bridge (new) 117�118, 117

aesthetics 122Runnymede Bridge (old) 112�114, 113,

114aesthetics 122construction sequences 113, 114

safety, risk mitigation 26�27Second Severn Bridge 131�136, 139

construction, cantilever phase 138wind loads 133�134, 134

section propertiescomposite structures 165�166examples 167steel 165, 165

semi-integral bridges 31�32, 31definitions 29loadingsdead 32live 32soil 32thermal 32

serviceablity limit state 3, 11�12Severn Bridge

Second 131�136, 139wind loads 133�134, 134

shear connectorsassessments 160�161, 160, 161bar connectors, capacity 14beam bridges, numbers 26box girder bridges, composite 94�95,

95channel connectors, capacity 14

181

Index

shear connectors (continued )flexible 13, 13

tension 13hoop connectors, capacity 14rigid, behaviour 14�15shear studs, capacity 14, 26

shear lag, continuous bridges 61�63, 62shear planes, connectors 15, 15shear studs, capacity 14, 26skew effects, portal structures, integral

bridges 40, 40, 41�42, 41slabsbeam bridges

depths 18design parameters 25�26, 26

trusses 98�99viaducts

arching 75�76, 75insitu stitches 74�75, 74interaction curves 76�77, 76launching 73�74limiting shear stress 77punching shear capacity 77, 77shear resistance 77

slenderness parameter, through girderbridges 63

soil loadings, portal structures, integralbridges 39, 39

soil pressure coefficients 30�31, 30soil–structure interactions 30�31, 32span ranges, composite bridges 1�2, 2span–depth ratiosbeam and slab bridges 16, 17continuous bridges 46trusses 99

stainless steel 142steelbeams, ultimate design shear resistance

9bending

cold rolling 118induction 118

buckling limits 6�8, 8composite structures, effective lengths

8, 8compressive loads, limitations 9corrosion

atmospheric 42blast cleaning 43cladding resistance 104rates 42submergence 42weathering 34

elastic modulus 6

fatigue 11girders

fabrication 9�10, 10welding 10

high-strength 110welding 110

paintingcosts 34systems 43�44

properties 2recycled 27�28reinforcement 6

permanent formwork 37, 37section properties 165, 165stainless 142strength, assessments 160stress–strain curves 6, 7structural 6, 8temperatures, low 11tensile loads, limitations 8�9yield strengths 6, 7

steel beam and concrete slab bridges seebeam bridges

Stonecutters Bridge (Hong Kong) 130towers 141�142, 141, 143�144, 144

submerged arc welding (SAW) 10superstructures, viaducts 69

temperaturesbridge movements 29�30concrete curing, reinforcement control

3�5differential 44�45low, brittle steel 11

through girder bridges (U deck)grillage analysis 61, 61limitations 59�60railways 59�60, 59shear lag 62�63slenderness parameter 63uses 58

tied arched bridges 122�123, 123construction sequences 126intersections 127�128, 127

torsional properties, composite structures170, 170

towerscable-stayed bridges

forms 139�140inclination 140, 140top anchorages 140�141, 141

truss bridgesbearing stresses 108buckling 108�109

182

Index

continuous 109, 109design criteria 100jointsbolted 102�103, 102, 105�106welded 102

launch sequences 106, 107patch loadings 107�108, 108

limiting compressive stresses 101, 101loadingschords 104�105, 105dead 104�105

member types 101slabs, formation 98�99span–depth ratios 99railway bridges 99

types 98underslung 100, 100advantages 99�100

weight–stiffness analysis 99�100, 100two-girder system, viaducts 67, 67

U deck bridges see through girder bridgesultimate limit state 3

shear planes 15, 15

viaductsbearings, expansion joints 69�71, 70concrete boxes, prestressed 68�69, 68construction methodsconnectors 82�83, 83crane erection 71�73, 72and piers 82slab launching 73�74, 74

cost benefits 66

definitions 66forms 66�69, 67, 68haunching, moments 78�79, 78noise emissions 93�94, 94slabsarching 75, 75design 74�75insitu stitches 74, 74interaction curves 76�77, 76limiting shear stress 77punching shear capacity 77, 77shear resistance 77

superstructures 69two-girder system 67�68, 67

vibration frequencies, natural 57�58, 57

Walsall Road Bridge 50�51, 50steelwork details 52

Wanxian Bridge (China) 113, 115weight–stiffness analysis, trusses 99�100,

100welding

details, box girder bridges 90, 91high-strength steel 110joints 102metal arc 10submerged arc 10

wind loadscable-stayed bridgesflutter 134, 135static 132typhoons 142vortices 134, 134, 135

wind tunnel testing 135

183

Index