steel-concrete composite bridges
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enjoyTRANSCRIPT
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Steelconcrete compositebridges
David Collings
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Published by Thomas Telford Publishing, Thomas Telford Ltd,
1 Heron Quay, London E14 4JD.
www.thomastelford.com
Distributors for Thomas Telford books are
USA: ASCE Press, 1801 Alexander Bell Drive, Reston, VA 20191-4400, USA
Japan:Maruzen Co. Ltd, Book Department, 310 Nihonbashi 2-chome,
Chuo-ku, Tokyo 103
Australia:DA Books and Journals, 648 Whitehorse Road, Mitcham 3132,Victoria
First published 2005
Figures 5.2, 10.10, 11.2 courtesy of Benaim
Figure 10.9 courtesy of T Hambly
Figures 5.4, 5.5 courtesy of Amec Group Ltd
Figure 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 and
Patents Act 1988, no part of this publication may be reproduced, stored in a retrieval system
or 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 imply
that 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 expressed
in this publication provide a safe and accurate guide, no liability or responsibility can be accepted
in this respect by the author or publishers.
Typeset by Academic Technical, Bristol
Printed and bound in Great Britain by MPG Books, Bodmin
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Dedication
For my father
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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 29Soilstructure interaction 30Example 3.1 31Weathering steel 34Compact sections 38Portal frame structures 38Example 3.2 38Effects of skew 40Example 3.3 41
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Painting 42Shrinkage 44Differential temperature 44
4. Continuous bridges 46
Introduction 46
Motorway widening 47Momentshear 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 78Introduction 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
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8. Trusses 98
Introduction 98Example 8.1 99Member type 101Steel sections under axial load 101Joints in steelwork 102Example 8.2 103
Enclosure 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 118
Nodes in tubular structures 118Aesthetics 120Tied arches 122Example 9.3 123Arch buckling 124
10. Cable-stayed bridges 129
Introduction 129Deckstay connection 130Example 10.1 131High-strength concrete 131
Buckling interaction 137Shear connection 138Towers 139Tower top 140Example 10.2 141Stainless steel 142Strain-limited composite section 143
11. Prestressed steelconcrete composite bridges 145
Introduction 145Displacement of supports 145
Prestress 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
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12. Assessment of composite bridges 155
Introduction 155History 155Structure types 157Inspection 157Loads 157Materials 159
Testing 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 steelconcrete composite sections 165Section properties for cracked steelconcrete composite sections withreinforcement 166
Appendix C: Section properties for examples 167
Appendix D: Plastic section properties for steelconcrete compositesections 168
Appendix E: Torsional properties for steelconcrete compositesections 170
Appendix F: Momentaxial load interaction for compactsteelconcrete composite sections 171
References 172
Index 177
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ForewordThe bridge crossing it, with its numberless short spans and lack of bigness, beauty and
romance 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 a
shock of elation as the train had moved slowly along the bridge, carrying him with it, and
he gazed downward upon flowing waters, again he marvelled at what men could do; at the
power 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 BridgeEngineering[139]. This book expands upon that chapter and provides details of moresteelconcrete 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 Engineeringand wish to find moredetail on steelconcrete 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.
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AcknowledgementsMany 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 theDoncaster 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 Brunels Paddington Bridge.
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Notation
A areaAa steel areaAac composite sectionAc concrete areaAs reinforcing steel areaB widthD depth of girder, rigidityE Youngs 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 area
J 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 connectors
Npk 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
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Q variable loadQl longitudinal shearR reactionS Strouhal numberT torsion, tension, periodV shear force, wind speedVarch punching shear resistance
Vcf 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 eccentricity
f 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 member
y distancez lever arm
axial contribution factor, prestress lossfl partial load factorfm partial material factorf3 partial factor (BS 5400) deflection, settlement" strain angle slenderness parameter
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creep function dynamic increment
Subscriptsa steelac steelconcrete composite
b bottomc concretecr critical bucklingcs steelconcrete 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
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Steelconcrete compositebridges
David Collings
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Published by Thomas Telford Publishing, Thomas Telford Ltd,
1 Heron Quay, London E14 4JD.
www.thomastelford.com
Distributors for Thomas Telford books are
USA: ASCE Press, 1801 Alexander Bell Drive, Reston, VA 20191-4400, USA
Japan:Maruzen Co. Ltd, Book Department, 310 Nihonbashi 2-chome,
Chuo-ku, Tokyo 103
Australia: DA Books and Journals, 648 Whitehorse Road, Mitcham 3132,Victoria
First published 2005
Figures 5.2, 10.10, 11.2 courtesy of Benaim
Figure 10.9 courtesy of T Hambly
Figures 5.4, 5.5 courtesy of Amec Group Ltd
Figure 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 and
Patents Act 1988, no part of this publication may be reproduced, stored in a retrieval system
or 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 imply
that 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 expressed
in this publication provide a safe and accurate guide, no liability or responsibility can be accepted
in this respect by the author or publishers.
Typeset by Academic Technical, Bristol
Printed and bound in Great Britain by MPG Books, Bodmin
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Dedication
For my father
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Index
Page numbers for figures and illustrations are shown in italics. Bridges cited are in theUK unless otherwise stated.
A13 London bridge 152153aesthetics
colours 4344
detail 122fashion 121political influences 120proportion 122scale 121122visual unity 121
Ah Kai Sha Bridge (China) 149150, 149analysis
cable-stayed bridges 142143continuous bridges 5051, 51grillage
beam and slab bridges 19, 19
integral bridges 33
34, 33, 35through girder bridges 61, 61
approximation methods 164arched bridges
bucklinganalysis 125127, 125loadings 124125, 124
composite bowstring 123124composite interaction curves 116,
116
composite tubular arches 117compression members 114116,
116construction
falsework 113, 114sequences 113, 114
curved sections, fabrication 118forms 111, 111geometric ratios 112loadings
abnormal 112113analysis 112113, 117118
stiffening 113, 113thrust 111112tied 122124, 123
construction sequences 126intersections 127128, 127
tubular nodesjoint capacities 119120, 119, 120K joints 119, 119profiling 120X joints 119, 119
atmospheric corrosion, steel 42
bar connectors, capacity 14beam and slab bridges
analysis, grillage 19, 19
construction, non-composite stage 20,20
girdersbracing 2024, 21, 22, 24design 20, 2223, 22flange stability 23maximum loading 20vertical stiffeners 24, 24web thickness 2324
loadingsdead 18, 18, 19HA vehicular 18, 19
HB vehicular 18, 19risk mitigation 2627shear connectors, numbers 26slabs
depths 18design parameters 2526, 26HB vehicular loadings 25, 25
spandepth ratios 16, 17beams seegirdersbearing stresses, truss bridges 108
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bearingscontinuous bridges, stiffeners 55viaducts, expansion joints 6971, 70
boltsHSFG, properties 103truss joints 102103, 102, 105106
box girder bridgesbracing, torsional analysis 97
composite, 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, 91
stiffness requirements 87, 88types 8788
longitudinal distortional warping8687, 87
prestressed concrete 151, 152153corrugated webs 151152, 152
railway bridgesbending stresses 90deflection limits 9293details 89finite element analysis 9091high speed lines 9293, 92
loadings 88shear stresses 8890skew crossings 92, 92weld details 90, 91
steel 85torsional distortion 8586, 86uses 85
bridge designcodes of practice 23environmental issues
concrete substitutes 28energy use 27
recycled steel 27
28British Standards seecodes of practicebuckling interaction coefficients, cable-
stayed bridges 137138, 137
cable-stayed bridgesanalysis 142143anchorages, forces 129130, 129axial loadings 139back spans, concrete 130, 130
buckling interaction coefficients137138, 137
cable load analysis 136cable-out scenarios 136construction, cantilever phase 138extra-dosed 153154, 153loadings
dead 132
highway 132wind 132136, 133, 134, 142
stay-deck connections 130131, 130towers
analysis 143144, 144forms 139140, 141, 141inclination 140, 140top anchorages 140141, 141
channel connectors, capacity 14codes of practice
bridge design 23, 1617European 17
colours, aesthetics of 43
44composite actions
curves 116, 116interface connections 12modular ratio 1112
composite bowstring arched bridges123124
composite bridgesassessments 155
cased beams 161162shear connections 160161, 160, 161
definitions 1
embedded joists 156
157, 156history 155156inspections 157life cycles 162163loadings
highway 157158, 158railway 158159, 159
slab formation 157span ranges 12, 2
composite structureseffective lengths 8, 8momentaxial load interaction 171
plastic modulus 38plastic section properties 168169,
168
section properties 165166torsional properties 170, 170
composites, definitions 1concrete
bending moments 56, 5corrosion, chloride contaminated water
151, 162
178
Index
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crackingcauses 5354hogging limits 5455, 54
creep 5heat, reinforcement control 35high-strength 131132
tensile strength 131lightweight 8384
modulus 3, 4properties
compressive strength 2, 3tensile strength 3
shrinkage 44, 44strain curve 4, 5
strength, assessments 159strengthening 162stressstrain curves 3, 4substitutes 28
concrete boxes, prestressed, viaducts6869, 68
concrete structures, moment rounding5153, 52
connectorsbox girder bridges 97, 97capacity 14continuous bridges, fatigue stresses
6465, 64number of 12shear
flexible 13, 13rigid 14
shear planes 15, 15
constructionbeam and slab bridges 20, 20continuous bridges 55, 55tied arched bridges 126viaducts
connectors 8283, 83crane erection 7173, 72and piers 82slab launching 7374
continuous bridgesanalysis 5051, 51deflections
construction phase 55, 56long-term 57predicting 5657railway limits 5556vibration frequency effects 58
fatigue stress, assessments 6364frequencies, natural 5758, 57hogging, limiting 5455, 54loadings 50moment rounding 5153, 52
motorway widening 4749, 48piers
bearing stiffeners 55steelwork bracing 5253, 52
shear lag 6163, 62slabs, pour sequences 56spandepth ratios 46through girder types 5861, 59
uses 46
47continuous truss bridges 109, 109corrosion
concrete, chloride contaminated water151, 162
stainless steel 142steel
atmospheric 42blast cleaning 43cladding resistance 104rates of 42submergence 42
weathering 34
deflectionscontinuous bridges
construction phase 55, 56long-term 57predicting 5657railway limits 5556vibration frequency effects 58
limits, high-speed railway lines 9293Doncaster North Viaduct 6869, 68
bearing layout 7071, 70
construction 71
72, 72slab design 74
double composite piersflanges 81, 81loadings 8081, 81stress build-up 82
environmental issuesaesthetics
colour 4344detail 122fashion 121
proportion 122scale 121122surroundings 120121visual unity 121
bridge constructionconcrete substitutes 28energy use 27recycled steel 2728
noise emissions 9394, 94European codes of practice 17
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expansion jointsviaducts
bearings 6971, 70uses 69
fatiguerailway bridges 11steel 11
fatigue stresscontinuous bridges
assessments 6364connectors 6465
flexible connectors, types 13, 13floods, steel, corrosion 42frequencies, continuous bridges, natural
5758, 57
girdersbottom flange, stresses 3435bracing
cross 21, 21ineffective 21, 21piers 5253, 52plan 21, 21U-frame 21, 21
cased, assessments 161162fabrication 910, 10
welding 10flange stability 23longitudinal-shear flow 35, 37, 37momentshear interaction 49, 49vertical stiffeners 24, 24
websshear capacity 49slenderness effect 8182thickness 2324
haunchingforms of 79, 79longitudinal shear 7980viaducts, moments 7879, 78
high-strength concrete 131132tensile strength 131
high-strength steel 110
welding 110highway bridges
continuous motorway 47, 47fatigue, assessments 64motorway widening 4749, 48noise emissions 9394, 94vehicular loadings
abnormal 112113HA 18, 19, 132, 132, 158HB 18, 19, 2526, 25
Himi Bridge (Japan) 153hogging, limiting 5455, 54hoop connectors, capacity 14HSFG bolts, properties 103
inspections, composite bridges 157integral bridges
see also semi-integral bridges
analysis, grillage 33
34, 33, 35deck slabs, shrinkage 44, 44definitions 29girders
bottom flange stresses 3435longitudinal-shear flow 35, 37,
37
portal structuresdesign 29, 29, 38, 38skew effects 40, 40, 4142, 41soil loadings 39, 39
reinforcement, details 37, 37
soil pressure coefficients 30
31,30
soilstructure interactions 3031uses of 29
jointsbolted 102103, 102, 105106tubular nodes
capacities 119120, 119, 120K 119, 119profiling 120X 119, 119
welded 102
Kuala Lumpur highway intersection 96,97
launch sequencestruss bridges 106, 107
patch loadings 107108, 108viaducts, slabs 7374, 74
limit statesserviceablity 3, 1112ultimate 3
longitudinal shear, haunching 79
80low temperatures, steel, brittle 11
Maupre Bridge (France) 91, 91metal arc welding (MAW) 10moment rounding 5153, 52momentaxial load interaction, composite
structures 171momentbending interaction, girders 49,
49
180
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motorwayswidening
costs 47highway bridges 4749, 48
Nanny Bridge 4142, 41Nantenbach Bridge 109noise emissions
railway bridges 93
94vehicular 93viaducts 9394, 94vibration frequencies 9394
resund Bridge (DenmarkSweden) 109
paintingsteel 4344
costs 34piers
continuous bridges, bearing stiffeners 55
double composite 80
81, 81steelwork, bracing 5253, 52
plastic modulus, composite structures 38plastic section properties, composite
structures 168169, 168political influences, aesthetics 120portal structures
integral bridgesdesign 29, 29, 38, 38skew effects 40, 40, 4142, 41soil loadings 39, 39
prestressed composite box girders 151,
152
153corrugated webs 151152, 152
prestressed composite bridgesconstruction stresses 149, 150extra-dosed 153154, 153limiting stresses 147148stress analysis 147148, 147support displacement 145146
prestressingdefinitions 145losses
concrete creep 149
concrete shrinkage 148misalignment 148relaxation 148slip 148
tendonsbonded 146, 147deviators 146unbonded 146147
Quakers Yard Bridge 1618, 17
railway bridgesbox girder bridges, steel 8893, 89, 91,
92
deflection limits 5556, 6162expansion joints 69fatigue
assessments 64steel 11
loading assessments 158
159, 159noise emissions 9394, 94through deck 5960, 59trusses, spandepth ratios 99
reinforcing steel 6permanent formwork 37, 37
rigid connectorsbehaviour 1314static strengths 14
Rittoh Bridge (Japan) 153River Blyth Bridge 3134, 31, 34, 35
steelwork details 36
road bridges see highway bridgesRunnymede Bridge (new) 117118, 117
aesthetics 122Runnymede Bridge (old) 112114, 113,
114
aesthetics 122construction sequences 113, 114
safety, risk mitigation 2627Second Severn Bridge 131136, 139
construction, cantilever phase 138wind loads 133134, 134
section propertiescomposite structures 165166examples 167steel 165, 165
semi-integral bridges 3132, 31definitions 29loadings
dead 32live 32soil 32thermal 32
serviceablity limit state 3, 1112
Severn BridgeSecond 131136, 139
wind loads 133134, 134shear connectors
assessments 160161, 160, 161bar connectors, capacity 14beam bridges, numbers 26box girder bridges, composite 9495,
95
channel connectors, capacity 14
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shear connectors (continued)flexible 13, 13
tension 13hoop connectors, capacity 14rigid, behaviour 1415shear studs, capacity 14, 26
shear lag, continuous bridges 6163, 62shear planes, connectors 15, 15
shear studs, capacity 14, 26skew effects, portal structures, integral
bridges 40, 40, 4142, 41slabs
beam bridgesdepths 18design parameters 2526, 26
trusses 9899viaducts
arching 7576, 75insitu stitches 7475, 74interaction curves 7677, 76
launching 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 3031, 30soilstructure interactions 3031, 32span ranges, composite bridges 12, 2spandepth ratios
beam and slab bridges 16, 17continuous bridges 46trusses 99
stainless steel 142steel
beams, ultimate design shear resistance9
bendingcold rolling 118induction 118
buckling limits 68, 8composite structures, effective lengths
8, 8compressive loads, limitations 9corrosion
atmospheric 42blast cleaning 43cladding resistance 104rates 42submergence 42weathering 34
elastic modulus 6
fatigue 11girders
fabrication 910, 10welding 10
high-strength 110welding 110
paintingcosts 34
systems 43
44properties 2recycled 2728reinforcement 6
permanent formwork 37, 37section properties 165, 165stainless 142strength, assessments 160stressstrain curves 6, 7structural 6, 8temperatures, low 11tensile loads, limitations 89
yield strengths 6, 7steel beam and concrete slab bridges see
beam bridgesStonecutters Bridge (Hong Kong) 130
towers 141142, 141, 143144, 144submerged arc welding (SAW) 10superstructures, viaducts 69
temperaturesbridge movements 2930concrete curing, reinforcement control
35
differential 44
45low, brittle steel 11
through girder bridges (U deck)grillage analysis 61, 61limitations 5960railways 5960, 59shear lag 6263slenderness parameter 63uses 58
tied arched bridges 122123, 123construction sequences 126intersections 127128, 127
torsional properties, composite structures170, 170
towerscable-stayed bridges
forms 139140inclination 140, 140top anchorages 140141, 141
truss bridgesbearing stresses 108buckling 108109
182
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continuous 109, 109design criteria 100joints
bolted 102103, 102, 105106welded 102
launch sequences 106, 107patch loadings 107108, 108
limiting compressive stresses 101, 101
loadingschords 104105, 105dead 104105
member types 101slabs, formation 9899spandepth ratios 99
railway bridges 99types 98underslung 100, 100
advantages 99100weightstiffness analysis 99100, 100
two-girder system, viaducts 67, 67
U deck bridges seethrough girder bridgesultimate limit state 3
shear planes 15, 15
viaductsbearings, expansion joints 6971, 70concrete boxes, prestressed 6869, 68construction methods
connectors 8283, 83crane erection 7173, 72and piers 82
slab launching 73
74, 74cost benefits 66
definitions 66forms 6669, 67, 68haunching, moments 7879, 78noise emissions 9394, 94slabs
arching 75, 75design 7475insitu stitches 74, 74
interaction curves 76
77, 76limiting shear stress 77punching shear capacity 77, 77shear resistance 77
superstructures 69two-girder system 6768, 67
vibration frequencies, natural 5758, 57
Walsall Road Bridge 5051, 50steelwork details 52
Wanxian Bridge (China) 113, 115weightstiffness analysis, trusses 99100,
100welding
details, box girder bridges 90, 91high-strength steel 110joints 102metal arc 10submerged arc 10
wind loadscable-stayed bridges
flutter 134, 135static 132typhoons 142
vortices 134, 134, 135wind tunnel testing 135
183
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