bridge design to eurocodes worked examples...bridge design to eurocodes worked examples worked...

EUR 25193 EN - 2012

Bridge Design to Eurocodes Worked examples

Worked examples presented at the Workshop ldquoBridge Design to Eurocodesrdquo Vienna 4-6 October 2010

Support to the implementation harmonization and further development of the Eurocodes

Y Bouassida E Bouchon P Crespo P Croce L Davaine S Denton M Feldmann R Frank G Hanswille W Hensen B Kolias N Malakatas G Mancini M Ortega G Sedlacek G Tsionis

Editors A Athanasopoulou M Poljansek A Pinto

G Tsionis S Denton

The mission of the JRC is to provide customer-driven scientific and technical support for the conception development implementation and monitoring of EU policies As a service of the European Commission the JRC functions as a reference centre of science and technology for the Union Close to the policy-making process it serves the common interest of the Member States while being independent of special interests whether private or national European Commission Joint Research Centre Contact information Address JRC ELSA Unit TP 480 I-21027 Ispra (VA) Italy E-mail eurocodesjrceceuropaeu Tel +39-0332-789989 Fax +39-0332-789049 httpwwwjrceceuropaeu Legal Notice Neither the European Commission nor any person acting on behalf of the Commission is responsible for the use which might be made of this publication

Europe Direct is a service to help you find answers to your questions about the European Union

Freephone number ()

00 800 6 7 8 9 10 11

() Certain mobile telephone operators do not allow access to 00 800 numbers or these calls may be billed

A great deal of additional information on the European Union is available on the Internet It can be accessed through the Europa server httpeuropaeu JRC 68415 EUR 25193 EN ISBN 978-92-79-22823-0 ISSN 1831-9424 doi 10278882360 Luxembourg Publications Office of the European Union 2012 copy European Union 2012 Reproduction is authorised provided the source is acknowledged Printed in Italy

i

Acknowledgements

The work presented in this report is a deliverable within the framework of the Administrative

Arrangement SI2558935 under the Memorandum of Understanding between the Directorate-General

for Enterprise and Industry of the European Commission (DG ENTR) and the Joint Research Centre

(JRC) on the support to the implementation harmonisation and further development of the

Eurocodes

ii

iii

Table of Contents

Acknowledgements i

Table of contents iii

List of authors and editors xi

Foreword xiii

Introduction xv

Chapter 1

Introduction to the design example

11 Introduction 3

12 Geometry of the deck 3

121 LONGITUDINAL ELEVATION 3

122 TRANSVERSE CROSS-SECTION 3

123 ALTERNATIVE DECKS 4

13 Geometry of the substructure 5

131 PIERS 5

132 ABUTMENTS 7

133 BEARINGS 7

14 Design specifications 8

141 DESIGN WORKING LIFE 8

142 NON-STRUCTURAL ELEMENTS 8

143 TRAFFIC DATA 9

144 ENVIRONMENTAL CONDITIONS 10

145 SOIL CONDITIONS 11

146 SEISMIC DATA 11

147 OTHER SPECIFICATIONS 11

15 Materials 11

16 Details on structural steel and slab reinforcement 12

161 STRUCTURAL STEEL DISTRIBUTION 12

162 DESCRIPTION OF THE SLAB REINFORCEMENT 15

iv

17 Construction process 16

171 LAUNCHING OF THE STEEL GIRDERS 16

172 SLAB CONCRETING 16

Chapter 2

Basis of design (EN 1990)

21 Introduction 21

22 EN 1990 Section 1 ndash General 21

23 EN 1990 Section 2 - Requirements 21

24 EN 1990 Section 3 ndash Principles of limit state design 22

241 DESIGN SITUATIONS 22

242 ULTIMATE LIMIT STATES 23

243 SERVICEABILITY LIMIT STATES 23

25 EN 1990 Section 4 ndash Basic variables 24

251 ACTIONS 24

252 MATERIAL AND PRODUCTS PROPERTIES 25

26 EN 1990 Section 5 ndash Structural analysis and design assisted by testing 26

27 EN 1990 Section 6 ndash Limit states design and Annex A2 ndash Application for bridges 26

271 DESIGN VALUES 26


273 SINGLE SOURCE PRINCIPLE 27

274 SPECIAL CASES IN THE APPLICATION OF EQU 28

275 COMBINATIONS OF ACTIONS 29

276 LIMIT STATE VERIFICATIONS 31

28 Conclusions 32

29 Summary of key concepts 33

CHAPTER 3

Actions on bridge deck and piers (EN 1991)

Part A Wind and thermal action on bridge deck and piers

31 Introduction 37

32 Brief description of the procedure 37

v

33 Wind actions on the deck 40

331 BRIDGE DECK DURING ITS SERVICE LIFE WITHOUT TRAFFIC 40

332 BRIDGE DURING ITS SERVICE LIFE WITH TRAFFIC 43

333 BRIDGE UNDER CONSTRUCTION (MOST CRITICAL CASE ABD TERMINATION OF PUSHING)

43

334 VERTICAL WIND FORCES ON THE BRIDGE DECK (Z-DIRECTION)

45

335 WIND FORCES ALONG THE BRIDGE DECK (Y-DIRECTION) 46

34 Wind actions on the piers 46

341 SQUAT RECTANGULAR PIER 250x500x1000 46

342 lsquoHIGHrsquo CIRCULAR CYLINDRICAL PIER Oslash400x 4000 47

35 Thermal actions 48

Part B Action during execution accidental actions and traffic loads

36 Introduction 50

37 Actions during execution 50

371 LAUNCHING PHASE 52

38 Accidental actions 55

381 IMPACT OF VEHICLES ON THE BRIDGE SUBSTRUCTURE 56

382 IMPACT OF VEHICLES ON THE BRIDGE SUPERSTRUCTURE 56

39 Traffic loads 57

391 STATIC LOAD MODELS 58

392 GROUPS OF TRAFFIC LOADS ON ROAD BRIDGES 60

393 LOAD COMBINATIONS FOR THE CASE STUDY 61

394 FATIGUE LOAD MODELS 65

395 FATIGUE ASSESSMENT OF THE COMPOSITE BRIDGE 67

CHAPTER 4

Bridge deck modelling and structural analysis

41 Introduction 79

42 Shear lag effect 79

421 GLOBAL ANALYSIS 79

422 SECTION ANALYSIS 80

vi

43 Concrete creep effect (modular ratios) 81

431 SHORT TERM MODULA RATIO 81

432 LONG TERM MODULAR RATIO 81

44 Elastic mechanical properties of the cross sections 83

441 UN-CRACKED COMPOSITE BEHAVIOR 83

442 CKRACKED COMPOSITE BEHAVIOR 84

45 Actions modelling 85

451 SELF-WEIGHT 85

452 NON-STRUCTURAL EQUIPMENTS 85

453 CONCRETE SHRINKAGE IN THE COMPOSITE DECK 86

454 ROAD TRAFFIC 87

46 Global analysis 90

47 Main results 91

471 VERTICAL SUPPORT REACTIONS 92

472 INTERNAL FORCES AND MOMENTS 92

473 STRESSES AT ULS 92

CHAPTER 5 93

Concrete bridge design (EN 1992-2)

51 Introduction 97

52 Local verifications in the concrete slab 97

521 DURABILITY ndash CPVER TO REINFORCEMENT 97

522 TRANSVERSE REINFORCEMENT VERIFICATIONS 99

523 LONGITUDINAL REINFORCEMENT VERIFICATIONS 116

524 PUNCHING SHEAR (ULS) 118

53 Second order effects in the high piers 121

531 MAIN FEATURES OF THE PIERS523 FORCES AND MOMENTS ON TOP OF THE PIERS

121

532 FORCES AND MOMENTS ON TOP OF THE PIERS 122

533 SECOND ORDER EFFECTS 122

vii

CHAPTER 6

Composite bridge design (EN 1994-2)

61 Verification of cross-section at mid-span P1-P2 127

611 GEOMETRY AND STRESSES 127

612 DETERMINING THE CROSS-SECTION CLASS (ACCORDING TO EN1994-2 552)

127

613 PLASTIC SECTION ANALYSIS 130

62 Verification of cross-section at internal support P1 132



132


63 Alternative double composite cross-section at internal support P-1 139


142

632 PLASTIC SECTION ANALYSIS BENDING AND RESISTANCE CHECK

144

633 SOME COMMENTS ABOUT EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE

144

64 Verification of the Serviceability Limit Sates (SLS) 145

65 Stresses control at Serviceability Limit States 145

651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE 145

652 CONTROL OF STRESS IN REINFORCEMENTSTEEL BARS 146

653 STRESS LIMITATION IN STRUCTURAL STEEL 147

654 ADDITIONAL VERIFICATION OF FATIGUE UDER A LOW NUMBER OF CYCLES

150

655 LIMITATION OF WEB BREATHING 151

66 Control of cracking for longitudinal global bending 151

661 MAXIMUM VALUE OF CRACK WIDTH 151

662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA 152

663 CONTROL OF CRACKING UNDER DIRECT LOADING 153

664 CONTROL OF CRACKING UNDER INDIRECT LOADING 155

67 Shear connection at steel-concrete interface 156

671 RESISTANCE OF HEADED STUDS 156

672 DETAILING OF SHEAR CONNECTION 157

viii

673 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS

160

674 CONNECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE

163

675 SYNOPSIS OF THE DESIGN EXAMPLE 165

676 DESIGN OF THE SHEAR CONNECTION FOR THE FATIGUE ULS COMBINATION OF ACTIONS

166

677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECK ENDS

171

CHAPTER 7

Geotechnical aspects of bridge design (EN 1997)

71 Introduction 177

72 Geotechnical data 177

73 Ultimate limit states 183

731 SUPPORT REACTIONS 183

732 GENERAL THE 3 DESIGN APPROACHES OF EUROCODE 7 185

74 Abutment C0 189

741 BEARING CAPACITY (ULS) 189

742 SLIDING (ULS) 192

75 Pier P1 (Squat Pier) 193


752 SETTLEMENT (SLS) 195

76 Seismic design situations 196

CHAPTER 8

Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)

81 Introduction 201

82 Example of ductile pier 201

821 BRIDGE CONFIGURATION ndash DESIGN CONCEPT 201

822 SEISMIC STRUCTURAL SYSTEM 203

823 FUNDAMENTAL MODE ANALYSIS IN THE LONGITUDINAL DIRECTION

205

824 MULTIMODE RESPONSE ANALYSIS 206

825 DESIGN ACTION EFFECTS AND VERIFICATION 209

826 BEARINGS AND ROADWAY JOINTS 219

ix

827 CONCLUSION FOR DESIGN CONCEPT 224

83 Example of limited ductile piers 224


832 DESIGN SEISMIC ACTION 225

833 SEISIC ANALYSIS 226

834 VERIFICATIONS OF PIERS 237

835 BEARINGS AND JOINTS 239

84 Example of seismic isolation 241


842 DESIGN FOR HORIZONTAL NON-SEISMIC ACTIONS 247

843 DESIGN SEISMI ACTION 249


845 FUNDAMENTAL MODE METHOD 257

846 NON-LINERTIME HISTORY ANALYSIS 262

847 VERIFICATION OF THE ISOLATION SYSTEM 269

848 VERIFICATION OF SUBSTRUCTURE 271

849 DESIGN ACTION EFFECTS FOR THE FOUNDATION 278

8410 COMPARISON WITH FUNDAMENTAL MODE METHOD 279

APPENDICES 283

APPENDIX A A-1

Design of steel bridges Overview of key contents of EN 1993

APPENDIX B B-1

A sample analytical method for bearing resistance calculation

APPENDIX C C-1

Examples of a method to calculate settlements for spread foundations

APPENDIX D D-1

Generation of semi-artificial accelerograms for time-history analysis through modification of natural records

x

xi

List of authors and editors

Authors

Introduction

Steve Denton Parsons Brinckerhoff Chairman of CENTC250 Horizontal Group Bridges

Georgios Tsionis University of Patras Secretary of CENTC250 Horizontal Group Bridges

Chapter 1 ndash Introduction to the design example

Pilar Crespo Ministry of Public Works (Spain)

Laurence Davaine French Railway Bridge Engineering Department (SNCF IGOA)

Chapter 2 ndash Basis of design (EN 1990)


Chapter 3 ndash Actions on bridge decks and piers (EN 1991)

Nikolaos Malakatas Ministry of Infrastructures Transports and Networks (Greece)

Pietro Croce Department of Civil Engineering University of Pisa Italy

Chapter 4 ndash Bridge deck modeling and design


Chapter 5 ndash Concrete bridge design (EN 1992)

Emmanuel Bouchon Large Bridge Division SetraCTOA Paris France

Giuseppe Mancini Politecnico di Torino Italy

Chapter 6 ndash Composite bridge design (EN 1994-2)

Miguel Ortega Cornejo IDEAM SA University ldquoEuropea de Madridrsquo Spain

Joel Raoul Large Bridge Division SetraCTOA Ecole Nationale de Ponts et Chausses Paris France

Chapter 7 ndash Geotechnical aspects of bridge design (EN 1997)

Roger Frank University Paris-Est Ecole den Ponts ParisTech Navier-CERMES

Yosra Bouassida University Paris-Est Ecole den Ponts ParisTech Navier-CERMES

Chapter 8 ndash Overview of seismic issues for bridge design (EN 1998-1 EN 1998-2)

Basil Kolias DENCO SA Athens

Appendix A ndash Design of steel bridges Overview of key content of EN 1993

Gerhard Hanswille Bergische Universitat

Wolfang Hensen PSP - Consulting Engineers

xii

Markus Feldmann RWTH Aachen University

Gerhard Sedlacek RWTH Aachen University

Editors

Adamantia Athanasopoulou Martin Poljansek Artur Pinto

European Laboratory for Structural Assessment

Institute for the Protection and Security of the Citizen

Joint Research Centre European Commission

Georgios Tsionis Steve Denton

CENTC250 Horizontal Group Bridges

xiii

Foreword

The construction sector is of strategic importance to the EU as it delivers the buildings and infrastructure needed by the rest of the economy and society It represents more than 10 of EU GDP and more than 50 of fixed capital formation It is the largest single economic activity and the biggest industrial employer in Europe The sector employs directly almost 20 million people In addition construction is a key element for the implementation of the Single Market and other construction relevant EU Policies eg Environment and Energy

In line with the EUrsquos strategy for smart sustainable and inclusive growth (EU2020) Standardization will play an important part in supporting the strategy The EN Eurocodes are a set of European standards which provide common rules for the design of construction works to check their strength and stability against live and extreme loads such as earthquakes and fire

With the publication of all the 58 Eurocodes parts in 2007 the implementation of the Eurocodes is extending to all European countries and there are firm steps towards their adoption internationally The Commission Recommendation of 11 December 2003 stresses the importance of training in the use of the Eurocodes especially in engineering schools and as part of continuous professional development courses for engineers and technicians noting that they should be promoted both at national and international level

In light of the Recommendation DG JRC is collaborating with DG ENTR and CENTC250 ldquoStructural Eurocodesrdquo and is publishing the Report Series lsquoSupport to the implementation harmonization and further development of the Eurocodesrsquo as JRC Scientific and Technical Reports This Report Series include at present the following types of reports

1 Policy support documents ndash Resulting from the work of the JRC and cooperation with partners and stakeholders on lsquoSupport to the implementation promotion and further development of the Eurocodes and other standards for the building sector

2 Technical documents ndash Facilitating the implementation and use of the Eurocodes and containing information and practical examples (Worked Examples) on the use of the Eurocodes and covering the design of structures or their parts (eg the technical reports containing the practical examples presented in the workshops on the Eurocodes with worked examples organized by the JRC)

3 Pre-normative documents ndash Resulting from the works of the CENTC250 Working Groups and containing background information andor first draft of proposed normative parts These documents can be then converted to CEN technical specifications

4 Background documents ndash Providing approved background information on current Eurocode part The publication of the document is at the request of the relevant CENTC250 Sub-Committee

5 ScientificTechnical information documents ndash Containing additional non-contradictory information on current Eurocodes parts which may facilitate implementation and use preliminary results from pre-normative work and other studies which may be used in future revisions and further development of the standards The authors are various stakeholders involved in Eurocodes process and the publication of these documents is authorized by the relevant CENTC250 Sub-Committee or Working Group

Editorial work for this Report Series is assured by the JRC together with partners and stakeholders when appropriate The publication of the reports type 3 4 and 5 is made after approval for publication from the CENTC250 Co-ordination Group

The publication of these reports by the JRC serves the purpose of implementation further harmonization and development of the Eurocodes However it is noted that neither the Commission nor CEN are obliged to follow or endorse any recommendation or result included in these reports in the European legislation or standardization processes

xiv

This report is part of the so-called Technical documents (Type 2 above) and contains a comprehensive description of the practical examples presented at the workshop ldquoBridge Design to the Eurocodesrdquo with emphasis on worked examples of bridge design The workshop was held on 4-6 October 2010 in Vienna Austria and was co-organized with CENTC250Horizontal Group Bridges the Austrian Federal Ministry for Transport Innovation and Technology and the Austrian Standards Institute with the support of CEN and the Member States The workshop addressed representatives of public authorities national standardisation bodies research institutions academia industry and technical associations involved in training on the Eurocodes The main objective was to facilitate training on Eurocode Parts related to Bridge Design through the transfer of knowledge and training information from the Eurocode Bridge Parts writers (CENTC250 Horizontal Group Bridges) to key trainers at national level and Eurocode users

The workshop was a unique occasion to compile a state-of-the-art training kit comprising the slide presentations and technical papers with the worked example for a bridge structure designed following the Eurocodes The present JRC Report compiles all the technical papers prepared by the workshop lecturers resulting in the presentation of a bridge structure analyzed from the point of view of each Eurocode

The editors and authors have sought to present useful and consistent information in this report However it must be noted that the report is not a complete design example and that the reader may identify some discrepancies between chapters Users of information contained in this report must satisfy themselves of its suitability for the purpose for which they intend to use it

We would like to gratefully acknowledge the workshop lecturers and the members of CENTC250 Horizontal Group Bridges for their contribution in the organization of the workshop and development of the training material comprising the slide presentations and technical papers with the worked examples We would also like to thank the Austrian Federal Ministry for Transport Innovation and Technology especially Dr Eva M Eichinger-Vill and the Austrian Standards Institute for their help and support in the local organization of the workshop

It is also noted that the chapters presented in the report have been prepared by different authors and reflecting the different practices in the EU Member States both lsquorsquo and lsquorsquo are used as decimal separators

All the material prepared for the workshop (slides presentations and JRC Report) is available to download from the ldquoEurocodes Building the futurerdquo website (httpeurocodesjrceceuropaeu)

Ispra November 2011

Adamantia Athanasopoulou Martin Poljansek Artur Pinto European Laboratory for Structural Assessment (ELSA)

Institute for the Protection and Security of the Citizen (IPSC)

Joint Research Centre (JRC) - European Commission

Steve Denton George Tsionis CENTC250 Horizontal Group Bridges

xv

Introduction

The Eurocodes are currently in the process of national implementation towards becoming the Europe-

wide means for structural design of civil engineering works

As part of the strategy and general programme for promotion and training on the Eurocodes a

workshop on bridge design to Eurocodes was organised in Vienna in October 2010 The main

objective of this workshop was to transfer background knowledge and expertise The workshop aimed

to provide state-of-the-art training material and background information on Eurocodes with an

emphasis on practical worked examples

This report collects together the material that was prepared and presented at the workshop by a

group of experts who have been actively involved in the development of the Eurocodes It

summarises important points of the Eurocodes for the design of concrete steel and composite road

bridges including foundations and seismic design The worked examples utilise a common bridge

project as a basis although inevitably they are not exhaustive

THE EUROCODES FOR THE DESIGN OF BRIDGES

The Eurocodes

The Eurocodes listed in the Table I constitute a set of 10 European standards (EN) for the design of

civil engineering works and construction products They were produced by the European Committee

for Standardization (CEN) and embody national experience and research output together with the

expertise of international technical and scientific organisations The Eurocodes suite covers all

principal construction materials all major fields of structural engineering and a wide range of types of

structures and products

Table I Eurocode parts

EN 1990 Eurocode Basis of structural design EN 1991 Eurocode 1 Actions on structures EN 1992 Eurocode 2 Design of concrete structures EN 1993 Eurocode 3 Design of steel structures EN 1994 Eurocode 4 Design of composite steel and concrete structures EN 1995 Eurocode 5 Design of timber structures EN 1996 Eurocode 6 Design of masonry structures EN 1997 Eurocode 7 Geotechnical design EN 1998 Eurocode 8 Design of structures for earthquake resistance EN 1999 Eurocode 9 Design of aluminium structures

From March 2010 the Eurocodes were intended to be the only Standards for the design of structures

in the countries of the European Union (EU) and the European Free Trade Association (EFTA) The

Member States of the EU and EFTA recognise that the Eurocodes serve as

a means to prove compliance of buildings and civil engineering works with the essential

requirements of the Construction Products Directive (Directive 89106EEC) particularly Essential

Requirement 1 ldquoMechanical resistance and stabilityrdquo and Essential Requirement 2 ldquoSafety in case

of firerdquo

a basis for specifying contracts for construction works and related engineering services

xvi

a framework for drawing up harmonised technical specifications for construction products (ENs

and ETAs)

The Eurocodes were developed under the guidance and co-ordination of CENTC250 ldquoStructural

Eurocodesrdquo The role of CENTC250 and its subcommittees is to manage all the work for the

Eurocodes and to oversee their implementation The Horizontal Group Bridges was established within

CENTC250 with the purpose of facilitating technical liaison on matters related to bridges and to

support the wider strategy of CENTC250 In this context the strategy for the Horizontal Group

Bridges embraces the following work streams maintenance and evolution of Eurocodes development

of National Annexes and harmonisation promotion (trainingguidance and international) future

developments and promotion of research needs

Bridge Parts of the Eurocodes

Each Eurocode except EN 1990 is divided into a number of parts that cover specific aspects The

Eurocodes for concrete steel composite and timber structures and for seismic design comprise a

Part 2 which covers explicitly the design of road and railway bridges These parts are intended to be

used for the design of new bridges including piers abutments upstand walls wing walls and flank

walls etc and their foundations The materials covered are i) plain reinforced and prestressed

concrete made with normal and light-weight aggregates ii) steel iii) steel-concrete composites and iv)

timber or other wood-based materials either singly or compositely with concrete steel or other

materials Cable-stayed and arch bridges are not fully covered Suspension bridges timber and

masonry bridges moveable bridges and floating bridges are excluded from the scope of Part 2 of

Eurocode 8

A bridge designer should use EN 1990 for the basis of design together with EN 1991 for actions EN

1992 to EN 1995 (depending on the material) for the structural design and detailing EN 1997 for

geotechnical aspects and EN 1998 for design against earthquakes The main Eurocode parts used for

the design of concrete steel and composite bridges are given in Table II

The ten Eurocodes are part of the broader family of European standards which also include material

product and execution standards The Eurocodes are intended to be used together with such

normative documents and through reference to them adopt some of their provisions Fig I

schematically illustrates the use of Eurocodes together with material (eg concrete and steel) product

(eg bearings barriers and parapets) and execution standards for the design and construction of a

bridge

xvii

Table II Overview of principal Eurocode parts used for the design of concrete steel and composite bridges and bridge elements

EN Part Scope Concrete Steel Composite EN 1990 Basis of design radic radic radic EN 1990A1 Bridges radic radic radic EN 1991-1-1 Self-weight radic radic radic EN 1991-1-3 Snow loads radic radic radic EN 1991-1-4 Wind actions radic radic radic EN 1991-1-5 Thermal actions radic radic radic EN 1991-1-6 Actions during execution radic radic radic EN 1991-1-7 Accidental actions radic radic radic EN 1991-2 Traffic loads radic radic radic EN 1992-1-1 General rules radic radic EN 1992-2 Bridges radic radic EN 1993-1-1 General rules radic radic EN 1993-1-5 Plated elements radic radic EN 1993-1-7 Out-of-plane loading radic radic EN 1993-1-8 Joints radic radic EN 1993-1-9 Fatigue radic radic EN 1993-1-10 Material toughness radic radic EN 1993-1-11 Tension components radic radic EN 1993-1-12 Transversely loaded plated structures radic radic EN 1993-2 Bridges radic radic EN 1993-5 Piling radic radic EN 1994-1-1 General rules radic EN 1994-2 Bridges radic EN 1997-1 General rules radic radic radic EN 1997-2 Testing radic radic radic EN 1998-1 General rules seismic actions radic radic radic EN 1998-2 Bridges radic radic radic EN 1998-5 Foundations radic radic radic

Figure I Use of Eurocodes with product material and execution standards for a bridge

xviii

THE DESIGN EXAMPLE

The worked examples in this report refer to the same structure However some modifications andor

extensions are introduced to cover some specific issues that would not otherwise be addressed

details are given in the pertinent chapters Timber bridges are not treated in this report although their

design is covered by the Eurocodes

The following assumptions have been made

the bridge is not spanning a river and therefore no hydraulic actions are considered

the climatic conditions are such that snow actions are not considered

the soil properties allow for the use of shallow foundations

the recommended values for the Nationally Determined Parameters are used throughout

The example structure shown in Fig II is a road bridge with three spans (600 m + 800 m + 600 m)

The continuous composite deck is made up of two steel girders with I cross-section and a concrete

slab with total width 120 m Alternative configurations namely transverse connection at the bottom of

the steel girders and use of external tendons are also studied Two solutions are considered for the

piers squat and slender piers with a height 100 m and 400 m respectively The squat piers have a

50times25 m rectangular cross-section while the slender piers have a circular cross-section with external

diameter 40 m and internal diameter 32 m For the case of slender piers the deck is fixed on the

piers and free to move on the abutments For the case of squat piers the deck is connected to each

pier and abutment through triple friction pendulum isolators The piers rest on rectangular shallow

footings The abutments are made up of gravity walls that rest on rectangular footings

The configuration of the example bridge was chosen for the purpose of this workshop It is not

proposed as the optimum solution and it is understood that other possibilities exist It is also noted

that the example is not fully comprehensive and there are aspects that are not covered

Figure II Geometry of the example bridge

OUTLINE OF THE REPORT

Following the introduction Chapter 1 describes the geometry and materials of the example bridge as

well as the main assumptions and the detailed structural calculations Each of the subsequent

chapters presents the main principles and rules of a specific Eurocode and their application on the

example bridge The key concepts of basis of design namely design situations limit states the single

source principle and the combinations of actions are discussed in Chapter 2 Chapter 3 deals with

the permanent wind thermal traffic and fatigue actions and their combinations The use of FEM

analysis and the design of the deck and the piers for the ULS and the SLS including the second-

order effects are presented in Chapters 4 and 5 respectively Chapter 6 handles the classification of

xix

composite cross-sections the ULS SLS and fatigue verifications and the detailed design for creep

and shrinkage Chapter 7 presents the settlement and resistance calculations for the pier three

design approaches for the abutment and the verification of the foundation for the seismic design

situation Finally Chapter 8 is concerned with the conceptual design for earthquake resistance

considering the alternative solutions of slender or squat piers the latter case involves seismic

isolation and design for ductile behaviour

Steve Denton Chairman of Horizontal Group Bridges

Georgios Tsionis University of Patras Secretary of Horizontal Group Bridges

CHAPTER 6

Composite bridge design (EN1994-2)

Miguel ORTEGA CORNEJO

Project Manager IDEAM SA

Prof at University ldquoEuropea de Madridrdquo Spain

Joeumll RAOUL

Assistant to the Director of Large Bridge Division SeacutetraCTOA

Prof at ldquoEcole Nationale de Ponts et Chausseacutesrdquo Paris France

Convenor EN-1994-2

Chapter 6 Composite bridge design (EN1994-2) - M Ortega Cornejo J Raoul

126


127

61 Verification of cross-section at mid-span P1-P2

611 GEOMETRY AND STRESSES

At mid-span P1-P2 in ULS the concrete slab is in compression across its whole thickness Its contribution is therefore taken into account in the cross-section resistance The stresses in Fig 61 are subsequently calculated with the composite mechanical properties and obtained by summing the various steps whilst respecting the construction phases

The internal forces and moments in this cross-section are MEd = 6389 MNmiddotm VEd = 125 MN

Fig 61 Stresses at ULS in cross-section at mid-span P1-P2

Note The sign criteria for stresses are according to EN-1994-2 (+) tension and (ndash) compression


Lower flange is in tension therefore it is Class 1 The upper flange is composite and connected following the recommendations of EN1994-2 66 therefore it is Class 1

To classify the steel web the position of the Plastic Neutral Axis (PNA) is determined as follows

o Design plastic resistance of the concrete in compression

γ= = times =ck

c cc

fF A MN

085 085middot3519484 38643

150 (force of frac12 slab)

Note that the design compressive strength of concrete is γ

= ckcd

c

ff (EN-1994-2 2412)

EN-1994 differs from EN-1992-1-1 316 (1) in which an additional coefficient αcc is


128

applied α

γ= cc ck

cdc

ff

middot αcc takes account of the long term effects on the compressive

strength and of unfavourable effects resulting from the way the loads are applied

The value for αcc is to be given in each National annex EN-1994-2 used the value 100 without permitting national choice for several reasons1

- The plastic stress block for use in resistance of composite sections defined in EN-1994 6212 (figure 62) consist of a stress 085fcd extending to the neutral axis as shown in Figs 62 and 63

Fig 62 Rectangular stress blocks for concrete in compression at ULS (figure 21 of1)

Fig 63 Detail of the stress block for concrete al ULS (figure 61 of1)

- Predictions using the stress block of EN-1994 have been verified against the results for composite members conducted independently from the verifications for concrete bridges

- The EN-1994 block is easier to apply The Eurocode 2 rule for rectangular block (EN-1992-1-1 317 (3)) was not used in Eurocode 4 because resistance formulae became complex where the neutral axis is close to or within the steel flange adjacent to concrete slab

- Resistance formulae for composite elements given in EN-1994 are based on calibrations using stress block with αcc=100

o The reinforcing steel bars in compression are neglected

o Design plastic resistance of the structural steel upper flange (1 flange)

1 See ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo CR Hendy and RP Johnson


129

γ= = times times =y uf

s uf s ufM

fF A MN

0

345(10 004) 1380

10

Note that for the thickness 16lttle 40 mm fy=345 MPa o Design plastic resistance of the structural steel web (1 web)

γ= = times times =y w

s w s wM

fF A MN

0

345(272 0018) 16891

10

o Design plastic resistance of the structural steel lower flange (1 flange)

γ= = times times =y lf

s lf s lfM

fF A MN

0

345(120 004) 1656

10

Fig 64 Plastic neutral axis and design of plastic resistance moment at mid span P1-P2

As le + + c s uf s w s lfF F F F (38643 le 4725) and + ge + c s uf s w s lfF F F F (5244 ge 33451) it is

concluded that the PNA is located in the structural steel upper flange at a distance x from the upper extreme fibre of this flange

The internal axial forces equilibrium of the cross section leads to the location of the PNA

minusminus minus + + + =c s uf s uf s w s lf

xF F x F F F

(004 )middot middot 0

004

minus minus + minus + + =x x38643 345middot 138 345middot 16891 1656 0 X=00125 m=125 mm

As the PNA is located in the upper steel flange (Fig 64) the whole web and the bottom flange are in tension and therefore in Class 1 (EN-1993-1-1 552)

Conclusion The cross-section at mid-span P1-P2 is in Class 1 and is checked by a plastic section analysis


130

This is what usually happens in composite bridges in sagging areas with cross sections in class 1 with the PNA near or in the upper concrete slab or at least in class 2 with only a small upper part of the compressed web

613 PLASTIC SECTION ANALYSIS

6131 Bending resistance check

The design plastic resistance moment is calculated from the position of the PNA according to EN1994-2 6212(1) (see Fig 63)

MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)

MplRd = 7959 MNmiddotm

MEd = 6389 MNmiddotm le MplRd =7959 MNmiddotm is then verified

The cross-section at adjacent support P1 is in Class 3 but there is no need to reduce MplRd by a factor 09 because the ratio of lengths of the spans adjacent to P1 is 075 which is not less than 06 (EN1994-2 6213(2))

6132 Shear resistance check

As τ

εη

= = ge =w

w

hk

t272 31

15111 51360018

the web (stiffened by the vertical stiffeners) should be

checked in terms of shear buckling according to EN-1993-1-5 51

The maximum design shear resistance is given by VRd = min(VbwRd VplaRd) where VbwRd is the shear buckling resistance according to EN-1993-1-5 5 and VplaRd is the resistance to vertical shear according to EN-1993-1-1 626

η

γ

times times= + = =le times

timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2720middot1810 1063

3middot 3 110 (EN 1993-1-5 52)

Given the distribution of the transverse bracing frames in the span P1-P2 (spacing a = 8 m) a vertical frame post is located in the studied cross-section (as for the cross-section at support P1) The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 221 MN

As the vertical frame posts are assumed to be rigid

τ = + = + times =

whk

a

2 2272534 4 534 4 5802

8 is the shear buckling coefficient according to EN-

1993-1-5 Annex A3

( ) ( )π π

σν

times= = =

times

times times timestimes

wE

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 188312

12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)

ττ σ= = times =cr Ek MPa5802 8312 4822

(EN-1993-1-5 53)


131

λττ

= = = =y w y ww

crcr

f f 345

076 076 20324822middot 3

is the slenderness of the panel according to EN-1993-

1-5 53 As wλ is ge108 then

The factor for the contribution of the web to the shear buckling resistance χw is

( ) ( )χ

λ= = =

++w

w

137 1370501

07 203207(Table 51 of EN-1993-1-5 53)

Finally the contribution of the web to the shear buckling resistance is

χ

γ

times times times= = =

timestimesw y w w

bw Rd

M

f h tV MN -6

1

0501 345 2720 184441

3 3middot1 1010

If we neglect the contribution of the flanges to the shear buckling resistance asymp 0bf RdV then

= + = + le =b Rd bw Rd bf Rd b Rd

V V V MN V MN

444 0 1063 444

And η

γ


timesy w w

pl a Rd

M

f h tV E MN -6

0

12 345 2720 181170

3 3 10 (EN 1993-1-1 626)

So as VEd = 221 MNle VRd = min(VbwRd VplaRd)= min(444 1170)=444 then is verified

6133 Bending and vertical shear interaction

According to EN-1994-2 6224 if the vertical shear force VEd does not exceed half the shear resistance VRd obtained before there is no need to check the interaction M V (Fig 65)

In our case VEd = 221lt05middot444=222 MN then there is no need to check the interaction M-V

Fig 65 Shear-Moment interaction for class 1 and 2 cross-sections (a) with shear buckling and

without shear buckling (b) (Figure 66 of 1)


132

62 Verification of cross-section at internal support P1


At internal support P1 in ULS the concrete slab is in tension across its whole thickness Its contribution is therefore neglected in the cross-section resistance The stresses in Fig 66 are subsequently calculated and obtained by summing the various steps whilst respecting the construction phases

Fig 66 Stresses at ULS in cross-section at internal support P1

Note The sign criteria for stresses are according to EN-1994-2 + tension and ndash compression

The internal forces and moments in this cross-section are

MEd = -10935 MNmiddotm

VEd = 812 MN


The upper flange is in tension therefore is in Class 1 (EN 1993-1-1 552)

The lower flange is in compression and then must be classified according to (EN 1993-1-1 Table 52)

minus minus= = =lf wb t

c mm1200 26

587 2 2

ε= = le = times =lf

ct

587 2354891 9 9 8033

120 295

(Lower flange tlf=120 mm fylf=295 MPa)


133

Then the lower flange is in Class 1

The web is in tension in its upper part and in compression in its lower part The position of the Plastic Neutral Axis (PNA) is determined as follows

o The slab is cracked and its contribution is neglected

o Ultimate force of the tensioned upper reinforcing steel bars (φ 20130 mm) (located in the slab)

γ= = times times =sk

s ss

fF A m MN-4 2

1 1

500144996 10 6304


o Ultimate force of the tensioned lower reinforcing steel bars (φ 16130 mm) (located in the slab)


s ss

fF A m MN-4 2

2 2

50092797 10 4034




s uf s ufM

fF A MN

0

295(12 012) 354

10

o Design plastic resistance of the total structural steel web (1 web)


s w s wM

fF A MN

0

345(256 0026) 22963

10

o Design plastic resistance of the structural steel lower flange (1 lower flange)


s lf s lfM

fF A MN

0

295(120 012) 4248

10

As + + le +1 2 s s s uf s w s lfF F F F F (4573le6544) and + + + ge1 2 s s s uf s w s lfF F F F F (6870le4248)

the PNA is deduced to be located in the steel web

If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section leads to the location of the PNA

minus+ + + minus minus =s s s uf s w s w s w s lf

x xF F F F F F F1 2 (256 ) 0

256 256

6304+4034+354+897middotX-22963+897middotX-4248=0 X=1098 m

Over half of the steel web is in compression (the lower part) 256-1098=1462 m

α = = = gtw

w

h xh

- 256 - 10980571 050

256

Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α gt050 then

The limiting slenderness between Class 2 and Class 3 is given by


134

εα

= = gtgt = =minus minus

ct

235456middot

256 456 3459846 58590026 13 1 13middot0571 1

The steel web is at least in Class 3 and reasoning is now based on the elastic stress distribution at ULS given in Fig 66 ψ= -(2682 2531) = -1059le -1 therefore the limiting slenderness between Class 3 and Class 4 is given by (EN-1993-1-1 55 and table 52)

( ) ( )ε ψ ψ= = le times = times + =times timesct

256 2359846 62 1- (- ) 62 1 1059 1059 10849

0026 345

It is concluded that the steel web is in Class 3

Conclusion The cross-section at support P1 is in Class 3 and is checked by an elastic section analysis

623 SECTION ANALYSIS

6231 Elastic bending verification

In the elastic bending verification the maximum stresses in the structural steel must be below the

yield strength σγ

le0

ys

M

f

As we have 29263 MPa in the upper steel flange and -27754 MPa in the lower steel flange which are below the limit of fyγM0=295MPa admitted in an elastic analysis for the thickness of 120 mm the bending resistance is verified

This verification could be made not with the extreme fibre stresses but with the stresses of the center of gravity of the flanges (EN-1993-1-1 621(9))

6232 Alternative Plastic bending verification (Effective Class 2 cross-section)

EN-1994-2 552(3) establishes that a cross-section with webs in Class 3 and flanges in Classes 1 or 2 may be treated as an effective cross-section in Class 2 with an effective web in accordance to EN-1993-1-1 6224


135

Fig 67 Effective class 2 cross-section at support P-1 Design plastic bending resistance

If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper part of the web then the internal axial forces equilibrium of the cross section leads to the location of the PNA

εγ γ

+ + + times minus times times times times minus =

y w y ws s s uf w w s lf

M M

f fF F F X t t F

1 2 0 0

2 20 0

6304+4034+354+897middotX-2middot3848-4248=0 then X=0495 m

And the hogging bending moment resistance of the effective class 2 cross-section is

MplRd=-(6304middot(0353+012+0495)+4034middot(013+012+0495)+354middot(006+0495)+444middot(04952) +3848middot(256-0495-04292)+4248middot(256-0495-006))= -12297 MNmiddotm

As = lt =10935 12253Ed pl RdM M the bending resistance is verified


As τ

εη

= = ge =w

w

hk

t256 31

9846 51360026




η

γ

times times times= + le = times =

timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2560 2610 1446

3 3middot1 10 (EN 1993-1-5 52)

Given the distribution of the bracing transverse frames (spacing a = 8 m) a vertical frame post is located in the cross-section at support P1 The shear buckling check is therefore performed in the adjacent web panel with the highest shear force The maximum shear force registered in this panel is VEd = 812 MN

The vertical frame posts are assumed to be rigid This yields


136

τ = + = + =

whk

a

2 2256534 4 534 4 575

8 is the shear buckling coefficient according to EN-1993-

1-5 Annex A3

( ) ( )π π

σν


minus times minus timesw

E

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 261958

12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)

ττ σ= = times =middot 575 1958 11258 cr Ek MPa (EN-1993-1-5 53)

λττ

= = = =y w y ww

crcr

f f 345076 076 133

11258middot 3 is the slenderness of the panel according to EN-

1993-1-5 53 As λw is ge108 then


( ) ( )χ

λ= = =

++w

w

137 1370675

07 13307(Table 51 of EN-1993-1-5 53)


χ

γminustimes times times

= = times =times

w y w wbw Rd

M

f h tV MN 6

1

0675 345 2560 2610 814

3 3 110


= + = + le =b Rd bw Rd bf Rd b RdV V V MN V MN 814 0 1446 814

And η


= = times =times

y w wpl a Rd

M

f h tV MN 6

0

12 345 2560 2610 1591

3 3 10 (EN 1993-1-1 626)

As VEd = 812 MNle VRd = min(VbwRd VplaRd)= min(814 1591)=814 the shear design force is lower than the shear buckling resistance

6234 Flange contribution to the shear buckling resistance

When the flange resistance is not fully used to resist the design bending moment and therefore MEdltMfRd the contribution from the flanges could be evaluated according to EN-1993-1-5 54

γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1

Note that in our case it is not strictly necessary the use of the shear buckling resistance of the flanges as seen in the previous paragraph but we will develop the calculation in an academic way

Where bf and tf must be taken for the flange which provides the smallest axial resistance with the condition that bf must be not larger than 15εtf on each side of the web

MfRd is the plastic bending resistance of the cross-section neglecting the web area


137

Fig 68 Design plastic bending resistance neglecting the web area

If we consider that the PNA is located at a distance x from the extreme upper fibre of the upper flange then the internal axial forces equilibrium of the cross section leads to the location of the PNA

( )minus+ + minus minus =s s s uf s uf s lf

xxF F F F F1 2

0120

012 012

( )minus+ + sdot minus sdot minus =

xx 0126304 4034 354 354 4248 0

012 012

Then x =01145 m

And the hogging bending moment resistance of the effective cross-section neglecting the web area is

MfRd=-2middot(6304middot(0353+01145)+4034middot(013+01145)+33777middot(011452)+1628middot(012-01145)2+4248middot(28-006-01145))= -11740 MNmiddotm

As = lt =Ed f RdM M 10935 11740 the bending resistance is verified without considering the

influence of the web and the shear resistance is already verified neglecting the contribution of the flanges therersquos no need no verify the interaction M-V However we will check the interaction M-V for the example

Once the bending resistance of the cross-section neglecting the web MfRd is obtained the contribution of the flanges to the shear buckling resistance can be evaluated as

γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1middot

As the upper flange is a composite flange made of the steel reinforcement and the steel upper flange itself we will take the lower steel flange (1200x120 mm2) to evaluate the contribution of the flanges to the shear buckling resistance

According to EN-1993-1-5 54 (1)

times times times= + = + =

times times

f f yf

w yw

b t fc a m

th f

2 2

2 2

16 16 1200 120 295025 8 025 3110

26 256 345


138

Then minus times = minus = times

timesbf RdV

226

1200 120 295 10935middot 1 0197 MN

3110 11 1174010

The shear buckling resistance is the sum of the contribution of the web = 814 bw RdV MN obtained

before and the contribution of the flanges = 0197 MNbf RdV so the total shear buckling resistance in this case is


The contribution of the flanges to shear buckling resistance represents in this case less than 25 which could be considered negligible as supposed before

According to EN-1993-1-5 55 the shear verification is

η = le3

10Ed

b Rd

VV

and in this case η = =3

81209975

814 without considering the contribution of the

flanges to the shear buckling resistance

6235 Bending and shear interaction

The interaction M-V should be considered according to EN-1993-1-5 71 (1) As the design shear force is higher than 50 of the shear buckling resistance then is has to be verified

η η

+ minus minus le

f Rd

pl Rd

MM

21 3

1 2 1 10

Where

η = Ed

pl Rd

MM1

and η = Ed

bw Rd

VV3

Fig 69 Shear-Moment interaction for Class 3 and 4 cross-sections according to clause 71 of EN-1993-1-5 (Figure 67 of1)


139

This criterion should be verified according to EN-1993-1-5 71 (2) at all sections other than those located at a distance less than hw2 from a support with vertical stiffener

If we consider the internal shear forces and moments of the section located over P-1 (x=60m)VEd=8124MN MEd=-10935mMN and the section located at X=625 m VEd=7646MN MEd=-9186mMN we could obtain the values of the design shear force and bending moment of the section located at X=6125 m which approximately is at hw2 from the support as an average of both values on the safe side

Then we will verify the interaction for the design internal forces and moments

VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN

That leads to η = =1

1006050818

12297 η = =3

788509686

814 and

[ ]η η+ minus minus = + minus times minus = le

f Rd

pl Rd

M

M

2 21 3

117401 2 1 0818 1 2 09686 1 0858 1

12297

So the interaction M-V is verified

Note that we have considered that MplRd is the value obtained before for the effective class 2 cross-section

63 Alternative double composite cross-section at internal support P-1

As an alternative to the simple composite cross-section located at the hogging bending moments area it is possible to design a double composite cross-section with a bottom concrete slab located between the two steel girders connected to them

The double composite action in hogging areas is an economical alternative to reduce the steel weight of the compressed bottom flange

Compression stresses from negative bending usually keep the bottom slab uncracked so bending and torsional stiffness in these areas are noticeably higher than those classically obtained with steel sections Double composite action greatly improves the deformational and dynamic response both to bending and torsion

The main structural advantage of the double composite action is related to the bridge response at ultimate limit state Cross-sections along the whole bridge are in Class 1 or Class 2 not only in sagging areas but also usually in hogging areas Thus instability problems at ultimate limit state are avoided not only at the bottom flange because of its connection to the concrete but also in webs due to the low position of the neutral axis in an ultimate limit state

As a result a safe and economical design is possible using a global elastic analysis with cross-section elastoplastic resistances both in sagging and hogging areas There is even enough capacity for almost reaching global plasticity in ULS by means of adequate control of elastoplastic rotations with no risk of brittle instabilities This constitutes a structural advantage of the cross sections with double composite action solution when compared to the more classical twin girder alternatives

Fig 610 shows two examples of road bridges bridge over river Mijares (main span 64 m) in Betxi-Borriol (Castelloacuten Spain) and bridge over river Jarama (main span 75 m) in Madrid Spain with double composite action in hogging areas


140

Fig 610 Two examples of road composite bridges with double composite action in hogging

areas

Fig 611 shows a view of Viaduct ldquoArroyo las Piedrasrdquo in the Spanish High Speed Railway Line Coacuterdoba-Maacutelaga This is the first composite steel-concrete Viaduct of the Spanish railway lines with a main span of 635 m

In High Speed bridges the typical twin girder solution for road bridges must improve their torsional stiffness in order to respond to the high speed railway requirements In this case in hogging areas the double composite action is materialized not only for bending but also for torsion

The double composite action was extended to the whole length of the deck to allow the torsion circuit to be closed A strict box cross section is obtained in sagging areas with the use of discontinuous precast slabs only connected to the steel girders for torsion and not for bending

Fig 611 Example of a High Speed Railway Viaduct with double composite action


141

Fig 612 Cross-section at support P-1 with double composite action Design plastic bending

resistance

Back to our case study if we change the lower steel flange from 1200x120 mm2 to a smaller one of 1000x60 mm2 plus a 050 m thick bottom slab of concrete C3545 (Fig 612) we could verify the bending resistance to compare both cross sections We could also resize the upper steel flange or even the upper slab reinforcement but for this example we will keep the original ones and only change the lower steel flange

Fig 613 shows a classical solution for composite road bridges with double composite action The bottom concrete slab in hogging areas is extended to a length of 20 or 25 of the main span The maximum thickness at support cross section is 050 m and the minimum thickness at the end of the slab is 025 m Fig 613 defines in red line the thickness distribution of the bottom concrete slab and in green the lower steel flange reduction

Fig 613 Alternative steel distribution of the double composite main girder and bottom

concrete slab thickness


142

For the example we are only calculating the ultimate bending resistance of the double composite cross section at support P-1 but it is necessary to clarify some aspects treated by EN-1994-2 related to the double composite action

EN 1994-2 establishes in 5422 (2) the modular ratio simplified method for considering the creep and shrinkage of concrete in a simple composite cross-section For double composite cross sections this simplified method is not fully applicable

EN-1994-2 5422 (10) requires that for double composite cross section with both slabs un-cracked (eg in the case of pre-stressing) the effects of creep and shrinkage should be determined by more accurate methods

Strictly speaking in our case we do not have double composite action with both slabs un-cracked because the upper slab will be cracked and we will neglect its contribution and only consider the upper reinforcement so what we have in hogging areas is a simple composite cross-section with the reinforcement of the upper slab and bottom concrete in compression


The upper flange is in tension therefore it is in Class 1 (EN 1993-1-1 552)


minus minus= = =

1000 26487 mm

2 2lf wb t

c

ε= = le = =487 235

8116 10middot 10middot 837560 335lf

ct



The upper part of the web is in tension and the lower part is in compression The position of the Plastic Neutral Axis (PNA) is determined as follows

o The tensioned upper slab is cracked and we neglect its contribution


γminus= = times =times4 2

1 1

500144996 10 6304 MN

115sk

s ss

fF A m (force of frac12 slab)



2 2

50092797 10 4034 MN

115sk

s ss



γ= = times times =

0

295(12 012) 354 MN

10y uf

s uf s ufM

fF A


143


γ= = times times =

0

345(262 0026) 2350 MN

10y w

s w s wM

fF A


γ= = times times =

0

335(100 006) 201 MN

10y lf

s lf s lfM

fF A

o Design plastic resistance of the bottom concrete slab in compression

γtimes

= = times times =inf

085 085 3535 05 347 MN

150ck

c cc

fF A

As + + le + +1 2 infs s s uf s w s lf cF F F F F F

(4573le783) and

+ + + ge +1 2 infs s s uf s w s lf cF F F F F F (6923le548) the PNA is located in the steel web

If we consider that the PNA is located at a distance x from the upper extreme fibre of the web then the internal axial forces equilibrium of the cross-section gives the location of the PNA

minus+ + + minus minus minus =1 2 inf

(262 )0

262 262s s s uf s w s w s w s lf c

x xF F F F F F F F


Only around 30 of the steel web is in compression (the lower part) 262-1815=0805 m

αminus minus

= = = le262 1815

0307 050262

w

w

h xh

Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if αlt050 then

Therefore the limiting slenderness between Class 2 and Class 3 is given by

εα

times= = lt = =

235415

262 415 34510076 111560026 0307

ct

According to this the steel web is in Class 2

However the part of the web in touch with the bottom concrete slab is laterally connected to it so only 0305 m of the total length under compression (0805 m) could have buckling problems If we take this into consideration the actual depth of the web considered for the classification of the compressed panel is 1815+0305=212m instead of 262 m considered before

With this new values αminus minus

= = = le

212 18150144 050

212w

w

h xh

Then according to EN-1993-1-1 55 and table 52 (sheet 1 of 3) if α lt050 then



144

εα

times= = lt = =

23536

212 36 3458154 206330026 0144

ct

The steel web could be in fact classified as Class 1

Conclusion The cross-section at support P1 with double composite action is in Class 2 (due to the lower steel flange) and can be checked by plastic section analysis as we said at the beginning of this section

632 PLASTIC SECTION ANALYSIS BENDING RESISTANCE CHECK

If we consider that the PNA is located at a distance x=1815 m from the upper extreme fibre of the upper part of the web then the hogging bending moment resistance of the Class 2 cross-section is

MplRd=-(6304middot(0353+012+1815)+4034middot(013+012+1815)+354middot(006+1815)+ 1628middot(11852) +722middot(08052)+3472middot(0805-025)+201middot(0805+0062))= -14285 MNmiddotm

In comparison with the simple composite action cross-section we have significantly increased the bending moment resistance locally reducing the amount of structural steel just by adding the bottom concrete slab connected to the steel girders

For the final verification MEd should be lower than the ultimate bending resistance MplRd For the example we havenrsquot recalculated the new design bending moment MEd increased by the self weight of the bottom concrete something that of course should had been done in a real case

633 SOME COMMENTS ABOUT AN EVENTUAL CRUSHING OF THE EXTREME FIBRE OF THE BOTTOM CONCRETE

EN-1994-2 6212 (2) establishes that for a composite cross-section with structural steel grade S420 or S460 if the distance between the PNA (xpl) and the extreme fiber of the concrete slab in compression exceeds 15 of the overall depth of the cross section (h) the design resistance moment MRd should be taken as βmiddotMRd reduced by the β factor defined on figure 63 of EN-1994-2 This figure limits this ratio to a maximum value of 40

Although this paragraph applies to the steel grade we could consider limiting the maximum ratio xplh to avoid an eventual crushing of the concrete

In standard composite bridges in sagging bending moment areas the ratio xplh is usually below the limit of 015 This value generally varies from 010 to 015 so there is not a practical incidence of the reduction of the bending moment resistance

Meanwhile in composite cross-sections with double composite action in hogging bending moment areas the ratio xplh is usually around 25-30 The incidence of the β factor in a real case of double composite action has not a very big influence barely reducing the plastic bending moment resistance of the composite cross-section from 94 to 91 of its total plastic bending resistance

In our case study for the alternative double composite cross-section this ratio is xplh=08653216=0269 This value leads to a β factor of 093 so the reduced bending moment resistance would be βmiddotMRd =093middot(-14285)=-13285 MNmiddotm

In our case study we have considered the resistance of the bottom concrete equal to the upper concrete C3545 but in practice it is not unusual to use higher resistance in the bottom concrete C4050 C4555 or even C5060


145

64 Verification of the Serviceability Limit States (SLS)

EN-1994-2 71 (1) establishes that a composite bridge shall be designed such that all the relevant SLS are satisfied according to the principles of EN-1990 34 The limit states that concern are

o The functioning of the structure or structural members under normal use

o The comfort of people

o The ldquoappearancerdquo of the construction work This is related with such criteria as high deflections and extensive cracking rather than aesthetics

At SLS under global longitudinal bending the following should be verified

o Stress limitation and web breathing according to EN-1994 72

o Deformations deflections and vibrations according to EN-1994 73

o Cracking of concrete according to EN-1994 74

In this case study we are only analyzing the stress limitation and the cracking of concrete And we will not carry out a deflection or vibration control that should be done according to EN-1994 73

65 Stresses control at Serviceability Limit States

651 CONTROL OF COMPRESSIVE STRESS IN CONCRETE

EN-1994-2 722 (1) establishes that the excessive creep and microcraking of concrete shall be avoided by limiting the compressive stress in concrete EN-1994-2 722 (2) refers to EN-1992-1-1 and EN-1992-2 72 for that limitation

EN-1992-1-1 72 (2) recommends to limit the compressive stress in concrete under the characteristic combination to a value of k1middotfck (k1 is a nationally determined parameter and the recommended value is 060) so as to control the longitudinal cracking of concrete and also recommends to limit compressive stress in concrete under the quasi-permanent loads to k2middotfck (k2 is a national parameter and the recommended value is 045) in order to admit linear creep assumption

Fig 614 shows the maximum and minimum normal stresses of the upper concrete slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The results for all cross-sections of the bridge are very far from both compression limits 06middotfck=-21 MPa or 045middotfck=-1575 MPa


146

Fig 614 Concrete slab stress under the characteristic SLS combination

652 CONTROL OF STRESS IN REINFORCEMENT STEEL BARS

Tensile stresses in the reinforcement shall be limited in order to avoid inelastic strain unacceptable cracking or deformation according to EN-1992-1-1 72(4)

Fig 615 Upper reinforcement layer stress under the characteristic SLS combination


147

Unacceptable cracking or deformation may be assumed to be avoided if under the characteristic combination of loads the tensile stress in the reinforcement does not exceed k3middotfsk and where the stress is caused by an imposed deformation the tensile stress should not exceed k4middotfsk k3 and k4 are nationally determined parameters and the recommended values are k3= 08 and k4= 10)

Fig 615 shows the maximum and minimum normal stresses of the upper reinforcement layer of the slab calculated in two different hypotheses upper slab cracked or uncracked under the characteristic SLS combination The stress results for all cross-sections of the bridge are widely verified for the example very far from both tensile limits 08middotfsk=400 MPa or 10middotfsk=500 MPa

Note that the stresses calculated with a contributing concrete strength are not equal to zero at the deck ends because of the shrinkage self-balanced stresses (isostatic or primary effects of shrinkage)

When McEd is negative the tension stiffening term ∆σs should be added to the stress values in Fig 52 calculated without taking the concrete strength into account This term ∆σs is in the order of 100 MPa (see paragraph 663)

653 STRESS LIMITATION IN STRUCTURAL STEEL

EN-1994-2 722 (5) refers to EN-1993-2 73 for the stress limitation in structural steel under SLS

For the characteristic SLS combination of actions considering the effect of shear lag in flanges and the secondary effects caused by deflections (if applicable) the following criteria for the normal and shear stresses in the structural steel should be verified (EN-1993-2 73 equations 71 72 and 73)

σγ

le

yEd ser

M ser

f

τγ

lesdot

3y

Ed ser

M ser

f

σ τγ

+ sdot le2 2

3 yEd ser Ed ser

M ser

f

The partial factor γMser is a national parameter and the recommended value is 10 according to EN-1993-2 72 (note 2)

Strictly speaking the Von Mises criterion of the third equation only makes sense if it is calculated with concomitant stress values

For the verification of the stresses control at SLS the stresses should be considered on the external faces of the steel flanges and not in the flange midplane (EN-1993-1-1 621 (9))

Figs 616 and 617 show the maximum and minimum normal stresses of the upper and lower steel flanges calculated in two different hypotheses upper slab cracked or uncracked

The normal stresses for all cross-sections of the bridge are far from the limit of the yield strength which depends on the steel plate thickness (Figs 616 and 617)

σγ

le

yEd ser

M ser

f


148

Fig 616 Upper steel flange stress under the characteristic SLS combination

Fig 617 Lower steel flange stress under the characteristic SLS combination

These figures make it clear that the normal stress calculated in the steel flanges without taking the concrete strength into account are logically equal to zero at both deck ends However this is not true for the stresses calculated by taking the concrete strength into account as the self-balanced stresses from shrinkage (still called isostatic effects or primary effects of shrinkage in EN1994-2) were then taken into account


149

Fig 618 shows the maximum and minimum shear stresses in the centroid of the cross section calculated in two different hypotheses upper slab cracked or uncracked The shear stress results for all cross-sections of the bridge are very far from the limit

τγ

le = =times

35520496

3 3 10y

Ed ser

M ser

fMPa

Fig 618 Shear stress in the centre of gravity of the cross-section under the characteristic SLS combination

To be safe without increasing the number of stress calculations (and because this criterion is widely verified for the example see Figs 619 and 620) the Von Mises criterion has been assessed for each steel flange by considering the maximum normal stress in this flange and the maximum shear stress in the web (ie non-concomitant stresses and hypotheses on the safe side)

Figs 619 and 620 show the maximum and minimum stresses applying the Von Mises safety criterion described in both steel flanges All cross-sections of the bridge are very far from the limit

σ τγ

+ le2 2

3 yEd ser Ed ser

M ser

f


150

Fig 619 Von Mises criterion in the upper flange under the characteristic SLS combination

Fig 620 Von Mises criterion in the lower flange under the characteristic SLS combination

654 ADDITIONAL VERIFICATION OF FATIGUE UNDER A LOW NUMBER OF CYCLES

According to EN-1993-2 73 (2) it is assumed that the nominal stress range in the structural steel framework due to the SLS frequent load combination is limited to


151

σγ

∆ le

15 yfre

M ser

f

This criterion is used to ensure that the frequent variations remain confined in the strictly linear part (+- 075 fy) of the structural steel stress-strain relationship With this any fatigue problems for a low number of cycles are avoided

655 LIMITATION OF WEB BREATHING

Every time a vehicle crosses the bridge the web gets slightly deformed out of its plane according to the deformed shape of the first buckling mode and then returns to its initial shape This repeated deformation called web breathing is likely to generate fatigue cracks at the weld joint between web and flange or between web and vertical stiffener

According to EN-1993-2 74 (2) for webs without longitudinal stiffeners (or for a sub-panel in a stiffened web) the web breathing occurrence can be avoided for road bridges if

le + le30 40 300w

w

hL

t

Where L is the span length in m but not less than 20 m

For the design example

o in end-span hwtw = 1511 le 30+4middot60=270

o in central span hwtw = 1511 le 300

Generally speaking this criterion is widely verified for road bridges Otherwise EN1993-2 defines a more accurate criterion (EN-1993 74 (3)) if EN-1993-2 74 (2) is not satisfied based on

o the critical plate buckling stresses of the unstiffened web (or of the sub-panel)

σcr = kσmiddotσE and τcr = kτmiddotσE

o the stresses σxEdser and τxEdser for frequent SLS combination of actions (calculated at a particular point where fatigue crack initiation could occur)

σ τ

σ τ+ le

2 2

1111x Ed ser x Ed ser

cr cr

66 Control of cracking for longitudinal global bending

661 MAXIMUM VALUE OF CRACK WIDTH

The maximum values of the crack width are defined in EN-1992-1-1 731 table 71N depending on the exposure class (EN-1992-1-1 4 table 41)

For the example we assume that the upper reinforcement of the slab located under the waterproofing layer is XC3 exposure class and the lower reinforcement of the slab is XC4


152

According to EN-1992-1-1 731 table 71N for exposure classes XC3 and XC4 the recommended value of the maximum crack width wmax is 03 mm under the quasi-permanent load combination

We will also verify the crack width limited to wmax=03 mm under indirect non-calculated actions (restrained shrinkage) in the tensile zone for the characteristic SLS combination of actions

662 CRACKING OF CONCRETE MINIMUM REINFORCEMENT AREA

The simplified procedure of EN-1994-2 742 (1) requires a minimum reinforcement area for the composite beams given by

σ= s s c ct eff ct sA k k kf A

Where

fcteff is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur fcteff may be taken as fctm=32 MPa for a concrete C3545 (according to EN-1992-1-1 table 31)

k is a coefficient which accounts for the effect of non-uniform self balanced stresses It may be taken equal to 080 (EN-1994-2 742 (1))

ks is a coefficient which accounts for the effect of the reduction of the normal force of the concrete slab due to initial cracking and local slip of the shear connection which may be taken equal to 090 (EN-1994-2 742 (1))

kc is a coefficient which takes into account the stress distribution within the section immediately prior to cracking and is given by

( )= + le

+ 0

103 10

1 2cc

kh z

hc is the thickness of the concrete slab excluding any haunch or ribs In our case hc=0307 m

z0 is the vertical distance between the centroid of the uncracked concrete flange and the uncracked composite section calculated using the modular ratio n0 for short term loading In our case for P-1 cross section z0=102677-(0109+03072)= 0764 m and for the P1P2 mid-span cross-section z0=066854-(0109+03072)= 0406 m

σs is the maximum stress permitted in the reinforcement immediately after cracking This may be taken as its characteristic yield strength fsk (according to EN-1994-2 742) In our case fsk=500 MPa

Act is the area of the tensile zone caused by direct loading and primary effect of shrinkage immediately prior to cracking of the cross section For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2

Then

( )= + = le

+ times

103 113 10

1 0307 2 0764ck for the support P-1 cross-section hence kc=10

( )= + = le

+ times

103 102 10

1 0307 2 0406ck for the mid-span P-1-P-2 cross-section hence kc=10

= times times times times times = =6 2 2min 09 10 08 32 1950 10 500 89856 8985sA mm cm for half of slab (6 m)


153

As we have φ 20130 in the upper reinforcement level and φ 16130 in the lower reinforcement level the reinforcement area is (24166+15466) cm2mmiddot60m=23779 cm2gtgt Asmin so the minimum reinforcement of the slab is verified

663 CONTROL OF CRACKING UNDER DIRECT LOADING

According to EN-1994-2 743 (1) when the minimum reinforcement calculated before (according to EN-1994-2 742) is provided the limitation of crack widths may generally be achieved by limiting the maximum bar diameter (according to EN-1994-2 table 71) and limiting the maximum bar spacing (according to table 72 of EN-1994-2 743) Both limits depend on the stress in the reinforcement and the crack width

Table 61 Maximum bar diameter for high bond bars (EN-1994-2 743 table 72)

Steel Stresses σs (Nmm2)

Maximum bar diameter φlowast (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm

160 200 240 280 320 360 400 450

40 32 20 16 12 10 8 6

32 25 16 12 10 8 6 5

25 16 12 8 6 5 4 -

The maximum bar diameter φ for the minimum reinforcement may be obtained according to EN-1994-2 742 (2)

φ φ=

0

ct eff

ct

ff

Where φlowast is obtained of table 71 of EN-1994 and fct0 is a reference strength of 29 MPa

Table 62 Maximum bar spacing for high bond bars (EN-1994-2 743 table 72)


Maximum bar spacing (mm) for design crack width wk wk=04 mm wk=03 mm wk=02 mm

160 200 240 280 320 360

300 300 250 200 150 100

300 250 200 150 100 50

200 150 100 50 - -

The stresses in the reinforcement should be determined taking into account the effect of tension stiffening of concrete between cracks In EN-1994-2 743 (3) there is a simplified procedure for calculating this


154

In a composite beam where the concrete slab is assumed to be cracked stresses in reinforcement increase due to the effect of tension stiffening of concrete between cracks compared with the stresses based on a composite section neglecting concrete

The direct tensile stress in the reinforcement σs due to direct loading may be calculated according to EN-1994-2 743 (3)

σ σ σ= + ∆0s s s

With σα ρ

∆ =04 ctm

sst s

f and α =st

a a

AIA I

Where

σs0 is the stress in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension

fctm is the mean tensile strength of the concrete For a concrete C3545 (according to EN-1992-1-1 table 31) fctm=32 MPa

ρs is the reinforcement ratio given by ρ = ss

ct

AA

Act is the area of the tensile zone For simplicity the area of the concrete section within the effective width may be used In our case Act=195 m2

As is the area of all layers of longitudinal reinforcement within the effective concrete area

A I are area and second moment of area respectively of the effective composite section neglecting concrete in tension

Aa Ia are area and second moment of area respectively of the structural steel section

Although there could be another section of the bridge with higher tensile stresses in the reinforcement due to the sequence of the concreting phase we will check for the application example only two cross sections over the support P-1 which normally would be the worst section and mid span P-1P-2

At the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) hence

ρminustimes

= =423779 10

001219195s and the mid-span P-1P-2 cross-section As=18559 cm2 (φ 16130 + φ

16130 in 6 m) hence ρminustimes

= =418559 10

000952195s

The value of αst at the P-1cross-section isαtimes

= =times

03543 058321232

03305 05076st while in the mid-span P-1P-2

cross-section αtimes

= =times

01555 024561416

01369 01969st

Then the effect of tension-stiffening at the P-1 cross-section is

σtimes

∆ = =times

04 328523

1232 001219s MPa


155

Meanwhile in the mid span P-1P-2 σtimes

∆ = =times

04 329495

1416 00s MPa

As the tensile stresses in the reinforcement caused by the internal forces acting on the composite section calculated neglecting concrete in tension are

o Support P-1 cross section σs0 =6594 MPa

o Mid span P-1P-2 cross section σs0 =2745 MPa

Then the direct tensile stresses in reinforcement σs due to direct loading (according to EN-1994-2 743) are

o Support P-1 cross section σs =σs0 +∆σs =6594+8523=15117 MPa

o Mid span P-1P-2 cross section σs =σs0 +∆σs =2745+9495=1224 MPa

As both values are below 160 MPa according to table 62 the maximum bar spacing for the design crack width wk=03mm is 300 mm As we have 130 mm the maximum bar spacing is verified

According to table 61 the maximum bar diameter φ for the minimum reinforcement should be 32 mm and

φ = =32

32 353129

mm

As the example verifies the minimum reinforcement established by EN-1994-2 742 (1) the actual maximum diameter used in the longitudinal steel reinforcement is φ 20 lower than the limit established by EN-1994-2 742 (2) and the bar spacing also verifies the limits established by EN-1994-2 742 (3) then the crack width is controlled

664 CONTROL OF CRACKING UNDER INDIRECT LOADING

It has to be verified that the crack widths remain below 03 mm using the indirect method in the tensile zones of the slab for characteristic SLS combination of actions This method assumes that the stress in the reinforcement is known But that is not true under the effect of shrinkages (drying endogenous and thermal shrinkage) The following conventional calculation is then suggested

From the expression of the minimum reinforcement area for the composite beams given by EN-1994-2 742 (1) σ= s s c ct eff ct sA k k kf A

we can get

σ = s s c ct eff ct sk k kf A A

Letacutes consider that this is the stress in the reinforcement due to shrinkage at the cracking instant

In our case for the P-1 cross-section As=23779 cm2 (φ 20130 + φ 16130 in 6 m) and the mid span P-1P-2 cross section As=18559 cm2

This gives

o Support P-1 cross section σs=09x10x08x32x195 (23779x10-4)=18894 MPa

o Mid-span P-1P-2 cross section σs=09x10x08x32x195 (18559x10-4)=24208 MPa

High bond bars with diameter φ= 20 mm have been chosen in the upper reinforcement layer of the slab at the support cross-section and φ= 16 mm at the mid-span P-1P-2 cross section This gives

o Support P-1 cross-section φlowast= φmiddot2932=18125 mm


156

o Mid-span P-1P-2 cross-section φlowast= φmiddot2932=145 mm

The maximum reinforcement stress is obtained by linear interpolation in Table 71 in EN1994-2

o Support P-1 cross-section 23018 MPa gt18894 MPa

o Mid-span P-1P-2 cross-section 25500 MPagt24208 MPa

Hence both sections are verified

67 Shear connection at steel-concrete interface

671 RESISTANCE OF HEADED STUDS

The design shear resistance of a headed stud (Fig 622) (PRd) automatically welded in accordance with EN-14555 is defined in EN-1994-2 663

= (1) (2)min( )Rd Rd RdP P P

P(1)Rd is the design resistance when the failure is due to the shear of the steel shank toe of the stud

π

γ=

2

(1)08

4u

Rdv

df

P

P(2)Rd is the design resistance when the failure is due to the concrete crushing around the shank of the

stud

α

γ=

2(2) 029 ck cm

Rdv

d f EP

With

α = +

02 1schd

for 3le schd

le4

α = 10 for schd

gt4

Where

γv is the partial factor The recommended value is γv=125

d is the diameter of the shank of the headed stud (16ledle25mm)

fu is the specified ultimate tensile strength of the material of the stud (fule500MPa)

fck is the characteristic cylinder compressive strength of the concrete In our case fck=35 MPa

Ecm is the secant modulus of elasticity of concrete (EN-1992-1-1 312 table 31) In our case Ecm=22000(fcm10)03=3407714 MPa (fcm=fck+8 MPa)

hsc is the overall nominal height of the stud


157

In our case if we consider headed studs of steel S-235-J2G3 of diameter d=22 mm height hsc=200 mm and fu=450 MPa then

π timestimes times

= = times

2

(1) 6

2208 450

4 01095 10 N=01095 MN125RdP

= = gtgt200

909 422

schd

α = 10 and times sdot times

= =times2

(2) 029 1 22 35 340771401226 MN

125RdP

Then = 01095 MNRdP Each row of 4 headed studs (Fig 621) resist at ULS sdot =4 0438 MNRdP

For Serviceability State Limit EN-1994 722 (6) refers to 681 (3) Under the characteristic combination of actions the maximum longitudinal shear force per connector should not exceed ksmiddotPRd (the recommended value for ks=075)

Then sdot = times075 01095 MN=00766 MNs Rd

k P Each row of 4 headed studs (Fig 621) resist at SLS sdot sdot =4 03064 MNs Rdk P

Fig 621 Detail of headed studs connection

672 DETAILING OF SHEAR CONNECTION

The following construction detailing applies for in-situ poured concrete slabs (EN-1994-2 665) When the slab is precast these provisions may be reviewed paying particular attention to the various instability problems (buckling in the composite upper flange between two groups of shear connectors for example) and to the lack of uniformity of the longitudinal shear flow at the steel-concrete interface (EN-1994-2 6655 (4))

Maximum longitudinal spacing between rows of connectors

According to EN-1994-2 6655 (3) to ensure a composite behaviour of the main girder the maximum longitudinal center to center spacing (s) between two successive rows of connectors is limited to smax le min (800 mm 4 hc) with hc the concrete slab thickness

When verifying the mid-span P1P2 cross-section (see paragraph 612) it was considered that the upper structural steel flange in compression was a Class 1 element as it was connected to the concrete slab


158

However if we consider the upper flange non-connected to the upper concrete slab according to EN-1993-1-1 table 52 sheet 2 of 3 ctf = ((1000-18)2)40=12275 and that would result a Class 4 flange

as times =fct =12275gt14middot =14 235 345 1155 In order to classify a compressed upper flange connected to the slab as a Class 1 or 2 because of the restraint from shear connectors the headed studs rows should be sufficiently close to each other to prevent buckling between two successive rows (EN-1994-2 6655(2)) This gives an additional criterion in smax

lemaxs 22 235ft fy if the concrete slab is solid and there is contact over the full length

lemaxs 15 235ft fy if the concrete slab is not in contact over the full length (eg slab with transverse ribs) This is not our case

Where tf is the thickness of the upper flange and fy the yield strength of the steel flange

Table 63 summarizes the results of applying both conditions to our case

Table 63 Maximum longitudinal spacing for rows of studs

Upper Steel flange tf (mm) fy (Nmm2) smax eD

40 55 80

120

345 335 325 295

726 800 800 800

297 414

Only applies for flanges in compression (not in tension)

This criterion is supplemented by EN-1994-2 6655(2) defining a maximum distance between the longitudinal row of shear connectors closest to the free edge of the upper flange in compression ndash to which they are welded ndash and the free edge itself (Fig 622)

le times9 235D fe t fy

Fig 622 Detailing

Minimum distance between the edge of a connector and the edge of a plate According to EN-1994-2 6-6-5-6 (2) the distance eD between the edge of a headed stud and the edge of a steel plate must not be less than 25 mm in order to ensure the correct stud welding


159

In this example (Fig 621) minus minus

= minus = minus = gt0 1000 750 22114 25

2 2 2 2f

D

b b de

Minimum dimensions of the headed studs According to EN-1994-2 6657 (1) and (2) the height of a stud should not be less than 3middotd where d is the diameter of the shank and the head of the stud should have a diameter not less than 15middotd and a depth of at least 04middotd (Fig 623)

Fig 623 Minimum dimensions of a headed stud

As we have studs of d=22 mm the head should have a diameter over 33 mm and a depth of at least 88 mm With a total height of the studs of 200 mm we are far from the limit of 3middotd=66 mm

EN-1994-2 also establishes a condition between the diameter of the connector and the thickness of the steel plate (EN-1994-2 6657 (3)) For studs welded to steel plates in tension subjected to fatigue loading the diameter of the stud should be

le sdot15 fd t

This is widely satisfied in the example with tfmin=55mm in the tensile area and d=22mm

This limitation also applies to steel webs This verification allows the use of the detail category ∆τc = 90 MPa

Clause 6657 (5) establishes that the limit for other elements than plates in tension or webs is dle25middottf

Minimum spacing between rows of connectors

According to EN-1994-2 6656 (4) the longitudinal spacing of studs in the direction of the shear force should be not less than 5d=110 mm in our case while the spacing in the transverse direction to the shear force should be not less than 25d in solid slabs or 4d in other cases In our example 25d=55 mm Both limits are widely fulfilled in the example with strans=250 mm

Criteria related to the stud anchorage in the slab

Where a concrete haunch is used between the upper structural steel flange and the soffit of the concrete slab the sides of the haunch should lie outside a line drawn 45ordm from the outside edge of the connector (Fig 622) (EN-1994-2 6654 (1))

Clause 6654 (2) establishes that the nominal concrete lateral cover from the side of the haunch to the connector should not be less than 50 mm and the clear distance between the lower face of the stud head and the lower reinforcement layer should be not less than 40 mm according to clause


160

6654 (2) This value could be reduced to 30 mm if no concrete haunch is used (EN-1994-2 6651 (1)) (see Fig 622)

Figs 624 and 625 show a general view and a detail of the connection with headed studs of the upper flange of a composite bridge and Fig 626 shows the connection of the lower flange of the main steel girders in a double composite cross-section

Figs 624 amp 625 View and detail of an upper flange connection

Fig 626 View of the lower flange connection of a steel girder


When the structure behaviour remains elastic in a given cross-section each load case from the global longitudinal bending analysis produces a longitudinal shear force per unit length νLk at the interface between the concrete slab and the steel main girder For a girder with uniform moment of area (S) subjected to a continuous bending moment this shear force per unit length is easily deduced from the cross-section properties and the internal forces and moments the girder is subjected to

ν =c k

L k

S VI


161

Where

νLk is the longitudinal shear force per unit length at the interface concrete-steel

Sc is the moment of area of the concrete slab with respect to the centre of gravity of the composite cross-section

I is the second moment of area of the composite cross-section

Vk is the shear force for the considered load case and coming from the elastic global cracked analysis

According to EN-1994-2 6621 (2) to calculate normal stresses when the composite cross-section is ultimately (characteristic SLS combination of actions in this paragraph) subjected to a negative bending moment McEd the concrete is taken as cracked and does not contribute to the cross-section strength But to calculate the shear force per unit length at the interface even if McEd is negative the characteristic cross-section properties Sc and I are calculated by taking the concrete strength into account (uncracked composite behaviour of the cross-section)

The final shear force per unit length is obtained by adding algebraically the contributions of each single load case and considering the construction phases As for the normal stresses calculated with an uncracked composite behaviour of the cross-section the modular ratio used in Sc and I is the same as the one used to calculate the corresponding shear force contribution for each single load case

For SLS combination of actions the structure behaviour remains entirely elastic and the longitudinal global bending calculation is performed as an envelope Thus the value of the shear force per unit length is determined in each cross-section at abscissa x by

ν ν ν = min max( ) max ( ) ( )L k k kx x x

Fig 627 shows the variations in this longitudinal shear force per unit length for the characteristic SLS combination of actions for the case of the example

In each cross-section of the deck there should be enough studs to resist all the shear force per unit length

The following should be therefore verified at all abscissa x

ν le sdot sdot ( ) ( P )iL k s Rd

i

Nx kL

with

sdot = sdot sdot 1 4s RD s RD of studk P k P

Where

νLk is the shear force per unit length in the connection under the characteristic SLS combination

Ni is the number of rows of 4 headed studs φ 22mm and h=200 mm located at the length Li

Li is the length of a segment with constant row spacing

ksmiddotPRd=4middot ks middotPRd of 1 stud =03064 MN is the SLS resistance of a row of 4 headed studs calculated in 71

For the example we have divided the total length of the bridge into segments delimited by the following abscissa x in (m) corresponding with nodes of the design model

00 60 125 250 350 420 500 625

800 875 1000 1080 1125 1200 1320 1400

1500 1625 1700 1760 1875 1940 2000


162

For example for the segment [500 m 625 m] around the support P1 the shear force per unit length obtained in absolute value for characteristic SLS combination of actions is as follows (in MNm)

Table 64 Shear force per unit length at SLS at segment 50-625 m

x (m) 50+ 54- 54+ 60- 60+ 625-

νLk (MNm) 0842 0900 0900 0989 0943 0906

The maximum SLS shear force per unit length to be considered is therefore 0989 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)

( )ν

sdot= =

(4middot P ) 03064 MN031 m

max ( ) 0989 MNms Rd

L k

k

x on a safe side 030 m

Fig 627 illustrates this elastic design of the connection for characteristic SLS combination of actions The curve representing the shear force per unit length that the shear connectors are able to take up thus encompasses fully the curve of the SLS design shear force per unit length

The corresponding values of row spacing obtained for the design of the connection in SLS are summarized in paragraph 675 of this chapter Note that we have considered regular spacing jumps from 50 to 50 mm

Fig 627 SLS shear force per unit length resisted by the headed studs


163


6741 Elastic design

Whatever the behaviour of the bridge at ULS ndash elastic in all cross-sections or elasto-plastic in some cross-sections ndash the design of the connection at ULS starts by an elastic calculation of the shear force per unit length at the interface steel-concrete by elastic analysis with the cross-sections properties of the uncracked section taking into account the effects of construction (EN-1994 6622 (4)) following the same procedure as made for SLS in the previous paragraph

In each cross-section the shear force per unit length at ULS is therefore given by

ν ν ν= min max( ) max ( ) ( )L Ed Ed Edx x x

With

ν =c Ed

L Ed

S VI

Where

νLEd is the design longitudinal shear force per unit length at the concrete-steel interface

Sc is the moment of area of the concrete slab with respect to the centre of gravity of the

composite cross-section


VEd is the design shear force for the considered load case and coming from the elastic global cracked analysis considering the constructive procedure

Fig 628 shows the variations in this design longitudinal shear force per unit length for the ULS combination of actions for the case of the example

According to EN-1994-2 6612 (1) the number of shear connectors (headed studs) per unit length constant per segment should verify the following two criteria

o locally in each segment ldquoirdquo the shear force per unit length should not exceed by more than 10 what the number of shear connectors per unit length can resist

ν le sdot sdot ( ) 11 iL Ed RD

i

Nx PL

with

= sdot 1 4RD RD of studP P

Where



PRd=4middotPRd of 1 stud =0438 MN is the ULS resistance of a row of 4 headed studs calculated in 71

o over every segment length (Li) the number of shear connectors should be sufficient so that the total design shear force does not exceed the total design shear resistance


164

ν leinti+1

i

x

x

( ) ( )L Ed i RDx dx N P with


Where xi and xi+1 designates the abscissa at the border of the segment Li

For the design of the connection at ULS we have considered the same segment division as used for the SLS verification

In the example for the segment [500 m 625 m] around the support P1 the design shear force per unit length obtained in absolute value for ULS combination of actions is as follows (in MNm)

Table 65 Design shear force per unit length at ULS at segment 50-625 m

x (m) 50+ 54- 54+ 60- 60+ 625-

νLEd (MNm) 1124 1203 1203 1323 1264 1213

The maximum ULS design shear force per unit length to be resisted is therefore 1323 MNm which is guaranteed providing the stud rows are placed at the maximum spacing of (4 studs per row)

( )ν

times sdot times= = 1

110 (4 P ) 11 0438 MN0365 m

max ( ) 1323 MNmRd stud

L kEd x

And the second condition

νsdot

= leinti+1

i

x 1

x

(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud

L Ed x dx MNs

Then sge(4middotPRd of 1 stud)1232= 04381232=0355 m then on the safe side the spacing for this segment would be s=035 m

Fig 628 illustrates the elastic design of the connection for the Ultimate Limit State (ULS) combination of actions


165

Fig 628 ULS shear force per unit length resisted by the headed studs

6742 Design with plastic zones in sagging bending areas

If a cross-section with a positive bending moment at ULS has partially yielded the previous elastic calculation made for the ULS combination of actions should be supplemented (EN-1994-2 6622 (1))

As far as the structure behaviour is no longer elastic the relationship between the shear force per unit length and the global internal forces and moments is no longer linear Therefore the previous elastic calculation becomes inaccurate In a plastic zone the shear connection is normally heavily loaded and a significant bending moment redistribution occurs between close cross-sections

In our case although the mid-span cross-sections are Class 1 sections no yielding occurs as we can see on Fig 61 with a medium tensile value for the lower flange of 3429MPa lt fy=345MPa There is therefore no need to perform the more complex calculations established by EN-1994-2 in clauses 6622 (2) and (3)

675 SYNOPSIS OF THE DESIGN EXAMPLE

Paragraphs 673 and 674 summarize respectively the connection design at SLS and ULS Fig 629 shows the results of the spacing of rows of 4 headed stud connectors resulting from the design at SLS (red solid line) the design at ULS (orange solid line) and the results of applying the maximum spacing requirements (green solid line) defined in paragraph 671 according to EN-1994-2


166

Fig 629 Envelope of spacing of rows of 4 connectors after connection dimensioning

As described before we have used an engineering criterion of dimensioning the spacing of rows of connectors with 50 mm steps This figure also shows the final envelope (in black dotted line) resulting from the three mentioned conditions and with the provision of symmetrical spacing design of the connection in the total length of the bridge Although that could not be theoretically necessary constructively thinking it is absolutely convenient

Note that in general the SLS criteria nearly always govern the design over the ULS requirements except for the sections around the mid-span In these zones the spacing just necessary to resist the SLS shear flow becomes too large to avoid buckling in the steel flange between two successive stud rows And then the governing criterion becomes the construction detailing


In this paragraph we summarize the fatigue verification that has to be performed to confirm the design of the connection already performed in previous paragraphs under SLS and ULS combination of actions

Once the connection is designed and decided the final spacing of rows of connectors fatigue ULS of the connectors has to be verified according to EN-1994-2 section 68

The fatigue load model FLM3 induces the following stress ranges

o ∆τ shear stress range in the stud shank calculated at the level of its weld on the upper structural steel flange

Unlike normal stress range the shear stresses at the steel-concrete interface are calculated using the uncracked cross-section mechanical properties The shear stress for the basic combination of non-cyclic loads (EN1992-1-1 683) has therefore no influence ∆τ is thus deduced from variations in the shear force per unit length under the FLM3 crossing only ndash noted ∆νLFLM3 ndash by taking account of its transverse location on the


167

pavement and using the short term modular ratio n0 ∆τ also depends on the local shear connector density and the nominal value of the stud shank area

ντ

π∆

∆ =

32

4

L FLM

i

i

NdL

Where



d is the diameter of the shank of the headed stud

∆νLFLM3 is the variations in the shear force per unit length under the FLM3 crossing

o ∆σp normal stress range in the upper steel flange to which the studs are welded

6761 Equivalent constant amplitude stress range

For verification of stud shear connectors based on nominal stress ranges the equivalent constant range of shear stress ∆τE2 for two million cycles is given by (EN-1994-2 6862(1))

∆τE2 = λvmiddot∆τ

Where

∆τ is the range of shear stress due to fatigue loading related to the cross-sectional area of the shank of the stud πd24 with d the diameter of the shank

λv is the damage equivalent factor depending on the spectra and the slope m of the fatigue curve

For bridges the damage equivalent factor λv for headed studs in shear should be determined from λv= λv1middotλv2middotλv3middotλv4 (EN-1994-2 6862 (3))

Factors λv2 to λv4 should be determined in accordance with EN-1993-2 952 (3) to (6) but using exponents 8 and 18 instead of 5 and 15 to allow for the relevant slope m=8 of the fatigue strength curve for headed studs given in EN-1994-2 683 (3)

o λv1 is the factor for damage effect of traffic According to EN-1994-2 6862 (4) λv1=155 for road bridges up to 100 m span

o λv2 is the factor for the traffic volume

λ

=

18

12

0 0

obsmv

NQQ N

Where

=

sumsum

188

1i i

mi

n QQ

n (EN-1993-2 952 (3)) is the average gross weight (kN) of the

lorries in the slow lane

Q0=480KN


168

N0=05x106

Nobs is the total number of lorries per year in the slow lane In this example we have Nobs=05x106 equivalent to a road or motorway with medium rates of lorries (EN-1991-2 table 45 (n))

Qi is the gross weight in kN of the lorry i in the slow lane

ni is the number of lorries of gross weight Qi in the slow lane

Table 66 Traffic assumption for obtaining λv2

Lorry Q (kN) Long distance

1 2 3 4 5

200 310 490 390 450

20 5

50 15 10

If we substitute table 66 values into the previous equations then we obtain

Qm1=45737 kN

λ = =245737 0952

480v

o λv3 is the factor for the design life of the bridge For 100 years of design life then λv3=10 according to EN-1993-2 952 (5)

o λv4 takes into account the effects of the heavy traffic on the other additional slow lane defined in the example In the case of a single slow lane λv4=10

In the present case the factor depends on the transverse influence of each slow lane on the internal forces and moments in the main girders

ηλ

η

= +

188

2 2 24

1 1 1

1 mv

m

N QN Q

η = minus12

eb

With

e is the eccentricity of the FLM3 load with respect to the bridge deck axis (in the example +- 175 m)

b is the distance between the main girders (in the example 70 m)

η = + =11 175 0752 70

and η = minus =21 175 0252 70


169

The factor η1 represents the maximum influence of the transverse location of the traffic slow lanes on the fatigue-verified main girder N1=N2 (same number of heavy vehicles in each slow lane) and Qm1=Qm2 (same type of lorry in each slow lane) will be considered for the example

This gives finally λv4=10

Then λv=155middot0952middot10middot10=1477

For the upper steel plate a stress range ∆σE is defined according to EN-1994-2 6861 (2)

σ λφ σ σ∆ = minusE max minf f

Where

σmaxf and σminf are the maximum and minimum stresses due to the maximum and minimum internal bending moments resulting from the combination of actions defined in EN-1992-1-1 683 (3)

ψ ψge gt

+ + + +

sum sum 11 1 2

1 1 k j k i k i fat

j iG P Q Q Q

λ is the damage equivalent factor calculated according to EN-1993-2 952 for road bridges with the relevant slope of the fatigue strength curve m=5

φ is a damage equivalent impact factor For road bridges φ = 10 (EN-1994-2 6861 (7)) however φ is increased when crossing an expansion joint according to EN-1991-2 461(6) φ

=13[1-D26]ge10 where D (in m) is the distance between the detail verified for fatigue and the expansion joint (with Dle6m)

6762 Fatigue verifications

For stud connectors welded to a steel flange that is always in compression under the relevant combination of actions (see paragraph 761) the fatigue assessment should be made by checking the criterion which corresponds to a crack propagation in the stud shank

γ τ τ γminus∆ le ∆2 Ff E c Mf s

Where

∆τE2 is the equivalent constant range of shear stress for two millions cycles

∆τE2 = λvmiddot∆τ (see paragraph 761)

∆τc is the reference value of fatigue strength at 2 million cycles ∆τc=90 MPa

γFf is the fatigue partial factor According to EN-1993-2 93 the recommended value is γFf=10

γMfs is the partial factor for verification of headed studs in bridges According to EN-1994-2 2412 (6) the recommended value is γMfs=10

Meanwhile where the maximum stress in the steel flange to which studs connectors are welded is tensile under the relevant combination the interaction at any cross-section between shear stress range ∆τE in the weld of the stud connector and the normal stress range ∆σE in the steel flange should be verified according to EN-1994-2 6872 (2)


170

γ σσ γ

∆le

∆E2

c

10

Ff

Mf

γ ττ γ

∆le

∆E2

c

10

Ff

Mf s and

γ σ γ τσ γ τ γ

∆ ∆+ le

∆ ∆E2 E2

c c

13

Ff Ff

Mf Mf s

Where

∆σE is the stress range in the flange connected (see paragraph 761)

∆σc is the reference value of fatigue strength at 2 million cycles ∆σc=80 MPa

γMf is the partial factor defined by EN-1993-1-9 table 31 For safe life assessment method with high consequences of the upper steel flange failure of the bridge γMf=135

In general once the connection at the steel-concrete interface is designed under the SLS and ULS combination of actions and the final spacing of connectors is decided fulfilling the maximum spacing limits established by EN-1994-2 (see paragraphs 672 to 675) the fatigue ULS verification does not influence the design of the connection

Figure 630 shows the verification of the connection under the fatigue ULS for the case of the example and Figure 631 shows the spacing of the rows of 4 studs under the fatigue ULS

Fig 630 Fatigue verification of the connection


171

Fig 631 Spacing of the rows of connectors under the fatigue ULS


The shear force per unit length at the steelconcrete interface used in the previous calculations only takes account of hyperstatic (or secondary) effects of shrinkage and thermal actions It is therefore necessary to also verify according to EN-1994-2 6624 (1) that sufficient shear connectors have been put in place at both free deck ends to anchor the shear force per unit length coming from the isostatic (or primary) effects of shrinkage and thermal actions

The first step is to calculate ndash in the cross-section at a distance Lv from the free deck end (anchorage length) ndash the normal stresses due to the isostatic effects of the shrinkage (envelope of short-term and long-term calculations) and thermal actions

Integrating these stresses over the slab area gives the longitudinal shear force at the steelconcrete interface for the two considered load cases

The second step is to determine the maximum longitudinal spacing between stud rows over the length Lv which is necessary to resist the corresponding shear force per unit length The calculation is performed for ULS combination of actions only In this case EN1994-2 6624 (3) considers that the studs are ductile enough for the shear force per unit length vLEd to be assumed constant over the anchorage length Lv This length is taken as equal to beff which is the effective slab width in the global analysis at mid-end span (6 m for this example)

All calculations performed for the design example a maximum longitudinal shear force of 215 MN is obtained at the steelconcrete interface under shrinkage action (obtained with the long-term calculation) and 114 MN under thermal actions

This therefore gives VLEd = 10x215 + 15x114 = 386 MN for ULS combination of actions


172

Notice that according to EN-1992-1-1 2421 (1) the recommended partial factor for shrinkage action is γSH=10

The design value of the shear flow νLEd (at ULS) and then the maximum spacing smax over the anchorage length Lv= beff between the stud rows are as follows

ν = = 0643 MNmL Ed

L Edeff

V

b (rectangular shear stress block)

ν= = = 1

max

4 04380681 m

0643Rd stud

L Ed

Ps

This spacing is significantly higher than the one already obtained through previous verifications (see Fig 79) As it is generally the case the anchorage of the shrinkage and thermal actions at the free deck ends does not govern the connection design

Notes

o To simplify the design example the favourable effects of the permanent loads are not taken into account (self-weight and non-structural bridge equipments) Anyway they cause a shear flow which is in the opposite direction to the shear flow caused by shrinkage and thermal actions So the suggested calculation is on the safe side

Note that it is not always true For instance for a cross-girder in a cantilever outside the main steel girder and connected to the concrete slab the shear flow coming from external load cases should be added to the shear flow coming from shrinkage and thermal actions Finally the shear flow for ULS combination of these actions should be anchored at the free end of the cross-girder

o EN1994-2 6624(3) suggests that the same verification could be performed by using the shear flow for SLS combination of actions and a triangular variation between the end cross-section and the one at the distance Lv However this will never govern the connection design and it is not explicitly required by section 7 of EN1994-2 dealing with the SLS justifications


173

References

EN-1992-1-1 Eurocode 2 Design of concrete structures Part 1-1 General rules and rules for buildings

EN-1992-2 Eurocode 2 Design of concrete structures Part 2 Concrete bridges- Design and detailing rules

EN-1993-1-1 Eurocode 3 Design of steel structures Part 1-1 General rules and rules for buildings EN-1993-1-5 Eurocode 3 Design of steel structures Part 1-5 Platted steel structures EN-1993-2 Eurocode 3 Design of steel structures Part 2 Steel bridges EN-1994-1-1 Eurocode 4 Design of composite steel and concrete structures Part 1-1 General rules

and rules for buildings EN-1994-2 Eurocode 4 Design of composite steel and concrete structures Part 2 General rules and

rules for bridges LDavaine F Imberty J Raoul 2007 ldquoGuidance book Eurocodes 3 and 4 Application to steel-

concrete composite road bridgesrdquoSeacutetra CR Hendy and RP Johnson 2006 ldquoDesignersrsquo Guide to EN-1994-2 Eurocode 4 Design of

composite steel and concrete structures Part 2 General rules and rules for bridgesrdquo Great Britain Thomas Telford


174

Acknowledgements

Table of Contents


Foreword

13Introduction

Introduction


The Eurocodes


THE DESIGN EXAMPLE


CHAPTER 6 - Composite bridge design (EN 1994-2)










622 DETERMINING THE CORSS-SECTION CLASS (ACCORDING TO EN1994-2 552)








631 Determining the cross-section Class (ACCORDING to EN1994-2 552)





651 control of COMPRESSIVE stress in concrete

652 control of stress in reinforcement steel bars

653 stress limitation in structural steel


655 limitation of web breathing



662 CRACKING OF CONCRETE MINIMUM REINFIRCEMENT AREA




671 resistance of headed studs RESISTANCE OF HEADED STUDS



674 CONECTION DESIGN FOR THE ULS COMBINATION OF ACTIONS OTHER THAN FATIGUE

6741 Elastic design






677 INFLUENCE OF SHRINKAGE AND THERMAL ACTION ON THE CONNECTION DESIGN AT BOTH DECKS ENDS

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 CHS ltFEFF4f7f75288fd94e9b8bbe5b9a521b5efa7684002000410064006f006200650020005000440046002065876863900275284e8e9ad88d2891cf76845370524d53705237300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c676562535f00521b5efa768400200050004400460020658768633002gt13 CHT ltFEFF4f7f752890194e9b8a2d7f6e5efa7acb7684002000410064006f006200650020005000440046002065874ef69069752865bc9ad854c18cea76845370524d5370523786557406300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c4f86958b555f5df25efa7acb76840020005000440046002065874ef63002gt13 CZE 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 DAN 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 DEU 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 ESP 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 ETI 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 FRA 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 GRE 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HEB 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HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke Stvoreni PDF dokumenti mogu se otvoriti Acrobat i Adobe Reader 50 i kasnijim verzijama)13 HUN 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 ITA 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 JPN ltFEFF9ad854c18cea306a30d730ea30d730ec30b951fa529b7528002000410064006f0062006500200050004400460020658766f8306e4f5c6210306b4f7f75283057307e305930023053306e8a2d5b9a30674f5c62103055308c305f0020005000440046002030d530a130a430eb306f3001004100630072006f0062006100740020304a30883073002000410064006f00620065002000520065006100640065007200200035002e003000204ee5964d3067958b304f30533068304c3067304d307e305930023053306e8a2d5b9a306b306f30d530a930f330c8306e57cb30818fbc307f304c5fc59808306730593002gt13 KOR ltFEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020ace0d488c9c80020c2dcd5d80020c778c1c4c5d00020ac00c7a50020c801d569d55c002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002egt13 LTH 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ltFEFF0049007a006d0061006e0074006f006a00690065007400200161006f00730020006900650073007400610074012b006a0075006d00750073002c0020006c0061006900200076006500690064006f00740075002000410064006f00620065002000500044004600200064006f006b0075006d0065006e007400750073002c0020006b006100730020006900720020012b00700061016100690020007000690065006d01130072006f00740069002000610075006700730074006100730020006b00760061006c0069007401010074006500730020007000690072006d007300690065007300700069006501610061006e006100730020006400720075006b00610069002e00200049007a0076006500690064006f006a006900650074002000500044004600200064006f006b0075006d0065006e007400750073002c0020006b006f002000760061007200200061007400760113007200740020006100720020004100630072006f00620061007400200075006e002000410064006f00620065002000520065006100640065007200200035002e0030002c0020006b0101002000610072012b00200074006f0020006a00610075006e0101006b0101006d002000760065007200730069006a0101006d002egt13 NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 50 en hoger)13 NOR 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 POL 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 PTB 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 RUM ltFEFF005500740069006c0069007a00610163006900200061006300650073007400650020007300650074010300720069002000700065006e007400720075002000610020006300720065006100200064006f00630075006d0065006e00740065002000410064006f006200650020005000440046002000610064006500630076006100740065002000700065006e0074007200750020007400690070010300720069007200650061002000700072006500700072006500730073002000640065002000630061006c006900740061007400650020007300750070006500720069006f006100720103002e002000200044006f00630075006d0065006e00740065006c00650020005000440046002000630072006500610074006500200070006f00740020006600690020006400650073006300680069007300650020006300750020004100630072006f006200610074002c002000410064006f00620065002000520065006100640065007200200035002e00300020015f00690020007600650072007300690075006e0069006c006500200075006c0074006500720069006f006100720065002egt13 RUS 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 SKY ltFEFF0054006900650074006f0020006e006100730074006100760065006e0069006100200070006f0075017e0069007400650020006e00610020007600790074007600e100720061006e0069006500200064006f006b0075006d0065006e0074006f0076002000410064006f006200650020005000440046002c0020006b0074006f007200e90020007300610020006e0061006a006c0065007001610069006500200068006f0064006900610020006e00610020006b00760061006c00690074006e00fa00200074006c0061010d00200061002000700072006500700072006500730073002e00200056007900740076006f00720065006e00e900200064006f006b0075006d0065006e007400790020005000440046002000620075006400650020006d006f017e006e00e90020006f00740076006f00720069016500200076002000700072006f006700720061006d006f006300680020004100630072006f00620061007400200061002000410064006f00620065002000520065006100640065007200200035002e0030002000610020006e006f0076016100ed00630068002egt13 SLV ltFEFF005400650020006e006100730074006100760069007400760065002000750070006f0072006100620069007400650020007a00610020007500730074007600610072006a0061006e006a006500200064006f006b0075006d0065006e0074006f0076002000410064006f006200650020005000440046002c0020006b006900200073006f0020006e0061006a007000720069006d00650072006e0065006a016100690020007a00610020006b0061006b006f0076006f00730074006e006f0020007400690073006b0061006e006a00650020007300200070007200690070007200610076006f0020006e00610020007400690073006b002e00200020005500730074007600610072006a0065006e006500200064006f006b0075006d0065006e0074006500200050004400460020006a00650020006d006f0067006f010d00650020006f0064007000720065007400690020007a0020004100630072006f00620061007400200069006e002000410064006f00620065002000520065006100640065007200200035002e003000200069006e0020006e006f00760065006a01610069006d002egt13 SUO 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 SVE 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 TUR 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 UKR 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 ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing Created PDF documents can be opened with Acrobat and Adobe Reader 50 and later)13 gtgt13 Namespace [13 (Adobe)13 (Common)13 (10)13 ]13 OtherNamespaces [13 ltlt13 AsReaderSpreads false13 CropImagesToFrames true13 ErrorControl WarnAndContinue13 FlattenerIgnoreSpreadOverrides false13 IncludeGuidesGrids false13 IncludeNonPrinting false13 IncludeSlug false13 Namespace [13 (Adobe)13 (InDesign)13 (40)13 ]13 OmitPlacedBitmaps false13 OmitPlacedEPS false13 OmitPlacedPDF false13 SimulateOverprint Legacy13 gtgt13 ltlt13 AddBleedMarks false13 AddColorBars false13 AddCropMarks false13 AddPageInfo false13 AddRegMarks false13 ConvertColors ConvertToCMYK13 DestinationProfileName ()13 DestinationProfileSelector DocumentCMYK13 Downsample16BitImages true13 FlattenerPreset ltlt13 PresetSelector MediumResolution13 gtgt13 FormElements false13 GenerateStructure false13 IncludeBookmarks false13 IncludeHyperlinks false13 IncludeInteractive false13 IncludeLayers false13 IncludeProfiles false13 MultimediaHandling UseObjectSettings13 Namespace [13 (Adobe)13 (CreativeSuite)13 (20)13 ]13 PDFXOutputIntentProfileSelector DocumentCMYK13 PreserveEditing true13 UntaggedCMYKHandling LeaveUntagged13 UntaggedRGBHandling UseDocumentProfile13 UseDocumentBleed false13 gtgt13 ]13gtgt setdistillerparams13ltlt13 HWResolution [2400 2400]13 PageSize [612000 792000]13gtgt setpagedevice13

The mission of the JRC is to provide customer-driven scientific and technical support for the conception development implementation and monitoring of EU policies As a service of the European Commission the JRC functions as a reference centre of science and technology for the Union Close to the policy-making process it serves the common interest of the Member States while being independent of special interests whether private or national European Commission Joint Research Centre Contact information Address JRC ELSA Unit TP 480 I-21027 Ispra (VA) Italy E-mail eurocodesjrceceuropaeu Tel +39-0332-789989 Fax +39-0332-789049 httpwwwjrceceuropaeu Legal Notice Neither the European Commission nor any person acting on behalf of the Commission is responsible for the use which might be made of this publication

Europe Direct is a service to help you find answers to your questions about the European Union

Freephone number ()

00 800 6 7 8 9 10 11

() Certain mobile telephone operators do not allow access to 00 800 numbers or these calls may be billed

A great deal of additional information on the European Union is available on the Internet It can be accessed through the Europa server httpeuropaeu JRC 68415 EUR 25193 EN ISBN 978-92-79-22823-0 ISSN 1831-9424 doi 10278882360 Luxembourg Publications Office of the European Union 2012 copy European Union 2012 Reproduction is authorised provided the source is acknowledged Printed in Italy

i

Acknowledgements





Eurocodes

ii

iii

Table of Contents

Acknowledgements i



Foreword xiii

Introduction xv

Chapter 1


11 Introduction 3






131 PIERS 5

132 ABUTMENTS 7

133 BEARINGS 7




143 TRAFFIC DATA 9



146 SEISMIC DATA 11


15 Materials 11




iv




Chapter 2


21 Introduction 21








251 ACTIONS 24










28 Conclusions 32


CHAPTER 3



31 Introduction 37


v





43


45







36 Introduction 50






39 Traffic loads 57






CHAPTER 4


41 Introduction 79




vi








451 SELF-WEIGHT 85



454 ROAD TRAFFIC 87


47 Main results 91




CHAPTER 5 93


51 Introduction 97








121



vii

CHAPTER 6





127





132




142


144


144







150










viii


160


163



166


171

CHAPTER 7


71 Introduction 177





74 Abutment C0 189







CHAPTER 8


81 Introduction 201





205




ix



















APPENDICES 283

APPENDIX A A-1


APPENDIX B B-1


APPENDIX C C-1


APPENDIX D D-1


x

xi


Authors

Introduction



























xii



Editors







xiii

Foreword












xiv







Ispra November 2011





xv

Introduction














The Eurocodes















of firerdquo


xvi


and ETAs)



















Eurocode 8










bridge

xvii




xviii

THE DESIGN EXAMPLE

































xix









CHAPTER 6





Joeumll RAOUL



Convenor EN-1994-2


126


127











γ= = times =ck

c cc

fF A MN

085 085middot3519484 38643



= ckcd

c

ff (EN-1994-2 2412)



128

applied α

γ= cc ck

cdc

ff














129


s uf s ufM

fF A MN

0

345(10 004) 1380

10



s w s wM

fF A MN

0

345(272 0018) 16891

10



s lf s lfM

fF A MN

0

345(120 004) 1656

10






xF F x F F F


004





130





MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)





As τ

εη

= = ge =w

w

hk

t272 31

15111 51360018




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2720middot1810 1063

3middot 3 110 (EN 1993-1-5 52)



τ = + = + times =

whk

a

2 2272534 4 534 4 5802


1993-1-5 Annex A3

( ) ( )π π

σν

times= = =

times


wE

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 188312

12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)


(EN-1993-1-5 53)


131

λττ

= = = =y w y ww

crcr

f f 345

076 076 20324822middot 3




( ) ( )χ

λ= = =

++w

w

137 1370501

07 203207(Table 51 of EN-1993-1-5 53)


χ

γ


timestimesw y w w

bw Rd

M

f h tV MN -6

1

0501 345 2720 184441

3 3middot1 1010



V V V MN V MN

444 0 1063 444

And η

γ


timesy w w

pl a Rd

M

f h tV E MN -6

0

12 345 2720 181170

3 3 10 (EN 1993-1-1 626)








132








VEd = 812 MN





c mm1200 26

587 2 2


ct

587 2354891 9 9 8033

120 295



133






s ss

fF A m MN-4 2

1 1

500144996 10 6304




s ss

fF A m MN-4 2

2 2

50092797 10 4034




s uf s ufM

fF A MN

0

295(12 012) 354

10



s w s wM

fF A MN

0

345(256 0026) 22963

10



s lf s lfM

fF A MN

0

295(120 012) 4248

10





x xF F F F F F F1 2 (256 ) 0

256 256



α = = = gtw

w

h xh

- 256 - 10980571 050

256




134

εα


ct

235456middot

256 456 3459846 58590026 13 1 13middot0571 1



256 2359846 62 1- (- ) 62 1 1059 1059 10849

0026 345






yield strength σγ

le0

ys

M

f






135



εγ γ



M M

f fF F F X t t F

1 2 0 0

2 20 0






As τ

εη

= = ge =w

w

hk

t256 31

9846 51360026




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2560 2610 1446

3 3middot1 10 (EN 1993-1-5 52)




136

τ = + = + =

whk

a

2 2256534 4 534 4 575


1-5 Annex A3

( ) ( )π π

σν



E

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 261958

12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)


λττ

= = = =y w y ww

crcr

f f 345076 076 133


1993-1-5 53 As λw is ge108 then


( ) ( )χ

λ= = =

++w

w

137 1370675

07 13307(Table 51 of EN-1993-1-5 53)


χ


= = times =times

w y w wbw Rd

M

f h tV MN 6

1

0675 345 2560 2610 814

3 3 110



And η


= = times =times

y w wpl a Rd

M

f h tV MN 6

0

12 345 2560 2610 1591

3 3 10 (EN 1993-1-1 626)




γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1





137




xxF F F F F1 2

0120

012 012


xx 0126304 4034 354 354 4248 0

012 012

Then x =01145 m






γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1middot




times times

f f yf

w yw

b t fc a m

th f

2 2

2 2

16 16 1200 120 295025 8 025 3110

26 256 345


138


timesbf RdV

226

1200 120 295 10935middot 1 0197 MN

3110 11 1174010






η = le3

10Ed

b Rd

VV


81209975





η η

+ minus minus le

f Rd

pl Rd

MM

21 3

1 2 1 10

Where

η = Ed

pl Rd

MM1

and η = Ed

bw Rd

VV3



139




VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN


1006050818

12297 η = =3

788509686

814 and


f Rd

pl Rd

M

M

2 21 3

117401 2 1 0818 1 2 09686 1 0858 1

12297











140


areas






141


resistance






142








minus minus= = =

1000 26487 mm

2 2lf wb t

c

ε= = le = =487 235


ct







1 1

500144996 10 6304 MN

115sk

s ss




2 2

50092797 10 4034 MN

115sk

s ss



γ= = times times =

0

295(12 012) 354 MN

10y uf

s uf s ufM

fF A


143


γ= = times times =

0

345(262 0026) 2350 MN

10y w

s w s wM

fF A


γ= = times times =

0

335(100 006) 201 MN

10y lf

s lf s lfM

fF A


γtimes


085 085 3535 05 347 MN

150ck

c cc

fF A


(4573le783) and




(262 )0


x xF F F F F F F F



αminus minus

= = = le262 1815

0307 050262

w

w

h xh



εα

times= = lt = =

235415

262 415 34510076 111560026 0307

ct




= = = le

212 18150144 050

212w

w

h xh




144

εα

times= = lt = =

23536

212 36 3458154 206330026 0144

ct
















145

















146






147








σγ

le

yEd ser

M ser

f

τγ

lesdot

3y

Ed ser

M ser

f

σ τγ

+ sdot le2 2

3 yEd ser Ed ser

M ser

f






σγ

le

yEd ser

M ser

f


148





149


τγ

le = =times

35520496

3 3 10y

Ed ser

M ser

fMPa




σ τγ

+ le2 2

3 yEd ser Ed ser

M ser

f


150






151

σγ

∆ le

15 yfre

M ser

f





le + le30 40 300w

w

hL

t









σ τ

σ τ+ le

2 2


cr cr






152






Where





( )= + le

+ 0

103 10

1 2cc

kh z





Then

( )= + = le

+ times

103 113 10


( )= + = le

+ times

103 102 10




153







160 200 240 280 320 360 400 450

40 32 20 16 12 10 8 6

32 25 16 12 10 8 6 5

25 16 12 8 6 5 4 -


φ φ=

0

ct eff

ct

ff





160 200 240 280 320 360

300 300 250 200 150 100

300 250 200 150 100 50

200 150 100 50 - -



154



σ σ σ= + ∆0s s s

With σα ρ

∆ =04 ctm

sst s

f and α =st

a a

AIA I

Where




ct

AA







ρminustimes

= =423779 10



= =418559 10

000952195s


= =times

03543 058321232



= =times

01555 024561416

01369 01969st


σtimes

∆ = =times

04 328523

1232 001219s MPa


155


∆ = =times

04 329495

1416 00s MPa









φ = =32

32 353129

mm





we can get




This gives






156











π

γ=

2

(1)08

4u

Rdv

df

P


stud

α

γ=

2(2) 029 ck cm

Rdv

d f EP

With

α = +

02 1schd

for 3le schd

le4

α = 10 for schd

gt4

Where








157


π timestimes times

= = times

2

(1) 6

2208 450

4 01095 10 N=01095 MN125RdP

= = gtgt200

909 422

schd


= =times2

(2) 029 1 22 35 340771401226 MN

125RdP












158









40 55 80

120

345 335 325 295

726 800 800 800

297 414




Fig 622 Detailing



159


= minus = minus = gt0 1000 750 22114 25

2 2 2 2f

D

b b de





le sdot15 fd t










160







ν =c k

L k

S VI


161

Where













i

Nx kL

with


Where






00 60 125 250 350 420 500 625

800 875 1000 1080 1125 1200 1320 1400

1500 1625 1700 1760 1875 1940 2000


162



x (m) 50+ 54- 54+ 60- 60+ 625-

νLk (MNm) 0842 0900 0900 0989 0943 0906


( )ν

sdot= =

(4middot P ) 03064 MN031 m


L k

k






163


6741 Elastic design




With

ν =c Ed

L Ed

S VI

Where










i

Nx PL

with


Where






164

ν leinti+1

i

x

x







x (m) 50+ 54- 54+ 60- 60+ 625-

νLEd (MNm) 1124 1203 1203 1323 1264 1213


( )ν


110 (4 P ) 11 0438 MN0365 m


L kEd x


νsdot

= leinti+1

i

x 1

x

(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud

L Ed x dx MNs




165









166











167


ντ

π∆

∆ =

32

4

L FLM

i

i

NdL

Where









Where







λ

=

18

12

0 0

obsmv

NQQ N

Where

=

sumsum

188

1i i

mi

n QQ



Q0=480KN


168

N0=05x106






1 2 3 4 5

200 310 490 390 450

20 5

50 15 10


Qm1=45737 kN

λ = =245737 0952

480v




ηλ

η

= +

188

2 2 24

1 1 1

1 mv

m

N QN Q

η = minus12

eb

With



η = + =11 175 0752 70

and η = minus =21 175 0252 70


169






Where


ψ ψge gt

+ + + +

sum sum 11 1 2

1 1 k j k i k i fat

j iG P Q Q Q







Where








170

γ σσ γ

∆le

∆E2

c

10

Ff

Mf

γ ττ γ

∆le

∆E2

c

10

Ff

Mf s and


∆ ∆+ le

∆ ∆E2 E2

c c

13

Ff Ff

Mf Mf s

Where








171










172



ν = = 0643 MNmL Ed

L Edeff

V


ν= = = 1

max

4 04380681 m

0643Rd stud

L Ed

Ps


Notes





173

References









174

Acknowledgements

Table of Contents


Foreword

13Introduction

Introduction


The Eurocodes


THE DESIGN EXAMPLE








































6741 Elastic design







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ltFEFF005400610074006f0020006e006100730074006100760065006e00ed00200070006f0075017e0069006a007400650020006b0020007600790074007600e101590065006e00ed00200064006f006b0075006d0065006e0074016f002000410064006f006200650020005000440046002c0020006b00740065007200e90020007300650020006e0065006a006c00e90070006500200068006f006400ed002000700072006f0020006b00760061006c00690074006e00ed0020007400690073006b00200061002000700072006500700072006500730073002e002000200056007900740076006f01590065006e00e900200064006f006b0075006d0065006e007400790020005000440046002000620075006400650020006d006f017e006e00e90020006f007400650076015900ed007400200076002000700072006f006700720061006d0065006300680020004100630072006f00620061007400200061002000410064006f00620065002000520065006100640065007200200035002e0030002000610020006e006f0076011b006a016100ed00630068002egt13 DAN 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 DEU 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 ESP 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 ETI 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 FRA 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 GRE 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 HEB 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 HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke Stvoreni PDF dokumenti mogu se otvoriti Acrobat i Adobe Reader 50 i kasnijim verzijama)13 HUN 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 ITA 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 JPN ltFEFF9ad854c18cea306a30d730ea30d730ec30b951fa529b7528002000410064006f0062006500200050004400460020658766f8306e4f5c6210306b4f7f75283057307e305930023053306e8a2d5b9a30674f5c62103055308c305f0020005000440046002030d530a130a430eb306f3001004100630072006f0062006100740020304a30883073002000410064006f00620065002000520065006100640065007200200035002e003000204ee5964d3067958b304f30533068304c3067304d307e305930023053306e8a2d5b9a306b306f30d530a930f330c8306e57cb30818fbc307f304c5fc59808306730593002gt13 KOR ltFEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020ace0d488c9c80020c2dcd5d80020c778c1c4c5d00020ac00c7a50020c801d569d55c002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002egt13 LTH 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 LVI 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 NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 50 en hoger)13 NOR 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 POL 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 PTB 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 RUM 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 RUS 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 SKY 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 SLV 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 SUO 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 SVE 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 TUR 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 UKR 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 ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing Created PDF documents can be opened with Acrobat and Adobe Reader 50 and later)13 gtgt13 Namespace [13 (Adobe)13 (Common)13 (10)13 ]13 OtherNamespaces [13 ltlt13 AsReaderSpreads false13 CropImagesToFrames true13 ErrorControl WarnAndContinue13 FlattenerIgnoreSpreadOverrides false13 IncludeGuidesGrids false13 IncludeNonPrinting false13 IncludeSlug false13 Namespace [13 (Adobe)13 (InDesign)13 (40)13 ]13 OmitPlacedBitmaps false13 OmitPlacedEPS false13 OmitPlacedPDF false13 SimulateOverprint Legacy13 gtgt13 ltlt13 AddBleedMarks false13 AddColorBars false13 AddCropMarks false13 AddPageInfo false13 AddRegMarks false13 ConvertColors ConvertToCMYK13 DestinationProfileName ()13 DestinationProfileSelector DocumentCMYK13 Downsample16BitImages true13 FlattenerPreset ltlt13 PresetSelector MediumResolution13 gtgt13 FormElements false13 GenerateStructure false13 IncludeBookmarks false13 IncludeHyperlinks false13 IncludeInteractive false13 IncludeLayers false13 IncludeProfiles false13 MultimediaHandling UseObjectSettings13 Namespace [13 (Adobe)13 (CreativeSuite)13 (20)13 ]13 PDFXOutputIntentProfileSelector DocumentCMYK13 PreserveEditing true13 UntaggedCMYKHandling LeaveUntagged13 UntaggedRGBHandling UseDocumentProfile13 UseDocumentBleed false13 gtgt13 ]13gtgt setdistillerparams13ltlt13 HWResolution [2400 2400]13 PageSize [612000 792000]13gtgt setpagedevice13

i

Acknowledgements





Eurocodes

ii

iii

Table of Contents

Acknowledgements i



Foreword xiii

Introduction xv

Chapter 1


11 Introduction 3






131 PIERS 5

132 ABUTMENTS 7

133 BEARINGS 7




143 TRAFFIC DATA 9



146 SEISMIC DATA 11


15 Materials 11




iv




Chapter 2


21 Introduction 21








251 ACTIONS 24










28 Conclusions 32


CHAPTER 3



31 Introduction 37


v





43


45







36 Introduction 50






39 Traffic loads 57






CHAPTER 4


41 Introduction 79




vi








451 SELF-WEIGHT 85



454 ROAD TRAFFIC 87


47 Main results 91




CHAPTER 5 93


51 Introduction 97








121



vii

CHAPTER 6





127





132




142


144


144







150










viii


160


163



166


171

CHAPTER 7


71 Introduction 177





74 Abutment C0 189







CHAPTER 8


81 Introduction 201





205




ix



















APPENDICES 283

APPENDIX A A-1


APPENDIX B B-1


APPENDIX C C-1


APPENDIX D D-1


x

xi


Authors

Introduction



























xii



Editors







xiii

Foreword












xiv







Ispra November 2011





xv

Introduction














The Eurocodes















of firerdquo


xvi


and ETAs)



















Eurocode 8










bridge

xvii




xviii

THE DESIGN EXAMPLE

































xix









CHAPTER 6





Joeumll RAOUL



Convenor EN-1994-2


126


127











γ= = times =ck

c cc

fF A MN

085 085middot3519484 38643



= ckcd

c

ff (EN-1994-2 2412)



128

applied α

γ= cc ck

cdc

ff














129


s uf s ufM

fF A MN

0

345(10 004) 1380

10



s w s wM

fF A MN

0

345(272 0018) 16891

10



s lf s lfM

fF A MN

0

345(120 004) 1656

10






xF F x F F F


004





130





MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)





As τ

εη

= = ge =w

w

hk

t272 31

15111 51360018




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2720middot1810 1063

3middot 3 110 (EN 1993-1-5 52)



τ = + = + times =

whk

a

2 2272534 4 534 4 5802


1993-1-5 Annex A3

( ) ( )π π

σν

times= = =

times


wE

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 188312

12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)


(EN-1993-1-5 53)


131

λττ

= = = =y w y ww

crcr

f f 345

076 076 20324822middot 3




( ) ( )χ

λ= = =

++w

w

137 1370501

07 203207(Table 51 of EN-1993-1-5 53)


χ

γ


timestimesw y w w

bw Rd

M

f h tV MN -6

1

0501 345 2720 184441

3 3middot1 1010



V V V MN V MN

444 0 1063 444

And η

γ


timesy w w

pl a Rd

M

f h tV E MN -6

0

12 345 2720 181170

3 3 10 (EN 1993-1-1 626)








132








VEd = 812 MN





c mm1200 26

587 2 2


ct

587 2354891 9 9 8033

120 295



133






s ss

fF A m MN-4 2

1 1

500144996 10 6304




s ss

fF A m MN-4 2

2 2

50092797 10 4034




s uf s ufM

fF A MN

0

295(12 012) 354

10



s w s wM

fF A MN

0

345(256 0026) 22963

10



s lf s lfM

fF A MN

0

295(120 012) 4248

10





x xF F F F F F F1 2 (256 ) 0

256 256



α = = = gtw

w

h xh

- 256 - 10980571 050

256




134

εα


ct

235456middot

256 456 3459846 58590026 13 1 13middot0571 1



256 2359846 62 1- (- ) 62 1 1059 1059 10849

0026 345






yield strength σγ

le0

ys

M

f






135



εγ γ



M M

f fF F F X t t F

1 2 0 0

2 20 0






As τ

εη

= = ge =w

w

hk

t256 31

9846 51360026




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2560 2610 1446

3 3middot1 10 (EN 1993-1-5 52)




136

τ = + = + =

whk

a

2 2256534 4 534 4 575


1-5 Annex A3

( ) ( )π π

σν



E

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 261958

12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)


λττ

= = = =y w y ww

crcr

f f 345076 076 133


1993-1-5 53 As λw is ge108 then


( ) ( )χ

λ= = =

++w

w

137 1370675

07 13307(Table 51 of EN-1993-1-5 53)


χ


= = times =times

w y w wbw Rd

M

f h tV MN 6

1

0675 345 2560 2610 814

3 3 110



And η


= = times =times

y w wpl a Rd

M

f h tV MN 6

0

12 345 2560 2610 1591

3 3 10 (EN 1993-1-1 626)




γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1





137




xxF F F F F1 2

0120

012 012


xx 0126304 4034 354 354 4248 0

012 012

Then x =01145 m






γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1middot




times times

f f yf

w yw

b t fc a m

th f

2 2

2 2

16 16 1200 120 295025 8 025 3110

26 256 345


138


timesbf RdV

226

1200 120 295 10935middot 1 0197 MN

3110 11 1174010






η = le3

10Ed

b Rd

VV


81209975





η η

+ minus minus le

f Rd

pl Rd

MM

21 3

1 2 1 10

Where

η = Ed

pl Rd

MM1

and η = Ed

bw Rd

VV3



139




VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN


1006050818

12297 η = =3

788509686

814 and


f Rd

pl Rd

M

M

2 21 3

117401 2 1 0818 1 2 09686 1 0858 1

12297











140


areas






141


resistance






142








minus minus= = =

1000 26487 mm

2 2lf wb t

c

ε= = le = =487 235


ct







1 1

500144996 10 6304 MN

115sk

s ss




2 2

50092797 10 4034 MN

115sk

s ss



γ= = times times =

0

295(12 012) 354 MN

10y uf

s uf s ufM

fF A


143


γ= = times times =

0

345(262 0026) 2350 MN

10y w

s w s wM

fF A


γ= = times times =

0

335(100 006) 201 MN

10y lf

s lf s lfM

fF A


γtimes


085 085 3535 05 347 MN

150ck

c cc

fF A


(4573le783) and




(262 )0


x xF F F F F F F F



αminus minus

= = = le262 1815

0307 050262

w

w

h xh



εα

times= = lt = =

235415

262 415 34510076 111560026 0307

ct




= = = le

212 18150144 050

212w

w

h xh




144

εα

times= = lt = =

23536

212 36 3458154 206330026 0144

ct
















145

















146






147








σγ

le

yEd ser

M ser

f

τγ

lesdot

3y

Ed ser

M ser

f

σ τγ

+ sdot le2 2

3 yEd ser Ed ser

M ser

f






σγ

le

yEd ser

M ser

f


148





149


τγ

le = =times

35520496

3 3 10y

Ed ser

M ser

fMPa




σ τγ

+ le2 2

3 yEd ser Ed ser

M ser

f


150






151

σγ

∆ le

15 yfre

M ser

f





le + le30 40 300w

w

hL

t









σ τ

σ τ+ le

2 2


cr cr






152






Where





( )= + le

+ 0

103 10

1 2cc

kh z





Then

( )= + = le

+ times

103 113 10


( )= + = le

+ times

103 102 10




153







160 200 240 280 320 360 400 450

40 32 20 16 12 10 8 6

32 25 16 12 10 8 6 5

25 16 12 8 6 5 4 -


φ φ=

0

ct eff

ct

ff





160 200 240 280 320 360

300 300 250 200 150 100

300 250 200 150 100 50

200 150 100 50 - -



154



σ σ σ= + ∆0s s s

With σα ρ

∆ =04 ctm

sst s

f and α =st

a a

AIA I

Where




ct

AA







ρminustimes

= =423779 10



= =418559 10

000952195s


= =times

03543 058321232



= =times

01555 024561416

01369 01969st


σtimes

∆ = =times

04 328523

1232 001219s MPa


155


∆ = =times

04 329495

1416 00s MPa









φ = =32

32 353129

mm





we can get




This gives






156











π

γ=

2

(1)08

4u

Rdv

df

P


stud

α

γ=

2(2) 029 ck cm

Rdv

d f EP

With

α = +

02 1schd

for 3le schd

le4

α = 10 for schd

gt4

Where








157


π timestimes times

= = times

2

(1) 6

2208 450

4 01095 10 N=01095 MN125RdP

= = gtgt200

909 422

schd


= =times2

(2) 029 1 22 35 340771401226 MN

125RdP












158









40 55 80

120

345 335 325 295

726 800 800 800

297 414




Fig 622 Detailing



159


= minus = minus = gt0 1000 750 22114 25

2 2 2 2f

D

b b de





le sdot15 fd t










160







ν =c k

L k

S VI


161

Where













i

Nx kL

with


Where






00 60 125 250 350 420 500 625

800 875 1000 1080 1125 1200 1320 1400

1500 1625 1700 1760 1875 1940 2000


162



x (m) 50+ 54- 54+ 60- 60+ 625-

νLk (MNm) 0842 0900 0900 0989 0943 0906


( )ν

sdot= =

(4middot P ) 03064 MN031 m


L k

k






163


6741 Elastic design




With

ν =c Ed

L Ed

S VI

Where










i

Nx PL

with


Where






164

ν leinti+1

i

x

x







x (m) 50+ 54- 54+ 60- 60+ 625-

νLEd (MNm) 1124 1203 1203 1323 1264 1213


( )ν


110 (4 P ) 11 0438 MN0365 m


L kEd x


νsdot

= leinti+1

i

x 1

x

(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud

L Ed x dx MNs




165









166











167


ντ

π∆

∆ =

32

4

L FLM

i

i

NdL

Where









Where







λ

=

18

12

0 0

obsmv

NQQ N

Where

=

sumsum

188

1i i

mi

n QQ



Q0=480KN


168

N0=05x106






1 2 3 4 5

200 310 490 390 450

20 5

50 15 10


Qm1=45737 kN

λ = =245737 0952

480v




ηλ

η

= +

188

2 2 24

1 1 1

1 mv

m

N QN Q

η = minus12

eb

With



η = + =11 175 0752 70

and η = minus =21 175 0252 70


169






Where


ψ ψge gt

+ + + +

sum sum 11 1 2

1 1 k j k i k i fat

j iG P Q Q Q







Where








170

γ σσ γ

∆le

∆E2

c

10

Ff

Mf

γ ττ γ

∆le

∆E2

c

10

Ff

Mf s and


∆ ∆+ le

∆ ∆E2 E2

c c

13

Ff Ff

Mf Mf s

Where








171










172



ν = = 0643 MNmL Ed

L Edeff

V


ν= = = 1

max

4 04380681 m

0643Rd stud

L Ed

Ps


Notes





173

References









174

Acknowledgements

Table of Contents


Foreword

13Introduction

Introduction


The Eurocodes


THE DESIGN EXAMPLE








































6741 Elastic design








ii

iii

Table of Contents

Acknowledgements i



Foreword xiii

Introduction xv

Chapter 1


11 Introduction 3






131 PIERS 5

132 ABUTMENTS 7

133 BEARINGS 7




143 TRAFFIC DATA 9



146 SEISMIC DATA 11


15 Materials 11




iv




Chapter 2


21 Introduction 21








251 ACTIONS 24










28 Conclusions 32


CHAPTER 3



31 Introduction 37


v





43


45







36 Introduction 50






39 Traffic loads 57






CHAPTER 4


41 Introduction 79




vi








451 SELF-WEIGHT 85



454 ROAD TRAFFIC 87


47 Main results 91




CHAPTER 5 93


51 Introduction 97








121



vii

CHAPTER 6





127





132




142


144


144







150










viii


160


163



166


171

CHAPTER 7


71 Introduction 177





74 Abutment C0 189







CHAPTER 8


81 Introduction 201





205




ix



















APPENDICES 283

APPENDIX A A-1


APPENDIX B B-1


APPENDIX C C-1


APPENDIX D D-1


x

xi


Authors

Introduction



























xii



Editors







xiii

Foreword












xiv







Ispra November 2011





xv

Introduction














The Eurocodes















of firerdquo


xvi


and ETAs)



















Eurocode 8










bridge

xvii




xviii

THE DESIGN EXAMPLE

































xix









CHAPTER 6





Joeumll RAOUL



Convenor EN-1994-2


126


127











γ= = times =ck

c cc

fF A MN

085 085middot3519484 38643



= ckcd

c

ff (EN-1994-2 2412)



128

applied α

γ= cc ck

cdc

ff














129


s uf s ufM

fF A MN

0

345(10 004) 1380

10



s w s wM

fF A MN

0

345(272 0018) 16891

10



s lf s lfM

fF A MN

0

345(120 004) 1656

10






xF F x F F F


004





130





MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)





As τ

εη

= = ge =w

w

hk

t272 31

15111 51360018




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2720middot1810 1063

3middot 3 110 (EN 1993-1-5 52)



τ = + = + times =

whk

a

2 2272534 4 534 4 5802


1993-1-5 Annex A3

( ) ( )π π

σν

times= = =

times


wE

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 188312

12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)


(EN-1993-1-5 53)


131

λττ

= = = =y w y ww

crcr

f f 345

076 076 20324822middot 3




( ) ( )χ

λ= = =

++w

w

137 1370501

07 203207(Table 51 of EN-1993-1-5 53)


χ

γ


timestimesw y w w

bw Rd

M

f h tV MN -6

1

0501 345 2720 184441

3 3middot1 1010



V V V MN V MN

444 0 1063 444

And η

γ


timesy w w

pl a Rd

M

f h tV E MN -6

0

12 345 2720 181170

3 3 10 (EN 1993-1-1 626)








132








VEd = 812 MN





c mm1200 26

587 2 2


ct

587 2354891 9 9 8033

120 295



133






s ss

fF A m MN-4 2

1 1

500144996 10 6304




s ss

fF A m MN-4 2

2 2

50092797 10 4034




s uf s ufM

fF A MN

0

295(12 012) 354

10



s w s wM

fF A MN

0

345(256 0026) 22963

10



s lf s lfM

fF A MN

0

295(120 012) 4248

10





x xF F F F F F F1 2 (256 ) 0

256 256



α = = = gtw

w

h xh

- 256 - 10980571 050

256




134

εα


ct

235456middot

256 456 3459846 58590026 13 1 13middot0571 1



256 2359846 62 1- (- ) 62 1 1059 1059 10849

0026 345






yield strength σγ

le0

ys

M

f






135



εγ γ



M M

f fF F F X t t F

1 2 0 0

2 20 0






As τ

εη

= = ge =w

w

hk

t256 31

9846 51360026




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2560 2610 1446

3 3middot1 10 (EN 1993-1-5 52)




136

τ = + = + =

whk

a

2 2256534 4 534 4 575


1-5 Annex A3

( ) ( )π π

σν



E

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 261958

12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)


λττ

= = = =y w y ww

crcr

f f 345076 076 133


1993-1-5 53 As λw is ge108 then


( ) ( )χ

λ= = =

++w

w

137 1370675

07 13307(Table 51 of EN-1993-1-5 53)


χ


= = times =times

w y w wbw Rd

M

f h tV MN 6

1

0675 345 2560 2610 814

3 3 110



And η


= = times =times

y w wpl a Rd

M

f h tV MN 6

0

12 345 2560 2610 1591

3 3 10 (EN 1993-1-1 626)




γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1





137




xxF F F F F1 2

0120

012 012


xx 0126304 4034 354 354 4248 0

012 012

Then x =01145 m






γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1middot




times times

f f yf

w yw

b t fc a m

th f

2 2

2 2

16 16 1200 120 295025 8 025 3110

26 256 345


138


timesbf RdV

226

1200 120 295 10935middot 1 0197 MN

3110 11 1174010






η = le3

10Ed

b Rd

VV


81209975





η η

+ minus minus le

f Rd

pl Rd

MM

21 3

1 2 1 10

Where

η = Ed

pl Rd

MM1

and η = Ed

bw Rd

VV3



139




VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN


1006050818

12297 η = =3

788509686

814 and


f Rd

pl Rd

M

M

2 21 3

117401 2 1 0818 1 2 09686 1 0858 1

12297











140


areas






141


resistance






142








minus minus= = =

1000 26487 mm

2 2lf wb t

c

ε= = le = =487 235


ct







1 1

500144996 10 6304 MN

115sk

s ss




2 2

50092797 10 4034 MN

115sk

s ss



γ= = times times =

0

295(12 012) 354 MN

10y uf

s uf s ufM

fF A


143


γ= = times times =

0

345(262 0026) 2350 MN

10y w

s w s wM

fF A


γ= = times times =

0

335(100 006) 201 MN

10y lf

s lf s lfM

fF A


γtimes


085 085 3535 05 347 MN

150ck

c cc

fF A


(4573le783) and




(262 )0


x xF F F F F F F F



αminus minus

= = = le262 1815

0307 050262

w

w

h xh



εα

times= = lt = =

235415

262 415 34510076 111560026 0307

ct




= = = le

212 18150144 050

212w

w

h xh




144

εα

times= = lt = =

23536

212 36 3458154 206330026 0144

ct
















145

















146






147








σγ

le

yEd ser

M ser

f

τγ

lesdot

3y

Ed ser

M ser

f

σ τγ

+ sdot le2 2

3 yEd ser Ed ser

M ser

f






σγ

le

yEd ser

M ser

f


148





149


τγ

le = =times

35520496

3 3 10y

Ed ser

M ser

fMPa




σ τγ

+ le2 2

3 yEd ser Ed ser

M ser

f


150






151

σγ

∆ le

15 yfre

M ser

f





le + le30 40 300w

w

hL

t









σ τ

σ τ+ le

2 2


cr cr






152






Where





( )= + le

+ 0

103 10

1 2cc

kh z





Then

( )= + = le

+ times

103 113 10


( )= + = le

+ times

103 102 10




153







160 200 240 280 320 360 400 450

40 32 20 16 12 10 8 6

32 25 16 12 10 8 6 5

25 16 12 8 6 5 4 -


φ φ=

0

ct eff

ct

ff





160 200 240 280 320 360

300 300 250 200 150 100

300 250 200 150 100 50

200 150 100 50 - -



154



σ σ σ= + ∆0s s s

With σα ρ

∆ =04 ctm

sst s

f and α =st

a a

AIA I

Where




ct

AA







ρminustimes

= =423779 10



= =418559 10

000952195s


= =times

03543 058321232



= =times

01555 024561416

01369 01969st


σtimes

∆ = =times

04 328523

1232 001219s MPa


155


∆ = =times

04 329495

1416 00s MPa









φ = =32

32 353129

mm





we can get




This gives






156











π

γ=

2

(1)08

4u

Rdv

df

P


stud

α

γ=

2(2) 029 ck cm

Rdv

d f EP

With

α = +

02 1schd

for 3le schd

le4

α = 10 for schd

gt4

Where








157


π timestimes times

= = times

2

(1) 6

2208 450

4 01095 10 N=01095 MN125RdP

= = gtgt200

909 422

schd


= =times2

(2) 029 1 22 35 340771401226 MN

125RdP












158









40 55 80

120

345 335 325 295

726 800 800 800

297 414




Fig 622 Detailing



159


= minus = minus = gt0 1000 750 22114 25

2 2 2 2f

D

b b de





le sdot15 fd t










160







ν =c k

L k

S VI


161

Where













i

Nx kL

with


Where






00 60 125 250 350 420 500 625

800 875 1000 1080 1125 1200 1320 1400

1500 1625 1700 1760 1875 1940 2000


162



x (m) 50+ 54- 54+ 60- 60+ 625-

νLk (MNm) 0842 0900 0900 0989 0943 0906


( )ν

sdot= =

(4middot P ) 03064 MN031 m


L k

k






163


6741 Elastic design




With

ν =c Ed

L Ed

S VI

Where










i

Nx PL

with


Where






164

ν leinti+1

i

x

x







x (m) 50+ 54- 54+ 60- 60+ 625-

νLEd (MNm) 1124 1203 1203 1323 1264 1213


( )ν


110 (4 P ) 11 0438 MN0365 m


L kEd x


νsdot

= leinti+1

i

x 1

x

(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud

L Ed x dx MNs




165









166











167


ντ

π∆

∆ =

32

4

L FLM

i

i

NdL

Where









Where







λ

=

18

12

0 0

obsmv

NQQ N

Where

=

sumsum

188

1i i

mi

n QQ



Q0=480KN


168

N0=05x106






1 2 3 4 5

200 310 490 390 450

20 5

50 15 10


Qm1=45737 kN

λ = =245737 0952

480v




ηλ

η

= +

188

2 2 24

1 1 1

1 mv

m

N QN Q

η = minus12

eb

With



η = + =11 175 0752 70

and η = minus =21 175 0252 70


169






Where


ψ ψge gt

+ + + +

sum sum 11 1 2

1 1 k j k i k i fat

j iG P Q Q Q







Where








170

γ σσ γ

∆le

∆E2

c

10

Ff

Mf

γ ττ γ

∆le

∆E2

c

10

Ff

Mf s and


∆ ∆+ le

∆ ∆E2 E2

c c

13

Ff Ff

Mf Mf s

Where








171










172



ν = = 0643 MNmL Ed

L Edeff

V


ν= = = 1

max

4 04380681 m

0643Rd stud

L Ed

Ps


Notes





173

References









174

Acknowledgements

Table of Contents


Foreword

13Introduction

Introduction


The Eurocodes


THE DESIGN EXAMPLE








































6741 Elastic design








iii

Table of Contents

Acknowledgements i



Foreword xiii

Introduction xv

Chapter 1


11 Introduction 3






131 PIERS 5

132 ABUTMENTS 7

133 BEARINGS 7




143 TRAFFIC DATA 9



146 SEISMIC DATA 11


15 Materials 11




iv




Chapter 2


21 Introduction 21








251 ACTIONS 24










28 Conclusions 32


CHAPTER 3



31 Introduction 37


v





43


45







36 Introduction 50






39 Traffic loads 57






CHAPTER 4


41 Introduction 79




vi








451 SELF-WEIGHT 85



454 ROAD TRAFFIC 87


47 Main results 91




CHAPTER 5 93


51 Introduction 97








121



vii

CHAPTER 6





127





132




142


144


144







150










viii


160


163



166


171

CHAPTER 7


71 Introduction 177





74 Abutment C0 189







CHAPTER 8


81 Introduction 201





205




ix



















APPENDICES 283

APPENDIX A A-1


APPENDIX B B-1


APPENDIX C C-1


APPENDIX D D-1


x

xi


Authors

Introduction



























xii



Editors







xiii

Foreword












xiv







Ispra November 2011





xv

Introduction














The Eurocodes















of firerdquo


xvi


and ETAs)



















Eurocode 8










bridge

xvii




xviii

THE DESIGN EXAMPLE

































xix









CHAPTER 6





Joeumll RAOUL



Convenor EN-1994-2


126


127











γ= = times =ck

c cc

fF A MN

085 085middot3519484 38643



= ckcd

c

ff (EN-1994-2 2412)



128

applied α

γ= cc ck

cdc

ff














129


s uf s ufM

fF A MN

0

345(10 004) 1380

10



s w s wM

fF A MN

0

345(272 0018) 16891

10



s lf s lfM

fF A MN

0

345(120 004) 1656

10






xF F x F F F


004





130





MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)





As τ

εη

= = ge =w

w

hk

t272 31

15111 51360018




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2720middot1810 1063

3middot 3 110 (EN 1993-1-5 52)



τ = + = + times =

whk

a

2 2272534 4 534 4 5802


1993-1-5 Annex A3

( ) ( )π π

σν

times= = =

times


wE

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 188312

12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)


(EN-1993-1-5 53)


131

λττ

= = = =y w y ww

crcr

f f 345

076 076 20324822middot 3




( ) ( )χ

λ= = =

++w

w

137 1370501

07 203207(Table 51 of EN-1993-1-5 53)


χ

γ


timestimesw y w w

bw Rd

M

f h tV MN -6

1

0501 345 2720 184441

3 3middot1 1010



V V V MN V MN

444 0 1063 444

And η

γ


timesy w w

pl a Rd

M

f h tV E MN -6

0

12 345 2720 181170

3 3 10 (EN 1993-1-1 626)








132








VEd = 812 MN





c mm1200 26

587 2 2


ct

587 2354891 9 9 8033

120 295



133






s ss

fF A m MN-4 2

1 1

500144996 10 6304




s ss

fF A m MN-4 2

2 2

50092797 10 4034




s uf s ufM

fF A MN

0

295(12 012) 354

10



s w s wM

fF A MN

0

345(256 0026) 22963

10



s lf s lfM

fF A MN

0

295(120 012) 4248

10





x xF F F F F F F1 2 (256 ) 0

256 256



α = = = gtw

w

h xh

- 256 - 10980571 050

256




134

εα


ct

235456middot

256 456 3459846 58590026 13 1 13middot0571 1



256 2359846 62 1- (- ) 62 1 1059 1059 10849

0026 345






yield strength σγ

le0

ys

M

f






135



εγ γ



M M

f fF F F X t t F

1 2 0 0

2 20 0






As τ

εη

= = ge =w

w

hk

t256 31

9846 51360026




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2560 2610 1446

3 3middot1 10 (EN 1993-1-5 52)




136

τ = + = + =

whk

a

2 2256534 4 534 4 575


1-5 Annex A3

( ) ( )π π

σν



E

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 261958

12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)


λττ

= = = =y w y ww

crcr

f f 345076 076 133


1993-1-5 53 As λw is ge108 then


( ) ( )χ

λ= = =

++w

w

137 1370675

07 13307(Table 51 of EN-1993-1-5 53)


χ


= = times =times

w y w wbw Rd

M

f h tV MN 6

1

0675 345 2560 2610 814

3 3 110



And η


= = times =times

y w wpl a Rd

M

f h tV MN 6

0

12 345 2560 2610 1591

3 3 10 (EN 1993-1-1 626)




γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1





137




xxF F F F F1 2

0120

012 012


xx 0126304 4034 354 354 4248 0

012 012

Then x =01145 m






γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1middot




times times

f f yf

w yw

b t fc a m

th f

2 2

2 2

16 16 1200 120 295025 8 025 3110

26 256 345


138


timesbf RdV

226

1200 120 295 10935middot 1 0197 MN

3110 11 1174010






η = le3

10Ed

b Rd

VV


81209975





η η

+ minus minus le

f Rd

pl Rd

MM

21 3

1 2 1 10

Where

η = Ed

pl Rd

MM1

and η = Ed

bw Rd

VV3



139




VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN


1006050818

12297 η = =3

788509686

814 and


f Rd

pl Rd

M

M

2 21 3

117401 2 1 0818 1 2 09686 1 0858 1

12297











140


areas






141


resistance






142








minus minus= = =

1000 26487 mm

2 2lf wb t

c

ε= = le = =487 235


ct







1 1

500144996 10 6304 MN

115sk

s ss




2 2

50092797 10 4034 MN

115sk

s ss



γ= = times times =

0

295(12 012) 354 MN

10y uf

s uf s ufM

fF A


143


γ= = times times =

0

345(262 0026) 2350 MN

10y w

s w s wM

fF A


γ= = times times =

0

335(100 006) 201 MN

10y lf

s lf s lfM

fF A


γtimes


085 085 3535 05 347 MN

150ck

c cc

fF A


(4573le783) and




(262 )0


x xF F F F F F F F



αminus minus

= = = le262 1815

0307 050262

w

w

h xh



εα

times= = lt = =

235415

262 415 34510076 111560026 0307

ct




= = = le

212 18150144 050

212w

w

h xh




144

εα

times= = lt = =

23536

212 36 3458154 206330026 0144

ct
















145

















146






147








σγ

le

yEd ser

M ser

f

τγ

lesdot

3y

Ed ser

M ser

f

σ τγ

+ sdot le2 2

3 yEd ser Ed ser

M ser

f






σγ

le

yEd ser

M ser

f


148





149


τγ

le = =times

35520496

3 3 10y

Ed ser

M ser

fMPa




σ τγ

+ le2 2

3 yEd ser Ed ser

M ser

f


150






151

σγ

∆ le

15 yfre

M ser

f





le + le30 40 300w

w

hL

t









σ τ

σ τ+ le

2 2


cr cr






152






Where





( )= + le

+ 0

103 10

1 2cc

kh z





Then

( )= + = le

+ times

103 113 10


( )= + = le

+ times

103 102 10




153







160 200 240 280 320 360 400 450

40 32 20 16 12 10 8 6

32 25 16 12 10 8 6 5

25 16 12 8 6 5 4 -


φ φ=

0

ct eff

ct

ff





160 200 240 280 320 360

300 300 250 200 150 100

300 250 200 150 100 50

200 150 100 50 - -



154



σ σ σ= + ∆0s s s

With σα ρ

∆ =04 ctm

sst s

f and α =st

a a

AIA I

Where




ct

AA







ρminustimes

= =423779 10



= =418559 10

000952195s


= =times

03543 058321232



= =times

01555 024561416

01369 01969st


σtimes

∆ = =times

04 328523

1232 001219s MPa


155


∆ = =times

04 329495

1416 00s MPa









φ = =32

32 353129

mm





we can get




This gives






156











π

γ=

2

(1)08

4u

Rdv

df

P


stud

α

γ=

2(2) 029 ck cm

Rdv

d f EP

With

α = +

02 1schd

for 3le schd

le4

α = 10 for schd

gt4

Where








157


π timestimes times

= = times

2

(1) 6

2208 450

4 01095 10 N=01095 MN125RdP

= = gtgt200

909 422

schd


= =times2

(2) 029 1 22 35 340771401226 MN

125RdP












158









40 55 80

120

345 335 325 295

726 800 800 800

297 414




Fig 622 Detailing



159


= minus = minus = gt0 1000 750 22114 25

2 2 2 2f

D

b b de





le sdot15 fd t










160







ν =c k

L k

S VI


161

Where













i

Nx kL

with


Where






00 60 125 250 350 420 500 625

800 875 1000 1080 1125 1200 1320 1400

1500 1625 1700 1760 1875 1940 2000


162



x (m) 50+ 54- 54+ 60- 60+ 625-

νLk (MNm) 0842 0900 0900 0989 0943 0906


( )ν

sdot= =

(4middot P ) 03064 MN031 m


L k

k






163


6741 Elastic design




With

ν =c Ed

L Ed

S VI

Where










i

Nx PL

with


Where






164

ν leinti+1

i

x

x







x (m) 50+ 54- 54+ 60- 60+ 625-

νLEd (MNm) 1124 1203 1203 1323 1264 1213


( )ν


110 (4 P ) 11 0438 MN0365 m


L kEd x


νsdot

= leinti+1

i

x 1

x

(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud

L Ed x dx MNs




165









166











167


ντ

π∆

∆ =

32

4

L FLM

i

i

NdL

Where









Where







λ

=

18

12

0 0

obsmv

NQQ N

Where

=

sumsum

188

1i i

mi

n QQ



Q0=480KN


168

N0=05x106






1 2 3 4 5

200 310 490 390 450

20 5

50 15 10


Qm1=45737 kN

λ = =245737 0952

480v




ηλ

η

= +

188

2 2 24

1 1 1

1 mv

m

N QN Q

η = minus12

eb

With



η = + =11 175 0752 70

and η = minus =21 175 0252 70


169






Where


ψ ψge gt

+ + + +

sum sum 11 1 2

1 1 k j k i k i fat

j iG P Q Q Q







Where








170

γ σσ γ

∆le

∆E2

c

10

Ff

Mf

γ ττ γ

∆le

∆E2

c

10

Ff

Mf s and


∆ ∆+ le

∆ ∆E2 E2

c c

13

Ff Ff

Mf Mf s

Where








171










172



ν = = 0643 MNmL Ed

L Edeff

V


ν= = = 1

max

4 04380681 m

0643Rd stud

L Ed

Ps


Notes





173

References









174

Acknowledgements

Table of Contents


Foreword

13Introduction

Introduction


The Eurocodes


THE DESIGN EXAMPLE








































6741 Elastic design








iv




Chapter 2


21 Introduction 21








251 ACTIONS 24










28 Conclusions 32


CHAPTER 3



31 Introduction 37


v





43


45







36 Introduction 50






39 Traffic loads 57






CHAPTER 4


41 Introduction 79




vi








451 SELF-WEIGHT 85



454 ROAD TRAFFIC 87


47 Main results 91




CHAPTER 5 93


51 Introduction 97








121



vii

CHAPTER 6





127





132




142


144


144







150










viii


160


163



166


171

CHAPTER 7


71 Introduction 177





74 Abutment C0 189







CHAPTER 8


81 Introduction 201





205




ix



















APPENDICES 283

APPENDIX A A-1


APPENDIX B B-1


APPENDIX C C-1


APPENDIX D D-1


x

xi


Authors

Introduction



























xii



Editors







xiii

Foreword












xiv







Ispra November 2011





xv

Introduction














The Eurocodes















of firerdquo


xvi


and ETAs)



















Eurocode 8










bridge

xvii




xviii

THE DESIGN EXAMPLE

































xix









CHAPTER 6





Joeumll RAOUL



Convenor EN-1994-2


126


127











γ= = times =ck

c cc

fF A MN

085 085middot3519484 38643



= ckcd

c

ff (EN-1994-2 2412)



128

applied α

γ= cc ck

cdc

ff














129


s uf s ufM

fF A MN

0

345(10 004) 1380

10



s w s wM

fF A MN

0

345(272 0018) 16891

10



s lf s lfM

fF A MN

0

345(120 004) 1656

10






xF F x F F F


004





130





MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)





As τ

εη

= = ge =w

w

hk

t272 31

15111 51360018




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2720middot1810 1063

3middot 3 110 (EN 1993-1-5 52)



τ = + = + times =

whk

a

2 2272534 4 534 4 5802


1993-1-5 Annex A3

( ) ( )π π

σν

times= = =

times


wE

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 188312

12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)


(EN-1993-1-5 53)


131

λττ

= = = =y w y ww

crcr

f f 345

076 076 20324822middot 3




( ) ( )χ

λ= = =

++w

w

137 1370501

07 203207(Table 51 of EN-1993-1-5 53)


χ

γ


timestimesw y w w

bw Rd

M

f h tV MN -6

1

0501 345 2720 184441

3 3middot1 1010



V V V MN V MN

444 0 1063 444

And η

γ


timesy w w

pl a Rd

M

f h tV E MN -6

0

12 345 2720 181170

3 3 10 (EN 1993-1-1 626)








132








VEd = 812 MN





c mm1200 26

587 2 2


ct

587 2354891 9 9 8033

120 295



133






s ss

fF A m MN-4 2

1 1

500144996 10 6304




s ss

fF A m MN-4 2

2 2

50092797 10 4034




s uf s ufM

fF A MN

0

295(12 012) 354

10



s w s wM

fF A MN

0

345(256 0026) 22963

10



s lf s lfM

fF A MN

0

295(120 012) 4248

10





x xF F F F F F F1 2 (256 ) 0

256 256



α = = = gtw

w

h xh

- 256 - 10980571 050

256




134

εα


ct

235456middot

256 456 3459846 58590026 13 1 13middot0571 1



256 2359846 62 1- (- ) 62 1 1059 1059 10849

0026 345






yield strength σγ

le0

ys

M

f






135



εγ γ



M M

f fF F F X t t F

1 2 0 0

2 20 0






As τ

εη

= = ge =w

w

hk

t256 31

9846 51360026




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2560 2610 1446

3 3middot1 10 (EN 1993-1-5 52)




136

τ = + = + =

whk

a

2 2256534 4 534 4 575


1-5 Annex A3

( ) ( )π π

σν



E

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 261958

12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)


λττ

= = = =y w y ww

crcr

f f 345076 076 133


1993-1-5 53 As λw is ge108 then


( ) ( )χ

λ= = =

++w

w

137 1370675

07 13307(Table 51 of EN-1993-1-5 53)


χ


= = times =times

w y w wbw Rd

M

f h tV MN 6

1

0675 345 2560 2610 814

3 3 110



And η


= = times =times

y w wpl a Rd

M

f h tV MN 6

0

12 345 2560 2610 1591

3 3 10 (EN 1993-1-1 626)




γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1





137




xxF F F F F1 2

0120

012 012


xx 0126304 4034 354 354 4248 0

012 012

Then x =01145 m






γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1middot




times times

f f yf

w yw

b t fc a m

th f

2 2

2 2

16 16 1200 120 295025 8 025 3110

26 256 345


138


timesbf RdV

226

1200 120 295 10935middot 1 0197 MN

3110 11 1174010






η = le3

10Ed

b Rd

VV


81209975





η η

+ minus minus le

f Rd

pl Rd

MM

21 3

1 2 1 10

Where

η = Ed

pl Rd

MM1

and η = Ed

bw Rd

VV3



139




VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN


1006050818

12297 η = =3

788509686

814 and


f Rd

pl Rd

M

M

2 21 3

117401 2 1 0818 1 2 09686 1 0858 1

12297











140


areas






141


resistance






142








minus minus= = =

1000 26487 mm

2 2lf wb t

c

ε= = le = =487 235


ct







1 1

500144996 10 6304 MN

115sk

s ss




2 2

50092797 10 4034 MN

115sk

s ss



γ= = times times =

0

295(12 012) 354 MN

10y uf

s uf s ufM

fF A


143


γ= = times times =

0

345(262 0026) 2350 MN

10y w

s w s wM

fF A


γ= = times times =

0

335(100 006) 201 MN

10y lf

s lf s lfM

fF A


γtimes


085 085 3535 05 347 MN

150ck

c cc

fF A


(4573le783) and




(262 )0


x xF F F F F F F F



αminus minus

= = = le262 1815

0307 050262

w

w

h xh



εα

times= = lt = =

235415

262 415 34510076 111560026 0307

ct




= = = le

212 18150144 050

212w

w

h xh




144

εα

times= = lt = =

23536

212 36 3458154 206330026 0144

ct
















145

















146






147








σγ

le

yEd ser

M ser

f

τγ

lesdot

3y

Ed ser

M ser

f

σ τγ

+ sdot le2 2

3 yEd ser Ed ser

M ser

f






σγ

le

yEd ser

M ser

f


148





149


τγ

le = =times

35520496

3 3 10y

Ed ser

M ser

fMPa




σ τγ

+ le2 2

3 yEd ser Ed ser

M ser

f


150






151

σγ

∆ le

15 yfre

M ser

f





le + le30 40 300w

w

hL

t









σ τ

σ τ+ le

2 2


cr cr






152






Where





( )= + le

+ 0

103 10

1 2cc

kh z





Then

( )= + = le

+ times

103 113 10


( )= + = le

+ times

103 102 10




153







160 200 240 280 320 360 400 450

40 32 20 16 12 10 8 6

32 25 16 12 10 8 6 5

25 16 12 8 6 5 4 -


φ φ=

0

ct eff

ct

ff





160 200 240 280 320 360

300 300 250 200 150 100

300 250 200 150 100 50

200 150 100 50 - -



154



σ σ σ= + ∆0s s s

With σα ρ

∆ =04 ctm

sst s

f and α =st

a a

AIA I

Where




ct

AA







ρminustimes

= =423779 10



= =418559 10

000952195s


= =times

03543 058321232



= =times

01555 024561416

01369 01969st


σtimes

∆ = =times

04 328523

1232 001219s MPa


155


∆ = =times

04 329495

1416 00s MPa









φ = =32

32 353129

mm





we can get




This gives






156











π

γ=

2

(1)08

4u

Rdv

df

P


stud

α

γ=

2(2) 029 ck cm

Rdv

d f EP

With

α = +

02 1schd

for 3le schd

le4

α = 10 for schd

gt4

Where








157


π timestimes times

= = times

2

(1) 6

2208 450

4 01095 10 N=01095 MN125RdP

= = gtgt200

909 422

schd


= =times2

(2) 029 1 22 35 340771401226 MN

125RdP












158









40 55 80

120

345 335 325 295

726 800 800 800

297 414




Fig 622 Detailing



159


= minus = minus = gt0 1000 750 22114 25

2 2 2 2f

D

b b de





le sdot15 fd t










160







ν =c k

L k

S VI


161

Where













i

Nx kL

with


Where






00 60 125 250 350 420 500 625

800 875 1000 1080 1125 1200 1320 1400

1500 1625 1700 1760 1875 1940 2000


162



x (m) 50+ 54- 54+ 60- 60+ 625-

νLk (MNm) 0842 0900 0900 0989 0943 0906


( )ν

sdot= =

(4middot P ) 03064 MN031 m


L k

k






163


6741 Elastic design




With

ν =c Ed

L Ed

S VI

Where










i

Nx PL

with


Where






164

ν leinti+1

i

x

x







x (m) 50+ 54- 54+ 60- 60+ 625-

νLEd (MNm) 1124 1203 1203 1323 1264 1213


( )ν


110 (4 P ) 11 0438 MN0365 m


L kEd x


νsdot

= leinti+1

i

x 1

x

(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud

L Ed x dx MNs




165









166











167


ντ

π∆

∆ =

32

4

L FLM

i

i

NdL

Where









Where







λ

=

18

12

0 0

obsmv

NQQ N

Where

=

sumsum

188

1i i

mi

n QQ



Q0=480KN


168

N0=05x106






1 2 3 4 5

200 310 490 390 450

20 5

50 15 10


Qm1=45737 kN

λ = =245737 0952

480v




ηλ

η

= +

188

2 2 24

1 1 1

1 mv

m

N QN Q

η = minus12

eb

With



η = + =11 175 0752 70

and η = minus =21 175 0252 70


169






Where


ψ ψge gt

+ + + +

sum sum 11 1 2

1 1 k j k i k i fat

j iG P Q Q Q







Where








170

γ σσ γ

∆le

∆E2

c

10

Ff

Mf

γ ττ γ

∆le

∆E2

c

10

Ff

Mf s and


∆ ∆+ le

∆ ∆E2 E2

c c

13

Ff Ff

Mf Mf s

Where








171










172



ν = = 0643 MNmL Ed

L Edeff

V


ν= = = 1

max

4 04380681 m

0643Rd stud

L Ed

Ps


Notes





173

References









174

Acknowledgements

Table of Contents


Foreword

13Introduction

Introduction


The Eurocodes


THE DESIGN EXAMPLE








































6741 Elastic design








v





43


45







36 Introduction 50






39 Traffic loads 57






CHAPTER 4


41 Introduction 79




vi








451 SELF-WEIGHT 85



454 ROAD TRAFFIC 87


47 Main results 91




CHAPTER 5 93


51 Introduction 97








121



vii

CHAPTER 6





127





132




142


144


144







150










viii


160


163



166


171

CHAPTER 7


71 Introduction 177





74 Abutment C0 189







CHAPTER 8


81 Introduction 201





205




ix



















APPENDICES 283

APPENDIX A A-1


APPENDIX B B-1


APPENDIX C C-1


APPENDIX D D-1


x

xi


Authors

Introduction



























xii



Editors







xiii

Foreword












xiv







Ispra November 2011





xv

Introduction














The Eurocodes















of firerdquo


xvi


and ETAs)



















Eurocode 8










bridge

xvii




xviii

THE DESIGN EXAMPLE

































xix









CHAPTER 6





Joeumll RAOUL



Convenor EN-1994-2


126


127











γ= = times =ck

c cc

fF A MN

085 085middot3519484 38643



= ckcd

c

ff (EN-1994-2 2412)



128

applied α

γ= cc ck

cdc

ff














129


s uf s ufM

fF A MN

0

345(10 004) 1380

10



s w s wM

fF A MN

0

345(272 0018) 16891

10



s lf s lfM

fF A MN

0

345(120 004) 1656

10






xF F x F F F


004





130





MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)





As τ

εη

= = ge =w

w

hk

t272 31

15111 51360018




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2720middot1810 1063

3middot 3 110 (EN 1993-1-5 52)



τ = + = + times =

whk

a

2 2272534 4 534 4 5802


1993-1-5 Annex A3

( ) ( )π π

σν

times= = =

times


wE

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 188312

12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)


(EN-1993-1-5 53)


131

λττ

= = = =y w y ww

crcr

f f 345

076 076 20324822middot 3




( ) ( )χ

λ= = =

++w

w

137 1370501

07 203207(Table 51 of EN-1993-1-5 53)


χ

γ


timestimesw y w w

bw Rd

M

f h tV MN -6

1

0501 345 2720 184441

3 3middot1 1010



V V V MN V MN

444 0 1063 444

And η

γ


timesy w w

pl a Rd

M

f h tV E MN -6

0

12 345 2720 181170

3 3 10 (EN 1993-1-1 626)








132








VEd = 812 MN





c mm1200 26

587 2 2


ct

587 2354891 9 9 8033

120 295



133






s ss

fF A m MN-4 2

1 1

500144996 10 6304




s ss

fF A m MN-4 2

2 2

50092797 10 4034




s uf s ufM

fF A MN

0

295(12 012) 354

10



s w s wM

fF A MN

0

345(256 0026) 22963

10



s lf s lfM

fF A MN

0

295(120 012) 4248

10





x xF F F F F F F1 2 (256 ) 0

256 256



α = = = gtw

w

h xh

- 256 - 10980571 050

256




134

εα


ct

235456middot

256 456 3459846 58590026 13 1 13middot0571 1



256 2359846 62 1- (- ) 62 1 1059 1059 10849

0026 345






yield strength σγ

le0

ys

M

f






135



εγ γ



M M

f fF F F X t t F

1 2 0 0

2 20 0






As τ

εη

= = ge =w

w

hk

t256 31

9846 51360026




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2560 2610 1446

3 3middot1 10 (EN 1993-1-5 52)




136

τ = + = + =

whk

a

2 2256534 4 534 4 575


1-5 Annex A3

( ) ( )π π

σν



E

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 261958

12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)


λττ

= = = =y w y ww

crcr

f f 345076 076 133


1993-1-5 53 As λw is ge108 then


( ) ( )χ

λ= = =

++w

w

137 1370675

07 13307(Table 51 of EN-1993-1-5 53)


χ


= = times =times

w y w wbw Rd

M

f h tV MN 6

1

0675 345 2560 2610 814

3 3 110



And η


= = times =times

y w wpl a Rd

M

f h tV MN 6

0

12 345 2560 2610 1591

3 3 10 (EN 1993-1-1 626)




γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1





137




xxF F F F F1 2

0120

012 012


xx 0126304 4034 354 354 4248 0

012 012

Then x =01145 m






γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1middot




times times

f f yf

w yw

b t fc a m

th f

2 2

2 2

16 16 1200 120 295025 8 025 3110

26 256 345


138


timesbf RdV

226

1200 120 295 10935middot 1 0197 MN

3110 11 1174010






η = le3

10Ed

b Rd

VV


81209975





η η

+ minus minus le

f Rd

pl Rd

MM

21 3

1 2 1 10

Where

η = Ed

pl Rd

MM1

and η = Ed

bw Rd

VV3



139




VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN


1006050818

12297 η = =3

788509686

814 and


f Rd

pl Rd

M

M

2 21 3

117401 2 1 0818 1 2 09686 1 0858 1

12297











140


areas






141


resistance






142








minus minus= = =

1000 26487 mm

2 2lf wb t

c

ε= = le = =487 235


ct







1 1

500144996 10 6304 MN

115sk

s ss




2 2

50092797 10 4034 MN

115sk

s ss



γ= = times times =

0

295(12 012) 354 MN

10y uf

s uf s ufM

fF A


143


γ= = times times =

0

345(262 0026) 2350 MN

10y w

s w s wM

fF A


γ= = times times =

0

335(100 006) 201 MN

10y lf

s lf s lfM

fF A


γtimes


085 085 3535 05 347 MN

150ck

c cc

fF A


(4573le783) and




(262 )0


x xF F F F F F F F



αminus minus

= = = le262 1815

0307 050262

w

w

h xh



εα

times= = lt = =

235415

262 415 34510076 111560026 0307

ct




= = = le

212 18150144 050

212w

w

h xh




144

εα

times= = lt = =

23536

212 36 3458154 206330026 0144

ct
















145

















146






147








σγ

le

yEd ser

M ser

f

τγ

lesdot

3y

Ed ser

M ser

f

σ τγ

+ sdot le2 2

3 yEd ser Ed ser

M ser

f






σγ

le

yEd ser

M ser

f


148





149


τγ

le = =times

35520496

3 3 10y

Ed ser

M ser

fMPa




σ τγ

+ le2 2

3 yEd ser Ed ser

M ser

f


150






151

σγ

∆ le

15 yfre

M ser

f





le + le30 40 300w

w

hL

t









σ τ

σ τ+ le

2 2


cr cr






152






Where





( )= + le

+ 0

103 10

1 2cc

kh z





Then

( )= + = le

+ times

103 113 10


( )= + = le

+ times

103 102 10




153







160 200 240 280 320 360 400 450

40 32 20 16 12 10 8 6

32 25 16 12 10 8 6 5

25 16 12 8 6 5 4 -


φ φ=

0

ct eff

ct

ff





160 200 240 280 320 360

300 300 250 200 150 100

300 250 200 150 100 50

200 150 100 50 - -



154



σ σ σ= + ∆0s s s

With σα ρ

∆ =04 ctm

sst s

f and α =st

a a

AIA I

Where




ct

AA







ρminustimes

= =423779 10



= =418559 10

000952195s


= =times

03543 058321232



= =times

01555 024561416

01369 01969st


σtimes

∆ = =times

04 328523

1232 001219s MPa


155


∆ = =times

04 329495

1416 00s MPa









φ = =32

32 353129

mm





we can get




This gives






156











π

γ=

2

(1)08

4u

Rdv

df

P


stud

α

γ=

2(2) 029 ck cm

Rdv

d f EP

With

α = +

02 1schd

for 3le schd

le4

α = 10 for schd

gt4

Where








157


π timestimes times

= = times

2

(1) 6

2208 450

4 01095 10 N=01095 MN125RdP

= = gtgt200

909 422

schd


= =times2

(2) 029 1 22 35 340771401226 MN

125RdP












158









40 55 80

120

345 335 325 295

726 800 800 800

297 414




Fig 622 Detailing



159


= minus = minus = gt0 1000 750 22114 25

2 2 2 2f

D

b b de





le sdot15 fd t










160







ν =c k

L k

S VI


161

Where













i

Nx kL

with


Where






00 60 125 250 350 420 500 625

800 875 1000 1080 1125 1200 1320 1400

1500 1625 1700 1760 1875 1940 2000


162



x (m) 50+ 54- 54+ 60- 60+ 625-

νLk (MNm) 0842 0900 0900 0989 0943 0906


( )ν

sdot= =

(4middot P ) 03064 MN031 m


L k

k






163


6741 Elastic design




With

ν =c Ed

L Ed

S VI

Where










i

Nx PL

with


Where






164

ν leinti+1

i

x

x







x (m) 50+ 54- 54+ 60- 60+ 625-

νLEd (MNm) 1124 1203 1203 1323 1264 1213


( )ν


110 (4 P ) 11 0438 MN0365 m


L kEd x


νsdot

= leinti+1

i

x 1

x

(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud

L Ed x dx MNs




165









166











167


ντ

π∆

∆ =

32

4

L FLM

i

i

NdL

Where









Where







λ

=

18

12

0 0

obsmv

NQQ N

Where

=

sumsum

188

1i i

mi

n QQ



Q0=480KN


168

N0=05x106






1 2 3 4 5

200 310 490 390 450

20 5

50 15 10


Qm1=45737 kN

λ = =245737 0952

480v




ηλ

η

= +

188

2 2 24

1 1 1

1 mv

m

N QN Q

η = minus12

eb

With



η = + =11 175 0752 70

and η = minus =21 175 0252 70


169






Where


ψ ψge gt

+ + + +

sum sum 11 1 2

1 1 k j k i k i fat

j iG P Q Q Q







Where








170

γ σσ γ

∆le

∆E2

c

10

Ff

Mf

γ ττ γ

∆le

∆E2

c

10

Ff

Mf s and


∆ ∆+ le

∆ ∆E2 E2

c c

13

Ff Ff

Mf Mf s

Where








171










172



ν = = 0643 MNmL Ed

L Edeff

V


ν= = = 1

max

4 04380681 m

0643Rd stud

L Ed

Ps


Notes





173

References









174

Acknowledgements

Table of Contents


Foreword

13Introduction

Introduction


The Eurocodes


THE DESIGN EXAMPLE








































6741 Elastic design








vi








451 SELF-WEIGHT 85



454 ROAD TRAFFIC 87


47 Main results 91




CHAPTER 5 93


51 Introduction 97








121



vii

CHAPTER 6





127





132




142


144


144







150










viii


160


163



166


171

CHAPTER 7


71 Introduction 177





74 Abutment C0 189







CHAPTER 8


81 Introduction 201





205




ix



















APPENDICES 283

APPENDIX A A-1


APPENDIX B B-1


APPENDIX C C-1


APPENDIX D D-1


x

xi


Authors

Introduction



























xii



Editors







xiii

Foreword












xiv







Ispra November 2011





xv

Introduction














The Eurocodes















of firerdquo


xvi


and ETAs)



















Eurocode 8










bridge

xvii




xviii

THE DESIGN EXAMPLE

































xix









CHAPTER 6





Joeumll RAOUL



Convenor EN-1994-2


126


127











γ= = times =ck

c cc

fF A MN

085 085middot3519484 38643



= ckcd

c

ff (EN-1994-2 2412)



128

applied α

γ= cc ck

cdc

ff














129


s uf s ufM

fF A MN

0

345(10 004) 1380

10



s w s wM

fF A MN

0

345(272 0018) 16891

10



s lf s lfM

fF A MN

0

345(120 004) 1656

10






xF F x F F F


004





130





MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)





As τ

εη

= = ge =w

w

hk

t272 31

15111 51360018




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2720middot1810 1063

3middot 3 110 (EN 1993-1-5 52)



τ = + = + times =

whk

a

2 2272534 4 534 4 5802


1993-1-5 Annex A3

( ) ( )π π

σν

times= = =

times


wE

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 188312

12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)


(EN-1993-1-5 53)


131

λττ

= = = =y w y ww

crcr

f f 345

076 076 20324822middot 3




( ) ( )χ

λ= = =

++w

w

137 1370501

07 203207(Table 51 of EN-1993-1-5 53)


χ

γ


timestimesw y w w

bw Rd

M

f h tV MN -6

1

0501 345 2720 184441

3 3middot1 1010



V V V MN V MN

444 0 1063 444

And η

γ


timesy w w

pl a Rd

M

f h tV E MN -6

0

12 345 2720 181170

3 3 10 (EN 1993-1-1 626)








132








VEd = 812 MN





c mm1200 26

587 2 2


ct

587 2354891 9 9 8033

120 295



133






s ss

fF A m MN-4 2

1 1

500144996 10 6304




s ss

fF A m MN-4 2

2 2

50092797 10 4034




s uf s ufM

fF A MN

0

295(12 012) 354

10



s w s wM

fF A MN

0

345(256 0026) 22963

10



s lf s lfM

fF A MN

0

295(120 012) 4248

10





x xF F F F F F F1 2 (256 ) 0

256 256



α = = = gtw

w

h xh

- 256 - 10980571 050

256




134

εα


ct

235456middot

256 456 3459846 58590026 13 1 13middot0571 1



256 2359846 62 1- (- ) 62 1 1059 1059 10849

0026 345






yield strength σγ

le0

ys

M

f






135



εγ γ



M M

f fF F F X t t F

1 2 0 0

2 20 0






As τ

εη

= = ge =w

w

hk

t256 31

9846 51360026




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2560 2610 1446

3 3middot1 10 (EN 1993-1-5 52)




136

τ = + = + =

whk

a

2 2256534 4 534 4 575


1-5 Annex A3

( ) ( )π π

σν



E

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 261958

12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)


λττ

= = = =y w y ww

crcr

f f 345076 076 133


1993-1-5 53 As λw is ge108 then


( ) ( )χ

λ= = =

++w

w

137 1370675

07 13307(Table 51 of EN-1993-1-5 53)


χ


= = times =times

w y w wbw Rd

M

f h tV MN 6

1

0675 345 2560 2610 814

3 3 110



And η


= = times =times

y w wpl a Rd

M

f h tV MN 6

0

12 345 2560 2610 1591

3 3 10 (EN 1993-1-1 626)




γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1





137




xxF F F F F1 2

0120

012 012


xx 0126304 4034 354 354 4248 0

012 012

Then x =01145 m






γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1middot




times times

f f yf

w yw

b t fc a m

th f

2 2

2 2

16 16 1200 120 295025 8 025 3110

26 256 345


138


timesbf RdV

226

1200 120 295 10935middot 1 0197 MN

3110 11 1174010






η = le3

10Ed

b Rd

VV


81209975





η η

+ minus minus le

f Rd

pl Rd

MM

21 3

1 2 1 10

Where

η = Ed

pl Rd

MM1

and η = Ed

bw Rd

VV3



139




VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN


1006050818

12297 η = =3

788509686

814 and


f Rd

pl Rd

M

M

2 21 3

117401 2 1 0818 1 2 09686 1 0858 1

12297











140


areas






141


resistance






142








minus minus= = =

1000 26487 mm

2 2lf wb t

c

ε= = le = =487 235


ct







1 1

500144996 10 6304 MN

115sk

s ss




2 2

50092797 10 4034 MN

115sk

s ss



γ= = times times =

0

295(12 012) 354 MN

10y uf

s uf s ufM

fF A


143


γ= = times times =

0

345(262 0026) 2350 MN

10y w

s w s wM

fF A


γ= = times times =

0

335(100 006) 201 MN

10y lf

s lf s lfM

fF A


γtimes


085 085 3535 05 347 MN

150ck

c cc

fF A


(4573le783) and




(262 )0


x xF F F F F F F F



αminus minus

= = = le262 1815

0307 050262

w

w

h xh



εα

times= = lt = =

235415

262 415 34510076 111560026 0307

ct




= = = le

212 18150144 050

212w

w

h xh




144

εα

times= = lt = =

23536

212 36 3458154 206330026 0144

ct
















145

















146






147








σγ

le

yEd ser

M ser

f

τγ

lesdot

3y

Ed ser

M ser

f

σ τγ

+ sdot le2 2

3 yEd ser Ed ser

M ser

f






σγ

le

yEd ser

M ser

f


148





149


τγ

le = =times

35520496

3 3 10y

Ed ser

M ser

fMPa




σ τγ

+ le2 2

3 yEd ser Ed ser

M ser

f


150






151

σγ

∆ le

15 yfre

M ser

f





le + le30 40 300w

w

hL

t









σ τ

σ τ+ le

2 2


cr cr






152






Where





( )= + le

+ 0

103 10

1 2cc

kh z





Then

( )= + = le

+ times

103 113 10


( )= + = le

+ times

103 102 10




153







160 200 240 280 320 360 400 450

40 32 20 16 12 10 8 6

32 25 16 12 10 8 6 5

25 16 12 8 6 5 4 -


φ φ=

0

ct eff

ct

ff





160 200 240 280 320 360

300 300 250 200 150 100

300 250 200 150 100 50

200 150 100 50 - -



154



σ σ σ= + ∆0s s s

With σα ρ

∆ =04 ctm

sst s

f and α =st

a a

AIA I

Where




ct

AA







ρminustimes

= =423779 10



= =418559 10

000952195s


= =times

03543 058321232



= =times

01555 024561416

01369 01969st


σtimes

∆ = =times

04 328523

1232 001219s MPa


155


∆ = =times

04 329495

1416 00s MPa









φ = =32

32 353129

mm





we can get




This gives






156











π

γ=

2

(1)08

4u

Rdv

df

P


stud

α

γ=

2(2) 029 ck cm

Rdv

d f EP

With

α = +

02 1schd

for 3le schd

le4

α = 10 for schd

gt4

Where








157


π timestimes times

= = times

2

(1) 6

2208 450

4 01095 10 N=01095 MN125RdP

= = gtgt200

909 422

schd


= =times2

(2) 029 1 22 35 340771401226 MN

125RdP












158









40 55 80

120

345 335 325 295

726 800 800 800

297 414




Fig 622 Detailing



159


= minus = minus = gt0 1000 750 22114 25

2 2 2 2f

D

b b de





le sdot15 fd t










160







ν =c k

L k

S VI


161

Where













i

Nx kL

with


Where






00 60 125 250 350 420 500 625

800 875 1000 1080 1125 1200 1320 1400

1500 1625 1700 1760 1875 1940 2000


162



x (m) 50+ 54- 54+ 60- 60+ 625-

νLk (MNm) 0842 0900 0900 0989 0943 0906


( )ν

sdot= =

(4middot P ) 03064 MN031 m


L k

k






163


6741 Elastic design




With

ν =c Ed

L Ed

S VI

Where










i

Nx PL

with


Where






164

ν leinti+1

i

x

x







x (m) 50+ 54- 54+ 60- 60+ 625-

νLEd (MNm) 1124 1203 1203 1323 1264 1213


( )ν


110 (4 P ) 11 0438 MN0365 m


L kEd x


νsdot

= leinti+1

i

x 1

x

(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud

L Ed x dx MNs




165









166











167


ντ

π∆

∆ =

32

4

L FLM

i

i

NdL

Where









Where







λ

=

18

12

0 0

obsmv

NQQ N

Where

=

sumsum

188

1i i

mi

n QQ



Q0=480KN


168

N0=05x106






1 2 3 4 5

200 310 490 390 450

20 5

50 15 10


Qm1=45737 kN

λ = =245737 0952

480v




ηλ

η

= +

188

2 2 24

1 1 1

1 mv

m

N QN Q

η = minus12

eb

With



η = + =11 175 0752 70

and η = minus =21 175 0252 70


169






Where


ψ ψge gt

+ + + +

sum sum 11 1 2

1 1 k j k i k i fat

j iG P Q Q Q







Where








170

γ σσ γ

∆le

∆E2

c

10

Ff

Mf

γ ττ γ

∆le

∆E2

c

10

Ff

Mf s and


∆ ∆+ le

∆ ∆E2 E2

c c

13

Ff Ff

Mf Mf s

Where








171










172



ν = = 0643 MNmL Ed

L Edeff

V


ν= = = 1

max

4 04380681 m

0643Rd stud

L Ed

Ps


Notes





173

References









174

Acknowledgements

Table of Contents


Foreword

13Introduction

Introduction


The Eurocodes


THE DESIGN EXAMPLE








































6741 Elastic design








vii

CHAPTER 6





127





132




142


144


144







150










viii


160


163



166


171

CHAPTER 7


71 Introduction 177





74 Abutment C0 189







CHAPTER 8


81 Introduction 201





205




ix



















APPENDICES 283

APPENDIX A A-1


APPENDIX B B-1


APPENDIX C C-1


APPENDIX D D-1


x

xi


Authors

Introduction



























xii



Editors







xiii

Foreword












xiv







Ispra November 2011





xv

Introduction














The Eurocodes















of firerdquo


xvi


and ETAs)



















Eurocode 8










bridge

xvii




xviii

THE DESIGN EXAMPLE

































xix









CHAPTER 6





Joeumll RAOUL



Convenor EN-1994-2


126


127











γ= = times =ck

c cc

fF A MN

085 085middot3519484 38643



= ckcd

c

ff (EN-1994-2 2412)



128

applied α

γ= cc ck

cdc

ff














129


s uf s ufM

fF A MN

0

345(10 004) 1380

10



s w s wM

fF A MN

0

345(272 0018) 16891

10



s lf s lfM

fF A MN

0

345(120 004) 1656

10






xF F x F F F


004





130





MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)





As τ

εη

= = ge =w

w

hk

t272 31

15111 51360018




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2720middot1810 1063

3middot 3 110 (EN 1993-1-5 52)



τ = + = + times =

whk

a

2 2272534 4 534 4 5802


1993-1-5 Annex A3

( ) ( )π π

σν

times= = =

times


wE

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 188312

12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)


(EN-1993-1-5 53)


131

λττ

= = = =y w y ww

crcr

f f 345

076 076 20324822middot 3




( ) ( )χ

λ= = =

++w

w

137 1370501

07 203207(Table 51 of EN-1993-1-5 53)


χ

γ


timestimesw y w w

bw Rd

M

f h tV MN -6

1

0501 345 2720 184441

3 3middot1 1010



V V V MN V MN

444 0 1063 444

And η

γ


timesy w w

pl a Rd

M

f h tV E MN -6

0

12 345 2720 181170

3 3 10 (EN 1993-1-1 626)








132








VEd = 812 MN





c mm1200 26

587 2 2


ct

587 2354891 9 9 8033

120 295



133






s ss

fF A m MN-4 2

1 1

500144996 10 6304




s ss

fF A m MN-4 2

2 2

50092797 10 4034




s uf s ufM

fF A MN

0

295(12 012) 354

10



s w s wM

fF A MN

0

345(256 0026) 22963

10



s lf s lfM

fF A MN

0

295(120 012) 4248

10





x xF F F F F F F1 2 (256 ) 0

256 256



α = = = gtw

w

h xh

- 256 - 10980571 050

256




134

εα


ct

235456middot

256 456 3459846 58590026 13 1 13middot0571 1



256 2359846 62 1- (- ) 62 1 1059 1059 10849

0026 345






yield strength σγ

le0

ys

M

f






135



εγ γ



M M

f fF F F X t t F

1 2 0 0

2 20 0






As τ

εη

= = ge =w

w

hk

t256 31

9846 51360026




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2560 2610 1446

3 3middot1 10 (EN 1993-1-5 52)




136

τ = + = + =

whk

a

2 2256534 4 534 4 575


1-5 Annex A3

( ) ( )π π

σν



E

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 261958

12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)


λττ

= = = =y w y ww

crcr

f f 345076 076 133


1993-1-5 53 As λw is ge108 then


( ) ( )χ

λ= = =

++w

w

137 1370675

07 13307(Table 51 of EN-1993-1-5 53)


χ


= = times =times

w y w wbw Rd

M

f h tV MN 6

1

0675 345 2560 2610 814

3 3 110



And η


= = times =times

y w wpl a Rd

M

f h tV MN 6

0

12 345 2560 2610 1591

3 3 10 (EN 1993-1-1 626)




γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1





137




xxF F F F F1 2

0120

012 012


xx 0126304 4034 354 354 4248 0

012 012

Then x =01145 m






γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1middot




times times

f f yf

w yw

b t fc a m

th f

2 2

2 2

16 16 1200 120 295025 8 025 3110

26 256 345


138


timesbf RdV

226

1200 120 295 10935middot 1 0197 MN

3110 11 1174010






η = le3

10Ed

b Rd

VV


81209975





η η

+ minus minus le

f Rd

pl Rd

MM

21 3

1 2 1 10

Where

η = Ed

pl Rd

MM1

and η = Ed

bw Rd

VV3



139




VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN


1006050818

12297 η = =3

788509686

814 and


f Rd

pl Rd

M

M

2 21 3

117401 2 1 0818 1 2 09686 1 0858 1

12297











140


areas






141


resistance






142








minus minus= = =

1000 26487 mm

2 2lf wb t

c

ε= = le = =487 235


ct







1 1

500144996 10 6304 MN

115sk

s ss




2 2

50092797 10 4034 MN

115sk

s ss



γ= = times times =

0

295(12 012) 354 MN

10y uf

s uf s ufM

fF A


143


γ= = times times =

0

345(262 0026) 2350 MN

10y w

s w s wM

fF A


γ= = times times =

0

335(100 006) 201 MN

10y lf

s lf s lfM

fF A


γtimes


085 085 3535 05 347 MN

150ck

c cc

fF A


(4573le783) and




(262 )0


x xF F F F F F F F



αminus minus

= = = le262 1815

0307 050262

w

w

h xh



εα

times= = lt = =

235415

262 415 34510076 111560026 0307

ct




= = = le

212 18150144 050

212w

w

h xh




144

εα

times= = lt = =

23536

212 36 3458154 206330026 0144

ct
















145

















146






147








σγ

le

yEd ser

M ser

f

τγ

lesdot

3y

Ed ser

M ser

f

σ τγ

+ sdot le2 2

3 yEd ser Ed ser

M ser

f






σγ

le

yEd ser

M ser

f


148





149


τγ

le = =times

35520496

3 3 10y

Ed ser

M ser

fMPa




σ τγ

+ le2 2

3 yEd ser Ed ser

M ser

f


150






151

σγ

∆ le

15 yfre

M ser

f





le + le30 40 300w

w

hL

t









σ τ

σ τ+ le

2 2


cr cr






152






Where





( )= + le

+ 0

103 10

1 2cc

kh z





Then

( )= + = le

+ times

103 113 10


( )= + = le

+ times

103 102 10




153







160 200 240 280 320 360 400 450

40 32 20 16 12 10 8 6

32 25 16 12 10 8 6 5

25 16 12 8 6 5 4 -


φ φ=

0

ct eff

ct

ff





160 200 240 280 320 360

300 300 250 200 150 100

300 250 200 150 100 50

200 150 100 50 - -



154



σ σ σ= + ∆0s s s

With σα ρ

∆ =04 ctm

sst s

f and α =st

a a

AIA I

Where




ct

AA







ρminustimes

= =423779 10



= =418559 10

000952195s


= =times

03543 058321232



= =times

01555 024561416

01369 01969st


σtimes

∆ = =times

04 328523

1232 001219s MPa


155


∆ = =times

04 329495

1416 00s MPa









φ = =32

32 353129

mm





we can get




This gives






156











π

γ=

2

(1)08

4u

Rdv

df

P


stud

α

γ=

2(2) 029 ck cm

Rdv

d f EP

With

α = +

02 1schd

for 3le schd

le4

α = 10 for schd

gt4

Where








157


π timestimes times

= = times

2

(1) 6

2208 450

4 01095 10 N=01095 MN125RdP

= = gtgt200

909 422

schd


= =times2

(2) 029 1 22 35 340771401226 MN

125RdP












158









40 55 80

120

345 335 325 295

726 800 800 800

297 414




Fig 622 Detailing



159


= minus = minus = gt0 1000 750 22114 25

2 2 2 2f

D

b b de





le sdot15 fd t










160







ν =c k

L k

S VI


161

Where













i

Nx kL

with


Where






00 60 125 250 350 420 500 625

800 875 1000 1080 1125 1200 1320 1400

1500 1625 1700 1760 1875 1940 2000


162



x (m) 50+ 54- 54+ 60- 60+ 625-

νLk (MNm) 0842 0900 0900 0989 0943 0906


( )ν

sdot= =

(4middot P ) 03064 MN031 m


L k

k






163


6741 Elastic design




With

ν =c Ed

L Ed

S VI

Where










i

Nx PL

with


Where






164

ν leinti+1

i

x

x







x (m) 50+ 54- 54+ 60- 60+ 625-

νLEd (MNm) 1124 1203 1203 1323 1264 1213


( )ν


110 (4 P ) 11 0438 MN0365 m


L kEd x


νsdot

= leinti+1

i

x 1

x

(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud

L Ed x dx MNs




165









166











167


ντ

π∆

∆ =

32

4

L FLM

i

i

NdL

Where









Where







λ

=

18

12

0 0

obsmv

NQQ N

Where

=

sumsum

188

1i i

mi

n QQ



Q0=480KN


168

N0=05x106






1 2 3 4 5

200 310 490 390 450

20 5

50 15 10


Qm1=45737 kN

λ = =245737 0952

480v




ηλ

η

= +

188

2 2 24

1 1 1

1 mv

m

N QN Q

η = minus12

eb

With



η = + =11 175 0752 70

and η = minus =21 175 0252 70


169






Where


ψ ψge gt

+ + + +

sum sum 11 1 2

1 1 k j k i k i fat

j iG P Q Q Q







Where








170

γ σσ γ

∆le

∆E2

c

10

Ff

Mf

γ ττ γ

∆le

∆E2

c

10

Ff

Mf s and


∆ ∆+ le

∆ ∆E2 E2

c c

13

Ff Ff

Mf Mf s

Where








171










172



ν = = 0643 MNmL Ed

L Edeff

V


ν= = = 1

max

4 04380681 m

0643Rd stud

L Ed

Ps


Notes





173

References









174

Acknowledgements

Table of Contents


Foreword

13Introduction

Introduction


The Eurocodes


THE DESIGN EXAMPLE








































6741 Elastic design








viii


160


163



166


171

CHAPTER 7


71 Introduction 177





74 Abutment C0 189







CHAPTER 8


81 Introduction 201





205




ix



















APPENDICES 283

APPENDIX A A-1


APPENDIX B B-1


APPENDIX C C-1


APPENDIX D D-1


x

xi


Authors

Introduction



























xii



Editors







xiii

Foreword












xiv







Ispra November 2011





xv

Introduction














The Eurocodes















of firerdquo


xvi


and ETAs)



















Eurocode 8










bridge

xvii




xviii

THE DESIGN EXAMPLE

































xix









CHAPTER 6





Joeumll RAOUL



Convenor EN-1994-2


126


127











γ= = times =ck

c cc

fF A MN

085 085middot3519484 38643



= ckcd

c

ff (EN-1994-2 2412)



128

applied α

γ= cc ck

cdc

ff














129


s uf s ufM

fF A MN

0

345(10 004) 1380

10



s w s wM

fF A MN

0

345(272 0018) 16891

10



s lf s lfM

fF A MN

0

345(120 004) 1656

10






xF F x F F F


004





130





MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)





As τ

εη

= = ge =w

w

hk

t272 31

15111 51360018




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2720middot1810 1063

3middot 3 110 (EN 1993-1-5 52)



τ = + = + times =

whk

a

2 2272534 4 534 4 5802


1993-1-5 Annex A3

( ) ( )π π

σν

times= = =

times


wE

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 188312

12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)


(EN-1993-1-5 53)


131

λττ

= = = =y w y ww

crcr

f f 345

076 076 20324822middot 3




( ) ( )χ

λ= = =

++w

w

137 1370501

07 203207(Table 51 of EN-1993-1-5 53)


χ

γ


timestimesw y w w

bw Rd

M

f h tV MN -6

1

0501 345 2720 184441

3 3middot1 1010



V V V MN V MN

444 0 1063 444

And η

γ


timesy w w

pl a Rd

M

f h tV E MN -6

0

12 345 2720 181170

3 3 10 (EN 1993-1-1 626)








132








VEd = 812 MN





c mm1200 26

587 2 2


ct

587 2354891 9 9 8033

120 295



133






s ss

fF A m MN-4 2

1 1

500144996 10 6304




s ss

fF A m MN-4 2

2 2

50092797 10 4034




s uf s ufM

fF A MN

0

295(12 012) 354

10



s w s wM

fF A MN

0

345(256 0026) 22963

10



s lf s lfM

fF A MN

0

295(120 012) 4248

10





x xF F F F F F F1 2 (256 ) 0

256 256



α = = = gtw

w

h xh

- 256 - 10980571 050

256




134

εα


ct

235456middot

256 456 3459846 58590026 13 1 13middot0571 1



256 2359846 62 1- (- ) 62 1 1059 1059 10849

0026 345






yield strength σγ

le0

ys

M

f






135



εγ γ



M M

f fF F F X t t F

1 2 0 0

2 20 0






As τ

εη

= = ge =w

w

hk

t256 31

9846 51360026




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2560 2610 1446

3 3middot1 10 (EN 1993-1-5 52)




136

τ = + = + =

whk

a

2 2256534 4 534 4 575


1-5 Annex A3

( ) ( )π π

σν



E

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 261958

12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)


λττ

= = = =y w y ww

crcr

f f 345076 076 133


1993-1-5 53 As λw is ge108 then


( ) ( )χ

λ= = =

++w

w

137 1370675

07 13307(Table 51 of EN-1993-1-5 53)


χ


= = times =times

w y w wbw Rd

M

f h tV MN 6

1

0675 345 2560 2610 814

3 3 110



And η


= = times =times

y w wpl a Rd

M

f h tV MN 6

0

12 345 2560 2610 1591

3 3 10 (EN 1993-1-1 626)




γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1





137




xxF F F F F1 2

0120

012 012


xx 0126304 4034 354 354 4248 0

012 012

Then x =01145 m






γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1middot




times times

f f yf

w yw

b t fc a m

th f

2 2

2 2

16 16 1200 120 295025 8 025 3110

26 256 345


138


timesbf RdV

226

1200 120 295 10935middot 1 0197 MN

3110 11 1174010






η = le3

10Ed

b Rd

VV


81209975





η η

+ minus minus le

f Rd

pl Rd

MM

21 3

1 2 1 10

Where

η = Ed

pl Rd

MM1

and η = Ed

bw Rd

VV3



139




VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN


1006050818

12297 η = =3

788509686

814 and


f Rd

pl Rd

M

M

2 21 3

117401 2 1 0818 1 2 09686 1 0858 1

12297











140


areas






141


resistance






142








minus minus= = =

1000 26487 mm

2 2lf wb t

c

ε= = le = =487 235


ct







1 1

500144996 10 6304 MN

115sk

s ss




2 2

50092797 10 4034 MN

115sk

s ss



γ= = times times =

0

295(12 012) 354 MN

10y uf

s uf s ufM

fF A


143


γ= = times times =

0

345(262 0026) 2350 MN

10y w

s w s wM

fF A


γ= = times times =

0

335(100 006) 201 MN

10y lf

s lf s lfM

fF A


γtimes


085 085 3535 05 347 MN

150ck

c cc

fF A


(4573le783) and




(262 )0


x xF F F F F F F F



αminus minus

= = = le262 1815

0307 050262

w

w

h xh



εα

times= = lt = =

235415

262 415 34510076 111560026 0307

ct




= = = le

212 18150144 050

212w

w

h xh




144

εα

times= = lt = =

23536

212 36 3458154 206330026 0144

ct
















145

















146






147








σγ

le

yEd ser

M ser

f

τγ

lesdot

3y

Ed ser

M ser

f

σ τγ

+ sdot le2 2

3 yEd ser Ed ser

M ser

f






σγ

le

yEd ser

M ser

f


148





149


τγ

le = =times

35520496

3 3 10y

Ed ser

M ser

fMPa




σ τγ

+ le2 2

3 yEd ser Ed ser

M ser

f


150






151

σγ

∆ le

15 yfre

M ser

f





le + le30 40 300w

w

hL

t









σ τ

σ τ+ le

2 2


cr cr






152






Where





( )= + le

+ 0

103 10

1 2cc

kh z





Then

( )= + = le

+ times

103 113 10


( )= + = le

+ times

103 102 10




153







160 200 240 280 320 360 400 450

40 32 20 16 12 10 8 6

32 25 16 12 10 8 6 5

25 16 12 8 6 5 4 -


φ φ=

0

ct eff

ct

ff





160 200 240 280 320 360

300 300 250 200 150 100

300 250 200 150 100 50

200 150 100 50 - -



154



σ σ σ= + ∆0s s s

With σα ρ

∆ =04 ctm

sst s

f and α =st

a a

AIA I

Where




ct

AA







ρminustimes

= =423779 10



= =418559 10

000952195s


= =times

03543 058321232



= =times

01555 024561416

01369 01969st


σtimes

∆ = =times

04 328523

1232 001219s MPa


155


∆ = =times

04 329495

1416 00s MPa









φ = =32

32 353129

mm





we can get




This gives






156











π

γ=

2

(1)08

4u

Rdv

df

P


stud

α

γ=

2(2) 029 ck cm

Rdv

d f EP

With

α = +

02 1schd

for 3le schd

le4

α = 10 for schd

gt4

Where








157


π timestimes times

= = times

2

(1) 6

2208 450

4 01095 10 N=01095 MN125RdP

= = gtgt200

909 422

schd


= =times2

(2) 029 1 22 35 340771401226 MN

125RdP












158









40 55 80

120

345 335 325 295

726 800 800 800

297 414




Fig 622 Detailing



159


= minus = minus = gt0 1000 750 22114 25

2 2 2 2f

D

b b de





le sdot15 fd t










160







ν =c k

L k

S VI


161

Where













i

Nx kL

with


Where






00 60 125 250 350 420 500 625

800 875 1000 1080 1125 1200 1320 1400

1500 1625 1700 1760 1875 1940 2000


162



x (m) 50+ 54- 54+ 60- 60+ 625-

νLk (MNm) 0842 0900 0900 0989 0943 0906


( )ν

sdot= =

(4middot P ) 03064 MN031 m


L k

k






163


6741 Elastic design




With

ν =c Ed

L Ed

S VI

Where










i

Nx PL

with


Where






164

ν leinti+1

i

x

x







x (m) 50+ 54- 54+ 60- 60+ 625-

νLEd (MNm) 1124 1203 1203 1323 1264 1213


( )ν


110 (4 P ) 11 0438 MN0365 m


L kEd x


νsdot

= leinti+1

i

x 1

x

(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud

L Ed x dx MNs




165









166











167


ντ

π∆

∆ =

32

4

L FLM

i

i

NdL

Where









Where







λ

=

18

12

0 0

obsmv

NQQ N

Where

=

sumsum

188

1i i

mi

n QQ



Q0=480KN


168

N0=05x106






1 2 3 4 5

200 310 490 390 450

20 5

50 15 10


Qm1=45737 kN

λ = =245737 0952

480v




ηλ

η

= +

188

2 2 24

1 1 1

1 mv

m

N QN Q

η = minus12

eb

With



η = + =11 175 0752 70

and η = minus =21 175 0252 70


169






Where


ψ ψge gt

+ + + +

sum sum 11 1 2

1 1 k j k i k i fat

j iG P Q Q Q







Where








170

γ σσ γ

∆le

∆E2

c

10

Ff

Mf

γ ττ γ

∆le

∆E2

c

10

Ff

Mf s and


∆ ∆+ le

∆ ∆E2 E2

c c

13

Ff Ff

Mf Mf s

Where








171










172



ν = = 0643 MNmL Ed

L Edeff

V


ν= = = 1

max

4 04380681 m

0643Rd stud

L Ed

Ps


Notes





173

References









174

Acknowledgements

Table of Contents


Foreword

13Introduction

Introduction


The Eurocodes


THE DESIGN EXAMPLE








































6741 Elastic design








ix



















APPENDICES 283

APPENDIX A A-1


APPENDIX B B-1


APPENDIX C C-1


APPENDIX D D-1


x

xi


Authors

Introduction



























xii



Editors







xiii

Foreword












xiv







Ispra November 2011





xv

Introduction














The Eurocodes















of firerdquo


xvi


and ETAs)



















Eurocode 8










bridge

xvii




xviii

THE DESIGN EXAMPLE

































xix









CHAPTER 6





Joeumll RAOUL



Convenor EN-1994-2


126


127











γ= = times =ck

c cc

fF A MN

085 085middot3519484 38643



= ckcd

c

ff (EN-1994-2 2412)



128

applied α

γ= cc ck

cdc

ff














129


s uf s ufM

fF A MN

0

345(10 004) 1380

10



s w s wM

fF A MN

0

345(272 0018) 16891

10



s lf s lfM

fF A MN

0

345(120 004) 1656

10






xF F x F F F


004





130





MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)





As τ

εη

= = ge =w

w

hk

t272 31

15111 51360018




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2720middot1810 1063

3middot 3 110 (EN 1993-1-5 52)



τ = + = + times =

whk

a

2 2272534 4 534 4 5802


1993-1-5 Annex A3

( ) ( )π π

σν

times= = =

times


wE

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 188312

12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)


(EN-1993-1-5 53)


131

λττ

= = = =y w y ww

crcr

f f 345

076 076 20324822middot 3




( ) ( )χ

λ= = =

++w

w

137 1370501

07 203207(Table 51 of EN-1993-1-5 53)


χ

γ


timestimesw y w w

bw Rd

M

f h tV MN -6

1

0501 345 2720 184441

3 3middot1 1010



V V V MN V MN

444 0 1063 444

And η

γ


timesy w w

pl a Rd

M

f h tV E MN -6

0

12 345 2720 181170

3 3 10 (EN 1993-1-1 626)








132








VEd = 812 MN





c mm1200 26

587 2 2


ct

587 2354891 9 9 8033

120 295



133






s ss

fF A m MN-4 2

1 1

500144996 10 6304




s ss

fF A m MN-4 2

2 2

50092797 10 4034




s uf s ufM

fF A MN

0

295(12 012) 354

10



s w s wM

fF A MN

0

345(256 0026) 22963

10



s lf s lfM

fF A MN

0

295(120 012) 4248

10





x xF F F F F F F1 2 (256 ) 0

256 256



α = = = gtw

w

h xh

- 256 - 10980571 050

256




134

εα


ct

235456middot

256 456 3459846 58590026 13 1 13middot0571 1



256 2359846 62 1- (- ) 62 1 1059 1059 10849

0026 345






yield strength σγ

le0

ys

M

f






135



εγ γ



M M

f fF F F X t t F

1 2 0 0

2 20 0






As τ

εη

= = ge =w

w

hk

t256 31

9846 51360026




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2560 2610 1446

3 3middot1 10 (EN 1993-1-5 52)




136

τ = + = + =

whk

a

2 2256534 4 534 4 575


1-5 Annex A3

( ) ( )π π

σν



E

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 261958

12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)


λττ

= = = =y w y ww

crcr

f f 345076 076 133


1993-1-5 53 As λw is ge108 then


( ) ( )χ

λ= = =

++w

w

137 1370675

07 13307(Table 51 of EN-1993-1-5 53)


χ


= = times =times

w y w wbw Rd

M

f h tV MN 6

1

0675 345 2560 2610 814

3 3 110



And η


= = times =times

y w wpl a Rd

M

f h tV MN 6

0

12 345 2560 2610 1591

3 3 10 (EN 1993-1-1 626)




γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1





137




xxF F F F F1 2

0120

012 012


xx 0126304 4034 354 354 4248 0

012 012

Then x =01145 m






γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1middot




times times

f f yf

w yw

b t fc a m

th f

2 2

2 2

16 16 1200 120 295025 8 025 3110

26 256 345


138


timesbf RdV

226

1200 120 295 10935middot 1 0197 MN

3110 11 1174010






η = le3

10Ed

b Rd

VV


81209975





η η

+ minus minus le

f Rd

pl Rd

MM

21 3

1 2 1 10

Where

η = Ed

pl Rd

MM1

and η = Ed

bw Rd

VV3



139




VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN


1006050818

12297 η = =3

788509686

814 and


f Rd

pl Rd

M

M

2 21 3

117401 2 1 0818 1 2 09686 1 0858 1

12297











140


areas






141


resistance






142








minus minus= = =

1000 26487 mm

2 2lf wb t

c

ε= = le = =487 235


ct







1 1

500144996 10 6304 MN

115sk

s ss




2 2

50092797 10 4034 MN

115sk

s ss



γ= = times times =

0

295(12 012) 354 MN

10y uf

s uf s ufM

fF A


143


γ= = times times =

0

345(262 0026) 2350 MN

10y w

s w s wM

fF A


γ= = times times =

0

335(100 006) 201 MN

10y lf

s lf s lfM

fF A


γtimes


085 085 3535 05 347 MN

150ck

c cc

fF A


(4573le783) and




(262 )0


x xF F F F F F F F



αminus minus

= = = le262 1815

0307 050262

w

w

h xh



εα

times= = lt = =

235415

262 415 34510076 111560026 0307

ct




= = = le

212 18150144 050

212w

w

h xh




144

εα

times= = lt = =

23536

212 36 3458154 206330026 0144

ct
















145

















146






147








σγ

le

yEd ser

M ser

f

τγ

lesdot

3y

Ed ser

M ser

f

σ τγ

+ sdot le2 2

3 yEd ser Ed ser

M ser

f






σγ

le

yEd ser

M ser

f


148





149


τγ

le = =times

35520496

3 3 10y

Ed ser

M ser

fMPa




σ τγ

+ le2 2

3 yEd ser Ed ser

M ser

f


150






151

σγ

∆ le

15 yfre

M ser

f





le + le30 40 300w

w

hL

t









σ τ

σ τ+ le

2 2


cr cr






152






Where





( )= + le

+ 0

103 10

1 2cc

kh z





Then

( )= + = le

+ times

103 113 10


( )= + = le

+ times

103 102 10




153







160 200 240 280 320 360 400 450

40 32 20 16 12 10 8 6

32 25 16 12 10 8 6 5

25 16 12 8 6 5 4 -


φ φ=

0

ct eff

ct

ff





160 200 240 280 320 360

300 300 250 200 150 100

300 250 200 150 100 50

200 150 100 50 - -



154



σ σ σ= + ∆0s s s

With σα ρ

∆ =04 ctm

sst s

f and α =st

a a

AIA I

Where




ct

AA







ρminustimes

= =423779 10



= =418559 10

000952195s


= =times

03543 058321232



= =times

01555 024561416

01369 01969st


σtimes

∆ = =times

04 328523

1232 001219s MPa


155


∆ = =times

04 329495

1416 00s MPa









φ = =32

32 353129

mm





we can get




This gives






156











π

γ=

2

(1)08

4u

Rdv

df

P


stud

α

γ=

2(2) 029 ck cm

Rdv

d f EP

With

α = +

02 1schd

for 3le schd

le4

α = 10 for schd

gt4

Where








157


π timestimes times

= = times

2

(1) 6

2208 450

4 01095 10 N=01095 MN125RdP

= = gtgt200

909 422

schd


= =times2

(2) 029 1 22 35 340771401226 MN

125RdP












158









40 55 80

120

345 335 325 295

726 800 800 800

297 414




Fig 622 Detailing



159


= minus = minus = gt0 1000 750 22114 25

2 2 2 2f

D

b b de





le sdot15 fd t










160







ν =c k

L k

S VI


161

Where













i

Nx kL

with


Where






00 60 125 250 350 420 500 625

800 875 1000 1080 1125 1200 1320 1400

1500 1625 1700 1760 1875 1940 2000


162



x (m) 50+ 54- 54+ 60- 60+ 625-

νLk (MNm) 0842 0900 0900 0989 0943 0906


( )ν

sdot= =

(4middot P ) 03064 MN031 m


L k

k






163


6741 Elastic design




With

ν =c Ed

L Ed

S VI

Where










i

Nx PL

with


Where






164

ν leinti+1

i

x

x







x (m) 50+ 54- 54+ 60- 60+ 625-

νLEd (MNm) 1124 1203 1203 1323 1264 1213


( )ν


110 (4 P ) 11 0438 MN0365 m


L kEd x


νsdot

= leinti+1

i

x 1

x

(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud

L Ed x dx MNs




165









166











167


ντ

π∆

∆ =

32

4

L FLM

i

i

NdL

Where









Where







λ

=

18

12

0 0

obsmv

NQQ N

Where

=

sumsum

188

1i i

mi

n QQ



Q0=480KN


168

N0=05x106






1 2 3 4 5

200 310 490 390 450

20 5

50 15 10


Qm1=45737 kN

λ = =245737 0952

480v




ηλ

η

= +

188

2 2 24

1 1 1

1 mv

m

N QN Q

η = minus12

eb

With



η = + =11 175 0752 70

and η = minus =21 175 0252 70


169






Where


ψ ψge gt

+ + + +

sum sum 11 1 2

1 1 k j k i k i fat

j iG P Q Q Q







Where








170

γ σσ γ

∆le

∆E2

c

10

Ff

Mf

γ ττ γ

∆le

∆E2

c

10

Ff

Mf s and


∆ ∆+ le

∆ ∆E2 E2

c c

13

Ff Ff

Mf Mf s

Where








171










172



ν = = 0643 MNmL Ed

L Edeff

V


ν= = = 1

max

4 04380681 m

0643Rd stud

L Ed

Ps


Notes





173

References









174

Acknowledgements

Table of Contents


Foreword

13Introduction

Introduction


The Eurocodes


THE DESIGN EXAMPLE








































6741 Elastic design







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Quality 3013 gtgt13 AntiAliasGrayImages false13 CropGrayImages true13 GrayImageMinResolution 30013 GrayImageMinResolutionPolicy OK13 DownsampleGrayImages true13 GrayImageDownsampleType Bicubic13 GrayImageResolution 30013 GrayImageDepth -113 GrayImageMinDownsampleDepth 213 GrayImageDownsampleThreshold 15000013 EncodeGrayImages true13 GrayImageFilter DCTEncode13 AutoFilterGrayImages true13 GrayImageAutoFilterStrategy JPEG13 GrayACSImageDict ltlt13 QFactor 01513 HSamples [1 1 1 1] VSamples [1 1 1 1]13 gtgt13 GrayImageDict ltlt13 QFactor 01513 HSamples [1 1 1 1] VSamples [1 1 1 1]13 gtgt13 JPEG2000GrayACSImageDict ltlt13 TileWidth 25613 TileHeight 25613 Quality 3013 gtgt13 JPEG2000GrayImageDict ltlt13 TileWidth 25613 TileHeight 25613 Quality 3013 gtgt13 AntiAliasMonoImages false13 CropMonoImages true13 MonoImageMinResolution 120013 MonoImageMinResolutionPolicy OK13 DownsampleMonoImages true13 MonoImageDownsampleType Bicubic13 MonoImageResolution 120013 MonoImageDepth -113 MonoImageDownsampleThreshold 15000013 EncodeMonoImages true13 MonoImageFilter CCITTFaxEncode13 MonoImageDict ltlt13 K -113 gtgt13 AllowPSXObjects false13 CheckCompliance [13 None13 ]13 PDFX1aCheck false13 PDFX3Check false13 PDFXCompliantPDFOnly false13 PDFXNoTrimBoxError true13 PDFXTrimBoxToMediaBoxOffset [13 00000013 00000013 00000013 00000013 ]13 PDFXSetBleedBoxToMediaBox true13 PDFXBleedBoxToTrimBoxOffset [13 00000013 00000013 00000013 00000013 ]13 PDFXOutputIntentProfile ()13 PDFXOutputConditionIdentifier ()13 PDFXOutputCondition ()13 PDFXRegistryName ()13 PDFXTrapped False1313 CreateJDFFile false13 Description ltlt13 ARA 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 ESP 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HEB 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HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke Stvoreni PDF dokumenti mogu se otvoriti Acrobat i Adobe Reader 50 i kasnijim verzijama)13 HUN 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 NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 50 en hoger)13 NOR 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 POL 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 PTB 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 RUM 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 SKY 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 SUO 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 SVE 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 TUR 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 UKR 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 ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing Created PDF documents can be opened with Acrobat and Adobe Reader 50 and later)13 gtgt13 Namespace [13 (Adobe)13 (Common)13 (10)13 ]13 OtherNamespaces [13 ltlt13 AsReaderSpreads false13 CropImagesToFrames true13 ErrorControl WarnAndContinue13 FlattenerIgnoreSpreadOverrides false13 IncludeGuidesGrids false13 IncludeNonPrinting false13 IncludeSlug false13 Namespace [13 (Adobe)13 (InDesign)13 (40)13 ]13 OmitPlacedBitmaps false13 OmitPlacedEPS false13 OmitPlacedPDF false13 SimulateOverprint Legacy13 gtgt13 ltlt13 AddBleedMarks false13 AddColorBars false13 AddCropMarks false13 AddPageInfo false13 AddRegMarks false13 ConvertColors ConvertToCMYK13 DestinationProfileName ()13 DestinationProfileSelector DocumentCMYK13 Downsample16BitImages true13 FlattenerPreset ltlt13 PresetSelector MediumResolution13 gtgt13 FormElements false13 GenerateStructure false13 IncludeBookmarks false13 IncludeHyperlinks false13 IncludeInteractive false13 IncludeLayers false13 IncludeProfiles false13 MultimediaHandling UseObjectSettings13 Namespace [13 (Adobe)13 (CreativeSuite)13 (20)13 ]13 PDFXOutputIntentProfileSelector DocumentCMYK13 PreserveEditing true13 UntaggedCMYKHandling LeaveUntagged13 UntaggedRGBHandling UseDocumentProfile13 UseDocumentBleed false13 gtgt13 ]13gtgt setdistillerparams13ltlt13 HWResolution [2400 2400]13 PageSize [612000 792000]13gtgt setpagedevice13

x

xi


Authors

Introduction



























xii



Editors







xiii

Foreword












xiv







Ispra November 2011





xv

Introduction














The Eurocodes















of firerdquo


xvi


and ETAs)



















Eurocode 8










bridge

xvii




xviii

THE DESIGN EXAMPLE

































xix









CHAPTER 6





Joeumll RAOUL



Convenor EN-1994-2


126


127











γ= = times =ck

c cc

fF A MN

085 085middot3519484 38643



= ckcd

c

ff (EN-1994-2 2412)



128

applied α

γ= cc ck

cdc

ff














129


s uf s ufM

fF A MN

0

345(10 004) 1380

10



s w s wM

fF A MN

0

345(272 0018) 16891

10



s lf s lfM

fF A MN

0

345(120 004) 1656

10






xF F x F F F


004





130





MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)





As τ

εη

= = ge =w

w

hk

t272 31

15111 51360018




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2720middot1810 1063

3middot 3 110 (EN 1993-1-5 52)



τ = + = + times =

whk

a

2 2272534 4 534 4 5802


1993-1-5 Annex A3

( ) ( )π π

σν

times= = =

times


wE

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 188312

12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)


(EN-1993-1-5 53)


131

λττ

= = = =y w y ww

crcr

f f 345

076 076 20324822middot 3




( ) ( )χ

λ= = =

++w

w

137 1370501

07 203207(Table 51 of EN-1993-1-5 53)


χ

γ


timestimesw y w w

bw Rd

M

f h tV MN -6

1

0501 345 2720 184441

3 3middot1 1010



V V V MN V MN

444 0 1063 444

And η

γ


timesy w w

pl a Rd

M

f h tV E MN -6

0

12 345 2720 181170

3 3 10 (EN 1993-1-1 626)








132








VEd = 812 MN





c mm1200 26

587 2 2


ct

587 2354891 9 9 8033

120 295



133






s ss

fF A m MN-4 2

1 1

500144996 10 6304




s ss

fF A m MN-4 2

2 2

50092797 10 4034




s uf s ufM

fF A MN

0

295(12 012) 354

10



s w s wM

fF A MN

0

345(256 0026) 22963

10



s lf s lfM

fF A MN

0

295(120 012) 4248

10





x xF F F F F F F1 2 (256 ) 0

256 256



α = = = gtw

w

h xh

- 256 - 10980571 050

256




134

εα


ct

235456middot

256 456 3459846 58590026 13 1 13middot0571 1



256 2359846 62 1- (- ) 62 1 1059 1059 10849

0026 345






yield strength σγ

le0

ys

M

f






135



εγ γ



M M

f fF F F X t t F

1 2 0 0

2 20 0






As τ

εη

= = ge =w

w

hk

t256 31

9846 51360026




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2560 2610 1446

3 3middot1 10 (EN 1993-1-5 52)




136

τ = + = + =

whk

a

2 2256534 4 534 4 575


1-5 Annex A3

( ) ( )π π

σν



E

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 261958

12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)


λττ

= = = =y w y ww

crcr

f f 345076 076 133


1993-1-5 53 As λw is ge108 then


( ) ( )χ

λ= = =

++w

w

137 1370675

07 13307(Table 51 of EN-1993-1-5 53)


χ


= = times =times

w y w wbw Rd

M

f h tV MN 6

1

0675 345 2560 2610 814

3 3 110



And η


= = times =times

y w wpl a Rd

M

f h tV MN 6

0

12 345 2560 2610 1591

3 3 10 (EN 1993-1-1 626)




γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1





137




xxF F F F F1 2

0120

012 012


xx 0126304 4034 354 354 4248 0

012 012

Then x =01145 m






γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1middot




times times

f f yf

w yw

b t fc a m

th f

2 2

2 2

16 16 1200 120 295025 8 025 3110

26 256 345


138


timesbf RdV

226

1200 120 295 10935middot 1 0197 MN

3110 11 1174010






η = le3

10Ed

b Rd

VV


81209975





η η

+ minus minus le

f Rd

pl Rd

MM

21 3

1 2 1 10

Where

η = Ed

pl Rd

MM1

and η = Ed

bw Rd

VV3



139




VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN


1006050818

12297 η = =3

788509686

814 and


f Rd

pl Rd

M

M

2 21 3

117401 2 1 0818 1 2 09686 1 0858 1

12297











140


areas






141


resistance






142








minus minus= = =

1000 26487 mm

2 2lf wb t

c

ε= = le = =487 235


ct







1 1

500144996 10 6304 MN

115sk

s ss




2 2

50092797 10 4034 MN

115sk

s ss



γ= = times times =

0

295(12 012) 354 MN

10y uf

s uf s ufM

fF A


143


γ= = times times =

0

345(262 0026) 2350 MN

10y w

s w s wM

fF A


γ= = times times =

0

335(100 006) 201 MN

10y lf

s lf s lfM

fF A


γtimes


085 085 3535 05 347 MN

150ck

c cc

fF A


(4573le783) and




(262 )0


x xF F F F F F F F



αminus minus

= = = le262 1815

0307 050262

w

w

h xh



εα

times= = lt = =

235415

262 415 34510076 111560026 0307

ct




= = = le

212 18150144 050

212w

w

h xh




144

εα

times= = lt = =

23536

212 36 3458154 206330026 0144

ct
















145

















146






147








σγ

le

yEd ser

M ser

f

τγ

lesdot

3y

Ed ser

M ser

f

σ τγ

+ sdot le2 2

3 yEd ser Ed ser

M ser

f






σγ

le

yEd ser

M ser

f


148





149


τγ

le = =times

35520496

3 3 10y

Ed ser

M ser

fMPa




σ τγ

+ le2 2

3 yEd ser Ed ser

M ser

f


150






151

σγ

∆ le

15 yfre

M ser

f





le + le30 40 300w

w

hL

t









σ τ

σ τ+ le

2 2


cr cr






152






Where





( )= + le

+ 0

103 10

1 2cc

kh z





Then

( )= + = le

+ times

103 113 10


( )= + = le

+ times

103 102 10




153







160 200 240 280 320 360 400 450

40 32 20 16 12 10 8 6

32 25 16 12 10 8 6 5

25 16 12 8 6 5 4 -


φ φ=

0

ct eff

ct

ff





160 200 240 280 320 360

300 300 250 200 150 100

300 250 200 150 100 50

200 150 100 50 - -



154



σ σ σ= + ∆0s s s

With σα ρ

∆ =04 ctm

sst s

f and α =st

a a

AIA I

Where




ct

AA







ρminustimes

= =423779 10



= =418559 10

000952195s


= =times

03543 058321232



= =times

01555 024561416

01369 01969st


σtimes

∆ = =times

04 328523

1232 001219s MPa


155


∆ = =times

04 329495

1416 00s MPa









φ = =32

32 353129

mm





we can get




This gives






156











π

γ=

2

(1)08

4u

Rdv

df

P


stud

α

γ=

2(2) 029 ck cm

Rdv

d f EP

With

α = +

02 1schd

for 3le schd

le4

α = 10 for schd

gt4

Where








157


π timestimes times

= = times

2

(1) 6

2208 450

4 01095 10 N=01095 MN125RdP

= = gtgt200

909 422

schd


= =times2

(2) 029 1 22 35 340771401226 MN

125RdP












158









40 55 80

120

345 335 325 295

726 800 800 800

297 414




Fig 622 Detailing



159


= minus = minus = gt0 1000 750 22114 25

2 2 2 2f

D

b b de





le sdot15 fd t










160







ν =c k

L k

S VI


161

Where













i

Nx kL

with


Where






00 60 125 250 350 420 500 625

800 875 1000 1080 1125 1200 1320 1400

1500 1625 1700 1760 1875 1940 2000


162



x (m) 50+ 54- 54+ 60- 60+ 625-

νLk (MNm) 0842 0900 0900 0989 0943 0906


( )ν

sdot= =

(4middot P ) 03064 MN031 m


L k

k






163


6741 Elastic design




With

ν =c Ed

L Ed

S VI

Where










i

Nx PL

with


Where






164

ν leinti+1

i

x

x







x (m) 50+ 54- 54+ 60- 60+ 625-

νLEd (MNm) 1124 1203 1203 1323 1264 1213


( )ν


110 (4 P ) 11 0438 MN0365 m


L kEd x


νsdot

= leinti+1

i

x 1

x

(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud

L Ed x dx MNs




165









166











167


ντ

π∆

∆ =

32

4

L FLM

i

i

NdL

Where









Where







λ

=

18

12

0 0

obsmv

NQQ N

Where

=

sumsum

188

1i i

mi

n QQ



Q0=480KN


168

N0=05x106






1 2 3 4 5

200 310 490 390 450

20 5

50 15 10


Qm1=45737 kN

λ = =245737 0952

480v




ηλ

η

= +

188

2 2 24

1 1 1

1 mv

m

N QN Q

η = minus12

eb

With



η = + =11 175 0752 70

and η = minus =21 175 0252 70


169






Where


ψ ψge gt

+ + + +

sum sum 11 1 2

1 1 k j k i k i fat

j iG P Q Q Q







Where








170

γ σσ γ

∆le

∆E2

c

10

Ff

Mf

γ ττ γ

∆le

∆E2

c

10

Ff

Mf s and


∆ ∆+ le

∆ ∆E2 E2

c c

13

Ff Ff

Mf Mf s

Where








171










172



ν = = 0643 MNmL Ed

L Edeff

V


ν= = = 1

max

4 04380681 m

0643Rd stud

L Ed

Ps


Notes





173

References









174

Acknowledgements

Table of Contents


Foreword

13Introduction

Introduction


The Eurocodes


THE DESIGN EXAMPLE








































6741 Elastic design








xi


Authors

Introduction



























xii



Editors







xiii

Foreword












xiv







Ispra November 2011





xv

Introduction














The Eurocodes















of firerdquo


xvi


and ETAs)



















Eurocode 8










bridge

xvii




xviii

THE DESIGN EXAMPLE

































xix









CHAPTER 6





Joeumll RAOUL



Convenor EN-1994-2


126


127











γ= = times =ck

c cc

fF A MN

085 085middot3519484 38643



= ckcd

c

ff (EN-1994-2 2412)



128

applied α

γ= cc ck

cdc

ff














129


s uf s ufM

fF A MN

0

345(10 004) 1380

10



s w s wM

fF A MN

0

345(272 0018) 16891

10



s lf s lfM

fF A MN

0

345(120 004) 1656

10






xF F x F F F


004





130





MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)





As τ

εη

= = ge =w

w

hk

t272 31

15111 51360018




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2720middot1810 1063

3middot 3 110 (EN 1993-1-5 52)



τ = + = + times =

whk

a

2 2272534 4 534 4 5802


1993-1-5 Annex A3

( ) ( )π π

σν

times= = =

times


wE

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 188312

12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)


(EN-1993-1-5 53)


131

λττ

= = = =y w y ww

crcr

f f 345

076 076 20324822middot 3




( ) ( )χ

λ= = =

++w

w

137 1370501

07 203207(Table 51 of EN-1993-1-5 53)


χ

γ


timestimesw y w w

bw Rd

M

f h tV MN -6

1

0501 345 2720 184441

3 3middot1 1010



V V V MN V MN

444 0 1063 444

And η

γ


timesy w w

pl a Rd

M

f h tV E MN -6

0

12 345 2720 181170

3 3 10 (EN 1993-1-1 626)








132








VEd = 812 MN





c mm1200 26

587 2 2


ct

587 2354891 9 9 8033

120 295



133






s ss

fF A m MN-4 2

1 1

500144996 10 6304




s ss

fF A m MN-4 2

2 2

50092797 10 4034




s uf s ufM

fF A MN

0

295(12 012) 354

10



s w s wM

fF A MN

0

345(256 0026) 22963

10



s lf s lfM

fF A MN

0

295(120 012) 4248

10





x xF F F F F F F1 2 (256 ) 0

256 256



α = = = gtw

w

h xh

- 256 - 10980571 050

256




134

εα


ct

235456middot

256 456 3459846 58590026 13 1 13middot0571 1



256 2359846 62 1- (- ) 62 1 1059 1059 10849

0026 345






yield strength σγ

le0

ys

M

f






135



εγ γ



M M

f fF F F X t t F

1 2 0 0

2 20 0






As τ

εη

= = ge =w

w

hk

t256 31

9846 51360026




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2560 2610 1446

3 3middot1 10 (EN 1993-1-5 52)




136

τ = + = + =

whk

a

2 2256534 4 534 4 575


1-5 Annex A3

( ) ( )π π

σν



E

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 261958

12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)


λττ

= = = =y w y ww

crcr

f f 345076 076 133


1993-1-5 53 As λw is ge108 then


( ) ( )χ

λ= = =

++w

w

137 1370675

07 13307(Table 51 of EN-1993-1-5 53)


χ


= = times =times

w y w wbw Rd

M

f h tV MN 6

1

0675 345 2560 2610 814

3 3 110



And η


= = times =times

y w wpl a Rd

M

f h tV MN 6

0

12 345 2560 2610 1591

3 3 10 (EN 1993-1-1 626)




γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1





137




xxF F F F F1 2

0120

012 012


xx 0126304 4034 354 354 4248 0

012 012

Then x =01145 m






γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1middot




times times

f f yf

w yw

b t fc a m

th f

2 2

2 2

16 16 1200 120 295025 8 025 3110

26 256 345


138


timesbf RdV

226

1200 120 295 10935middot 1 0197 MN

3110 11 1174010






η = le3

10Ed

b Rd

VV


81209975





η η

+ minus minus le

f Rd

pl Rd

MM

21 3

1 2 1 10

Where

η = Ed

pl Rd

MM1

and η = Ed

bw Rd

VV3



139




VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN


1006050818

12297 η = =3

788509686

814 and


f Rd

pl Rd

M

M

2 21 3

117401 2 1 0818 1 2 09686 1 0858 1

12297











140


areas






141


resistance






142








minus minus= = =

1000 26487 mm

2 2lf wb t

c

ε= = le = =487 235


ct







1 1

500144996 10 6304 MN

115sk

s ss




2 2

50092797 10 4034 MN

115sk

s ss



γ= = times times =

0

295(12 012) 354 MN

10y uf

s uf s ufM

fF A


143


γ= = times times =

0

345(262 0026) 2350 MN

10y w

s w s wM

fF A


γ= = times times =

0

335(100 006) 201 MN

10y lf

s lf s lfM

fF A


γtimes


085 085 3535 05 347 MN

150ck

c cc

fF A


(4573le783) and




(262 )0


x xF F F F F F F F



αminus minus

= = = le262 1815

0307 050262

w

w

h xh



εα

times= = lt = =

235415

262 415 34510076 111560026 0307

ct




= = = le

212 18150144 050

212w

w

h xh




144

εα

times= = lt = =

23536

212 36 3458154 206330026 0144

ct
















145

















146






147








σγ

le

yEd ser

M ser

f

τγ

lesdot

3y

Ed ser

M ser

f

σ τγ

+ sdot le2 2

3 yEd ser Ed ser

M ser

f






σγ

le

yEd ser

M ser

f


148





149


τγ

le = =times

35520496

3 3 10y

Ed ser

M ser

fMPa




σ τγ

+ le2 2

3 yEd ser Ed ser

M ser

f


150






151

σγ

∆ le

15 yfre

M ser

f





le + le30 40 300w

w

hL

t









σ τ

σ τ+ le

2 2


cr cr






152






Where





( )= + le

+ 0

103 10

1 2cc

kh z





Then

( )= + = le

+ times

103 113 10


( )= + = le

+ times

103 102 10




153







160 200 240 280 320 360 400 450

40 32 20 16 12 10 8 6

32 25 16 12 10 8 6 5

25 16 12 8 6 5 4 -


φ φ=

0

ct eff

ct

ff





160 200 240 280 320 360

300 300 250 200 150 100

300 250 200 150 100 50

200 150 100 50 - -



154



σ σ σ= + ∆0s s s

With σα ρ

∆ =04 ctm

sst s

f and α =st

a a

AIA I

Where




ct

AA







ρminustimes

= =423779 10



= =418559 10

000952195s


= =times

03543 058321232



= =times

01555 024561416

01369 01969st


σtimes

∆ = =times

04 328523

1232 001219s MPa


155


∆ = =times

04 329495

1416 00s MPa









φ = =32

32 353129

mm





we can get




This gives






156











π

γ=

2

(1)08

4u

Rdv

df

P


stud

α

γ=

2(2) 029 ck cm

Rdv

d f EP

With

α = +

02 1schd

for 3le schd

le4

α = 10 for schd

gt4

Where








157


π timestimes times

= = times

2

(1) 6

2208 450

4 01095 10 N=01095 MN125RdP

= = gtgt200

909 422

schd


= =times2

(2) 029 1 22 35 340771401226 MN

125RdP












158









40 55 80

120

345 335 325 295

726 800 800 800

297 414




Fig 622 Detailing



159


= minus = minus = gt0 1000 750 22114 25

2 2 2 2f

D

b b de





le sdot15 fd t










160







ν =c k

L k

S VI


161

Where













i

Nx kL

with


Where






00 60 125 250 350 420 500 625

800 875 1000 1080 1125 1200 1320 1400

1500 1625 1700 1760 1875 1940 2000


162



x (m) 50+ 54- 54+ 60- 60+ 625-

νLk (MNm) 0842 0900 0900 0989 0943 0906


( )ν

sdot= =

(4middot P ) 03064 MN031 m


L k

k






163


6741 Elastic design




With

ν =c Ed

L Ed

S VI

Where










i

Nx PL

with


Where






164

ν leinti+1

i

x

x







x (m) 50+ 54- 54+ 60- 60+ 625-

νLEd (MNm) 1124 1203 1203 1323 1264 1213


( )ν


110 (4 P ) 11 0438 MN0365 m


L kEd x


νsdot

= leinti+1

i

x 1

x

(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud

L Ed x dx MNs




165









166











167


ντ

π∆

∆ =

32

4

L FLM

i

i

NdL

Where









Where







λ

=

18

12

0 0

obsmv

NQQ N

Where

=

sumsum

188

1i i

mi

n QQ



Q0=480KN


168

N0=05x106






1 2 3 4 5

200 310 490 390 450

20 5

50 15 10


Qm1=45737 kN

λ = =245737 0952

480v




ηλ

η

= +

188

2 2 24

1 1 1

1 mv

m

N QN Q

η = minus12

eb

With



η = + =11 175 0752 70

and η = minus =21 175 0252 70


169






Where


ψ ψge gt

+ + + +

sum sum 11 1 2

1 1 k j k i k i fat

j iG P Q Q Q







Where








170

γ σσ γ

∆le

∆E2

c

10

Ff

Mf

γ ττ γ

∆le

∆E2

c

10

Ff

Mf s and


∆ ∆+ le

∆ ∆E2 E2

c c

13

Ff Ff

Mf Mf s

Where








171










172



ν = = 0643 MNmL Ed

L Edeff

V


ν= = = 1

max

4 04380681 m

0643Rd stud

L Ed

Ps


Notes





173

References









174

Acknowledgements

Table of Contents


Foreword

13Introduction

Introduction


The Eurocodes


THE DESIGN EXAMPLE








































6741 Elastic design








xii



Editors







xiii

Foreword












xiv







Ispra November 2011





xv

Introduction














The Eurocodes















of firerdquo


xvi


and ETAs)



















Eurocode 8










bridge

xvii




xviii

THE DESIGN EXAMPLE

































xix









CHAPTER 6





Joeumll RAOUL



Convenor EN-1994-2


126


127











γ= = times =ck

c cc

fF A MN

085 085middot3519484 38643



= ckcd

c

ff (EN-1994-2 2412)



128

applied α

γ= cc ck

cdc

ff














129


s uf s ufM

fF A MN

0

345(10 004) 1380

10



s w s wM

fF A MN

0

345(272 0018) 16891

10



s lf s lfM

fF A MN

0

345(120 004) 1656

10






xF F x F F F


004





130





MplRd = 38643 x (02505 + 00125) + (00125 x 10) x 34510 x (001252)+ (00275 x 10) x (34510) x (002752)+16891 x (00275+2722)+1656 x (00275+272+0042)





As τ

εη

= = ge =w

w

hk

t272 31

15111 51360018




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2720middot1810 1063

3middot 3 110 (EN 1993-1-5 52)



τ = + = + times =

whk

a

2 2272534 4 534 4 5802


1993-1-5 Annex A3

( ) ( )π π

σν

times= = =

times


wE

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 188312

12 1- 12 1- 03 2720 (EN-1993-1-5 Annex A1)


(EN-1993-1-5 53)


131

λττ

= = = =y w y ww

crcr

f f 345

076 076 20324822middot 3




( ) ( )χ

λ= = =

++w

w

137 1370501

07 203207(Table 51 of EN-1993-1-5 53)


χ

γ


timestimesw y w w

bw Rd

M

f h tV MN -6

1

0501 345 2720 184441

3 3middot1 1010



V V V MN V MN

444 0 1063 444

And η

γ


timesy w w

pl a Rd

M

f h tV E MN -6

0

12 345 2720 181170

3 3 10 (EN 1993-1-1 626)








132








VEd = 812 MN





c mm1200 26

587 2 2


ct

587 2354891 9 9 8033

120 295



133






s ss

fF A m MN-4 2

1 1

500144996 10 6304




s ss

fF A m MN-4 2

2 2

50092797 10 4034




s uf s ufM

fF A MN

0

295(12 012) 354

10



s w s wM

fF A MN

0

345(256 0026) 22963

10



s lf s lfM

fF A MN

0

295(120 012) 4248

10





x xF F F F F F F1 2 (256 ) 0

256 256



α = = = gtw

w

h xh

- 256 - 10980571 050

256




134

εα


ct

235456middot

256 456 3459846 58590026 13 1 13middot0571 1



256 2359846 62 1- (- ) 62 1 1059 1059 10849

0026 345






yield strength σγ

le0

ys

M

f






135



εγ γ



M M

f fF F F X t t F

1 2 0 0

2 20 0






As τ

εη

= = ge =w

w

hk

t256 31

9846 51360026




η

γ


timesy w w

b Rd bw Rd bf Rd

M

f h tV V V MN -6

1

12 345 2560 2610 1446

3 3middot1 10 (EN 1993-1-5 52)




136

τ = + = + =

whk

a

2 2256534 4 534 4 575


1-5 Annex A3

( ) ( )π π

σν



E

w

EtMPa

h

2 2 2 5 2

2 2 2 2

21 10 261958

12 1 12 1 03 2560 (EN-1993-1-5 Annex A1)


λττ

= = = =y w y ww

crcr

f f 345076 076 133


1993-1-5 53 As λw is ge108 then


( ) ( )χ

λ= = =

++w

w

137 1370675

07 13307(Table 51 of EN-1993-1-5 53)


χ


= = times =times

w y w wbw Rd

M

f h tV MN 6

1

0675 345 2560 2610 814

3 3 110



And η


= = times =times

y w wpl a Rd

M

f h tV MN 6

0

12 345 2560 2610 1591

3 3 10 (EN 1993-1-1 626)




γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1





137




xxF F F F F1 2

0120

012 012


xx 0126304 4034 354 354 4248 0

012 012

Then x =01145 m






γ

= minus

f f yf Edbf Rd

M f Rd

b t f MV

c M

22

1

1middot




times times

f f yf

w yw

b t fc a m

th f

2 2

2 2

16 16 1200 120 295025 8 025 3110

26 256 345


138


timesbf RdV

226

1200 120 295 10935middot 1 0197 MN

3110 11 1174010






η = le3

10Ed

b Rd

VV


81209975





η η

+ minus minus le

f Rd

pl Rd

MM

21 3

1 2 1 10

Where

η = Ed

pl Rd

MM1

and η = Ed

bw Rd

VV3



139




VEd=(8124+7646)2=7885 MN and MEd=(-10935-9186)2=-100605 mMN


1006050818

12297 η = =3

788509686

814 and


f Rd

pl Rd

M

M

2 21 3

117401 2 1 0818 1 2 09686 1 0858 1

12297











140


areas






141


resistance






142








minus minus= = =

1000 26487 mm

2 2lf wb t

c

ε= = le = =487 235


ct







1 1

500144996 10 6304 MN

115sk

s ss




2 2

50092797 10 4034 MN

115sk

s ss



γ= = times times =

0

295(12 012) 354 MN

10y uf

s uf s ufM

fF A


143


γ= = times times =

0

345(262 0026) 2350 MN

10y w

s w s wM

fF A


γ= = times times =

0

335(100 006) 201 MN

10y lf

s lf s lfM

fF A


γtimes


085 085 3535 05 347 MN

150ck

c cc

fF A


(4573le783) and




(262 )0


x xF F F F F F F F



αminus minus

= = = le262 1815

0307 050262

w

w

h xh



εα

times= = lt = =

235415

262 415 34510076 111560026 0307

ct




= = = le

212 18150144 050

212w

w

h xh




144

εα

times= = lt = =

23536

212 36 3458154 206330026 0144

ct
















145

















146






147








σγ

le

yEd ser

M ser

f

τγ

lesdot

3y

Ed ser

M ser

f

σ τγ

+ sdot le2 2

3 yEd ser Ed ser

M ser

f






σγ

le

yEd ser

M ser

f


148





149


τγ

le = =times

35520496

3 3 10y

Ed ser

M ser

fMPa




σ τγ

+ le2 2

3 yEd ser Ed ser

M ser

f


150






151

σγ

∆ le

15 yfre

M ser

f





le + le30 40 300w

w

hL

t









σ τ

σ τ+ le

2 2


cr cr






152






Where





( )= + le

+ 0

103 10

1 2cc

kh z





Then

( )= + = le

+ times

103 113 10


( )= + = le

+ times

103 102 10




153







160 200 240 280 320 360 400 450

40 32 20 16 12 10 8 6

32 25 16 12 10 8 6 5

25 16 12 8 6 5 4 -


φ φ=

0

ct eff

ct

ff





160 200 240 280 320 360

300 300 250 200 150 100

300 250 200 150 100 50

200 150 100 50 - -



154



σ σ σ= + ∆0s s s

With σα ρ

∆ =04 ctm

sst s

f and α =st

a a

AIA I

Where




ct

AA







ρminustimes

= =423779 10



= =418559 10

000952195s


= =times

03543 058321232



= =times

01555 024561416

01369 01969st


σtimes

∆ = =times

04 328523

1232 001219s MPa


155


∆ = =times

04 329495

1416 00s MPa









φ = =32

32 353129

mm





we can get




This gives






156











π

γ=

2

(1)08

4u

Rdv

df

P


stud

α

γ=

2(2) 029 ck cm

Rdv

d f EP

With

α = +

02 1schd

for 3le schd

le4

α = 10 for schd

gt4

Where








157


π timestimes times

= = times

2

(1) 6

2208 450

4 01095 10 N=01095 MN125RdP

= = gtgt200

909 422

schd


= =times2

(2) 029 1 22 35 340771401226 MN

125RdP












158









40 55 80

120

345 335 325 295

726 800 800 800

297 414




Fig 622 Detailing



159


= minus = minus = gt0 1000 750 22114 25

2 2 2 2f

D

b b de





le sdot15 fd t










160







ν =c k

L k

S VI


161

Where













i

Nx kL

with


Where






00 60 125 250 350 420 500 625

800 875 1000 1080 1125 1200 1320 1400

1500 1625 1700 1760 1875 1940 2000


162



x (m) 50+ 54- 54+ 60- 60+ 625-

νLk (MNm) 0842 0900 0900 0989 0943 0906


( )ν

sdot= =

(4middot P ) 03064 MN031 m


L k

k






163


6741 Elastic design




With

ν =c Ed

L Ed

S VI

Where










i

Nx PL

with


Where






164

ν leinti+1

i

x

x







x (m) 50+ 54- 54+ 60- 60+ 625-

νLEd (MNm) 1124 1203 1203 1323 1264 1213


( )ν


110 (4 P ) 11 0438 MN0365 m


L kEd x


νsdot

= leinti+1

i

x 1

x

(4 P )( ) 15407 (in 125 m)=1232 MNm Rd stud

L Ed x dx MNs




165









166











167


ντ

π∆

∆ =

32

4

L FLM

i

i

NdL

Where









Where







λ

=

18

12

0 0

obsmv

NQQ N

Where

=

sumsum

188

1i i

mi

n QQ



Q0=480KN


168

N0=05x106






1 2 3 4 5

200 310 490 390 450

20 5

50 15 10


Qm1=45737 kN

λ = =245737 0952

480v




ηλ

η

= +

188

2 2 24

1 1 1

1 mv

m

N QN Q

η = minus12

eb

With



η = + =11 175 0752 70

and η = minus =21 175 0252 70


169






Where


ψ ψge gt

+ + + +

sum sum 11 1 2

1 1 k j k i k i fat

j iG P Q Q Q







Where








170

γ σσ γ

∆le

∆E2

c

10

Ff

Mf

γ ττ γ

∆le

∆E2

c

10

Ff

Mf s and


∆ ∆+ le

∆ ∆E2 E2

c c

13

Ff Ff

Mf Mf s

Where








171










172



ν = = 0643 MNmL Ed

L Edeff

V


ν= = = 1

max

4 04380681 m

0643Rd stud

L Ed

Ps


Notes





173

References









174

Acknowledgements

Table of Contents


Foreword

13Introduction

Introduction


The Eurocodes


THE DESIGN EXAMPLE








































6741 Elastic design








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