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The Behaviour and Design ofSteel Structures to EC3

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The Behaviour and Designof Steel Structures to EC3

Fourth edition

N.S. Trahair, M.A. Bradford,D.A. Nethercot, and L. Gardner

First edition published 1977Second edition 1988, revised second edition published 1988Third edition Australian (AS4100) published 1998Third edition British (BS5950) published 2001

Fourth edition published 2008byTaylor & Francis2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN

Simultaneously published in the USA and CanadabyTaylor & Francis270 Madison Ave, NewYork, NY 10016

Taylor & Francis is an imprint of theTaylor & Francis Group,an informa business

1977, 1988, 2001, 2008 N.S. Trahair, M.A. Bradford,D.A. Nethercot, and L. Gardner

All rights reserved. No part of this book may be reprinted orreproduced or utilised in any form or by any electronic,mechanical, or other means, now known or hereafterinvented, including photocopying and recording, or in anyinformation storage or retrieval system, without permission inwriting from the publishers.

The publisher makes no representation, express or implied,with regard to the accuracy of the information contained in this book andcannot accept any legal responsibility or liability for any efforts oromissions that may be made.

British Library Cataloguing in Publication DataA catalogue record for this book is available from the British Library

Library of Congress Cataloging in Publication DataThe behaviour and design of steel structures to EC3 / N.S. Trahair

. . . [et al.]. 4th ed.p. cm.

Includes bibliographical references and index.1. Building, Iron and steel. I. Trahair, N.S.

TA684.T7 2008624.1821dc22 2007016421

ISBN10: 0415418658 (hbk)ISBN10: 0415418666 (pbk)ISBN10: 0203935934 (ebk)

ISBN13: 9780415418652 (hbk)ISBN13: 9780415418669 (pbk)ISBN13: 9780203935934 (ebk)

This edition published in the Taylor & Francis e-Library, 2007.

To purchase your own copy of this or any of Taylor & Francis or Routledgescollection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.

ISBN 0-203-93593-4 Master e-book ISBN

Contents

Preface ixUnits and conversion factors xGlossary of terms xiNotations xv

1 Introduction 1

1.1 Steel structures 11.2 Design 31.3 Material behaviour 81.4 Member and structure behaviour 141.5 Loads 171.6 Analysis of steel structures 211.7 Design of steel structures 24

References 30

2 Tension members 33

2.1 Introduction 332.2 Concentrically loaded tension members 332.3 Eccentrically and locally connected tension members 372.4 Bending of tension members 392.5 Stress concentrations 402.6 Design of tension members 422.7 Worked examples 452.8 Unworked examples 48

References 49

3 Compression members 50

3.1 Introduction 503.2 Elastic compression members 51

vi Contents

3.3 Inelastic compression members 553.4 Real compression members 613.5 Design of compression members 623.6 Restrained compression members 653.7 Other compression members 743.8 Appendix elastic compression members 783.9 Appendix inelastic compression members 813.10 Appendix effective lengths of compression members 833.11 Appendix torsional buckling 883.12 Worked examples 893.13 Unworked examples 96

References 98

4 Local buckling of thin-plate elements 100

4.1 Introduction 1004.2 Plate elements in compression 1024.3 Plate elements in shear 1134.4 Plate elements in bending 1184.5 Plate elements in bending and shear 1214.6 Plate elements in bearing 1244.7 Design against local buckling 1264.8 Appendix elastic buckling of plate elements

in compression 1394.9 Worked examples 1414.10 Unworked examples 151

References 152

5 In-plane bending of beams 154

5.1 Introduction 1545.2 Elastic analysis of beams 1565.3 Bending stresses in elastic beams 1575.4 Shear stresses in elastic beams 1635.5 Plastic analysis of beams 1755.6 Strength design of beams 1835.7 Serviceability design of beams 1895.8 Appendix bending stresses in elastic beams 1905.9 Appendix thin-walled section properties 1915.10 Appendix shear stresses in elastic beams 1955.11 Appendix plastic analysis of beams 197

Contents vii

5.12 Worked examples 2055.13 Unworked examples 224

References 225

6 Lateral buckling of beams 227

6.1 Introduction 2276.2 Elastic beams 2286.3 Inelastic beams 2376.4 Real beams 2396.5 Design against lateral buckling 2406.6 Restrained beams 2456.7 Cantilevers and overhanging beams 2536.8 Braced and continuous beams 2566.9 Rigid frames 2616.10 Monosymmetric beams 2636.11 Non-uniform beams 2666.12 Appendix elastic beams 2686.13 Appendix effective lengths of beams 2736.14 Appendix monosymmetric beams 2746.15 Worked examples 2756.16 Unworked examples 290

References 291

7 Beam-columns 295

7.1 Introduction 2957.2 In-plane behaviour of isolated beam-columns 2967.3 Flexuraltorsional buckling of isolated

beam-columns 3117.4 Biaxial bending of isolated beam-columns 3197.5 Appendix in-plane behaviour of elastic beam-columns 3237.6 Appendix flexuraltorsional buckling of

elastic beam-columns 3267.7 Worked examples 3297.8 Unworked examples 343

References 345

8 Frames 347

8.1 Introduction 3478.2 Triangulated frames 348

viii Contents

8.3 Two-dimensional flexural frames 3508.4 Three-dimensional flexural frames 3728.5 Worked examples 3738.6 Unworked examples 386

References 388

9 Joints 392

9.1 Introduction 3929.2 Joint components 3929.3 Arrangement of joints 3969.4 Behaviour of joints 3989.5 Common joints 4069.6 Design of bolts 4109.7 Design of bolted plates 4149.8 Design of welds 4179.9 Appendix elastic analysis of joints 4209.10 Worked examples 4239.11 Unworked examples 431

References 432

10 Torsion members 433

10.1 Introduction 43310.2 Uniform torsion 43610.3 Non-uniform torsion 44910.4 Torsion design 46110.5 Torsion and bending 46610.6 Distortion 46910.7 Appendix uniform torsion 47110.8 Appendix non-uniform torsion 47310.9 Worked examples 47810.10 Unworked examples 484

References 485

Index 487

Preface

This fourth British edition has been directed specifically to the design of steel structures inaccordance with Eurocode 3 Design of Steel Structures. The principal part of this is Part1-1:General Rules and Rules for Buildings and this is referred to generally in the text asEC3. Also referred to in the text are Part 1-5: Plated Structural Elements, and Part 1-8:Design Of Joints, which are referred to as EC3-1-5 and EC3-1-8. EC3 will be accompaniedby NationalAnnexes which will contain any National Determined Parameters for the UnitedKingdom which differ from the recommendations given in EC3.

Designers who have previously used BS5950 (which is discussed in the third Britishedition of this book) will see a number of significant differences in EC3. One of the moreobvious is the notation. The notation in this book has been changed generally so that it isconsistent with EC3.

Another significant difference is the general absence of tables of values computed fromthe basic design equations which might be used to facilitate manual design. Some design-ers will want to prepare their own tables, but in some cases, the complexities of the basicequations are such that computer programs are required for efficient design. This is espe-cially the case for members under combined compression and bending, which are discussedin Chapter 7. However, the examples in this book are worked in full and do not rely on suchdesign aids.

EC3 does not provide approximations for calculating the lateral buckling resistancesof beams, but instead expects the designer to be able to determine the elastic bucklingmoment to be used in the design equations. Additional information to assist designers inthis determination has been given in Chapter 6 of this book. EC3 also expects the designerto be able to determine the elastic buckling loads of compression members. The additionalinformation given in Chapter 3 has been retained to assist designers in the calculation ofthe elastic buckling loads.

EC3 provides elementary rules for the design of members in torsion. These are gener-alised and extended in Chapter 10, which contains a general treatment of torsion togetherwith a number of design aids.

The preparation of this fourth British edition has provided an opportunity to revise thetext generally to incorporate the results of recent findings and research. This is in accordancewith the principal objective of the book, to provide students and practising engineers withan understanding of the relationships between structural behaviour and the design criteriaimplied by the rules of design codes such as EC3.

N.S. Trahair, M.A. Bradford, D.A. Nethercot, and L. GardnerApril 2007

Units and conversion factors

Units

While most expressions and equations used in this book are arranged so that theyare non-dimensional, there are a number of exceptions. In all of these, SI un