Basic Structural Theory

BASIC STRUCTURAL THEORY
This book introduces the basic equations of the theory of structures. Conventional presentations of these equations follow the ideas of elastic analysis, introduced nearly two hundred years ago. The present text is written against the background of advances made in structural theory during the last fifty years, notably by the introduction of the so-called plastic theory.Tests on real structures in the twentieth century revealed that structural states predicted by elastic analysis cannot in fact be observed in practice, whereas plastic ideas can be used to give accurate estimates of strength. Strength is discussed in the first part of this book without reference to equations of elastic deformation. However, the designer is concerned also with stiffness, for whichelastic analysis is needed, and the standard equations (suitable, for example, for computer programming) are presented. Finally, stability is analyzed, which again is essentially an elastic phenomenon, and it is shown that a higher factor of safety is required to guard against buckling than is required to guarantee straightforward strength. The emphasis throughout this book is on the derivation andapplication of the structural equations, rather than on details of their solution (nowadays best done by computer), and the numerical examples are deliberately kept simple. Jacques Heyman is former Head of the Department of Engineering at the University of Cambridge and the author of fourteen books, including The stone skeleton, Elements of the theory of structures, Structural analysis: ahistorical approach, Elements of stress analysis and the two-volume set, Plastic design of frames: Volume 1, Fundamentals and Volume 2, Applications, with Lord Baker. He is a Fellow of the Society of Antiquaries, the Institution of Civil Engineers and the Royal Academy of Engineering, and an Honorary Fellow of the Royal Institute of British architects. He was a consulting engineer for a number of Englishcathedrals and a member of the Architectural Advisory Panel for Westminster Abbey and the Cathedrals Fabric Commission for England. He also has served on many British Standards committees. Professor Heyman’s The stone skeleton won the Choice Outstanding Academic Books Award in 1996.

Books by the author

Plastic design of portal frames Beams and framed structures Plastic design of frames (2volumes) Coulomb’s memoir on statics Equilibrium of shell structures Elements of stress analysis The masonry arch The stone skeleton Elements of the theory of structures Arches, vaults and buttresses Structural analysis: a historical approach The science of structural engineering

Basic Structural Theory
Jacques Heyman
University of Cambridge

CAMBRIDGE UNIVERSITY PRESS

Cambridge, NewYork, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521897945 © Jacques Heyman 2008 This publication is in copyright. Subject to statutory exception and to the provision ofrelevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2008

ISBN-13 978-0-511-39692-2 ISBN-13 978-0-521-89794-5

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Contents

Preface

page vii

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Structural assumptions 1.2 Structural equations 3 6 8 8 17 20 26 39 48

2 Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . ....