STRUCTURAL MECHANICS Available from the authors of Structural Mechanics 4T STRUMEC A TEACHING PACKAGE consisting of 10 COMPUTER BASED TUTORIALS • each tutorial relates to a programme of study in this text • each tutorial consists of 30 to 50 questions and problems • each tutorial can be used for self-assessment or examination • each tutorial gives instant feedback on performance • these tutorials are highly visual and student friendly in presentation 150 OVERHEAD TRANSPARENCIES • match each programme of study • ensure a high level of class presentation TWO TEXT BOOKS • Structural Mechanics from the Foundations of Engineering Series • Structural Mechanics from the College Work Out Series 4TSTRUMEC ... a comprehensive and integrated package for the teaching of Structural Mechanics, available for purchase by any University and College. For further details write to: Ray Hulse, Associate Dean, School of the Built Environment, Coventry University, Coventry, CVl 5FB. FOUNDATIONS OF ENGINEERING Series Editor: G. E. Drabble Structural Mechanics Jack Cain Formerly Senior Course Tutor Civil Engineering Coventry University Ray Hulse Head of Academic Programmes School of The Built Environment Coventry University ~ MACMillAN © J. A. Cain and R. Hulse 1990 All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No paragraph of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, 90 Tottenham Court Road, London WI P 9HE. Any person who does any unauthorised act in relation to this publication may be liable to criminal prosecution and civil claims for damages. First published 1990 by MACMILLAN PRESS LTD Houndmills, Basingstoke, Hampshire RG21 6XS and London Companies and representatives throughout the world ISBN 978-0-333-48078-6 ISBN 978-1-349-10542-7 (eBook) DOI 10.1007/978-1-349-10542-7 A catalogue record for this book is available from the British Library. 13 12 II 10 9 8 7 6 04 03 02 01 00 99 98 A Solutions Manual is available from the Publishers ISBN 978-0-333-68790-1 To Pat and Jean FOUNDATIONS OF ENGINEERING SERIES J. A. Cain and R. Hulse Structural Mechanics G. E. Drabble Dynamics R. G. Powell Electromagnetism P. Silvester Electric Circuits J. Simonson Thermodynamics M. Widden Fluid Mechanics Series Standing Order If you would like to receive future titles in this series as they are published, you can make use of our standing order facility. To place a standing order please contact your bookseller or, in case of difficulty,write to us at the address below with your name and address and the name of the series. Please state with which title you wish to begin your standing order. (If you live outside the United Kingdom we may not have the rights for your area, in which case we will forward your order to the publisher concerned.) Customer Services Department, Macmillan Distribution Ltd Houndmills, Basingstoke, Hampshire RG21 6XS, England CONTENTS Series Editor's Foreword Vlll Authors' Preface ix How to use this book xi Programme 1 Revision of the Fundamentals of Statics 1 2 Simple Structures (Loads and Reactions) 27 3 Pin Jointed Frame Structures 69 4 Shearing Forces and Bending Moments 99 5 Stress Analysis (Direct Stresses) 137 6 Bending Stresses 163 7 Combined Bending and Direct Stresses 197 8 Shear Stresses 225 9 Torsional Stresses 259 10 Stress Transformations and Mohr's Circle of Stress 287 11 Composite Sections 315 12 Beam Deflections and Rotations 349 13 Strain Energy 383 14 Virtual Work 407 Index 435 SERIES EDITOR'S FOREWORD This series of programmed texts has been written specifically for first year students on degree courses in engineering. Each book covers one of the core subjects required by electrical, mechanical, civil or general engineering students, and the contents have been designed to match the first year requirements of most universities and polytechnics. The layout of the texts is based on that of the well-known text, Engineering Mathematics by K. Stroud (first published by Macmillan in 1970, and now in its third edition). The remarkable success of this book owes much to the skill of its author, but it also shows that students greatly appreciate a book which aims primarily to help them to learn their chosen subjects at their own p~ce. The authors of this present series acknowledge their debt to Mr Stroud, and hope that by adapting his style and methods to their own subjects they have produced equally helpful and popular texts. Before publication of each text the comments of a class of first year students, of some recent engineering graduates and of some lecturers in the field have been obtained. These helped to identify any points which were particularly difficult or obscure to the average reader or which were technically inaccurate or misleading. Subsequent revisions have eliminated the difficulties which were highlighted at this stage, but it is likely that, despite these efforts, a few may have passed unnoticed. For this the authors and publishers apologise, and would welcome criticisms and suggestions from readers. Readers should bear in mind that mastering any engineering subject requires considerable effort. The aim of these texts is to present the material as simply as possible and in a way which enables students to learn at their own pace, to gain confidence and to check their understanding. The responsibility for learning is, however, still very much their own. G. E. DRABBLE V111 AUTHORS PREFACE I This book contains fourteen programmes incorporating material which will be found in most first year undergraduate and HND syllabuses in Strength of Materials and Structural Analysis. The book is intended for use by students of Engineering and Building as a first text in Structural Mechanics as taught in most Polytechnic and University departments of Engineering and Construction. The aim of the text is to provide a sound understanding of fundamental principles of Structural Mechanics by presenting the principles and concepts involved in a distinctive programmed learning format whereby the student can work and learn at his/her own pace and test his/her understanding by answering a series of carefully constructed questions and graded practical problems. Although it is assumed that students using the book will have some grasp of elementary mechanics, the first chapter provides useful revision of the basic principles of statics which provide the foundation material for the rest of the book. Subsequent chapters deal with concepts of structural form and types of loading. Techniques for analysing statically determinate pin jointed frame structures and simply supported and cantilevered beams are introduced. The drawing of shear force and bending moment diagrams for beams subjected to different types of loading is given comprehensive coverage. A number of programmes cover stress analysis including analysis and design of structures subjected to direct, bending, shear or torsional stress. Problems involving combined bending and axial loading are also considered. The analysis of complex stress situations using Mohr's Circle of Stress forms the basis of one complete programme, as does the analysis of composite sections under different stress situations including thermal loading. Later programmes show how the deflection of statically determinate beams may be calculated using integration techniques, and Strain Energy and Virtual Work methods are introduced as a foundation for further more advanced study. The book is suitable for general class use and for individual study supported by seminar and/or tutorial work. It is appreciated that the coverage of the text may be a little greater than that required for some courses and that the last few programmes may, in many courses, form part of second year work. This is intentional as the earlier programmes are suitable for use by HND students or those undergraduates on Building Courses where the depth of study of Structural Mechanics may not be so great. Engineering undergraduates will find that most of the text will be required in their first year studies and the more able student, by grasping the subject matter more quickly, will be able to work to the end of the book thereby gaining an early introduction to second year studies. Throughout the book the emphasis is on student centred learning with the intention of providing the student with a sound grasp of the fundamental principles of Structural ix