An Introduction to Structural Mechanics

368 Pages·2001·4.196 MB·English

by  Paul Smith

Introduction to Structural
Mechanics
P. S. Smith
Introduction to Structural Mechanics

P. S. Smith

School of Engineering

University of East London
© P. S. Smith 2001
All rights reserved. No reproduction, copy or transmission of
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Any person who does any unauthorized act in relation to this
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The author has asserted his right to be identified as
the author of this work in accordance with the
Copyright, Designs and Patents Act 1988.
First published 2001 by
PALGRAVE MACMILLAN
Houndmills, Basingstoke, Hampshire RG21 6XS and
175 Fifth Avenue, New York, N.Y. 10010
Companies and representatives throughout the world
PALGRAVE MACMILLAN is the new global academic imprint of
St. Martin’s Press LLC Scholarly and Reference Division and
Palgrave Publishers Ltd (formerly Macmillan Press Ltd).
ISBN 0–333–96255–9
This book is printed on paper suitable for recycling and
made from fully managed and sustained forest sources.
A catalogue record for this book is available
from the British Library.
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Printed and bound in Great Britain by
J.W. Arrowsmith Ltd, Bristol
Contents

Preface ix

1. Basic Concepts and Load Path 1
1.1 Introduction 1
1.2 Equilibrium 1
Example 1.1 7
1.3 Load Paths – Determination of Load 12
Example 1.2 19
Example 1.3 20
Example 1.4 23
Example 1.5 24
Further Problems 1 27

2. Section Properties and Moment of Resistance 31
2.1 Introduction 31
2.2 Section Properties 32
Example 2.1 38
Example 2.2 43
Example 2.3 47
Example 2.4 49
Example 2.5 52
Example 2.6 55
Example 2.7 58
Example 2.8 59
2.3 Moment of Resistance 61
Example 2.9 61
Example 2.10 64
Example 2.11 65
Example 2.12 69
Example 2.13 70
Example 2.14 71
Example 2.15 72
Example 2.16 73
Example 2.17 75
Further Problems 2 79
iv Contents
3. Analysis of Beams 83
3.1 Introduction 83
3.2 Types of Beams, Loads and Supports 84
3.3 Determination of the Static Determinacy
of Structures 90
Example 3.1 92
Example 3.2 94
Example 3.3 95
Example 3.4 96
Example 3.5 97
3.4 Beam Reactions 97
Example 3.6 99
Example 3.7 100
Example 3.8 102
Example 3.9 104
Example 3.10 105
Example 3.11 107
Example 3.12 111
Example 3.13 113
Example 3.14 114
Example 3.15 115
Example 3.16 116
Example 3.17 118
Example 3.18 118
3.5 Shear Force and Bending Moment
Diagrams 119
Example 3.19 120
Example 3.20 124
Example 3.21 126
Example 3.22 129
Example 3.23 132
Example 3.24 134
Example 3.25 137
Example 3.26 140
Example 3.27 144
Example 3.28 146
Example 3.29 149
Example 3.30 151
Example 3.31 153
Contents v
Example 3.32 155
Example 3.33 159
Example 3.34 160
Example 3.35 161
Example 3.36 162
Example 3.37 163
Further Problems 3 165

4. Three Pin Frames 169
4.1 Introduction 169
4.2 Layout of Three Pin Frames 170
4.3 Determination of Reactions 173
Example 4.1 174
Example 4.2 176
Example 4.3 178
Example 4.4 180
Example 4.5 182
Example 4.6 183
Example 4.7 185
Example 4.8 188
4.4 Axial Thrust Diagrams 189
4.5 Analysis of Three Pin Frames 192
Example 4.9 193
Example 4.10 198
Example 4.11 201
Example 4.12 207
Example 4.13 208
Example 4.14 209
Example 4.15 210
Example 4.16 211
Further Problems 4 213

5. Deflection of Beams and Frames 217
5.1 Introduction 217
5.2 Effects of Supports and Load Patterns 217

5.3 Sketching Displacements 220
Example 5.1 221
vi Contents
Example 5.2 222
Example 5.3 223
Example 5.4 224
Example 5.5 226
Example 5.6 227
Example 5.7 228
5.4 Macaulay’s Method 232
Example 5.8 233
Example 5.9 236
Example 5.10 238
Example 5.11 242
Example 5.12 244
Example 5.13 247
Example 5.14 249
Example 5.15 252
Example 5.16 254
Example 5.17 257
Further Problems 5 261

6. Pin Jointed Frames 265
6.1 Introduction 265
6.2 Methods of Analysis 267
Example 6.1 269
Example 6.2 273
6.3 Method of Resolution of Forces at Joints 276
Example 6.3 277
Example 6.4 281
Example 6.5 285
Example 6.6 292
Example 6.7 293
Example 6.8 294
Example 6.9 295
Example 6.10 296
Example 6.11 297
Example 6.12 298
Example 6.13 299
Example 6.14 300
Example 6.15 301
Further Problems 6 303
Contents vii

7. Torsion and Torque 305
7.1 Introduction 305
7.2 Torsion and Torque Diagrams 307
Example 7.1 309
Example 7.2 310
7.3 Simple Torsion Problems 311
Example 7.3 315
Example 7.4 315
Example 7.5 317
Example 7.6 318
Example 7.7 320
Example 7.8 321
Example 7.9 322
Example 7.10 323
Further Problems 7 325

8. Combined Stress 329
8.1 Introduction 329
8.2 Direct and Bending Stresses 329
Example 8.1 337
Example 8.2 339
Example 8.3 341
Example 8.4 343
Example 8.5 344
Example 8.6 347
Example 8.7 349
Example 8.8 350
Further Problems 8 353

Index 355
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Preface

In writing this book I was mindful of the comments of both students and practitioners
gathered over more than twenty years in civil engineering, latterly in education. Most centred on the
fact that, having learned the background and basic theory, you are left trying to find suitable
situations and examples of application of the acquired knowledge. Tracking a problem through
often helps to gel the theory, and with practice can focus the mind on what is trying to be achieved.
In this text you will find both theory and worked examples side-by-side. The examples start
from a fundamental level and progress to more difficult, intricate and taxing problems. Early
examples assume little or no experience in the subject matter but soon propel you forward to
solving complex, practical-based structural systems. The emphasis is on problem-based learning,
and the procedures adopted are reinforced by their application to a plentiful supply of worked
examples.
You are invited to reinforce you understanding of the structural theories and applications, or
to use the examples as a reference to test your ability to apply your knowledge to the various
problems presented here. Each chapter commences by providing details of the basic theory and
procedures to be adopted in the solutions, supported by worked examples to demonstrate the
application, and concluded with further problems to test your understanding.
To both aspiring and practising engineers this book will provide a powerful learning or
revision text which will enable you to test and develop your understanding of structural analysis.