Stress, Strain, and Structural Dynamics: An Interactive Handbook of Formulas, Solutions, and MATLAB Toolboxes

961 Pages·2005·40.38 MB·English

by  Bingen Yang

Stress, Strain, and
Structural Dynamics
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Stress, Strain, and
Structural Dynamics
An Interactive Handbook of Formulas,
Solutions, and MATLAB Toolboxes
Bingen Yang
University of Southern California
Amsterdam Boston Heidelberg London New York Oxford
Paris San Diego San Francisco Singapore Sydney Tokyo
Elsevier Academic Press
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Library of Congress Cataloging-in-Publication Data
Yang, Bingen.
Stress, strain, and structural dynamics.
p. cm.
Includes bibliographical references.
1. Strains and stresses. 2. Structural dynamics. I. Title.
TA648.3.Y36 2004
624.1'7-dc22
2004022861
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
ISBN: 0-12-787767-3
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To my parents,
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My daughters Sonia and Tanya
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Contents
Preface xv
Acknowledgements xvii
Chapter 1 Introduction 1
1.1 The Making of This Book 1
1.2 How to Use This Book 4
Part I Strength of Materials 7
Chapter 2
Static Analysis of Euler-Bernoulli Beams 9
2.1 Getting Started 9
2.2 Beam Theory 11
2.2.1 Static Problem 11
2.2.2 Solution Methods 16
2.2.3 Fundamentals of Euler-Bernoulli Beams 23
2.3 Static Analysis by the Toolbox 25
2.3.1 System Setup 26
2.3.2 Response to External Forces 28
2.3.3 Response to Boundary Disturbances 33
2.3.4 Total Response 34
2.3.5 Exact Analytical Solutions 36
2.3.6 Other Useful Functions 40
2.4 Moments of Inertia of Beam Cross-Section Area 42
2.5 Quick Solution Guide 46
2.6 References 51
Chapter 3
Static Analysis of Bars, Shafts, and Strings 53
3.1 Getting Started 53
3.2 System Description 55
3.3 Static Analysis by the Toolbox 59
3.3.1 System Setup 59
VII
3.3.2 Response to External Forces 60
3.3.3 Response to Boundary Disturbances 63
3.3.4 Total Response 65
3.4 Stepped Bars and Shafts 67
3.4.1 System Description 67
3.4.2 Solution by the Toolbox 68
3.5 The Distributed Transfer Function Method 74
3.6 Quick Solution Guide 78
3.7 References 83
Chapter 4 Buckling Analysis of Columns 85
4.1 Getting Started 85
4.2 Uniform Columns 87
4.2.1 Column Buckling Theory 87
4.2.2 Solution by the Toolbox 91
4.2.3 Eccentric Loading 96
4.2.4 Beam-Column Problem 100
4.2.5 Geometric Imperfection 104
4.3 Stepped and Nonuniform Columns 109
4.3.1 Constrained Stepped Columns 109
4.3.2 Nonuniform Columns 116
4.4 The Distributed Transfer Function Method 123
4.5 Quick Solution Guide 127
4.6 References 133
Chapter 5 Stress Analysis in Two-Dimensional Problems 135
5.1 Getting Started 135
5.2 Plane Stress and Strain 136
5.2.1 In-Plane Stresses 136
5.2.2 In-Plane Strains 142
5.2.3 Strain Rosette 147
5.2.4 Hooke's Law 149
5.2.5 Criteria of Failure 151
5.3 Quick Solution Guide 155
5.4 References 156
Part II Structural Mechanics 157
Chapter 6
Static Analysis of Constrained Multispan Beams 159
6.1 Getting Started 159
6.2 System Description 161
6.3 Solution by the Toolbox 166
6.3.1 System Setup 166
6.3.2 Response to External Forces 171
6.3.3 Response to Boundary Disturbances 176
6.3.4 Response to Support Settlement 178
6.3.5 Total Response 181
6.3.6 Influence Lines 183
6.4 The Distributed Transfer Function Method 189
viii Contents
6.5 Quick Solution Guide
6.6 References 200
Chapter 7 Static Analysis of Plane Trusses 201
7.1 Getting Started 201
7.2 System Description 203
7.3 Solution by the Toolbox 205
7.3.1 System Setup 205
7.3.2 Response to External Forces 210
7.3.3 Support Settlement 213
7.3.4 Fabrication Errors and Thermal Effects 216
7.3.5 Total Response 220
7.4 The Stiffness Method 224
7.5 Quick Solution Guide 230
7.6 References 235
Chapter 8 Stati c Analysis of Plane Frames 237
8.1 Getting Started 237
8.2 System Description 240
8.3 Solution by the Toolbox 243
8.3.1 System Setup 243
8.3.2 Response to External Forces 248
8.3.3 Response to Settlement of Supports 252
8.3.4 Total Response 256
8.3.5 Response of Frame Members 260
8.4 The Distributed Transfer Function Method 263
8.5 Quick Solution Guide 268
8.6 References 276
Part III Dynamics and Vibrations 277
Chapter 9 Dynamics of Particles and Rigid Bodies 279
9.1 Getting Started 279
9.2 Dynamics of Particles 280
9.2.1 Preliminaries 280
9.2.2 Kinematics 284
9.2.3 Kinetics of Single Particle 286
9.2.4 Particle Motion via Numerical Integration 289
9.2.5 Systems of Particles 297
9.2.6 Central Force Motion 303
9.3 Dynamics of Rigid Bodies in Plane Motion 307
9.3.1 Plane Motion 307
9.3.2 Mass Moments of Inertia 310
9.3.3 Kinetics 314
9.3.4 Simulation of Dynamic Response 317
9.4 Rigid Body Dynamics in Three Dimensions 323
9.4.1 Kinematics 323
9.4.2 Inertia Properties 327
9.4.3 Energy and Momentum 335
Contents