Table Of ContentINTRODUCTION TO STRUCTURES, 2"d Edition
"Talking of education, people have now a-days" (said he) "got a strange opinion that every
thing should be taught by lectures. Now, I cannot see that lectures can do so much good as
reading the books from which the lectures are taken. I know nothing that can be best
taught by lectures, except where experiments are to be shewn. You may teach chymestry
by lectures - You might teach making of shoes by lectures!"
James Boswell: Life ofS amuel Johnson, 1766 (1709-1784)
Dedicated to
Frank DiMaggio
Professor Emeritus, Columbia University
ABOUT OUR AUTHOR
William R Spillers, formerly Professor of Civil Engineering in
Rensselaer Polytechnic Institute, Troy, New Yorlc, is now
Professor of Civil Engineering at The New Jersey Institute of
Technology, Newark, NJ where he was Departmental Chairman
1990 - 1998. He is a structural engineer with an international
reputation in areas of computer applications to structures, design
theory, and fabric structures. He has written extensively in these
areas, with well over 120 published articles and 9 books,
including the first edition of Introduction to Structures (Ellis
Horwood Limited 1985). He holds engineering degrees from the
University of California at Berkeley (BS 1955, MS 1956) and
Colwnbia University (PhD 1961 ), and was a Guggenheim Fellow
in 1968 and an NSF Fellow in 1975.
He has combined a strong academic career as a consultant
structural engineer on major projects around the world. This
duality has given a unique flavour to his work particularly on
computer applications in structures when his Automated
Structural Analysis (Pergamon Press 1972) was one of the first
texts to introduce computer applications into the undergraduate
curriculwn. His text on structural optimisation, Iterative
Structural Design (North Holland 1975), was one of the first texts
on this subject; and his Basic Questions ofD esign Theory (North
Holland 1975) describes a National Science Foundation
symposiwn he organised, which turned out to be the origin of
present day design theory. Introduction to Structures continues
this tradition of combining a strong academic approach with
industrial engineering practice.
Introduction to Structures, 2nd Edition
William R. Spillers
Professor of Civil and Environmental Engineering
New Jersey Institute of Technology
Newark USA
Oxford Cambridge Philadelphia New Delhi
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First published by Horwood Publishing Limited, 2002
Reprinted by Woodhead Publishing Limited, 2011
© W. R. Spillers, 2002
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British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
ISBN 978-1-898563-94-5
Printed by Lightning Source
Contents
Foreword
1. Introduction and Review I
I.I Modeling 1
1.2 Notation 6
1.3 Rigid body mechanics 9
1.3.l The tripod 14
1.3.2 The two-bar truss 15
1.4 The concept of stress resultants 15
1.5 Exercises 20
2. Statically Determinate Stnictures 24
2.1 Introduction 24
2.2 Statically determinate trusses 26
2.2.1 Plane trusses 28
2.2.1.1 The method ofj oints 32
2.2.1.2 The method of sections 35
2.2.1.3 Geometric instability 37
2.2.2 Space tmsses 40
2.2.2.1 The method ofj oints 42
2.2.2.2 The method of sections 45
2 2.2.3 The Schwedler dome 45
2.3 Frames 46
2.3.l Equilibrium equations of straight plane beams 47
2.3.2 Plane frames and arches 50
2.3.2.1 The three-hinged arch 53
2.3.3 Space frames 56
2.3.3.1 Ditf. equations for cwved beams 61
2.4 Membrane shells 63
2.4.1 A symmetric spherical shell under its own weight 63
2.5 Exercises 66
3. Deflections of Stl1ldures 73
3.1 Vutual work for trusses 74
3.1.l Member stiffness 74
3.1.2 Member/joint displacement relationships 75
3.1.3 Virtual work for a truss element 76
3.1.4 Virtual worli:: for truss structures 77
3.1.5 Some truss examples 78
3.1.6 Williot geomeby 81
3.2 VJrtual work for plane frames 83
3.2.1 The moment-:anvature relationship 84
3.2.2 The virtual work equation 88
3,2.3 A note on the integral of the product of two functions 90
3.2.4 Virtualworkforplaneframes 91
3.2.4.1 Applications 95
3.3 More general applications 95
3.4 Computation of discontinuities 96
3.5 Real structures versus virtual structures 96
3.6 Exercises 98
4. Statically Indeterminate Structures 103
4.1 The force method 106
4.1.1 A single degree of freedom system 106
4.1.2 A tw<Hlegree of freedom system 107
4.1.3 The general case 109
4.2 The displacement method 113
4.2.l A structure with a single degree of freedom 113
4.2.2 A structure with two degrees of freedom 115
4.2.3 A three-degree of freedom system 118
4.2.4 A pile problem 120
4.3 Exercises 122
5. Plastic Analysis 131
5.1 Introduction 131
5.2 The concept of a plastic hinge 135
5.3 Proportional loading 138
5.4 Moment redistribution 138
5.5 Analysis theorems 138
5.5.1 The~ work equation 139
5.5.2 The work energy equation 139
5.5.3 The lower bound theorem 141
5.5.4 The upper bound theorem 142
5.6 Computing plastic collapse loads 144
5.7 Extensions 148
5.7.l Interaction formulas 148
5.7.2 Repeated loading 150
5.7.3 Shakedown 151
5.7.4 Common sense 153
5.8 Exercises 154
6. Uses of Cables 162
6.1 Plane cables 164
6.1.l Particular solutions 166
6.1.2 Some examples: The parabola versus the catenary 168
6.1.3 A cable loaded by concentrated forces 170
6.2 Beams with cables 171
6.3 A statically determinate suspension bridge 176
6.4 A simple example of an air-supported structure 177
6.4.l The grid methodofshape1inding 179
6.5 Cables in three dimensions 181
6.6 Exercises 182
7. Moment Distribution 185
7 .1 Member sttll'ne§ and joint distribution 185
7 .2 Frame problems and sidesway 190
7.3 Generalizations and extensions 193
7.3.l A Vierendeel 'truss' example 197
7 .3.2 Temperature and settlement 199
7.3.3 Variable moment of inertia. 199
7 .4 Exercises 201
8. Influence Lines and their Application 204
8.1 The Mueller-BresJau principle 206
8.2 An example from building design 207
8.3 Moving loads 209
8.4 Placing moving loads for maximum moment 210
8.5 Exercises 211
9. References 213
Appendix 1. The Rotation Matrix 217
Appendix2. Geometric Instability 221
Appendixl. Discontinuous Functions 222
Appendix4. The Frenet Formulas 225
AppendixS. Kinematics of Curved Beams 228
Appendix(;. The Degree of Statical Indeterminacy 230
.some
Appendix7. Beam Solutions 233
Appendix I. A Transcendental Equation 234
Appendix9. The Effect of Prestn& 235
Index 239
Foreword
Over the past 20 years massive changes have occurred in the practice of structural
analysis. Those of us who graduated from an engineering school in the 1950s were
taught relatively simple skills and hoped that we would never he asked to analyze
structures with more than three redundants. Today a structure with 300 redundants
is not considered large or thought to present any particular problem for analysis. In
fact, a highly reliable solution for such a structure is usually available at a modest
price. We have thus gone from a situation in which the analysis of a highly
indeterminate structure posed considerable difficulty to one in which analysis
capabilities are readily available and cheap.
Educational institutions have for the most part been slow to respond to these
changes. While we did institute computer programming courses quickly and in
some cases graduate courses in computer-aided structural analysis, surveys have
shown that the undergraduate curriculum -the backbone of professional engineering
- is roughly the same as it was 20 to 30 years ago. To the extent that we teach
engineering, not computer programming, this lack of response to the advent of the
computer may have been appropriate. But in the long run the computer will surely
have its impact upon the way we teach structures. While not presuming to know
how matters will eventually turn out, it is the thesis of this text that because of the
computer (if for no other reason) structural engineers must know more today.
The question is, of course, how to know more. As far as this text is concerned that
question is answered in two ways. In terms of depth, an attempt has been made to
discuss three-dimensional problems more than has been common in the past. In
terms of scope, the text moves through statically indeterminate structures and on
some plastic analysis. In order to do this it has been necessary to omit some (in this
context) redundant topics such as the conjugate beam and the three-moment
equations.
Otherwise, the outline of this text is straightforward. It moves logically from
statically determinate structures to the computation of displacements to the analysis
of statistically indeterminate structures. Then follow four supplementary chapters
dealing with plastic analysis, cables, moment distribution, and influence lines. In
terms of style, there is a tendency to include more material than the reader might
want on first reading. That is done in the hope that he or she will return for a second
look and even try the references which are indicated.
There is a 200-year tradition in structures. As a result, those of us who call
ourselves structural engineers spend much time learning -really taking -from others.
In my own case this includes not only teachers and colleagues but also long
suffering students at both Columbia University and Rensselaer Polytechnic Institute
to whom I am grateful. What we have shared is a common interest in how structures
work.
