Structural analysis volume 2. Statically indeterminate structures.

401 Pages·2018·5.455 MB·English

by  Khalfallah, Salah

Structural Analysis 2
In memory of my father, Tahar
In memory of my wife, Mrs Nadjet Khalfallah-Boudaa
To my family
20 Ramadhan 1437 AH
Series Editor
Gilles Pijaudier-Cabot
Structural Analysis 2

Statically Indeterminate Structures

Salah Khalfallah
First published 2018 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as
permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced,
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© ISTE Ltd 2018
The rights of Salah Khalfallah to be identified as the author of this work have been asserted by him in
accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Control Number: 2018946933

British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-78630-339-4
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Chapter 1. Introduction to Statically Indeterminate
Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. External static indeterminacy . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3. Internal static indeterminacy . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.1. Truss structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.2. Beam and frame structures . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.3. Crossbeams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4. Kinematic static indeterminacy . . . . . . . . . . . . . . . . . . . . . . . . 11
1.5. Statically indeterminate structural analysis methods . . . . . . . . . . . . 15
1.6. Superposition principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.7. Advantages and disadvantages of statically indeterminate structures . . . 17
1.7.1. Advantages of statically indeterminate structures . . . . . . . . . . . 18
1.7.2. Disadvantages of statically indeterminate structures . . . . . . . . . 19
1.8. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.9. Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Chapter 2. Method of Three Moments . . . . . . . . . . . . . . . . . . . . . 25
2.1. Simple beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2. Continuous beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.3. Applying Clapeyron's theorem . . . . . . . . . . . . . . . . . . . . . . . . 43
2.3.1. Beam with two spans . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.3.2. Beam with support settlements . . . . . . . . . . . . . . . . . . . . . . 46
2.3.3. Beam with cantilever . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.4. Focus method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
vi Structural Analysis 2
2.4.1. Left focus method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.4.2. Right focus method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.4.3. Focus method with loaded bays . . . . . . . . . . . . . . . . . . . . . 57
2.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2.6. Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Chapter 3. Method of Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.1. Beam with one degree of static indeterminacy . . . . . . . . . . . . . . . 67
3.2. Beam with many degrees of static indeterminacy . . . . . . . . . . . . . 72
3.3. Continuous beam with support settlements . . . . . . . . . . . . . . . . . 77
3.4. Analysis of a beam with two degrees of static indeterminacy . . . . . . 80
3.5. Analysis of a beam subjected to a moment . . . . . . . . . . . . . . . . . 84
3.6. Analysis of frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.6.1. Frame with two degrees of static indeterminacy . . . . . . . . . . . . 87
3.6.2. Frame with cantilever . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.6.3. Frame with many degrees of static indeterminacy . . . . . . . . . . 100
3.6.4. Frame with oblique bars . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.7. Analysis of truss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.7.1. Internally statically indeterminate truss . . . . . . . . . . . . . . . . . 114
3.7.2. Externally statically indeterminate truss . . . . . . . . . . . . . . . . 121
3.7.3. Internally and externally statically indeterminate truss . . . . . . . . 125
3.8. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
3.9. Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Chapter 4. Slope-Deflection Method . . . . . . . . . . . . . . . . . . . . . . 137
4.1. Relationship between deflections and transmitted moments . . . . . . . 137
4.2. Fixed-end moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
4.2.1. Bi-hinged beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
4.2.2. Simply supported beam . . . . . . . . . . . . . . . . . . . . . . . . . . 142
4.3 Rigidity factor and transmission coefficient . . . . . . . . . . . . . . . . . 142
4.4. Beam analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
4.4.1. Single span beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
4.4.2. Continuous beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
4.4.3. Continuous beam with cantilever . . . . . . . . . . . . . . . . . . . . 153
4.4.4. Beam with support settlements . . . . . . . . . . . . . . . . . . . . . . 156
4.4.5. Beam subjected to a moment . . . . . . . . . . . . . . . . . . . . . . . 160
4.5. Analysis of frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
4.5.1. Frame without sidesway . . . . . . . . . . . . . . . . . . . . . . . . . . 164
4.5.2. Frames with sidesway . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
4.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
4.7. Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
Contents vii
Chapter 5. Moment-Distribution Method . . . . . . . . . . . . . . . . . . . 213
5.1. Hypotheses of the moment-distribution method . . . . . . . . . . . . . . 213
5.2. Presentation of the moment-distribution method . . . . . . . . . . . . . . 214
5.2.1. Distribution of a moment around a rigid joint . . . . . . . . . . . . . 214
5.2.2. Distribution procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
5.3. Continuous beam analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
5.3.1. Beam with support settlement . . . . . . . . . . . . . . . . . . . . . . 220
5.3.2. Beam with cantilever . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
5.3.3. Beam subjected to a moment . . . . . . . . . . . . . . . . . . . . . . . 227
5.4. Analysis of frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
5.4.1. Frame without sidesway . . . . . . . . . . . . . . . . . . . . . . . . . . 229
5.4.2. Frame with sidesway . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
5.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
5.6. Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
Chapter 6. Influence Lines of Statically
Indeterminate Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
6.2. Influence lines of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
6.2.1. Beam with one degree of static indeterminacy . . . . . . . . . . . . . 272
6.2.2. Beam with two degrees of static indeterminacy . . . . . . . . . . . . 279
6.3. Influence lines of frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
6.4. Influence lines of trusses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
6.4.1. Internally statically indeterminate truss . . . . . . . . . . . . . . . . . 292
6.4.2. Externally statically indeterminate truss . . . . . . . . . . . . . . . . 300
6.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
6.6. Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
Chapter 7. Statically Indeterminate Arch Analysis . . . . . . . . . . . . 309
7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
7.2. Classification of arches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
7.3. Semicircular arch under concentrated load . . . . . . . . . . . . . . . . . 311
7.4. Parabolic arch under concentrated load . . . . . . . . . . . . . . . . . . . 321
7.5. Semicircular arch under distributed load . . . . . . . . . . . . . . . . . . . 326
7.6. Parabolic arch under distributed load . . . . . . . . . . . . . . . . . . . . . 331
7.7. Semicircular arch fixed under concentrated load . . . . . . . . . . . . . . 337
7.8. Statically indeterminate tied arch . . . . . . . . . . . . . . . . . . . . . . . 345
7.9. Arch with many degrees of freedom . . . . . . . . . . . . . . . . . . . . . 350
7.10. Influence lines of statically indeterminate arch . . . . . . . . . . . . . . 356
viii Structural Analysis 2
7.10.1. Influence lines of bi-hinged arch . . . . . . . . . . . . . . . . . . . . 356
7.10.2. Influence line of fixed-end arch . . . . . . . . . . . . . . . . . . . . . 360
7.11. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
7.12. Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379