Structural Stability in Engineering Practice

467 Pages·1999·17.644 MB·\467

by  Lajos Kollar (Author)

Structural Stability in
Engineering Practice
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Structural Stability in
Engineering Practice
Edited by
Lajos Kollar
Technical University Budapest
First published 1999 by E & FN Spon
11 New Fetter Lane, London EC4P 4EE
Simultaneously published in the USA and Canada
by E & FN Spon, an imprint of Routledge
29 West 35th Street, New York, NY 10001
E & FN Spon is an imprint of the Taylor & Francis Group
© 1999 E&FN Spon
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British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloging in Publication Data
Structural stability in engineering practice / edited by L. Kollar.
p. cm.
Includes bibliographical references.
1. Structural stability. 2. Load factor design. I. Kollar, Lajos
TA656.S778 1999
624. I'71-dc21 99-14295
CIP
ISBN 0-419-23790-9
Contents
Preface xi
1 Loss of stability and post-buckling behaviour Lajos Kollar 1
1.1 The main kinds of loss of stability of 'centrally' loaded (geometrically perfect)
structures 2
1.1.1 Symmetric stable bifurcation 2
1.1.2 Symmetric unstable bifurcation 3
1.1.3 Asymmetric bifurcation 4
1.1.4 The degenerating case of the symmetric bifurcation 5
1.1.5 General remarks 6
1.2 The imperfection sensitivity of the structures 7
1.3 Loss of stability with a limit point (divergence of equilibrium; snapping through) 11
1.4 The influence of plasticity 13
1.5 Some practical points of view for estimating the post-critical behaviour 16
1.6 Evaluation of buckling experiments by the generalized Southwell plot 20
2 Summation theorems concerning critical loads of bifurcation Tiber Tamai 23
2.1 On the summation theorems 23
2.2 The Southwell theorem 26
2.3 Dunkerley type theorems and formulae 30
2.3.1 The Dunkerley theorem 30
2.3.2 The Foppl-Papkovich theorem 35
2.3.3 The Kollar conjecture 43
2.3.4 The Melon theorem 51
2.3.5 The Rankine formula 55
2.4 Conclusions 56
3 Interaction of different buckling modes in the post-buckling range Lajos Kollar 59
3.1 Description of the phenomenon 59
3.2 The post-buckling load-bearing capacity of a braced column 60
3.3 The post-buckling load-bearing capacity of the ribbed plate 69
3.4 The post-buckling load-bearing behaviour of the box bar 74
3.5 The interaction of the buckling modes of cylindrical shells 80
3.5.1 Nonlinear shell equations 80
VI
3.5.2 The eigenfunctions of the cylindrical shell 82
3.5.3 The post-buckling behaviour of the shell 84
4 Stability of elastic structures with the aid of the catastrophe theory Zsolt Caspar 88
4.1 Statement of the problem 88
4.2 Definitions 89
4.3 Thorn's theorem 90
4.4 The cuspoid catastrophes 92
4.4.1 The fold catastrophe 92
4.4.2 The cusp catastrophe 93
4.4.3 The swallowtail catastrophe 95
4.4.4 The butterfly catastrophe 96
4.5 The umbilic catastrophes 97
4.5.1 The elliptic umbilic 97
4.5.2 The hyperbolic umbilic 99
4.6 Imperfection-sensitivity of structures 100
4.6.1 What kind of catastrophes arise? 100
4.6.2 The method 100
4.6.3 The fold catastrophe 102
4.6.4 The cusp catastrophe 106
4.6.5 Higher order cuspoid catastrophes 115
4.6.6 The umbilic catastrophes 117
4.7 Probability of the instability 127
5 Buckling of frames Josef Appeltauer, Lajos Kollar 129
5.1 General theory of frame buckling Josef Appeltauer 129
5.1.1 Description of the phenomena 129
5.1.2 Mechanical models describing the various kinds of loss of stability 130
5.1.3 Bifurcation 135
5.1.4 Divergence 145
5.1.5 Snapping through 153
5.1.6 Practical applications 155
5.1.7 Conclusions 161
5.2 Approximate stability analysis of frames by the buckling analysis of the
individual columns Lajos Kollar 161
5.2.1 Basic principles of the method 161
5.2.2 Stability investigation of braced frames 167
5.2.3 Stability investigation of unbraced frames 175
6 Application of the sandwich theory in the stability analysis of structures
Istvan Hegedus and Laszlo P. Kollar 187
6.1 Assumptions, definitions 188
6.2 Sandwich beam with thin faces (Timoshenko-beam) 190
6.3 Sandwich beam with thick faces 195
6.3.1 Incompressible core 195
Vll
6.3.2 Compressible core 199
6.4 Models based on the sandwich beam with thick faces 204
6.4.1 Beams with flexural deformations only (S = oo or 5 = 0) 205
6.4.2 Beams with shear deformations only (Dy = oo and DI = 0) 205
6.4.3 Sandwich beam with thin faces (£>j = 0) 207
6.4.4 Beam on an elastic foundation which restrains the rotations -
Csonka-beam (DQ = oo) 207
6.4.5 Sandwich beam with thick faces on an elastic foundation which restrains
the rotations 209
6.4.6 Sandwich beam with thick faces on an elastic foundation which restrains
the displacements 209
6.4.7 Isotropic sandwich plate 210
6.4.8 Orthotropic sandwich plate 213
6.4.9 Orthotropic shallow sandwich shell 215
6.4.10 Multi-layered sandwich cantilever beam 216
6.5 Approximate expressions for the calculation of the buckling load 217
6.5.1 Parallel and serial connections of beams (Foppl-Papkovich's and
Southwetfs theorem) 217
6.5.2 Cantilever beams on elastic foundation which restrains the rotation 221
6.5.3 Multi-layered sandwich beam 222
6.6 Some applications of the sandwich theory in structural engineering 223
6.6.1 Discrete structures with regular built-up 223
6.6.2 Exact analysis of discrete structures using the theory of difference equa-
tions 223
6.6.3 Trusses 226
6.6.4 Laced (Vierendeel) column 230
6.6.5 Frames and shear walls 235
6.6.6 Combined torsional and in-plane buckling of multistorey buildings 238
7 Bracing of building structures against buckling Lajos Kottar and Karoly Zalka 242
7.1 Basic principles 242
7.2 The necessary stiffness of the bracing core 243
7.2.1 The bending stiffness of the bracing core 243
7.2.2 The torsional stiffness of the bracing core 245
7.2.3 Generalization of the results. Spatial behaviour 251
7.3 The necessary strength of the bracing core 256
7.4 Bracing system of shear walls and cores 258
7.4.1 The equivalent column 259
7.4.2 Uniformly distributed load over the height 262
7.4.3 Concentrated load at top floor level 265
7.4.4 Supplementary remarks 265
7.5 Stability analysis of the columns of the building 268
7.5.1 Sway critical loads 269
7.5.2 Sway versus nonsway critical loads 272
7.5.3 Conclusions 273
Vlll
8 Buckling of arches and rings Lajos Kollar 276
8.1 Buckling of bars with curved axis (arches) in their own plane 277
8.1.1 Buckling of rings and arches with circular axis 277
8.1.2 Arches with noncircular axes. 285
8.1.3 Snapping through of flat arches 291
8.1.4 Buckling of arches with thin-walled, open cross sections 299
8.1.5 Buckling of arches with hangers or struts 308
8.2 Lateral buckling of rings and arches 321
8.2.1 Lateral buckling of centrally compressed arches with circular axis 321
8.2.2 Buckling of centrally compressed arches with axes other than circular 327
8.2.3 Lateral buckling of centrally compressed arches loaded by hangers or
struts 329
8.2.4 Post-critical behaviour of laterally buckling arches. 335
8.2.5 Lateral buckling of arches bent in the plane of the arch 335
9 Special stability problems of beams and trusses Lajos Kollar 339
9.1 Problems of lateral stability of beams 339
9.1.1 The governing differential equations of lateral buckling and some
conclusions 340
9.1.2 The energy method for determining the critical loads of suspended
beams 344
9.1.3 Determination of the critical load by the summation theorem 349
9.2 Lateral stability of the nodes of plane trusses 353
9.3 Snapping through of shell-beams in the plane of bending 356
10 Stability of viscoelastic structures Gyorgy Ijjas 358
10.1 Introduction 358
10.1.1 General remarks 358
10.1.2 Material properties 358
10.2 Various kinds of creep buckling 359
10.3 Structures made of fluid-type material, exhibiting symmetric unstable
post-critical behaviour 363
10.3.1 Description of the phenomenon 363
10.3.2 The pseudo-equilibrium surface 365
10.3.3 The total potential energy 368
10.3.4 Supplementary remarks 371
10.4 Structures made of solid-type material, exhibiting symmetric unstable
post-critical behaviour 371
10.4.1 Description of the phenomenon 371
10.4.2 The pseudo-equilibrium surface 373
10.4.3 The total potential energy 375
10.4.4 Supplementary remarks 376
10.5 Structures made of DischingeMype material, exhibiting symmetric
unstable post-critical behaviour 376
10.5.1 Description of the phenomenon 376
IX
10.5.2 The pseudo-equilibrium surface 378
10.5.3 The total potential energy 379
10.5.4 Supplementary remarks 380
10.6 Structures made of fluid-type material, exhibiting symmetric stable post-critical
behaviour 380
10.6.1 Description of the phenomenon 380
10.6.2 The pseudo-equilibrium surface 382
10.6.3 The total potential energy 382
10.6.4 Supplementary remarks 383
10.7 Structures made of solid-type material, exhibiting symmetric stable post-critical
behaviour 384
10.7.1 Description of the phenomenon 384
10.7.2 The pseudo-equilibrium surface 384
10.7.3 The total potential energy 386
10.8Creep of the dashpot 386
10.9 Two remarks about the problems appearing in the literature 387
10.9.1 Importance of the degree of approximations 387
10.9.2 Importance of the elastic behaviour 388
11 Buckling under dynamic loading Lajos Kollar 389
11.1 Description of the dynamic loading process 389
11.2 Buckling of an initially curved bar under a falling load 391
11.3 Generalizations 395
12 Stability paradoxes Lajos Kollar 398
12.1 Structures behaving differently from common engineering sense 398
12.1.1 Instability of blown-up rubber balloons 398
12.1.2 The buckling length in the case of a load of varying direction, passing
through a fixed point 402
12.1.3 Instability of a bar in tension 403
12.1.4 Structures with infinitely great critical forces 404
12.1.5 Structures with abruptly changing rigidity characteristics 405
12.2 Destabilizing by stiffening and stabilizing by softening 407
12.2.1 Stabilizing by increasing the length 407
12.2.2 The destabilizing effect of an additional support 410
12.2.3 Paradoxes with torsional buckling 411
12.2 A The destabilizing effect of damping in the case of nonconservative
forces 412
References 415
Author Index 443
Subject Index 449