Structural Stability in Engineering Practice

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ISBN: 9780419237907 | 0419237909
Cover: Hardcover
Copyright: 8/3/1999

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Stability is an essential requisite in the design and manufacture of all structures, and engineers need a good understanding of critical loading factors in structure design. This book illustrates the various problems associated with attaining stability, and provides the results for practical use by the design engineer.

Preface

Loss of stability and post-buckling behaviour

(22)

Lajos Kollar

The main kinds of loss of stability of `centrally' loaded (geometrically perfect) structures

(5)

Symmetric stable bifurcation

(1)

Symmetric unstable bifurcation

(1)

Asymmetric bifurcation

(1)

The degenerating case of the symmetric bifurcation

(1)

General remarks

(1)

The imperfection sensitivity of the structures

(4)

Loss of stability with a limit point (divergence of equilibrium; snapping through)

(2)

The influence of plasticity

(3)

Some practical points of view for estimating the post-critical behaviour

(4)

Evaluation of buckling experiments by the generalized Southwell plot

(3)

Summation theorems concerning critical loads of bifurcation

(36)

Tibor Tarnai

On the summation theorems

(3)

The Southwell theorem

(4)

Dunkerley type theorems and formulae

(26)

The Dunkerley theorem

(5)

The Foppl-Papkovich theorem

(8)

The Kollar conjecture

(8)

The Melan theorem

(4)

The Rankine formula

(1)

Conclusions

(3)

Interaction of different buckling modes in the post-buckling range

(29)

Lajos Kollar

Description of the phenomenon

(1)

The post-buckling load-bearing capacity of a braced column

(9)

The post-buckling load-bearing capacity of the ribbed plate

(5)

The post-buckling load-bearing behaviour of the box bar

(6)

The interaction of the buckling modes of cylindrical shells

(8)

Nonlinear shell equations

(2)

The eignefunctions of the cylindrical shell

(2)

The post-buckling behaviour of the shell

(4)

Stability of elastic structures with the aid of the catastrophe theory

(41)

Zsolt Gaspar

Statement of the problem

(1)

Definitions

(1)

Thom's theorem

(2)

The cuspoid catastrophes

(5)

The fold catastrophe

(1)

The cusp catastrophe

(2)

The swallowtail catastrophe

(1)

The butterfly catastrophe

(1)

The umbilic catastrophes

(3)

The elliptic umbilic

(2)

The hyperbolic umbilic

(1)

Imperfection-sensitivity of structures

100

(27)

What kind of catastrophes arise?

100

(1)

The method

100

(2)

The fold catastrophe

102

(4)

The cusp catstrophe

106

(9)

Higher order cuspoid catastrophes

115

(2)

The umbilic catastrophes

117

(10)

Probability of the instability

127

(2)

Buckling of frames

129

(58)

Josef Appeltauer

Lajos Kollar

General theory of frame buckling

129

(32)

Josef Appeltauer

Description of the phenomena

129

(1)

Mechanical models describing the various kinds of loss of stability

130

(5)

Bifurcation

135

(10)

Divergence

145

(8)

Snapping through

153

(2)

Practical applications

155

(6)

Conclusions

161

(1)

Approximate stability analysis of frames by the buckling analysis of the individual columns

161

(26)

Lajos Kollar

Basic principles of the method

161

(6)

Stability investigation of braced frames

167

(8)

Stability investigation of unbraced frames

175

(12)

Application of the sandwich theory in the stability analysis of structures

187

(55)

Istvan Hegedus

Laszlo P. Kollar

Assumptions, definitions

188

(2)

Sandwich beam with thin faces (Timoshenko-beam)

190

(5)

Sandwich beam with thick faces

195

(9)

Incompressible core

195

(4)

Compressible core

199

(5)

Models based on the sandwich beam with thick faces

204

(13)

Beams with flexural deformations only (S = ∞ or S = 0)

205

(1)

Beams with shear deformations only (D0 = ∞ and D0 = 0)

205

(2)

Sandwich beam with thin faces (D0 = 0)

207

(1)

Beam on an elastic foundation which restrains the rotations-Csonka-beam (D0 = ∞)

207

(2)

Sandwich beam with thick faces on an elastic foundation which restrains the rotations

209

(1)

Sandwich beam with thick faces on an elastic foundation which restrains the displacements

209

(1)

Isotropic sandwich plate

210

(3)

Orthotropic sandwich plate

213

(2)

Orthotropic shallow sandwich shell

215

(1)

Multi-layered sandwich cantilever beam

216

(1)

Approximate expressions for the calculation of the buckling load

217

(6)

Parallel and serial connections of beams (Foppl-Papkovich's and Southwell's theorem)

217

(4)

Cantiliver beams on elastic foundation which restrains the rotation

221

(1)

Multi-layered sandwich beam

222

(1)

Some applications of the sandwich theory in structural engineering

223

(19)

Discrete structures with regular built-up

223

(1)

Exact analysis of discrete structures using the theory of difference equations

223

(3)

Trusses

226

(4)

Laced (Vierendeel) column

230

(5)

Frames and shear walls

235

(3)

Combined torsional and in-plane buckling of multistorey buildings

238

(4)

Bracing of building structures against buckling

242

(34)

Lajos Kollar

Karoly Zalka

Basic principles

242

(1)

The necessary stiffiness of the bracing core

243

(13)

The bending stiffness of the bracing core

243

(2)

The torsional stiffness of the bracing core

245

(6)

Generalization of the results. Spatial behaviour

251

(5)

The necessary strength of the bracing core

256

(2)

Bracing system of shear walls and cores

258

(10)

The equivalent column

259

(3)

Uniformly distributed load over the height

262

(3)

Concentrated load at top floor level

265

(1)

Supplementary remarks

265

(3)

Stability analysis of the columns of the building

268

(8)

Sway critical loads

269

(3)

Sway versus nonsway critical loads

272

(1)

Conclusions

273

(3)

Buckling of arches and rings

276

(63)

Lajos Kollar

Buckling of bars with curved axis (arches) in their own plane

277

(44)

Buckling of rings and arches with circular axis

277

(8)

Arches with noncircular axes

285

(6)

Snapping through of flat arches

291

(8)

Buckling of arches with thin-walled, open cross sections

299

(9)

Buckling of arches with hangers or struts

308

(13)

Lateral buckling of rings and arches

321

(18)

Lateral buckling of centrally compressed arches with circular axis

321

(6)

Buckling of centrally compressed arches with axes other than circular

327

(2)

Lateral buckling of centrally compressed arches loaded by hangers or struts

329

(6)

Post-critical behaviour of laterally buckling arches

335

(1)

Lateral buckling of arches bent in the plane of the arch

335

(4)

Special stability problems of beams and trusses

339

(19)

Lajos Kollar

Problems of lateral stability of beams

339

(14)

The governing differential equations of lateral buckling and some conclusions

340

(4)

The energy method for determining the critical loads of suspended beams

344

(5)

Determination of the critical load by the summation theorem

349

(4)

Lateral stability of the nodes of plane trusses

353

(3)

Snapping through of shell-beams in the plane of bending

356

(2)

Stability of viscoelastic structures

358

(31)

Gyorgy Ijjas

Introduction

358

(1)

General remarks

358

(1)

Material properties

358

(1)

Various kinds of creep buckling

359

(4)

Structures made of fluid-type material, exhibiting symmetric unstable post-critical behaviour

363

(8)

Description of the phenomenon

363

(2)

The pseudo-equilibrium surface

365

(3)

The total potential energy

368

(3)

Supplementary remarks

371

(1)

Structures made of solid-type material, exhibiting symmetric unstable post-critical behaviour

371

(5)

Description of the phenomenon

371

(2)

The pseudo-equilibrium surface

373

(2)

The total potential energy

375

(1)

Supplementary remarks

376

(1)

Structures made of Dischinger-type material, exhibiting symmetric unstable post-critical behaviour

376

(4)

Description of the phenomenon

376

(2)

The pseudo-equilibrium surface

378

(1)

The total potential energy

379

(1)

Supplementary remarks

380

(1)

Structures made of fluid-type material, exhibiting symmetric stable post-critical behaviour

380

(4)

Description of the phenomenon

380

(2)

The pseudo-equilibrium surface

382

(1)

The total potential energy

382

(1)

Supplementary remarks

383

(1)

Structures made of solid-type material, exhibiting symmetric stable post-critical behaviour

384

(2)

Description of the phenomenon

384

(1)

The pseudo-equilibrium surface

384

(2)

The total potential energy

386

(1)

Creep of the dashpot

386

(1)

Two remarks about the problems appearing in the literature

387

(2)

Importance of the degree of approximations

387

(1)

Importance of the elastic behaviour

388

(1)

Buckling under dynamic loading

389

(9)

Lajos Kollar

Description of the dynamic loading process

389

(2)

Buckling of an initially curved bar under a falling load

391

(4)

Generalizations

395

(3)

Stability paradoxes

398

(17)

Lajos Kollar

Structures behaving differently from common engineering sense

398

(9)

Instability of blown-up rubber balloons

398

(4)

The buckling length in the case of a load of varying direction, passing through a fixed point

402

(1)

Instability of a bar in tension

403

(1)

Structures with infinitely great critical forces

404

(1)

Structures with abruptly changing rigidity characteristics

405

(2)

Destabilizing by stiffening and stabilizing by softening

407

(8)

Stabilizing by increasing the length

407

(3)

The destabilizing effect of an additional support

410

(1)

Paradoxes with torsional buckling

411

(1)

The destabilizing effect of damping in the case of nonconservative forces

412

(3)

References

415

(28)

Author Index

443

(6)

Subject Index

449

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Structural Stability in Engineering Practice

Summary

Table of Contents

Supplemental Materials