Structural Stability in Engineering Practice

by KOLLAR; LASZLO P

• ISBN13: 9780419237907
• ISBN10: 0419237909
• Edition: 1st
• Format: Hardcover
• Copyright: 1999-08-03
• Publisher: CRC Press

Summary

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.

Table of Contents

Preface	xi
Loss of stability and post-buckling behaviour	1	(22)
Lajos Kollar
The main kinds of loss of stability of `centrally' loaded (geometrically perfect) structures	2	(5)
Symmetric stable bifurcation	2	(1)
Symmetric unstable bifurcation	3	(1)
Asymmetric bifurcation	4	(1)
The degenerating case of the symmetric bifurcation	5	(1)
General remarks	6	(1)
The imperfection sensitivity of the structures	7	(4)
Loss of stability with a limit point (divergence of equilibrium; snapping through)	11	(2)
The influence of plasticity	13	(3)
Some practical points of view for estimating the post-critical behaviour	16	(4)
Evaluation of buckling experiments by the generalized Southwell plot	20	(3)
Summation theorems concerning critical loads of bifurcation	23	(36)
Tibor Tarnai
On the summation theorems	23	(3)
The Southwell theorem	26	(4)
Dunkerley type theorems and formulae	30	(26)
The Dunkerley theorem	30	(5)
The Foppl-Papkovich theorem	35	(8)
The Kollar conjecture	43	(8)
The Melan theorem	51	(4)
The Rankine formula	55	(1)
Conclusions	56	(3)
Interaction of different buckling modes in the post-buckling range	59	(29)
Lajos Kollar
Description of the phenomenon	59	(1)
The post-buckling load-bearing capacity of a braced column	60	(9)
The post-buckling load-bearing capacity of the ribbed plate	69	(5)
The post-buckling load-bearing behaviour of the box bar	74	(6)
The interaction of the buckling modes of cylindrical shells	80	(8)
Nonlinear shell equations	80	(2)
The eignefunctions of the cylindrical shell	82	(2)
The post-buckling behaviour of the shell	84	(4)
Stability of elastic structures with the aid of the catastrophe theory	88	(41)
Zsolt Gaspar
Statement of the problem	88	(1)
Definitions	89	(1)
Thom's theorem	90	(2)
The cuspoid catastrophes	92	(5)
The fold catastrophe	92	(1)
The cusp catastrophe	93	(2)
The swallowtail catastrophe	95	(1)
The butterfly catastrophe	96	(1)
The umbilic catastrophes	97	(3)
The elliptic umbilic	97	(2)
The hyperbolic umbilic	99	(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