Britvec / Irvine / Hartnett The Stability of Elastic Systems

Pergamon Unified Engineering Series
1. Auflage 2014
ISBN: 978-1-4831-8517-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 480 Seiten, Web PDF

The Stability of Elastic Systems presents some of the most important aspects of the stability and the non-linear behavior at finite deformations of several types of structural elastic systems, which are important for a more precise understanding of the static performance of such systems. This book is divided into eight chapters that aim to complete parts of classical, eigenvalue, theories of buckling and to demonstrate the important role played by finite deformations in the theoretical analyses of stability. Other chapters discuss the properties of prismatic members and the post-buckling behavior of plane frameworks. A chapter describes the elastic buckling and stability of statically determinate space frameworks. The remaining chapters cover the elastic buckling of statically indeterminate pin-jointed systems and space frameworks. These chapters also examine the non-conservative aspects of structural systems. This book will be of great value to practicing engineers and students.

Autoren/Hrsg.

Britvec, S. J.

Irvine, Thomas F.

Hartnett, James P.

Inhaltsverzeichnis

1;Front Cover;1
2;The Stability of
Elastic Systems;4
3;Copyright Page;5
4;Table of Contents;8
5;Preface;12
6;Introduction;14
7;Chapter
1. Principal Forms of Equilibrium Paths and their Stability;20
7.1;1-1 CONSERVATIVE ELASTIC SYSTEMS
– GENERALIZED COORDINATES;21
7.2;1-2 THE TOTAL POTENTIAL ENERGY FUNCTION
– PRINCIPAL ORTHOGONAL COORDINATES OF DEFORMATION;45
7.3;1-3 EQUILIBRIUM STATES AND STABILITY – CRITICAL STATES CRITICAL AND NON
– CRITICAL COORDINATES;55
7.4;1-4 BRANCHING OF EQUILIBRIUM PATHS AT A CRITICAL POINT –
THE BUCKLING BEHAVIOR;63
7.5;1-5 STABILITY OF EQUILIBRIUM NEAR A SIMPLE
BRANCHING POINT;72
7.6;1-6 SYMMETRY IN THE CRITICAL COORDINATE AT A SIMPLE
BRANCHING POINT;77
7.7;1-7 PERFECT ELASTIC SYSTEMS
DEPENDING ON SEVERAL LOAD PARAMETERS–EQUILIBRIUM HYPER-SURFACES;81
7.8;1-8 ELASTIC STRUCTURAL SYSTEMS WITH NON-ORTHOGONAL GENERALIZED COORDINATES
– SOLUTION OF THE NON-LINEAR EQUILIBRIUM EQUATIONS AT A BRANCHING POINT;102
7.9;1-9 SEVERAL CRITICAL COORDINATES
– BRANCHING POINTS OF SYSTEMS WITH SEVERAL DEGREES OF FREEDOM;109
7.10;1-10 SYMMETRICAL ELASTIC STRUCTURAL SYSTEMS –
COMPLETE SYMMETRY;117
7.11;1-11 BUCKLING OF GEOMETRICALLY IMPERFECT ELASTICSY STEMS
– EQUILIBRIUM PATHS OF IMPERFECT SYSTEMS;124
7.12;1-12 EQUILIBRIUM PATHS OF IMPERFECT SYMMETRICAL SYSTEMS;131
7.13;1-13 ADJACENT BRANCHING POINTS
– COUPLED MODES OF ELASTIC BUCKLING;140
8;Chapter
2. Analysis of Prismatic Members as Constitutive Elements of a System;156
8.1;2-1 BUCKLING OF COMPRESSIVE MEMBERS IN A PLANE
– FLEXURAL ELASTICA;157
8.2;2-2 TRANSVERSE DEFORMATIONS;166
8.3;2-3 GEOMETRICAL COMPATIBILITY;166
8.4;2-4 COORDINATES OF DEFORMATION OF COMPRESSIVE MEMBERS;167
8.5;2-5 INTERNAL FORCES;168
8.6;2-6 INTERNAL ENERGY;169
8.7;2-7 SUMMARY OF BASIC EQUATIONS FOR COMPRESSIVE MEMBERS
– GENERALIZED EQUILIBRIUM EQUATIONS;170
8.8;2-8 INFLECTIONAL ELASTICA OF TENSILE MEMBERS;171
8.9;2-9 SUMMARY OF BASIC EQUATIONS FOR INFLECTIONAL
TENSILE MEMBERS;178
8.10;2-10 NON-INFLECTIONAL ELASTICA OF TENSILE MEMBERS
NON-SYMMETRICAL CASES;179
8.11;2-11 SUMMARY OF BASIC EQUATIONS FOR NON-SYMMETRICAL,
NON-INFLECTIONAL TENSILE MEMBERS;187
8.12;2-12 SUMMARY OF BASIC EQUATIONS FOR SYMMETRICAL
TENSILE MEMBERS;187
8.13;2-13 CATEGORIES OF PRACTICAL DEFORMATIONS;188
8.14;2-14 GENERALIZED EQUILIBRIUM EQUATIONS FOR SINGLE MEMBERS
– BUCKLING OF PRISMATIC BARS;188
8.15;2-15 THE FIRST-ORDER THEORY;203
8.16;2-16 PIN-ENDED MEMBERS OR COLUMNS;206
9;Chapter
3. Elastic Buckling and Stability of Statically Determinate Plane Frameworks;215
9.1;3-1 GENERAL FORMS OF THE FORCE-DISPLACEMENT
RELATIONSHIPS FOR PERFECT MEMBERS;216
9.2;3-2 ELASTIC BUCKLING OF ISOSTATIC FRAMES IN EQUILIBRIUM
GENERALTHEORY;216
9.3;3-3 ELASTIC STABILITY IN STATICAL EQUILIBRIUM;224
9.4;3-4 APPLICATIONS OF THE THEORY
– TESTS ON MODEL FRAMES;225
9.5;3-5 EXPERIMENTAL DETERMINATION OF CRITICAL STATES –
THE SOUTHWELL PLOT;250
9.6;3-6 THE ENERGY METHOD
– THE TOTAL POTENTIAL ENERGY SURFACES OF STATICALLY DETERMINATE FRAMEWORKS;253
9.7;3-7 GRAPHICAL SOLUTION;266
10;Chapter 4. Elastic Buckling of Continuous
Rigidly-jointed Plane Frameworks;268
10.1;4-1 CRITICAL STATES-DISTINCTIONS BETWEEN BRACED
AND UNBRACED FRAMES;268
10.2;4-2 CRITICAL LOADING SYSTEMS OF UNBRACED FRAMES;274
10.3;4-3 GEOMETRICAL COMPATIBILITY CONDITIONS OF UNBRACED FRAMES;275
10.4;4-4 CONTINUITY CONDITIONS OF UNBRACED FRAMES;277
10.5;4-5 STATICAL EQUILIBRIUM OF THE UNBUCKLED FRAME;278
10.6;4-6 STATICAL EQUILIBRIUM OF THE BUCKLED FRAME;279
10.7;4-7 THE NON-LINEAR EQUATIONS OF POST-CRITICAL
EQUILIBRIUM STATES;283
10.8;4-8 SOLUTION OF THE NON-LINEAR EQUATIONS OF POST
– CRITICAL EQUILIBRIUM STATES;285
11;Chapter
5. Elastic Buckling of Rigidly-jointed Plane Trusses;288
11.1;5-1 THE FIRST-ORDER THEORY -STATICAL EQUILIBRIUM OF
THE UNBUCKLED TRUSS;288
11.2;5-2 STATICAL EQUILIBRIUM OF THE BUCKLED TRUSS;289
11.3;5-3 THE INITIAL BUCKLING CONDITION AND THE POST-CRITICAL
EQUILIBRIUM STATES;293
11.4;5-4 TESTS ON MODEL FRAMES;303
11.5;5-5 AN ALTERNATIVE SOLUTION OF THE NON-LINEAR
EQUILIBRIUM EQUATIONS;308
11.6;5-6 AXIALLY-HYPERSTATIC RIGIDLY-JOINTED BRACED FRAMEWORKS
– COMPATIBILITY CONDITIONS OF FLEXURAL CONTRACTIONS OF THE MEMBERS;322
12;Chapter
6. Elastic Buckling and Stability of Statically Determinate Space Frameworks;331
12.1;6-1 GENERAL FORCE-DISPLACEMENT EQUILIBRIUM PATHS
FOR PERFECT MEMBERS;331
12.2;6-2 GEOMETRICAL COMPATIBILITY CONDITIONS IN SPACE;332
12.3;6-3 CRITICAL EQUILIBRIUM STATES;336
12.4;6-4 STATICAL EQUILIBRIUM OF THE BUCKLED FRAMEWORK;337
12.5;6-5 THE POST-CRITICAL EQUILIBRIUM PATHS;337
12.6;6-6 STABILITY OF CRITICAL EQUILIBRIUM STATES;338
12.7;6-7 MODEL ISOSTATIC SPACE FRAMES;339
12.8;6-8 TWO EXAMPLES OF STATICAL EQUILIBRIUM IN THE ELASTIC POST-BUCKLING
OF ISOSTATIC SPACE FRAMES;339
12.9;6-9 THE ENERGY METHOD-THE TOTAL POTENTIAL ENERGY SURFACES OF STATICALLY DETERMINATE SPACE FRAMEWORKS;347
13;Chapter
7. Elastic Buckling of Statically Indeterminate Pin-jointed Systems and Space Frameworks;348
13.1;7-1 FLEXURAL BUCKLING OF HYPERSTATIC
PIN-JOINTED FRAMEWORKS;348
13.2;7-2 ULTIMATE CRITICAL STATES;360
13.3;7-3 STATICAL DETERMINATION OF ULTIMATE CRITICAL LOADS;362
13.4;7-4
DETERMINATION OF ULTIMATE CRITICAL LOADS BY THE PRINCIPLE OF VIRTUAL WORK;372
13.5;7-5 ULTIMATE CRITICAL STATES IN THE CASE OF
SEVERAL LOAD PARAMETERS;375
13.6;7-6 ELEMENTS OF ELASTIC LIMIT-DESIGN;378
13.7;7-7 GEOMETRY AND KINEMATICS OF SPHERICAL RETICULATED
SHELLS AND SOME SPACE ELEMENTS;382
13.8;7-8 SOME THREE-DIMENSIONAL SYMMETRICAL ELEMENTS
AND THEIR COMBINATIONS;387
13.9;7-9 THE SNAP-THROUGH PROBLEM;390
13.10;7-10 DIMENSIONAL MODEL ANALYSIS OF THE ELASTIC STABILITY
OF STRUCTURES;395
13.11;7-11 GEOMETRICAL COMPATIBILITY CONDITIONS IN HYPERSTATIC
SYSTEMS;399
13.12;7-12 EQUILIBRIUM OF HYPERSTATIC PIN-JOINTED SYSTEMS IN
POST-BUCKLING;399
13.13;7-13 TEST OF A HYPERSTATIC MODEL FRAME;400
13.14;7-14 THE TOTAL POTENTIAL ENERGY SURFACES OF HYPERSTATIC
FRAMEWORKS;405
14;Chapter
8. Non-conservative Aspects of Structural Systems;409
14.1;8-1 PLASTIC FLEXURAL BUCKLING OF COLUMNS AT FINITE
DEFORMATIONS–COLUMN MODEL;409
14.2;8-2 STATICAL EQUILIBRIUM OF THE BUCKLED COLUMN;412
14.3;8-3 INITIAL PLASTIC BUCKLING STRESS;413
14.4;8-4 PLASTIC POST-BUCKLING OF COLUMNS OR PIN-JOINTED
MEMBERS-POST-CRITICAL EQUILIBRIUM SURFACES;419
14.5;8-5 PLASTIC BUCKLING OF PIN-JOINTED STRUCTURAL SYSTEMS;422
14.6;8-6 BUCKLING OF IMPERFECTION-SENSITIVE STRUCTURES
UNDER DYNAMIC LOADING-EXISTING MODELS AND ESTIMATES;424
14.7;8-7 DYNAMIC BUCKLING OF RIGIDLY-JOINTED FRAMEWORKS
AND SIMILAR SYSTEMS UNDER STEP-LOADING;434
14.8;8-8 QUASI-STATIC CRITERIA;440
15;Appendix I;442
16;Appendix II:
Effect of Axial Extensibility on the Equilibrium Configurations of Elastic Bars;445
17;Appendix ..I: Buckling Characteristics of a Single Member of the Frame;447
18;Appendix IV:
Motion of the System Near a Critical State;450
19;Appendix V:
Developments of the More Accurate Solutions for Prismatic Members Under Large Axial forces in the Initial Stages of Plane Buckling;453
20;Appendix VI:
Prismatic Members Under Small Axial Forces in the Initial Stages of Plane Buckling;459
21;Appendix VII:
Two Exercises on Portal Frames;463
22;Referencestand Related Bibliography;468
23;Index;474