Karnovsky / Lebed Advanced Methods of Structural Analysis

1. Auflage 2010
ISBN: 978-1-4419-1047-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 593 Seiten

Advanced Methods of Structural Analysis aims to help its readers navigate through the vast field of structural analysis. The book aims to help its readers master the numerous methods used in structural analysis by focusing on the principal concepts, as well as the advantages and disadvantages of each method. The end result is a guide to mastering the many intricacies of the plethora of methods of structural analysis. The book differentiates itself from other volumes in the field by focusing on the following: •Extended analysis of beams, trusses, frames, arches and cables •Extensive application of influence lines for analysis of structures •Simple and effective procedures for computation of deflections •Introduction to plastic analysis, stability, and free vibration analysis Authors Igor A. Karnovsky and Olga Lebed have crafted a must-read book for civil and structural engineers, as well as researches and students with an interest in perfecting structural analysis. Advanced Methods of Structural Analysis also offers numerous example problems, accompanied by detailed solutions and discussion of the results.

Autoren/Hrsg.

Karnovsky, Igor A.

Lebed, Olga

Inhaltsverzeichnis

1;Preface;6
2;Acknowledgments;10
3;Contents;12
4;Introduction;19
5;Part I Statically Determinate Structures;23
5.1;1 Kinematical Analysis of Structures;24
5.1.1;1.1 Classification of Structures by KinematicalViewpoint;24
5.1.2;1.2 Generation of Geometrically UnchangeableStructures;26
5.1.3;1.3 Analytical Criteria of the InstantaneouslyChangeable Structures;28
5.1.4;1.4 Degrees of Freedom;32
5.1.5;Problems;34
5.2;2 General Theory of Influence Lines;36
5.2.1;2.1 Analytical Method for Construction of InfluenceLines;36
5.2.1.1;2.1.1 Influence Lines for Reactions;37
5.2.1.1.1;2.1.1.1 Simply Supported Beam (Fig.2.1);37
5.2.1.1.2;2.1.1.2 Simply Supported Beam with Overhang (Fig.2.2);39
5.2.1.1.3;2.1.1.3 Cantilevered Beam (Fig.2.3);40
5.2.1.2;2.1.2 Influence Lines for Internal Forces;41
5.2.1.2.1;2.1.2.1 Bending Moment Mk;41
5.2.1.2.2;2.1.2.2 Influence Line Qk;43
5.2.1.2.3;2.1.2.3 Discussion;45
5.2.2;2.2 Application of Influence Lines for Fixed andMoving Loads;48
5.2.2.1;2.2.1 Fixed Loads;48
5.2.2.2;2.2.2 Moving Loads;51
5.2.3;2.3 Indirect Load Application;54
5.2.4;2.4 Combining of Fixed and Moving Load Approaches;56
5.2.5;2.5 Properties of Influence Lines;57
5.2.6;Problems;58
5.3;3 Multispan Beams and Trusses;60
5.3.1;3.1 Multispan Statically Determinate Beams;60
5.3.1.1;3.1.1 Generation of Multispan Statically Determinate Hinged Beams;60
5.3.1.2;3.1.2 Interaction Schemes and Load Path;61
5.3.1.3;3.1.3 Influence Lines for Multispan HingedBeams;63
5.3.1.4;3.1.4 Summary;66
5.3.2;3.2 The Generation of Statically Determinate Trusses;68
5.3.2.1;3.2.1 Simple Trusses;68
5.3.2.2;3.2.2 Compound Trusses;69
5.3.2.3;3.2.3 Complex Trusses;70
5.3.3;3.3 Simple Trusses;70
5.3.4;3.4 Trusses with Subdivided Panels;75
5.3.4.1;3.4.1 Main and Auxiliary Trusses and Load Path;76
5.3.4.2;3.4.2 Baltimore and Subdivided Warren Trusses;78
5.3.5;3.5 Special Types of Trusses;82
5.3.5.1;3.5.1 Three-Hinged Trusses;82
5.3.5.2;3.5.2 Trusses with a Hinged Chain;85
5.3.5.3;3.5.3 Complex Trusses;89
5.3.5.4;3.5.4 Summary;91
5.3.6;Problems;93
5.4;4 Three-Hinged Arches;98
5.4.1;4.1 Preliminary Remarks;98
5.4.1.1;4.1.1 Design Diagram of Three-Hinged Arch;98
5.4.1.2;4.1.2 Peculiarities of the Arches;99
5.4.1.3;4.1.3 Geometric Parameters of Circularand Parabolic Arches;100
5.4.2;4.2 Internal Forces;101
5.4.3;4.3 Influence Lines for Reactions and Internal Forces;107
5.4.3.1;4.3.1 Influence Lines for Reactions;109
5.4.3.2;4.3.2 Influence Lines for Internal Forces;109
5.4.3.2.1;4.3.2.1 Bending Moment;109
5.4.3.2.2;4.3.2.2 Shear Force;110
5.4.3.2.3;4.3.2.3 Axial Force;112
5.4.3.2.4;4.3.2.4 Properties of the Influence Lines for Internal Forces;113
5.4.3.3;4.3.3 Application of Influence Lines;113
5.4.4;4.4 Nil Point Method for Construction of InfluenceLines;115
5.4.4.1;4.4.1 Bending Moment;115
5.4.4.2;4.4.2 Shear Force;116
5.4.4.3;4.4.3 Axial Force;117
5.4.5;4.5 Special Types of Arches;118
5.4.5.1;4.5.1 Askew Arch;118
5.4.5.1.1;4.5.1.1 Reactions and Bending Moment at Section k;119
5.4.5.1.2;4.5.1.2 Influence Lines for Thrust and Bending Moment Mk.;120
5.4.5.2;4.5.2 Parabolic Arch with Complex Tie;121
5.4.5.2.1;4.5.2.1 Reactions and Bending Moment at Section k;122
5.4.5.2.2;4.5.2.2 Influence Lines for Thrust and Bending Moment at the Section k;123
5.4.6;Problems;124
5.5;5 Cables;129
5.5.1;5.1 Preliminary Remarks;129
5.5.1.1;5.1.1 Direct and Inverse Problems;130
5.5.1.2;5.1.2 Fundamental Relationships;131
5.5.2;5.2 Cable with Neglected Self-Weight;133
5.5.2.1;5.2.1 Cables Subjected to Concentrated Load;133
5.5.2.1.1;5.2.1.1 Direct Problem;134
5.5.2.1.2;5.2.1.2 Inverse Problem;135
5.5.2.2;5.2.2 Cable Subjected to Uniformly DistributedLoad;136
5.5.2.2.1;5.2.2.1 Direct Problem;136
5.5.2.2.2;5.2.2.2 Inverse Problem;137
5.5.3;5.3 Effect of Arbitrary Load on the Thrust and Sag;142
5.5.4;5.4 Cable with Self-Weight;145
5.5.4.1;5.4.1 Fundamental Relationships;145
5.5.4.2;5.4.2 Cable with Supports Located at the SameLevel;147
5.5.4.3;5.4.3 Cable with Supports Locatedon the Different Elevations;150
5.5.4.3.1;5.4.3.1 Saddle Point Within the Span;150
5.5.4.3.2;5.4.3.2 Saddle Point Outside of the Span;152
5.5.5;5.5 Comparison of Parabolic and Catenary Cables;155
5.5.6;5.6 Effect of Axial Stiffness;157
5.5.6.1;5.6.1 Elastic Cable with Concentrated Load;157
5.5.6.2;5.6.2 Elastic Cable with Uniformly DistributedLoad;159
5.5.7;Problems;160
5.6;6 Deflections of Elastic Structures;164
5.6.1;6.1 Introduction;164
5.6.2;6.2 Initial Parameters Method;166
5.6.3;6.3 Maxwell–Mohr Method;178
5.6.3.1;6.3.1 Deflections Due to Fixed Loads;178
5.6.3.2;6.3.2 Deflections Due to Change of Temperature;184
5.6.3.3;6.3.3 Summary;189
5.6.4;6.4 Displacement Due to Settlement of Supports and Errors of Fabrication;189
5.6.5;6.5 Graph Multiplication Method;195
5.6.6;6.6 Elastic Loads Method;204
5.6.7;6.7 Reciprocal Theorems;208
5.6.7.1;6.7.1 Theorem of Reciprocal Works(Betti Theorem);208
5.6.7.2;6.7.2 Theorem of Reciprocal Unit Displacements (Maxwell Theorem);209
5.6.7.3;6.7.3 Theorem of Reciprocal Unit Reactions (Rayleigh First Theorem);211
5.6.7.4;6.7.4 Theorem of Reciprocal Unit Displacements and Reactions (Rayleigh Second Theorem);212
5.6.7.5;6.7.5 Summary;212
5.6.8;Problems;214
6;Part II Statically Indeterminate Structures;228
6.1;7 The Force Method;229
6.1.1;7.1 Fundamental Idea of the Force Method;229
6.1.1.1;7.1.1 Degree of Redundancy, Primary Unknowns and Primary System;229
6.1.1.2;7.1.2 Compatibility Equation in Simplest Case;232
6.1.2;7.2 Canonical Equations of Force Method;235
6.1.2.1;7.2.1 The Concept of Unit Displacements;235
6.1.2.2;7.2.2 Calculation of Coefficients and Free Termsof Canonical Equations;237
6.1.3;7.3 Analysis of Statically Indeterminate Structures;240
6.1.3.1;7.3.1 Continuous Beams;240
6.1.3.2;7.3.2 Analysis of Statically IndeterminateFrames;242
6.1.3.3;7.3.3 Analysis of Statically IndeterminateTrusses;251
6.1.3.4;7.3.4 Analysis of Statically Indeterminate Arches;255
6.1.4;7.4 Computation of Deflections of Redundant Structures;261
6.1.5;7.5 Settlements of Supports;264
6.1.6;7.6 Temperature Changes;269
6.1.7;Problems;277
6.2;8 The Displacement Method;288
6.2.1;8.1 Fundamental Idea of the Displacement Method;288
6.2.1.1;8.1.1 Kinematical Indeterminacy;289
6.2.1.2;8.1.2 Primary System and Primary Unknowns;291
6.2.1.3;8.1.3 Compatibility Equation. Concept of UnitReaction;292
6.2.2;8.2 Canonical Equations of Displacement Method;293
6.2.2.1;8.2.1 Compatibility Equations in General Case;293
6.2.2.2;8.2.2 Calculation of Unit Reactions;294
6.2.2.3;8.2.3 Properties of Unit Reactions;296
6.2.2.4;8.2.4 Procedure for Analysis;297
6.2.3;8.3 Comparison of the Force and Displacement Methods;308
6.2.3.1;8.3.1 Properties of Canonical Equations;309
6.2.4;8.4 Sidesway Frames with Absolutely Rigid Crossbars;311
6.2.5;8.5 Special Types of Exposures;313
6.2.5.1;8.5.1 Settlements of Supports;313
6.2.5.2;8.5.2 Errors of Fabrication;317
6.2.6;8.6 Analysis of Symmetrical Structures;319
6.2.6.1;8.6.1 Symmetrical and Antisymmetrical Loading;319
6.2.6.2;8.6.2 Concept of Half-Structure;320
6.2.7;Problems;322
6.3;9 Mixed Method;330
6.3.1;9.1 Fundamental Idea of the Mixed Method;330
6.3.1.1;9.1.1 Mixed Indeterminacy and PrimaryUnknowns;330
6.3.1.2;9.1.2 Primary System;331
6.3.2;9.2 Canonical Equations of the Mixed Method;333
6.3.2.1;9.2.1 The Matter of Unit Coefficientsand Canonical Equations;333
6.3.2.2;9.2.2 Calculation of Coefficients and Free Terms;334
6.3.2.3;9.2.3 Computation of Internal Forces;335
6.3.3;Problems;336
6.4;10 Influence Lines Method;339
6.4.1;10.1 Construction of Influence Lines by the ForceMethod;339
6.4.1.1;10.1.1 Continuous Beams;341
6.4.1.2;10.1.2 Hingeless Nonuniform Arches;347
6.4.1.2.1;10.1.2.1 Unit Coefficients;350
6.4.1.2.2;10.1.2.2 Free Terms;350
6.4.1.2.3;10.1.2.3 Reactions of Support A;351
6.4.1.2.4;10.1.2.4 Bending Moment at Crown C;352
6.4.1.3;10.1.3 Statically Indeterminate Trusses;355
6.4.1.3.1;10.1.3.1 Influence Line for Primary Unknown X1;358
6.4.2;10.2 Construction of Influence Linesby the Displacement Method;360
6.4.2.1;10.2.1 Continuous Beams;362
6.4.2.1.1;10.2.1.1 Influence Line for Primary Unknown Z1;362
6.4.2.1.2;10.2.1.2 Influence Line for Bending Moment Mk;364
6.4.2.1.3;10.2.1.3 Influence Line for Shear Force Qk;365
6.4.2.2;10.2.2 Redundant Frames;369
6.4.3;10.3 Comparison of the Force and DisplacementsMethods;371
6.4.4;10.4 Kinematical Method for Construction of InfluenceLines;374
6.4.5;Problems;380
6.5;11 Matrix Stiffness Method;385
6.5.1;11.1 Basic Idea and Concepts;385
6.5.1.1;11.1.1 Finite Elements;386
6.5.1.2;11.1.2 Global and Local Coordinate Systems;386
6.5.1.3;11.1.3 Displacements of Joints and Degreesof Freedom;387
6.5.2;11.2 Ancillary Diagrams;388
6.5.2.1;11.2.1 Joint-Load (J-L) Diagram;388
6.5.2.2;11.2.2 Displacement-Load (Z-P) Diagram;392
6.5.2.3;11.2.3 Internal Forces-Deformation (S-e)Diagram;393
6.5.3;11.3 Initial Matrices;395
6.5.3.1;11.3.1 Vector of External Joint Loads;395
6.5.3.2;11.3.2 Vector of Internal Unknown Forces;396
6.5.4;11.4 Resolving Equations;397
6.5.4.1;11.4.1 Static Equations and Static Matrix;397
6.5.4.2;11.4.2 Geometrical Equations and DeformationMatrix;402
6.5.4.3;11.4.3 Physical Equations and Stiffness Matrix in Local Coordinates;403
6.5.5;11.5 Set of Formulas and Procedure for Analysis;406
6.5.5.1;11.5.1 Stiffness Matrix in Global Coordinates;406
6.5.5.2;11.5.2 Unknown Displacements and InternalForces;407
6.5.5.3;11.5.3 Matrix Procedures;408
6.5.6;11.6 Analysis of Continuous Beams;409
6.5.7;11.7 Analysis of Redundant Frames;420
6.5.8;11.8 Analysis of Statically Indeterminate Trusses;426
6.5.9;11.9 Summary;430
6.5.10;Problems;431
7;Part III Special Topics;437
7.1;12 Plastic Behavior of Structures;438
7.1.1;12.1 Idealized Stress–Strain Diagrams;438
7.1.2;12.2 Direct Method of Plastic Analysis;442
7.1.3;12.3 Fundamental Methods of Plastic Analysis;445
7.1.3.1;12.3.1 Kinematical Method;445
7.1.3.2;12.3.2 Static Method;445
7.1.4;12.4 Limit Plastic Analysis of Continuous Beams;447
7.1.4.1;12.4.1 Static Method;448
7.1.4.2;12.4.2 Kinematical Method;450
7.1.5;12.5 Limit Plastic Analysis of Frames;456
7.1.5.1;12.5.1 Beam Failure;457
7.1.5.2;12.5.2 Sidesway Failure;459
7.1.5.3;12.5.3 Combined Failure;459
7.1.5.4;12.5.4 Limit Combination Diagram;459
7.1.6;Problems;460
7.2;13 Stability of Elastic Systems;464
7.2.1;13.1 Fundamental Concepts;464
7.2.2;13.2 Stability of Structures with Finite Number Degreesof Freedom;468
7.2.2.1;13.2.1 Structures with One Degree of Freedom;468
7.2.2.2;13.2.2 Structures with Two or More Degreesof Freedom;473
7.2.3;13.3 Stability of Columns with Rigid and ElasticSupports;476
7.2.3.1;13.3.1 The Double Integration Method;476
7.2.3.1.1;13.3.1.1 Uniform Clamped-Free Column;476
7.2.3.1.2;13.3.1.2 Uniform Columns with Elastic Supports;478
7.2.3.2;13.3.2 Initial Parameters Method;481
7.2.4;13.4 Stability of Continuous Beams and Frames;486
7.2.4.1;13.4.1 Unit Reactions of the Beam-Columns;486
7.2.4.2;13.4.2 Displacement Method;488
7.2.4.3;13.4.3 Modified Approach of the DisplacementMethod;496
7.2.5;13.5 Stability of Arches;498
7.2.5.1;13.5.1 Circular Arches Under Hydrostatic Load;499
7.2.5.2;13.5.2 Complex Arched Structure:Arch with Elastic Supports;505
7.2.6;13.6 Compressed Rods with Lateral Loading;506
7.2.6.1;13.6.1 Double Integration Method;507
7.2.6.2;13.6.2 Initial Parameters Method;509
7.2.6.3;13.6.3 P-Delta Analysis of the Frames;514
7.2.6.4;13.6.4 Graph Multiplication Methodfor Beam-Columns;517
7.2.6.4.1;13.6.4.1 Simply Supported Beam-Column;518
7.2.6.4.2;13.6.4.2 Fixed-Free Beam-Column;518
7.2.7;Problems;519
7.3;14 Dynamics of Elastic Systems;527
7.3.1;14.1 Fundamental Concepts;527
7.3.1.1;14.1.1 Kinematics of Vibrating Processes;527
7.3.1.2;14.1.2 Forces Which Arise at Vibrations;527
7.3.1.3;14.1.3 Degrees of Freedom;529
7.3.1.4;14.1.4 Purpose of Structural Dynamics;533
7.3.1.5;14.1.5 Assumptions;533
7.3.2;14.2 Free Vibrations of Systems with Finite Number Degrees of Freedom: Force Method;534
7.3.2.1;14.2.1 Differential Equations of Free Vibration in Displacements;534
7.3.2.2;14.2.2 Frequency Equation;535
7.3.2.3;14.2.3 Mode Shapes Vibration and Modal Matrix;536
7.3.3;14.3 Free Vibrations of Systems with Finite Number Degrees of Freedom: Displacement Method;544
7.3.3.1;14.3.1 Differential Equations of Free Vibrationin Reactions;544
7.3.3.2;14.3.2 Frequency Equation;546
7.3.3.3;14.3.3 Mode Shape Vibrations and Modal Matrix;546
7.3.3.4;14.3.4 Comparison of the Force and DisplacementMethods;552
7.3.4;14.4 Free Vibrations of One-Span Beams with Uniformly Distributed Mass;552
7.3.4.1;14.4.1 Differential Equation of Transversal Vibration of the Beam;554
7.3.4.2;14.4.2 Fourier Method;555
7.3.4.3;14.4.3 Krylov–Duncan Method;557
7.3.5;Problems;560
8;Bibliography;600
9;Index;602