Neal Structural Theorems and Their Applications

The Commonwealth and International Library: Structures and Solid Body Mechanics Division
1. Auflage 2013
ISBN: 978-1-4831-3902-9
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 208 Seiten, Web PDF

Structural Theorems and Their Applications is an account of the various structural theorems and their applications. Topics covered range from the principles of superposition to virtual work and energy concepts, calculation of deflections, and analysis of indeterminate structures using the compatibility and equilibrium methods. Reciprocal theorems and theorems of plastic analysis for plane frames are also discussed. This book is comprised of eight chapters and begins with an overview of the problems of structural analysis and the importance of the principle of virtual work in this regard, followed by an analysis of the principles of superposition. The next chapter is devoted to virtual work and energy concepts such as strain energy and complementary energy. The principle of virtual work is used in the subsequent chapters as the basis for all of the indirect methods of structural analysis described in the text, including the analysis of indeterminate structures using the compatibility method and the equilibrium method. The principle of virtual work is also used to prove the reciprocal theorems and to establish the various theorems of plastic and incremental collapse for framed structures. This monograph will be of interest to mechanical and structural engineers.

Autoren/Hrsg.

Neal, B. G.

Inhaltsverzeichnis

1;Front Cover;1
2;Structural Theorems and their Applications;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;9
6;CHAPTER 1. THE PROBLEMS OF STRUCTURAL ANALYSIS;12
6.1;1.1. Introduction;12
6.2;1.2. Basic conditions;13
6.3;1.3. Exclusion of gross deformations;15
6.4;1.4. Statically determinate and indeterminate structures;19
6.5;1.5. Choice of variables;21
6.6;1.6. Direct and indirect approaches;25
7;CHAPTER 2. PRINCIPLES OF SUPERPOSITION;27
7.1;2.1. Introduction;27
7.2;2.2. Superposition of force systems;27
7.3;2.3. Superposition of displacements;33
7.4;2.4. Superposition for linear elastic structures;36
7.5;2.5. Symmetry and skew-symmetry;40
8;CHAPTER 3. VIRTUAL WORK AND ENERGY CONCEPTS;47
8.1;3.1. Introduction;47
8.2;3.2. Principle of Virtual Work;48
8.3;3.3. Virtual Work transformations;53
8.4;3.4. Strain energy;61
8.5;3.5. Complementary energy;65
8.6;3.6. Total potential;68
9;CHAPTER 4. INDETERMINATE STRUCTURES BY THE COMPATIBILITY METHOD;69
9.1;4.1. Introduction;69
9.2;4.2. Truss with single redundancy;70
9.3;4.3. Truss with several redundancies;77
9.4;4.4. Proof of Engesser's Theorem of Compatibility;82
9.5;4.5. Lack of fit;85
9.6;4.6. Castigliano's Theorem of Compatibility;88
9.7;4.7. Further applications of Virtual Work;90
10;CHAPTER 5. CALCULATION OF DEFLECTIONS;104
10.1;5.1. Introduction;104
10.2;5.2. Statically determinate truss;105
10.3;5.3. Statically indeterminate truss;108
10.4;5.4. First Theorem of Complementary Energy;112
10.5;5.5. Castigliano's Theorem (Part II);113
10.6;5.6. Further examples;115
11;CHAPTER 6. INDETERMINATE STRUCTURES BY THE EQUILIBRIUM METHOD;124
11.1;6.1. Introduction;124
11.2;6.2. Truss with two deformation variables;125
11.3;6.3. Lack of fit;134
11.4;6.4. Theorem of Minimum Potential Energy;136
11.5;6.5. Castigliano's Theorem (Part I);142
11.6;6.6. Beams and frames;143
12;CHAPTER 7. RECIPROCAL THEOREMS;152
12.1;7.1. Introduction;152
12.2;7.2. Proofs of reciprocal theorems;153
12.3;7.3. Influence lines for redundant structures;157
12.4;7.4. Influence lines by model analysis;161
13;CHAPTER 8. THEOREMS OF PLASTIC ANALYSIS FOR PLANE FRAMES;164
13.1;8.1. Introduction;164
13.2;8.2. Plastic and incremental collapse;166
13.3;8.3. Plastic collapse theorems;175
13.4;8.4. Upper and lower bounds on .c;180
13.5;8.5. Shake-down and incremental collapse theorems;183
13.6;8.6. Trial and error method for determining .s;189
14;APPENDIX A. PROOF OF PRINCIPLE OF VIRTUAL WORK FOR PLANE FRAMES;194
15;BIBLIOGRAPHY;202
16;RECOMMENDED FURTHER READING;205
17;INDEX;206