Structural Theorems and Their Applications

PrefaceChapter 1. The Problems of Structural Analysis 1.1. Introduction 1.2. Basic Conditions 1.3. Exclusion of Gross Deformations 1.4. Statically Determinate and Indeterminate Structures 1.5. Choice of Variables 1.6. Direct and Indirect ApproachesChapter 2. Principles of Superposition 2.1. Introduction 2.2. Superposition of Force Systems 2.3. Superposition of Displacements 2.4. Superposition for Linear Elastic Structures 2.5. Symmetry and Skew-SymmetryChapter 3. Virtual Work and Energy Concepts 3.1. Introduction 3.2. Principle of Virtual Work 3.3. Virtual Work Transformations 3.4. Strain Energy 3.5. Complementary Energy 3.6. Total PotentialChapter 4. Indeterminate Structures by the Compatibility Method 4.1. Introduction 4.2. Truss with Single Redundancy 4.3. Truss with Several Redundancies 4.4. Proof of Engesser's Theorem of Compatibility 4.5. Lack of Fit 4.6. Castigliano's Theorem of Compatibility 4.7. Further Applications of Virtual WorkChapter 5. Calculation of Deflections 5.1. Introduction 5.2. Statically Determinate Truss 5.3. Statically Indeterminate Truss 5.4. First Theorem of Complementary Energy 5.5. Castigliano's Theorem (Part II) 5.6. Further ExamplesChapter 6. Indeterminate Structures by the Equilibrium Method 6.1. Introduction 6.2. Truss with Two Deformation Variables 6.3. Lack of Fit 6.4. Theorem of Minimum Potential Energy 6.5. Castigliano's Theorem (Part I) 6.6. Beams and FramesChapter 7. Reciprocal Theorems 7.1. Introduction 7.2. Proofs of Reciprocal Theorems 7.3. Influence Lines for Redundant Structures 7.4. Influence Lines by Model AnalysisChapter 8. Theorems of Plastic Analysis for Plane Frames 8.1. Introduction 8.2. Plastic and Incremental Collapse 8.3. Plastic Collapse Theorems 8.4. Upper and Lower Bounds on ¿c 8.5. Shake-Down and Incremental Collapse Theorems 8.6. Trial and Error Method for Determining ¿8Appendix A. Proof of Principle of Virtual Work for Plane FramesBibliographyRecommended Further ReadingIndex