Matrix Methods of Structural Analysis

PrefaceChapter 1. Introduction 1.1. The Aim of Matrix Methods 1.2. Linearity 1.3. Superposition 1.4. Methods of Structural AnalysisChapter 2. Vectors and Matrices 2.1. Vectors 2.2. Matrices 2.3. Matrix Inversion 2.4. Coordinate Transformations 2.5. The Principal Axes Problem 2.6. The Solution of Simultaneous Equations and the Inversion of Matrices 2.7. The Linear Programming ProblemChapter 3. Basic Relationships and Definitions 3.1. Notation for Loads and Displacements 3.2. A Note on Sign Conventions 3.3. Stiffness and Flexibility Matrices 3.4. Equilibrium and Compatibility Conditions: Virtual WorkChapter 4. The Equilibrium Method 4.1. The Analysis of a Plane Pin-Jointed Truss 4.2. The Analysis of a Plane Rigid-Jointed Truss 4.3. The Assembly of the Stiffness Matrix of a Structure 4.4. Stiffness Matrices for a Straight Uniform Member in a Space Structure 4.5. The Analysis of Plane Grillages 4.6. The Analysis of Pin-Jointed Space Trusses 4.7. Pin-Joints in Rigid-Jointed Structures 4.8. Temperature Stresses and Lack of Fit 4.9. Dynamic ProblemsChapter 5. Stiffness, Flexibility and Equilibrium Matrices for Single Members 5.1. Equilibrium Equations and Rigid-Body Displacements 5.2. Products of Equilibrium Matrices 5.3. Flexibility and Stiffness Matrices for a General Linear Member 5.4. Coordinate Transformations of Flexibility and Equilibrium Matrices 5.5. Members Formed From Elements Connected in Series 5.6. The Effect of Joints of Finite Size 5.7. Semi-Rigid Joint ConnectionsChapter 6. Connection Matrices and Determinate Systems 6.1. Formulation of the Equilibrium Method Using Connection Matrices 6.2. an Alternative Formulation of the Equilibrium Method 6.3. The Analysis of Determinate Structures 6.4. Determinate Structures with Rigid Joints: Tree StructuresChapter 7. The Compatibility Method 7.1. The Analysis of a Pinpointed Truss 7.2. The Analysis of a Rigid-Jointed Frame 7.3. General Features of the Compatibility Method 7.4. Axial Forces in Rigid-Jointed Frames 7.5. A Derivation of the Compatibility Equations by Virtual Work 7.6. Combinations of Release Systems 7.7. The Collapse Load of a Rigid-Plastic StructureChapter 8. Transfer Matrices 8.1. The Transfer Matrix of a Single Member 8.2. an Example of the Use of Transfer Matrices 8.3. The Effect of Intermediate Supports 8.4. a Comparison of the Transfer Matrix Method and the Equilibrium Method 8.5. Rigid Supports and Flexible Joints 8.6. The Application of Transfer Matrices to Vibration ProblemsChapter 9. Computational Problems 9.1. Single and Repetitive Problems 9.2. Ill-Conditioning in Matrix Processes 9.3. Numerical Checks in Matrix Processes 9.4. Operations on Banded Matrices 9.5. The Use of Sub-StructuresChapter 10. The Analysis of Non-linear Structures 10.1. Stiffness Matrices for a Uniform Member with Axial Thrust 10.2. The Determination of Elastic Critical Loads 10.3. a General Method for Analyzing Non-linear Structures 10.4. The Analysis of Guyed Masts 10.5. Some Problems of Collapse Analysis