Matrix Methods of Structural Analysis

Preface to the Second EditionChapter 1. Introduction 1.1. The Value of a Systematic Approach 1.2. A Structure as an Assembly of Elements 1.3. Boundaries and Nodes 1.4. Linearity and Superposition 1.5. How Analytical Methods are Built upChapter 2. The Main Variables and Relationships 2.1. Nodal VariablesâEURLoads and Displacements 2.2. Element VariablesâEURStress-Resultants and Deformations 2.3. Equilibrium and Compatibility Conditions: Virtual Work 2.4. Coordinate TransformationsChapter 3. The Elastic Properties of Single Elements (a) Line Elements 3.1. Stress-Resultant and Deformation Vectors for a General Plane Member 3.2. The Straight Uniform Beam: Two Dimensional Analysis 3.3. The Straight Uniform Beam: Three-Dimensional Analysis 3.4. Straight Uniform Members with Pinned Ends 3.5. Straight Uniform Members in Plane Grillages 3.6. Curved and Non-Uniform Plane Members 3.7. Segmented Members 3.8. The Effect of Joints of Finite Size 3.9. Flexible Joint Connections 3.10. The Calculation of Equivalent Joint Loads 3.11. The Replacement of Distributed MassChapter 4. The Elastic Properties of Single Elements (b) An Introduction to Area and Volume Elements 4.1. The Basic Equations of Plane Stress 4.2. The Simple Triangular Element 4.3. The Simple Rectangular Element 4.4. Body Forces and Initial Strains 4.5. Transformation of Axes 4.6. The Replacement of Distributed Mass 4.7. More Complex ElementsChapter 5. The Equilibrium or Displacement Method 5.1. The Analysis of a Plane Pin-Jointed Truss 5.2. The Analysis of a Plane Rigid-Jointed Truss 5.3. The Assembly of the Stiffness Matrix of a Structure 5.4. Settlement and Partial Restraint 5.5. Dynamic ProblemsChapter 6. The Equilibrium Equations of a Complete Structure 6.1. Setting up the Equilibrium Equations 6.2. An Alternative Form of the Equilibrium Method 6.3. The Analysis of Determinate Structures 6.4. Determinate Structures with Rigid Joints: Tree StructuresChapter 7. Plastic Analysis and Design 7.1. Ideal Rigid-Plastic Behavior 7.2. Setting up the Equilibrium Equations 7.3. Plastic Collapse under Proportional Loading 7.4. Duality and the Mechanism Approach 7.5. The Shakedown Problem 7.6. Minimum-Weight Design for Single and Multiple Loadings 7.7. A Compact Procedure for Finding the Collapse Load FactorChapter 8. The Compatibility or Force Method 8.1. The Analysis of a Pin-Jointed Truss 8.2. The Analysis of a Rigid-Jointed Frame 8.3. Applications to More Complex Skeletal Structures 8.4. Axial Forces in Rigid-Jointed Frames 8.5. An Algebraic Procedure for Transforming the Equilibrium EquationsChapter 9. Transfer Matrices 9.1. Transfer Matrices for Single Structural Elements 9.1.1. The Equations for a Line Element 9.1.2. The Equations for a Joint 9.2. An Example of the Use of Transfer Matrices 9.3. A Problem Involving Intermediate Supports 9.4. A Comparison Between the Transfer Matrix and Equilibrium Methods 9.5. Rigid Supports and Flexible Joints 9.6. Vibration ProblemsChapter 10. The Analysis of Non-linear Structures 10.1. Stiffness Matrices for a Straight 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. Non-linear Problems Associated with Plastic Collapse Analysis 10.6. Elastic-Plastic AnalysisChapter 11. Problems of Size and Accuracy 11.1. The Solution of Large Sets of Load/Displacement Equations 11.2. The Use of Sub-Structures 11.3. Numerical Checks for Computer Analyses 11.4. Ill-Conditioning in Structural AnalysisA Summary of the Main EquationsAppendix. Vectors and Matrices A.1. Vectors A.2. Matrices A.3. Matrix Inversion A.4.