Matrix Structural Analysis

Preface

Chapter One Matrix Algebra

1.1 Introduction

1.2 Definitions

1.3 Matrix Algebra Manipulation

1.4 Simultaneous Linear Algebraic Equations

1.5 Supplementary Problems

1.6 Suggested Computer Exercises

Chapter Two Fundamental Concepts and Principles

2.1 Introduction

2.2 Generalized Forces and Displacements

2.3 Structural Behavior

2.4 Structural System and Its Constituent Elements

2.5 Energy Theorems in Structural Analysis

2.6 Basic Thermo-Elastic Relations

2.7 Strain and Complementary Strain Energies

2.8 Principles of Superposition

2.9 Reciprocal Theorems

2.10 Supplementary Problems

Chapter Three Direct Stiffness Matrix Method

3.1 Introduction

3.2 General Discussion

3.3 Aggregate and Element Stiffness Matrices

3.4 Sign Convention

3.5 Axial Rod Element Stiffness Matrix

3.6 Coordinate Transformation Matrix

3.7 Linear Spring Stiffness Matrix

3.8 Torsional Rod and Torsional Spring Stiffness Matrices

3.9 Rectilinear Beam Element Stiffness Matrix

3.10 Special Cases for the Rectilinear Beam Element

3.11 Curved Beam Element—Stiffness Matrix

3.12 Structures with Distributed Loads

3.13 Structures with Thermal Loads

3.14 Supplementary Problems

3.15 Suggested Computer Exercises

Chapter Four Element Stiffness Matrices of Lifting Surface Type Structures

4.1 Introduction

4.2 Spar or Rib Element Stiffness Matrix

4.3 Rectangular Shear Panel Element Stiffness Matrix

4.4 Trapezium Shear Panel Element Stiffness Matrix

4.5 Triangular Membrane Element Stiffness Matrix

4.6 Rectangular Membrane Element Stiffness Matrix

4.7 Supplementary Problems

Chapter Five Matrix Force Method

5.1 Introduction

5.2 General Theory of the Force Method

5.3 Analysis of Truss-Structures by the Force Matrix Method

5.4 Analysis of Rigid Frame and Beam Structures by the Force Matrix Method

5.5 Supplementary Problems

Chapter Six Analysis of Nonlinear Truss-Structures by the Stiffness Method

6.1 Introduction

6.2 Modified Stiffness Matrix Method for the Nonlinear Analysis of Truss-Type Structures

6.3 Algorithm for Nonlinear Analysis

Chapter Seven Analysis by Structural Partitioning

7.1 Introduction

7.2 Procedure of Analysis by Structural Partitioning Using the Stiffness Matrix Method

7.3 Theory Development for the Analysis by Structural Partitioning

7.4 Substructure Displacements and Forces with Common Boundary Nodes Fixed

7.5 Substructure Displacements and Forces with Common Boundary Nodes Relaxed

7.6 Structure Displacements and Internal Forces

7.7 Supplementary Problems

7.8 Suggested Computer Exercises

References

Index