Automated Structural Analysis

Preface

Chapter One Graphs, Networks, and Structures

1.1 Introduction

1.2 Graph Theory

1.3 Piping Networks

1.3.1 An Example

1.4 Skeletal Structures

1.4.1 Types of Structures Considered

1.4.2 Requirements for a Solution

Chapter Two The Node Method for Trusses

2.1 Introduction

2.2 The Truss

2.3 A Formal Description of the Truss Problem

2.4 A Decomposition

2.5 Exercises

2.5.1 Discussion of Exercise 3

Chapter Three A General Statement of the Node Method

3.1 Introduction

3.2 The Node Method

3.3 The Decomposition

3.4 Exercises

Chapter Four The Node Method for Plane Frames

4.1 The Plane Frame

4.2 Rotation of Coordinates

4.3 A Formal Description of the Plane Frame

4.4 A Decomposition

4.5 A Simple Example

4.6 Exercises

Chapter Five The Node Method for Space Frames

5.1 The Space Frame

5.2 A Formal Description of the Space Frame

5.3 A Decomposition

Chapter Six Some Generalizations

6.1 Introduction

6.2 Member Loads, Temperature, Lack of Fit, etc.

6.3 Examples

6.4 An Alternative Formulation for Temperature and Lack of Fit

6.5 Exercises

Chapter Seven The Primitive Stiffness Matrix

7.1 Introduction

7.2 Member Stiffness Obtained from the Cantilever Flexibility

7.3 Adding Flexibilities to Approximate a Curved Member

7.4 Singular Stiffness Matrices

7.5 The Effect of Shear

7.6 Exercises

Chapter Eight The Mesh Method

8.1 Introduction

8.2 The Mesh Method Derived from the Node Method

8.3 The Mesh Law

8.4 An Alternative Formulation

8.5 Exercises

Chapter Nine Miscellaneous Theorems

Chapter Ten Kron's Methods

10.1 Introduction

10.2 Tearing and Interconnecting

10.3 K-Partitioning

10.4 Method of Substructures

References

Appendices

A.1 Matrices and Vectors

A.2 The Classical Methods of Structural Analysis

A.3 Beams and Rods

A.4 Gaussian Elimination

A.5 The Solution of Large Systems

Computer Programs

General Comments

P.1 The Node Method for Plane Trusses

P.2 The Node Method for Space Trusses

P.3 The Node Method for Plane Frames

P.4 The Node Method for Space Frames

P.5 The Mesh Method for Plane Frames

P.6 A Program for Large Space Trusses

P.7 Adding Flexibilities

P.8 Plastic Analysis of Plane Frames

Index