Matrix Analysis of Structures

This book takes a fresh, student-oriented approach to teaching the material covered in the senior- and first-year graduate-level matrix structural analysis course taken by civil engineering majors. Unlike traditional texts for this course that are difficult to read, Kassimali takes special care to provide understandable and exceptionally clear explanations of concepts, step-by-step procedures for analysis, flowcharts, and interesting and modern examples, producing a technically and mathematically accurate presentation of the subject.

1 INTRODUCTION

1

(22)

1.1 Historical Background

2

(1)

1.2 Classical, Matrix, and Finite-Element Methods of Structural Analysis

3

(1)

1.3 Flexibility and Stiffness Methods

4

(1)

1.4 Classification of Framed Structures

5

(5)

1.5 Analytical Models

10

(2)

1.6 Fundamental Relationships for Structural Analysis

12

(8)

1.7 Linear versus Nonlinear Analysis

20

(1)

1.8 Software

21

(1)

Summary

22

(1)

2 MATRIX ALGEBRA

23

(25)

2.1 Definition of a Matrix

24

(1)

2.2 Types of Matrices

25

(2)

2.3 Matrix Operations

27

(11)

2.4 Gauss-Jordan Elimination Method

38

(6)

Summary

44

(1)

Problems

45

(3)

3 PLANE TRUSSES

48

(79)

3.1 Global and Local Coordinate Systems

49

(3)

3.2 Degrees of Freedom

52

(6)

3.3 Member Stiffness Relations in the Local Coordinate System

58

(9)

3.4 Finite-Element Formulation Using Virtual Work

67

(9)

3.5 Coordinate Transformations

76

(9)

3.6 Member Stiffness Relations in the Global Coordinate System

85

(4)

3.7 Structure Stiffness Relations

89

(16)

3.8 Procedure for Analysis

105

(17)

Summary

122

(1)

Problems

123

(4)

4 COMPUTER PROGRAM FOR ANALYSIS OF PLANE TRUSSES

127

(34)

4.1 Data Input

128

(11)

4.2 Assignment of Structure Coordinate Numbers

139

(3)

4.3 Generation of the Structure Stiffness Matrix

142

(5)

4.4 Formation of the Joint Load Vector

147

(2)

4.5 Solution for Joint Displacements

149

(2)

4.6 Calculation of Member Forces and Support Reactions

151

(7)

Summary

158

(2)

Problems

160

(1)

5 BEAMS

161

(87)

5.1 Analytical Model

162

(8)

5.2 Member Stiffness Relations

170

(14)

5.3 Finite-Element Formulation Using Virtual Work

184

(6)

5.4 Member Fixed-End Forces Due to Loads

190

(6)

5.5 Structure Stiffness Relations

196

(9)

5.6 Structure Fixed-Joint Forces and Equivalent Joint Loads

205

(8)

5.7 Procedure for Analysis

213

(10)

5.8 Computer Program

223

(21)

Summary

244

(1)

Problems

244

(4)

6 PLANE FRAMES

248

(91)

6.1 Analytical Model

249

(6)

6.2 Member Stiffness Relations in the Local Coordinate System

255

(12)

6.3 Coordinate Transformations

267

(8)

6.4 Member Stiffness Relations in the Global Coordinate System

275

(8)

6.5 Structure Stiffness Relations

283

(15)

6.6 Procedure for Analysis

298

(18)

6.7 Computer Program

316

(17)

Summary

333

(1)

Problems

334

(5)

7 MEMBER RELEASES AND SECONDARY EFFECTS

339

(73)

7.1 Member Releases in Plane Frames and Beams

340

(20)

7.2 Computer Implementation of Analysis for Member Releases

360

(1)

7.3 Support Displacements

361

(23)

7.4 Computer Implementation of Support Displacement Effects

384

(5)

7.5 Temperature Changes and Fabrication Errors

389

(17)

Summary

406

(1)

Problems

407

(5)

8 THREE-DIMENSIONAL FRAMED STRUCTURES

412

(82)

8.1 Space Trusses

413

(15)

8.2 Grids

428

(23)

8.3 Space Frames

451

(38)

Summary

489

(1)

Problems

489

(5)

9 SPECIAL TOPICS AND MODELING TECHNIQUES

494

(69)

9.1 The Structure Stiffness Matrix Including Restrained Coordinates--An Alternative Formulation of the Stiffness Method

495

(6)

9.2 Approximate Matrix Analysis of Rectangular Building Frames

501

(8)

9.3 Condensation of Degrees of Freedom, and Substructuring

509

(16)

9.4 Inclined Roller Supports

525

(3)

9.5 Offset Connections

528

(4)

9.6 Semirigid Connections

532

(4)

9.7 Shear Deformations

536

(4)

9.8 Nonprismatic Members

540

(3)

9.9 Solution of Large Systems of Stiffness Equations

543

(16)

Summary

559

(1)

Problems

560

(3)

APPENDIX A COMPUTER SOFTWARE

563

(2)

APPENDIX B FLEXIBILITY METHOD

565

(7)

BIBLIOGRAPHY

572

(2)

ANSWERS TO SELECTED PROBLEMS

574

(13)

INDEX

587

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Matrix Analysis of Structures

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