Matrix Structural Analysis

The field of structural analysis has experienced profound change in the past three decades. This book presents a rigorous, concise development of the concepts of modern matrix structural analysis with emphasis on techniques and methods which are the basis for the Finite Element Method. The material is presented in a traditional manner. Basic analytical tools set the groundwork for understanding more complex concepts. Meaningful examples which illustrate the underlying theories and procedures are provided throughout the text, presented in a step-by-step format to promote understanding.

Lewis P. Felton and Richard B. Nelson are the authors of Matrix Structural Analysis, published by Wiley.

Basic Concepts

1

(71)

Introduction

1

(2)

Types of Structural Elements

3

(6)

Typical One-Dimensional Elements

4

(3)

Typical Two-Dimensional Elements

7

(2)

Three-Dimensional Elements

9

(1)

Overview of the Concepts of Structural Analysis

9

(2)

The Theorem of Virtual Work

10

(1)

Loads

11

(3)

Material Behavior

14

(2)

Review of Equilibrium Equations

16

(11)

Concentrated Forces

16

(1)

Equilibrium of Forces

17

(1)

Moment of Force

18

(2)

Equilibrium of Moments

20

(2)

Free-Body Diagrams

22

(1)

Statically Equivalent Systems of Forces

22

(1)

Treatment of Distributed Forces

23

(4)

Analytic Models

27

(27)

Connections

28

(6)

Supports

34

(20)

Determinacy and Indeterminacy

54

(9)

Stability and Instability

63

(3)

Preview

66

(6)

Statically Determinate Trusses

72

(47)

Introduction

72

(1)

Equilibrium of Axially Loaded Bars

72

(4)

Internal Forces in Statically Determinate Trusses

76

(19)

Statical Stability/Instability and Determinacy/Indeterminacy

95

(2)

Deformations of Axially Loaded Bars

97

(7)

Direct Calculation of Truss Displacements

104

(15)

Statically Determinate Frames

119

(50)

Introduction

119

(1)

Equilibrium of Beams

119

(2)

Internal Forces in Statically Determinate Frames

121

(18)

Shear and Bending Moment Diagrams

127

(10)

Alternate Representations of Bending Moment

137

(2)

Deformations of Beams

139

(5)

Direct Calculation of Beam Displacements

144

(25)

Solution of Differential Equations

145

(11)

Moment-Area Method

156

(13)

Virtual Work

169

(60)

Introduction

169

(1)

Virtual Work for Truss Joints

170

(2)

Virtual Work for Axially Loaded Bars

172

(3)

Virtual Work for Trusses

175

(17)

Virtual Work for Beams

192

(13)

Virtual Work for Frames

205

(11)

Summary

216

(13)

Introduction to Analysis of Indeterminate Structures: Force Method

229

(119)

Introduction

229

(1)

Redundant Forces

229

(3)

Trusses

232

(31)

Basic Formulation

234

(14)

Matrix Formulation

248

(13)

Matrix Formulation for Structures with General Element Flexibility

261

(2)

Frames

263

(44)

Basic Formulation

265

(12)

Flexibility Matrix for Beams

277

(7)

Matrix Formulation

284

(11)

Combined Bending and Axial Behavior

295

(5)

General Axial Behavior

300

(7)

Miscellaneous Considerations

307

(20)

Support Settlement

307

(4)

Structures Composed of Several Types of Elements

311

(7)

Initial Deformations

318

(3)

Effect of Moment-Bearing Joints on Truss Behavior

321

(6)

Computing Deflections

327

(21)

Symmetry

348

(34)

Introduction

348

(1)

Behavioral Symmetry for Beams

348

(4)

Betti's Theorem for Linearly Elastic Bernoulli-Euler Beams

349

(2)

Maxwell's Reciprocal Relationship

351

(1)

Physical Symmetry

352

(30)

Structures Symmetric With Respect to a Line

353

(19)

Structures Symmetric With Respect to a Point

372

(10)

Influence Lines

382

(26)

Introduction

382

(1)

Moving Loads and Influence Lines

383

(5)

Virtual Work and Influence Lines

388

(20)

Influence Lines for Statically Determinate Structures

388

(2)

Influence Lines for Indetermine Structures: The Muller-Breslau Principle

390

(10)

Influence Lines for Trusses

400

(8)

Introduction to the Displacement Method

408

(91)

Introduction

408

(1)

System Displacements

409

(9)

Analysis of Trusses

418

(16)

Analysis of Frames

434

(41)

Stiffness Matrix for Beams

434

(2)

Matrix Formulation

436

(7)

Equilibrium by Virtual Work

443

(25)

Fixed-End Moments From Betti's Theorem

468

(7)

Miscellaneous Considerations

475

(24)

Support Settlement

475

(3)

Structures Composed of Several Types of Elements

478

(21)

Displacement Method: Advanced Formulation

499

(73)

Introduction

499

(1)

Force-Displacement Stiffness Matrix for Beams

500

(5)

Equilibrium Equations

505

(3)

Force-Displacement Stiffness Matrix for Axially Loaded Bars

508

(1)

Combined Bending and Axial Behavior

509

(13)

Element Stiffness Matrix in Global Coordinates

522

(9)

Direct Stiffness Method

531

(15)

General Support Motions

538

(2)

Direct Stiffness Method for Trusses

540

(6)

Miscellaneous Considerations

546

(26)

Support Settlement

546

(4)

Structures Comosed of Several Types of Elements

550

(4)

Effect of Joint Dimensions

554

(6)

Releases

560

(12)

Energy Concepts and Approximations

572

(60)

Introduction

572

(1)

Basic Energy Forms

573

(17)

Strain Energy

574

(5)

Symmetry of Stiffness and Flexibility Matrices

579

(2)

Positive Definiteness of Strain Energy

581

(2)

Convexity of Strain Energy

583

(3)

Partial Derivative of Strain Energy; Castigliano's Theorem, Part I

586

(1)

Deformation Energy; Castigliano's Theorem, Part II

587

(1)

External Potential Energy

588

(1)

Total Potential Energy; Stationary and Minimum Values

588

(2)

Effects of Approximations

590

(10)

Constrained Displacements

590

(5)

Incompatible Displacements

595

(1)

Approximations in the Force Method

596

(4)

Generalized Displacements and Forces

600

(6)

Approximate Displacement Patterns

604

(2)

Applications to Structures Composed of One-Dimensional Elements

606

(26)

Strain Energy of Bars and Beams

607

(4)

Examples of Rayleigh-Ritz Method

611

(21)

Introduction to Finite Element Analysis

632

(41)

Introduction

632

(1)

Basic Reqirements

632

(3)

Stiffness Matrix and Force Vector for Assumed Displacements

635

(8)

Development Using Energy

635

(3)

Development Using Virtual Work

638

(2)

Approximate Solutions as Best Fits

640

(3)

Examples of Finite Element Analysis

643

(30)

Appendix A Fixed-End Moments and Forces

673

(8)

Appendix B Moment Distribution Method for Frame Analysis

681

(16)

Index

697

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Matrix Structural Analysis

Summary

Author Biography

Table of Contents

Supplemental Materials