Matrix Sturctural Analysis

, by McGuire, William; Gallagher, Richard H.; Ziemian, Ronald D.

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ISBN: 9780471129189 | 0471129186
Cover: Hardcover
Copyright: 7/1/1999

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Entire book and illustrative examples have been edited extensively, and several chapters repositioned. Imperial units are used instead of SI units in many of the examples and problems, particularly those of a nonlinear nature that have strong implications for design, since the SI system has not been fully assimilated in practice.

Symbols

xvii

Chapter 1 Introduction

(8)

1.1 A Brief History of Structural Analysis

(1)

1.2 Computer Programs

(5)

1.2.1 Computational Flow and General Purpose Programs

(2)

1.2.2 The Program MASTAN2

(2)

References

(1)

Chapter 2 Definitions and Concepts

(22)

2.1 Degrees of Freedom

(2)

2.2 Coordinate Systems and Conditions of Analysis

(3)

2.3 Structure Idealization

(2)

2.4 Axial Force Element--Force-Displacement Relationships

(3)

2.4.1 Element Stiffness Equations

(2)

2.4.2 Element Flexibility Equations

(1)

2.5 Axial Force Element--Global Stiffness Equations

(1)

2.6 Examples

(6)

2.7 Problems

(5)

Chapter 3 Formation of the Global Analysis Equations

(25)

3.1 Direct Stiffness Method--The Basic Equations

(8)

3.2 Direct Stiffness Method--The General Procedure

(7)

3.3 Some Features of the Stiffness Equations

(1)

3.4 Indeterminacy

(2)

3.5 Problems

(6)

References

(1)

Chapter 4 Stiffness Analysis of Frames--I

(37)

4.1 Stress-Strain Relationships

(2)

4.2 Work and Energy

(2)

4.3 Reciprocity

(2)

4.4 Flexibility-Stiffness Transformations

(4)

4.4.1 Stiffness to Flexibility Transformation

(1)

4.4.2 Flexibility to Stiffness Transformation

(3)

4.5 The Framework Element Stiffness Matrix

(8)

4.5.1 Axial Force Member

(1)

4.5.2 Pure Torsional Member

(1)

4.5.3 Beam Bent About Its z Axis

(4)

4.5.4 Beam Bent About Its y Axis

(1)

4.5.5 Complete Element Stiffness Matrix

(1)

4.6 A Commentary on Deformations and Displacement Variables

(2)

4.6.1 Neglected Deformations

(1)

4.6.2 Displacement Variables

(1)

4.7 Examples

(12)

4.8 Problems

(4)

References

(1)

Chapter 5 Stiffness Analysis of Frame--II

(44)

5.1 Coordinate Transformations

(15)

5.1.1 Transformation Matrices

(4)

5.1.2 Transformation of Degrees of Freedom

(1)

5.1.3 Transformations and Energy

(2)

5.1.4 Rectangular Transformation Matrices

100

(8)

5.2 Loads Between Nodal Points

108

(12)

5.3 Self-Straining--Initial and Thermal Strain Conditions

120

(10)

5.3.1 Initial Strain Problems

122

(3)

5.3.2 Thermal Strain Problems

125

(5)

5.4 Problems

130

(7)

Chapter 6 Virtual Work Principles

137

(37)

6.1 Principle of Virtual Displacements--Rigid Bodies

138

(4)

6.2 Principle of Virtual Displacements--Deformable Bodies

142

(2)

6.3 Virtual Displacement Analysis Procedure and Detailed Expressions

144

(6)

6.3.1 General Procedure

144

(1)

6.3.2 Internal Virtual Work

145

(3)

6.3.3 External Virtual Work

148

(2)

6.4 Construction of Analytical Solutions by the Principal of Virtual Displacements

150

(8)

6.4.1 Exact Solutions

150

(3)

6.4.2 Approximate Solutions and the Significance of the Chosen Virtual Displacements

153

(1)

6.4.3 Examples

154

(4)

6.5 Principle of Virtual Forces

158

(12)

6.5.1 Equations of Equilibrium

158

(3)

6.5.2 Characteristics of Virtual Force Systems

161

(1)

6.5.3 Formulation of the Virtual Forces Principle

162

(2)

6.5.4 Construction of Analytical Solutions by the Virtual Forces Principle

164

(6)

6.6 Problems

170

(3)

References

173

(1)

Chapter 7 Virtual Work Principles in Framework Analysis

174

(42)

7.1 Description of the Displaced State of Elements

175

(6)

7.1.1 Definition of the Shape Function Mode of Description

175

(1)

7.1.2 Formulation of Shape Functions

176

(4)

7.1.3 Characteristics of Shape Functions

180

(1)

7.2 Virtual Displacements in the Formulation of Element Stiffness Equations

181

(3)

7.2.1 Construction of Expressions for Real and Virtual Displacements

181

(1)

7.2.2 Virtual Displacements Formula for an Element Stiffness Matrix

182

(1)

7.2.3 Application to Standard Axial, Torsional, and Flexural Elements

183

(1)

7.3 Nonuniform Elements

184

(2)

7.4 Nonuniform Torsion

186

(8)

7.4.1 An Element Stiffness Matrix

187

(3)

7.4.2 Application and Examples

190

(4)

7.5 Loads Between Nodal Points and Initial Strain Effect--A General Approach

194

(5)

7.6 Virtual Forces in the Formulation of Element Force-Displacement Equations

199

(10)

7.6.1 Construction of Element Equations by the Principle of Virtual Forces

199

(4)

7.6.2 Further Applications--Shearing Deformations and Curved Elements

203

(6)

7.7 Problems

209

(5)

References

214

(2)

Chapter 8 Nonlinear Analysis of Frames--An Introduction

216

(26)

8.1 Nonlinear Behavior, Analysis, and Design

216

(18)

8.1.1 Sources of Nonlinearity

217

(1)

8.1.2 Levels of Analysis

218

(2)

8.1.3 Examples from Established Theory

220

(10)

8.1.4 A Commentary on Stability

230

(4)

8.2 A Matrix Approach

234

(1)

8.3 The Equations of Analysis and Their Solution

235

(4)

8.3.1 Equation Solution--The Options

236

(1)

8.3.2 A Fundamental Problem

237

(2)

8.4 Problems

239

(2)

References

241

(1)

Chapter 9 Geometric Nonlinear and Elastic Critical Load Analysis

242

(27)

9.1 Geometric Stiffness Matrices for Planar Elements

243

(11)

9.1.1 Axial Force Member

243

(2)

9.1.2 Combined Bending and Axial Force

245

(1)

9.1.3 Examples of Plane Structure Analysis

246

(8)

9.2 Combined Torsion and Axial Force

254

(3)

9.3 Three Dimensional Geometric Nonlinear Analysis--An Overview

257

(2)

9.4 Examples of Three Dimensional Structure Analysis

259

(4)

9.5 Problems

263

(5)

References

268

(1)

Chapter 10 Material Nonlinear Analysis

269

(32)

10.1 Nonlinear Material Behavior

269

(5)

10.1.1 Plasticity Theory

270

(2)

10.1.2 Plastic Analysis

272

(1)

10.1.3 Further Considerations

273

(1)

10.2 A Plastic Hinge Method For Ductile Frames

274

(4)

10.2.1 The Yield Surface and a Plastic Reduction Matrix

274

(3)

10.2.2 Definition of the Yield Surface

277

(1)

10.3 Inelastic Critical Load Theory

278

(1)

10.4 Examples

279

(1)

10.5 The Yield Surface Concept--A Brief Survey of Further Applications

290

(4)

10.5.1 Spread of Plasticity

290

(2)

10.5.2 Multiple Yield Surfaces

292

(1)

10.5.3 Reinforced Concrete Members

293

(1)

10.6 Problems

294

(5)

References

299

(2)

Chapter 11 Solution of Linear Algebraic Equations

301

(38)

11.1 The Basic Choice--Direct Inversion versus Elimination or Iteration

302

(1)

11.2 Direct Elimination Methods

302

(8)

11.2.1 Gauss Elimination

304

(3)

11.2.2 Cholesky Method

307

(3)

11.3 Iterative Methods

310

(6)

11.3.1 Gauss-Seidel and Jacobi Iterations

310

(2)

11.3.2 Conjugate Gradient Method

312

(4)

11.4 Sparseness and Bandedness

316

(1)

11.5 Frontal Solvers

317

(5)

11.6 Errors

322

(3)

11.6.1 The Condition Number

326

(1)

11.6.2 Estimate of Condition Number

327

(2)

11.6.3 Error Estimates and Preconditioning

329

(4)

11.6.4 Detecting, Controlling, and Correcting Error

333

11.7 Problems

325

References

337

(2)

Chapter 12 Solution of Nonlinear Equilibrium Equations

339

(36)

12.1 Incremental Analysis

339

(1)

12.2 Incremental Single-Step Methods

340

(5)

12.2.1 Euler Method

341

(1)

12.2.2 Second-Order Runge-Kutta Methods

341

(4)

12.3 Incremental-Iterative Methods

345

(6)

12.3.1 Load Control Method

347

(1)

12.3.2 Displacement Control Methods

348

(1)

12.3.3 Work Control Method

349

(1)

12.3.4 Constant Arc Length Methods

349

(1)

12.3.5 Modified Iterative Technique

349

(1)

12.3.6 Convergence Criteria

350

(1)

12.4 Automatic Load Incrementation

351

(1)

12.4.1 Change in Stiffness

351

(1)

12.4.2 Number of Iterations

352

(1)

12.5 Element Result Calculations

352

(3)

12.5.1 Updating Deformed Geometry

352

(1)

12.5.2 Force Recovery

352

(3)

12.6 Plastic Hinge Constraints

355

(3)

12.7 Limit Point and Post-Limit Analysis

358

(2)

12.8 Critical Load Analysis--An Eigenproblem

360

(10)

12.8.1 Reduction to Standard Form

361

(2)

12.8.2 Polynomial Expansion

363

(1)

12.8.3 Power Method

364

(3)

12.8.4 Inverse Iteration

367

(3)

12.9 Problems

370

(3)

References

373

(2)

Chapter 13 Special Analysis Procedures

375

(44)

13.1 Condensation

376

(1)

13.2 Substructuring

377

(8)

13.3 Constraints

385

(3)

13.4 Joint Coordinates

388

(5)

13.5 Connections and Joints

393

(10)

13.5.1 Flexible Connections

393

(5)

13.5.2 Finite Joint Size

398

(5)

13.6 Symmetry and Antisymmetry

403

(5)

13.7 Reanalysis Techniques

408

(5)

13.8 Problems

413

(5)

References

418

(1)

Appendix A Nonlinear Analysis--A Further Look

419

(25)

A.1 Virtual Displacement Principles in Lagrangian Formulations

420

(5)

A.2 An Updated Lagrangian Formulation and Its Linearization

425

(1)

A.3 Application to the Framework Element

426

(5)

A.4 Finite Rotations and Equilibrium in the Deformed Configuration

431

(6)

A.4.1 The Finite Rotation Equation

432

(1)

A.4.2 Application of the Finite Rotation Equation to the Framework Element

433

(4)

A.5 Nonuniform Torsion

437

(4)

References

441

(3)

Appendix B On Rigid Body Motion and Natural Deformation

444

(7)

B.1 The Nature of the Problem

444

(1)

B.2 Distinguishing Between Rigid Body Motion and Natural Deformation

445

(2)

B.3 Critique of Force Recovery Methods

447

(3)

B.3.1 The Natural Deformation Approach

447

(1)

B.3.2 The Elementary Approach

448

(2)

References

450

(1)

Author Index

451

(2)

Subject Index

453

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Matrix Sturctural Analysis

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