Structural Analysis Using Classical and Matrix Methods

by McCormac, Jack C.

Edition: 4th

ISBN13: 9780470036082

ISBN10: 0470036087

Format: Hardcover

Pub. Date: 2006-10-13

Publisher(s): WILEY

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Summary

Presenting an introduction to elementary structural analysis methods and principles, this book will help readers develop a thorough understanding of both the behavior of structural systems under load and the tools needed to analyze those systems. Throughout the chapters, they'll explore both statically determinate and statically indeterminate structures. And they'll find hands-on examples and problems that illustrate key concepts and give them opportunity to apply what they've learned.

Author Biography

Jack C. McCormac is Alumni Distinguished Professor o Civil Engineering, Emeritus at Clemson University. He holds a BS in civil engineering from the Citadel, an MS in civil engineering from Massachusetts Institute of Technology, and a Doctor of Letters from Clemson University. His contributions to engineering education and the engineering profession have been recognized by many, including the American Society for Engineering Education, the American Institute of Steel Construction, and the American Concrete Institute. Professor McCormac was included in the International Who's Who in Engineering, and was named by the Engineering News-Record as one of the top 125 engineers or architects in the world in the last 125 years for his contributions to the construction industry. He was one of only two educators living in the world today to receive this honor.

Professor McCormac belongs to the American Society of Civil Engineers and served as the principal civil engineering grader for the National Council of Examiners for Engineering and Surveying for many years.

Dedication

vii

Preface

xiii

PART ONE: STATICALLY DETERMINATE STRUCTURES

(572)

Introduction

(13)

Structural Analysis and Design

(1)

History of Structural Analysis

(3)

Basic Principles of Structural Analysis

(1)

Structural Components and Systems

(1)

Structural Forces

(2)

Structural Idealization (Line Diagrams)

(2)

Calculation Accuracy

(1)

Checks on Problems

(1)

Impact of Computers on Structural Analysis

(2)

Structural Loads

(27)

Introduction

(1)

Structural Safety

(1)

Specifications and Building Codes

(3)

Types of Structural Loads

(1)

Dead Loads

(1)

Live Loads

(2)

Live Load Impact Factors

(1)

Live Loads on Roofs

(1)

Rain Loads

(2)

Wind Loads

(3)

Simplified ASCE Procedure for Estimating Wind Loads

(2)

Detailed ASCE Procedure for Estimating Wind Loads

(1)

Seismic Loads

(2)

Equivalent Lateral Force Procedure for Estimating Seismic Loads

(3)

Snow Loads

(3)

Other Loads

(1)

Problems for Solution

(2)

System Loading and Behavior

(14)

Introduction

(1)

Tributary Areas

(4)

Influence Areas

(1)

Live Load Reduction

(2)

Loading Conditions for Allowable Stress Design

(2)

Loading Conditions for Strength Design

(3)

Concept of the Force Envelope

(1)

Problems for Solution

(1)

Reactions

(38)

Equilibrium

(1)

Moving Bodies

(1)

Calculation of Unknowns

(1)

Types of Support

(2)

Stability, Determinacy, and Indeterminacy

(3)

Unstable Equilibrium and Geometric Instability

(1)

Sign Convention

(1)

Free-Body Diagrams

(1)

Horizontal and Vertical Components

(1)

Reactions by Proportions

(1)

Reactions Calculated by Equations of Statics

(3)

Principle of Superposition

(1)

The Simple Cantilever

(1)

Cantilevered Structures

(2)

Reaction Calculations for Cantilevered Structures

(2)

Arches

(1)

Three-Hinged Arches

(5)

Uses of Arches and Cantilevered Structures

(1)

Cables

(5)

Problems for Solution

(7)

Shearing Force and Bending Moment

(22)

Introduction

(2)

Shear Diagrams

(1)

Moment Diagrams

(1)

Relations Among Loads, Shearing Forces, and Bending Moments

(1)

Moment Diagrams Drawn from Shear Diagrams

(7)

Shear and Moment Diagrams for Statically Determinate Frames

106

(4)

Shearing Force and Bending Moment Equations

110

(2)

Problems for Solution

112

(5)

Introduction to Plane Trusses

117

(26)

Introduction

117

(1)

Assumptions for Truss Analysis

118

(1)

Truss Notation

119

(1)

Roof Trusses

120

(1)

Bridge Trusses

121

(1)

Arrangement of Truss Members

122

(1)

Statical Determinacy of Trusses

123

(4)

Methods of Analysis and Conventions

127

(2)

Method of Joints

129

(5)

Computer Analysis of Statically Determinate Trusses

134

(1)

Example Computer Problem

135

(3)

Problems for Solution

138

(5)

Plane Trusses, Continued

143

(25)

Analysis by the Method of Sections

143

(1)

Application of the Method of Sections

144

(7)

Method of Shears

151

(2)

Zero-Force Members

153

(2)

When Assumptions Are Not Correct

155

(1)

Simple, Compound, and Complex Trusses

156

(1)

The Zero-Load Test

157

(2)

Stability

159

(2)

Equations of Condition

161

(1)

Problems for Solution

162

(6)

Three-Dimensional or Space Trusses

168

(17)

Introduction

168

(1)

Basic Principles

168

(1)

Equations of Static Equilibrium

169

(2)

Stability of Space Trusses

171

(1)

Special Theorems Applying to Space Trusses

171

(1)

Types of Support

172

(1)

Illustrative Examples

173

(5)

Solution Using Simultaneous Equations

178

(2)

Example Problem with SABLE32

180

(2)

Problems for Solution

182

(3)

Influence Lines for Beams

185

(19)

Introduction

185

(1)

The Influence Line Defined

185

(1)

Influence Lines for Simple Beam Reactions

186

(1)

Influence Lines for Simple Beam Shearing Forces

187

(1)

Influence Lines for Simple Beam Moments

188

(1)

Qualitative Influence Lines

189

(5)

Uses of Influence Lines; Concentrated Loads

194

(1)

Uses of Influence Lines: Uniform Loads

195

(1)

Common Simple Beam Formulas from Influence Lines

196

(1)

Determining Maximum Loading Effects Using Influence Lines

197

(1)

Maximum Loading Effects Using Beam Curvature

198

(1)

Impact Loading

199

(2)

Problems for Solution

201

(3)

Truss Influence Lines and Moving Loads

204

(21)

Influence Lines for Trusses

204

(1)

Arrangement of Bridge Floor Systems

204

(2)

Influence Lines for Truss Reactions

206

(1)

Influence Lines for Member Forces of Parallel-Chord Trusses

206

(2)

Influence Lines for Members Forces of Nonparallel Chord Trusses

208

(2)

Influence Lines for K Truss

210

(1)

Determination of Maximum Forces

211

(2)

Counters in Bridge Trusses

213

(2)

Live Loads for Highway Bridges

215

(4)

Live Loads for Railway Bridges

219

(1)

Maximum Values for Moving Loads

220

(3)

Problems for Solution

223

(2)

Deflections and Angle Changes Using Geometric Methods

225

(23)

Introduction

225

(1)

Sketching Deformed Shapes of Structures

225

(5)

Reasons for Computing Deflections

230

(2)

The Moment-Area Theorems

232

(2)

Application of the Moment-Area Theorems

234

(7)

Analysis of Fixed-End Beams

241

(2)

Maxwell's Law of Reciprocal Deflections

243

(2)

Problems for Solution

245

(3)

Deflections and Angle Changes Using Geometric Methods Continued

248

(16)

The Method of Elastic Weights

248

(1)

Application of the Method of Elastic Weights

249

(5)

Limitations of the Elastic-Weight Method

254

(1)

Conjugate-Beam Method

255

(2)

Summary of Conjugate Beams

257

(1)

Equilibrium

257

(1)

Summary of Beam Relations

258

(1)

Application of the Conjugate Method to Beams

258

(2)

Long Term Deflections

260

(1)

Application of the Conjugate Method to Frames

261

(1)

Problems for Solution

261

(3)

Deflection and Angle Changes Using Energy Methods

264

(33)

Introduction to Energy Methods

264

(1)

Conservation of Energy Principle

264

(1)

Virtual Work or Complementary Virtual Work Method

265

(2)

Truss Deflections by Virtual Work

267

(2)

Application of Virtual Work to Trusses

269

(4)

Deflections of Beams and Frames by Virtual Work

273

(1)

Example Problems for Beams and Frames

274

(7)

Rotations or Angle Changes by Virtual Work

281

(2)

Introduction to Castigliano's Theorems

283

(1)

Castigliano's Second Theorem

284

(5)

Problems for Solution

289

(8)

PART TWO: STATICALLY INDETERMINATE STRUCTURES

Classical Methods

Introduction to Statically Indeterminate Structures

297

(8)

Introduction

297

(1)

Continuous Structures

298

(2)

Advantages of Statically Indeterminate Structures

300

(2)

Disadvantages of Statically Indeterminate Structures

302

(1)

Methods of Analyzing Statically Indeterminate Structures

302

(2)

Looking Ahead

304

(1)

Force Methods of Analyzing Statically Indeterminate Structures

305

(17)

Beams and Frames with One Redundant

305

(9)

Beams and Frames with Two or More Redundants

314

(2)

Support Settlement

316

(4)

Problems for Solution

320

(2)

Force Methods for Analyzing Statically Indeterminate Structures Continued

322

(25)

Analysis of Externally Redundant Trusses

322

(4)

Analysis of Internally Redundant Trusses

326

(3)

Analysis of Trusses Redundant Internally and Externally

329

(1)

Temperature Changes, Shrinkage, Fabrication Errors, and So On

330

(2)

Castigliano's First Theorem

332

(9)

Analysis Using Computers

341

(1)

Problems for Solution

342

(5)

Influence Lines for Statically Indeterminate Structures

347

(16)

Influence Lines for Statically Indeterminate Beams

347

(6)

Qualitative Influence Lines

353

(3)

Influence Lines for Statically Indeterminate Trusses

356

(4)

Problems for Solution

360

(3)

Slope Deflection: A Displacement Method of Analysis

363

(26)

Introduction

363

(1)

Derivation of Slope-Deflection Equations

363

(3)

Application of Slope Deflection to Continuous Beams

366

(3)

Continuous Beams with Simple Ends

369

(2)

Miscellaneous Items Concerning Continuous Beams

371

(1)

Analysis of Beams with Support Settlement

372

(2)

Analysis of Frames---No Sides way

374

(2)

Analysis of Frames with Sidesway

376

(6)

Analysis of Frames with Sloping Legs

382

(1)

Problems for Solution

382

(7)

PART THREE: STATICALLY INDETERMINATE STRUCTURES

Common Methods in Current Practice

Approximate Analysis of Statically Indeterminate Structures

389

(24)

Introduction

389

(1)

Trusses with Two Diagonals in Each Panel

390

(1)

Continuous Beams

391

(4)

Analysis of Building Frames for Vertical Loads

395

(3)

Analysis of Portal Frames

398

(2)

Analysis of Building Frames for Lateral Loads

400

(7)

Approximate Analyses of Frame Compared to ``Exact'' Analysis by SABLE32

407

(1)

Moment Distribution

408

(1)

Analysis of Vierendeel ``Trusses''

408

(2)

Problems for Solution

410

(3)

Moment Distribution for Beams

413

(20)

Introduction

413

(2)

Basic Relations

415

(2)

Definitions

417

(2)

Sign Convention

419

(1)

Application of Moment Distribution

419

(5)

Modification of Stiffness for Simple Ends

424

(1)

Shearing Force and Bending Moment Diagrams

425

(3)

Computer Solution with SABLE32

428

(2)

Problems for Solution

430

(3)

Moment Distribution for Frames

433

(28)

Frames with Sidesway Prevented

433

(2)

Frames with Sidesway

435

(2)

Sidesway Moments

437

(10)

Frames with Sloping Legs

447

(4)

Multistory Frames

451

(4)

Computer Analysis of Frame

455

(2)

Problems for Solution

457

(4)

Introduction to Matrix Methods

461

(9)

Structural Analysis Using the Computer

461

(1)

Matrix Methods

461

(1)

Review of Matrix Algebra

462

(1)

Force and Displacement Methods of Analysis

462

(1)

Introduction to the Force or Flexibility Method

463

(5)

Problems for Solution

468

(2)

Fundamentals of the Displacement or Stiffness Method

470

(24)

Introduction

470

(1)

General Relationships

470

(2)

Stiffness Equations for Axial Force Members

472

(6)

Stiffness Equations for Flexural Members

478

(9)

Stiffness Matrix for Combined Axial and Flexural Members

487

(2)

Characteristics of Stiffness Matrices

489

(1)

Relation Between Stiffness and Flexibility Matrices

490

(2)

Problems for Solution

492

(2)

Stiffness Matrices for Inclined Members

494

(24)

General

494

(1)

Axial Force Members

494

(6)

Flexural Members

500

(10)

Loading Between Nodes

510

(5)

Problems for Solution

515

(3)

Additional Matrix Procedures

518

(55)

General

518

(1)

Addition of Stiffness Equations

518

(2)

Stiffness Matrices for Inclined Members

520

(3)

Stiffness Equations for Structures with Enforced Displacements

523

(1)

Stiffness Equations for Structures with Members Experiencing Temperature Changes

524

(2)

Stiffness Equations for Structures Whose Members Have Incorrect Lengths

526

(1)

Applications of Matrix Partitioning

526

(1)

Condensation

527

(1)

Band Width of Stiffness Matrices for General Structures

528

(3)

Problems for Solution

531

(2)

APPENDICES

Appendix A The Catenary Equation

533

(5)

Appendix B Matrix Algebra

538

(15)

B.1 Introduction

538

(1)

B.2 Matrix Definitions and Properties

538

(1)

B.3 Special Matrix Types

539

(1)

B.4 Determinant of a Square Matrix

540

(1)

B.5 Adjoint Matrix

541

(1)

B.6 Matrix Arithmetic

542

(5)

B.7 Gauss's Method for Solving Simultaneous Equations

547

(1)

B.8 Special Topics

548

(5)

Appendix C Wind, Seismic, and Snow Load Tables and Figures

553

(12)

Appendix D Computer Analysis of Various Structures Using SAP2000

565

(8)

D.1 Introduction

565

(1)

D.2 Analysis of Plane Trusses

565

(2)

D.3 Analysis of Space Trusses

567

(1)

D.4 Analysis of Statically Indeterminate Plane Trusses

568

(2)

D.5 Analysis of Composite Structures

570

(1)

D.6 Analysis of Continuous Beams and Frames

571

(2)

Glossary

573

(6)

Index

579

Structural Analysis Using Classical and Matrix Methods

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