Advanced Mechanics of Materials

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ISBN: 9780133969610 | 0133969614
Cover: Paperback
Copyright: 8/28/1998

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Treats topics by extending concepts and procedures a step or two beyond elementary mechanics of materials andemphasizes the physical view-- mathematical complexity is not used where it is not needed.Includes new coverage of symmetry considerations, rectangular plates in bending, plastic action in plates, and critical speed of rotating shafts. Expands the coverage of fatigue, the reciprocal theorem, semi-inverse problems in elasticity, thermal stress, and buckling.

PREFACE

1 ORIENTATION. REVIEW OF ELEMENTARY MECHANICS OF MATERIALS

(27)

1.1 Methods of Stress Analysis

(2)

1.2 Terminology

(2)

1.3 Properties of a Plane Area

(4)

1.4 Axial Loading. Pressure Vessels

(2)

1.5 Torsion

(1)

1.6 Beam Stresses

(2)

1.7 Beam Deflections

(1)

1.8 Symmetry Considerations. Static Indeterminacy

(3)

1.9 Plastic Deformation. Residual Stress

(1)

1.10 Other Remarks

(9)

2 STRESS, PRINCIPAL STRESSES, STRAIN ENERGY

(23)

2.1 Preliminary Remarks

(2)

2.2 Principal Stresses: Theory

(3)

2.3 Principal Stresses: Calculations

(2)

2.4 Octahedral and Maximum Shear Stress

(2)

2.5 Stress-Strain-Temperature Relations

(2)

2.6 Strain Energy Density

(2)

2.7 Stress Concentration

(3)

2.8 Contact Stress

(7)

3 FAILURE AND FAILURE CRITERIA

(26)

3.1 Introduction

(1)

3.2 Isotropic Material, Brittle Failure

(4)

3.3 Isotropic Material, Ductile Failure

(2)

3.4 Anisotropic Materials

(1)

3.5 Introduction to Fracture Mechanics

(4)

3.6 Introduction to Fatigue

(14)

4 APPLICATIONS OF ENERGY METHODS

(56)

4.1 Introduction

(5)

4.2 Reciprocal Theorems

(2)

4.3 Strain Energy in Terms of Loads

(3)

4.4 Unit Load Method

(3)

4.5 Example Solutions with Straight Members

(3)

4.6 Curved Members

(4)

4.7 Statistically Indeterminate Problems

(6)

4.8 Formulas from Geometric Considerations

103

(2)

4.9 Strain Energy in Terms of Displacements

105

(2)

4.10 Principle of Stationary Potential Energy

107

(3)

4.11 Rayleigh-Ritz Method

110

(4)

4.12 Trigonometric Series

114

(2)

4.13 Finite Element Method

116

(17)

5 BEAMS ON AN ELASTIC FOUNDATION

133

(28)

5.1 Introduction

133

(2)

5.2 Basic Equations, Winkler Foundation

135

(3)

5.3 Semi-Infinite Beams with Concentrated End Loads

138

(2)

5.4 Infinite Beams with Concentrated Loads

140

(3)

5.5 Example Problems

143

(4)

5.6 Uniformly Distributed Load

147

(3)

5.7 Beams of Finite Length

150

(11)

6 CURVED BEAMS

161

(29)

6.1 Introduction. Strain Distribution

161

(3)

6.2 Circumferential Stress

164

(3)

6.3 Numerical Examples

167

(3)

6.4 Radial Stress and Shear Stress

170

(4)

6.5 Sections Having Thin Flanges

174

(5)

6.6 Closed Sections with Thin Walls

179

(1)

6.7 Deflections of Sharply Curved Beams

180

(10)

7 ELEMENTS OF THEORY OF ELASTICITY

190

(41)

7.1 Introduction

190

(3)

7.2 Displacements, Strains, and Compatibility

193

(2)

7.3 Equilibrium Equations and Boundary Conditions

195

(3)

7.4 Stress Field Solution for Plane Stress Problems

198

(3)

7.5 Polynomial Solutions in Cartesian Coordinates

201

(2)

7.6 Displacements Calculated from Stresses

203

(2)

7.7 Plane Stress Problems in Polar Coordinates

205

(2)

7.8 Circular Hole

207

(3)

7.9 Concentrated Force Loading

210

(3)

7.10 Thermal Stress

213

(3)

7.11 Torsion. Warping Function

216

(3)

7.12 Torsion. Prandtl Stress Function

219

(2)

7.13 Inelastic Material Behavior

221

(10)

8 PRESSURIZED CYLINDERS AND SPINNING DISKS

231

(30)

8.1 Governing Equations

231

(2)

8.2 Pressurized Cylinders

233

(4)

8.3 Shrink Fits. Compound Cylinders

237

(5)

8.4 Spinning Disks, Part I

242

(3)

8.5 Spinning Disks, Part II

245

(2)

8.6 Plastic Action in Thick-Walled Cylinders

247

(4)

8.7 Plastic Action in Spinning Disks

251

(10)

9 TORSION

261

(53)

9.1 Introduction. Saint-Venant Torsion Theory

261

(2)

9.2 Membrane Analogy

263

(2)

9.3 Membrane Analogy for Thin-Walled Open Sections

265

(3)

9.4 Remarks and Formulas

268

(3)

9.5 Pure Twist of Thin-Walled Tubes of One Cell

271

(4)

9.6 Pure Twist of Thin-Walled Multicell Tubes

275

(3)

9.7 Torsion with Restraint of Warping: I Sections

278

(5)

9.8 Sectorial Area

283

(3)

9.9 Sectorial Properties

286

(3)

9.10 Warping of Thin-Walled Cross Sections in Pure Torsion

289

(3)

9.11 Stresses in Open Sections When Beta is Not Constant

292

(1)

9.12 Torsion with Restraint of Warping: General Sections

293

(2)

9.13 Bimoment

295

(3)

9.14 Large Rotation, Axial Load, and Pretwisting

298

(4)

9.15 Torsion with Plastic Action

302

(12)

10 UNSYMMETRIC BENDING AND SHEAR CENTER

314

(32)

10.1 Unsymmetric Bending of Straight Beams

314

(3)

10.2 Numerical Examples

317

(2)

10.3 Beam Deflections in Unsymmetric Bending

319

(4)

10.4 Transverse Shear Stress and Shear Flow

323

(4)

10.5 Shear Center: Introduction

327

(3)

10.6 Shear Center: Special Open Section

330

(3)

10.7 Shear Center: General Open Sections

333

(3)

10.8 Shear Center: Remarks

336

(10)

11 PLASTICITY IN STRUCTURAL MEMBERS AND COLLAPSE ANALYSIS

346

(3)

11.1 Introduction

346

(1)

11.2 Stress and Deflection in Loading and Unloading

347

(3)

11.3 Plastic Action in Bending

350

(3)

11.4 Plastic Hinges in Beams

353

(3)

11.5 Collapse Analysis of Beams

356

(5)

11.6 Collapse Analysis of Plane Frames and Arches

361

(4)

11.7 General Theorems

365

(2)

11.8 Interaction: Bending and Axial Force

367

(3)

11.9 Interaction: Some Additional Relations

370

(9)

12 PLATE BENDING

379

(32)

12.1 Introduction. Assumptions and Limitations

379

(2)

12.2 Governing Equations in Cartesian Coordinates

381

(2)

12.3 Uniform Bending. Boundary Conditions

383

(4)

12.4 Series Solution for Rectangular Plates. Selected Results

387

(2)

12.5 Governing Equations for Axisymmetric Plates

389

(3)

12.6 Solution of Simple Axisymmetric Problems

392

(3)

12.7 Selected Solutions for Axisymmetric Plates

395

(2)

12.8 Superposition Solutions for Axisymmetric Plates

397

(2)

12.9 Plastic Collapse Analysis of Plates

399

(12)

13 SHELLS OF REVOLUTION WITH AXISYMMETRIC LOADS

411

(32)

13.1 Introduction

411

(1)

13.2 Geometry and Terminology

412

(1)

13.3 Membrane Forces and Stresses

413

(3)

13.4 Applications of Membrane Theory

416

(3)

13.5 Membrane Shells of Uniform Strength

419

(2)

13.6 Bending Theory of Cylindrical Shells

421

(2)

13.7 Bending Formulas for Edge Loads

423

(2)

13.8 Applications of Bending Theory

425

(5)

13.9 The Reinforcing Ring

430

(13)

14 BUCKLING AND INSTABILITY

443

(28)

14.1 Introduction. Elementary Theory

443

(3)

14.2 An Energy Method

446

(3)

14.3 Beam-Columns: Classical Theory

449

(2)

14.4 Beam-Columns: Approximations

451

(2)

14.5 Inelastic Buckling

453

(2)

14.6 Plates: Buckling, Effective Width, and Failure

455

(5)

14.7 Additional Buckling Problems

460

(2)

14.8 Remarks about Stability, Buckling, and Collapse

462

(9)

REFERENCES

471

(6)

INDEX

477

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Advanced Mechanics of Materials

Summary

Table of Contents

Supplemental Materials