Engineering Solid Mechanics: Fundamentals and Applications

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ISBN: 9780849316074 | 0849316073
Cover: Hardcover
Copyright: 12/22/1998

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Engineering Solid Mechanics bridges the gap between elementary approaches to strength of materials and more advanced, specialized versions on the subject.The book provides a basic understanding of the fundamentals of elasticity and plasticity, applies these fundamentals to solve analytically a spectrum of engineering problems, and introduces advanced topics of mechanics of materials - including fracture mechanics, creep, superplasticity, fiber reinforced composites, powder compacts, and porous solids.Text includes:· stress and strain, equilibrium, and compatibility· elastic stress-strain relations· the elastic problem and the stress function approach to solving plane elastic problems· applications of the stress function solution in Cartesian and polar coordinates· Problems of elastic rods, plates, and shells through formulating a strain compatibility function as well as applying energy methods· Elastic and elastic-plastic fracture mechanics· Plastic and creep deformation· Inelastic deformation and its applications This book presents the material in an instructive manner, suitable for individual self-study. It emphasizes analytical treatment of the subject, which is essential for handling modern numerical methods as well as assessing and creating software packages. The authors provide generous explanations, systematic derivations, and detailed discussions, supplemented by a vast variety of problems and solved examples.Primarily written for professionals and students in mechanical engineering, Engineering Solid Mechanics also serves persons in other fields of engineering, such as aerospace, civil, and material engineering.

Chapter 1 Analysis of Stress

(48)

1.1 Rigid and Deformable Bodies

(1)

1.2 Body Forces and Surface Tractions

(1)

1.3 Concept of Stress and Strain

(1)

1.4 The State of Stress at a Point

(4)

1.5 Cartesian Stress Components

(2)

1.6 Some Special States of Stress

(1)

1.6.1 Plane Stress

(1)

1.6.2 Plane Strain

(1)

1.6.3 Axial Symmetry

(1)

1.6.4 Free Torsion

(1)

1.7 Stress Equations of Equilibrium

(12)

1.7.1 Cartesian Coordinates

(4)

1.7.2 Cylindrical Polar Coordinates

(3)

1.7.3 Spherical Polar Coordinates

(1)

1.7.4 Curvilinear Coordinates

(3)

1.8 Stress Transformation Law

(6)

1.9 Plane Stress Transformation -- Mohr's Circle of Stress

(2)

1.10 Principal Stresses

(5)

1.11 Maximum Shear Stresses

(4)

1.12 Octahedral Shear Stress -- Pure Shear

(1)

1.13 Mean (Hydrostatic) Stress and Deviatoric Stresses

(2)

1.14 A Note on the Stress Equations

(1)

Problems

(7)

References

(1)

Chapter 2 Analysis of Strain

(52)

2.1 Infinitesimal Strains

(5)

2.1.1 Normal Strain

(1)

2.1.2 Shear Strain

(2)

2.1.3 Volumetric Strain

(2)

2.2 Infinitesimal Strain-Displacement Relations

(8)

2.2.1 Cartesian Coordinates

(5)

2.2.2 Cylindrical Polar Coordinates

(2)

2.2.3 Spherical Polar Coordinates

(1)

2.3 Strain Compatibility Conditions

(5)

2.3.1 Cartesian Coordinates

(2)

2.3.2 Cylindrical Polar Coordinates

(1)

2.3.3 Spherical Polar Coordinates

(2)

2.4 Strain Tensor

(4)

2.5 Some Special States of Strain

(3)

2.5.1 Plane Strain

(1)

2.5.2 Plane Stress

(1)

2.5.3 Axial Symmetry

(1)

2.5.4 Free Torsion

(2)

2.6 Principal Strains -- Maximum and Octahedral Shear Strains

(2)

2.7 Mean Strain Dilatation and Strain Deviations

(2)

2.8 Mohr's Circle of Strain

(2)

2.9 Strain Gauge Rosettes

(2)

2.10 Notes on Finite Strains

(5)

2.11 Strain Rate-Velocity Relations

(3)

Problems

(9)

References

(2)

Chapter 3 Elastic Stress-Strain Relations

101

(54)

3.1 Introduction

101

(1)

3.2 Basic Assumptions: Elasticity, Homogeneity, and Isotropy

101

(2)

3.2.1 Elasticity

101

(1)

3.2.2 Homogeneity

102

(1)

3.2.3 Isotropy

103

(1)

3.3 Hooke's Law for Homogeneous Isotropic Materials

103

(5)

3.3.1 Simple Loading

103

(1)

3.3.2 Triaxial Loading

104

(4)

3.4 Relations Among the Elastic Constants

108

(2)

3.5 Inverse Form of Hooke's Law

110

(2)

3.6 Dilatation and Distortion

112

(2)

3.7 Thermoelastic Stress-Strain Relations

114

(2)

3.8 Strain Energy for an Elastic Isotropic Solid

116

(6)

3.9 Strain Energy for a Solid Obeying Hooke's Law

122

(6)

3.10 Some Elastic Energy Theorems

128

(7)

3.10.1 Principle of Work

128

(1)

3.10.2 Principle of Virtual Work

129

(2)

3.10.3 Principle of Stationary Potential Energy

131

(1)

3.10.4 Castigliano's Theorems

132

(3)

3.11 Generalized Hooke's Law

135

(11)

3.11.1 Anisotropic Elasticity

135

(5)

3.11.2 Application to Fiber-Reinforced Composites

140

(6)

3.12 Note on Composite Elastic Constants

146

(1)

3.13 Stress-Strain Relations for Large Elastic Deformation

146

(4)

Problems

150

(4)

References

154

(1)

Chapter 4 Solution of the Elastic Problem

155

(50)

4.1 The Elastic Problem

155

(1)

4.2 Boundary Conditions

156

(3)

4.3 Saint-Venant's Principle

159

(1)

4.4 Uniqueness and Semi-Inverse Method of Elastic Solution

160

(1)

4.5 Example of Solution in Terms of Stress: Pressurized Thick-Walled Sphere

161

(3)

4.6 The Elastic Plane Problem

164

(6)

4.6.1 Plane Strain Formulation

165

(2)

4.6.2 Plane Stress Formulation

167

(2)

4.6.3 Deduction of Plane Stress Equations from Plane Strain Equations

169

(1)

4.7 Stress Function Formulation for Plane Elastic Problems

170

(1)

4.8 Governing Equations in Terms of a Stress Function in Cartesian Coordinates

171

(12)

4.8.1 Plane Strain

171

(3)

4.8.2 Plane Stress

174

(1)

4.8.3 Thermoelastic Plane Problem

174

(1)

4.8.3.1 Thermoelastic Plane Strain

174

(1)

4.8.3.2 Thermoelastic Plane Stress

175

(7)

4.8.4 Finding a Stress Function in Cartesian Coordinates

182

(1)

4.9 Governing Equations in Terms of a Stress Function in Polar Coordinates

183

(12)

4.9.1 Plane Strain

183

(2)

4.9.2 Plane Stress

185

(2)

4.9.3 Axisymmetric Plane Problems

187

(1)

4.9.3.1 Axisymmetric Problems without Body Forces

187

(2)

4.9.3.2 Axisymmetric Problems with Centrifugal Body Forces

189

(2)

4.9.3.3 Axisymmetric Problems with Radial Temperature Gradient

191

(4)

4.9.4 A Note on Finding a Stress Function in Polar Coordinates

195

(1)

4.10 A Glossary of Stress Functions for Some Plane Problems

195

(5)

4.10.1 Cartesian Coordinates

195

(2)

4.10.2 Polar Coordinates

197

(3)

Problems

200

(3)

References

203

(2)

Chapter 5 Elastic Plane Problems in Cartesian Coordinates

205

(38)

5.1 Introduction

205

(1)

5.2 Problems Solved in Terms of Algebraic Polynomials

205

(24)

5.2.1 Retaining Wall Subjected to Hydrostatic Pressure

209

(4)

5.2.2 Simply Supported Beam under Uniformly Distributed Load

213

(7)

5.2.3 Cantilever Beam Subjected to an End Load

220

(1)

5.2.3.1 Stresses

220

(2)

5.2.3.2 Displacements

222

(7)

5.3 Problems Solved in Terms of Trigonometric Stress Functions

229

(5)

5.3.1 Simply Supported Beam under Laterally Distributed Sinusoidal Load on Both Sides

230

(2)

5.3.2 Simply Supported Beam under Two Equal Lateral Loads at the Middle of the Span

232

(1)

5.3.3 Bar subjected to Two Equal and Opposite Axial Loads

233

(1)

5.4 A Note on Some Other Forms of Stress Functions

234

(3)

Problems

237

(4)

References

241

(2)

Chapter 6 Elastic Plane Problems in Polar Coordinates

243

(76)

6.1 Introduction

243

(1)

6.2 Axisymmetric Problems

243

(30)

6.2.1 Thick-Walled Cylinder Subjected to Uniform Internal and/or External Pressure

243

(3)

6.2.1.1 Cylinder Subjected to Internal Pressure Only

246

(1)

6.2.1.2 Cylinder Subjected to External Pressure Only

247

(3)

6.2.2 Thick-Walled Cylinder Subjected to Steady-State Radial Thermal Gradient

250

(1)

6.2.2.1 Plane Strain

250

(3)

6.2.2.2 Plane Stress

253

(1)

6.2.2.3 Other End Conditions

254

(1)

6.2.3 Cylinder Compounding by Shrink Fit

255

(7)

6.2.4 Rotating Disk of Uniform Thickness

262

(1)

6.2.4.1 Annular Rotating Disk of Constant Thickness

262

(2)

6.2.4.2 Solid Rotating Disk of Constant Thickness

264

(2)

6.2.5 Rotating Solid Disk of Uniform Strength (De Laval Disk)

266

(3)

6.2.6 Rotating Drums and Rotors

269

(1)

6.2.7 Rotating Disks and Rotors Subjected to Radial Thermal Gradients

270

(3)

6.3 Axially Nonsymmetric Problems

273

(30)

6.3.1 Bending of a Circularly Curved Beam

274

(1)

6.3.1.1 Beam Subjected to an End Shearing Force

274

(6)

6.3.1.2 Beam Subjected to Pure Bending

280

(2)

6.3.1.3 Beam Subjected to an End Moment and a Normal Force

282

(1)

6.3.1.4 Beam Subjected to an Inclined End Force

282

(1)

6.3.2 Thermal Stresses in Curved Beams

283

(3)

6.3.3 Wedge Subjected to a Concentrated Load at its Vertex

286

(1)

6.3.3.1 Force Acting Along a Wedge Axis

286

(3)

6.3.3.2 Force Perpendicular to the Wedge Axis

289

(1)

6.3.3.3 Force Inclined to the Wedge Axis

290

(2)

6.3.3.4 Bending Moment Acting at the Vertex

292

(3)

6.3.4 Concentrated Line Load Acting on the Edge of a Straight Boundary

295

(1)

6.3.4.1 Force Acting Normal to the Boundary

295

(1)

6.3.4.2 Force Acting Along the Boundary

296

(1)

6.3.4.3 Force Acting Inclined to the Boundary

297

(1)

6.3.5 Uniformly Distributed Line Load Acting on the Edge of a Straight Boundary

297

(2)

6.3.6 Circular Solid Disk Subjected to Two Equal and Opposite Diametral Loads

299

(2)

6.3.7 Concentrated Load Acting on a Rectangular Beam

301

(2)

6.4 Stresses Concentration Around a Small Circular Hole

303

(8)

Problems

311

(7)

References

318

(1)

Chapter 7 Elastic Rods Subjected to General Loading

319

(122)

7.1 Introduction

319

(1)

7.2 Stress Resultants

319

(3)

7.2.1 Note on Sign Convention for Stress Resultants

321

(1)

7.3 Bending of Rods

322

(23)

7.3.1 Bending Stresses

322

(4)

7.3.2 Elastic Curve in Bending

326

(4)

7.3.3 Bending of Curved Beams

330

(4)

7.3.3.1 Determination of the Location of the Neutral Axis

334

(2)

7.3.3.2 Approximate Determination of the Neutral Axis

336

(1)

7.3.3.3 Maximum Stresses

337

(1)

7.3.3.4 Bending of a Curved Beam by Lateral Forces Acting in the Plane of Its Axis

337

(2)

7.3.3.5 Strain Energy in Curved Beams

338

(1)

7.3.3.6 Comparison with Exact and Other Solutions

339

(2)

7.3.4 Thermoelastic Bending of Straight Bars

341

(4)

7.4 Shear Stresses in Rods

345

(14)

7.4.1 Rectangular Solid Section

347

(2)

7.4.2 Circular Solid Section

349

(3)

7.4.3 Thin-Walled Open Sections

352

(3)

7.4.3.1 Shear Center

355

(2)

7.4.4 Thin-Walled Closed Sections

357

(2)

7.5 Torsion of Bars

359

(17)

7.5.1 Saint-Venant's Free Torsion

360

(3)

7.5.2 Solid Circular Section

363

(2)

7.5.3 Solid Elliptical Section

365

(1)

7.5.4 Solid Rectangular Section

366

(2)

7.5.5 Thin-Walled Open Sections

368

(2)

7.5.6 Thin-Walled Closed Sections

370

(2)

7.5.7 Effect of Internal Stiffening Webs

372

(1)

7.5.8 Effect of End Constraint

373

(1)

7.5.8.1 Solid Sections

374

(1)

7.5.8.2 Thin-Walled Sections

375

(1)

7.6 Displacements in Rods -- Energy Approach

376

(22)

7.6.1 Application of Castigliano's Theorem

376

(8)

7.6.2 Mohr's Unit Load Method

384

(3)

7.6.3 A Note on the Deflection of Curved Beams

387

(4)

7.6.4 Application to Springs

391

(1)

7.6.4.1 Helical Compression Spring

391

(2)

7.6.4.2 Spiral Helical Compression Spring

393

(1)

7.6.4.3 Flat Compression Spring

394

(1)

7.6.4.4 Flat Torsion Spring

395

(3)

7.7 Buckling of Rods

398

(17)

7.7.1 Buckling of Columns

398

(1)

7.7.1.1 Equilibrium Approach

398

(5)

7.7.1.2 Minimum Potential Energy Solution: Rayleigh-Ritz Method

403

(7)

7.7.2 Beam-Columns

410

(2)

7.7.3 Lateral Buckling of Beams

412

(3)

7.8 Beams on Elastic Foundation

415

(10)

7.8.1 Infinitely Long Beams

416

(1)

7.8.1.1 Concentrated Force

416

(2)

7.8.1.2 Concentrated Moment

418

(2)

7.8.1.3 Uniform Load

420

(2)

7.8.2 Semi-Infinite Beams

422

(3)

7.8.3 Short Beams

425

(1)

Problems

425

(14)

References

439

(2)

Chapter 8 Some Problems of Elastic Plates and Shells

441

(120)

8.1 Introduction

441

(1)

8.2 State of Stress in Plates and Shells

441

(1)

8.3 Plate Equations in Cartesian Coordinates

442

(10)

8.3.1 Deformation Pattern

442

(2)

8.3.2 Stress Resultants

444

(1)

8.3.3 Equations of Equilibrium

445

(3)

8.3.4 Method of Solution: Pure Bending of a Plate

448

(1)

8.3.5 Effect of Thermal Gradient Throughout Plate Thickness

449

(1)

8.3.5.1 A Plate with Free Edges

449

(1)

8.3.5.2 A Plate with Clamped Edges

450

(1)

8.3.5.3 A Plate with Simply Supported Edges

451

(1)

8.4 Bending of Rectangular Plates -- Energy Approach

452

(14)

8.4.1 Uniformly Loaded Rectangular Plate Simply Supported Along Its Four Edges

452

(6)

8.4.2 Uniformly Loaded Rectangular Plate Clamped Along Its Four Edges

458

(7)

8.4.3 An Approximate Strip Method for Rectangular Plates

465

(1)

8.5 Axisymmetric Bending of Flat, Circular Plates

466

(20)

8.5.1 Solid Circular Plates

468

(1)

8.5.1.1 Simply Supported Plate Subjected to Uniform Pressure

468

(1)

8.5.1.2 All-Around Clamped Plate Subjected to Uniform Pressure

469

(3)

8.5.1.3 All-Around Clamped Plate Subjected to a Concentrated Force at the Center

472

(2)

8.5.1.4 Simply Supported Plate Subjected to a Concentrated Force at the Center

474

(1)

8.5.2 Annular Circular Plates

475

(1)

8.5.2.1 Simply Supported Annular Plate Subjected to Edge Moments

475

(2)

8.5.2.2 Simply Supported Annular Circular Plate Subjected to a Shearing Force at the Inner Edge

477

(1)

8.5.3 Other Loadings and Edge Conditions

478

(1)

8.5.4 Thermal Stresses in Circular Plates

479

(1)

8.5.4.1 Temperature Gradient Across the Thickness of a Disk with Free Edges

479

(1)

8.5.4.2 Temperature Gradient Across the Thickness of a Disk with All-Around Clamped Edges

480

(1)

8.5.4.3 Axisymmetric Radial Temperature Gradient

480

(2)

8.5.5 Comments on the Deflection of Circular Plates

482

(1)

8.5.5.1 Deflection Due to Shear

482

(1)

8.5.5.2 Large Deflection

483

(3)

8.6 Membrane Stresses in Axisymmetric Shells

486

(21)

8.6.1 Axisymmetric Shells Subjected to Uniform Pressure

486

(4)

8.6.2 Applications to Pressurized Containers

490

(1)

8.6.2.1 Spherical Shell

490

(1)

8.6.2.2 Circular Cylindrical Shell

491

(1)

8.6.2.3 Conical Shell

491

(1)

8.6.2.4 Toroidal Shell

492

(1)

8.6.3 Displacement in Axisymmetric Shells

493

(6)

8.6.4 Axisymmetric Shells Subjected to Gravity Loading

499

(1)

8.6.4.1 Hemispherical Liquid Container Freely Supported at Its Top Edge

499

(1)

8.6.4.2 Conical Liquid Container Freely Supported at Its Top Edge

500

(4)

8.6.4.3 Spherical Container on a Skirt Support

504

(3)

8.7 Bending of Thin-Walled Cylinders Subjected to Axisymmetric Loading

507

(33)

8.7.1 Problem Formulation

507

(6)

8.7.2 Long, Thin-Walled Pressurized Pipe with a Rigid Flange at its End

513

(4)

8.7.3 Short, Thin-Walled Pressurized Pipe with Two Rigid Flanges at Both Ends

517

(1)

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Engineering Solid Mechanics: Fundamentals and Applications

Summary

Table of Contents

Supplemental Materials

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Engineering Solid Mechanics: Fundamentals and Applications

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Table of Contents

Supplemental Materials

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