CHAPTER 3 LOAD DETERMINATION ___________________________________ 73

3.0

Introduction ................................................................................................... 73

3.1

Loading Classes.............................................................................................. 73

3.2

Free-Body Diagrams ........................................................................................ 75

3.3

Load Analysis ................................................................................................. 76

Three-Dimensional Analysis

76

Two-Dimensional Analysis

77

Static Load Analysis

78

3.4

Two-Dimensional, Static Loading Case Studies ............................................. 78

Case Study 1A: Bicycle Brake Lever Loading Analysis

79

Case Study 2A: Hand-Operated Crimping-Tool Loading Analysis

84

Case Study 3A: Automobile Scissors-Jack Loading Analysis

88

3.5

Three-Dimensional, Static Loading Case Study............................................. 93

Case Study 4A: Bicycle Brake Arm Loading Analysis

94

3.6

Dynamic Loading Case Study ........................................................................ 98

Case Study 5A: Fourbar Linkage Loading Analysis

98

3.7

Vibration Loading ........................................................................................ 101

Natural Frequency

102

Dynamic Forces

104

Case Study 5B: Fourbar Linkage Dynamic Loading Measurement

105

3.8

Impact Loading............................................................................................. 106

Energy Method

107

3.9

Beam Loading .............................................................................................. 111

Shear and Moment

111

Singularity Functions

112

Superposition

122

3.10 Summary ..................................................................................................... 123

3.11 References ................................................................................................... 125

3.12 Web References ............................................................................................ 126

3.13 Bibliography ................................................................................................. 126

3.14 Problems ...................................................................................................... 126

CHAPTER 4 STRESS, STRAIN, AND DEFLECTION ___________________________ 139

4.0

Introduction ................................................................................................. 139

4.1

Stress ............................................................................................................ 139

4.2

Strain ............................................................................................................ 143

4.3

Principal Stresses ......................................................................................... 143

4.4

Plane Stress and Plane Strain ....................................................................... 146

Plane Stress

146

Plane Strain

146

4.5

Mohr’s Circles .............................................................................................. 146

4.6

Applied Versus Principal Stresses ................................................................. 151

4.7

Axial Tension ............................................................................................... 152

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MACHINE DESIGN -

An Integrated Approach

4.8

Direct Shear Stress, Bearing Stress, and Tearout ......................................... 153

Direct Shear

153

Direct Bearing

154

Tearout Failure

154

4.9

Beams and Bending Stresses ....................................................................... 154

Beams in Pure Bending

155

Shear Due to Transverse Loading

158

4.10 Deflection in Beams ..................................................................................... 162

Deflection by Singularity Functions

164

Statically Indeterminate Beams

171

4.11 Castigliano’s Method ................................................................................... 173

Deflection by Castigliano’s Method

175

Finding Redundant Reactions with Castigliano’s Method

175

4.12 Torsion ......................................................................................................... 177

4.13 Combined Stresses ....................................................................................... 183

4.14 Spring Rates.................................................................................................. 185

4.15 Stress Concentration ................................................................................... 186

Stress Concentration Under Static Loading

187

Stress Concentration Under Dynamic Loading

188

Determining Geometric Stress-Concentration Factors

188

Designing to Avoid Stress Concentrations

191

4.16 Axial Compression - Columns ..................................................................... 193

Slenderness Ratio

193

Short Columns

193

Long Columns

193

End Conditions

195

Intermediate Columns

197

Eccentric Columns

200

4.17 Stresses in Cylinders ...................................................................................... 203

Thick-Walled Cylinders

204

Thin-Walled Cylinders

205

4.18 Case Studies in Static Stress and Deflection Analysis .................................. 205

Case Study 1B: Bicycle Brake Lever Stress and Deflection Analysis 206

Case Study 2B: Crimping-Tool Stress and Deflection Analysis

209

Case Study 3B: Automobile Scissors-Jack Stress and Deflection Analysis 214

Case Study 4B: Bicycle Brake Arm Stress Analysis

217

4.19 Summary ...................................................................................................... 221

4.20 References .................................................................................................... 227

4.21 Bibliography ................................................................................................. 228

4.22 Problems ...................................................................................................... 228

CHAPTER 5 STATIC FAILURE THEORIES _________________________________ 243

5.0

Introduction ................................................................................................. 243

5.1

Failure of Ductile Materials Under Static Loading ....................................... 245

The von Mises-Hencky or Distortion-Energy Theory

246

The Maximum Shear-Stress Theory

252

The Maximum Normal-Stress Theory

254

Comparison of Experimental Data with Failure Theories

254

 

xi

5.2

Failure of Brittle Materials Under Static Loading ....................................... 258

Even and Uneven Materials

258

The Coulomb-Mohr Theory

259

The Modified-Mohr Theory

260

5.3

Fracture Mechanics ..................................................................................... 265

Fracture-Mechanics Theory

266

Fracture Toughness Kc

269

5.4

Using The Static Loading Failure Theories ................................................. 273

5.5

Case Studies in Static Failure Analysis ........................................................ 274

Case Study 1C: Bicycle Brake Lever Failure Analysis

274

Case Study 2C: Crimping Tool Failure Analysis

277

Case Study 3C: Automobile Scissors-Jack Failure Analysis

280

Case Study 4C: Bicycle Brake Arm Factors of Safety

282

5.6

Summary .................................................................................................... 285

5.7

References .................................................................................................. 288

5.8

Bibliography ................................................................................................ 289

5.9

Problems ..................................................................................................... 290

CHAPTER 6 FATIGUE FAILURE THEORIES ________________________________ 303

6.0

Introduction ................................................................................................ 303

History of Fatigue Failure

303

6.1

Mechanism of Fatigue Failure .................................................................... 306

Crack Initiation Stage

307

Crack Propagation Stage

307

Fracture

308

6.2

Fatigue-Failure Models ................................................................................. 309

Fatigue Regimes

309

The Stress-Life Approach

311

The Strain-Life Approach

311

The LEFM Approach

311

6.3

Machine-Design Considerations ............................................................... 312

6.4

Fatigue Loads .............................................................................................. 313

Rotating Machinery Loading

313

Service Equipment Loading

314

6.5

Measuring Fatigue Failure Criteria ............................................................ 315

Fully Reversed Stresses

316

Combined Mean and Alternating Stress

322

Fracture-Mechanics Criteria

323

Testing Actual Assemblies

326

6.6

Estimating Fatigue Failure Criteria ............................................................. 327

Estimating the Theoretical Fatigue Strength Sf’ or Endurance Limit Se’ 328

Correction Factors to the Theoretical Fatigue Strength

330

Calculating the Corrected Fatigue Strength Sf

337

Creating Estimated S-N Diagrams

337

6.7

Notches and Stress Concentrations ............................................................. 342

Notch Sensitivity

343

6.8

Residual Stresses ........................................................................................ 347

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MACHINE DESIGN -

An Integrated Approach

6.9

Designing for High-Cycle Fatigue ............................................................... 352

6.10 Designing for Fully Reversed Uniaxial Stresses .......................................... 352

Design Steps for Fully Reversed Stresses with Uniaxial Loading: 353

6.11 Designing for Fluctuating Uniaxial Stresses ............................................... 360

Creating the Modified-Goodman Diagram

361

Applying Stress-Concentration Effects with Fluctuating Stresses 364

Determining the Safety Factor with Fluctuating Stresses

366

Design Steps for Fluctuating Stresses

369

6.12 Designing for Multiaxial Stresses in Fatigue .............................................. 376

Frequency and Phase Relationships

377

Fully Reversed Simple Multiaxial Stresses

377

Fluctuating Simple Multiaxial Stresses

378

Complex Multiaxial Stresses

379

6.13 A General Approach to High-Cycle Fatigue Design ..................................... 381

6.14 A Case Study in Fatigue Design ................................................................... 386

Case Study 6: Redesign of a Failed Laybar for a Water-Jet Power Loom 387

6.15 Summary ...................................................................................................... 399

6.16 References .................................................................................................... 403

6.17 Bibliography ................................................................................................. 406

6.18 Problems ...................................................................................................... 407