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
x
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
xii
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