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Contents
Chapter 2 Application of Probability to Mechanical Design
39
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Probability
39
Bayes Theorem
42
Decision Trees
44
Variance
47
A. Total Differential of the Variance
47
B. Card Sort Solution Estimate of Variance
51
C. Computer Estimate of Variance and Distribution
56
Safety Factors and Probability of Failure
56
Fatigue
66
A. Some Factors Influencing Fatigue Behavior
69
1. Surface condition, ka
70
2. Size and shape, kb
71
3. Reliability, kc
72
4. Temperature, ka
73
5. Stress concentration, ke
74
6. Residual stress, kf
79
7. Internal Structure, kg
81
8. Environment, kh
82
9. Surface treatment and hardening, ki
82
10. Fretting, kj
83
11. Shock or vibration loading, kk
84
12. Radiation, kt
84
13. Speed
84
14. Mean stress
85
B. Fatigue Properties of Materials
87
1. Bending
90
2. Contact
91
3. Low cycle fatigue using strain
93
C. ~rr--am curves
95
1. Mean curve
103
2. Card sort
105
D. Fatigue Considerations in Design Codes
107
E.
Summary for Fatigue Calculations
107
F. Monte Carlo Fatigue Calculations
113
G. Bounds on Monte Carlo Fatigue Calculations
126
1. The minimum Pf for a structural member stress s~ 126
2. t and Pf in terms of the safety factor N
129
H. Approximate Dimension Solution Using Cardsort
and Lower Material Bounds
131
References
134
Problems
137