Application of Probability to Mechanical Design
71
Hot rolled:
20919 + 0.05456,tt
ka =
a parabolic form
(2.58)
As forged:
20955 - 0.002666,t,
ka -
a parabolic form
(2.59)
The standard deviations [2.18] and coefficients of variation [2.51] are in
Table 2.4.
2. Size and Shape, k~
The subject of size and shape effects in design is discussed; the same general
conclusions and methods presented here also apply to fatigue loading.
For example, it is seen that the small bar has less volume of material exposed
to a high stress condition for a given loading and consequently should
exhibit a higher fatigue life than the larger bar. Some data illustrating this
effect are shown [2.15]. Shape (moment of inertia) also has an effect as shown
[2.15]. In design it is important to consider effects of size and shape, but by
proper attention to these factors a part several inches in diameter can
be designed to on the basis of fatigue data obtained on small specimens.
A rough guide presented by Castleberry, Juvinall, and Shigley is
- 1 for d < 0.30in.(2.26, 2.51)
0.85 0.3 < d < 2in.(2.26, 2.51)
kb = 1 (d - 0.30) 2 < d < 9in.(2.4)
(2.60)
15
0.65-0.75
4 _ cv ~ 5 to 6% min(2.18)
Table 2.4 ka standard deviations ~ and coefficients of variation
Surface finish
Shigley, Miscke [2.51]
Haugen [2.18]
Ground
Cv = 0.13
}a = 0.103
Cold drawn & machined
Cv = 0.06
~ = 0.0406
2780.5
Hot roiled
Cv =0.11
~a - (~.~/2)
2780.5
Forged
Cv = 0.08
~a =