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Fatigue Failure Resulting from Variable Loading 345
2 Modify S to determine S e .

e
p. 287 S e = k a k b k c k d k e k f S (6–18)
e
k a = aS b (6–19)
ut
Table 6–2 Factor a Exponent

Parameters for Marin Surface Finish S ut , kpsi S ut , MPa b
Surface Modification Ground 1.34 1.58 −0.085
Factor, Eq. (6–19) Machined or cold-drawn 2.70 4.51 −0.265
Hot-rolled 14.4 57.7 −0.718
As-forged 39.9 272. −0.995

Rotating shaft. For bending or torsion,
⎧
⎪ (d/0.3) −0.107 = 0.879d −0.107 0.11 ≤ d ≤ 2in
⎪
⎪
⎪ −0.157
0.91d 2 < d ≤ 10 in
⎨
p. 288 k b = (6–20)
⎪ (d/7.62) −0.107 = 1.24d −0.107 2.79 ≤ d ≤ 51 mm
⎪
⎪
1.51d 51 < 254 mm
⎪ −0.157
⎩
For axial,
k b = 1 (6–21)
Nonrotating member. Use Table 6–3, p. 290, for d e and substitute into Eq. (6–20)
for d.
⎧
⎪ 1 bending
⎨
p. 290 k c = 0.85 axial (6–26)
⎪
0.59 torsion
⎩
p. 291 Use Table 6–4 for k d, or
−3
−5
k d = 0.975 + 0.432(10 )T F − 0.115(10 )T F 2
3
−8
+ 0.104(10 )T − 0.595(10 −12 )T 4 (6–27)
F F
pp. 292–293, k e
Table 6–5
Reliability, % Transformation Variate z a Reliability Factor k e
Reliability Factor k e 50 0 1.000
Corresponding to 90 1.288 0.897
8 Percent Standard 95 1.645 0.868
Deviation of the 99 2.326 0.814
Endurance Limit 99.9 3.091 0.753

99.99 3.719 0.702
99.999 4.265 0.659
99.9999 4.753 0.620