Page 371 - Shigley's Mechanical Engineering Design

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346 Mechanical Engineering Design

pp. 293–294, k f
3 Determine fatigue stress-concentration factor, K f or K fs . First, find K t or K ts from
Table A–15.
p. 295 K f = 1 + q(K t − 1) or K fs = 1 + q(K ts − 1) (6–32)

Obtain q from either Fig. 6–20 or 6–21, pp. 295–296.
Alternatively,
K t − 1
p. 296 K f = 1 + √ (6–33)
1 + a/r
√ √
For a in units of in, and S ut in kpsi
√ −3 −5 2 −8 3
Bending or axial: a = 0.246 − 3.08(10 )S ut + 1.51(10 )S − 2.67(10 )S ut
ut
(6–35a)
√ −3 −5 2 −8 3
Torsion: a = 0.190 − 2.51(10 )S ut + 1.35(10 )S − 2.67(10 )S ut (6–35b)
ut
4 Apply K f or K fs by either dividing S e by it or multiplying it with the purely
reversing stress, not both.
5 Determine fatigue life constants a and b. If S ut ≥ 70 kpsi, determine f from
Fig. 6–18, p. 285. If S ut < 70 kpsi, let f = 0.9.
2
p. 285 a = ( fS ut ) /S e (6–14)
b =−[log( fS ut /S e )]/3 (6–15)
6 Determine fatigue strength S f at N cycles, or, N cycles to failure at a reversing
stress σ rev
(Note: this only applies to purely reversing stresses where σ m = 0).
p. 285 S f = aN b (6–13)
1/b
N = (σ rev /a) (6–16)
Fluctuating Simple Loading
For S e , K f or K fs , see previous subsection.
1 Calculate σ m and σ a . Apply K f to both stresses.
p. 301 σ m = (σ max + σ min )/2 σ a =|σ max − σ min |/2 (6–36)
2 Apply to a fatigue failure criterion, p. 306

σ m ≥ 0
Soderburg σ a /S e + σ m /S y = 1/n (6–45)
mod-Goodman σ a /S e + σ m /S ut = 1/n (6–46)
2
Gerber nσ a /S e + (nσ m /S ut ) = 1 (6–47)
2
2
ASME-elliptic (σ a /S e ) + (σ m /S y ) = 1/n 2 (6–48)
σ m < 0
p. 305 σ a = S e /n