Page 372 - Shigley's Mechanical Engineering Design

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Fatigue Failure Resulting from Variable Loading 347
Torsion. Use the same equations as apply for σ m ≥ 0, except replace σ m and σ a with
τ m and τ a , use k c = 0.59 for S e , replace S ut with S su = 0.67S ut [Eq. (6–54), p. 317],
and replace S y with S sy = 0.577S y [Eq. (5–21), p. 297]
3 Check for localized yielding.

p. 306 σ a + σ m = S y /n (6–49)
or, for torsion, τ a + τ m = 0.577S y /n

4 For finite-life fatigue strength, equivalent completely reversed stress (see Ex. 6–12,
pp. 313–314),

σ a
mod-Goodman σ rev =
1 − (σ m /S ut )
σ a
Gerber σ rev =
1 − (σ m /S ut ) 2
If determining the finite life N with a factor of safety n, substitute σ rev /n for σ rev in
Eq. (6–16). That is,
1/b
σ rev /n

N =
a

Combination of Loading Modes
See previous subsections for earlier definitions.

1 Calculate von Mises stresses for alternating and midrange stress states, σ and σ .

a m
When determining S e , do not use k c nor divide by K f or K fs . Apply K f and/or
K fs directly to each specific alternating and midrange stress. If axial stress is
present divide the alternating axial stress by k c = 0.85. For the special case of
combined bending, torsional shear, and axial stresses
p. 318

1/2

2

(σ a ) axial 2

σ = (K f ) bending (σ a ) bending + (K f ) axial + 3 (K fs ) torsion (τ a ) torsion
a
0.85
(6–55)
1/2

2 2

σ = (K f ) bending (σ m ) bending + (K f ) axial (σ m ) axial + 3 (K fs ) torsion (τ m ) torsion
m
(6–56)
2 Apply stresses to fatigue criterion [see Eqs. (6–45) to (6–48), p. 346 in previous
subsection].
3 Conservative check for localized yielding using von Mises stresses.

p. 306 σ + σ = S y /n (6–49)
m
a