Page 369 - Shigley's Mechanical Engineering Design

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344 Mechanical Engineering Design
¯
To evaluate the preceding equation we need S e and K f . The Marin factors are
¯
k a = 2.67S ¯ −0.265 LN(1, 0.058) = 2.67(87.6) −0.265 LN(1, 0.058)
ut
¯
k a = 0.816
k b = 1
k c = 1.23S ¯ −0.078 LN(1, 0.125) = 0.868LN(1, 0.125)
ut
¯
k c = 0.868
k d = k f = 1
¯
¯
and the endurance strength is
¯
S e = 0.816(1)(0.868)(1)(1)0.506(87.6) = 31.4 kpsi
The hole governs. From Table A–15–1 we find d/w = 0.50, therefore K t = 2.18. From
√
Table 6–15 a = 5/S ut = 5/87.6 = 0.0571, r = 0.1875 in. From Eq. (6–78) the
¯
fatigue stress-concentration factor is
2.18
¯
K f = = 1.91
2(2.18 − 1) 0.0571
1 + √
2.18 0.1875
The thickness t can now be determined from Eq. (1)
¯
K f ¯nF ¯ 1.91(2.65)1000
t ≥ = = 0.430 in
(w − d)S e (0.75 − 0.375)31 400
1
1
Use -in-thick strap for the workpiece. The -in thickness attains and, in the rounding
2 2
to available nominal size, exceeds the reliability goal.

The example demonstrates that, for a given reliability goal, the fatigue design factor
that facilitates its attainment is decided by the variabilities of the situation. Furthermore,
the necessary design factor is not a constant independent of the way the concept unfolds.
Rather, it is a function of a number of seemingly unrelated a priori decisions that are made
in giving definition to the concept. The involvement of stochastic methodology can be
limited to defining the necessary design factor. In particular, in the example, the design
factor is not a function of the design variable t; rather, t follows from the design factor.

6–18 Road Maps and Important Design Equations
for the Stress-Life Method

As stated in Sec. 6–15, there are three categories of fatigue problems. The important
procedures and equations for deterministic stress-life problems are presented here.

Completely Reversing Simple Loading
1 Determine S either from test data or

e
⎧
S ut ≤ 200 kpsi (1400 MPa)
⎪ 0.5S ut
⎨
p. 282 S = 100 kpsi S ut > 200 kpsi (6–8)

e
⎪
700 MPa S ut > 1400 MPa
⎩