Page 359 - Shigley's Mechanical Engineering Design

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334 Mechanical Engineering Design

EXAMPLE 6–17 Estimate the Marin loading factor k c for a 1–in-diameter bar that is used as follows.
(a) In bending. It is made of steel with S ut = 100LN(1, 0.035) kpsi, and the designer
intends to use the correlation S = 0.30 ut to predict S .

S

¯
e e

(b) In bending, but endurance testing gave S = 55LN(1, 0.081) kpsi.
e
(c) In push-pull (axial) fatigue, S ut = LN(86.2, 3.92) kpsi, and the designer intended to
use the correlation S = 0.30 ut .
S
¯

e
(d) In torsional fatigue. The material is cast iron, and S is known by test.

e
Solution (a) Since the bar is in bending,
Answer k c = (1, 0)
(b) Since the test is in bending and use is in bending,
Answer k c = (1, 0)
(c) From Eq. (6–73),
Answer (k c ) ax = 1.23(86.2) −0.0778 LN(1, 0.125)
k c = 1.23(86.2) −0.0778 (1) = 0.870
¯
ˆ σ kc = Ck c = 0.125(0.870) = 0.109
¯
(d) From Table 6–15, k c = 0.90, ˆσ kc = 0.07, and
¯
0.07
Answer C kc = = 0.08
0.90

The temperature factor k d is
k d = k d LN(1, 0.11) (6–75)
¯
where k d = k d , given by Eq. (6–27), p. 291.
¯
Finally, k f is, as before, the miscellaneous factor that can come about from a great
many considerations, as discussed in Sec. 6–9, where now statistical distributions, pos-
sibly from testing, are considered.

Stress Concentration and Notch Sensitivity
Notch sensitivity q was defined by Eq. (6–31), p. 295. The stochastic equivalent is

K f − 1
q = (6–76)
K t − 1

where K t is the theoretical (or geometric) stress-concentration factor, a deterministic
quantity. A study of lines 3 and 4 of Table 20–6, will reveal that adding a scalar to (or
subtracting one from) a variate x will affect only the mean. Also, multiplying (or divid-
ing) by a scalar affects both the mean and standard deviation. With this in mind, we can