Page 380 - Shigley's Mechanical Engineering Design

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Fatigue Failure Resulting from Variable Loading 355
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for 12 (10 ) cycles. Using the Gerber criterion, estimate the new endurance limit after
cycling.
(a) Use Miner’s method.
(b) Use Manson’s method.
6–63 Repeat Prob. 6–62 using the Goodman criterion.

Stochastic Problems
6–64 Solve Prob. 6–1 if the ultimate strength of production pieces is found to be Sut = 1030LN
(1, 0.0508) MPa.
6–65 The situation is similar to that of Prob. 6–14 wherein the imposed completely reversed axial
load F a = 3.8LN(1, 0.20) kip is to be carried by the link with a thickness to be specified by you,
the designer. Use the 1020 cold-drawn steel of Prob. 6–14 with Sut = 68LN (1, 0.28) and
Syt = 57LN(1, 0.058) kpsi. The reliability goal must exceed 0.99. Using the correlation method,
specify the thickness t.
6–66 A solid round steel bar is machined to a diameter of 32 mm. A groove 3 mm deep with a radius
of 3 mm is cut into the bar. The material has a mean tensile strength of 780 MPa. A completely
reversed bending moment M = 160 N · m is applied. Estimate the reliability. The size factor
should be based on the gross diameter. The bar rotates.
6–67 Repeat Prob. 6–66, with a completely reversed torsional moment of T = 160 N · m applied.
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6–68 A 1 -in-diameter hot-rolled steel bar has a 3 -in diameter hole drilled transversely through it. The
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bar is nonrotating and is subject to a completely reversed bending moment of M = 1500 lbf · in
in the same plane as the axis of the transverse hole. The material has a mean tensile strength of
76 kpsi. Estimate the reliability. The size factor should be based on the gross size. Use Table A–16
for K t .
6–69 Repeat Prob. 6–68, with the bar subject to a completely reversed torsional moment of 2000 lbf · in.

6–70 The plan view of a link is the same as in Prob. 6–30; however, the forces F are completely
reversed, the reliability goal is 0.998, and the material properties are S ut = 64LN(1, 0.045) kpsi
and S y = 54LN(1, 0.077) kpsi. Treat F a as deterministic, and specify the thickness h.

Computer Problems
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6–71 A 1 by 1 -in steel bar has a -in drilled hole located in the center, much as is shown in
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4 2 4
Table A–15–1. The bar is subjected to a completely reversed axial load with a deterministic load
of 1200 lbf. The material has a mean ultimate tensile strength of ¯ S ut = 80 kpsi.
(a) Estimate the reliability.
(b) Conduct a computer simulation to confirm your answer to part a.
6–72 From your experience with Prob. 6–71 and Ex. 6–19, you observed that for completely reversed
axial and bending fatigue, it is possible to
• Observe the COVs associated with a priori design considerations.
• Note the reliability goal.
• Find the mean design factor ¯n d that will permit making a geometric design decision that will
attain the goal using deterministic methods in conjunction with ¯n d .

Formulate an interactive computer program that will enable the user to find ¯n d . While the mater-
ial properties S ut , S y , and the load COV must be input by the user, all of the COVs associated with