Page 288 - Shigley's Mechanical Engineering Design

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Failures Resulting from Static Loading 263
5–84 A plate 100 mm wide, 200 mm long, and 12 mm thick is loaded in tension in the direction of the
length. The plate contains a crack as shown in Fig. 5–26 with the crack length of 16 mm. The
√
material is steel with K Ic = 80 MPa · m, and S y = 950 MPa. Determine the maximum possi-
ble load that can be applied before the plate (a) yields, and (b) has uncontrollable crack growth.
5–85 A cylinder subjected to internal pressure p i has an outer diameter of 14 in and a 1-in wall thick-
√
ness. For the cylinder material, K Ic = 72 kpsi · in, S y = 170 kpsi, and S ut = 192 kpsi. If the
cylinder contains a radial crack in the longitudinal direction of depth 0.5 in determine the pres-
sure that will cause uncontrollable crack growth.
5–86 A carbon steel collar of length 1 in is to be machined to inside and outside diameters, respec-
tively, of
D i = 0.750 ± 0.0004 in D o = 1.125 ± 0.002 in

This collar is to be shrink-fitted to a hollow steel shaft having inside and outside diameters,
respectively, of
d i = 0.375 ± 0.002 in d o = 0.752 ± 0.0004 in

These tolerances are assumed to have a normal distribution, to be centered in the spread interval,
and to have a total spread of ±4 standard deviations. Determine the means and the standard devi-
ations of the tangential stress components for both cylinders at the interface.
5–87 Suppose the collar of Prob. 5–44 has a yield strength of S y = N(95.5, 6.59) kpsi. What is the
probability that the material will not yield?
5–88 A carbon steel tube has an outside diameter of 75 mm and a wall thickness of 3 mm. The tube is
to carry an internal hydraulic pressure given as p = N(40, 2) MPa. The material of the tube has
a yield strength of S y = N(350, 29) MPa. Find the reliability using thin-wall theory.