Page 287 - Shigley's Mechanical Engineering Design

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262 Mechanical Engineering Design
These are shrink-fitted together. Find the nominal shrink-fit pressure and the von Mises stress in
each body at the fit surface.
5–72 Repeat Prob. 5–71 for maximum shrink-fit conditions.
5–73 A solid steel shaft has a gear with ASTM grade 20 cast-iron hub (E = 14.5 Mpsi) shrink-fitted
to it. The shaft diameter is 2.001 ± 0.0004 in. The specifications for the gear hub are

+ 0.0004
2.000 in
− 0.0000
1
ID with an OD of 4.00 ± in. Using the midrange values and the modified Mohr theory,
32
estimate the factor of safety guarding against fracture in the gear hub due to the shrink fit.
5–74 Two steel tubes are shrink-fitted together where the nominal diameters are 40, 45, and 50 mm.
Careful measurement before fitting determined the diametral interference between the tubes to be
0.062 mm. After the fit, the assembly is subjected to a torque of 900 N · m and a bending-moment
of 675 N · m. Assuming no slipping between the cylinders, analyze the outer cylinder at the inner
and outer radius. Determine the factor of safety using distortion energy with S y = 415 MPa.
5–75 Repeat Prob. 5–74 for the inner tube.
5–76 to For the problem given in the table, the specifications for the press fit of two cylinders are given
5–81 in the original problem from Chap. 3. If both cylinders are hot-rolled AISI 1040 steel, determine
the minimum factor of safety for the outer cylinder based on the distortion-energy theory.

Problem Number Original Problem, Page Number
5–76 3–110, 143
5–77 3–111, 143
5–78 3–112, 143
5–79 3–113, 143
5–80 3–114, 143
5–81 3–115, 143

5–82 For Eqs. (5–36) show that the principal stresses are given by

θ θ
K I
σ 1 = √ cos 1 + sin
2πr 2 2
θ θ
K I
σ 2 = √ cos 1 − sin
2πr 2 2
⎨ 0 (plane stress)
⎧
σ 3 = 2 θ
⎩ νK I cos (plane strain)
πr 2
1
5–83 Use the results of Prob. 5–82 for plane strain near the tip with θ = 0 and ν = . If the yield
3
strength of the plate is S y , what is σ 1 when yield occurs?
(a) Use the distortion-energy theory.
(b) Use the maximum-shear-stress theory. Using Mohr’s circles, explain your answer.