Page 373 - Shigley's Mechanical Engineering Design

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348 Mechanical Engineering Design
PROBLEMS

Problems marked with an asterisk (*) are linked to problems in other chapters, as summarized in
Table 1–1 of Sec. 1–16, p. 24.
Problems 6–1 to 6–63 are to be solved by deterministic methods. Problems 6–64 to 6–78 are
to be solved by stochastic methods. Problems 6–71 to 6–78 are computer problems.

Deterministic Problems
6–1 A 10-mm drill rod was heat-treated and ground. The measured hardness was found to be 300 Brinell.
Estimate the endurance strength in MPa if the rod is used in rotating bending.
6–2 Estimate S in kpsi for the following materials:

e
(a) AISI 1035 CD steel.
(b) AISI 1050 HR steel.
(c) 2024 T4 aluminum.
(d) AISI 4130 steel heat-treated to a tensile strength of 235 kpsi.
6–3 A steel rotating-beam test specimen has an ultimate strength of 120 kpsi. Estimate the life of the
specimen if it is tested at a completely reversed stress amplitude of 70 kpsi.
6–4 A steel rotating-beam test specimen has an ultimate strength of 1600 MPa. Estimate the life of
the specimen if it is tested at a completely reversed stress amplitude of 900 MPa.
6–5 A steel rotating-beam test specimen has an ultimate strength of 230 kpsi. Estimate the fatigue
strength corresponding to a life of 150 kcycles of stress reversal.
6–6 Repeat Prob. 6–5 with the specimen having an ultimate strength of 1100 MPa.
6–7 A steel rotating-beam test specimen has an ultimate strength of 150 kpsi and a yield strength of
135 kpsi. It is desired to test low-cycle fatigue at approximately 500 cycles. Check if this is pos-
sible without yielding by determining the necessary reversed stress amplitude.
6–8 Derive Eq. (6–17). Rearrange the equation to solve for N.
6
3
6–9 For the interval 10 ≤ N ≤ 10 cycles, develop an expression for the axial fatigue strength

(S ) ax for the polished specimens of 4130 used to obtain Fig. 6–10. The ultimate strength is
f
S ut = 125 kpsi and the endurance limit is (S ) ax = 50 kpsi.

e
6–10 Estimate the endurance strength of a 1.5-in-diameter rod of AISI 1040 steel having a machined
finish and heat-treated to a tensile strength of 110 kpsi.
6–11 Two steels are being considered for manufacture of as-forged connecting rods. One is AISI 4340
Cr-Mo-Ni steel capable of being heat-treated to a tensile strength of 260 kpsi. The other is a plain car-
bon steel AISI 1040 with an attainable S ut of 113 kpsi. If each rod is to have a size giving an equiva-
lent diameter d e of 0.75 in, is there any advantage to using the alloy steel for this fatigue application?
6–12 A 1-in-diameter solid round bar has a groove 0.1-in deep with a 0.1-in radius machined into it.
The bar is made of AISI 1020 CD steel and is subjected to a purely reversing torque of 1800 lbf · in.
For the S-N curve of this material, let f = 0.9.
(a) Estimate the number of cycles to failure.
(b) If the bar is also placed in an environment with a temperature of 750 F, estimate the number
◦
of cycles to failure.
6–13 A solid square rod is cantilevered at one end. The rod is 0.6 m long and supports a completely
reversing transverse load at the other end of ±2kN. The material is AISI 1080 hot-rolled steel.
4
If the rod must support this load for 10 cycles with a factor of safety of 1.5, what dimension
should the square cross section have? Neglect any stress concentrations at the support end.