Homework #07

DUE: Monday, November 21, 2016 before class in Box B in the MAE department.

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Problem 1

Determine the safety factors at points A and B for the bracket shown below. It is made of ASTM Class 50 Cast Iron (Table A-24). The variables have the following values: l = 6in, a = 8 in, d = 1.5 in, F = 1000 lb. Use the modified Mohr Theory.

Problem 2

(1) Estimate the endurance limit and the low cycle fatigue strength for an axially loaded ground steel specimen with \(S_{ut} = 150 \mathrm{ksi}\), \(d= 1.0 \mathrm{in}\), and \(T = 70^\circ \mathrm{F}\). (2) Determine the expected life for \(\sigma_a = 75 \mathrm{ksi}\) and \(\sigma_m=0 \mathrm{ksi}\).

Problem 3

Determine the required diameter for a round steel element that is axially loaded from -2500 to 2500 lb in fully reversed cycles. Assume it is ground, \(S_{ut} = 150 \mathrm{ksi}\), and is loaded at \(T = 70^\circ \mathrm{F}\). Determine the diameter for infinite life and \(10^3\) cycles.

Problem 4

Given a 2024-T3 aluminum specimen forged to \(2.0 \mathrm{in}\) round, determine the fatigue strength for \(3 \times 10^7\) cycles of loading for fully reversed torsion. Note that for non-ferrous metals, the unmodified fatigue strength is taken at \(N = 5 \times 10^8\) cycles (see Table A-24).

Problem 5

A simple hot rolled 1020 steel cantilever beam of length 0.6 m is loaded transversely at the end with a fully reversing load of \(\pm 5 \mathrm{kN}\). The beam has a rectangular cross section with a width of \(40 \mathrm{mm}\). What is the required height of the beam's cross section to guarantee safe operation up to \(N = 10^4 \mathrm{cycles}\) with a design factor of 2? Neglect any stress concentrations.