The shaft shown is made of AISI 1040 CD steel. It is machine finished and is subjected to a repeated bending stress of 15ksi. The diameter at the shoulder is 1.3in and will be used at a temperature of 400F. Estimate:
(a) The endurance limit at 95% reliability
(b) Endurance strength at 105 cycles and show on S-N plot 10
(c) Plot the design region by Modified Goodman theory and determine if failure is by yield or fatigue
(d) Find the factor of safety at the shoulder against fatigue at 105 cycles using the Modified Goodman Criterion
For the given AISI 1040 Steel, the ultimate strength is obtained from manuals as 90ksi. The r/d and D/d is calculated for the given dimensions. The theoretical stress concentration factor is obtained for the values of r/d and D/d. Then Ka, Kb, Kc, and Kd values are obtained for the given data and material specification (Refer Shigley). Once Ka, Kb, Kc, Kd are known, the endurance strength can then be obtained. The calculated endurance strength will be for 10^6 cycles. The SN curve is prepared and the endurance strength corresponding to the 10^5 cycles is obtained. Using the modified Goodman theory, the variation of σa with σm is plotted. Using the modified Goodman Theory, the factor os safety is computed for the given mean stress and amplitude stress.
Answer:
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