Question:

A steel tensile link has a mean yield strength of \(\bar{S}_{y}=27,000\) psi and a standard deviation on strength of \(S_{y}=4000\) psi. The variable applied stress has a mean value of \(\bar{\sigma}=13,000\) psi and a standard deviation \(s=3000\) psi. (a) What is the probability of failure taking place? Show the situation with carefully drawn frequency distributions. (b) The factor of safety is the ratio of the mean material strength divided by the mean applied stress. What factor of safety is required if the allowable failure rate is 5 percent? (c) If absolutely no failures can be tolerated, what is the lowest value of the factor of safety?

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