15. A reversing nominal stress  with 500 cylces is applied to a rotating-beam. The fatigue strength fraction is . If the ultimate strength of the beam is , and  and  are independent, determine the probability of failure using the First Order Second Moment Method.

Solution

The failure strength is given by

So the limit-state function is the reversing nominal stress subtracted from the failure strength. Failure occurs when.

where .

Using FOSM, we have

The probability of failure is then given by

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