61. A rotating-beam is subjected to a completely reversed stress. The fatigue strength fraction of the beam is  and the ultimate strength of the beam is . If the yield strength of the beam is  and the maximum probability of failure is designed to be , determine the maximum cycles of the reversed stress using the First Order Second Moment Method. Assume that  and  are independent.

Solution

The failure strength is

And thus the completed reversed stress is given by

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

where .

Using FOSM, we have

The probability of failure is then given by

Thus

Solving for  yields

Ans.