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.