17.
A bending moment 
is applied to a circular shaft
with a diameter of 
. If the yield strength is 
, determine the probability of
failure using the First Order Second Moment Method. Note that 
,
and 
are independent.
Solution
The bending stress is given by
Thus,
the limit-state function is the bending stress subtracted from the yield strength.
Failure occurs when
.
where
.
Using FOSM, we have
The probability of failure is then given by
