27.
A random force 
is applied to a brittle thin
plate with a 
-diameter hole in the center. The
plate has a width of 
and a thickness of 
.
If the stress concentration factor is 
and the yield strength of the
plate is 
, estimate the probability of
failure using the First Order Second Moment Method. Note that 
and
are independent.
Solution
The nominal stress is
Considering the effect of stress concentrations, the maximum stress is given by
The
limit-state function is the maximum stress subtracted from the yield strength.
Failure occurs when
.
where
.
Using FOSM, we have
The probability of failure is then given by
