18. A
truss undergoes a force 
. The diamter of rod BC is 
.
If the yield stress of rod BC is 
, and 
and
are independent, determine the
probability of failure using the First Order Second Moment Method.
Solution
Consider the force equilibrium of rod AB and rod AC
as shown in the figure below
According to the force equilibrium along with 
axis,
Then
Thus the compressible stress applied to rod BC is
The
limit-state function is actual stress subtracted from the yield strength.
Failure occurs when
.
where
.
Using FOSM, we have
The probability of failure is then given by
