12. The
size of a strut is 
in. The strut is subjected to an
eccentrial force 
with an offset of 
as
shown in the figure. If the yield strength of the strut is 
and 
and
are independent, determine the
probability of failure using the First Order Second Moment Method.
Solution
According
to the theory of short compression member, the maximum compressive stress occurs
at point 
, and its magnitude is
where
is the cross-section area of the
strut, 
is the distance between point and
axis 
, and 
is
the moment of inertia.
The
limit-state function is the maximum compression stress of the strut subtracted
from the yield strength. Failure occurs when
.
where
.
Using FOSM, we have
The probability of failure is then given by
