34.
A tube is subejcted to a load 
, shown in the figure. It has an
outside diameter of 
and insider diameter of 
. The lenghth of the tube is 
and the modulus of elasticity is 
.
The allowable transverse deflection is 
. If 
and
are independent, determine the
probability of failure using the First Order Second Moment Method. Note that
the maximum deflection is 
Solution
The maximum deflection happens at A, given by
The
limit-state function is the maximum deflection subtracted from allowable
transverse deflection. Failure occurs when
.
where
.
Using FOSM, we have
The probability of failure is then given by
