38. Rod OB is subjected to a force  as shown in the figure. The allowable stress of rod OA is . If rod OA has a round cross section with a diameter of , determine the probability of failure using the First Order Second Moment Method. Assume that ,  and  are independent.

Solution

Consider the free-body diagram of rod OB

According to the moment equilibrium of rod OB with respect to point B,

Solving for F_O yields

Thus the stress acting on the rod OA is

Thus the limit-state function is the actual stress subtracted from allowable stress. Failure occurs when,

where .

Using FOSM, we have

The probability of failure is then given by