25. An uniform load of  is applied to a rod OC shown in the figure. If the rod OD has a diameter of , and its yield strength is , determine the probability of failure using the First Order Second Moment Method. Note that  and  are independent.

Solution

Consider the free body diagram of rod OC shown in the figure.

Based on the moment equilibrium of rod OC with respect to point A,

Solving for  yields

Thus the compressed stress acting on rod OD is given by

The limit-state function is the actual compressed stress subtracted from the yield strength. Failure occurs when.

where .

Using FOSM, we have

The probability of failure is then given by