5-2. A rod has a diameter of 3 in, and it is subjected to a shear force of .  If the allowable shear stress is , determine the probability of failure of the rod. Assume that  and  are independent.              

Solution:

The first moment of the cross section area at the neutral axis is

The maximum shear stress is

Set , then , where

Thus, the probability of failure of the rod is

Ans.