6-11. An axial member force P is applied to the joint of a component as shown in the figure. Assume that P follows a normal distribution , and the allowable normal stress on the joint section follows . If the member is 1.2-in thick, determine the probabilities of failure of section AB and BC. Assume  and  are independent.

Solution:

,   

,     

Solve the above equations, we have

Thus, the normal stresses on section AB and BC are

Set , then , where

The probability of failure on section AB is

                                   Ans.

Set , then , where

The probability of failure on section BC is

Ans.