6-4.  A pole with a fixed bottom is used to support a weight as shown in the figure. The pole has a radius of 18 mm. The mass of the pole is negligible. If the allowable tensile stress of the pole follows , determine the probability of failure. Assume that  and  are independent.

Solution:

Section Properties

The maximum tensile stress is

Since , we have

Set , then , where

Thus, the probability of failure of the pole is obtained by

Ans.