6-8.  A random force  is acting on the center of a shaft that has a radius of 0.5 in. Determine the probability of failure at point A due to excessive normal stress. The allowable normal stress follows . Assume that , and  are independent.

Solution:

Section Properties

Normal Stress at Point A

Since , we have

Set , then , where

Thus, the probability of failure due to excessive normal stress is

Ans.