6-7.  A random force  is acting on a bar, which has a radius of 45 mm as shown in the figure. Determine the probability of failure at point B located at the left end due to excessive normal stres. The allowable normal stress follows . Assume that , and  are independent.

Solution:

Section Properties

Normal Stress at Point B

Since , we have

  (Negative value means compressive stress)               

  (Negative value means compressive stress)               

Set , then , where

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

Ans.