7-4. A cantilever is subject to a vertical force as shown. The dimensions of the cantilever are also shown in the figure.  If the allowable normal stress of the cantilever is, determine the probabilities of failure caused by excessive bending stress. Neglect the weight of the cantilever.

Solution:

Section properties:

The bending stress can be expressed by

When ,

Set , then , where

The probability of failure of the cantilever caused by excessive bending stress is

Ans.