1-26.  A cantilever is subject to a vertical random force  as shown in the figure. If the allowable shear strain at point C is , determine the probability of failure. Given that the cantilever has a Shear modulus of  .  and  are independent.

Solution:

Section Properties

Shear Stress

Shear Strain

Since , we have

Set , then , where

Thus, the probability of failure of the cantilever could be obtained by

Ans.