1-23.    A bolt passes through a board that is 2 inches thick and the board has a normally distributed allowable shear stress  psi.  If the washer has an outer diameter of 0.5 inches and a normally distributed load is applied  lb, what is the probability that the board will fail and the bolt head and washer will rip through the board?  Assume  and  are independent variables.

Solution

Internal loading: The shear force developed in the board due to the force  on the washer is determined by summing the forces in the y direction.

Average shear stress: The relevant area of the board is in².

We obtain

Probability of failure:

Since  lb and  psi are independent,  also follows a normal distribution.  .

 psi

 psi

Equation (1) can be written as

Ans.