4-8.  The system is used to support a normally distributed weight lb.  If the yield stress of rod AC is  psi, what is the probability of failure?  Consider only the normal stress at A.  The diameter of rod AC is d = 2 in.  Assume  and  are independent.

Solution

Sum the forces: The force at A_x can be found by summing the forces in the x and y directions and then take the moments about A.

;                    

For the probability of failure at A:

        (1)

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

 psi                                             (2)

psi                               (3)

Equation (1) can be written as

Ans.