1-20.    The system supports a normally distributed load  lb.  Determine the minimum diameter of bar BC if the allowable yield strength is  psi.  Let the maximum probability of failure for of bar BC be 10^-4.  Assume  and  are independent variables.  .

Solution

Sum the forces: The force in AC can be found by taking the moment about B or by first taking the moment about C then sum the forces in the y direction.

Alternative solution:

For the probability of failure in AC:

                                                                                                  (1)

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

 psi                         (2)

psi       (3)

Equation (1) can be written as

From (1), (2), (3), and some algebra we obtain

 in                    Ans.