45. A force  is applied to rod BC as shown in the figure. Rod AB has a round cross section and its yield strength is . If the maximum probability of failure is designed to be , determine the minimum diameter of rod AB and select a preferred diameter. Note that  and  are independent.

Solution

Consider the free-body diagram of rod BC

According to the moment equilibrium of rod BC with respect to point C,

Solving for F_B yields

Thus the stress acting on the rod AB is

Thus the limit-state function is the actual stress subtracted from the yield strength. Failure occurs when,

where .

Using FOSM, we have

The probability of failure is then given by

Thus

Solving for  yields

Thus  can be used.                                                                                                                    Ans.