41. A force  is applied to a truss shown in the figure. The yield strength of rod AB is . If the maximum probability of failure is designed to be , determine the minimum diameter of rod AB. Note that  and  are independent.

Solution

Consider the force equilibrium of rod OA and rod AB shown in the figure

According to the force equilibrium along with  axis, 

Then

Thus the tensile stress applied to rod AB is

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.