50. A rod OC is subjected to a uniform load of  as shown in the figure. The yield strength of rod OD is . If the maximum probability of failure is designed to be , determine the minimum diameter of rod OD using the First Order Second Moment Method and then select a preferred one. Note that  and  are independent.

Solution

Consider the free body diagram of rod OC shown in the figure.

Based on the moment equilibrium of rod OC with respect to point A,

Solving for  yields

Thus the compressed stress acting on rod OD is given by

The limit-state function is the actual compressed 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.