43. A bar with a circular cross section is subjectd to a force . The yield strength of the bar is . If the maximum probability of failure is designed to be , determine the minimum diameter using the First Order Second Moment Method and then select a preferred diameter. Note that  and  are independent.

Solution

The tensile stress of the bar is

The limit-state function is the actual tensile 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.