51. A brittle thin plate is subjected to a random force . The plate has a width of  and a hole in the center with a diameter of . The yield strength of the plate is . Assume the stress concentration factor is  and the maximum probability of failure is designed to be , estimate the minimum thickness of the plate using the First Order Second Moment Method.

Solution

The nominal stress is

With the effect of stress concentration, the maximum stress is given by

The limit-state function is the maximum 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.