59. An eccentric force  is applied to a strut with a square cross section shown in the figure. The yield strength of the strut is . If the maximum probability of failure is designed to be , determine the minimum side length of the square cross section using the theory of short compression member. Assume that  and  are independent.

Solution

Based on the theory of short compression member, the maximum compressive stress occurs at point , and is given by

where  is the cross-section area of the strut,  is the distance between point  and axis , and   is the moment of inertia.

The limit-state function is the maximum compression 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.