53. A tension rod has a length of  and a yield strength of  . The modulus of elasticity is . If the maximum probability of failure is designed to be , determine the allowable axial elongation using the First Order Second Moment Method.

Solution

Based on Hooke’s law, the tensile stress is given by

where  is the stain.

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

Ans.