62. A critical stress element is subjected to two normal stresses  and . The Poission’s ratio is  is 0.29 and the modulus of elasticity is . If the axial length of the element is  and allowable axial elongation is , determine the probability of failure using First Order Second Moment Method. Assume that  and  are independent.

Solution

The axial strain is

Therefore the axial elongation is given by

The limit-state function is the actual axial elongation subtracted from the allowable one. Failure occurs when.

where .

Using FOSM, we have

The probability of failure is then given by

Ans.