54. A tensile force  is applied to a rod. The rod has a diameter of   and a length of . The modulus of elasticity is  and the poission ratio is . If the allowable change in rod diameter is , estimate the probability of failure using the First Order Second Moment Method.

Solution

The tensile stress is

And the corresponding axial strain is given by

Then the lateral strain is

Thus the change in rod diameter is

The limit-state function is the actual change in rod diameter subtracted from the allowable one. Failure occurs when.

where .

Using FOSM, we have

The probability of failure is then given by