8. A shaft is designed to transmit a power  at . The shaft has a round cross section with a diameter of . If the allowable shear stress of the shaft is , estimate the probability of failure using the First Order Second Moment Method.

Solution

The transmitted power is

Thus the required torque is

And the maximum shear stress resulting from the torque is

The limit-state function is the actual maximum shear stress subtracted from the allowable one. Failure occurs when.

where .

Using FOSM, we have

The probability of failure is then given by