12. A shaft with a round cross section is designed to tranismit a power at . The diameter and the allowabe shear stress of the shaft are  and , respectively. If the maximum probability of failure is desinged to be , estimate the maximum power that the shaft can transimit using the First Order Second Moment Method. Note that  and  are independent.

Solution

The transmitted power is given by

Thus

And the maximum shear stress is

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

where .

Using FOSM, we have

The probability of failure is then given by

Thus

Solving for  yields

Ans.