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.