3-2.  The shaft rotates with  and transmits the power of . The allowable shear stress of the shaft is . Determinate the probability of failure of the shaft. Given that the  torsional stress-concentration factor is . Assuming that  and  are independent.

Solution:

The torque on the shaft is

The shear stress developed in the shaft is

Set , then , where

Thus, the probability of failure of the shaft is

Ans.