3-1.  A shaft has an outer diameter of 36 mm and an inner diameter of 26 mm. Two torques  and  are applied to the shaft as shown. If  and , determine the distribution of the maximum shear stress developed in the shaft. Assuming that  and  are independent.

Solution:

The maximum shear stress in the shaft could be obtianed by

Since  and  are independent,  also follows a normal distribution. We have

Thus,  follows a normal distribution .                                          Ans.