3-4.  A coupling connects the two shafts as shown. The torque  applied on the shafts follows a normal distribution . The diameter of the shafts is . Determine the distribution of the maximum shear stress of the shaft. Assume that the shear stress in the bolts is uniform.

Solution:

The maximum shear stress in the shaft could be obtianed by

Thus,  also follows a normal distribution. We have

Thus,  follows a normal distribution .                                       Ans.