5-5. Force  is exerting on the piston of a cylinder as shown in the figure. The diameter of the piston is 100 mm, and the cylinder has a wall thickness of 3 mm. Determine the distribution of the Hoop stress developped in the cylinder.

Solution:

Hoop Stress: Since , then thin wall analysis can be used. Thus, the hoop stress is

Since ,  also follows a normal distribution, and

Thus,  follows a normal distribution .                                           Ans.