5-6. Force F is exerting on the piston of a thin-walled cylinder as shown below. The diameter of the piston is 10 in, and the wall has a thickness of 3 in. If the internal pressure caused by F follows . Determine the distribution of the Hoop stress and longitudinal stress developped in the cylinder.

Solution:

Hoop Stress:

Since ,  also follows a normal distribution, and

Thus,  follows a normal distribution .                                          Ans.

Longitudinal stress:

Thus,  also follows a normal distribution, and

Thus,  follows a normal distribution .                                            Ans.