6-1.  The internal pressure of a gas tank is . The tank has an internal diameter of 18 in, and the wall thickness is 0.2 in. Determine the distribution of the Hoop stress and Longitudinal stress developed at point M, which is on the wall of the tank.  

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.

Longitudinal stress:

Thus,  also follows a normal distribution, and

Thus,  follows a normal distribution .                                           Ans.