Question

A thin-walled cylindrical pressure vessel is subjected to an internal gauge pressure, p=75 psip=75 psi. It had a wall thickness of 0.25 inches and an inner diameter of 8 inches. Use Mohr’s Circle to determine the absolute maximum shear stress in the pressure vessel when it is subjected to this pressure.

Answer 1

To solve this problem we must apply the concept related to the longitudinal effort and the effort of the hoop. The effort of the hoop is given as

`\sigma_h = (Pd)/(2t)`

Here,

P = Pressure

d = Diameter

t = Thickness

At the same time the longitudinal stress is given as,

`\sigma_l = (Pd)/(4t)`

The letters have the same meaning as before.

Then he hoop stress would be,

`\sigma_h = (Pd)/(2t)`

`\sigma_h = (75 * 8)/(2* 0.25)`

`\sigma_h = 1200psi`

And the longitudinal stress would be

`\sigma_l = (Pd)/(4t)`

`\sigma_l = (75* 8)/(4* 0.25)`

`\sigma_l = 600Psi`

The Mohr's circle is attached in a image to find the maximum shear stress, which is given as

`\tau_(max) = (\sigma_h)/(2)`

`\tau_(max) = (1200)/(2)`

`\tau_(max) = 600Psi`

Therefore the maximum shear stress in the pressure vessel when it is subjected to this pressure is 600Psi