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Strength of Materials: Thin Wall Pressure Vessels

A thin wall pressure vessel is a container that is under pressure that is considered to have a thin wall. To classify as a thin wall pressure vessel, the inner radius r is more than or 10 times greater than the thickness t; r/t > 10. If r/t = 10 then the predicted stress can be up to 4 % less than the actual stress. This error is due to the fact that as the thickness grows in relationship to the inner radius, there will be a greater variation of stress across the thickness. However, if it is said to be a thin wall pressure vessel then the stress difference isn't significant and it can be assumed as uniform.

When a thin wall pressure vessel is under stress, there can be multiple stresses that need to be considered. The first stress is called the circumferential or hoop stress. Refer to the figure and equation 1 below.

Pressure vessel hoop stress equation (1)

r = radius

t = thickness

Hoop Stress on a Pressure Vessel

The second stress that needs to be considered is the longitudinal stress. Refer to the figure and equation 2 below.

Pressure vessel longitudinal stress equation (2)

Longitudinal Stress on a Pressure Vessel

Types of Pressure Vessels

There are different types of pressure vessels, but the two that will be discussed here are cylinders and spheres. A pressure vessel that is cylindrical in shape has both a hoop stress and a longitudinal stress. The hoop stress however is normally always two time greater than the longitudinal stress. Due to this, hoses and other cylindrical type vessels will split on the wall instead of being pulled apart like it would under an axial load. Refer to the picture below.

Failure due to hoop stress on a pressure vessel

On the other hand pressure vessels that are spheres do not have a hoop stress. Instead they only have longitudinal stress. Due to this spherical pressure vessels can withstand larger pressures then pressure vessels that are cylinders.

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