How to Calculate Hoop Compression in a Pressure Vessel

Hoop compression stress is a function of wall thickness and pressure.

Hoop stress, or hoop compression stress, is a circumferential mechanical stress of a steel pressure cylinder that is brought on by internal or external pressure. The classic example of hoop stress is the stress applied to metal bands around a wooden barrel. It is a circumferential loading that is a function of the cross sectional radius of the cylinder, the vessel wall thickness and the intensity of the force being applied.

Instructions

1. Determine the vessel wall thickness as measured in inches. For instance, a common thin-walled vessel wall thickness (t) could be 1/8 inch (0.125 inches).

2. Determine the internal radius of the vessel as well as the internal pressure that is to be applied. For a thin-walled vessel, a common radius (r) would be 3 feet, and a reasonable internal pressure (P) would be 10 pounds per square inch (psi).

3. Determine the hoop compression stress using the formula σ = P x r / t. This calculates to be 10 x 3 / 0.125 or 240 psi.

References

• eFunda: Hoop Compression in Pressure Vessels
• eFormulae: Strength of Materials