What is Hoop Stress?

Hoop stress, also known as tangential stress, is the force exerted circumferentially (perpendicular to the axis and the radius) in both directions on every particle in the cylinder wall. It is a critical factor in mechanical engineering and materials science, particularly when designing pressure vessels, pipes, and tanks.

The Hoop Stress Formula (Barlow’s Formula)

For thin-walled cylinders (where the ratio of diameter to thickness is greater than 20), hoop stress is calculated using the following equation:

σθ = (P × D) / (2 × t)

Where:

• σθ: Hoop Stress (MPa, PSI)
• P: Internal Pressure
• D: Outer Diameter of the cylinder
• t: Wall Thickness

Importance in Engineering

Understanding hoop stress is essential to prevent catastrophic failures in pipeline infrastructure. If the internal pressure exceeds the material's yield strength, the pipe or vessel will undergo plastic deformation and eventually burst. Engineers use this calculator to determine the minimum wall thickness required for a specific material and operating pressure, often applying a safety factor to ensure long-term durability.

Frequently Asked Questions

Q: What is the difference between hoop stress and longitudinal stress?
A: Hoop stress acts around the circumference, while longitudinal stress acts parallel to the axis of the pipe. For thin-walled vessels, hoop stress is typically twice as high as longitudinal stress.

Q: When should I use the thick-wall formula?
A: If the wall thickness is more than 1/10th (or sometimes 1/20th) of the radius, you should use Lame's equations for thick-walled cylinders instead of this simplified hoop stress calculator.