Hoop Stress Calculator

Hoop (circumferential) stress is the dominant stress in a pressurized pipe or tank wall.

How the Math Works

The hoop stress formula σ = p·r ÷ t calculates the circumferential stress in a thin-walled pressure vessel. Here, p is the internal pressure, r is the vessel's radius, and t is the wall thickness. This equation arises from balancing the forces acting on a cylindrical segment: the internal pressure pushes outward, while the material's strength resists this force. The formula assumes the wall thickness is much smaller than the radius (t << r), making it ideal for pipes, tanks, and similar structures. Higher pressure or larger radius increases stress, while thicker walls reduce it, ensuring structural integrity.

Practical Applications

Engineers use this calculation to design pressure vessels like gas cylinders, pipelines, and storage tanks. By plugging in material properties and operating conditions, they determine the minimum wall thickness required to prevent failure. For example, if a tank must withstand 10 MPa pressure with a 1.5 m radius, the formula helps select a thickness that keeps stress below the material's yield strength. This prevents leaks, ruptures, or catastrophic failures, ensuring safety in industries ranging from automotive to aerospace where pressurized systems are common.

Day-to-Day Use

While you may not calculate hoop stress yourself, it directly impacts everyday products. The pressure in your car's tires, the safety of gas cylinders at home, or the reliability of water pipes relies on this principle. Manufacturers use the formula to ensure items like soda cans or balloons don't burst unexpectedly. Even in emergencies, understanding hoop stress helps assess damage—like identifying if a leaking pipe is due to excessive pressure or insufficient wall thickness—helping prevent accidents and maintain daily life's smooth operation.

Worked example

5 bar in a 0.3 m radius, 5 mm wall → 30 MPa.

FAQ