Hoop Stress Calculator

Hoop Stress Calculator:

Enter the values of internal pressure, P_(Pa), radius of the cylinder or sphere, r_(m) and wall thickness, t_(m) to determine the value of Hoop Stress, HS_(Pa).

Enter Internal Pressure :		Pa
Enter Radius :		m
Enter Thickness :		m
Result – Hoop Stress:		Pa

Hoop Stress Formula:

Hoop stress is a type of mechanical stress exerted in the circumferential direction of a cylindrical or spherical object, typically caused by internal or external pressure. This stress is vital in analyzing pressure vessels, pipelines, and tanks, ensuring they can withstand the forces without failure.

The circumferential or hoop stress arises due to the pressure acting perpendicular to the axis of the structure, tending to stretch the walls outward. Its magnitude depends on factors such as internal or external pressure, the radius of the cylinder or sphere, and the wall thickness.

Hoop stress calculations are essential for designing safe and efficient structures, as excessive stress can lead to material deformation or rupture. The relationship between pressure, radius, and thickness allows engineers to optimize material use while maintaining safety standards.

The formula for hoop stress is derived considering the equilibrium of forces acting on the walls of the structure. The stress increases with rising pressure or radius and decreases with greater wall thickness, making thickness a crucial design parameter.

Hoop Stress, HS_(Pa)Pascals equalsthe internal pressure, P_(Pa) in Pascals multiplied by the radius of the cylinder or sphere, r_(m) in metres, divided by the wall thickness, t_(m) in metres.

Hoop Stress, HS_(Pa) = P_(Pa) * r_(m) / t_(m)

HS_(Pa) = hoop stress in Pascals, Pa.

P_(Pa) = internal pressure in Pascals, Pa.

r_(m) = radius in metres, m.

t_(m) = thickness in metres, m.

Hoop Stress Calculation:

1.A cylindrical pressure vessel has an internal pressure of 2MPa, a radius of 0.5m, and a wall thickness of 0.02m. Calculate the hoop stress.

Given: P_(Pa) = 2 * 10⁶Pa, r_(m) = 0.5m, t_(m) = 0.02m.

Hoop Stress, HS_(Pa) = P_(Pa) * r_(m) / t_(m)

HS_(Pa) = 2 * 10⁶ * 0.5 / 0.02

HS_(Pa) = 50 * 10⁶Pa.

2.A pipeline with a radius of 0.3m and a wall thickness of 0.01m is subjected to a hoop stress of 90MPa. Determine the internal pressure.

Given: HS_(Pa) = 90 * 10⁶Pa, r_(m) = 0.3m, t_(m) = 0.01m.

Hoop Stress, HS_(Pa) = P_(Pa) * r_(m) / t_(m)

P_(Pa) = HS_(Pa) * t_(m) / r_(m)

P_(Pa) = 90 * 10⁶ * 0.01 / 0.3

P_(Pa) = 0.9 * 10³ / 0.3

P_(Pa) = 3 * 10⁶Pa.