Stress for Thin-Walled Spheres & Cylinders

Thin Walled Cylinder Stress Calculator

Summary
Cylindrical Hoop Stress Calculator
Cylindrical Axial / Spherical Hoop Stress Calculator

Summary

There are three primary mechanical stresses that can be applied to a spherical or cylindrically shaped object:

Hoop Stress
Axial Stress
Radial Stress

If the object/vessel has walls with a thickness less than one-tenth of the overall diameter, then these objects can be assumed to be ‘thin-walled’ and the following equations be used to estimate the stresses:

Cylinder Hoop Stress, $\sigma = \frac{P * r}{t}$
Cylinder Axial Stress, $\sigma =\frac{P*r}{2t}$
Sphere Hoop Stress, $\sigma =\frac{P*r}{2t}$
Radial Stress, $\sigma =\frac{-P}{2}$

In a sphere, hoop stress and axial stress have the same value.

Cylindrical Hoop Stress Calculator

Cylindrical Axial / Spherical Hoop Stress Calculator

Calculate the hoop stress in a thin-walled cylinder:
Formula:	$\sigma = \frac{P * r}{t}$
	P = pressure (+ve for internal pressure, -ve for external pressure) r = radius t = wall thickness
Pressure	Pa
Radius	m
Wall thickness	m

Result:	Pa

Calculate the axial stress in a thin-walled cylinder / hoop stress in a thin-walled sphere:
Formula:	$\sigma =\frac{P*r}{2t}$
	P = pressure (+ve for internal pressure, -ve for external pressure) r = radius t = wall thickness
Pressure	Pa
Radius	m
Wall thickness	m

Result:	Pa