Stress for Thin-Walled Spheres & Cylinders

Thin Walled Cylinder 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

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

Cylindrical Axial / Spherical Hoop Stress Calculator

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