# Stress in Thick-Walled Cylinders - or Tubes

## Radial and tangential stress in thick-walled cylinders or tubes with closed ends - with internal and external pressure

When a thick-walled tube or cylinder is subjected to internal and external pressure a hoop and longitudinal stress are produced in the wall.

### Online Thick Walled Pipe & Cylinder Calculator

The calculator below can be used to calculate the stress in tick walled pipes or cylinders with closed ends.

inside pressure (MPa, psi)

outside pressure (MPa, psi)

radius to point in the wall (mm, in)

### Stress in Axial Direction

The stress in axial direction at a point in the tube or cylinder wall can be expressed as:

σa = (pi ri2 - po ro2 )/(ro2 - ri2)                                   (1)

where

σa = stress in axial direction (MPa, psi)

pi = internal pressure in the tube or cylinder (MPa, psi)

po = external pressure in the tube or cylinder (MPa, psi)

ri = internal radius of tube or cylinder (mm, in)

ro = external radius of tube or cylinder (mm, in)

### Stress in Circumferential Direction - Hoop Stress

The stress in circumferential direction - hoop stress - at a point in the tube or cylinder wall can be expressed as:

σc = [(pi ri2 - po ro2) / (ro2 - ri2)] - [ri2 ro2 (po - pi) / (r2 (ro2 - ri2))]                                    (2)

where

σc = stress in circumferential direction (MPa, psi)

r = radius to point in tube or cylinder wall (mm, in) (ri < r < ro)

maximum stress when  r = ri (inside pipe or cylinder)

The stress in radial direction at a point in the tube or cylinder wall can be expressed as:

σr = [(pi ri2 - po ro2) / (ro2 - ri2)] + [ri2 ro2 (po - pi) / (r2 (ro2 - ri2))]                                  (3)

maximum stress when  r = ro (outside pipe or cylinder)

## Related Topics

• Mechanics - Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more
• Statics - Loads - force and torque, beams and columns

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