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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

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

Thick walled cylinder - stress due to pressure

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)

inside radius (mm, in)

outside radius (mm, in)

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)


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)


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)

Stress in Radial Direction

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)

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