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Engineering ToolBox > Stress in Thick-Walled Tubes or Cylinders

Radial and tangential stress in thick-walled tubes or cylinders with closed ends - 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

outside pressure

inside radius

outside radius

radius to point in the wall

Stress in Axial Direction

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

σ_a = (p_i r_i² - p_o r_o² )/(r_o² - r_i²) (1)

where

σ_a = stress in axial direction (MPa, psi)

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

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

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

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

Stress in Circumferential Direction - Hoop Stress

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

σ_c = [(p_i r_i² - p_o r_o²) / (r_o² - r_i²)] - [r_i² r_o² (p_o - p_i) / r² (r_o² - r_i²)] (2)

where

σ_c = stress in circumferential direction (MPa, psi)

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

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

Stress in Radial Direction

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

σ_r = [(p_i r_i² - p_o r_o²) / (r_o² - r_i²)] + [r_i² r_o² (p_o - p_i) / r² (r_o² - r_i²)] (3)

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