Stress in Thin-Walled Cylinders or Tubes

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

For the thin walled equations below the wall thickness is less than 1/20 of tube or cylinder diameter.

Hoop (Circumferential) Stress

The hoop stress is acting circumferential and perpendicular to the axis and the radius of the cylinder wall. The hoop stress can be calculated as

σ_h = p d / (2 t)                         (1)

where

σ_h = hoop stress (MPa, psi)

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

d = internal diameter of tube or cylinder (mm, in)

t = tube or cylinder wall thickness (mm, in)

Longitudinal (Axial) Stress

For a cylinder closed closed in both ends the internal pressure creates a force along the axis of the cylinder. The longitudinal stress caused by this force can be calculated as

σ_l = p d / (4 t)                               (2)

where

σ_l = longitudinal stress (MPa, psi)

Example - Stress in a Thin Walled Tube

The pressure in a thin walled tube with diameter 0.3 m and thickness 0.001 m is 1000 kPa (10 bar).

The hoop stress can be calculated 

σ_h = (1000 kPa) (0.3 m) / (2 (0.001 m))

    =  150000 kPa

    = 150 MPa  

The longitudinal stress can be calculated 

σ_h = (1000 kPa) (0.3 m) / (4 (0.001 m))

    =  75000 kPa

    = 75 MPa

Note that typical maximum allowable stress for carbon steel pipes is below 135 MPa.

Temperature ^oC
K
^oF

Length m
km
in
ft
yards
miles
naut miles

Area m²
km²
in²
ft²
miles²
acres

Volume m³
liters
in³
ft³
us gal

Weight kg_f
N
lbf

Velocity m/s
km/h
ft/min
ft/s
mph
knots

Pressure Pa
bar
mm H₂O
kg/cm²
psi
inches H₂O

Flow m³/s
m³/h
US gpm
cfm