# Stress in Thin-Walled Cylinders or Tubes

## Hoop and longitudinal stress thin-walled tubes or cylinders

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*.