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# 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

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

where

σh = 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

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

where

σl = 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

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

=  150000 kPa

= 150 MPa

The longitudinal stress can be calculated

σh = (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.

## Related Topics

### • Mechanics

Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.

### • Statics

Loads - forces and torque, beams and columns.

## Related Documents

### Fixed Pipes - Stress vs. Change in Temperature

Temperature changes introduces stress fixed pipes.

### Process Pipes - Allowable Stress vs. Temperature

Allowable wall stress in pipes according ASME M31.3.

### Rotating Bodies - Stress

Stress in rotating disc and ring bodies.

### Rotating Shafts - Torque

Torsional moments acting on rotating shafts.

### Stress

Stress is force applied on cross-sectional area.

### 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.

### Stress, Strain and Young's Modulus

Stress is force per unit area - strain is the deformation of a solid due to stress.

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