Thin-walled pressure vessel

A pressure-containing shell whose thickness is small relative to its curvature radius, allowing a membrane-stress approximation. For a cylindrical closed-end tube, pressure force balance gives hoop stress

P r / t

and axial stress

P r / (2 t)

, with the same radius convention and neglected end disturbances.

Table of contents
- Axial membrane stress Thin-walled pressure vessel
- Hoop stress Thin-walled pressure vessel

Axial membrane stress ( $σ_{z}$ )

 0  0

The longitudinal membrane stress carried by a shell. A thin cylindrical tube supporting its closed-end pressure load has

σ_{z} = P r / (2 t)

; external end loading or an open end changes that balance.

Hoop stress ( $σ_{θ}$ )

 0  0

The circumferential normal stress in a cylindrical or curved structure. In a thin cylindrical wall under internal pressure its membrane value is approximately