A thin cylindrical shell of diameter d, length l, and thickness t is subjected to an internal pressure p. The hoop stress in the shell is

Concept:

• Consider a thin pressure vessel having closed ends and contains fluid under a gauge pressure P. Then the walls of the cylinder will have longitudinal stress, circumferential stress and radial stress.
• As shown in the figure, a point of the shell having stresses from all sides i.e. tri-axial stresses.
• σL =  longitudinal stress (tensile), σr = radial stress (compressive), σh = circumferential stress (tensile).

As, σr <<<< σL and σh, therefore we neglect σr and assumed the bi-axial stresses.

Circumferential or hoop stress: \({σ _h} = \frac{{Pd}}{{2t}}\)

Longitudinal or axial stress: \({σ _L} = \frac{{Pd}}{{4t}}\)

where d is the internal diameter and t is the wall thickness of the cylinder.

• For the spherical shell, longitudinal stress and circumferential stress both are equal,

σh = σL = \(\frac{Pd}{4t}\)