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:
σh= Longitudinal or axial stress:
σL= where d is the internal diameter and t is the wall thickness of the cylinder.