Design of thin pressure vessel is based on

Explanation: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/hoop 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 = \(\frac{Pd}{4t}\)Hence, the design of thin pressure vessel is based on Longitudinal stress and Hoop stress.