SSC JE Civil Engineering 29-Oct-2020 Shift 1 Paper

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.
● ${\mathrm{\sigma }}_{\mathrm{L}}$ = longitudinal stress (tensile), ${\mathrm{\sigma }}_{\mathrm{r}}$ = radial stress (compressive), ${\mathrm{\sigma }}_{\mathrm{h}}$ = circumferential stress (tensile). As, and ${\mathrm{\sigma }}_{\mathrm{h}}$ , therefore we neglect ${\mathrm{\sigma }}_{\mathrm{r}}$ and assumed the bi-axial stresses.
Circumferential or hoop stress: ${\mathrm{\sigma }}_{\mathrm{h}}=\frac{\mathrm{Pd}}{2\mathrm{t}}$
Longitudinal or axial stress: ${\mathrm{\sigma }}_{\mathrm{L}}=\frac{\mathrm{Pd}}{4\mathrm{t}}$
where d is the internal diameter and t is the wall thickness of the cylinder.