Design of thin pressure vessel is based on
A. Hoop stress
B. Longitudinal stress
C. Both (1) and (2)
D. None of the above
Please scroll down to see the correct answer and solution guide.
Right Answer is: C
SOLUTION
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.
