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If p is internal pressure, d is diameter and t is thickness of wall for a thin cylindrical, shell, then the value of hoop stress will be:
1. td/4p
2. pd/4t
3. pd/2t
4. pt/4d

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Correct Answer - Option 3 : pd/2t

Concept:

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 as well as circumferential stress.

Circumferential or hoop stress: \({\sigma _h} = \frac{{pd}}{{2t}}\)

Longitudinal or axial stress: \({\sigma _L} = \frac{{pd}}{{4t}}\)

where ‘d’ is the internal diameter and ‘t’ is the wall thickness of the cylinder.

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