# Ratio of longitudinal stress to hoop stress in a thin cylinder is

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Ratio of longitudinal stress to hoop stress in a thin cylinder is
1. equal
2. half
3. one-fourth
4. four times

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Correct Answer - Option 2 : half

Explanation:

A thin pressure vessel having closed ends and contains a fluid under a gauge pressure ‘p’. Then the walls of the cylinder will have a longitudinal stress as well as a 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.

The ratio of longitudinal stress to hoop stress $= \frac{{\frac{{pd}}{{4t}}}}{{\frac{{pd}}{{2t}}}} = \frac{2}{4} = 0.5$