The variation of circumferential stress across the thickness of a thick cylinder is

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The variation of circumferential stress across the thickness of a thick cylinder is

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Uniform
Linear
Parabolic
None of the above

Answer 1

Explanation:

Thick Cylinder

A cylinder is considered to be ‘thick’ if the ratio of the inner diameter to the thickness of the wall is less than 20.

The Variation of the hoop stress and the radial stress on a thick cylinder,

The tangential stress varies parabolically from the maximum value at the inner radius to the minimum value at the outer radius.
The radial stress also varies parabolically but the maximum value is at the inner radius and at the outer radius the value is zero.

For a thick cylinder tangential stress is given by Lame's equation as follows,

\({σ _t} = \frac{{p\;{{\left( {{r_i}} \right)}^2}}}{{{{\left( {{r_0}} \right)}^2} - {{\left( {{r_i}} \right)}^2}}}\left[ {1 + \frac{{{{\left( {{r_0}} \right)}^2}}}{{{x^2}}}} \right]\)

Since, ro > ri and for the maximum value of σt, x = ri.

F1 M.J Madhu 04.04.20 D4

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The variation of circumferential stress across the thickness of a thick cylinder is

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