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Question

A thin cylinder of thickness t, width b and internal radius r is subjected to a pressure p on the entire internal surface. What is the change in radius of the cylinder? (μ is the Poisson's ratio and E is the modulus of elasticity) ?

A
p2r(2μ)Et
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B
pr2(2μ)Et
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C
pr2(2μ)2Et
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D
p(1μ)Etr2
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Solution

The correct option is C pr2(2μ)2Et
Hoop stress,σθ=prt
Longitudinal stress,σz=pr2t
Strain in circumferetial direction,
εθ=1E(σθμσz)=pr2tE(2μ)
Change in radius =εθ×r
=pr2(2μ)2Et

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