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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(2−μ)2EtHoop stress,σθ=prt Longitudinal stress,σz=pr2t Strain in circumferetial direction, εθ=1E(σθ−μσz)=pr2tE(2−μ) Change in radius =εθ×r =pr2(2−μ)2Et

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