Question

A solid circular bar of a certain material remains unchanged in volume when subjected to an uniaxial loading . Calculate Poisson’s ratio of material .( Take δV = 0 )​

Answer 1

Let L be the length, r be the radius of the wire.

Volume of the wire is

V=πr2L

Differentiating both sides, we get

ΔV=π(2rΔr)L+πr2ΔL

As the volume of the wire remains unchanged when it gets stretched, so ΔV=0. Hence

0=2πrLΔr+πr2ΔL

∴ΔL/LΔr/r=−21

Poisson′sratio=LongitudinalstrainLateralstrain=−ΔL/LΔr/r=21=0.5

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