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# Show that1. Volumetric strain = 3×longitudinal strain

Asked by rushabh1234 2nd December 2019, 10:02 PM
Let us assume a cube of length l is subjetced to volumetric stress.

Let Δl be the uniform change in all sides.

Change in volume ΔV = (l+Δl)3 - l3 = l3 + 3 l2 Δl + 3l (Δl)2 + (Δl)3 - l3 .................(1)

By neglecting higher order of Δl , we get ΔV = 3 l2 Δl

Hence volume strain,  ΔV/V = ( 3 l2 Δl ) / l3 = 3 Δl/l

From above eqn., we say volume strain equlas 3 times of longitudinal strain
Answered by Expert 4th December 2019, 9:10 AM
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