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Show that 1. Volumetric strain = 3×longitudinal strain
Asked by rushabh1234 | 02 Dec, 2019, 22:02: PM
answered-by-expert Expert Answer
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 Thiyagarajan K | 04 Dec, 2019, 09:10: AM

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