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Calculate Poisson's ratio and values of three modulii

Given:

A bar 30 mm in diameter was subjected to tensile load of 54 kN and the measured extension on 300 mm gauge length was 0.112 mm and change in diameter was 0.00366 mm.

Calculate Poisson's ratio and values of three modulii.

1 Answer
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Stress= 76.4N/mm2
Linear strain= 0.112/300=3.73 x 104
E=stress/strain= 204.6kN/mm2
Lateral strain= δd/d=0.00366/30=1.22 x 104
But lateral strain= (1/m)e=(1/m)(3.73 x 104)
1m(3.73104)=1.22104
1m=0.326

Again, Modulus of Rigidity (G)=E2(1+(1/m))=204.62(1+0.326)=77.2KN/mm2

Bulk Modulus (K)=E3(1(2/m))=196KN/mm2

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