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.

$Stress =$ $ 76.4 N/mm^2 \\ \; \\ $
$Linear $ $strain =$ $ 0.112/300 = 3.73 \\ \; \\ $ x $ 10^{-4} \\ \; \\ $
$ E = stress/strain = $ $ 204.6 kN/mm^2 \\ \; \\ $
$ Lateral $ $strain =$ $ δd/d = 0.00366/30 = 1.22 \\ \; \\ $ x $ 10^{-4} \\ \; \\ $
$But $ $lateral$ $ strain = $ $ (1/m)e = (1/m) (3.73 \\ \; \\ $ x $ 10^{-4})\\ \; \\ $
$ \\ \; \\ \dfrac{1}{m} \; (3.73 *10^{-4}) = 1.22 * 10^{-4}$
$ \\ \; \\ \therefore \dfrac{1}{m} \;=\; 0.326$

$Again, $ $ Modulus $ $ of$ $ Rigidity $ $ (G) = \dfrac {E} {2(1 + (1/m))} = \dfrac {204.6} {2(1 + 0.326)} = 77.2 KN/mm^2 $

$ Bulk $ $ Modulus$ $ (K) = \dfrac {E} {3(1 - (2/m))} = 196 KN/mm^2 $