A bar subjected to a tensile load 55 KN. Bar diameter=31 mm; Gauge length=300mm; extension=.115mm; change in diameter= 0.00367mm. Find: Poisson’s ratio, Young’s modulus, Bulk modulus, and modulus of rigidity.

Given data:

Tensile load(F)=55KN

Diameter(d)=31mm

Gauge Length (L)=300mm

Extension $(\Delta L)=0.115mm$

$\Delta d $Change in diameter=0.00567 mm

i) Poisson's ratio $\mu =\frac{lateral strain}{longitudinal strain}$

$\mu= \frac{\frac{0.00367}{31}}{\frac{0.115}{300}}$

$\mu=0.308$

2) Young's modulus=$\frac{stress}{strain}$

$E=\frac{55*10^3/\pi /4*31^2}{0.115/300}$

$E=190.09*10^3 N/mm^2$

3)$ E=3K(1-2\mu)$

$190.09*10^3=3K(1-2*0.308)$

$Bulk modulus(K)=165*10^3 N/mm^2$

4)$ E=2G(1+\mu)$

$190.09*10^3=2*G(1+0.308)$

Modulus of rigidity $G=72.664*10^3 N/mm^2$