A bar of size 3m long, 250 mm wide and 150 mm thick is subjected to pull of 50 kN. Find change in length, breadth and thickness. E= 2 X 10^5 N/mm^2 , Poisson’s ratio= 0.25. Calculate modulus of rigidity and bulk modulus. Also, find volumetric strain and change in volume.

Solution :

Given :

Length, $\quad L=3 ~m=3000~mm$

Width, $\quad b=250~mm$

Diameter or Thickness, $\quad d=150~mm$

Young Modulus, $\quad E=2×10^5~N/mm^2$

Poisson ratio, $\quad \mu =0.25$

$\begin{aligned}\sigma=\frac{P}{A} &=\frac{50 \times 10^{3}}{250 \times 150}\\ &=1.33 {~N} /{mm}^{2}\end{aligned}$

1) change in length (dL)

$\begin{aligned}dL=\frac{P L}{A E} &=\frac{50 \times 10^{3} \times 3000}{250 \times 150 \times …