A steel bar consists of two equal portions each 1 meter long, the respective diameters of each portion being 30 mm and 50 mm. Find the total strain energy of the bar when it is subjected to an axial pull of 150 kN. Take E= 200x103 N/mm2 for steel.

Data: P=150KN

$E=200*10^3 N/mm^2$

Stress $p_1=\frac{p}{A_1}$

$p_2=\frac{p}{A_2}$

$A_1=\frac{\pi}{4}*30^2$

$A_2=\frac{\pi}{4}*50^2$

Strain energy: $U=U_1+U_2$

$U=\frac{p_1^2}{2E}*A_1L_1+\frac{p_2^2}{2E}*A_2L_2$

$=\frac{150*10^3}{\frac{\pi}{4}*30^2}^2*\frac{\pi}{4}*30^2*1000+$ $\frac{150*10^3}{\frac{\pi}{4}*50^2}^2*\frac{\pi}{4}*50^2*1000$

$=79.577*10^3+28.64*10^3$

$=108.217*10^3 Nmm$