Question

What is the total strain energy of a member subjected to an axial stress f(E = Young's modulus)?

• A. $\left(\frac{f^2}{2E}\right)\times \text{volume of bar}$
• B. $\left(\frac{f}{E}\right)\times \text{volume of bar}$
• C. $\left(\frac{f^2}{2E}\right)\times \text{volume of bar}$
• D. $\left(\frac{f}{2E}\right)\times \text{volume of bar}$

Answer 1

The correct option is A $\left(\frac{f^2}{2E}\right)\times \text{volume of bar}$

Strain energy,
$U=\frac{1}{2}\times \text{Stree}\times \text{Strain}\times \text{Volume of bar}$
$=\frac{1}{2}\times f\times ϵ\times \text{Volume of bar}$
Since $ϵ=\frac{1}{E}$
$\therefore U=\frac{f^2}{2E}\times \text{Volume of bar}$