Question

The strain energy stored in a body of volume $V$ due to shear strain $\varphi$ is (shear modulus is $\eta$)

• A. $\frac{{\varphi }^{2}V}{2\eta }$
• B. $\frac{\varphi V^2}{2\eta }$
• C. $\frac{\varphi V^2}{\eta }$
• D. $\frac{1}{2}\eta \varphi V^2$

Answer 1

The correct option is D $\frac{1}{2}\eta \varphi V^2$

Shear strain$=\varphi$

$shearmodulus=\eta$

let $\Delta u=$ strain energy

$\frac{strainenergy}{volume}=\frac{\Delta u}{volume}=\frac{1}{2}\times stress\times strain$

$\frac{strainenergy}{volume}=\frac{\Delta u}{volume}=\frac{1}{2}\times stress\times strain$

$\Delta u=\frac{1}{2}\times \eta \times {\left(strain\right)}^2\times V$

$u=\frac{1}{2}\times \eta {\left(\varphi \right)}^{2}V$

$u=\frac{1}{2}\eta {\left(\varphi \right)}^{2}V$

Hence,

option $\left(D\right)$ is correct answer.