Question

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

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

Answer 1

Answer: (D)

Shear modulus $=\frac{\text { Shear stress }}{\text { Shear stress }}$
$\eta=\frac{\text { Shear stress }}{\phi}$
$\eta \phi=$ Shear stress
Strain energy per unit volume $=\frac{1}{2} \times$ shear stress $x$ shear strain
$\Rightarrow \frac{\text { Strain energy }}{\text { Volume }}=\frac{1}{2} \times \eta \dot{\eta} \times \phi \quad$ (Cross multiply volume)
Strain energy $=\frac{1}{2} \eta \phi^{2} V$