The strain energy stored in a body of volume | vedclass

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Question

(D) The shear modulus $\eta$ is defined as the ratio of shear stress to shear strain $\phi$: $\eta = \frac{	ext{Shear stress}}{\phi}$ Therefore,the s

Vedclass · Accepted Answer

$\frac{1}{2} \eta \phi^2 V$

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(D) The shear modulus $\eta$ is defined as the ratio of shear stress to shear strain $\phi$: $\eta = \frac{	ext{Shear stress}}{\phi}$ Therefore,the shear stress is given by: $	ext{Shear stress} = \eta \phi$ The strain energy per unit volume is given by the formula: $	ext{Energy density} = \frac{1}{2} 	imes 	ext{Shear stress} 	imes 	ext{Shear strain}$ Substituting the values: $\frac{	ext{Strain energy}}{V} = \frac{1}{2} 	imes (\eta \phi) 	imes \phi$ $\frac{	ext{Strain energy}}{V} = \frac{1}{2} \eta \phi^2$ Multiplying by volume $V$,we get the total strain energy: $	ext{Strain energy} = \frac{1}{2} \eta \phi^2 V$ Thus,the correct option is $D$.

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

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