Question

For the state of stress of pure shear t, the strain energy stored per unit volume in the elastic, homogeneous, isotropic material having elastic constants - Young's modulus, E and Poisson's ratio v will be

• A. $$\frac{\tau^2}{E}(1+\nu)$$
• B. $$\frac{\tau^2}{2E}(1+\nu)$$
• C. $$\frac{2\tau^2}{E}(1+\nu)$$
• D. $$\frac{\tau^2}{2E}(2+\nu)$$

Answer 1

Answer:

$$\frac{\tau^2}{E}(1+\nu)$$

Given: E = Young's modulus, v = Poisson's ratio; $E= 2G (1+ v) \Rightarrow 2G = E/(1 + v)$ Strain energy per unit volume =$\frac{\tau ^ 2}{2G} = \frac{\tau ^ 2}{E} (1 + \nu)$