Strain Energy due to Gradually Applied Load and Shear Stress

Q. A rectangular block of size $200mm\times 100mm\times 50mm$ is subjected to a shear stress of $500kg/c{m}^2$. If the modulus of rigidity of the material is $1\times {10}^{6}kg/c{m}^2$, the strain energy stored will be

1. $1000kg-cm$
2. $500kg-cm$
3. $125kg-cm$
4. $100kg-cm$

Q. The strain energy in a member is proportional to

1. total strain multiplied by the volume of the member
2. product of stress and the corresponding strain
3. product of strain and Young's modulus of the material
4. the maximum strain multiplied by the length of the member

Q. A mild steel bar of uniform cross-section A and length L is subjected to an axial load W. The strain energy stored in the bar would be

1. $\frac{WL}{2AE}$
2. $\frac{W^{2}L}{4AE}$
3. $\frac{WL}{4AE}$
4. $\frac{W^{2}L}{2AE}$

Q. A member having length L, cross-sectional area A and modulus of elasticity E is subjected to an axial load W. The strain energy stored in this member is

1. $\frac{W{L}^2}{AE}$
2. $\frac{W{L}^2}{2AE}$
3. $\frac{W^{2}L}{2AE}$
4. $\frac{W^{2}L}{AE}$

Q. What is the ratio of the strain energy in bar X to that in bar Y when the material of the two bars is the same? The cross-sectional areas are as indicated over the indicated lengths.

1. $1/3$
2. $2/3$
3. $4/3$
4. $1/6$