1. Strain energy stored in a member is given by

- 0.5 × stress × volume
- 0.5 × strain × volume
- 0.5 × stress × strain × volume
- 0.5 × stress × strain

2. Two uniform steel rods A and B of same length having diameters d and 2d are subjected to tensile forces P and 2P respectively. Then the strain energy in both rods will be

- rod A has more
- equal
- zero in both
- rod B has more

3. For a beam carrying a UDL, the strain energy will be maximum in case the beam is

- cantilever
- simply supported
- propped cantilever
- fixed at both ends

4. For linear elastic system, the top of displacement for strain energy is given by

- linear
- quadratic
- cubic
- quartic

5. A prismatic bar 1m long and 4 sq. cm in cross-sectional area is compressed by a force of 80 kN. If E = 200kN/sq.mm, the total strain energy stored in the bar is equal to

- 40 kN-mm
- 0.05 kN-mm
- 400 kN-mm
- 80 kN-mm

6. U_{1} and U_{2} are the strain energies stored in a prismatic bar due to axial tensile forces P_{1} and P_{2} respectively. The strain energy U stored in the same bar due to combined action of P_{1} and P_{2} will be

- U = U
_{1}× U_{2} - U = U
_{1}+ U_{2} - U > U
_{1}+ U_{2} - U < U
_{1}+ U_{2}

7. If a cantilever beam of length L is subjected to a point load P acting in the downward direction at its free end and the flexural rigidity (EI) of the beam is constant, the elastic strain energy due to bending would be

$\\a.\; \frac{PL}{6EI}\\ b. \; \frac{P^{2}L^{3}}{6EI}\\ c. \; \frac{P^{2}L^{2}}{3EI}\\ d. \; \frac{P^{2}L^{3}}{3EI}$

8. Strain energy per unit volume that a material can absorb without exceeding its proportional limit is called

- Strain hardening
- Shear modulus of material
- Bulk modulus of material
- Modulus of resilience

9. Which one of the following expression represents strain energy density?

- stress × strain
- (1/2) stress × strain
- (1/3) stress × strain
- (1/4) stress × strain

10. The strain energy stored in a simply supported beam of span ‘L’ and flexural rigidity EI due to central concentrated load W is given by

$\\a.\; \frac{W^{2}L^{2}}{48EI}\\ b.\; \frac{W^{2}L^{3}}{48EI}\\ c.\; \frac{W^{2}L^{2}}{96EI}\\ d.\; \frac{W^{2}L^{3}}{96EI}$

11. A bar of length L and cross-sectional area A is subjected to gradually applied load w. The strain energy stored in the bar is

$\\a.\; \frac{wL^{2}}{2AE}\\ b.\; \frac{wL^{2}}{AE}\\ c.\; \frac{w^{2}L}{AE}\\ d.\; \frac{w^{2}L}{2AE}$

12. A prismatic beam of uniform flexural rigidity EI is simply supported over a span, L. If a moment, M is applied at one support, the resulting bending strain energy is

$\\a.\; \frac{M^{2}L}{4EI}\\ b.\; \frac{ML^{2}}{EI}\\ c.\; \frac{M^{2}L}{6EI}\\ d.\; \frac{M^{2}L}{2EI}$

13. If the depth of a rectangular section is reduced to half, strain energy stored in the beam becomes

- 1/4 times
- 1/8 times
- 4 times
- 8 times

14. What will be the unit of strain energy density in SI system

- J/m
^{3} - J/m
^{3}s - Js/m
^{3} - Inlb/in
^{3}