Strain Energy MCQ – Strength of Materials

1. Strain energy stored in a member is given by

  1. 0.5 × stress × volume
  2. 0.5 × strain × volume
  3. 0.5 × stress × strain × volume
  4. 0.5 × stress × strain
Answer. c

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

  1. rod A has more
  2. equal
  3. zero in both
  4. rod B has more
Answer. b

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

  1. cantilever
  2. simply supported
  3. propped cantilever
  4. fixed at both ends
Answer. a

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

  1. linear
  2. quadratic
  3. cubic
  4. quartic
Answer. b

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/, the total strain energy stored in the bar is equal to

  1. 40 kN-mm
  2. 0.05 kN-mm
  3. 400 kN-mm
  4. 80 kN-mm
Answer. a

6. U1 and U2 are the strain energies stored in a prismatic bar due to axial tensile forces P1 and P2 respectively. The strain energy U stored in the same bar due to combined action of P1 and P2 will be

  1. U = U1 × U2
  2. U = U1 + U2
  3. U > U1 + U2
  4. U < U1 + U2
Answer. c

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}

Answer. b

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

  1. Strain hardening
  2. Shear modulus of material
  3. Bulk modulus of material
  4. Modulus of resilience
Answer. d

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

  1. stress × strain
  2. (1/2) stress × strain
  3. (1/3) stress × strain
  4. (1/4) stress × strain
Answer. b

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}

Answer. a

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}

Answer. a

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}

Answer. a

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

  1. 1/4 times
  2. 1/8 times
  3. 4 times
  4. 8 times
Answer. d

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

  1. J/m3
  2. J/m3s
  3. Js/m3
  4. Inlb/in3
Answer. a
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