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# MECHANICS OF SOLIDS IMPORTANT QUESTIONS

## [MOS] MECHANICS OF SOLIDS  IMPORTANT QUESTIONS

1. Explain the concept of stress. Define shear stress.

2. Define and explain Young’s modulus of elasticity.

3. Define stress, strain and elasticity.

4. Explain the salient features of a typical stress strain curve for a mild steel rod subjected to tension test.

5. Define stress, strain, elastic limit & Poisson’s ratio.

6. What is temperature stress. How will you evaluate it in a composite bar.

7. Describe the effect of temperature when the body is i) free to deform and ii) restrainted.

8. Explain Hooke’s Law and poisson’s ratio.

9. Define Young’s modulus and modulus of rigidity.

10. Define the term Bulk modulus & Modulus of rigidity.

11. Define strain energy and explain how it is stored in a body.

12. Explain the terms resilience, proof resilience and modulus of resilience.

13. Briefly explain instantaneous stresses.

14. State Hooks law and derive an expression for the deformation of a rod under axial load.

15. Deduce the expression to determine the elongation of a bar of tapering section.

16. A bar of uniform cross section A and length L is suspended from top.

Find the expression for the extension of the bar due to self weight only, If youngs modulus is E and unit weight of material is γ.

17. A circular of length L and cross sectional area A1 is kept inside a tube of same length and cross sectional area A2.

The composite rod is firmly held in between immovable walls at their ends.

If the temperature increases by an amount T°C from the stress free state. Find the stresses in the rod and tube using notations.

18. Derive the relationship between modulus of elasticity and modulus of rigidity.

19. Derive the relationship between modulus of elasticity and bulk modulus.

20. Derive the relationship between three moduli of elasticity.

21. Show that the volumetric strain of a cube subjected to normal stresses is equal to 3 times the linear strain.

22. Derive an expression for the strain energy density of a bar subjected to axial load applied gradually.

23. Prove that the stress developed due to suddenly applied load is twice that of gradually applied load.

24. Derive an expression for strain energy due to bending.

25. Derive an expression for strain energy due to shear.

26. Obtain the expressions for strain energy stored in a prismatic bar due to gradually applied and suddenly applied axial load.

27. Derive an expression for the strain energy of a prismatic bar hanging under its own weight.

## MODULE 3 AND 4

1. Define bending moment and shear force.

2. Define point of contraflexure and flexural rigidity

3. Explain the use of shear force and bending moment diagrams.

4. Explain the asssumptions made in the simple theory of bending.

5. What you mean by beams of uniform strength.

6. What is pure bending. Sketch a loading which causes pure bending in a simply supported beam.

7. Explain briefly bending stress distribution.

8. Define modulus of section. Explain the method of its derivation.

9. Define the section modulus. Derive the expression for rectangular cross section.

10. State and explain the theory of bending.

11. What do you mean by shear centre. Explain briefly its significance.

12. Derive the relationship between intensity, shear force and bending moment.

13. Draw the shear force and bending moment diagram for a cantilever of length L carrying a udl of ‘w’ per meter length over its entire length.

14. A beam of length L carries a udl and on two supports. How far from ends must the support be placed, if the greatest BM is to be as small as possible.

15. Draw the shear force and bending moment diagram for a cantilever of length L carrying a udl of ‘w’ per meter length acting over the half span from the free end.

16. Draw the bending moment diagram for a cantilever beam with uniformly varying load with intensity zero at the fixed and w at the free end.

17. A simply supported beam of span L carries a clockwise moment M at centre. Draw the BMD.

18. Derive the equation of pure bending of beam.

19. Derive the expression for the maximum shear stress in a circular section of radius R where F = shear force.

20. Obtain analytically the shear stress distribution of rectangular beam cross section.

21. Prove that the maximum shear stress in a circular section is 4/3 times the average stress.

22. Prove the maximum shear stress in rectangular cross section is 1.5 times the average shear stresses.

23. Obtain the expression for the shear stress at neutral axis for a triangular section with the base b and height h.

## MODULE 5 AND 6

1. Define Mohr’s circle. What are its uses.

2. Define principal stresses and principal strains.

3. Explain plain stress and Principal stress.

4. What is principal plane, principal stress, and plane of maximum shear.

5. Explain Mohr circle representation of stresses.

6. Explain why the plane of maximum shear stress and principal stress planes are inclined 45° to each other.

7. Differentiate between thin and thick cylinders. What are the assumptions made in Lame’s theory for thick cylinders.

8. Distinguish between thick and walled cylinders and compound cylinders.

9. What is the principle of compound cylinders. Sketch the stress distribution across the cross section of a compound cylinder.

10. Show that the planes containing maximum shear stress make an angle of 45° with the principal planes.

11. Explain why hollow shafts are more efficient in resisting torsion than solid shafts on the same weight.

12. Distinguish between closed coiled and open coiled springs.

13. Explain the terms torsional rigidity and polar modulus.

14. What are assumptions made in the theory of pure torsion.

15. Derive the expression for the stresses on an oblique plane of rectangular body, when the body is subjected to simple stress.

16. Derive the expression for normal stress on a plane inclined at an angle θ to x axis and subjected to normal stresses in x and y direction.

17. Show that the sum of normal stresses on two mutually perpendicular planes in a general two dimensional stress system is constant.

18. Show that in thin cylinders the circumferential stress is twice the longitudinal stress when subjected to an internal pressure.

19. Derive the expression for the hoop stress in thin cylinder (of diameter d and thickness t) subjected to an internal pressure of p.

20. What is hoop stress. Derive an expression for hoop stress in thin cylinders.

21. Derive an expression for hoop and longitudinal stresses in thin cylinder.

22. State and explain Lame’s equation for stress in thick cylinders.

23. Derive the expression for power transmission through circular shaft.

24. Show that hollow shaft is strongest than the solid shaft of same material, length and weight.

25. Derive the torsion formula for a prismatic shaft with circular cross section.