B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2009

Third Semester

Civil Engineering

CE 2201 — MECHANICS OF SOLIDS

(Regulation 2008)

Time : Three hours Maximum : 100 Marks

Answer ALL Questions

PART A — (10 × 2 = 20 Marks)

1. State Hooke’s law.

2. What is modulus of elasticity?

3. What is perfect frame?

4. State the two analytical methods for finding out the forces in the members of a perfect frame.

5. What is shear force in a beam?

6. What is bending moment in a beam?

7. What is slope of a beam?

8. What is deflection of a beam?

9. State the assumptions for shear stress in a circular shaft subjected to torsion.

10. What is stiffness of a spring?

PART B — (5 × 16 = 80 Marks)

11. (a) A hollow cylinder 2 m long has an outside diameter of 50 mm and inside diameter of 30 mm. If the cylinder is carrying a load of 25 kN, find the stress in the cylinder. Also find the deformation of the cylinder, if the value of modulus of elasticity for the cylinder material is 100 GPa.

Or

(b) A load of 5 kN is to be raised with the help of a steel wire. Find the minimum diameter of the wire, if the stress is not to exceed 100 MPa.

12. (a) A gas cylinder of internal diameter 40 mm is 5 mm thick. If the tensile stress in the material is not to exceed 30 MPa, find the maximum pressure which can be allowed in the cylinder.

Or

(b) A cylinderical shell of 500 mm diameter is required to withstand an internal pressure of 4 MPa. Find the minimum thickness of the shell, if maximum tensile strength for the plate material is 400 MPa and efficiency of the joints is 65%. Take factor of safety as 5.

13. (a) A cantilever beam of 2 m long carries a uniformly distributed load of 1.5 kN/m over a length of 1.6 m from the free end. Draw shear force and bending moment diagrams for the beam.

Or

(b) A simply supported beam 6 m long is carrying a uniformly distributed load of 5 kN/m over a length of 3 m from the right end. Draw shear force and bending moment diagrams for the beam and also calculate the maximum bending moment on the beam.

14. (a) A simply supported beam of span 3 m is subjected to a central load of 10 kN. Find the maximum slope and deflection of the beam. Take 4 6 mm 10 12 I × = and E = 200 GPa.

Or

(b) A steel joist, simply supported over a span of 6 m carries a point load of 50 kN at 1.2 m from the left hand support. Find the position and magnitude of the maximum deflection. Take 2 12 mm N 10 14 EI − × = .

15. (a) Find the angle of twist per metre length of a hollow shaft of 100 mm external diameter and 60 mm internal diameter, if the shear stress is not to exceed 35 MPa. Take modulus of rigidity G = 85 GPa.

Or

(b) A leaf spring is to be made of seven steel plates 65 mm wide and 6.5 mm thick. Calculate the length of the spring, so that it carries a central load of 2.75 kN, the bending stress being limited to 160 MPa. Also calculate the deflection at the centre of the spring. Take E for the spring material as 200 GPa.

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