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Posted By: sasi kala Member Level: Diamond Posted Date: 01 Jun 2008
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2007 Anna University B.E Mechanical CE 251 — STRENGTH OF MATERIALS Question paper
B.E./B.Tech. DEGREE EXAMINATION,
Fourth Semester
Mechanical Engineering
CE 251 — STRENGTH OF MATERIALS
Time : Three hours Maximum : 100 marks
Assume any additional data required and indicate it clearly.
Answer ALL questions.
PART A — (10 ? 2 = 20 marks)
1. Define : (a) Poisson’s ratio, (b) Rigidity modulus.
2. Write the two equations used to find the forces in compound bars made of two materials subjected to tension.
3. Define : (a) Shear force and (b) Bending moment at a section.
4. A clockwise moment M is applied at the free end of a cantilever. Draw the SF and BM diagrams for the cantilever.
5. Derive the relation between the shear force and bending moment, in bending theory.
6. Draw the shear stress distribution diagram for a rectangular beam with values at important points.
7. Write an expression for the angle of twist for a hollow circular shaft with external diameter D, internal diameter d, length l and rigidity modulus G.
8. Define stiffness of a helical spring and write an expression for it.
9. Normal stresses and and shear stress act at a point. Find the principal stresses and the principal planes.
10. A cantilever is subjected to a point load W at the free end. What is the slope and deflection at the free end?
PART B — (5 ? 16 = 80 marks)
11. Draw the SF and BM diagrams for the beam shown in Fig. Q. 11. Find the maximum values and their position. Give the values at important points in the diagram.
Fig. Q. 11
12. (a) Find the value of P and the change in length of each component and the total change in length of the bar shown in Fig. Q. 12 (a). E = 200 kN/mm2.
Fig. Q. 12 (a)
Or
(b) A bar 30 mm ? 30 mm ? 250 mm long was subjected to a pull of 90 kN in the direction of its length. The extension of the bar was found to be
0.125 mm, while the decrease in each lateral dimension was found to be 0.00375 mm. Find the Young’s modulus, Poisson’s ratio, rigidity modulus and bulk modulus for the material of the bar.
13. (a) A timber beam 150 mm wide and 300 mm deep is simply supported over a span of 4 metres. Find the maximum uniformly distributed load that the beam can carry if the bending stress is not to exceed 8 N/mm2.
Or
(b) Determine the diameter of a solid shaft transmitting 300 kW at 250 rpm. The maximum shear stress should not exceed 30 N/mm2 and the twist should not be more than one degree in a shaft length of 2 m.
G = 100 kN/mm2.
14. (a) A cylindrical shell 3 m long, 1 m internal diameter and 10 mm thick is subjected to an internal pressure of 1.5 N/mm2. Calculate the changes in length, diameter and volume of the cylinder. E = 200 kN/mm2, Poisson’s ratio = 0.3.
Or
(b) A point in a strained material is subjected to a horizontal tensile stress of 80 N/mm2 and a vertical compressive stress of 100 N/mm2. It is also accompanied by a shear stress of 50 N/mm2. Determine (i) principal stresses, (ii) principal planes and (iii) maximum shear stress and its planes.
15. (a) A 3 m long cantilever of uniform rectangular cross–section 150 mm wide and 300 mm deep is loaded with a point load of 3 kN at the free end and a udl of 2 kN/m over the entire length. Find the maximum deflection.
E = 210 kN/mm2. Use Macaulay’s method.
Or
(b) A simply supported beam of span 6 m is subjected to a udl of 2 kN/m over the entire span and a point load of 3 kN at 4 m from the left support. Find the deflection under the point load in terms of EI. Use strain energy method.
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