Mechanics Of Solids March06 Nr210302

NR

Code No: NR210302

II B.Tech I Semester Supplementary Examinations, March 2006 MECHANICS OF SOLIDS ( Common to Mechanical Engineering, Mechatronics, Metallurgy & Material Technology, Production Engineering and Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Define and explain the terms: i. ii. iii. iv.

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Modulus of Elasticity Modulus of Rigidity Poisson’s ratio Bulk Modulus.

(b) Two vertical rods one of steel and the other of copper are each rigidly fixed at the top and 600 mm apart. The diameter and length of each rod are 30 mm and 375 mm respectively. A cross bar fixed to the rods at the lower ends carries a load of 5 kN such that the cross bar remains horizontal even after loading. Find the stress in each rod and the position of the load on the bar. ES = 200 Gpa and EC = 100 Gpa. [10] 2. A steel rod 28 mm diameter is fixed concentrically in a brass tube of 42 mm outer diameter and 30 mm inner diameter. Both the rod and tube are 450 mm long. The compound rod is held between two stops which are exactly 450 mm apart and the temperature of the bar is raised by 700 C. [16] (a) Find the stresses in the rod and tube if the distance between the stops is increased by 0.30 mm. (b) Find the increase in the distance between the stops if the force exerted between them is 90 kN Take

ES = 200kN/mm2 ; Eb = 90kN/mm2 ;

αS = 11.2 × 10−6 per 0 C αb = 2.1 × 10−5 per 0 C

3. (a) Classify the beams based on support conditions with the help of neat sketches. [5] (b) What are the different types of loads. Give neat sketches to represent various types of loads. [3] (c) A simply supported beam of span ‘l’ is loaded with a triangular load with zero intensity at one end to w /unit length at the other end. Draw the shear fore diagram and bending moment diagram showing the salient values. [8] 4. (a) State the assumptions involved in the theory of simple bending. (b) Derive the Bending equation from fist principle. 1 of 2

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NR

Code No: NR210302

5. (a) What is moment area method? Explain the two Mohr’s theorems, as applicable to the slope and deflection of a beam. [6] (b) A cantilever of uniform cross-section of length l carries two point loads, W at the free end and 2W at a distance a from the free end. Find the maximum deflection due to this loading. [10] 6. (a) Explain horizontal and hoop stresses as applied to thin cylinders.

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(b) What thickness of metal would be required for cast-iron water pipe 90 cm in diameter under a head of 100m? Assume the permissible tensile stress for cast iron as 20 MN/ m2 . [8] 7. Derive an expression for the shear stress produced in a circular shaft which is subjected to torsion. What are the assumptions made in the above derivation ? [16] 8. An open coiled helical spring is made out of 10 mm diameter steel rod, the coils having 10 complete turns, and a mean diameter 80 mm, the angle of helix 150 . Calculate the deflection under an axial load of 250 N and the maximum intensities of direct and shear stresses induced in the section of the wire. If the axial load of 250 N is replaced by an axial torque of 6 N.m, calculate the angle of rotation about axis of the coil and actual deflection. N=0.85×105 N/mm2 and E=2.5×105 N/mm2 . [16] ?????

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