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Reg. No. : ..................................... Name : ........................................
Third Semester B.Tech. Degree Examination, June 2009 Branch : MECHANICAL ENGINEERING (2003 Scheme) 03-304 : Machanics of Solids (MNPU) Time : 3 Hours
Max. Marks : 100
Instruction : Answer all questions in Part A and any one question from each Module in Part B. Each full question in Part B carries 20 marks. PART – A I. i) State Hooke’s law and derive an expression for the deformation of a rod under axial load. ii) Explain clearly the concept and use of Mohr’s circle. iii) Differentiate plain stress and plain strain conditions giving exmples. iv) Define Elastic constants. Give the relation between them. v) Explain the use of shear force and bending moment diagrams. vi) Write down torsion formula and explain the terms. What is meant by torsional rigidity ? vii) What is the principle of compound cylinders ? Sketch the stress distribution across the cross section of a compound cylinder. viii) Differentiate between short and long columns. What is meant by slenderness ratio ? ix) Explain the terms resilience, proof resilience and modulus of resilience. x) State and explain castigliano’s theorems.
(10×4=40 Marks) P.T.O.
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PART – B MODULE – I II. Calculate the reactions at A and B for the beam shown in figure 1 and draw the shear force and bending moment diagram. Determine the maximum bending moment and bending stress. The moment of inertia of the beam section is 108mm4 and depth of the beam is 500 mm.
Fig. 1 III. A composite bar made up of aluminium and steel is held between two supports as shown in figure 2. The bars are stress free at a temperature of 38°C. What will be the stresses in the two bars when temperature is 21°C, if i) the supports are unyielding ii) the supports come nearer to each other by 0.1 mm. It can be assumed that the change of temperature is uniform all along the length of the bar. Es = 210 GPa. Eal = 74 GPa
αs = 11.7 × 10
−6
0 C;
−6
∞al = 23.4 × 10
Fig. 2
0 C
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MODULE – II IV. a) Determine the maximum power transmitted at 270 rpm by a mild steel hollow shaft of 40 mm internal diameter and 5 mm thick, if the allowable stress is 75 MPa and the angle of twist is not to exceed 1 degree in a length of 1.8 m. Assume G = 80 GPa for the shaft. b) Determine the maximum pressure a mild steel water pipe line of 0.3 m internal diameter and 3 mm thickness can sustain for an allowable stress of 120 MPa. Determine the change in volume of the pipe under the maximum pressure per metre length. Assume E = 210 GPa and Poisson’s ratio 0.3. V. A cantilever of span 4 m carries a u.d.l of 2 kN/m from free end to midpoint of the beam. Calculate the slope and deflection at the free end by moment area method. MODULE – III VI. a) What are the advantages of Rankine’s formula over Euler’s formula ? b) Two bars A and B are each 30 cm long and are of the same material. Bar A is 20 mm in diameter for a length of 10 cm and 40 mm in diameter for the remaining length. Bar B is 2 cm in diameter for 20 cm length and 4 cm in diameter for the remaining length. An axial blow given to A produces a maximum instantaneous stress of 200 MPa. Calculate the maximum instantaneous stress produced by the same blow on bar B. If each bar is stressed up to elastic limit calculate the ratio of energy stored by A and B at proof stress. VII. Find the Euler’s crushing load for a hollow cylindrical column made of cast iron 120 mm external diameter and 20 mm thick. The column is 4.2 m long one end fixed and the other end hinged. E = 80 kN/mm2. Compare this load with crushing load as given by Rankine’s formula using constants f cs = 550N/mm2, a =1/1600. (20×3=60 Marks) –––––––––––––––––––