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Reg. No. : ..................................... Name : ..........................................
Third Semester B.Tech. Degree Examination, November 2009 (2008 Scheme) Branch : Civil 08.302 : MECHANICS OF STRUCTURES Time : 3 Hours
Max. Marks : 100 PART – A
Answer all questions. I. a) Define stress, strain, Elastic limit and Poisson’s ratio. b) Derive the relationship between Modulus of elasticity (E) and Bulk modulus (K). c) Explain the terms shear stress and complementary shear. d) Define : 1) Point of contraflexure 2) Flexural rigidity e) A simply supported beam of length 4 m carries a point load of 40kN at the centre and is supported at ends. Find the cross-section of beam assuming depth to be twice the width. The maximum bending stress in beam is not to exceed 200 N/mm2. f) In case of pure bending show that the neutral axis coincides with the centroidal axis about which bending takes place. g) What are the assumptions made in derivation of the torsion equation ? h) Derive an expression for strain energy due to bending.
(8×5=40 Marks)
P.T.O.
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PART – B Module – I II. a) Sketch the stress strain curve of mild steel and explain the following : i) limit of proportionality ii) yield point iii) ultimate stress iv) breaking stress. b) Derive an expression for the elongation of a conical bar of length ‘l’ and base diameter ‘d’ under its own weight, if the density of its material is ‘w’ and the modulus of elasticity is E. c) A conical bar tapers uniformly from a diameter of 4cm to 1.5cm in a length of 40 cm. If an axial pull of 80 kN is applied at each end, determine the elongation of the bar taking modulus of elasticity E = 2 × 105 N/mm2. OR III. The composite bar shown in figure is 0.2 mm short of distance between the rigid supports at room temperature. What is the maximum temperature rise which will not produce stresses in the bar ? Given; cross sectional area of steel : cross sectional area of copper = 4:3
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Find the stresses induced when temperature rise is 40°C. αs = 12 × 10–6/°C
Es = 2 × 105 N/mm2
αc = 17.5 × 10–6/°C
Ec = 1.2 × 105N/mm 2.
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Module – II IV. In the truss shown in figure, determine : a) The reaction at A and D. b) The forces in members AB and AE by the method of joint. c) The forces in members BC, CE and by the method of section.
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OR V. A T section beam 300 mm deep and 150 mm wide has flange and web thickness of 30 mm. The length of the beam is 6 m and is simply supported at its ends. It carries a uniformly distributed load of intensity 5 kN/m over its entire length. In addition to the uniformly distributed load, it carries a concentrated load of 3kN at its middle. Draw the shear stress distribution diagram for the beam. 20 Module – III VI. Two shafts are made of same material and are of equal lengths. One of them is solid and another one is hollow. The ratio of inside and outside diameters for hollow shaft is 0.4. They are subjected to same torque and same maximum shear stress. Compare the weights of two shafts. 20 OR VII. A masonry retaining wall of trapezoidal section is 4 m high with a top width of 1 m and a bottom width of 3 m. It retains earth for the entire depth. Sketch the stress distribution diagram on the base of the wall. Take unit weight of soil 17kN/m3 and 20 weight of masonry 20kN/m3. Take coefficient of lateral earth pressure as 0.3. ————————