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Friday, 19 June 2015

Theory of elasticity -Model question paper for B.E/B.Tech Engineering



1(a) A semi- infinite elastic medium is subjected to a normal pressure of intensity ‘P’ distributed over a circular area of radius ‘a’ at x=0. Determine the stress distribution by using Fourier integral method. (8 Marks)
(b) A cantilever beam of rectangular cross-section 40 mm wide and 60 mm thick is 800 mm in length. It carries a load of 500 N at the free end. Determine the stresses in the cantilever at mid-length. (6 Marks)
(c) Determine the stress and displacement fields in an infinite medium due to equal and opposite point forces acting at different points along their common line of action. (6 Marks)
2(a) What are general solution to Biharmonic equation. (6 Marks)
(b) What is Winkler’s theory? Explain. (8 Marks)
(c) A circular disc of 8 cm diameter and 5 mm thick is subjected to diametral compression. If the applied load is 800 N, determine the stress distribution in the disc at the centre. (6 Marks)
3(a) An infinite plate contains an elliptical hole, with major and minor axes a and b. If the plate is under all round tension and the hole is unstressed, determine the hoop stress around the hole and show that the stress concentration factors at the ends of the major and minor axes are 2a/b and 2b/a respectively. (6 Marks)
(b) Explain St.Venant’s theory. (5 Marks)
(c) An elliptical shaft of semi axes a=0.05 m, b=0.025 m, and G=80 GPa is subjected to a twisting moment of 1200 π N.m. Determine the maximum shearing stress and the angle of twist per unit length. (4 Marks)
(d) Derive Bredt’s formula for the rate of twist in terms of the shear-stress distribution for the torsion of thin-walled sections. (5 Marks)
4(a) An 150 mm × 100 mm × 12 mm unequal angle bar is placed with the long leg vertical and used as a beam supported at each end, the span being 3 m. If load of 6500 N is placed at the mid length of the bar, determine the maximum stress due to bending. (6 Marks)
(b) Derive the generalized flexure formula. (5 Marks)
(c) A prismatic bar of 2a × 2b cross-section is bent by two equal and opposite couples. Determine the equations for the bent shape of the prismatic bar. (5 Marks)
(d) A point force of 500 N is applied normal to a semi-infinite solid. Determine the stress distribution at a depth of 50 mm and angular location of 150 with the line of action of the force. (4 Marks)
5(a) Describe membrane analogy for the bending of thin plates. How this analogy can be used to determine the deflection of a plate? (6 Marks)
(b) Derive Navier’s equations for the bending of a circular plate. What are the assumptions made? (10 Marks)
(c) A circular plate 50 mm diameter is clamped at the edge. Its deflection at the centre is limited to 1 mm when a pressure of 1 MPa is applied. Calculate the thickness of the plate and the maximum stress developed in it. E = 200 GPa, v=0.3. (4 Marks)
6(a) By neglecting bending stresses, derive the equations of equilibrium for shells of revolution. (8 Marks)
(b) A long circular pipe of radius 300 mm and wall thickness 10 mm is subjected to a uniform bending moment of 10 N-m and a shear force of 1600 N at one end. Determine the maximum deflection of the pipe. (4 Marks)
(c) What are different types of elastic foundations? Derive the differential equation for the elastic line of a beam resting on an elastic foundation. (8 Marks)
7(a) State and prove the Maxwell-Betti reciprocal theorem. (8 Marks)
(b) What are the various types of elements used for plane stress analysis. (4 Marks)
(c) What do you understand by interpolation function or shape function for an element? (4 Marks)
(d) A beam column of circular cross-section is 50 mm in diameter and 2 m long. It is simply supported at the ends and carries an axial compressive load of 3.5 kN. If a couple of 15 N-m is applied at the right end in the anti-clockwise direction, determine the deflection and maximum stress developed in the column at mid-span. Take E=2×105 N/mm2. (4 Marks)
8(a) Derive an expression for the deflection of a thin circular plate of radius ‘a’ heated on the lateral surface. (6 Marks)
(b) The temperature rise of a solid conductor of radius ‘b’ due to a uniform heat source is given by the formula T = λ (b2 - r2), where λ is a constant. If there are no external forces resisting longitudinal or radial expansion, determine the stress distribution in the conductor. (6 Marks)
(c) A 500 mm radius wheel supporting a 200 kN load rests on a rail 100 mm radius. The material of both is steel with E=2×103 N/mm2 and v=0.3. Determine the maximum contact pressure and the total contact area. (4 Marks)
(d) Distinguish between stress-concentration factor and strain-concentration factor. (4 Marks)

Material science and engineering- Model question paper for B.E/B.Tech Engineering
1(a)

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