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Tuesday, 7 July 2015

Mechanics of Materials- Model question paper for B.E/B.Tech Mechanical engineering



1(a) State St.Venant’s principle. (4 Marks)
(b) Write a brief note on properties of engineering materials.(6 Marks)
(c) Deduce a relation between Young’s modulus and Rigidity modulus. (6 Marks)
(d) A steel press has four tension members. Each member has a diameter of 16 mm. The largest load to be resisted by the press is to be 48 kN. Determine axial stress in the tension members. (4 Marks)
2(a) Prove that normal stress acting on maximum and minimum shear stress planes is the average of any two orthogonal normal stresses acting on the point. (8 Marks)
(b) Write a note on construction of Mohr’s circle. (8 Marks)
(c) A round bar of 30mm diameter is subjected to an axial compressive force P. Taking the allowable stresses for the material of the bar as 110 MPa in compression and 50 MPa in shear, determine the magnitude of maximum value of P which can be applied such that the member does not fail. (4 Marks)
3(a) The magnitude of bending moment at a section will be maximum or minimum when the shear force at that section is zero or changes its sign. Explain. (8 Marks)
(b) A 6m long beam simply supported its ends is subjected to UDL of 30 kN/m over 2 meters length from LHS support. Draw the SF and BM diagrams. (8 Marks)
(c) A 6 meters long beam is simply supported such that there is a over hang of L meters on either support. The beam is subjected to load W at its either ends. Determine W and L such that maximum bending moment and maximum shear stress induced in the beam are 30 kN-m and 15 kN respectively. (4 Marks)
4(a) What are the assumptions made during the derivation of equations related to theory of pure bending. (6 Marks)
(b) What is section modulus? Find the section modulus of a hollow circle. (6 Marks)
(c) A beam with I section has two equal flanges of each 220 mm wide and 12 mm thick. The web has 12 mm thickness and depth 460 mm. Determine the percentage of moment of resistance shared by the flanges and web, when the section is subjected to bending moment M. (8 Marks)
5(a) Derive the moment-curvature relationship for the deflected curve. (8 Marks)
(b) Macauleys method is an improved version of double integration method which can be used for finding the deflections of beams subjected to discontinuous loads. Explain. (8 Marks)
(c) A 2 meters long cantilever is subjected to UDL of 10 kN/m throughout its length and a vertically downward point load 20 kN at its free end. Taking E=200 GPa and maximum deflection as 0.3 mm, determine the width and depth of rectangular section. Depth of the section is twice the width. (4 Marks)
6(a) Show that shear stress distribution in any section of a shaft is directly proportional to the torque applied. (5 Marks)
(b) Explain the terms torsional rigidity and torsional flexibility. (6 Marks)
(c) Compare the mass of solid shaft with that of hollow shaft of same length, when they are made of same material and are to transmit same power at same speed. The outer diameter of hollow shaft is 1.4 times its inner diameter. Maximum shear stresses induced in both cases are equal. (5 Marks)
(d) A 1m long wire is hung in vertical position and disc is attatched at the bottom end. Diameter of the wire is 2 mm. Material of wire has yield stress in shear of 150 MPa. Determine the angle through which the disc can be rotated so that the wire does not yield. Take G= 80 GPa. (4 Marks)
7(a) Develop Euler’s buckling load formula for the column with both ends hinged. (6 Marks)
(b) Write a note on limitations of Euler’s formula. (4 Marks)
(c) Derive Rankine-Gordon formula. (6 Marks)
(d) A column 2.6 meters long with a square section of side 50 mm is to be replaced by a column with hollow square section of outer side 70 mm. Determine the wall thickness of the column and percentage saving in material. Both ends of the column are hinged. (4 Marks)
8(a) Show that the volumetric strain is the sum of longitudinal strain and twice the circumferential strain. (6 Marks)
(b) Radial and circumferential stresses in a thick wall pressure vessel vary parabolically across the section of the wall, while longitudinal stress is uniform throughout the cylinder. Explain. (6 Marks)
(c) A pressure vessel with outer and inner diameters of 400 mm and 320 mm respectively is subjected to an external pressure 8 MPa. Determine the circumferential stress induced at the inner and outer surfaces. (4 Marks)
(d) A water pipe with 500 mm diameter supplies water at 51 meters head. Taking allowable stress for pipe material as 30 MPa and efficiency of circumferential riveted joint as 80%, determine the thickness of the pipe. Specific weight of water is 9.81 kN/m3. (4 Marks)

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