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VTU Mechanical Engineering (Semester 3)
Mechanics of Materials
May 2016
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1(a) State Hooke's law. Sketch the typical stress - strain diagram for mild steel indicating all salient points and zones on it.
4 M
1(b) Derive an expression for the extension of uniformly tapering circular bar subjected to axial load.
8 M
1(c) A round bar with stepped portion is subjected to the forces as shown in fig Q1(c). Determine the magnitude of force P, such that net deformation in the bar does not exceed 1 mm. E for steel is 200 Gpa and Aluminium is 70 Gpa. Big end diameter and small end diameter of the tapering bar are 40mm and 12.5 respectively.
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8 M

2(a) Define Poisson's ratio. Derive an expression for volumetric strain of a rectangular bar, subjected to normal stress along the axis.
10 M
2(b) When a bar of 25mm diameter is subjected to a pull of 61kN, the extension on a 50mm gauge length is 0.1mm and decresase in diameter is 0.013mm. Calculate the values of elastic constant E, G, K and μ.
10 M

3(a) Derive an expression for the normal stress and shear stress on a plane inclined at 'θ' to the vertical axis in a biaxial stress system.
8 M
3(b) At a point in a loaded elastic member, there are normal stresses of 60MPa and 40MPa (bothe tensile) respectively, at right angles to each other with positive shear stress of 20MPa. Draw the Mohr's circle diagram and find i) Principle stresses and their plane ii) Maximum shear stress and its plane.
12 M

4(a) Derive an expression for strain energy stored in a plain bar subjected to axial load F.
5 M
4(b) Derive an expression for circumferential stress for thin cylinder.
5 M
4(c) T thick cylinder of 500mm inner diameter is subjected to an internal pressure of 9MPa. Taking the allowable stress for the material of the cylinder as 40MPa, determine the wall thickness of the cylinder.
10 M

5(a) Derive an expression to establish a relationship between the intensity of load, shear force and bending moment.
5 M
5(b) Draw the shear force and bending moment diagram for the beam shown in fig. Q5(b). Locate the point of contra flexure.
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15 M

6(a) List the assumptions made in simple bending theory and establish the relationship between bending stress and radius of curvature.
10 M
6(b) A uniform I - section beam is 100mm wide and 150mm deep with a flange thickness of 25mm and web thickness of 10mm. The beam is simply supported over a span of 5m. It carries a udl of 83.4kN/m throughout its length. Determine the bending stress in the beam.
10 M

7(a) Find the expression for the slope and deflection of a cantilever of length L carrying uniformly distributed load over whole length.
10 M
7(b) A beam of length 6mts is simply supported at its ends and carries two point loads of 48kN and 40kN at a distance of 1 m and 3 m respectively from the left supported. Find i) Deflection under each load ii) Maximum deflection iii) Point at which maximum deflection occurs. Take E = 2×105 Mpa and I = 85×106mm4.
10 M

8(a) Determine the diameter of the shaft which will transmit 440kW at 28. rpm, if maximum torsional shear stress is to be limited to 40N/mm2. Assume G = 84kN/mm2.
10 M
8(b) A solid round bar of 60mm diameter and 2.5m long is used as a strut. Find the safe compressive load for the strut if i) Both ends are hinged ii) Both ends are fixed. Take E = 2×105N/mm2 and factor safety = 3.
10 M

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