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VTU Mechanical Engineering (Semester 3)
Mechanics of Materials
June 2014
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) Define i) Stress ii) Hoke's law iii)Elasticity iv) Lateral strain
4 M
1 (b) Explain stress-strain relationship showing salient points on the diagram.
6 M
1 (c) A stepped bar is subjected to an external loading shown in fig Q1(c). calculated the change in the length of bar. Take E= 200 Gpa for steel, E=70 Gpa for aluminium and E=100GPa for copper.
img
10 M

2 (a) Define i) Poisson's ratio ii) Bulk modulus.
2 M
2 (b) Derive an expression for establishing the relationship between Young's modulus and modulus of rigidity.
6 M
2 (c) A 25 mm diameter steel rod passes concentrically through a bronze tube 400mm long and provided with nuts and washers which are adjusted initially so that there is no end play at 20°C. Assuming that there is no bronze when one of the nuts its tight end by giving at one-tenth of a turn, the pitch of the thered being 2.5mm, take E for steel =200 kN/mm2 and E for bronze=100 kN/mm2
12 M

3 (a) Define the principle planes and principal stresses.
4 M
3 (b) Explain procedure for constructing Mohr's circle, for an element acted upon by two tensile stresses and sher stresses.
6 M
3 (c) The state of stress in two dimensionally stressed body is as shown fig Q3(c). determine the principle planes, principle stresses, maximum shear stress and their planes.
10 M

4 (a) Define i) Strain energy ii)Work
3 M
4 (b) Prove that volumetric; strain in thin cylinder is given by \frac{Pd}{4tE}(5-4\mu ), with usual notations
7 M
4 (c) A.C.I pipe has 200 mm internal diameter and 50 mm metal thickness and carries water under a pressure of 5 N/mm2. Calculate the maximum and minimum intensities of circumferential stress and sketch the distribution of circumferential stress radial pressure across the section.
10 M

5 (a) Derive the relationship between load, shear and bending moment.
5 M
5 (b) Briefly explain the different types of loads.
3 M
5 (c) Draw the SFD and BMD for the loading pattern on the beam in FigQ5(c). indicate the point of contraflexure. Also locate the maximum BM with its magnitude
img
12 M

6 (a) What are the assumptions made in simple theory of bending?
4 M
6 (b) Prove that the maximum shear stress is 1.5 times the average shear stress in beam of rectangular cross- section.
6 M
6 (c) At a given position in a beam of uniform I-section is subjected to a bending moment of 100kN-m. Plot the variation of bending stress across the section.(Refer FigQ6(c))
img
10 M

7 (a) Derive the deflection equation for the beam in the standard form
EI\frac{d^{2}y}{dx^{2}}=M(x)
6 M
7 (b) For the beam loaded as shown in fig Q7(b), find the position and magnitude of maximum, deflection. Take I=4.3×108 and E=200kN/mm2.
img
14 M

8 (a) What are the assumptions made in simple theory of columns?
3 M
8 (b) Derive an expression for the critical load in a column subjected to compressive load, when one end is fixed and other end is free.
7 M
8 (c) Find the diameter of the shaft required to transmit 60kW at 150 RPM if the minimum torque is 25% more than the mean torque for a maximum shear stress of 60MPa. Find also the angle of twist in a length of 4m. Take G=80 Gpa.
10 M

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