Question Paper: Mechanics of Materials : Question Paper Jun 2014 - Mechanical Engineering (Semester 3) | Visveswaraya Technological University (VTU)
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## Mechanics of Materials - Jun 2014

### Mechanical Engineering (Semester 3)

TOTAL MARKS: 100
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks.
1 (a) Define i) Stress ii) Hoke's law iii)Elasticity iv) Lateral strain(4 marks) 1 (b) Explain stress-strain relationship showing salient points on the diagram.(6 marks) 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.
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(10 marks)
2 (a) Define i) Poisson's ratio ii) Bulk modulus.(2 marks) 2 (b) Derive an expression for establishing the relationship between Young's modulus and modulus of rigidity.(6 marks) 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 marks) 3 (a) Define the principle planes and principal stresses.(4 marks) 3 (b) Explain procedure for constructing Mohr's circle, for an element acted upon by two tensile stresses and sher stresses.(6 marks) 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 marks) 4 (a) Define i) Strain energy ii)Work(3 marks) 4 (b) Prove that volumetric; strain in thin cylinder is given by \frac{Pd}{4tE}(5-4\mu ), with usual notations(7 marks) 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 marks) 5 (a) Derive the relationship between load, shear and bending moment.(5 marks) 5 (b) Briefly explain the different types of loads.(3 marks) 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
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(12 marks)
6 (a) What are the assumptions made in simple theory of bending?(4 marks) 6 (b) Prove that the maximum shear stress is 1.5 times the average shear stress in beam of rectangular cross- section.(6 marks) 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))
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(10 marks)
7 (a) Derive the deflection equation for the beam in the standard form
EI\frac{d^{2}y}{dx^{2}}=M(x)
(6 marks)
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.
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(14 marks)
8 (a) What are the assumptions made in simple theory of columns?(3 marks) 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 marks) 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 marks)