JNTU
JNTU B.Tech II Year MECHANICS OF SOLIDS Previous Question Paper (April - 2018 - R15)
Note: This question paper contains two parts A and B. Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit.
Part A
(25 Marks)
State Hooke's law.
Answer
Hooke's law states that within the elastic limit, the stress applied to a material is directly proportional to the strain produced in it.
Distinguish between lateral strain and longitudinal strain.
Answer
Longitudinal strain is the ratio of change in length to the original length of a body in the direction of the applied force. Lateral strain is the ratio of change in width or diameter to the original width or diameter in a direction perpendicular to the applied force.
Define bending moment diagram.
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Differentiate between a simply supported beam and over hanging beam.
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State any two assumptions made in the theory of simple bending.
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The average shear stress in a beam of circular section of diameter 150mm is 3MPa. Evaluate the maximum shear stress.
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State Von-Mises theory of failure.
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List the methods to find the stresses on oblique plane.
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Define torsional rigidity.
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Define thin spherical shell. Name the stresses set up in a thin spherical shell.
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Part B
(50 Marks)
A composite tube consists of a steel tube 150mm internal diameter and 10mm thickness and an outer brass tube 170mm internal diameter and 10mm thickness. The two tubes are of the 150mm length. The compound tube carries an axial load of 1000kN. Determine (a) stress in the tubes (b) load carried by each tube and (c) amount of change in length. Take Es=2×105 N/mm2 and Eb=1×105 N/mm2.
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A rod is 2000mm long at a temperature of 10°C. Determine the expansion of the rod, when the temperature is raised to 80°C. If this expansion is prevented, evaluate the stresses induced in the material of the rod. Take E=2×105 N/mm2 and linear expansion of the material α=0.000012 per degree centigrade.
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Derive the relationship between modulus of elasticity and modulus of rigidity.
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A simply supported beam of length 5m carries a point load of 3kN at distance of 2m from the left end. Draw the S.F diagram for the beam.
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Derive the relationship between load, shear force and bending moment.
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An overhanging beam of length 8m is simply supported over 4m apart and overhang of 2m at each side. The beam carries two concentrated loads as shown in figure 1. Draw the shear force and bending moment diagrams.
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A rectangular beam 200 mm deep and 300mm wide is simply supported over a span of 8m. What uniformly distributed load per meter the beam may carry, if the bending stress is not to exceed 120 N/mm2.
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An I – section beam shown in figure 2, is simply supported over a span of 12m. If the maximum permissible bending stress is 80 N/mm2, what concentrated load can be carried at a distance of 4m from one support?
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A rectangular beam 100mm wide is subjected to a maximum shear force of 100kN. Estimate the depth of the beam if the maximum shear force is 6N/mm2.
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An I - section has the following dimensions. Top and bottom flanges=165mm×20mm. Web=200mm deep and 15mm thickness. If the maximum shear stress developed in the beam is 17N/mm2, compute the shear force to which the beam is subjected.
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At a point in a strained material the principal tensile stresses across two perpendicular planes are 80N/mm2 and 40N/mm2. Compute normal stress, shear stress and the resultant stress on a plane inclined at 20° with the minor principal stress. Also determine the obliquity.
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Write short note on maximum principal stress theory.
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The stresses induced at a critical point in a machine component made of steel 45C8 (σy = 380 N/mm2) are as follows: σx = 100 N/mm2; σy = 40 N/mm2; τxy = 80 N/mm2. Calculate the factor of safety by maximum shear stress theory.
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Compute the maximum torque transmitted by a solid shaft of diameter 100 mm if the maximum shear stress induced to the shaft is 50 N/mm2.
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Find the maximum shear stress induced in a solid circular shaft of diameter 150mm when the shaft transmits 150 kW power at 180 r.p.m.
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Derive an expression for longitudinal stress for a thin cylinder subjected to an internal pressure.
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A thin spherical vessel in the shape of spherical shell of 1.2m internal diameter and 12 mm shell thickness is subjected to pressure of 1.6 N/mm2. Estimate the hoop stress induced in the material of the vessel.
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