Mechanics Of Solids Nov2003 Or 210851

Code No: 210851 II B.Tech. I-Semester Supplementary Examinations, November-2003

OR

MECHANICS OF SOLIDS (Common to Chemical Engineering and Metallurgy and Material Techniques) Time: 3 hours Max. Marks: 70 Answer any FIVE questions All questions carry equal marks --1.a) State and explain Hooke’s law. b) The following data pertains to a tension test conducted in a laboratory. i) Diameter of the specimen = 15 mm ii) Length of the specimen = 200 mm iii) Extension under a load of 10 kN = 0.035 mm iv) Load at yield point = 110 kN v) Maximum load = 190 kN vi) Length of specimen after failure = 255 mm vii) Neck diameter = 12.25 mm Determine: (a) Young’s Modulus (b) Yield stress (c) Ultimate stress (d) Percentage elongation (e) Percentage reduction in area (f) Safe stress using a factor of safety of 1.5. 2.a)

b)

3.a) b)

Obtain the following relation between the three elastic constants from the first  9 KG  principle E =  .  3K + G  A rod of diameter 100mm and 1m long is subjected to a pull of 200 kN in the direction of its length. The extension of rod was found to be 0.15 mm, while the decrease in diameter was 0.007 mm. Find the Young’s modulus, Poisson’s ratio, modulus of rigidity and bulk modulus of the material. Define bending moment and shear force at a section of beam. Draw the bending moment diagram for a over hanging beam shown in the figure. Find the maximum sagging and hogging BM. Also find the point of contraflexure.

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Code No:210851 4.a) b)

5.a) b)

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OR

Show that for a circular cross-section, the maximum shear stress is 4/3 times the average shear stress. Draw the shear stress distribution for an I shaped section of a beam shown in figure, if the shear force is 200 kN the I-section is symmetric.

Obtain an expression for the differential equation for the classic line of a loaded beam. Obtain an expression for maximum slope and maximum deflection in a simply supported beam of span ‘l’, carrying a ud1 of ‘W’ kN/m over the entire span.

6.a) b)

Distinguish between thin and thick cylinders. A cylindrical shell is 3 m long, 1 m in diameter, thickness of wall is 10 mm, the internal fluid pressure is 1.5 N/mm2. Calculate the change in dimensions of the shell and maximum intensity of shear stress induced. Given E = 200 Gpa and Poisson’s ratio = 0.3.

7.

For the state of stresses shown in figure. Calculate the a) Normal stresses on plane AB inclined at 400 as shown. b) Principal stress and their planes. c) Maximum shearing stresses and their planes. d) Normal stress on the plane of maximum shear.

8.a) b)

Derive the torsion equation with usual notations. A solid steel shaft of an automobile axle is required to transmit a torque of 20 kN-m. If the shear stress is not to exceed 70 N/mm 2 and the angle of twist is limited to 0.2 degree per meter, find a suitable diameter for the shaft. Given G=84 Gpa. -*-*-*-