Mehcanics Of Solids Ii May2003 Or 220156

Code No:220156

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II-B.Tech. II-Semester Supplementary Examinations, April/May 2003. MECHANICS OF SOLIDS-II (Civil Engineering) Time: 3 hours Max.Marks:70 Answer any FIVE questions All questions carry equal marks --1.a) An element in a stressed material has tensile stress of 500 MN/m2 and a compressive stress of 350 MN/m2 acting on two mutually perpendicular planes and equal shear stress of 100MN/m2 on these planes. Find principal stresses and position of the principal planes. Find also maximum shearing stress. b) A short metallic column of 500mm2 cross-sectional area carries an axial compressive load of 100 kN. For a plane inclined at 60o with the direction of load, calculate (i) Normal stress (ii) tangential stress (iii) Resultant stress and (iv) maximum shear stress. 2.a) b)

3.a) b)

4.a)

b)

Explain (i) Maximum strain energy theory and (ii) maximum principal stress theory. A cylindrical shell made of mild steel plate and 1.2m in diameter is to be subjected to an internal pressure of 1.5 MN/m2 . If the material yields at 200 MN/m2, calculate the thickness of the plate on the basis of the following two theories, assuming a factor of safety 3 in each case. (i)Maximum shear stress theory and (ii) Maximum shear strain energy theory. A solid shaft of 200mm. diameter has the same cross – sectional area as that of a hollow shaft of the same material with inside diameter of 150mm. Find the ratio of the power transmitted by the two shafts at the same speed. A hollow shaft is subjected to a torque of 40 kNm and a bending moment of 30 kNm. The internal diameter of the shaft is one-half the external diameter. If the maximum shear stress is not to exceed 80 MN/m2 , find the diameter of the shaft. A closely coiled spring, made out of 10mm. square rod has 12 coils of 120mm. mean diameter. Find the maximum permissible axial load for this spring, if the maximum shear stress is limited to 260 N/mm2 . Also calculate the deflection under the load and the stiffness of the spring. Take N= 0.84 x 105 N/mm2. A leaf spring has 12 plates, each 50mm. wide and 5mm thick, the longest plate being 600mm. long. The greatest bending stress is not to exceed 180 N/mm2 and the central deflection is 15mm. Estimate the magnitude of the greatest central load that can be applied to the spring. E=0.206 x 106 N/mm2.

Contd…2.

Code No:220156

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5.

A bronze liner of 60mm. external diameter is to be shrunk on a steel rod of 48mm diameter. If the maximum stress in the liner is limited to 144 MN/m2, Calculate: i) Maximum radial pressure between liner and rod. ii) Difference between the liner bore and shaft diameter before shrinking. Take Es = 200 GN/m2 ; Eb = 90 GN/m2; Poisson’s ratio for both steel and bronze = 0.3.

6.

Compare the Crippling loads given by Rankine’s and Euler’s formulae for a tubular strut 2.25m. long having outer and inner diameters of 37.5mm and 32.5mm loaded through pin-joint at both ends. Take yield stress as 315 MN/m2, Rankine constant = 1/7500 and E=200 GN/m2. If elastic limit for the material is taken as 200 MN/m2, then for what length of the strut does the Euler formula cease to apply?

7.a) b)

Explain the various limitations of the Euler’s formula. A mild steel column is of hollow circular section with 120mm as external diameter and 90mm as internal diameter. The column is 3m long hinged at both the ends and has to carry a load of 80 kN at an eccentricity of 20mm from the geometrical axis. Calculate the maximum and minimum intensities of stresses. Also calculate the maximum permissible eccentricity so that no tension is induced any where in the section. Take E=2.05 x 105 N/mm2.

8.

A 40mm x 40mm x 5mm angle is used as a simply supported beam over a span of 2.4 metres. It carries a load of 200 N along the vertical axis passing through the centroid of the section. Determine the resulting bending stresses on the outer corners of the section, along the middle section of the beam. Take E=200 GN/m2.

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