53102-mt----advanced Mechanics Of Solids

NR

Code No: 53102/MT M.Tech. – I Semester Supplementary Examinations, September, 2008

ADVANCED MECHANICS OF SOLIDS (Common to Machine Design/ Design for Manufacturing) Time: 3hours

Max. Marks:60 Answer any FIVE questions All questions carry equal marks ---

1.a) b)

What is the importance of shear center? A channel section has flanges 60mm × 10mm and web 80 mm × 5mm. Determine the position of its shear center.

2.

A simply supported beam of span 1m carries a concentrated load of 10kN located at it’s mid span. The cross-section of the beam is shown in figure.1. Find the maximum deflection if E=100Gpa and plane of loading makes 400 to the plane of the web.

Contd…2.,

Code No: 53102/MT 3.a) b)

4.

::2::

Derive the expression for h2 of a rectangular section of curved beam of width b and depth d. The radius of curvature from centroidal axis is R. A curved beam of rectangular cross-section of width 20 mm and depth 40 mm is subjected to pure pending moment of +600 N-m. The beam is curved in a plane parallel depth. The mean radius of curvature is 50 mm. Plot the variation of stresses across the section. Figure.2 shows the dimensions of a double celled cross-section in the form of a rectangle and a triangle. A torque of 4 kN-m is applied. Calculate the shear stress in the rectangular part, triangular part and in the web. Also find the angle of twist per metre length.

Contd…3.,

Code No: 53102/MT 5.a) b)

6.a) b) 7.a)

b)

8.a) b)

::3::

Derive the expression for the thickness of disc of uniform strength in terms of radius r. A steam turbine rotor is running at 4200 rpm. It is to be designed for uniform strength for a stress of 85 MN/m2. If the thickness of the rotor at the center is 25 mm and density of it’s material is 800 kg/m3 find the thickness of the rotor at a radii of 100 mm, 200 mm and 350 mm. Obtain the stress-strain-Temperature relation for isotropic elastic plate. What is the strain energy of a plate? A 2m-long steel bar(E=210 Gpa) of 75 mm χ 75 mm cross section rests with a side on a rubber foundation (k=24Mpa). If a concentrated load of P=20 kN is applied at one end of the beam, determine i) the maximum deflection and ii) the maximum bending stress. A series of springs spaced at a distance of 1.5 m, supports a long thin-walled steel tube having E=206.8 Gpa. A weight of 6.7 kN acts down at mid length of the tube. The average diameter of the tube is 0.1m, and the moment of inertia of its section is 6 × 10−6 m4. Take the spring constant of each support to be k=10kN/m. Find the maximum moment and maximum deflection, assuming negligible tube weight. What are the contact stresses? How the contact stresses influence the failure of a member?

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