Download JNTUA M.Tech 1st Sem 2017 Feb 9D15103 Advanced Mechanics of Solids Question Paper

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Code: 9D15103

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M.Tech I Semester Regular & Supplementary Examinations January/February 2017

ADVANCED MECHANICS OF SOLIDS

(Machine Design)

Time: 3 hours

Max. Marks: 60

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Answer any FIVE questions

All questions carry equal marks

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1. Determine the shear center location C for an aircraft semi-circular box beam whose cross section is shown in figure below.
2. The masonry column carries an eccentric load P = 12 kN as shown in the figure below:
   1. Locate the points on the cross section where the neutral axis crosses the y- and the z-axes.

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   2. Determine the maximum tensile and compressive normal stresses.
3. The curved beam in figure is subjected to a load P = 120 kN. The dimensions of section BC are also shown in figure below. Determine the circumferential stress at B and radial stress at the junction of the flange and web at section BC.
4. 1. What is Prandtl elastic membrane analogy? Explain.
   2. A rod with rectangular cross section is used to transmit torque to a machine frame with a width of 40 mm. The first 3 m length of the rod has a depth of 60 mm, and the remaining 1.5 m length has a depth of 30 mm. The rod is made of steel for which G = 77.5 GPa. For T₁ = 750 N-m and T2 = 400 N-m, determine the maximum shear stress in the rod. Determine the angle of twist of the free end.

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   Contd. in page 2

5. Derive the stresses for two bodies in line contact: Loads normal and tangent to contact area.
6. What is plane stress and plane strain? Explain with suitable example.
7. For a solid in a state of plane stress, show that if there are body forces Px, Py per unit volume in the direction of the axes x, y respectively, the compatibility equation can be expressed in the form: ∇² (σx + σy) = (1 + ν)(∂Px/∂x + ∂Py/∂y)

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8. 1. What do you mean by compatibility equations? What is the necessity of compatibility equations? Write the compatibility equations in Cartesian co-ordinates.
   2. In planar problems, stress components are expressed in Cartesian co-ordinate system where as the location at which stress is considered is defined in polar co-ordinates. Why such mixed approach adopted? Discuss.
9. 1. Derive the equations of equilibrium in polar co-ordinates for radial direction & tangential direction.
   2. The stress components at a point are σx = −50, σy = 30, σz = 20. Txy = −60, tyz = 40, Txz = 50 MPa. Determine the principle stresses and principle directions.

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