Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech II MECHANICS OF SOLIDS AND MECHANICS OF FLUIDS Previous Question Paper (March - 2022 - R16)
Answer any five questions. All questions carry equal marks.
Main
Derive the relation between the Modulus of Elasticity and Modulus of Rigidity.
Answer
Consider a square element ABCD of side length 'a' subjected to pure shear stress τ on all four faces. This state of stress is equivalent to a tensile stress of magnitude τ on the diagonal AC and a compressive stress of magnitude τ on the diagonal BD. The strain in the diagonal AC is given by the sum of the longitudinal strain due to tensile stress and the lateral strain due to compressive stress:
Alternatively, the shear strain γ is related to the modulus of rigidity G by τ = Gγ. For a small shear deformation, the diagonal AC elongates by (aγ/√2). The strain in the diagonal is:
Equating the two expressions for ε:
Simplifying, we obtain the relation:
A load of 175 N falls through a height of 40 mm on to a collar rigidly attached to the lower end of a vertical bar 1.8 m long and of 1.8 cm2 cross-sectional area. The upper end of the vertical bar is fixed. Determine the maximum instantaneous stress induced in the bar. E=2×105 N/mm2.
Answer
Given: Load (W) = 175 N, Height (h) = 40 mm, Length (L) = 1800 mm, Area (A) = 180 mm2, Modulus of Elasticity (E) = 2×105 N/mm2.
The formula for maximum instantaneous stress (σ) in a bar subjected to an impact load is:
Substituting the values:
The maximum instantaneous stress induced in the bar is 66.71 N/mm2.
A rod whose ends are fixed to rigid supports, is heated so that rise in temperature is T °C. Prove that the thermal strain and thermal stresses set up in the rod are given by, Thermal strain = αT and Thermal stress = αTE where α = Co-efficient of linear expansion.
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Derive strain energy equation for sudden loading.
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Derive the pure bending equation.
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In a simply supported beam carrying un-symmetrical load how will you locate the point of maximum bending moment?
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An I-section shown in figure 1 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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Find the power that can be transmitted by a 60mm diameter shaft at 160rpm, if the permissible shear stress is 80N/mm2 and the maximum torque 30% greater than the mean torque.
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Maximum shear stress developed on the surface of a solid circular shaft under pure Torsion is 240 MPa. If the shaft diameter is doubled, and then what is the maximum shear stress developed corresponding to the same torque?
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A shaft is required for transmitting a power of 60 kW running at a speed of 750 rpm. If the available shaft material has permissible shear strength of 36 N/mm2 and rigidity modulus of 96 kN-mm2. Design a hollow shaft such that the inner diameter is 0.6 times the outer diameter.
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The right limb of a simple U-tube manometer containing mercury is open to the atmosphere while the left limb is connected to a pipe in which a fluid of specific gravity 0.9 is flowing. The center of the pipe is 12cm below the level of the mercury in the right limb. Find the pressure of fluid in the pipe if the difference of mercury level in the two limbs is 20 cm.
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State the Newton’s law of viscosity and give examples of its application.
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What are the surface and body forces associated with fluid flow? How are they incorporated in Euler’s equation?
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Briefly discuss the physical principle based on which the Navier-Stokes equation is derived.
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