JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II AEROSPACE VEHICLE STRUCTURES – I Previous Question Paper (March - 2022 - R13)
Answer any five questions. All questions carry equal marks.
Main
Write the Airy’s equations proposed on a stress function φ and also write the biharmonic equation.
Answer
Airy's stress function φ is a scalar function used to solve two-dimensional elasticity problems by satisfying the equilibrium equations and compatibility conditions. In the absence of body forces, the stress components in terms of the Airy stress function are defined as:
The biharmonic equation, which ensures the compatibility of strains in the two-dimensional plane stress or plane strain state, is expressed as:
A rectangular bar of cross-section area 14400 mm2 is subjected to an axial load of 24 kN. Determine the normal and shear stresses on a section which is inclined at an angle of 30° with normal cross-section of the bar.
Answer
Given: Area (A) = 14400 mm2, Axial load (P) = 24 kN = 24000 N, Angle of inclination (θ) = 30°.
First, calculate the axial stress (σx) on the normal cross-section:
Using the transformation equations for a plane stress state where σy = 0 and τxy = 0, the stresses on the inclined plane are:
- Normal stress (σn):σn = σx cos2θ = 1.667 × cos2(30°) = 1.667 × 0.75 = 1.25 N/mm2
- Shear stress (τn):τn = σx sinθ cosθ = 1.667 × sin(30°) × cos(30°) = 1.667 × 0.5 × 0.866 = 0.722 N/mm2
Write the compatibility equations and biharmonic equation for two-dimensional elasticity continuum.
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A large thin plate is subjected to certain boundary conditions on its thin edges (with its large faces free of stress), leading to the stress function
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Determine the slope at the left support, deflection under the load and maximum deflection of a simply supported beam of length 10 m, which is carrying a point load of 10 kN at a distance 6 m from the left end. Take E = 2 × 105 N/mm2 and I = 1 × 108 mm4.
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Find the slope and deflection of simply supported beam carrying a uniformly distributed load over the entire length using moment-area method.
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How will you apply Clapeyron’s theorem of three moments to a continuous beam with simply supported ends and continuous beam with fixed end supports?
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A continuous beam ABCD of length 15 m rests on four supports covering 3 equal spans and carries a uniformly distributed load of 1.5 kN/m length. Calculate the moments at the supports.
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Derive equation for the deflection of a continuous beam under elastic foundation.
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Compute the maximum bending moment, maximum deflection and the maximum bending stress for a railroad rail subjected to a single wheel load of 100 kN. The foundation modulus k = 15 MN/m2. Assume that I = 400 × 10-8 m4, E = 200 GN/m2, the depth of the rail is 180 mm and that the distance of the centroidal axis of the cross-section of the rail from the top surface is 100 mm.
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Find the expressions for maximum deflection and bending moment of beam under concentrated load.
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A steel column is of rectangular cross-section 4 cm × 6 cm and is having initial curvature given by
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How will you justify that Rankine’s formula is applicable for all lengths of columns, ranging from short to long columns.
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Determine Euler’s crippling load for an I-section joist 30cm × 15cm × 2cm and 5 m long which is used as a strut with both ends fixed. Take Young’s modulus for the joist as 2 × 105 N/mm2.
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What is meant by semi-monocoque structure? Explain with suitable example.
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Determine the internal energy stored within an elastic bar subjected to an axial tensile force P.
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