Jawaharlal Nehru Technological University
Jawaharlal Nehru Technological University B.Tech II AEROSPACE VEHICLE STRUCTURES I Previous Question Paper (December - 2017 - R13)
Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit.
Part A
What is Airy’s stress function in theory of elasticity?
Answer
Airy’s stress function, denoted by φ, is a scalar function used to solve two-dimensional elasticity problems. It satisfies the biharmonic equation ∇⁴φ = 0, where the stress components are derived from the second partial derivatives of φ, ensuring that the equilibrium equations are automatically satisfied.
Define the term ‘obliquity’ and how it is determined?
Answer
Obliquity is the angle made by the resultant stress vector acting on a plane with the normal to that plane. It is determined by the ratio of the shear stress (τ) to the normal stress (σ) acting on the plane, calculated as tan θ = τ/σ, where θ is the angle of obliquity.
What is redundancy in structure engineering?
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What is meant by externally and internally indeterminate structures?
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What are the different types of elastic foundation?
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What are basic assumptions for bending of curved beams?
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What is the slenderness ratio for a column?
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What is the effective length of a column for various end conditions?
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State the Rayleigh-Ritz method.
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Distinguish between semi monocoque and monocoque structure.
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Part B
What are the basic assumptions in theory of elasticity? And derive the equations of equilibrium and compatibility equations?
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An element cube is subjected to tensile stresses of 30 N/mm2 and 10 N/mm2 acting on two mutually perpendicular planes and a shear stress of 10 N/mm2 on these planes. Draw the Mohr’s circle of stresses and determine the magnitudes, directions of principal stresses and also the greatest shear stress.
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Consider a statically determinate beam with a general loading having a definite cross-sectional area. If its material obeys Hook’s law then develop a relationship between M, E, I and the slope of deflection from first principle. Discuss various boundary conditions and explain their significance. Explain with one such example.
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A cantilever beam of span L is subjected to clockwise moment M At the free end. Find the slope and deflection at the free end, assuming uniform flexural rigidity, EI.
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A beam simply supported at ends and subjected to a concentrated load W at the centre is deflected by an amount y1 at the centre. The central deflection of the same beam when subjected to two concentrated loads W equally spaced on the span is y2. Calculate the ratio of the two deflections, y1 and y2.
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Determine the thickness of a square foundation of side 1 m required, if it were to carry a concentrated load of 1 MN and a concentrated clockwise moment of 0.1 MNm. Assume that the foundation rests on an elastic foundation with spring constant, Ks = 12 N/mm2, the Young’s modulus of the foundation is 20 GPa and that the maximum permissible normal stresses on the foundation is 10 MPa.
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Derive the Winkler-Bach formula for curved beams.
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A cylindrical column 150 mm external diameter, 100 mm internal diameter and 7 m long is hinged at both ends. Calculate the (a) Euler’s crippling load (b) Crippling load as given by Rankine’s formula. E = 80 GPa, σc = 550 MPa and constant ‘a’ = 1/1600. Determine also the length for which two formulae would give the same crippling load.
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A steel bar of solid circular cross section is 50 mm in diameter. The bar is pinned at each end and subjected to axial compression. If the proportional limit of the material is 210 MPa and E is 200 GPa, determine the minimum length for which Euler formula is valid. Also determine the value of Euler buckling load if the column has minimum length.
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State the first Castigliano’s theorem and derive the appropriate expression which represents the theorem.
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Calculate the total strain energy stored in a cantilever beam of span L subjected to concentrated load, P at the free end assuming uniform flexural rigidity EI.
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State and prove the Maxwell’s reciprocal theorem. Explain in details the conditions under which this theorem holds.
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A simply supported beam of length L carries a concentrated load anywhere on the span. Determine the deflection of the beam at the point of application of the load by making use of Castigliano’s theorems.
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