JNTU
JNTU B.Tech II Year AEROSPACE VEHICLE STRUCTURES-I Previous Question Paper (May - 2019 - R15)
Note: This question paper contains two parts A and B. 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
Define Airy’s stress function in theory of elasticity.
Answer
Airy's stress function, denoted by φ, is a scalar function used in two-dimensional elasticity to determine the stress state of a body. It is defined such that the stress components satisfy the equilibrium equations identically in the absence of body forces. For a plane stress or plane strain problem, the stress components are expressed as:
For the solution to be valid, the function must satisfy the biharmonic equation ∇4φ = 0, which ensures compatibility of strains.
Illustrate the Mohr circle for different stress conditions.
Answer
The Mohr circle is a graphical representation of the state of stress at a point, where the horizontal axis represents normal stress (σ) and the vertical axis represents shear stress (τ). Different stress conditions are illustrated as follows:
- Uniaxial Tension: The circle is centered at (σ/2, 0) on the σ-axis with a radius of σ/2, passing through the origin and the point (σ, 0).
- Pure Shear: The circle is centered at the origin (0, 0) with a radius equal to the shear stress magnitude (τ), extending to τ and -τ on both axes.
- Biaxial Stress: If principal stresses σ1 and σ2 have the same sign, the circle lies entirely on one side of the τ-axis with a diameter defined by the distance between σ1 and σ2. If they have opposite signs, the circle crosses the τ-axis, indicating a state of combined tension and compression.
- Hydrostatic Stress: Since σ1 = σ2 = σ3, the circle collapses into a single point on the σ-axis at (σ, 0), representing zero shear stress in all planes.
Discuss the order of redundancy.
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Distinguish between statically determinate and statically indeterminate structures.
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State at least four functions for infinite beam.
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Distinguish between a finite beam and an infinite beam.
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Discuss at least four limitations of Euler’s column theory.
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Classify the columns used in the aircraft structures.
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State and explain Maxwell’s reciprocal Theorem.
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Formulate an expression for thin walled closed section beams subjected to torsion.
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Part B
A rectangular block of material is subjected to a tensile stress of 100 N/mm2 on one plane and a tensile 50 N/mm2 on a plane at right angles, together with shear stress of 60 N/mm2 on the same planes. Calculate magnitude and direction, the principal planes and the magnitude of the greater shear stress.
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State the equations of static equilibrium of a three dimensional elastic body.
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Describe stress - strain relationship for 2D elastic body.
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Show that the following are Airy’s stress functions and examine the stress distribution represented by them.
ii) φ = Ax3
iii) φ = A(x4 - 3x2y2)
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A steel grider of uniform section, 13 m long is simply supported at its ends. It carries concentrated loads of 90 kN and two points 3 m and 4.5 m from the two ends respectively. Calculate:
a) The deflection of the girder at the points under the two loads
b) The maximum deflections. Take: I = 64×10-4 m4 and E= 210 GPa.
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Develop an expression for the deflection of simply supported beam subjected to concentrated load W at the center of the beam.
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A wooden beam of cross-section 80 mm × 240 mm rests on an earth foundation. The modulus of elasticity of wood is 10 GN/m2 and modulus of foundation is 5 MN/m2. A uniformly distributed load of 2 kN/m acts on the middle portion of this very long beam over a span of 2 m. Compute the maximum deflection and the maximum bending stress in the beam.
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A semi-infinite steel bar (E = 200 GPa) has a square cross section (b = h = 80 mm) and rests on a Winkler foundation of modulus ko = 0.25 N/mm2/mm. A downward force of 50 kN is applied to the end. Find the maximum and minimum deflections and their locations. Also find Maximum Flexural stress and its location.
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Describe the Winkler Constant.
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Examine the various empirical relations used to predict the failure loads of columns.
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A hollow cylinder of 150 mm external diameter 15 mm thick and 3 m long is hinged at one end and fixed at other. Calculate the ratio of Euler and Rankine load.
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Develop an expression for the crippling load of a column when its one end is fixed and the other end is free.
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Discuss different types of instability in columns.
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Calculate the shear flow, shear stress, angle of twist of a rectangular cross section whose outer width and height are 200 mm and 100 mm respectively. The uniform thickness (t) of the tube is 4 mm. The tube is subjected to torque of 10 kN-m.
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Determine the shear flow, shearing stress and angle of twists in the each of the four walls of such tubing when it is subjected to a torque of 2700 N-m.
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