JNTU
JNTU B.Tech II AEROSPACE VEHICLE STRUCTURES I Previous Question Paper (April/May - 2023 - R13)
Part A is compulsory. In Part B, Answer any one question from each unit.
Part A
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Write the equations for maximum and minimum stresses of maximum strain energy theory.
Answer
According to the maximum strain energy theory (Beltrami-Haigh theory), failure occurs when the strain energy per unit volume reaches the strain energy at the yield point in a simple tension test. For a triaxial stress state, the condition is:
For a biaxial stress state (σ₃ = 0), the maximum and minimum principal stresses are determined by the yield criterion:
Define elastic axis. Why we need to locate it for any cross- section?
Answer
The elastic axis is the locus of points through which a transverse load must be applied to cause the beam to bend without twisting. It is essential to locate this axis in aerospace structures to decouple bending and torsional deformations, preventing aeroelastic instabilities like flutter and ensuring the structural integrity of thin-walled wings and fuselages.
State the principles of redundant analysis.
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Write about the effect of intermediate supports.
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How would you explain Point of contra-flexure for a beam with uniform cross section?
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Explain why Initial curvature leads to an eccentric effect to the column.
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Discuss briefly about short, medium and long columns.
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List and explain the modes of structural instabilities.
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What is Maxwell’s reciprocal deflection theory?
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Summarize the assumptions of shear flow of closed section beams.
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Part B
Explain how the stiffness matrix can be built for a uniform beam. Express the equations in matrix forms.
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Illustrate a graphical method-Mohr’s circle and derive the relations for principal stresses.
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Figure 1 shown below shows the state of stress at a point. Find the location of principal planes, principal stresses and maximum shear stress analytically and graphically.
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Derive Clapeyron’s Three moment equation for a continues beam with constant flexural rigidity.
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Discuss in detail the deflection of beams with discrete elastic supports using singularity methods.
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What is Redundancy and Do the complete redundant analysis for the following beam as shown below using appropriate method (figure 2)?
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With the help of a neat sketch, explain the plane truss and space truss.
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The Pratt – truss shown below has four bays of 5m, each with a height of 5m. It carries a load of 200KN at each lower joint. The lower chord members are each 2500 mm² in section. While the upper chord members are 4000 mm² in section. The verticals have a Sectional area of 2000 mm² and the diagonals 4250 mm². Calculate the central deflection Take E = 200 kN/mm² (figure 3).
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Derive the equations of deflections for a typical curved beam by taking appropriate example.
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A rod 2m in length and a rectangular cross-section 88mm and 44mm is supported horizontally through pin joints. It carries a vertical load of 3.3kW/m length and an axial thrust of 110kW. If E=208 kN/mm²; calculate the max. Stress induced.
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What is Euler’s theory of buckling of columns? What are the assumptions of the Euler’s theory?
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Derive an expression for maximum compressive stress acting on a beam column which is pinned at both ends.
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Discuss about the classifications of columns with give some examples.
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Derive the expression for equivalent length of a column, which is fixed at one end and hinged at other end? What is buckling factor? and derive Rankine’s Formula?
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Determine the shear flow distribution in thin-walled-section shown in figure 4 due to shear load Sy = 1000 N applied through the shear center of the section.
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A beam ABCDE of length L and uniform section is simply supported at it ends. It is subjected to loads each of magnitude P, applied at B, C and D. LAB = LBC = LCD = LDE. Compute the deflection at C using unit load method.
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Calculate the vertical displacement at the center of the simply supported beam of length L, having a uniformly distributed load w, and flexural rigidity EI using strain energy method.
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Use the principle of virtual work to determine the support reactions in the beam ABCD shown in Figure 5.
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