JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III Year AIRCRAFT STRUCTURAL ANALYSIS Previous Question Paper (October - 2020 - R16)
Answer any five questions. All questions carry equal marks.
Main
Derive an equation for the critical stress in a thin flat plate due to buckling.
Answer
For a thin rectangular plate of length a, width b, and thickness t, subjected to a uniform compressive stress σ, the governing differential equation for out-of-plane deflection w is given by the plate bending equation:
where D is the flexural rigidity, D = Et³ / (12(1 - ν²)). Assuming a simply supported boundary condition, the deflection is represented by the double sine series:
Substituting this into the governing equation leads to the expression for the buckling stress:
For the minimum critical buckling stress, we set n = 1. The equation becomes:
where k is the buckling coefficient defined as (mb/a + a/mb)². The value of k depends on the aspect ratio (a/b) and the number of half-waves m in the direction of loading.
Explain about buckling of flat plates in compression with neat sketches and graphs. Also discuss about End fixity of plates.
Answer
When a flat plate is subjected to in-plane compressive loads, it remains flat until the load reaches a critical value, at which point it undergoes sudden out-of-plane deformation (buckling). The load-deflection graph shows a bifurcation point where the plate transitions from a stable flat state to a buckled state. Unlike columns, thin plates possess significant post-buckling strength because the stress redistributes toward the supported edges.
End fixity refers to the boundary conditions at the edges of the plate. The buckling coefficient k varies significantly based on these conditions:
- Simply supported edges allow rotation but no displacement, resulting in a lower k value.
- Clamped (fixed) edges restrict both rotation and displacement, significantly increasing the stiffness of the plate and leading to a higher k value.
- The effective length of the plate is adjusted by an end fixity factor, similar to column theory, where higher degrees of constraint increase the critical buckling load.
The beam shown in figure 1 is assumed to have a complete tension field web. If the cross-sectional areas of the flanges and stiffeners are 250 mm2 and 200 mm2 respectively and the elastic section modulus of each flange is 600 mm3, determine the maximum stress in a flange and also whether or not the stiffeners buckle. The thickness of the web is 2 mm and the second moment of area of a stiffener about an axis in the plane of the web is 2000 mm4. E = 70000 N/mm2.
Answer
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Derive the relation between bending moment and shear force of an unsymmetrical cross-section.
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Discuss in brief about torsion of an arbitrary section beam with neat sketch.
Answer
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The cantilever beam shown in Figure 2 is uniformly tapered along its length in both x and y directions and carries a load of 100 kN at its free end. Calculate the forces in the booms and the shear flow distribution in the walls at a section 2 m from the built-in end if the booms resist all the direct stresses while the walls are effective only in shear. Each corner boom has a cross-sectional area of 900 mm2, while both central booms have cross-sectional areas of 1200 mm2.
Answer
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Determine the position of shear center S for the thin-walled, open cross-section shown in figure 3. The thickness t is constant.
Answer
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Idealize the box section shown in figure 4 into an arrangement of direct stress-carrying booms positioned at the four corners and panels which are assumed to carry only shear stresses.
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Determine the torsion bending constant for the thin-walled beam shown in figure 5 and also derive an expression for the angle of twist at its free end.
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Determine the shear flow distribution in the web of the tapered beam shown in Figure 6 below, at a section midway its length. The web of the beam has a thickness of 2 mm and is fully effective in resisting direct stress. The beam tapers symmetrically about its horizontal centroidal axis, and the cross-sectional area of each flange is 400 mm2.
Answer
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