JNTU
JNTU B.Tech III AEROSPACE VEHICLE STRUCTURES II Previous Question Paper (September 2021 - R13)
Answer any five questions. All questions carry equal marks.
Main
Determine the deflected form of the thin rectangular plate a × b is simply supported along its edges. It supports an in-plane tensile force Nx per unit length and carries a uniformly distributed load of intensity q0.
Answer
For a thin rectangular plate of dimensions a × b, simply supported on all edges, the governing differential equation for deflection w(x, y) under a transverse load q(x, y) and an in-plane tensile force Nx is given by:
where D is the flexural rigidity of the plate, defined as D = Et³ / (12(1 - ν²)).
Given the simply supported boundary conditions at x = 0, a and y = 0, b, the deflection w(x, y) can be expressed using a double Fourier sine series:
The uniformly distributed load q₀ can also be represented by a Fourier sine series:
where the coefficients qmn are calculated as:
Substituting these series into the governing equation, the coefficients Wmn are determined by equating terms:
Substituting the expression for qmn, the final deflected form is:
for m, n = 1, 3, 5, ... . This series converges rapidly, and the first term (m=1, n=1) provides a good approximation for the maximum deflection at the center of the plate.
A simply supported beam has a span of 2.4m and carries a central concentrated load of 10 kN. The flanges of the beam each have a cross-sectional area of 300 mm2 while that of the vertical web stiffeners is 280 mm2. If the depth of the beam, measured between the centroids of area of the flanges, is 350 mm and the stiffeners are symmetrically arranged about the web and spaced at 300 mm intervals, determine the maximum axial load in a flange and the compressive load in a stiffener. It may be assumed that the beam web, of thickness 1.5 mm, is capable of resisting diagonal tension only.
Answer
To determine the maximum axial load in the flange and the compressive load in the stiffener for a beam acting in pure diagonal tension (Wagner beam), we first establish the shear force and bending moment. The beam is simply supported with a span L = 2.4 m and a central load P = 10 kN. The maximum shear force V = P/2 = 5 kN, and the maximum bending moment M = (P × L)/4 = (10 kN × 2.4 m)/4 = 6 kNm.
The axial load in the flange (F) is calculated by dividing the bending moment by the depth of the beam (h = 350 mm = 0.35 m):
For the stiffener load, we assume the web acts in pure diagonal tension at an angle θ. For a web where the stiffeners are spaced at distance 'd' = 300 mm, the compressive load (Ps) in the stiffener is given by the vertical component of the diagonal tension force in the web:
Assuming the optimal diagonal tension angle θ = 45° for a standard Wagner beam analysis:
Thus, the maximum axial load in the flange is 17.14 kN, and the compressive load in each stiffener is 4.29 kN.
A thin-walled beam has the cross-section shown in Figure 1. Determine the direct stress distribution produced by a hogging bending moment Mx.
Answer
Sign in to view the complete answer paper.
Calculate the position of the shear centre of the thin-walled unsymmetrical channel section as shown in Figure 2.
Answer
Sign in to view the complete answer paper.
The thin-walled single cell beam shown in figure 3 has been idealized into a combination of direct stress carrying booms and shear stress only carrying walls. If the section supports a vertical shear load of 10 kN acting in a vertical plane through booms 3 and 6, calculate the distribution of shear flow around the section. Boom areas: B1 = B8 = 200 mm2, B2 = B7 = 250 mm2, B3 = B6 = 400 mm2, B4 = B5 = 100 mm2.
Answer
Sign in to view the complete answer paper.
The fuselage section shown in Figure 4 is subjected to a bending moment of 100 kNm applied in the vertical plane of symmetry. If the section has been completely idealized into a combination of direct stress carrying booms and shear stress only carrying panels, determine the direct stress in each boom.
Answer
Sign in to view the complete answer paper.
Derive the expression of the torsion bending constant for an open section beam fully built-in at one end.
Answer
Sign in to view the complete answer paper.
Find the shear flow in each web of the beam shown in Figure 5. Plot the distribution of axial load along each stiffening member when P1 = 20 kN and P2 = 10 kN. All dimensions are in cm.
Answer
Sign in to view the complete answer paper.