Chapter 3_Wing Box - 1 Chapter 3 Wing Box Sizing 3.1 Shear center Decoupling of bending and torsion 3.2 Sizing of wing box 3.3 Wing divergence 3.4

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Unformatted text preview: 1 Chapter 3 Wing Box Sizing 3.1 Shear center: Decoupling of bending and torsion 3.2 Sizing of wing box 3.3 Wing divergence 3.4 Aileron reversal 3.4 Flutter 2 3.1 Shear Center: Decoupling of Bending and Torsion Analysis of wing bending and torsion can be decoupled through the use of shear center. To appreciate this, let’s first consider a cantilever beam of rectangular cross-section. (1) A resultant force acting through edge A of the cross-section will cause the cross- section to move up and rotate clockwise. (2) A resultant force acting through edge B of the cross-section will cause the cross- section to move up and rotate counter-clockwise. (3) A resultant force acting through the centroid of the cross-section will cause the cross- section to move up without rotation. For cross-sections of arbitrary shape, there exists a point in the cross-section through which a shear force can be applied to translate the section without inducing the rotation of the section. This point is called shear center (s.c.) of the cross-section. Note : For a rectangular section, the shear center coincides with the geometric centroid. x z z y V y V z V z V z V z s.c. A B 3 A resultant force that does not act through the shear center can be transformed into an equivalent load system of a force that acts through the shear center and a torque around the shear center. This allows decoupling into a torsion problem and a bending problem that can be solved separately. The locus of shear center is called the elastic axis. = a s.c. P s.c. P + s.c. Pure bending Pure torsion Pa s.c. . P Pa = elastic axis wing , tail or canard 4 For a wing section, the aerodynamic center (a.c.) is used as the reference point to place resultant force ( ) L and moment ( ) ac M corresponding to aerodynamic pressure over the wing surface. Then the resultant force and moment with respect to the shear center is shown below: Note : The shear center is also used to decouple the effect of other loads such as wing weight, wing fuel weight etc into pure bending and pure torsion. L a.c. s.c. ac M e s.c. t ea M L s.c. L s.c. ea M = + Pure bending Pure torsion L : lift M : moment about the a.c. e : the dsitance between the a.c and the s.c. ea M : moment about the s.c. cos ea ac M M L e α = + α : angle of attack 5 3.2 Sizing of wing box Total lift: L nW = ( 1 ) where : W Mg = aircraft total weight n : design load factor Note : design load factor = 1.5 × limit load factor The effect of gravity and inertia force: The inertia forces (due to wing mass and fuel mass) and weight acts in the direction opposite to the lift. Accordingly, they relieve the load on the wing. In the initial design, the wing mass, fuel mass and their distribution is still unknown....
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Chapter 3_Wing Box - 1 Chapter 3 Wing Box Sizing 3.1 Shear center Decoupling of bending and torsion 3.2 Sizing of wing box 3.3 Wing divergence 3.4

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