project2 - V(y) UFID 0087-1745 W(y) 1. Derive the...

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W(y) V(y) UFID 0087-1745 1. Derive the relationship for the transverse shear force V and bending moment M as a function of span location y for the wing box. Elliptic case We know the following from phase 1: Where, ,and Since w(y) is the distributed force per unit span, and assuming the airplane is at straight and level flight, we use statics to derive the shear force distribution (V) as follows: z y Figure 1 FBD of wing. As we can see, the forces of w(y) should equal the forces of V(y). Thus, the sear force of the elliptical wing results as follows:
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(eqn. 1) To find the moment distribution, we simply integrate the shear with respect to y as follows: where the limits of integration are from zero to the tip of the wing. After doing this complex integration, the equation of the moment distribution is: (eqn. 2) The bending moment is highest at the wing root according to this equation, as expected. Average case For the average case, we use the same approach using the following values:
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2. Plot the shear force and bending moment diagrams for half the span. Elliptic case Figure 2. Shear diagram of elliptic wing
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Figure 3. Bending moment diagram of elliptic wing Average case Figure 4. Shear force diagram (average case)
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Figure 5. Bending moment diagram (average case) 3. Calculate the transverse shear force V and bending moment M at the wing-box root section. Also find the Torque T about the quarter chord at the wing root section. Elliptic case At the root section, y=0. Thus from equation 1: = -814.196 lb This indicates that the shear force is at maximum at the rood, as expected. To find the bending moment, we use the same approach using equation 2:
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= 0 lb-in Average case = -1046.55 lb =lb-in To find the torque about the quarter chord, we first have to derive the equation of the line of D(y) as follows: 41.875” D(y)
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Figure 6. Quarter chord of wing section Thus, to find the slope of the dashed blue line, we use the following approach: 41.875
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This note was uploaded on 08/27/2011 for the course AEROSPACE 3115C taught by Professor Bakcer during the Spring '10 term at University of Florida.

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project2 - V(y) UFID 0087-1745 W(y) 1. Derive the...

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