Question

An aircraft wing has an aerodynamic load q1(x)= q0 * (1 – (x/L)^2) that acts upward in a distributed manner as shown. under very specific conditions the load function is parabolic. the wing mass results in 200 pounds at 7 feet from the edge of fuselage and will act downward L is wing length and is 24 feet at the fuse ledge the Max value of the parabola is q0= equals 200 lbs/ ft based on given parameters what reactions on the wing must the fuse lage provide for equilibrium

200 lbs/ft qr(x) fuse lage Wing 1-24 ft Wo lbs

Answer 1

Solution Net aerodynamic force = area, 2. = 90(1-()%) Arca A-3 4 Area 4-6 2 111237) on 1943 81] A = 9.2.20 33 = 290 This force is acting at centroid, "Izan = 2.15 - $)=4042 ZdA ime, 9o cm 2 / 2904 .

& 1274 1983 from TR, 'I W = 200 lb V " A= 2 2 2 A = {(200) (24) A = 3200 16 Reactions R, and Rz can be determined by torque equations For equilibrium, (Torque), =0 f tTorque) so W(7) + A(Xcm) - R 2 (L) = 0 (200)(7) + (3200)(9) - R2(24) = | R2 = 1258.34 .lbl El Torque la so Ri (L) - (W)(L-7) – A(L-2cm) = 0 R(24) -(200)(24-7)-(3200X24 – 9) =0 R1 =2141.67 lb

The loads at ends 1 and 2 respectively are 1258.34 lb and 2141.67 lb