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Aerospace structures, exam, 19/09/2016 ² Datas:  Area of upper stringers : 150 mm²  Area of bottom stringer : 450 mm²  Height h : 200 mm  Thickness of all panels : 2 mm  Lenght of the beam : 1.3 m  Force F : 2 500 N  Beam characteristics : G = 27 GPa, E = 70 GPa. The horizontal force is applied at the right corner of the rigid body. The beam section has the semi-monocoque structure pre sented on the right. The force is introduced in the semi - monocoque section by a rib, however NO RIB CALCULATIONS ARE REQUIRED to solve the problem. The semi -monocoque section stringers already takes into account the areas of panels (no further calculations are needed). EXERCISE 1 1. Compute the position of the shear center of the semi-monocoque section. 2. Compute the internal forces in the beam in the 2 following cases: a. The force axis passes through the semi-monocoque structure centroid; b. The force axis passes through the shear center position. 3. Compute the torsional stiffness of the beam k θ by considering a unit moment applied to the system. Compute the bending stiffness EJ y according to the semi -monocoque section. 4. Compute the displacement δ of the point of application of the force considering torsional stiffness kθ and the bending stiffness EJy. EXERCISE 2 Ritz approximation. For both bending and torsion problems, choose the correct set of trial functions among the proposed ones (justify your choice) and solve the problem by writing the final symbolic equation obtained (solving the equation is not required). For the bending problem :  Set #1 : (z-L) and (z-L)²  Set #2 : z² and z3  Set #3 : (z-L)² and (z-L)3 For the torsion problem :  Set #1 : (z-L) and (z-L)²  Set #2 : z² and z3  Set #3 : (z-L)² and (z-L)3 z x q3 y δ Rigid body F q1 q5 q4 q2 h h h