WrittenTest June 13 2023

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Course of Aerospace Structures Written test, June 13 th, 2023 Name Surname Person code: Exercise 1 The beam structure sketched in the figure is loaded at pointC by the forceF, applied thex direction. Compute the displacement, in thex direction, of pointC. Neglect shear deformation. The coordinates of the points are given, with respect to the sketched reference system, in the data. (Unit for result: mm) Data A : (0; 1000; 0) mm B : (1000; 1000; 0) mm C : (1000; 0; 0) mm D : (1000; 0; 1000) mm F = 1000.0 N EIxx = EIyy = GJ = 1 × 1010 N mm 2 EA = 1 × 104 N Answer Exercise 2 Compute the critical buckling loadF of the beam structure sketched in the figure. Note that the hinge and the two sliders prevent the out of plane displacement both in thex and y directions. (Unit for result: N) Data l = 4 m EIxx = 3 × 1010 N mm 2 EIyy = 2 × 1010 N mm 2 Answer Exercise 3 Consider the semi-monocoque cross-section sketched in the figure. All the paneles have thickness equal to t. Compute, with respect to the sketched reference system, thex coordinate of the shear center. (Unit for result: mm) Data t = 1 mm A1 = 500 mm 2 A2 = 250 mm 2 l1 = 200 mm l2 = 300 mm E = 70000 MPa ν = 0.3 Answer Exercise 4 Consider the 3-D beam semi-monocoque beam model sketched in the figure, loaded at its extremity by the vertical forceF, that is aligned to the panel going from stringer #1 to stringer #3. Compute the axial force in the concentrated area #1 (area equal to A) at a distance equal tos/2 from the clamp. (Unit for result: N) Data A = 100 mm 2 t = 1 mm l = 0.3 m s = 10 m F = 1000 N E = 70000 MPa ν = 0.3; Answer 2 Exercise 5 Consider the three-dimensional beam sketched in the figure, and loaded by the vertical forceF. By re- sorting to the Ritz method, and adopting the simplest possible polynomial…