WrittenTesy Jul 05 2023

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Course of Aerospace Structures Written test, July 5 th, 2023 Name Surname Person code: Exercise 1 The beam sketched in the figure is clamped at one end. A displacementv is prescribed at the other end, still leaving the beam extremity free to rotate. This is (of course) accomplished by applying a forceF at the extremity whose actual value of the force is not given (only the prescribed displacementv is known). Compute the beam bending momentMxx at z = l/3 (from the clamp). Neglect shear deformation. (Unit for result: N mm) Data l = 3000 mm v = 5 mm EIxx = EIyy = 1 × 1012 N mm 2 EA = 1 × 104 N Answer Exercise 2 The beam structure sketched in the figure has a prescribed rotationθz, around the z axis, at point C (a moment is applied there, leaving free the three displacement components and the other two rotation components). Compute the reaction force in they direction transmitted by the constraint of pointB. Neglect shear deformation. The coordinates of the points are given, with respect to the sketched reference system, in the data. The bending and torsional stinness of the beams are given with respect to local reference systems, with thez axis aligned with the beam axis. Be careful with the measurement units. (Unit for result: N) Data A : (0; 1000; 0) mm B : (1000; 1000; 0) mm C : (1000; 1000; 1000) mm θz = 5 o EIxx = EIyy = 1 × 1010 N mm 2 GJ = 2 × 1011 N mm 2 Answer Exercise 3 Approximate the critical buckling loadF of the structure sketched in the figure by resorting to a poly- nomial approximation of the beam transverse displacement truncated to one unknown coefficient. The stiffness of the linear spring attached at the beam extremity is equal tok. Neglect shear deformation. (Unit for result: N) Data EA = 1 × 108 N l = 3 m EIxx = EIyy = 1 ×1012 N mm 2 k = 500 N /mm…