WrittenTest Jan 25 2023

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Course of Aerospace Structures Written test, Jan 25 th, 2023 Name Surname Person code: Exercise 1 The beam sketched in the figure, with bending stiffnessEI, is loaded by the concentrated forceF. Compute the bending moment at pointA. (Unit for result: N mm) Data a = 400 mm b = 800 mm EA = 1.0 × 105 N EI = 6.0 × 1010 Nmm2 K = 100 N /mm F = 5000 N Answer Exercise 2 The FE mesh sketched in the figure has two bilinear planar element and eight nodes. It is loaded by the distributed load sketched in the figure, with a maximum load per unit of length equal tof. Compute the virtual external work for the unitary virtual vertical displacement of node 5. (Unit for result: N mm) Data a = 4 mm b = 6 mm f = 20 N /mm Answer Exercise 3 The semi-monocoque beam cross section model in the figure is loaded by a concentrated momentMz. It has six stringers, each with concentrated area A. Compute the derivative of the cross section rotations angle with respect to the beam axis. (Unit for result: rad/mm) Data a = 600 mm b = 300 mm A = 500 mm 2 t1 = 1 mm t2 = 2 mm E = 70000 MPa ν = 0.3 Mz = 5 × 106 Nmm Answer Exercise 4 Consider the semi-monocoque cross section model sketched in the figure. Compute the x positions of the shear center. (Unit for result: mm) Data a = 400 mm b = 800 mm t1 = 1 mm t2 = 2 mm t3 = 3 mm A1 = 500 mm 2 A2 = 1000 mm 2 E = 70000 MPa ν = 0.3 Answer 2 Exercise 5 The beam sketched in the figure is loaded by the concentrated forceF at x = l and by the distributed force for unit of lengthq. By resorting to the displacement method, and using a trigonometric approximation with only one term, estimate the vertical displacement in they direction of point A (the point at x = l/2 from the hinge). Account for the axial pre-stress. (Unit for result: mm) Data q = 1.2 N/mm Fx = 10000 N…