WrittenTest Feb 15 2023

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Course of Aerospace Structures Written test, Feb 15 th, 2023 Name Surname Person code: Exercise 1 The semi-monocoque beam sketched in the figure is loaded at the free end by the vertical forceF, applied along the lefmost panel. Compute the upper right stringer axial stressσzz at point B. (Unit for result: MPa) Data a = 400 mm l = 12000 mm E = 70000.0 MPa ν = 0.3 A1 = 200 mm 2 A2 = 400 mm 2 F = 5000 N Answer Exercise 2 The beam sketched in the figure is loaded by a distributed force for unit of length with butterfly distri- bution and null resultantq(x) = −q + 2qx/l. By resorting to the displacement method, and using a trigonometric approximation for the vertical dis- placement v, with the first and second term (i.e.v ≈ a sin(πx/l) + b sin(2πx/l) ), estimate the rotation θ at point A (the point atx = l/2 from the hinge). Account for the axial pre-stress. Note: R sin( cπx l )xdx = − lx cπ cos( cπx l ) + l2 π2c2 sin( cπx l ). (Unit for result: rad) Data q = 100 N /mm Fx = 10000 N EA = 1 × 108 N EI = 1 × 1011 Nmm2 l = 4000 mm Answer Exercise 3 The beam in the figure, with the sketched triangular cross section, is loaded by a distributed traction force per unit of lengthf. By resorting to a FE model of the beam withone linear element estimate the axial displacement of the free end. (Unit for result: mm) Data a = 1 cm l = 1 m f = 100 × 102 N/m E = 70000 MPa ν = 0.3 Answer Exercise 4 Consider the 3-D beam sketched in the figure, loaded by the forceF. The axial stiffnessEA, torsional stiffnessGJ and bending stiffnessesEIxx and EIyy are the same for the three beams. The spring has stiffnessK. Compute the vertical displacementv at the extremity of beam 1. (Unit for result: mm) Data E = 70000 MPa ν = 0.3 l1 = 1000 mm l2 = 500 mm l3 = 250 mm EA = 800 ∗ E N GJ = 1000 ∗ G Nmm2 EIxx…