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. Dipartimento di Ingegneria Aerospaziale AAEERROOSSPPAACCEE SSTTRRUUCCTTUURREE Written Test 04 th July 2011 ________________________________________ LAST NAME ________________________________________ FIRST NAME ____________________ MATRICOLA Problem 1: Consider the tapered beam with an hollow circular section shown in figure, which is loaded by a uniform distribution of axial forces per unit length rz. The inner radius R 0 of the section is constant, whereas the outer radius linearly varies from R 1 to R 2. 1) Apply the Ritz-Raleigh approach to find the approximate solution of the problem, considering a simple single-term linear approximation of the axial displacement. 2) Apply a force method to evaluate the normal stress in the central section of the beam (z = L/2) according to the De Saint Venaint Solution for axially loaded beams. 3) Apply a stress recovery procedure for the evaluation of the same stress value considering the approximate solution provided by Ritz-Raleigh method. Compare and discuss the results obtained by the force and displacement method. Problem 2: Calculate the position of the shear centre for the semi-monocoque section presented in the figure. R0 z R1 R0 R1 DATA r z = 200 N/mm R0 = 35 mm R1 = 50 mm R2 = 40 mm L = 1 m E = 70000 MPa L q1 q2 q4 q5 a 2a q6 a a q3 a q7 DATA A = 400 mm 2 for all the stringers t = 3 mm for all the panels a = 400 mm