18 07 11

Page 1

. Dipartimento di Ingegneria Aerospaziale AAEERROOSSPPAACCEE SSTTRRUUCCTTUURREE Written Test 18 th July 2011 ________________________________________ LAST NAME ________________________________________ FIRST NAME ____________________ MATRICOLA Problem 1: For the beam system in the figure below: 1) calculate the deflection δ at the free end of beam #3; 2) consider the system as an assembly of the three elements #1 #2 and #3 and apply a displacement-based method; In particular: - choose the proper type of stiffness matrix for each element (the stiffness matrix of a free beam in a plane is provided); - build the global stiffness matrix and the force vector for the unconstrained system; - apply the constraints and write (without solving) the equation for the solution of the static problem. Problem 2: Calculate the torsional stiffness of the following semi-monocoque section: DATA E = 70000 N/mm ; J = 500000 mm 4; A = 8000 mm 2 for all the sections F = 2000 N ; W = 650 Nm L1 = 0.5 m ; L 2 = L 3 = 1.2 m ; F W δ L1 L2 L3 #1 #2 #3 [ ]                                 − −−− − − − − = l EJ l EJ l EJ l EJ l EJ l EJ l EJ l EJ l EA l EA l EJ l EJ l EJ l EJ l EJ l EJ l EJ l EJ l EA l EA K 460260 612 0612 0 0000 260460 612 0612 0 0000 22 2323 22 2323 q1 DATA A = 4000 mm 2 for all the stringers t1 = t2 = t 3 = t 4 = 10mm t5 = t 6 = 15 mm R1 = 1400 mm R2 = 1800 mm q2 q3 q4 q5 q6 R1 R2