10 02 11

Pagina 1

. Dipartimento di Ingegneria Aerospaziale AAEERROOSSPPAACCEE SSTTRRUUCCTTUURREESS Written Test 10 th February 2011 ________________________________________ COGNOME ________________________________________ NOME ____________________ MATRICOLA Problem 1: For the statically indeterminate system in the figure below: 1) find the indeterminate reaction in the spring by applying the PCVW and calculate the expressions of internal forces; 2) determine the linear system for the approximation of the axis displacement w y, by applying a Ritz-Raleigh method with a two-terms approximation: ( ) ( ) 2211 q zNq zNwy += . Choose the admissible set of shape functions among the following ones: a) 2 21 ; zNzN == b) 3 2 2 1 ; zNzN == Problem 2: A rib introduces a force system in the semi-monocoque section that is represented in the figure below. The thickness of the panels is provided in the table. 1) Evaluate and draw the internal forces in the rib, considering the axis shown in the figure. 2) Calculate the distance from the application point of the force at the left to the shear centre of the semi-monocoque section. 2F F K DATA F 3000 N L 600 mm k 2000 N /mm E 70 GPa J 2500000 mm 4 L L y z z Reference system for Ritz -Raleigh method q1 F A A A A A A q2 q3 q4 q5 q6 a a 2a 2a panel thickness #1 t #2 2t #3 2/3t #4 2t #5 t #6 t t DATA F 2400 N A 200 mm 2 a 300 mm t 2 mm a F 3a