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Course of Spacecraft Structures Written test, July 10 th, 2017 Exercise 1 Consider the structure in the figure. The three beams are characterized by axial stiffnessEA, bending stiffness EJ and torsional stiffnessGJ. The two ends are fixed, while two forces of intensityP are applied as illustrated in the sketch. Determine the reaction forces at the two fixed ends and plot the internal actions. Data EA = 1.8e6 N EJxx = EJyy = EJ = 3.75e6 N mm 2 GJ = 3.00e6 N mm 2 l = 1000 mm P = 1.5 kN Exercise 2 A thin-walled beam section is modeled according to the semi-monocoque scheme, as reported in the fig- ure. All the panels have thickness equal to 1mm, while the lumped area of the stringers, viz. including the contribution of the panels, is equal toA; the dimensionsa, b and c are reported below. An internal shear force T is considered as reported in the figure. Determine: 1. the state of internal shear stress; 2. the position of the shear center of the section. Data A = 200 mm2 a = 300 mm b = 200 mm c = 100 mm T = 3000 N Question 1 Discuss and illustrate mathematically the relation between the Principle of Complementary Virtual Works (PCVW) and the compatibility conditions. 1