2023 02 15 Solutions SS

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Course of Space Structures  February 15 th, 2023 Course of Space Structures Written test, February 15 th, 2023 Question 1  T rue/F alse (put a T (true) or F (false) at the end of the sentence) 1. The solution obtained using the Ritz method guarantees that the equilibrium conditions are satis ed at any point of the domain: F 2. A three-node truss element allows linear axial strains to be represented: T Question 2  Multiple Choice (circle the correct answer) 1. The Mindlin and Kirchho plate models: (a) share the same boundary conditions (b) are characterized by same essential but dierent natural conditions (c) are characterized by dierent essential and natural conditions 2. A beam is characterized by non-negligible shear deformability. (a) The solution has to be evaluated with a force-based approach (b) The solution has to be evaluated with a displacement-based approach (c) The Timoshenko model has to be preferred over the Euler-Bernoulli one Course of Space Structures  February 15 th, 2023 Exercise 1 Consider the three-beam system in the gure. The beams are connected each other at 90 degrees and have length equal to l, bending stiness EJ and torsional stiness GJ. The eect of shear deformability is assumed to be negligible. A uniformly distributed load of intensity q is applied as shown in the gure. Determine the reaction force V by solving the problem with a force-based approach. (Unit for result: N ) Data l = 1000 mm EJ = 10 10 Nmm 2 GJ = 2EJ q = 1 N/mm 2