SS test 2025 a2

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Course of Space Structures  February 7 th, 2025 Course of Space Structures Written test, February 7 th, 2025 Question 1  T rue/F alse (put a T (true) or F (false) at the end of the sentence) 1. For an Euler-Bernoulli beam modeled with nite elements, shear deformation is inherently included in the stiness matrix formulation: F 2. Consider the FEM analysis of a system of trusses. The evaluation of the internal forces requires the nodal displacements to be expressed in the truss local reference system: T Question 2  Multiple Choice (circle the correct answer) 1. In the Principle of Virtual Work, the virtual displacements: (a) must be consistent with the structure's compatibility conditions (b) can violate compatibility conditions, but must satisfy equilibrium (c) represent the physical displacements of the structure in case of linear behaviour 2. The Ritz method is equivalent to the nite element method when: (a) the trial functions are piecewise polynomials over subdomains and the amplitudes are the nodal displacements (b) the trial functions are part of a complete set and respectful of the essential conditions (c) the boundary conditions are imposed by removing the relevant rows and columns Course of Space Structures  February 7 th, 2025 Exercise 1 Consider the assembly of one-dimensional elements in the gure. All the structural members share the same stiness properties, EA and EJ , denoting the axial and the bending stiness, respectively. Shear deformability is negligible. Part of the structure is constrained with a continuous elastic support of stiness h. The external loads consist in a concentrated force P and a concentrated moment W . Model the structure using 3 nite elements and evaluate the nodal displacements. Data L = 1000 mm α = π/6 rad EA = 10 6 N EJ =…