SS test 2025 a1

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Course of Space Structures  January 21 st, 2025 Course of Space Structures Written test, January 21 st, 2025 Question 1  T rue/F alse (put a T (true) or F (false) at the end of the sentence) 1. The Euler-Bernoulli beam theory assumes that cross-sections remain plane and perpendicular to the neutral axis after deformation: T 2. For a concentrated load, the solution to the Euler-Bernoulli equilibrium equation exhibits discontinuities in the second derivative of the de ection: F Question 2  Multiple Choice (circle the correct answer) 1. In the Ritz method, the coe cients of the trial functions are determined: (a) By solving a system of algebraic equations derived from minimizing the total potential energy (b) By satisfying the strong form of the governing dierential equation (c) By using the boundary conditions directly 2. Hermite polynomials are used as shape functions in Euler-Bernoulli beam elements because: (a) they ensure zero transverse shear deformation (b) they provide continuity of both displacement and slope across elements (c) they optimize the computation of internal forces Course of Space Structures  January 21 st, 2025 Exercise 1 Consider the structure in the gure, which is composed of 3 beams with stinesses EA and EJ . The eect of shear deformability is neglected. The structure is loaded with a uniformly distributed load of intensity q. In addition, the structure is loaded by means of the prescribed displacement u and the rotation θ, as shown in the gure. Model the structure using 3 nite elements and determine the reaction force W . Data L = 800 mm EA = 7.2 × 106 N EJ = 2.3438 × 109 N mm2 q = 1.0 N/mm u = 1.0 mm θ = 1.0 deg The stiness matrix and the shape functions for the Euler-Bernoulli beam element are summarized below: K = 2EJ l3   6 −3l −6…