Exam of modelling part 300625

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Course of Space Structures  June 30 th, 2025 Course of Space Structures Written test, June 30 th, 2025 Question 1  T rue/F alse (put a T (true) or F (false) at the end of the sentence) 1. Consider a three-node truss element with shape functions Ni. The central node is 3. The shape function N3 is the linear combination of N1 and N2: F 2. The Ritz method cannot be applied for a plate problem where all the edges are free: F Question 2  Multiple Choice (circle the correct answer) 1. Consider a 2-node nite element based on the Timoshenko beam theory. The beam element is subjected to a vertical uniformly distributed load. The consistent set of nodal loads is given by: (a) Two nodal forces (b) Two nodal forces and two nodal bending moments (c) Two bending moments 2. The reduced integration technique in a 2-node Timoshenko beam nite element consists in: (a) Integrating the bending and shear energy with 2 Gauss points (b) Integrating the bending and shear energy with 1 Gauss point (c) Integrating the bending energy and the shear energy with 1 and 2 Gauss points, respectively Course of Space Structures  June 30 th, 2025 Exercise 1 The structure in the gure is made of two beams with bending and torsional stinesses EJi and GJi, respectively. Each beam has length L. The structure is xed at one end. The other end is loaded with a concentrated force P and is elastically restrained by a torsional spring of stiness kt. A torsional moment per unit length, uniformly distributed and with magnitude mt, is applied to the second beam. Find the exact solution of the problem using a displacement-based approach and assuming the Euler-Bernoulli model for the bending part. In particular, report the expression of the internal bending and torsional moments using the reference systems in the…