25 01 2022 Modeling of Space Structures First Part Exam of Space Structures

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Course of Space Structures  Modeling of Space Structures Written test, January 25 th, 2022 Exercise 1 Model the structure in the gure by using four 2-node nite elements. The horizontal and vertical mem- bers are made of aluminum, whose Young's modulus is E; they have square sections with dimensions a and b, respectively. The eect of shear deformability is assumed to be negligible. Solve the problem and determine the reaction force R. (Unit for result: N ) Data l1 = 1000 mm l2 = 300 mm a = 100 mm b = 10 mm E = 72 GPa P = 5 × 104 N The stiness matrix and the shape functions for the Euler-Bernoulli beam element are summarized below: K = 2EJ l3   6 −3l −6 −3l −3l 2l2 3l l 2 −6 3 l 6 3 l −3l l 2 3l 2l2   with: l: element length, ξ = ξ l N1 = 1 − 3ξ 2 + 2ξ 3 N2 =l ( −ξ + 2ξ 2 −ξ 3) N3 = 3ξ 2 − 2ξ 3 N4 =l ( ξ 2 −ξ 3) Exercise 2 Consider the structure in the gure. It is composed of two perpendicular beams connected each other in the middle. The two beams are simply supported (rotation allowed around the dashed line). Shear deformability is negligible. Solve the problem exactly and determine the reaction force R. (Unit for result: N ) Data l = 2000 mm EJ = 1.0 × 1011 Nmm 2 P = 9 kN 5