compito chimici 2018718

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Test on 18/07/2018 Student:______________________________________________________ Id. Number:______________ Please note that: correct solution of exercise 1 is mandatory to pass the exam. Exercise 1 Consider the structural scheme depicted in Figure 1 (a) for a very high distillation column. The struct ure is subject to the uniform distributed horizontal load q, which schematizes the wind forces, applied on the continuous vertical beam ABC . The axial and bending stiffness of the cross sect ions are denoted as EA and EI , respectively. By neglecting the shear deformability of the structural elements and assuming that EA = EI /L 2, 1. sketch the diagrams of the internal forces (axial force, shear force, bending moment) in the structure. Figure 1. Exercise 2 Consider the cross section depicted in Figure 2. The section is subjected to: (a) a shear force V = 1 kN (defining with the horizontal axis an angle equal to 30°) applied to the centroid G, and (b) to a bending moment M = 0.5 kNm. 1. Evaluate the position of the centroid G. 2. Evaluate the position of the shear center C 3. Disregarding the effect of the torsional moment ensuing from the shear force V being applied in G, evaluate and sketch the distributions of tangential and normal stresses along the beam cross section centerline. Figure 2 Exercise 3 By applying Prandtl’s membrane analogy to a shaft with a rectangular cross section of sides b and a (with b>> a) derive the expression for the shear stresses due to torsion.