2016 11 24

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Master of Science in Mechanical Engineering Politecnico di Milano Course of Machine Design 2 (Prof. S. Beretta, Prof. M. Giglio, Prof.ssa L. Vergani) Written test – 24.11.2016 Name: Surname: Polimi-ID: Exercise 1. Figure 1 shows a clamped beam with the distributed load q applied to the right side. The total length of the beam is l. Prove that the maximum vertical displacement f of the beam is given by: ݂= 41 ∙ݍ∙݈ସ 384 ∙ܧ∙ܬ Figure 1: The clamped beam with the distributed load. q f l/2 l/2 Exercise 2. The process column shown in Figure 2 is subjected to three loads: 1) the static inner pressure p, 2) the distributed wind load q1 till H/2, and 3) the distributed wind load q2 from H/2 to the top. Questions: 1) Perform the static assessment (full plasticity) of the process column at its base, that is section K-K. Consider that the structure from K-K to the ground is a clamp. 2) Given the formulation of the displacement in Exercise 1, evaluate the total displacement at the top of the column. Data: Height of the column, H = 35 m Inner diameter, d = 2 m Inner pressure, p = 1.6 MPa Wall thickness, t = 15 mm Distributed load, q1 = 1200 N/m Distributed load, q2 = 1800 N/m Material: Fe410, YS = 255 MPa Figure 2: The process column K K H/2 H/2 q2 q1 Exercise 3. Figure 3 shows the scheme of a stirrer, made of a vertical shaft with 4 paddles at the lower extremity. At the top of the shaft there is a gear transmission applying a constant torque T. The shaft has two supports, A and B. Figure 4 shows the dimensions of the shaft. Suppose that the 4 reaction forces between the paddles and the fluid are only tangential and applied at the paddles extremities. The shaft was peened and has residual stresses σres. Questions: 1) plot the diagrams of the internal forces in the shaft; 2) perform…