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Exercise 2. Discuss how you could integrate analytically the Paris equation and how you integrate it (providing a simple algorithm scheme) when the analytical solution cannot be used. Discuss two examples for which you cannot apply the analytical solution. 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 – 08.09.2017 Name: Surname: Polimi-ID: Do not write here 1 2 3 4 TOTAL Exercise 1. The boundary conditions of the beam AD are: 1) a clamp at point A, created by a fillet weld, see Figure 1.b, and 2) two supports at points B and D. The beam AD lays along axis x. The beam CE lays along axis z and it is connected with AD by a shrink fit, as in Figure 1.c. Figure 1.a shows the force F applied at point E. This force is applied from E to C during the exercise. Determine: 1) the bending and torque diagrams in beams AD and CE as a function of the position of force F along CE; 2) the minimum elastic interference to avoid slipping at the fitting in point C between CE and AD; 3) the static assessment at point B; 4) the dimension of the weld (throat size) in order to sustain the maximum static load in A. a. b. c. Figure 1: a. The structure; b. Detail of the weld at the clamp A; c. Detail of the fitting at point C. A B C D a a/2 a/2 F E b x y z Data a = 300 mm, b = 100 mm geometric data F = 1000 N loading force d = 20 mm diameter of the beam AD (circular cross section) dfit = 30 mm outer diameter of the beam CE at point C (at the fitting) S355 (Fe510) steel material of the beams Kt,f = Kt,t = 1.3 stress concentration factor in section B f = 0.2 friction coefficient L = 25 mm length of engagement in point C, between beams EC and AD Exercise 3. Figure 2 shows a shaft with…