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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 – 05.07.2016 Name: Surname: Polimi-ID: Do not write here 1 2 3 4 TOTAL Exercise 1. Figure 1 shows a beam with four supports placed in A, B, C, and D. The span length is l. The first span (AB) is subjected to a distributed load, p, whereas in CD a midspan load, F is applied. Requests: a. Calculate the diagram of bending moments b. Calculate the maximum deflection in CD c. Choose the beam profile that satisfies the displacement-based assessment: 𝛿 ≤ 𝑙 800⁄ Data: p = 5 N/mm F = 30 kN l = 4000 mm Material: steel (Fe430) Beam profile (HE) Figure 1 – Scheme of the beam. Exercise 2. A program for nondestructive in-service inspection of a plant is under planning. The plant under consideration contains, among other components, a wide plate (100 mm thick) in which long surfaces cracks may appear (shape factor 1.13). The plate is loaded by a membrane stress, which varies according to Figure 2. This loading history is repeated with a cycle of one day and night. It is judged that the nondestructive testing is capable of detecting crack with a depth larger than 1 mm. From previous fatigue testing of the material, it is judged that the following equation is applicable: 𝑑𝑎 𝑑𝑁 = 10−6 ( Δ𝐾𝐼 Δ𝐾0 ) 4 m/cycle, ∆𝐾0 = 20 𝑀𝑃𝑎√𝑚 The material has a fracture toughness of 71 𝑀𝑃𝑎√𝑚 and a yield strength of 650 MPa. According to the standard that applies to the plant, the safety factor, with respect to fracture should be at least 2.2. After checking if LEFM can be applied, estimate by use of the data provided, how often inspections of the plate should be performed. Figure 2 – Loading history for one cycle (day and night). Exercise 3.…