Exam 2023 06 28 WT1 text

Pagina 1

Exercise 1. Consider the document storage shelves shown in Figure 1, a couple of forces are loaded on the handle, at point A, as P (compressive force) and R (radial force). A pulley at point F is the one for moving the shelf with force F. F is along axis x (fixed in space) , P is along axis y’ and R is along axis x’, the last two forces rotating in space together with the structure (Figure 1). All the forces are constant in magnitude . All the beams are made by the material presented in the table below with a hollow cross -section of external diameter, de=5 mm, and internal diameter di=4.5 mm. At the status, the shaft is rotating at a constant angular speed . Figure 1 It is required to: (1) Determine the values of the force F and the reaction forces (2) Draw the internal forces for the structure, separately for the different loads (F, P and R) Also, ignoring the axial and shear forces: (3) Perform the static assessment for point C on the handle part (ABC) . (4) Perform the fatigue assessment for the support point E on the moved part (CDEF). Data: Loads Fatigue parameters: 𝑅 = 600 𝑁 𝑏2 = 0.85 𝑃 = 200 𝑁 𝑏3 = 0.85 q = 0.9 𝐾𝑡𝑏 = 1.5 (for supports and corner points ) 𝐾𝑡𝑡 = 1.4 (for supports and corner points ) Geometry Material: Ductile steel 𝐴𝐵 = 270 𝑚𝑚 𝜎𝑦 = 276 𝑀𝑃𝑎 𝐵𝐶 = 900 𝑚𝑚 𝜎𝑈𝑇𝑆 = 310 𝑀𝑃𝑎 𝐶𝐷 = 𝐷𝐸 = 𝐸𝐹 = 100 𝑚𝑚 D (diameter of pulley) = 900 mm Politecnico di Milano - Master of Science in Aeronautical Engineering Academic year 20 22-23 Course of Machine Design (Prof. M. Giglio) Written test 1 – June 28, 2023 NAME : SURNAME : Polimi-ID : Do not write here: 1 2 3 Total Exercise 2 The plate shown in the Figure 2 is subjected to a far -field stress composed by σ and τ. A crack with initial length 2𝑎 = 3 𝑚𝑚 is found in the middle of the plate . Assuming 𝜎 = 𝜎0(1 + 𝑠𝑖𝑛(𝜔𝑡)) and…