compito chimici 2019620

Pagina 1

Test on 20/06/2019 Student:______________________________________________________ Id. Number:______________ Please note that: correct solution of exercise 1 is mandatory to pass the exam. Exercise 1 Consider the piping segment depicted in Figure 1(a) . The structure is subjected to the uniform distrib uted vertical load w, which schematizes the weight of the pipe and thei r contents, applied on the continuous horizontal beam AB , and a positive thermal load ΔT. The bending stiffness of the cross sections is denoted as EI and the linear thermal expansion coefficient of the pipe is α = wL 3/( EI ΔT). By neglecting the axial and shear deformability of the structural elements: 1. Evaluate the reaction forces, 2. Sketch the diagrams of the internal forces (axial force, shear force, bending moment); (a) (b) Figure 1. Exercise 2 For the cross section schematically depicted in Figure 2: 1. Sketch the distribution of normal ( σ) and tangential ( τ) stresses assuming M = 30 kNm, V = 160 kN. 2. Check if the stress state at the intersection between the web and the upper flange is admissible according to the Von Mises strength criterion (assume f y = 200 MPa for the yielding strength of the material). Figure 2. Exercise 3 Apply Prandtl’s membrane analogy to a shaft with a rectangular cross section of width b and depth a to derive the equation of the maximum shear stress due to torsion. V M