Chemical Engineering - Mechanics of Solids and Structures II

Full exam

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 distributed vertical load w, which schematizes the weight of the pipe and their contents, applied on the continuous horizontal beam AB, and a positive thermal load DT. The bending stiffness of the cross sections is denoted as EI and the linear thermal expansion coefficient of the pipe is a = wL 3/(EI DT). 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 (s) and tangential (t) 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