Secondo parziale 18 6 2015

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Test on 18/06/2015 Student:______________________________________________________ Id. Number:______________ Exercise 1 Consider the U-shaped cross section, depicted in the figure below, having flanges of thickness p and the web of thickness q. The cross section is subjected to a shear force, V, inclined with respect to the vertical axis and applied at the centroid, G, of the cross-section. You should: 1. Find the position of the centroid. 2. Find the position of the shear center, if needed. 3. Evaluate and sketch along the centerline of the cross-section shown in the figure the distribution of shear stresses (that is the shear flow divided by the chord length); 4. Assuming the following material properties: E = 200000 MPa (Young modulus) and ν = 0.3 (Poisson coefficient), evaluate the value taken by the unit torsion angle α. G = E/2(1+ ν) Exercise 2 Answer one of the following theoretical questions: 1. Starting from the De Saint Venant cases, give the general equation for the solution of torsion for a generic cross-section, discuss them and explain other phenomena controlled by similar equations. 2. Derive the Euler critical load of a vertical cantilever.