HW9 - AE 321 Homework#9 Due Not Graded Do NOT hand in...

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1 AE 321 – Homework #9 Due: Not Graded. Do NOT hand in. Chapters 6, 7, 8: Torsion, Plane Problems and other problems 1. (a) Show that the stress function for the torsion of a long cylinder of solid triangular cross section (shown below) subjected to a given torque T is given by: ± x , y () = Cx ² y ² 2 3 h ³ ´ µ · ¸ x + 3 y ² 2 3 h ³ ´ µ · ¸ x + 1 3 h ³ ´ µ · ¸ (b) Find the stress, strain and displacement state for this bar assuming a homogeneous, isotropic linear elastic solid ( E and ± ) and no body forces. 2. (Old exam question) A long hollow linearly elastic, isotropic and homogeneous thick walled cylinder is loaded by a uniform axial pressure P and a net torque T as shown in the figure. (a) Briefly describe the concepts of (i) Superposition and (ii) Saint Venant's principle. (b) What are the boundary conditions on the end faces, the exterior lateral surface and the interior surface of the cylinder? (c) Find all stress components in the cylinder in terms of the loading P and T . Hint: Investigate using the known solution for torsion of a thick walled solid (as opposed to hollow) cylinder, i.e. 13 = ² μ ³ x 2 and 23 = ² x 1 with all other stresses zero and the angle of twist ± related to the net torque T by = 2 T b 4 .

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HW9 - AE 321 Homework#9 Due Not Graded Do NOT hand in...

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