Answer Happy

Problem 6 (a) First, using the membrane analogy, qualitatively assess the torsional resistance of the two cross-sections shown in the figure below (assume that the open cross-section remains open at all times, i.e., that the two ends never touch). Then, compute the ratio between the torsion constants of the two cross-sections when the thickness is 1/40th of the inner radius. Does the result correspond to your expectations from the membrane analogy? оо (b) A bar of length 3L and torsional rigidity µJ is built-in on both ends and is subjected to a uniformly distributed torque, mo, acting on part of its surface from x = 0 to x = L as shown in the figure below. No torque is applied after x = L. Calculate the bar rotation at location x = L using the governing differential equation based (GDE-based) approach for the torsion problem. X L mo 2L