Team Challenge # 2 The circular tube shown below is fixed at its left end and has a constant cross-section and uniform material properties. It is subject to a point torque, Q, at its free end, and a uniform distributed torque, q, is applied over its left half (0 x '/2). Prior to the application of the loads and supports, the tube is heated up by 20c. (a) Find H11 for the tube after heating. Assume that thermal expansion has no impact on E or v. (b) Using H from part (a), solve for the twist distribution in the tube, () for 0x L'. (c) Find the value and location of the maximum von Mises stress in the tube. R'o 91 R'i 11/2 Q1 Thermoelastic constitutive law (cylindrical coordinates): 1 p = [r v(a + 01)] + aT E 1 - = [a v( + r)] + aT = E 1 = = : [1 v(or + a)] + aT - Strain-displacement relationships (cylindrical coordinates): r = ; 1 = + ; = r r da 1 Material & Geometric Properties: L = 8m (at T) R = 0.1m (at To) R = 0.15m (at T) E = 2.5GPa v = 0.35 G = E/2(1+ v) a = 0.0025 -1 = 20c Q = 3000Nm 91 = 1000N