A bar AB with solid circular cross section (diameter d) is loaded by a distributed torque, t, which has a value of zero over the first half of the beam and then increases linearly over the second half until it reaches a value of to at the end of the beam, where x=L (see figure). The shear modulus is a constant, G. The total length of the bar is L. (A) Determine the angle of twist between the wall and x=L/2. (B) Determine the angle of twist between x=L/2 and the end of the bar (x=L). (C) Determine the maximum shear stress in the bar. linearly increasing distributed torque over second half of beam t(x=L/2)=0 t(x=L)=to B Problems (from Gere and Goodno, 9th edition): 1.7-1 A high-strength steel bar used in a large crane has a diameter d= 2.00 in. (see figure). The steel has a modulus of elasticity E = 29 x 106 psi and Poisson's ratio is v = 0.29. Because of clearance requirements, the diameter of the bar is limited to 2.001 in. when it is compressed by axial forces. What is the largest compressive load Pmax that is permitted? PROBLEM 1.7-1 1d axial Perpendicular EOM Global FBD Cut FBD P Elateral = -J Eaxtal EFx =0 Ad -Pmak antal JEE akhal Jacial - A =- Janial SFX=0 SE=0 Eaxlal= hoat E Easial - EA -N-P=0 0.001 ( == -0.29 P-P=0 0=0 N=-P LEA 0.001 = +0.29 Pmax (29x10 psi (#1 (2in)) Lmax = 157,080 165 157,080 165 or 157 kips 1000 165= | Kip