A 1.25-in.-diameter solid circular shaft is made of a material that is assumed to be elastoplastic with τY = 18 ksi and G = 11.2 × 106 psi. For an 8-ft length of the shaft, determine the maximum shearing stress and the angle of twist caused by a 7.5-kip·in. torque.

Problem #3: A circular shaft, fixed to the wall, is loaded as indicated in the figure below. Using all three failure criteria (Rankine's theory, Tresca criterion, and Von Mises criterion), determine the load magnitude, R, that causes yielding at point A on the cross-section. Assume the yield strength of the material is 64 ksi. Notes: . . ● Point A is at the mid-depth of the section and on the leftmost fiber (as viewed below). At the fixed base, the shaft will be subjected to a bending moment, a torsional moment, a shear force, and a normal force. Recall for a circular cross-section; 1=d¹ and/=d. Q does not need to be provided, as you should see herein. A 3 ft R 4 in. F T 2 ft 12R X