Suppose the shaft pictured below has dimensions d = 3 cm, D = 3.3 cm, and fillet radius r = 0.4 cm and is subjected to load P = 285 kN. Suppose the shaft is made from a material with yield strength Sy = 527 MPa. The nominal stress for this shaft is defined as onom 4P/(nd²). = load,max Assuming a stress concentration factor K+ = 1.5, calculate the maximum elastic stress elastic,max (i.e. assuming no yielding occurs) in the shaft: Telastic,max number (rtol=0.01, atol=1e-05) r -E •Hi- d - Assuming a perfectly plastic material, calculate the actual maximum stress (i.e. maximum value of load) developed in the shaft: number (rtol=0.01, atol=1e-05) MPa ? number (rtol=0.01, atol=1e-05) After the load is removed, find the magnitude of the maximum compressive residual stress in the shaft, Fresidual,max: Oresidual,max MPa MPa ?

4) A stepped steel shaft, shown below, is used in a spur gear reducer. The shaft is subjected to a constant axial stress (A=40 MPa), a constant bending stress due to loads by bearings and gears (M=60 MPa), and a steady torque (T=80 MPa) during shaft rotation. Neglect the stress concentration factors (we will cover this next week) that result from the stepped shaft geometry. The shaft is made of steel with Su=1006 MPa, Sy=648 MPa, and HB-229. The size of the shaft results in a gradient factor of CG=0.9. The shaft has a fine-ground finish. A 95% reliability is required. Calculate the safety factor relative to infinite life (106 cycles). If the safety factor is less than one (i.e., shaft fails), find the number of cycles to failure. (60) M d M

A circular hollow shaft is subjected to a torsional moment T = 30 kNm and a compressiveload P = 80 kN, as shown. The shaft has an outer diameter D = 120 mmand inner diameter d = 100 mm. Points A and B are on the surface of the shaft. (a)Calculate the direct and shear stress at point A. (b)Calculate the maximum,minimum and oriention of the max and min principal stresses at point A. (c)Calculate the maximum in-plane shear stress at point A and the orientation.