Question

The shaft shown in the figure is machined from AISI 1040 CD steel. The shaft rotates at 1600 rpm and is supported in rolling bearings at A and B. The applied forces are F1 = 2500 lbf and F2 = 1000 lbf. Determine the minimum fatigue factor of safety based on achieving infinite life. If infinite life is not predicted, estimate the number of cycles to failure. Also, check for yielding.

Answer 1

From a free-body diagram analysis, the bearing reaction forces are found to be 

$R_{A}= 2000$ lbf and $R_{B} = 1500$ lbf.The shear-force and bending-moment diagrams are shown. The critical location will be at the shoulder fillet between the 1-5/8 in and the 1-7/8 in diameters, where the bending moment is large, the diameter is smaller, and the stress concentration exists.

$M=16000−500(2.5)=14750 lbf$