The steel shaft shown in Figure 1 is machined from low carbon cold rolled steel SAE 1020 with
Sut = 65 kpsi, Sy = 38kpsi and E = 30Mpsi. The shaft is driven by a gear at B, drives a sheave at
D and supported by two deep groove ball bearings at A and C. The shear and bending moment
diagrams over the shaft length are shown in Figure 2. There are three locations of concern where
a moment occurs in combination with a stress concentration: point B at the step and end-mill key
seat under the gear ($M_B$ = 33 lb-in), point C at the right bearing where there is a step with a small
radius to fit to the bearing ($M_C$ = 63 lb-in) and point D at the sheave step ($M_D$ = 9 lb-in). The
diameters of the shaft are $d_0$ = 0.6 in, $d_1$ = 0.5 in, $d_2$ = 0.416 in and the radius of the fillets at B is
$r_B$ = 0.05in and C is $r_C$ = 0.0416in.
a) Using the modified Good-man criterion, calculate the minimum safety factor for infinite
life and check for yielding at the critical loaction B.
