A stepped steel shaft (as shown in Chapter 4, Figure 4.35) has D/d = 1.2, d = 30 mm,and

Chapter 17, Problem 17.26

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A stepped steel shaft (as shown in Chapter 4, Figure 4.35) has D/d = 1.2, d = 30 mm, and r = 3 mm. The surfaces are machined and the steel has a hardness of 200 Bhn and strength values of \(S_u\) = 700 MPa and \(S_y\) = 550 MPa. The rotating steel shaft used in a spur gear reducer is subjected to a constant bending moment and a steady torque which results in calculated stresses of 60 MPa bending and 80 MPa torsion. However, these are nominal values and do not take into account stress concentration caused by the stepped shaft (shoulder). The fatigue stress concentration caused by the shoulder of this steel shaft is \(K_f\) = 1.53 for bending and \(K_f\) = 1.28 for torsion. The modified endurance limit is 239 MPa. Determine the safety factor with respect to infinite fatigue life.