Problem 2. Consider a shaft with a diameter step as in Figure 2b. The dimensions are given as d = 40 mm, d = 48 mm, p= 1.00 mm. The material is a low-alloy steel with O = 1200 MPa. M) X S (Hint: safety factor X, can be used as a linear correction factor for eventual load M = (a) find kt and kf using both Peterson's and Neuber's approaches. (b) Assume the fatigue limit for smooth member is de = 0.50u, what completely reversed bending moment M can be applied for 106 cycles with a safety factor of 2.0? a Kt Kt 3.0 2.6 2.2 1.8 1.4 1.0 3.0 2.6 2.2 1.8 1.4 0 1.0 1 0 (a) 1.02 1.2 0.05 0.1 1.5 1.1 1.02 (c) 1.05 1.11 d 0.05 0.1 2 d/d = 2.0 0.15 p/d 2.0 d 0.2 S= P 4P , S= 0.25 0.3 AID) d M 32M d,3 d/d=1.43 3.0 2.6 2.2 1.8 1.4 1.0 3.0 2.6 2.2 1.8 1.4 0 d/d=2.0 1.5 1.2 1.1 1.02 (b) 1.02 1.05 1.111 2.0 d 0.05 0.1 0.15 0.2 0.25 p/d d M S= S= 32M ,3 Id CT 16T d,3 d/d=1.43 0.15 0.2 0.25 0.3 p/d1 Figure 2 Elastic stress concentration factors for notched circular shafts 0.3 1.0 0 0.05 0.1 0.15 0.2 0.25 0.3 p/d Notch sensitivity: q = kf-1 kt-1 Peterson's approach: q = 1 -3 log = 2.654 10-7 - 1.309 10- + 0.01103 , mm = 10loga (345 2070 MPa) Neuber's approach: q = 1 1+ For steels: log = -1.079 10-9 -3 +2.740 10-6-3.740 10 +0.6404 , mm = 10log B For aluminum alloys: (345