Question

A shoulder fillet has the dimensions D = 2.5”, d = 2.0”, and r = 0.06” (Kt = 2.552). The shaft is made from steel with an ultimate strength of 118 ksi with a machined surface finish. The shaft receives bending a bending moment that varies from +35 kip-in to -5 kip in. (a) Estimate the fatigue life of this shaft (b) What residual compressive stress would improve the life to 750,000. (Use the Smith-Watson-Topper approach to account for mean stress.) (c) How much should the life improve if the surface were ground instead of machined? (Compute the new N and compare to part (a).

could you please solve it using the numbers in the question, please don't post a past version of it as those are incorrect

Answer 1

x = 0.06 KA = 2.552 atened steel 6u = 118k Si prof per ____ a) fatigue life of the shaft. Mean Stress, 6m= 6max tbmin 6m = 35-5 = 15 kip 2 Stress, 6 = svyax - G и Amplitude 2 -= 35 US = 20 kip using Equation of Goodman line I 6m + 6a 1 - but se 2 Se = kako kako se For Steel, Se = 0.5 but Gut. = 118 ksi

- ka = surface tinish factor for machined Surface finish I Ka = a (but) as 4.51_b=-0.265 Ka = 4.SI (118) ka = 1.27 - -0. 265 K6 = - Size facter. For Dysomme K6=0.75 Kc Reliability factor. Assuming, aq, gggt. acliability ke=0.659 aks. ks = 1ta (4-1) [q=1T _= Kf= 1 + (2.552-1) t1.552 = 2.552 L s - 2.552 1.27X0.75X0.659 x 0.391 Sen SE OSX18 = 59 ksi.

I Se=0.2 48 59 = 14.48 Ksi from Equation bm & ba al but logo (0.9 but A -22026 Endurance test الجلد - كل - - log on. L - 0 1 2 3 4 5 logo four) → to go f118) = logis (0.99x118). = 109.. (106.2). - 2.026 Se = 14.48ksi. logen sattung Se = 10g (14.48) = 1.16 Fatigue life = 1028 Cycles

libe From = 750 x 103 smith watson - Topper approach ben - --- yo:75X10 Oy lo' 102 103 104 105 106 107 Reversals to failure → For 750x103 life cycle رجك عليه و2 . = C G for Ground surface, Ka= a(but) az 1.58 b -0.085. - Ka = 1.58 (118) { Key = 1.053 / Se = 1.053x0.75X0.65980.391 se = 0.203 X o 5X118 Se = 12. Si Se = logo (12) = 1.07 life = los cycles. Life improved = 781.58 Cycles /.