Question

A shaft is to be manufactured from a steel having an ultimate tensile strength of 420 MPa, and a yield stress of 305 MPa. The shaft has a solid circular cross section of diameter 50 mm and is subjected to a sinusoidally varying torque ranging from 60 Nm to 130 Nm. It has also been established that the shaft has a fully-corrected endurance limit of 129 MPa and that a torsional fatigue stress concentration factor, k_f = 2.1, exists at the point of interest. Use the Goodman criterion to calculate the factor of safety against fatigue failure in this case. Enter your answer to 1 decimal place.

Answer 1

Solutions tensile strength Gust = 42ompa Yield sweryth Gyt = 305mpg diamets of shast d = somm maximan Zorque Tmax = 130 N-m Miniman Torque Tminz 60nm. enderare limit se = 12ampa feelique correction factor & = 211 Kd = 1 kg a kd kl 20.47619 ym - MS Tomean = Tomanet Tmin - 130 +60 - Nm Tamplique = Tmax-Tmin = 130-60 = 35 m According to the stress theory Torque convert in to the shear shens. as listortion theory good cempore to maximam shear stress theory Sse=o.sse for maxim stray they, sse = 0.577 se for distortion theory Za = 16 Ta a 16x35x103 21:42 mpq. . ITX503 та 3 Zm= 16 Tm . 16895x10 23.87m84 ada TX 503

se = kako kako se Se = 0.47 16x129 = 60.8364 mpa Sse = 0.577 se Sse = 8511026 mpq Sus= 0.5877 bet Sus. = 0.579BX 420 = 242.48 mpa to Goodman fajhore. According ma zm Gq - Za 1:42 +387 at 35102 242.48 Pos (Fos= 17.72