Question

indi 2.. In the figure shown, shaft A, made of AISI 1020 hot-rolled steel, is welded to a fixed support and is subjected to loading by equal and opposite forces F via shaft B. A theoretical stress-concentration factor Kts of 1.6 is induced in the shaft by the -in weld fillet. The length of shaft A from the fixed support to the connection at shaft B is 2 ft. The load F cycles from 150 to 500 lbf. (a) For shaft A, find the factor of safety for infinite life using the Goodman fatigue failure criterion. (b) Repeat part (a) using the Gerber fatigue failure criterion -in

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Answer 1

1020 HR Sut= 55 kpsi , Sy= 30 kpi Given from table A-20 for ASI kus = 1:6 fmin = 150 uby fmo- soo liby L = 24 1 > d- / in - V8 in Let us find the notch sensitit 'a' we know It a for torsion ra= 0.190 - 2.51 (103) sut + 1.35(105) sut - 2:67 (158) ga ut ra s0.190 - 2.51x103 (55) +1:35x10 (55² -2.67 (108) tors3 fa- 0.088345 r in - 17 008834 1/8 q=0.8 q: 090007

Hatique Stress concentration facet Refus Ifs= it a shocu (kts-1) = t 0.8 (1.6-1) 1.48 The maximum torque is Tmoc = - fmox (1+1) 500(2) 1000 My in Torin = fmin (1+1) = Tmin= 180(2) > Tmin= 300 bal.in Tmoc 16 kgs Tmoc т3 16 (1.48) C1000) T (0.875)3 11251 poi Emina 16 kgs Train Td3 16x 1.48 (300) ↑ (0.875)3 3375 psi

I mean Tmox & Timin Tamplitude = Tmoc - Emin 2 ID 11251+ 3375 2 11251- 3375 7313 psi Tamplitude 3938 psc 3.938 kpsi 13332 I mean 7.313 kpsi Since the Strees is entirely shear according to mosc Shear Strees theory Sy/2 30x10 / Tmox 11251 the endurana limit se = 0.5 Sut and modifies sé = 27.5 kpsi fa= a slut Suyacefactor, - 0.5 (55) 0.718 Sunday 27 14.4 (55) 0.8105 effective diameter, de = 0:370 (7/8) 0.370 d de = 0.32375 -0.107 Sire fador , kb 0.8 79 de Ib = Qerses O. 9917 Load factor, kca 0.5a ( for torsion ) Sse= endurance lint at critical location Sse kako ko se - (0-8105)(0.9917) (0.59) 27.5 Sse = 13.0412 Ipsu Dince only shear loading is there tuum ate shear strength 550 = 0.67 Sot

5900 64(55) Sso 36.85 kosi for modiped goodman factor of sclety is Mt tamp & Tmean 8se SSU 3.938 13.0412 + 7.313 36.85 nt 1.998 factor of Safety according to modified goodnan is 1.9,98 6 for gerber criteid factor of syety is af - + Tamp Sse 2 łmean Sse Sso tamo 2 1 (30185 e) [ 3.938 13.0412 + 21 it 2(7.313) (13-0412) (36.85)(3.938) 313 ng 2.4978 factor of safety according to geben criteria 2.4978