Question

A rotating step shaft is loaded as shown, where the forces FA and FB are constant at 610 lbf and 305 lbf, respectively, and the torque Talternates from 0 to 1800 lbf-in. The shaft is to be considered simply supported at points and Cand is made of AISI 1045 CD steel with a fully corrected endurance limit of Se= 40 kpsi. Let Kf= 2.1 and Kfs = 1.7. Take the value of design factor to be 2.5. 6 in 6 in T, Determine the minimal acceptable diameter of section BC using the DE-Gerber criterion. The minimal acceptable diameter of section BC is in.

Answer 1

In the Solution; From the problem we can take the given data given Problem load is applied on the beam in two different planes i.e a-y Plane and z-x Plane. So, we will analyse the forces considen lering different plane at a time os follows. by

X-y Plane: - consider the FBD of the beam in a-y plane 600lbf 6 in ok Gin bin T +A Bkt T c hi R2: for beam to be in equilibrium: - Emo 30 (610x6) – 18 R2 = 0 :, R2 = 203.33 lbf E Fy = 0 RitiRz - 610 = Ri= 610 - 203:33 oRi Ri= 406.66 lbf Drow the SED, Tmo, and BMD as Hollows; - 466-66 $03:33 164 SED T TMD 2439-96 1219.98 BMD o

Shear force calculations - 3) SFO = R = 406.66 lbf - 203.341bf 406.66 - 610 - SFA = SFB = 203.34 lbf SFc = 203,33 7203.33 50 Twisting Morment; > Etx=0 TO +TC+T-T=0 To-To so → TO TA = 0 Тg -Т. Tc=T-Tzo Bending momenti Mo = 0 MA = R, x6 = 406.66 X6 : MA= 2439.96 lb-im → MB = (406-30 12 )-(610x6) > 4879-92 - 3650 MB 1219.92 16-im Mezo od

2-X planie- a consider the FBD of the beam in za 36576 Plane 6137 6072 sing Az TA BkiT --- 06 R3 Ry For beam to be ion equilibrium; - =0 Emo=0 (305x12) – 1884 8. Ry z 20 3.33 lbf 2 Fzzo R3 try 40606630 R3 = 305-203.33 - 101.67 261 Drow the SAD TMD and BMD 101067 lbf 203.33 SED T TMD 610 lbfin Smo

For combined stress problem from 7 MSST for 2+ 4 2 092 2. Syt n 2 77 5403056 Tid3 92.65 $(d3_0.48688 2 205 7 370.6 W 298.806 do t 77 2.5 23 (23 0.234) d= 0.499, 0.978 in s for safe result we will consider the targer value. 7. diameter of BC is de 0.978 in Note- All the calculations done in part (a) 8. (b) is for section BC. And the moment at point B is considered while calculating the bending stress because point Bis critical of the two: