Question

A rotating step shaft is loaded as shown, where the forces FA and FB are constant at 600 lbf and 300 lbf, respectively, and the torque T alternates from 0 to 1800 lbf in. The shaft is to be considered simply supported at points 0 and C, and is made of AISI 1045 CD steel with a fully corrected endurance limit of Se = 40 kpsi. Let Ki = 2.1 and K = 1.7. For a design factor of 2.5 determine the minimal acceptable diameter of section BC using the DE-Goodman criterion. FA = 600 lbf F = 300 lbf Problem 7-5

Answer 1

tо f = fоо 8% ot 6 Vo c Cz - --> X Se sop op PBagoodbf cy shaft) Here loadings are in two plane 1 x-y-plane 6 y-2-plane z" by (FBD of XY - planeta 02.100 ebt. Cza 200 lbf equilibrium A B fish static Now, shaft; of 1 T . 78938060 B & Boolbe " {ny@ 020 C₂ x 18 - 300 x1220 12C2 z 200 ebf las ebf 200 lbf {Fzzo . Cz+02 - 30020 (02 2100 ehf for Drawing 3FD & BMD consider i part oB; Os x S 12") 100 lbf Oki ts 2016) 71200 ebt in VIS foo 2, MA abrin mex) x BRO 2fz 20 T abfin . N(x) ( a 10020 los ebf 1 Tmol LA B & My @ 220 2) may - 100x = 0 2. MO lagx, abfin ET @x20 2) (Toxy =o)

for Be section, C12" <x5 18" 100 ebf VOC) MOR) 300 lbf V600) - 100 4.300 20 V012 - 200 ebft { 0 %) x 25 med) - 100x +300(x-12) M(X).2 200 (18-x) s ebfin) K 6" * " * (x-125 ET @ x20 2) T(x) - Tzo ebfin 1. Toga T can draw Tmo. SRO, BMD & " - from Macer; above epm we 2 Y-2-planer . Goo ebt AL T Oy 2 400 ebf Cyzl200 lb f 2) since; Y-2 plane loading is same as xy-plome loading. 2) all the SRO, BMD % 7m 0 0 0 simular with xy-plane , & al eon are also similar. A so we can directly draw similar SFD, BMD & TMD. L 400 ebf - RO A 2840 K MB 2 1200 lbf in Bmo1 Tmol

2002 a from above TMD & BMD e con tout so shear so shear le resuttaut forces FAQ J 4002 at A; RA 2 412: 3106 lbf tout moment at A i MAS 1940024 8002 MAR 2473. 8 634 ebfin tant Torque at A; Tazo ebt in Toni resultant At ③ t resultant at B, shear free : moment 11 Torque PB2 Bojat 2002 988.849 + lot o i at B.; MBO J 100 02 +12002 - Mg 2 109 7.0 5 Abfin Torque at Bi To SRA. 1 TB 2. TT ebf in from above values of loudings, that we can step B say is nowe more e loading since them at step B at A. there is small compared diameter. to at H & step is culso there so It is subjected to Band stress concentration also But A is not a - 30 step-B in smcell diameter Section is me Critical than Å be any other section in shaft - is sufe If sos a shaft step-B, we whole Transverse is is very small to shead & Bending other Compared Torsional neglect it. och laats shear steady Transverse - since; Bending moments are also steady. ~ But since shaft is natuting, critical element in shaft is subjected to reversed Bending moment & stresses. (. Ma2 Mp3 1894. Obra ebfing e shaft is safe. ath shear since, Stress, we Mм 2 o of in

88 ubkin Tmax a 1800 a) Now; & Taarina o ubfin Tmers & Tuin 1890 400 a gao ebfin Taz Tmas - Twin 2 1800- a goo est in for AISI 1045 CD steel; Sut a glasi & sya 74 ksa - By DE- Crosdman Centerian; [4 ( If ma)? + 3 ( Kes Tu j?] + 1 [acke Mm) ? + 3 (kps Tmj² we have; na 8,5 Keadil & Kfg 21.7 - Now; in 2 6 X se a 4o kepsa 240 x103 ps à xlos [4 (2.1x1097.0583) +3 clitx goog?] 3 4 + I [4 (2.1X0j? + 3(1-+*900279 gixlos in 1. d21-408 BC section Diameter of (Answer)