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241_Mechanics Homework Mechanics of Materials Solution

# 241_Mechanics Homework Mechanics of Materials Solution -...

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Unformatted text preview: PROBLEM 3 105 3.105 A hollow steel shalt is 0.9 m long and has the cross section shown. The steel ' is assumed to be elastoplastic with 1}, = 130 MPa and G = 77 GPa. Detemtine (a) the angle of twist at which the section ﬁrst becomes fully plastic, (1)) the corresponding magnitude of the applied torque. SOLUTION C‘ =é—d': o.o|S-M C1 = "lid! I: 0.035,“ (60 For ense‘i’ .D‘F Fully Pﬁas'i‘ic yid‘iina‘, FY = C, .. L’r; 10-9EISOwO") 1'40 2 -3 a - -_...—- -: ”-1“ . 6’0 7 80? q) C, G- (o.0/5‘K77 ,, to?) I r”! ‘- CL ’Z’r/ozgllo z 21H}? )c‘ -_-_— 2332’Y(C: _ (3,3) ‘ uCl?Dx/o‘)<0.r3333-—O.oi‘§a:} = ILLSQXIoa N-M = 14.8? kN~M an 3.106 A shalt of mild steel is machined to the shape shown and then twisted by torques of magnitude 45 kip'in. Assuming the steel to be elastoplastic with r, = 21 ksi, determine (a) the thickness of the plastic zone in portion CD of the shall, (1)) the length of the portion BE which remains fully elastic. SOLUTION (0..) In Fowi’tom CD C ='2Ld = LOO in TY = Jag’l’v = gcﬁgr t ~"}(I.Oo)3(’n‘\3-' 32.6137 mp.» ‘3 3 T=%E(l-%3 £3: neg}: n-%%l= 0.3;er £1: 0.71283 , [or =(o.7:28i(:.oot = 0.713 rub t, .- c—/o,,-o.237;n 4 (in) FDI- \]ie.poiin3 u‘i‘ Poi-«i E T“: Ty) C = C; J T” 40 R-p ivy .. TC _ 2T . 1'- : 2?— , (2) ‘io _ . 3 ty' EL ‘ “fag " CE 7T2: " WEE—)1. - LRIQG In Using Pm-Por‘i'ious gnawV +14? 5%?th LQS — Loam _ .35. :.25— l-00 ...
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