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250_Mechanics Homework Mechanics of Materials Solution

# 250_Mechanics Homework Mechanics of Materials Solution -...

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Unformatted text preview: 3.115 The hollow shaft AB is made of a steel which is assumed to be elastoplastic with r, = 145 MPa and G = 77 GPa. The magnitude T of the torque is slowly increased until the plastic zone ﬁrst reaches the inner surface; the torque is then removed. Determine (a) the maximum residual shearing stress, (b) the permanent angle of twist of the shalt. PROBLEM 3.115 SOLUTION inner rulim C, '-' 0.0l8m J outlaw rakes CI = 0.030 w. w J : 153(9, — f): 1(o.oso“- 049:3“) = l.l0'l‘iS'VlO"‘ m“ LOaJCnaI when ’0‘, readies inner :5¢.w~‘Fm-<:e.J +1"th 7.’= ”fr Ca. '3 a 7; "-‘ 211’; {Ga-ﬂair!) = i'ﬂ'fr'g‘ = gg'rfr(c:'ci) ‘3. cl = 231(l45xio‘3(0.0303— 0.0:?) = 6.4285310: N.” -31.. _ _ q» . _L_V._ ’Y‘— C: at! [o'ct Aﬂsg Y—%— --q)_ ’0 - _(1.2s 145x106) _ .2. _ , (QM-(ODWEWWOW - l3o.77vio m! . 7.4% UnPOJingf T= GﬂZSSNos v-m (define) AZ=AI£ Lg 6.923r)(o.03o) _ t. ’Z- --————-—-——--Lw7q§_xlo-‘ — l7‘l.i‘+ x10 Pa. Al F = c, 1": LW = «>th xio‘ Pa. .i07‘-iS’k'I0‘ L 1“,. c.6- cp’ ? (LTWL _ t awas'XI-RS) -1 9 GR]— h(77 woeful-IOWS'Ho“ - “H. 23x10 NJ : -5.3oﬁ Q85;JU¢.P: ’L’m :: no”. a— t' (Rev-E" CPA“? __ w: (a) M F=CL 1:“: t‘isxio‘-i74.H>¢IO‘ —29.H>-io‘P=.. - 2?.1 NHL 4 If ll ...
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