4 - Prob. 4.3-1. A bimetallic torsion bar consists of a...

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Unformatted text preview: Prob. 4.3-1. A bimetallic torsion bar consists of a steel core (G, = 75 GPa) of diameter d. = 25 mm around which is bonded a titanium sleeve (G, = 45 GPa) of inner diameter d.=25mmandouterdiameterd.=40mm.(a)lfthe maximum shear stress in the steel is 50 MP3, what is the total torque, 1} applied to the bimetallic bar? (b) What is thetotal twist angleoftbeeompositebarifitisZmlong? 9240/7an (é) Y T (1:)M‘L =wMI94 6 = Kept n)...“ I - ’1'" [2.6hm gin“ ‘ 5f . r9 = ZOOM!“ f lo 1% fl fr; ' fled/'f/fl’I/d/I'I/fl'luikn.’ afif' J“ (’6!!! [3" ’7' a an; 4:5 . ow , 7"! =0".ng mfl 27-wnrf 4564:. \(ZUMM)JDMp4 7) G c ,V _(_______ = ((wamu =(fitp ) a (I! L“ _ (7ffip‘ ) (/Z,fmm ) ¢5IQMfl4 l‘ he; 5 c 6’46 (mm 50mm ' , 4 ml ‘7“— : 5W? z 75am (0.0/25) ' 555 {/0 ) 7 fif/T’Jfle g[g4/y4 *44/2/4] = 1:0!" r .74— 4 I 9! g “4676 J,» =31 6/:- , 4r 7:54 -c/,-¢) ZJfO/m’MM 4jlum‘ 7: (fng/O-L%J)[ 7J'§/‘¢ {fiffxlotmvf 4371?: (aljax /0{Mm4)] {6) 7319/ fw’l/ [wry/c, ¢= {éfi—‘M = Maw/04%,! )flm) - 0, mega/m ‘¢t 0,/067 r‘fiI/‘ ’Prob.4.3-6. 11:esolidshaftinFig.P4.3-6ismadeofbnss thathasanaflowableshearmessfa. -'120M.Paanda shear modulusof elasticity G I- 39 GPa. The lengthof the shaftisL-Znyaudaverthislengththeallowable angle oftwistisofi...=0.10tad.lftheshaftistobesubjectedto amaximumtorqueofT-ZSkN°m.whatisthe-tequhed diametetoftheshafi? TE)‘ .1ng Tallow‘ 1; g dmi 5 (dszz‘x/CLE—twr. m. f‘ :20 a. '-' Wm. {L 100A; IL. 52TL , (bulow‘ . GIP _ Cl} =EC-Jdmin q 25 % L 2 a (dm'm.¢= 3 w, " 1r a. 0. or W dm‘m '71 (dmin)¢ = l0‘a.‘l mm Prob. 4.3-14. Solve Prob. 4.3-13 if the stated externally-ap- plied torque distribution is replaced by the cubically-varying I torque shown in Fig. P4344. g Q? & 16-394 / M Maximum WW r/rerf . fé//flrxtflm 1' fix) .IZ-MX = 0; 7h) fm= 7,; =x/fL/f)o/§ 1 4*— = 5[L[I'(2€)3]°/f =5 [5-21; LL: %[i—4(§)*(fl4] Max/mam rlur r/rcrf.‘ ' " ——-——————W m m m [mt/5+ Ly] 7;" (U = 31,, = ,7013 /ra/’ 441' __ 4 2;“ :ffo/g J {5) flnf/c a/Iéu/iif ¢,, 0 4 :o/ z é w) #02 =0 ‘1 [ [Mm/ma 4&1; z: 2 L =g;[;ra-ag} +%/—£—)’]0‘ s 45;: L‘ , {film/9‘ 558 = 14/4— {761’ Pmb. 4.4-5. (See the “generic torsion member” figure.) T-200N-m,d.-30mm,andd.-0mm. a) ' tree; as . . r. : Wedge; elcmenk £\ P’ZFn‘o: GnAn+ZTAn6inecose=o ’1 ‘5 Gn=‘2’Esinecose futA" 04 = "Este H n 1:(Ay.cOse) Lx Virgo gm An + "memes—awe) =0 9 73¢ = “Hoosze‘dnza _ = ‘T—cosze Tmnsme) 50 (0%wa = (TM-45‘» = fl: (Um); = 071(45") = "E rLYmJ = Int my): I m T1472) '1: "j‘E‘LE‘ maximum at}; outer surface, 50 ’E‘ 7i ‘waw— 7") IE» ooN-mYSOMnrD ‘3 ’TI'E‘Eommizl- (OMmqu = 51.121» Mfg (Gnu-QT = 5-4.? MPK (UMAXL =' " 5-4.7 Trnax = 57.? MPa, aw . Maximum normal stresses maXIMLUYI elnewr eb-ees (5 6 3.; M)T'\ K35??le Tmu= 57.7 MP“, mummy/V \(UWNT Tm" = 57.1 M Pal, Prob.4.4-10. L=4m,d.=40mm,d,=32mm,¢=0.25 ra¢de-28GP3. CO H L Erika? <b= GI? => L jHCZSCZEg )l Momma)” - (32mm24 K025 mph = 5204 m‘) =Z59. 6? gym T‘ZéON-m memmimlecfitmsi z demen}, ’6 yEFn=016nAn+ QIAncéinecose =0 \ => O‘n = ‘Zfeinecose EM“ /n ="E6'm29 own = _ = ,[xAncosey \€ix ‘50 O'ma-x Un( =T%%a — Trad—all.) ’T.(An8lh9) lo( 9.6? 'm 40m = 11' 40mm?“ 32mm " = 3-5 541% ©Mr=5i0 MP0» A uniform 1-in.-diameter steel shaft (0 = 12 x 10‘ psi) is supported by frictionless bearings and is used to transmit torques from gear B to gears atA and C as shown in Fig. P4.S-2, (a) Determine the maximum shear stress in element (1), (i.e., in segment AB), and the maximum shear stress in element (2). (b) Determine the relative rotation between the two ends; that is, determine ha I- ¢c - 434. {us-z 03W ‘ zemfi QaCBOH, E2211: amt: excision lbin.<1<2lein. 04x4 Him. (1 (2) (l x—GQEZ—e— x— a, 1200 km Fix ___3 le____x__,‘ <isoo “o‘il’l. 2MX”O= £199.!me (D W5. mgde Mel]! Ikflgoolb-l'n) , (Lnan I?” = TM? : ’IiUirfl'l $035.5 [251 [Tali Hal , (TM: 122 = -’1Tci5 = ram); 7mm. mail 7' 4,07 (Tm) = Lo,” ksi atrium ' 1;. 45%?) =7J—‘l—LV‘1SE.‘}S»35§ Uni.“ $1413 I @ ffgazq M‘Ps.‘ ¢2=U2 $11:$:’C§>A5 $¢VA=¢‘—¢k=¢‘+ 43‘ @ flb@+@+@ . rad . Cbc/A = ET. + LE. = 1.553 I (IO’EH‘EAJM'QQO Ib'in) + $437506") lbmflzoo Ho'm) = - (2.?6lthQ-H) m a] (pt/A = - Lf-H (210'?) ml ...
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4 - Prob. 4.3-1. A bimetallic torsion bar consists of a...

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