J. J.'- '-'.1J L.d 1V J L...,V./ 5-58. The two shafts are made of A-36 steel. Each has a diameter of 1 in., and they are supported by bearings at A, L and C, which allow free rotation. If the support at D is J fixed, determine the angle of twist of end B when the torques are agplied to tl1e assmbly as shown. r - fts t!?c; are mde - of A-36 steel. Each has a diameter of 1 in., and they are supported by bearings at A, B, and C, which allow free rotation. If the support at D is fixed, determine the angle of twist of end A when the torques are applied to the assembly as shown. -- 1-, " 0 80 lb. ft 30 in. Probs. 5-58/5-59 *-60. The two A-36 steel shafts AC and FD are coupled together using the meshed-gear arrangement shown. If A is a fixed support, determine the angle of twist at end F due to the applied torsional loading. Each shaft has a diameter of,.
.. ""1 5-58. The two shafts are made of A-36 steel. Each has a diameter of 1 in., and they are supported by bearings at A, B, and C, which allow free rotation. If the support at D is fixed, determine the angle of twist of end B when the torques are applied to the assembly as shown. '0""ok -f"'"". 030" -<-. ;... 'G 10,..""" - F.!1..L2120 II, O.JU3 "12,; 4"0 " Internal Torque: As shown on FBD. Angle of Twist: TL tpe=l JC 1 =y(0.54)(11.0)(1()6) [-60.0(12)(30)+20.0(12)(10)] c:::p-- - TF=-40.0Ib.Jt 0 4<>. lb.jt, o.sfe = - 0.01778 rad = 0.01778 rad 6 6 tpf = "4tPE = "4(0.01778) = 0.02667 rad Since there is no torque applied between F and B then tps = tp F = 0.02667 rod = 1.530 Ans 7;H =ZO.O IbJt../ 80 Ibj<:. t::.izoi 5-59. The two shafts are made of A-36 steel. Each has a diameter of 1 in., and they are supported by bearings at A, B, and C, which allow free rotation. If the support at D is fixed, determine the angle of twist of end A when tbe torques are applied to the assembly as sbown. F=.$L=120 16 0.;;]3 Internal Torque: As shown on FBD. Angle of Twist: TL tpe=l JC 1 = y(0.54)( 11.0)( 1()6) [-60.0( 12)(30) + 20.0( 12)( 10)] =-0.01778 rad =0.01778 fad 6 6 tpf ="4tPE= "4(0.01778) =0.02667 rad TGFLcF tpaif =---;a - -40(12)(10) - y(0.54)( 11.0)( 1()6) = -0.004445 fad =0.004445 rad tpa=tpf+tpaif = 0.02667 + 0.004445 = 0.03111 rad = 1. 780 Ans 7;H =,(,0.0Ibjt../ 'ff =-4<).0Ibft. a.5}t 801b.A C) f:.j,?o 16 O.5J-t. &Jt# 184
80 lb. ft, ju Ill. ( Probs. 5-58/5-59 *5-60. The two A-36 steel shafts AC and FD are coupled together using the meshed-gear arrangement shown. If A is a fixed support, determine the angle of twist at end F due to e applied torsional loading. Each shaft has a diameter of.:-j mm, and the journal bearings at F, B, and G allow free rotation. 40mm I 120 mm. E 18 N.m Prob.5-60
Ii.. *5-60. The two A-36 steel shafts AC and FD are coupled together using the meshed-gear arrangement shown. If A is a fixed support, determine the angle of twist at end F due to the applied torsional loading. Each shaft has a diameter of 30 rom, and the journal bearings at F, B, and G a,(lw frpp rotation. Internal Torq ue: As shown on FED. Angle of Twist: "'c = 'C' TL I.JJG - JG[6(1.5) +(-6)(0.5)] = 6.ooN.m2 JG 40 nun C -il J2 I"VG/D '. Ojmj" o.5m //' F:'<,=1500N. /8N. {;' O./Zrn "'D 0.04 2.00 = 0.12"'c = JG 1;;1>=-/8'OAJ.rY1 /81).", l DLED -18.0(0.5) -9.00 N. m2 9.00 N. ro2 rfieid = :J(; = JG - JG =---xi <PE=rflD+rflEJD 2.00 9.00 11.0 N. m2 = -+-=lg lg JG Since there is no torque berween E and F, then 11.00 rflf= rfle=r(0.oi5)'(75.0)(109) =0.001844 roo = 0.106 Ans bf=/50.0"; O.O+rn F=/ O.ON Tc.J{=b.OON'tr'I 71H=-(,.00 N.m 5-61. The assembly is made of A-36 steel and consists of a solid rod 15 rom in diameter connected to the inside of a tube using a rigid disk at B. Determine the angle of twist at A. The tube has an outer diameter of 30 rom and wall thickness of 3 rom. Internal Torque: As shown on FBD. Angle of Twist: TL "'A=2:- JG 50(0.3) 80(0.3) = + ;' (0.0075') 75.0( [09) ;'(0.Oi54-0.012') 75.0( 109) 50,,)"" 1:= 70.m = 0.04706 roo = 2.70 Ans 185
(C;;-76. The shaft is made of L2 tool steel, has a diameter 'of 40 mm, and is fixed at its ends A and B. If it is subjected to the couple, determine the maximum shear stress in regions AC and CB. ( 2kN 2kN ( 400-600m Prob.5-76
*5-76. The shaft is made of L2 tool steel, has a diameter of 40 mm, and is fixed at its ends A and B. If it is subjected to the couple, determine the maximum shear stress in regions AC and CB. '" an Equilibrium: Compatibility: 1A+1j, -2(0.1) =0 [ I] 400 '"'" 600./ '.,.. tpcia=tpcib 1A (0.4) - 1j, (0.6) JG-JG Solving Eqs. [I] and [2] yields : 1A=l.501j, [2].."'::, "" To 0'00l'? 1j, =0.080kN.m 1A=0.120kN'm Maximum Shear stress: 1Ac 0.12( IQ3)(Q.O2) - 9.55 MPa (AC>mu= J = r(0.024) 1j, c - O.OS( 1Q3)(Q.O2) - 6.37 MPa (CB)mu= J - r(0.024) Ans Ans 5-77. The bronze C86100 pipe has an outer diameter of 1.5 in. and a thickness of 0.125 in. The coupling on it at Cis being tightened using a wrench. If the torque developed at A is 125 Ib. in., determine the magnitude F of the couple forces. The pipe is fixed supported at end B. F '.._.-.-. Equilibrium: F(l2) -1j, -125 =0 [ I] Compatibility: E!PCIB=tpCIA 1j,(8) = 125( 10) JG JG 18 = 156.25 Ib. in. From Eq. [I], F( 12) -156.25-125 = 0 F =23.4Ib Ans, 'I 194
,..-------------- (1/6. - 5-60* A steel (G = 80 GPa) shaft 2.5 m long extends through and is attached to a hollow bronze (G = 40 GPa) shaft 1.5 m long, as shown in Fig. P5-60. Both shafts are fixed at the wall. When the two couples shown are applied to the shaft, determine (a) The maximum shearingstress in each of the materials. (b) The rotation of the right end of the shaft.!f/g- 5-62 The torsional assembly of Fig. P5-62 consists of an alu!l)ipum alloy (G = 28 GPa) segment AB securelyconnected to a steel (G = 80GPa) segment BCD by means of a flange cupling with four bolts. The diameters of both segments are 80 mm, the cross-sectional area of each bolt is 130mm2, FIG. P5-62 and the bolts are located 65 mm from the center of the shaft. If the cross shearing stress in the bolts is limited to 55 MPa, determine (a) The maximum torque T tat can be applied at section C. (b) The maximum shearing stress in the steel.
'. PROBLEM!I,' """"'" f' t /,,""T j-! -' I, -(77 I IboiT C. Ii) '-+! (f) rt.. cp EN 173 986 2C
, PROBLEM NAME DATE I ' z:;ill; 10:". 4t Jy;fnzjt(hrJ ': ; I 'n. j '" 12, If 2. "j ) '1 (, I 7- t:;\"-":-- 1.' J.6 J; ', ' J' "%""1 ' ',","-"-""" ' "'j """""'..:"-""i"""""'", ",,,,"'" """"- """',," '", <:; f,..r P P A(p<J ","'" rc,( CSh <, t t 7 J/' ( I <D"!'/r), /-4- JL"""! 6l ),,"/ " ė. '2.-,, j,... - """""'"- 1:?rl 1! """"""",, CJr ;,1' - " - :3 (/ ( '&>%2 " -Eftt') 'I EN 173 986 2C
'PROBLEM II) NAME DATE,IY'/'H<>.../' F /j ) 1+ /) - [ fif ; -J :, -7:> T,7 t, t",3 4-0 " """ """" """-+-"""'--""""""""-"'-"" 0 -ri.. 'f 'h't:)'1, I L tjllf;'c<. EN 173 986 2C
PROBLEM Ih/ F - t. L II The,Plniversity COLLEGEOF 0 Toledo ENGINEERING NAME DATE Ir {" 11 _!:1...3 / i prt ( ( ) ) I, 7 :. 7.0 2.' - 0y EN 113 9a6 2C
FIG. P5-54 5-54* Two 80-mm diameter solid circular steel (G = 80 GPa) and bronze (G = 45 GPa) shafts are rigidly connected and supp6rted as shown in Fig. P5-54. A torque T is applied at the junction of the two shafts as indicated. The allowable shearing stresses are 140MPafor the steel and 50 MPa for the - bronze. Determine (a) (b) The maximum torque T that can be applied. The angle of rotation of a section 1.25 m from the left support when the torque of part (a) is applied. 150 m(l1 100 mm 50 mm FIG. P5-58 5-58* A composite shaft consists 'Ofa hollow bronze (G = 40 GPa) cylinder with a I50-mm outside diameter and a 1O0-mminside diameter over a 50-mm diameter solid steel (G = 80 GPa) core. The two members are rigidly connected to a bar at the right end and to the wail at the left end as shown in Fig. P5-58. When the couple shown is applied to the shaft, determine (a) The rotation of bar AB. (1)) The maximum shearing stress in each of the members.
.". PROBLEM J-- r IIThe 7 NAME DATE Hi.nt f 8j I 011 L &>(flu; ",.', I.(s;X/;).( i ft- ". j, 1144.:x. '" c:i) - L.... T - -'- 2- v) d>l 2-- f" -,... ;(ltfiq'tl, j1tz-(l,'4r!r;, ",'t '. ( p", X ;f' 'f I i G d"7li(. ix"tj..- EN 173 986 2C
': 1 PROBLEM III' r-s-r COLLEGE OF ENGINEERING NAME DATE A/;' "" J '; G.f J'to J"':rr'L '- f& l( :c: c:.tjiu j"lt @" (i) T<fi:..IZ"i: IT(.. -- p q /,If/, M ) EN 173 986 2C
PROBLEM - - rf II The Ir-;niversity COLLEGE OF 0 Toledo ENGINEERING NAME DATE I "-;!A'i:: -, -' (J.I,. L - I I i t,,",",," d Vi i.,i."t?4f ( "'Jf '- C I G1)'i i EN 173 986 2C
5-87. The A-36 steel shaft is made from two segments: AC has a diameter of 0.5 in. and CB has a diameter of 1 in. If the shaft is fixed at its ends A and B and subjected tn llnlfnrm nl,trlhntp,n tornllf>: of no 1h. in./in. along o z.. - PROBLEMS 219 5-85Jhe two shafts are made of A-36 steel. Each has a eter of 25 mm and they are connected using the gears fixed to their ends. Their other ends are attached to fixed supports at A and B. They are also supported by journal bearings at C and D, which allow free rotation of the shafts along their axes. If a torque of 500 N. m is applied to the gear at E as shown, determine the reactions at A and B. 5-86. Determine the rotation of the gear at E in Probe 5-85. 50mm Probs. 5-85/5-86
PROBLEM 1./', I IIThe,r=;niversity COLLEGEOF 0 Toledo ENGINEERING NAME DATE (!) te:t.-",,/ 4't.../,; -+..1IId' --- T_";_,,,::...Ti,L,t ell' c.ll_.,'e.' J-O..-". C)...,.- M".TIi.'tI (, D,r,..,) TIJ.,.2 Tc r.. ;Yo (SJ, (: Q.." eti,' J,,'/"7 (j) If :f...: 2.)... d/r /' c:. Co G" "I i...,_._ ('It..',..'2.74'. - Ir {:' Ii 1E } l 3)... 1...,--- t.# III '1. "" EN 173 9a6 2C