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  1. 1. SOLUTIONS MANUALto accompanySixth EditionADVANCED MECHANICS OF MATERIALSARTHUR P.BORESIEmeritus Professor In Civil and Architectural Engineering The University of Wyoming and Laramie And Emeritus Professor In Theoretical and Applied Mechanics University of Illinois,Urbana-ChampaignRICHARD J.SCHMIDTProfessor Civil and Architectural Engineering The University of WyomingTo order books or for customer service call 1-800-CALI. -WILEY (225-5945). Copyright 2003 by John Wiley & Sons,lnc. Excerpts from this work may be reproduced by instructors for distribution on a notfor-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted.Any other reproduction or translation of this work beyond that permitted by Sections /07 or [08 ofthe [976 United States Copyright Act without the permission of the copyright owner is unlawful.Requestsfor permission orfurther information should be addressed to the Permissions Department,John Wiley & Sons,Inc,605 Third Avenue, New York,NY l0I58-00/2. ISBN 0-47]-27179-9United States of AmericaJohn Wiley & Sons,Inc.
  2. 2. ALLOY STEEL 5"""T'""- 5'7 F76. / -3 / -r FIG.1.5 YIELD nomrYIELD STREDGT14wPE1a YIELD Pot-01'Lowe)?vino pom? nqovluus OF QSlL/ EDCEui. 'rirnATe 71.-us/ .5 sI'iasuaqi{STRAIM AT Ftzncrurat. -'. Fez CENT ELa~sn'rioiv Assume-./.PMME 56617:;~cRmm Ta rare was on Tue Roz:Iasmm-Z(c-chi] (c) sue.Cc) 5'. (2) Marc Cb):Aw l: .LT: :7[9/v'yL(: '/ iill ex 1.. AL= **i-l. i. i -xtc/4-: -4 Eb/ QR - 1( /5) :705. '7 mm I sue (c) / ~1o (5): ,0),= Q/ /oo? o)= /1-72'~Mzl A7; = /2 3.2 / av (0/)l r-run nssemur:T, ', =C,= 5165) 5290* son Cc) ; (c/ _> / -U70 (a)lCr,"35:;= 37,7Mp, -7(65oo __ _ cps , _; {9../7+.3Mp.9P =60.23 MP3 /232oo A0, 7- '*-774j, =/7/ ,3 MP; F"fE!2 Pnessz/ rzE /5 APP/ ../ so:
  3. 4. (ct) Fiywua , gMm bah g I 2 *9-wt .F: Zv: (:: ,pa &"7" f: ~:: l / pug-574) ~ 4"?6/ Am / fwfI4',l7= l+P, ,L (09 Bygf-/ lv2)aw. Jll'1}. a.a-IQS 3 PSLS : Fa-l-4.. W (=9Var Frv-caimtcii. . , P E Vs " AL= L~. _3>(2rs_L_2 ELA L5. EQAQL-5 gt P :PE: /4 L4. 5 E, i4,i. :+i; ;it, L5' ' /4%; /75;-C/ -D, s~ .- My .1? t. 7.a. @9 , ,,w@@) Pm :/2:4. '44. l. S :(F-E_)[Ea/1a. ls) E5 H-L-Q.E5I9*; LA.n P :FEa. P4k. L$ 4 E, n,L, _-+Ea; i,i_,l'l" WWW M le awwm MA,24 __P_ ( Eq_A'a. [.gA Esp,5L, i-E, it. ,L,
  4. 5. _ Fl-0- coE, A.e
  5. 6. (C{)C0M4t; Ql/ U7xo%azoecazge /60/Vl L4vJ]-fxd 7(5410"6lll0~t (b>, , ;Z, v/ya? )J44 [wEf~Q-3)]cl 3 El;(5) (Cant-3
  6. 7. JWI2 EH2) x= o7P; >x: L _ Q gin t iw$5// ./ ea-rti, ai-21?. -4. -/ E5 75% blow the 13 A 50142LC.Jul:,0/A2. F ~~7Cel9= 0-3:4!Fn.AMl7"= .lafk) L:.7077- M,4444? A = l_{(-2077-L)2 (2770)(7-8D/ Crzx/ D7) :0.830 m CC)WEtt-(). X1~+=1'5Mo-A a, t7b&,7U; t. ofxizicet/ Ct (Fig.4) tut mww oi f}l. ,0g- W imam. wtvtttitna f75evCa, g=e( t9MJt7C5aZo1J Pa,4,daz. la: t Conl: -
  7. 8. .f-rdlr/7; .M .WWW .7ti7"5l W W M (ii) . $9! W / A ' 1,/3/ /J,I fmpfnil E/ "W .07; ' 9" MI 00" [, l0 / l/(I/ L}P "M Mil - ; .l W (L Sleel Vb/6/3: VC 3&3 (I Fpl . Fav M M(5.) M;N ill/ L :0.005 M (1,5)) WM 9% at ttL) 312.,C 1 ~ Witt/ MI tvrxioqll . e)W 9 b) y pg L N0t>)U'd gm t 7dl M 0'19;f H,,1 d-0./55g/ ml /1 . '0 -H Mmiw/ mM. .w P/41 / ,y-al). f,ce>""titan?
  8. 9. A 2 (6.S)(. Zoo +300) :3250 "W2/ i 7 _-.(6. 5)(36aJ( 19>) +(-s)(2td(3os.2;) =872ntM3 7-=2ii. s mm (at)G) 57 53-5,of F} MJB Me1514 ey-whomZ};: A+B-2i-Ml? ) :0 G ZTM, ,=3i5H2i)(t) ~l)(3)(-9:0(biT/ l7~rAo&. ZD~ri qcEgz. ,.@ , ; A=43lzH,5: 8Kil (C)lt/ titlt F. g.Q>) aEg-a. (C_)) M,in M4 y 7/"4"71& dhwwn (Howe).
  9. 10. l. Zl Conlf. Shear DiagramMomenl:DiagramFljUVe c.
  10. 11. 75.2. ? =f. tJ4 = @.s)[(ss.7-); )(, ,;.1+Y. ) _ Z- ;+Q00)(. s)(7I-95)in ? = 3-15(7847-7-y, )iin53s'@? ](a)k""(F-i~ 5),My 4nav; u2mm 4 V= .22Jis/ . E Z;of W:mum f, aS, T-tam Mr Ia =3-7-7/ ?XIDlmy,1l_jo Figurea.W it -4; Ft, t~n g. ;.'l'1mI7a): ,-_: .+2l0; ; +2!m; ),:[5D-30+20 + 1(0) +2(.3p). ;., z(5)]:-3.333 MP4. :g Ef"@'l2)i0-1 F5 a'; +d; ;+a7_;"$5 7 Q3)t*{'*'*3t)+(-5=77I)z~3.z1d1J, ;5 =29. 7:0 urnF~'7-I2.2, 7da4c1I'g~,1cjo# 4,, Y0- To l__x Z Fx 7. -U(5oI; trt9)-? o[a-9)-2;5[, ,9)=02+,= -T(S4iv-9)+ (, ,stuwi9)= o
  11. 18. 2. 0g= -390, 13:05; E34.@ Mgygzo),o"2ocr Ema":0, M ), @. ),amQCe) AL / Q=: /3/1, lY)=0) V): i'l/ ZNot dd Egw-(9 441a, ? 5.-, L.@ '620- rr)(a'o)(U'+ :40) =07%/ V-CI,0-T: 0MPa_) 0: __l0 Mpa)O:3': ~l1f0MP: ~nt[. ) @ 4
  12. 19. (M 37 Ewz zzywg ' (P3, 2. 1-.2 3) i-(
  13. 20. 0},: Xa:7+Wyy +' 0, =,; [:eo+2(co)+: o] =76.-0772 =1Oz+-mo},+J0;_;= +f; [tH) +2(lo)+2o_]By E-GJM 2-4),wk an Man 44( ).ET;=5'3ZT +5/-Z9*f+32.(,2 5 womydu W44 mg W -zw*%~W 574-Q? -7d, %e II :5D+D+10:lL0, I-l:5500) I3 :0 (C) By f= 3 W0 @- 20, 2:4, 422m,444 m, ,,~ 1; m. e I] : _4+53'. "..lg 11:33:77 09) T :* '1-3 I ea}. -.-/40 2. of(5)91 0 .45 / w%4"'l 'fMLo"CX_: Y)4'uoa4A oy7CE1,~u / Vlwb,k). L/rn4.u14/y--7% (qzotf):0 26:2: -a; ) + 26r; r; )=07lwa(Q) wgca 03':-roam,0', /V=50MPa,m a; y= (mpa,E;4.(3~.2.1) I, =.-40, I, _:u-534,,3:3 =0 (4) 77';475%-G? -wJ,r+-u0rf 4 new :0W 447:5 (4wc7-'4/4134M) aw0", : 50-257 MP4) d: :oJ g; :-70.2.5";MP4 0:)Cb) 8;, Eg. (e)m!2. v.3q),/(M446 :Ea, -;-r3) _ 70.297 MP4(C) 87 534(4) a/ m>@21); grog =,2;-l7:_41; . . 30, we795% T
  14. 25. (D Way x) 0}y; (7,T1,, ?=0-0:417, 4:1: 0,7?8J n=06; Efj? -4),7%, /.12/ Tu;/veo%L 25!,27,3; Wm,44 M % (xx;7;/ y,0g,W7] 7;}!U; z_)
  15. 26. may z; ;. (;, )) M rggaw, ,Q; l+a+M4ace;59' mm -0v47/"3n{=0-.318-/7767hHn=0 G r1;_'n5. uL'In =0 3 Q +'mL+177 -: .l 031I-{Lf4.Qj, ;4=:0 '787'+,M:I A /537) 14: at 0.0281
  16. 27. 511.4) [7 E5.4.(c)[email protected])/ur u/ rz L 7 zip cc: -o; )*+vrJ+
  17. 28. 33 Ej, @ + Wm,+2rr; , =0 97;+0/0+/ JV-3}"7 695:0 7350.907!/ ' "'3=0.e0? j f""0" 257, e5m,+/66+/3"'7)J:02 23- J +/77) J-H3 -/ /0 : aZg:7/}' me-;0,f/23) I7a=0.79
  18. 40. 2.410! I:0' + 7j+O_i, z=IO0/V170. rm 0;,40712 032 +y}y 0; .}__X0 -eabfo :0/f/ zoo 35*} I2'0'x7o;7 0?:0};55}:(Ta:*-90/00 5 0 3 0 : -7325 0; 0;,0;,0 -40 $0 03:;0'y+Oz-:2 50 75 0 0"1oo8-EMPQ, 03:-H-W MP4-;; :: 132,3 MP0./ mx [3 2. 2:
  19. 41. I Vxx +0},"(-_zz~= "90 -(,0 +4/0 . - -110I _{0;xO;7 0-xxoh 4 0;;0'7; : -90 70}+f-90-$'$}+}-60~90{ 3'0x7
  20. 42. .19, = .2.Lmgm/o. 4s50 = ./+3./3,-3437"and(g". _35) B 1 7/T546) / $1430 30. ____s. 15 $1 , =7/551 [. __9} Ea*-@20),a'3-s4oa"+17ooo=001- 0, 0? -5+cor-wzrzoz-4;) I :G75. 3 (,3.7)z+ (2 74.3); -pg 3.7] :/25593, 2 Tort 7- HK. I3WA-M X!95:9, 2:2, w4,. M4 out,/o'=I",>r= I. $6! Ef,4.[; {.t4(p). o, JQ. ?2F(rO', I,. ) +%-(Gr) '*'32g("0-z"r) -091315 + "5" :001 . . Y'2?qE. t+V; r%%"*'%9('a7r) iV'; -g-3 M " VB '0D1 20-?+_[)0"y. _,(_90Er _, '_0;Id;0 +-Br-:0 r-T572wwi E/4-Q-:91 vcw Wm Mu Ema: -so).
  21. 44. ;9;[r@as3o: rJ+? :,-Lr@~e)VzrJ +%$(rv; a rs>v'es? :'- reg,F(. ma.9) 1- r*(a~m9)B. =o,2 r(4., ;9)a; ,. +r(4.: .e) ? r + rCna)o; ,. + rams) _9zg1:+ r%%7 - r(m 590;,- r(M9) (I; ?4r"E, ;,p)5r =oii~*++--W +1r + Br-=9w, &,; J, ; ; V%, },4j , E;4.(; ;.;4). 'X*9~'13~> Idv mam?Ef4.L2-u4)-54 1&4-ecow W? ~7t#aIrfEfv-Q-%J: ;zJ24 5,. ,=0.
  22. 45. 4'9 Ef_Q_S-))X-= "'5-f-1 :1. oh? - d5 d5* 2? _.1 is;(R)X- 15? : ('*%LH +-m+%! n 3au 7% *3 E F Ma).we Omz (E)1*= (I mg q Ey. .; g;lCe)adv; ::2)*+'%3m+'''" (9) . 7(Ef""-Q7-53}.cane Ef4.23;)MmM/ J y
  23. 46. Before _c{eworma+/ on,vo/ ame :[6/v= (5'000}(/0o)(200),Afrer Jeformaf/ on,/e7 w/ o/+/1 a/ men; /on be increased 57 J T/ yec/ ep-f/ w 4/ Ifrvens/ an 5erom5 (W35).7:59 nal V0/ume= (902o)(/ pa+Jj/340+Serf/4/:7 7"/ {F 7"A/ a yo/ un7($ eyua/91!/65 5020 (too +g)[20o+ 25):5000(/ OM50") 53,.500 J + }? .320' :0: 0./9??mm Te d(5p/ azcernerlfj +4/('e5 of }/ ax/3 are12 =(05(, ]g'r *9): 5/I7 9/ ma :C0; 9/;nZ: (0 %= O E7uaf/ n (.2-7/ ) 7?: /sEX),:gLbxy:gxxp/ pa + , /., m,ma + x7(@ma+P5m, )= Q,S/59(0) e +67, S/ Ii(aj + ,7(co; "e-I/ has): -(f. "."_Z_. .Z1) 7/6 36 + xy (0; 29 ______L_: ,________: .__ Fm.P; /nc/ pa/J/ re(7('on X>, :0/ 2"/ )rfiv>, b?tan 29 =-* W 77
  24. 47. :.0. we s(0.z)2+ ( 0,aamj(0., )2 = Q20___/ >"/3 gm " .577 " EXX I 0.008.?-0.00/0 ~0. 00/25 :0.00026:2%, : 360, _g, gpa 5,,+ E/ n,m. . E7, 2 2 [(o. ooar}(o. g)(a) +(-o. aam)(_0-4)/0. 3)]:0.a073g/050.354, m, : 0540/;n, =o , (22.o. s'oo)' rnamze;a=02 cm =2 xn + mF3 M47iu0Lz000m.2: .Ha, ;:1,F0,0,5,0.0,0c.T230,44? TgL. )0/14?/710.4, uzo. o)=0 =do u_(o, a): o=c(, _((0,0) : . 0,025 =61, u(: ,1) = 0.oI2s'=0.01+-03 (B) M.43 : 0-0375' (awn
  25. 52. U/0:0) :0 :I9, ,1}'[o, z):0.0125:b,um,0) = a.0!15= 5: ,011,1). -.o. m2s=0.0.2:-0+b_, M. 53 :-. p. 011.9M (x, y) =0-ozsx -0-037;x/v(x, f) -_- 0.o1zsx +-0.01.25) 0.ot2.5xy(C)('7) Bar Ef4.@_), .2131}.=0.o2s 00.037:y,251;;:.0.olz5-0.12125!3,47: -0.03"/ Sx ,5%" =1'25 M'KXCA)"5; sMo')m9 ? -61),7tk.}Ju. m0J&i/ .4 0.00070 00.4 =%; _+J11[(, )+(, ?3. )f]=0025'. :7oL 25- D.038$9375')ro.0o078I75)7 0), ), . - $3; +-[B#; ,)-"6Jy]=0.01157:/25-0./20:01::+-o. o0o7'I. ?I1xCe) 5,:_; _(. 7"+g +%. };! .+g3,)=4.00030/17- 0.0!?190720: - 0.0010328/:5) +o. o0a7sI15x; ' E2? =6,7; =5,2. =0(C) FaraqoBcF. J.03)7tgM0p, ;m, g;M, ,, ,, M X-'--C"~ onzii 07:0 Z) A I B} Ef. ()I6%M4Q 2.51) (, d,4'/ y )(. :y: l4.4B)M:1-Lxx +4w*y7 + zxm 6,, -_ - o. o2u375
  26. 53. W (a) B} Ea= .,wk Wm W/ "7 f " /1%/ wI4 4/W E , : 3._. : 0_D10-D3757 #- Xu 0 0:15 -0- 0 0') 5,),=. 7 ='xy :_, _(%; x 1.3%) 5 0. 006z_. .o. o:%75x-0.004257M, ., ~:J13, x= y=/ , a4.a0Ero-Ga)/ W 6],Cow7a. wJi Jfa Zia /3/MM WW ""IWt e-: - .0 95/5 , : _(]_p,1;/22jyy'. '.. D.0D0703J fxy D IXX(8) 5; E7447) a4w(7(_Y}, M = ,!e, x+m2.4,7 +21:ex,= -M19 *5 B [E7~(aL)j amu WWWW WWW Le-; -L4')J '1 . ..o. oZ. c375j(-0-025), /op -_- -2.547, (0.o. u;37$
  27. 54. LL 2: H(Lx ; L_-X) 1- )7?) @3 U:B(L7-. XY) + X) (9)wlwu,Xcx)aMJ )/ (7)4; XmJy) .. 1L7(2z: nz/ /E;4.(_, g, ,,4og@ ; ,,. z;E; .[c) ua. (Co .
  28. 55. whu DaM4?EaM- 7/w,31 23414),62),axwV(f),we awu: f}(LxJx4-JBy"+Cy+D 3) u--. : l3(Ly-2%)) - Cx-I-E . _ (N'37 _E_616- =0 +. )_5", _L. 7_:2z)/ .. +.%: ;o+-0-F+0; F91,)1" L L + e?_~_'_)Y. _._ 731+ 7; = ;>0+O o+DX+3za. = 52, W 2 =0 4-0 M xo7 * :3} :70 +07Lw. c, 5:0, E2:-01, M42 C= F=0.
  29. 59. __ D +s/ 5;;= 5m 57):6'6) EX) 7' '"(15b" "~"6-) Ca) 87 Ewen) and Eo. ce)waP(F) r 1?u; %1ID,We /(gas;gt) 4.{(64-6c)7, ; [1 Eb-a. "'Y-_} 1 1.J/ Z6Gym5a_)> eyy-; ) Ex:5r'; c B] E;4.Ca) am!1-3;4.(e_) do-66/ / .-9c: z7c6v 2.10, wo19ZI'6' Z. -1 +(2a_" b E): -+6c)? -I] [/1B;574.09 awe 90(5) 072 E; -mf, { 1.10, we -pzowt120.215: ~1-1'1" =1=+ R6. =g(c, ,+a, ,)-R =5664+ 5'.0 _ 0-7(5'_, M _-0, coma E " " goo/ .900 gap/ , 000 '*V : _ 4,27 }$S,0 = 0.oo/23 tz;I-7;("7 *E7]I 200,000/0+ 1LX:gg0(/ +0.ooaoe) =6 / .60 mm d.80 :800 {/ +0.00/00)- &___. .__/ -7 L2 0'/0,,L/ ;-o, oo/ 3) =7,77/nm
  30. 70. Fwm FNL R78) YX] =355 64." c- Wfl 69.:0490250 66b :0.00/I40, c =-0.00/2 $= m Xxy= p.oo/ sf./3; Ta/ c I,l4Penc'/ ix A,E:72.0 &Pa) ,2 ; o.33.C09 Sac,a; ,_. =a',2=o; ,_. =z2/ L= ,4.Q3_.3z) udwa713:5? (er""5vrI O5):5 X9"_ 77~0 7/W0ce,0;x :0-3-3-, ~_I_o. oo25 r- o.33(-0.00/25)]:|I, g,u7 MP4- 7 m ,- =-34.34 MF4 W ~ -l_3;_3?[o. ooI2s+o.33c 00200)]0 = - 72'" (V0.00/$9) = = 4I-75MF X7 204-0033)By Ef4.Q.57), 6} =a(}x+%I+ I: -(r. ... -0m+0;; 1" '7_(l68.(=7- 34-34) + }I(I68*-;7L4-3g. ,>. g)7'+.4/.05"$7.16 I (07.83 :1 17$-?7 MP0OI-:7.! L ~10? -9} = -I-"7"IP;0.4133) . ,?49:0-st: ImI? :,7.? ./ISO0 II-Reatercncc ElementPrnscipnl shes:Element
  31. 71. i (am _ g; ,,. ,,)=31.0:-0;):;'{:7c. ~'1q+4ze7)2m. : (0183 MP0.5frc$5 ElementWM 0;,: 9o MP4, 07,:zzom J K =5oMPa,E$-5- G-30) >/ fa/ J6,9; : d; ,(~ V6,):3'5-I- (so o-270/20) =o. ooo.21L0000) = - 0.0003138:,&fa-(e)a4Q[9 of Exanyf/ e -? -I0 The I31CIPaI sfmmsY'Io: In/ e Eo Q'1(C)(-JiIC0'0w323)30. _ 0.0000102I3? E$. Q.3'I))f>r'fVJCIF4{ 57LI'5555 V9/471/79 0(x. ~1) axes are given by - U f 00: I"cr__0r :00; 2 . . -80+!00 + _ 2 1- ' 2. "I 50~ :/o i 101% :u2.%} -92./ MFATlu ; IwuP7e/ waf. /s, a,, .,. , /2 0;_e:0. QAWLV0'7: / /2.94, 4;:0, as:2.74 [Mm]By I: f
  32. 73. 10- 3-33; Swrcss compmea/ s are, /4 / WA,(Ex _ $0; 0/Y) 3 / M) 67: 50* f;3:J}-3 : y;5=0'-Bj Efd-(3.30)) (he Corres/ Pmo/ /1;; /4 57"/ '4/g Cam/ mic? /Zl. Sare_.I _ _ 3:. .. .(xx -J; -I-0-w(-30 7 245/00) 0 Fm,f-In J, ;.e{, '., y, 20 (gunre/ acwaie {rum flu XMClsJX :C0320 :o.737Z W:sin 29:0.34.20} 01:.o.Txm-, Core,by sg. .g. e1), gm :@.4:m)"(- 0-000 945) + Q.3ce20)7'(o.oooeL, )+2(v-r3r7)(a3~no ; = n Ewe =. ?.o| exIo""yy = -(J; y"V(; x)=0-0; :Va;:1 0.33x200. '65/IA: -" 71-eA (la)3,1 =25; . :_ 2% :_z.73L. r/o 5',22;.= Z21: ,2:_'ba1 susvxto E,5, 5,279 E?E;:s, zo C c)V? _z. = V32 - o_f. Z-9 -; .5?333x/ a"'5' E} 5),"' M45 _ :2 1.354? W430.574(5)44'-9 Wu:=7"W/0;) "2!MP5 (2 Q3 =1-rWa. , 3,7: n3oMPa,6;;=/ oamupa,,3=1L0Mr5 44-12057?:__=0) Ef. (3.. S'I)f. LMg V x _ _, [g,7L; up"9[2-I) "{"7") F511?-$=0.DDl*l:7 A Ey Z10- Q ,s: ssa, u57(-z~7)- - Evy = ; =zo; +:; ;, ~%v; a4z. vsu9/72+ TEo'_ur?5_ : _/2.27 (/2.27Z. >w54~) (63 551-rIn 3 .7eEfL@ M, j(e) 4914M:/251.9295+. -res;tfe 5""""M- 82. 37 F56. E77-/ a, -r/ rs Line. -r/ x OF 7:noozn mavaszz GD /5 290077/:/.2~cS9)q (0-'81)?/"V; ;p)/7760// F/95' C5136 =0,? ) 05 AA/ D V50 /7R( 57'/26:56.1" / -V trap/ >-pas/ ?: Gloxwvn '40) 4 75 2 / Min /4 ~ mm / s 1211* CROSS-SE-CT/ anc /912:. -A O/ S509 @429.Fox;c=2m7, C-'D =0.000833 < 6},(6) .0.00//75),ego =5:0 ;Q0005-33 5, ,.540- Eco:0.00/06? 4 e}__ED .94: V/ El-DEDJ gar B/ vies AD mm CD 425 smsrzc,4,. /o 030 =232.4/+ / a9oo(, oo/ :57) =250.57 / '7/a,mo =ago =21/ / ao{o.00/067) =22.5199 /17/0,,P =(2eo.57+ (/ .s)22599)6 83. 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