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Lr;= 2 (12S9)+2 {S:5"1,.)-1/,77-11f.s-3 =0("c.hcc.1= )
(t1.- Ld C .De pni"t of ihtcr.sccJion o rW )j ,'H, S,ound. Hoori-1:onro..! d,·,frtnce- fr-,;n, B +u c r' s
d.-=(22i")SiY) :'0°_ (iOin.)Co~ 300
::- 2.3"+0 ln.
'"'*',,:\) +~LMB':::D:
c •• j;j.} Wd - PC 18in.) -:= o~i~ (Iso 11)(Z.Slfo iYJ.) - P (IBill.) -;;.o
.w) 18in. p= +2.3.~jb P=23.4Ibj' ~
;GJ:~I' Z 'F:: O.: 2B+23.lt Ib -150 If:,=o~.;i,.i9 .. ~ B=+7.8.3Ih. o:=78.3Ibt ~"dl~ OJ)JJ~~!f j\-) ~qD ~J1' -l(~ (a.)+J Z"Mk:-=O:.~i~ 3 I 45kN (20k,tJ)(s'4m)+(2ktl)(3.Ltm)~<,i~ +(LfSkH)(o.5m)- 2 H (2.5m)::: O
f/:::+27.!f{,) .jj =27.,u!t~(b),t)' L Mft:::o:(ZOf::.r<)('Z,3Y") + (Lkt-iXo.Clrn)
_ (lf-5'1: N)( 2 rn)+ 2 K (1. SrYI) :::0K=-I- 6,OIf K=6.0ljf:t/1~
.!-ttt: Z F. =: 2 (27.lfb)+ 2 (t.otr)-2 0-2:l.f 5"= o (Chd~.s),,,,]) 71'J'Í~o" NI!c.. '8D<Ój: 8oCY'r] f~f3 c
(a.)+~LMB=D:(20 }çN)(2.b",)+ (2 k!1){ O.bm)
-(20kf/)( O.lfrn)- f (O.7rn).(.J) = Q
E=61f.b*;I~c:o
B 11-} c..p200.N
13 =0h
B; -;20 -2-1.0- b'+. b
B. -== + /06. 6 (f. I'!)'
2:::: /0(;.6 ktJr
e', /',~,,~
-t) ;EM" = O:VI (7.. L.ff t)ú:6 IX -t-(L501bXIVft) ú)) o:- (Suou U,)(7 H)+ 2D (IZH)= O
/ SOCúr.b10/-[- ~ ]) =' /"f':lB.3 -(v/+- IO'f.17)Wex:
(I)B 11' - f6k,"'S W = 600 Ib and
C I D c(", 1+5'" in Er (I):1 C. 2.:e]) _ () lO Li Ib
- 7 fi; 5 ft - 10 .
4l$ rtL"r = O: 2C +- 2(Cf6().1f. Ih) - (600 Ih)- (h-ú Ib) -(Som 16)", Q7 c=H~6~
(o) f = 1%5""/6 r. (b) ~ '= 960 Ib t ..
4.6 Sc.e Saiu"';'" of Probo Lr. 5 fuy clcrJv,d,OI ,,(- c1.(I):D:::-ILf5'8.J-(Wi-/Olf.J7)i.osC< (I)
V/'h~r, trvck' is 460";1' rú tip, w(, "''''v~ ])::. O ,!"\a.K",''''3 D= 00..>0'( vJ:= 3000 lI::, ,." El. (I)
/!.;'J-8.3-jIDI-f.17c"sC<:=0 {;{=62.D· ~
ft-.7 .'Replcu:...in:s 15 ~,'f' p/ P;'1 e;vd,o.,~ ohfc.-iM,.J
11:1 SolurioVl 6, 5;a.""pl,,; ?rcb. 11.2., I<I~ hc-V':
'ZM =0: .A - P (3 ft) -I- 8:/ (q Ft)· - ((; k'r~)(iI ir) -(G k'rr)(13 .ft) = O
?:= 3 73y - 'f8 k,f'> (I)-+ 52:' Me, :=0:
-A(CfU) f P({,ft)-(6k.psX2 fé)-(6k',p;)(lfft-)=oP -= 1.5' fi T 6 k'f-n (z)
S/me 13J\~ 3 O k.;~. Ôj,(I) l/di.:,P:::. J(30)-'r8 P ~ 'fZ kt"
Si",,,; ó::: A ::-30 k'fJ, Er (2) jicldJ0+ b ~ P ~ /.5(30) +- 6) Gl:lJ:: p ~ SI k0 <J
R.A"S~ ~-f valv-c.s f",. vJJ.,;c4 bea", ;v;11 Ix: ,C\f~ ;,S
6 k,.ps :5 f'5 LtZk"r> <$1
4-.6 T
3kH I fBA r d30
h-r~ 2.UmD,5m
+) Z!"IEl:= o:
J I:~I -/
0.75".1
(3 f::N1. 0.5 m) -I- r; (2.25m) - L2 (3 m) = ()Q = 0.5' I..N f' 0.7')-7; (I)
+ ) 2: N..D-=0: (3 ktJX z. 75....,) - Te (2.25",) - o. (0.7Sm) = c)
Q:=Jlki'l-3!ê (2)hr' Ú'ble (J.{- 1) nO!-!D ~e "i/aLi() ~:: ~ Cl,)d frtJrn (2), Q::: II kN.
(Df' cabl" a.f j) noi- fo be s/t1.c~ 7;;::0)0'1'-.1 from (11 Q ~ O.5h\
Fo, ne.i1her ca.ble fo Ix- sltltk; os kiY ::: Q:: íl kN ~
4-.9 Wc sh •• 1f lJh' 5js..(i) cmd (2) o.hro.,.Y).d ,.,) 'Rab. 4.r'3·For ~ ~./.f k.N) C1- (2) (/eUs.
Q:: /1- 3(lJ) o'
For TIJ ~ IfkN, Er (I) ;/eldJQ :: 0.5 +- {),75 (lf.) . () '::: 3.~ k;J. <:J
71,( 10a.1,·". 1'0 Ix. .54 fi: eabk "'VIr al,o nD/-6e slaef:. COY>1cin(tJ,j'
'>'r,'I'" CO>1dlfl'wJ~ cbrarnd il1 Prel,o lf.8: O.S k;J :: Q ~ 3.5 kN ~
39
T3~11:1/~NI I • L 1.71t1o.~':' ().75~
T-D
j)lQ.
r tE• I • .1
'0.75,.,
30 \~ 200 ti
+') '2 M", =0: (3 kNXO,'Jn,)-(J kNYO.1SNl) +1(2.Z~"')- Q (3 m ) -= OQ == 0.25 kN + 0.757.. (I).D
-1-) Lf'IJ)'" o: (; k.NXZ.7 S-,.,,)+ (i <1'1)(1.:;"")-75 (2.2:)M)-Q((). 75'",)= O
o.=:I':Jk.N-3T'à (2.)
fM- ,'1-1,:: foa.d"~'S -fufj-ddíc.<-.obln Mvtr núl:-bd!oc.I\"..:..d,
';"""""0" rY'vrr '101- ·xcuJ !f{,;;N.
/1,d'í"":r 0:5 Te, ~ 4- k N ;" q.(J...), ~ ha.ve
/3-3 ('-I) :: Q ~/3 -3(0) ./kN ~Q. ~ 13 kiJ
f'lok"/tlS' 0::- TJ) ~ 4- k/v ir, Er (1)/ vk /r,ol/r
().2.5"+ 0,7O:;(D) f Q:::. o.Z5"+ O.75'(If)0.2.5 klJ ~ Q s 3.25'" leH. (1+) <I
Cu-mb .."',·",s (3)ar0.(lf): JkN::Q~3.25k,'./ ~
5,'l1éC/ !Y1t'4imvM 1~V1~riJY". ;'1 Cfl0!e /l-EF ,', /..fo IcN)VI( fY\v, I- •• 1\0 h" v'<'
C0VY10M/'I1-S r~';oJ/fJ ob~;,<d I we C-<)vIc../C)(/'t' /i-.At!'Me. MI'-7/'l1 v",", /ot>c1 '"IIh.r'd Mj 6< rClik'd ts
4-0
Lr.19 1 nc. IO!J..;'''rl~ 01- r,,~pl.<..1-e ií <:')VI'I/"-}-(Y'f tIJ a
Cv <.Ir k of TY\ 0",<,-, r(800w)( q. :3 ,." -' o. 05" .m) :: 20 o rJ· ~ )
lhe. íO'" f,·I>1!. Cl {- f1~..,..{ B / 1h-("r~ fur", / r" vJr a li:. ()
f(]fN'1 ,;.. C4-1['/c; r-;'Ar- '\ bc. f'''-r't. /I~I "'.., ri. IV.H: fh"
S",,.,.,,,, /"<\AS,,,'fUt-!t A",; ótrl)),'f( SCI'1C~.
T
~
.B~B (a:) a=o200;)''''' _ _
().l.!"". ') . r.J::2H;l =0; B(o.'{m)-200rV.m::()t 8 ::-500 N
T~/t :3 -:::500 ri ~ j E -=- SOCJri <O- ~
t~ (b) o( ::- 90D
20~" -+~ 2:HA
-=6: 13 (0.2Srn)-2o!J tJ.rn::o
d B= 800N.8 ::800 N ~ j .ª :::BOON f ~
B (c) c<:: :5(/
+JZHi\-::o:(.3 Có~30' )(O.'!rn) -(BSin 30·XO. 2 5"")
- .2 DO N' "'1 = oB=Q03N
{3 -=: 'lo?>rL::f.30·;, ê ='10JN730' ~
B' L2C0 I)."" ~O·
JT
o.LJM
_1o'1\~1
f: 0,25"1
W ::::::(20 1!.:J)(Q. FI mA '-vi= 116.2. N
LF;..-=O: p,::::::D
~C'_ • T -WL..I)-O. 6E-
lSé -= J1{,.ZN-<&'l
4,20 75,.,.., D
~ D_
~
c1 C "'rB· ]j)0" ••.
t· O '!! ~~(J71< f-urLe.'o sh.ovJ.., fo •...m f.vf) C<)ufle~.
.05"M ::::0: A(200"" •..•)-ÚQ{,.2.tJ)(7S,.,""] = OA == 73. (, N
ê.-=73. (; N -... ,; f: -:=73. b t-J-
w -= (IS ..Qj)(Q.8 / mJs')vV::: 11..(7.1<;; N
+f'2'r; == O'. P -11.f7.J'5tJ-=U
fI=-I'-f7.2Nt 4
+ '2 F ::::O : T - 1os: 1 rj = O-"";>t. A-f) .
T;.D ::: 10:;' /1'1
.f:\(,·,,1tºl~
(tt)+J L.Mfl=O: 8h- P(d+375) = ()B(5'7.'t5) - p(lfB.ZI + 37~) :== O
B-=7.3b7P (I)(:~
FõY P=2SDN: B=7.3b7(ZSOAl) §.==/8T2f)------·~0~
(1)-1') Y/-(c:=D: 1\,J75'rnm)- P(37S-rf\M):::O O~t\/1",1\/,,::; p ~ 2:;0 N t1n,{ 'SOIV/hJ' fr;r At:: ~S;i~
. r.t -=- 1250 H 4 = 12)-Ot-lYLf(/' .~'"
!t,25 S'e< s~fvr •.v.., o~ Probo /.r.2Y fuI" P.8 d"~It,~t:J-of :sFr1V1Ct" ar..,{ f7X *riv"" 1-,'0>1 O F- ~,.;. (I) t1.n/~1(!l
(a..)The YlJo)/,((n t ó6()u/- C af- /),< force '!3é
C,i"'Cr ,ctJ GNli.!:J f1,-< sl,,,,.f t ~ tf..c S'fA rlf1<r m v, /- ",Iso 0<' 75 ;J'iT~&\€.Or 75x/o3 N,'lYrWl·._ ~vb(h'I\;'h'Y1!s fAt'r (.t!u-( fr:r liii:!,t1J75"mm),l'Ifo Cr(2),W( htlLl-r •
+5 L Me:::: o: 7S,,; 10;' i'/.m"1 - P(J 7S-rnm)=O Ôh~';I"
P=200f'( P=-2ooN~ <<:.
@çB = 11( 73 tJ '--<'- ef';;
Lr.Z9 f, ~LF;=o:10 2JJ" ,4x+(7':n6)ÚJs.2.0·-~'2..01b)c.oslD·=O_
r 110lb 751b It =1.t7.7/b A =47.7/b_~;<- -)I.. ~
18ft ")2.0 lb +-11: 5 :::0:
lA M fJ.d-32D/b-(/20I~,"n/o·_(7'5/J)s"fl2ú)----1'"' A - Ir '=' O~ t (içJ ~ 3 (,h 110 ~J =- 3 ó(, lI, 1 ~
'-1-) L l-\A '" o.' Mí\ +- (120 U,)c.o,10'( J8k)-(75' 16)C.I.S 2.o"(tsFc-) = OM =--85'7lb,!!: M = 8H /b.ft) 4
A -ft ~
-;-)7!'iA- = o ..
MA r (100 /b)4:,'ID·(J8H)-t;ÚJ~1.JJ·({cN~
=0Mr,=- /6.1/4 J;. - /772..7
Wc.. ><lO,,! IM,tlI::; 1co /6.f-(-
or-qoo ~ MA ~ '100
Sus,;-iM,v,~ e/Cfr<:l..S. ..o ••.. obfA"".-J fu. J'1,4:-100 ,; /6. '1 /y. r;, - 177 Z. 7 ~ 900
8 72, 7 ~/ 6, cri Lr 1. :: z. 6 77..7SI. 6th ç ~ ~ /5'8.0 16 <l'lJJ
J!f =/(Jr, 'Yr(bt= 75ff'1 I~ í
-I) LME; =0: I(20 WX7.z")+c2NJJln,,.,) I+ (20/<.,))(3. óm)+ (2DkJJ)(i/J~) I
_.( "'~ T)( >t. c;"")1- ME =- ()7. ''''
16m
1.<\....la.. 1.13_/Jl.... 'F tI~rt1é ~'\!
c 4. 5 >r>
-; 1-"lé
-=-(3.b «I) T- 36 o t...tJ.fY1
w( wA"r IMEI~ IOOkN.!'>1 Dr'" -IO{)k/l/,1"A ::t\_-:/CtJkN./fjc:
~ub \ h'iui-,y,J i1J~ -<,:><prc>ss,c.w' ob f-c;.,,,..,,/ fel" ME:
-100::; 3, bT - 3 b o::; lO OZ(,o == 3.GT 5: !f60
72.2kl'!.::: T-: /2.7.8f:JJ
+):2. M..D :::;. o:p(3o.s;nB) + Q(ú,wsV
- Q (2 a ws e) = ()3PS;r1 o = Q Cose
tzuv,. e -:: Q/3 P
v:::+CWJ-'(G/3 r)
Ii~]I
-I+)'ZMA ~ o:
M + (300 ;;)( jf,3.1Zmm)- (300N)(180.rlln)=0
1'1=(:300 tlXIBO-/63. 'l2)m"1 .
= 4, B 2 )/'m
L f=o.' fi.•..-JOON+(JOCJN)c.ns3S= oAA- .=' + 1.;0.2 J/
or ~ "'"I b 5: ';0
1+-, 3 5 (tJ-) Iric.n~k Af:!:. I~ iso~(~h"Wc ó"'"C-
CD =(BC)~., e :: .( c.>~~L 1-
+) 2:: Me""' o:P({c."se)- W(fur,n:::D
5ettr'h::J Co'> l3 = 2 (.,J~'-f - I :
pe (2c..os'{ -1) - V/e c..os f = c)
~~ vJ B' - oCo<' Z - 2.f' C07y - r -cos Q :=..!.. (vi"!: J v;! -f- 8)
Z ~ P P'
V~2~~-'[-i;(~±V;>B)J ~
0.) TriA0'!J1<. ABC is 1'$osc~l<s.
W" It I\Ve.
CD -= (8 e)cos f ::-(C-os f+) L Mc= o:W( {UJ'o fi:) - P (-{'~"nD) :=,,0
Scth'''3 5iY\e-=2..S"Y\~Cl>;f:
vlJ:.ú:,s Q - E 'P~ s;" Il c.,,,0: -= ()1- ~ 2
W-l P5in T =0e:= Z Sin-' (v/lz"p)
S·LJ \F-VJ 02.-'h.lL "" - - - -= . :;,z f. P 1f'.JJ .
i -= /4,5~ tJ= 21,0'.2,
ti ::-n lO (disc.o.rd)
C<J\ !l :::o,8Ido?- l2 -:=:- 32.5"3 oz.8 := G).l"
[.0' t ==- - 0, 51307..t!. -= /2G.J8~2-
f) = 25""2.. 8 o(d"!.t:McI)&-=-6'5'.1" ~
(6..) T ...•.o.r.'Jk !!-13C 1.5 Iso ':,ce/-o.Wc- hÁv~
A 8 -= Z ( AP) = 2.( 5 in iCD = f' C<J5 t
E/cYl'J a 1-,'"" of- S priYl3 :;r=(AB) - (lt8) .
8 &=-60
= ')! s in t -2t.s in 30·T-= +7.. = 2./ft(5in Jf- i)t s,"" B -
+~ 2:Me := o,' T (t úJS q ) - P( ts;" ()).=- (). 21d(Si'J~-t)[c,)$t -Pf. (2s;n!c.Ds!-)-c=.cJ
cosJ?:::o cr 2(fI..-P):;>in.f!- -1"i'{=:()2 ) L
&=- /co· (tr;vl"al) 5/'1 fi:::::: j kt.Z JJ,f-p
&o=-25in-'[±-fd/(Rf-P)J ~
4-.36íA~f
I'rcc-.•.
fi = 4/.8°
&=83.6°
(I) 3 non-c.o.--c.ur"'~nrJ nO~-for4.II<.Irc.o..(...J-loV'\,; .
0-. "1(\.J',) c.o""Fi<.rcl~ c..on~rrn.ivHd.
b. Retlc~,'""" 5\,0.7",,,,/11 Jel-"r",in~rc..
C. Eq..,i\i\"r"'·~ TY\O.;nrc..;"""J
A;x. '::' 6.b 7 k,'(l, AI"" /Ok/fJ.8 =- 12.02 k"pÁ56..3j §=-6.67k.'fí .•.....
(2.) Con~urren r r~C<Lh'''''1 (thlll0:1h ,q)0... Trus~ iMf('0P-"'1 C,ond,a;"",,-<,b. Read,'""" '.,.f-ú.r. in.hl-en ..,;,.",Je
c. No e,\v ,'i,'bn'uW\ ('LM/FO)
(3) 3 ~o~-(o»c.v,...,..ent, •..•o·-Fral1c!re~cJ;l,,)V1S.
a.Tr\Jt~ Cú,,",,?ldel'j c."",..,rrQ.;<M),b. Re",,,h'o,, .• çh.h·c",lIj de~("""nah:C, Ei..,,·lt'br;UM "",,,:,, 1''''1,>\,01
.e -= f "'-5x/r' t(4) Lf (\()"-co,,c..urrrnr, Mn - pc rAI/< I
f'"eú,C !-ro'n !>
0.. Tr..,\( eu"'pld-e1i (o'" S,{-'n.iVl<'J 'b, Reo.r. r,'oY1J 0u. t-_ i~ fC('l'l1:nc,te
c' [,u,[,l,r,l,/'" ""aiY1!u,l1edR ""r;,67 k"hl-"-)" B =(;.b7k,k4--~ 1-' -~ I
(A1 j-8~'" 10 k;F)(5)lf Conlv('T"Mr reo.â;o~s
(t'''i'W'5''' A')0.. Trul5 iTY\f0'(Kíl'1 l-a'f'\ r"l;neJ .b. 'R.e"d'IO~.S c1",t. i\\ile j~fMiM+e '
c. No ~uj(ilar:v'M (í~ fO)
(b) Z. r"~c.ho""s
Q.. I ('v\~ fC' (tla.l\i ú:>"Ç, Irú ,V1d6. RUlcf •."",,~ Aei-c,..,......,,,,,,,f-ec. &ju;[;ta,.;""" Yl"<;o.<"\-o-,,,, •• J
undcr S .,,~'" \0'" cl •.~':l
8 -= ~ == 5 l(;r5 t(7) 3 "" •..-c.oo'll,-",,,,,,rjJ\o<l-fcrúlkl
r<:'D.c. h'c'" >CL. IflJU Lo,.." F'1e*"l\ Ull"\sITa;y;db. Reolh'"", c1áaM;",af",c. ECI',Jii,bY"LJWO MAiV\t-a..'h".1
~::5k'rd; r:;::b.C7kif>-!'_-8. ;, 3 k,'/,," 2. 3G.1"
CE? 1. lt f'\LJ'\- 0<\lUYTeV\f, "'.M- r",ra Ilelr=th"un~
eL. Trl.iC" C<)Mple!-e.[j (.j",rro.i~p.{
b. Rec<ch;"..,>. :;f4/-.irv1cr.(ff\;n:../-tc.. 0ru;)'f,r;v •..•.VII" ,..••.rA:"''',),
LfV,c..=O: .flJ
= 5i<'"rl t
Lr.irl ºr- o.q lY1 -t
";:~IA~f-~ A-J
D C.
111;p
..z.
.8-'1. j~A-.;
]).D -:;-~I----,
c
kJ
(Ij 3 n''I'I'l"''leJl'Y,,,r,n'''''-f''ralki r~(h'o"r
0.. P.t..'h. """"'rl<\-(Ii' c.",,~tr"';n,<l
b. IÇ"""tT;<Nl1 ~tl "'l~ Jct-c...-.-\",,,f~c.. E1v1iibriv •.. """;,,tc..i,,<d.
A :: c.:: 245 N t
(2J 3 non-cú"ú.)rr'< •.•r,J\on"~/kl ("eAch'vr;;
0... Purc Co""'rl-dc.\~ (o"d,..";"",,,(D. Reo.( f-,'o-ú sffi+;eo..l1'[ c\e f-am:>'\1r .••c.. cCf •.•)l·ll'brl\,JY't\ ,....-(l ;."...,+o..; .•...-(J
I.§-= 0, -º: '" E?'== 2 '-15: N \
('3) lf nO"l-1.D",-vrrr"f,M''I- f"calkl rc""t,'olll0.. ?lG.f-c ~plcftl'1 (o~.,ir()..,'vJ.,.,{
6. k?~Cl.l h\,M\ srz-/: irdcrq"":"a.f-c
C, é'4l.JLI;br'·uM M";•....~,·.,..•;c(A = 3b8 1'1- j D = ]68 J.i--" (AJt'11 = 4~~.S 1'1)
'(Li-) 2 retJ.c. h-u,",s
. C\. Pla.fe rarhú\ ~ I.DV\dra;VW'c{
b. R""c!'\)n S da.hc.J11 det",,,,;,,,,,fe..c.. ~l.Jil,' bc:"'W\ """,;.,t",·", ••d uv,der
".:t;v<'\ loc.d,""'.sC=D==21.1':;N\ I
(5) 3 ()lY\-CO,,\lVf'l'1"vl+, r,o"'-porõ Il~ I rcoLl-'CiA0... P\?k CoJnple~l'1 (O'o'l\i'rn,'","'; fb. RE'~'~"Q"'~s hd-;(c.)~ d~ f-r••.•..;:'~+e 'c. =7 v,'I,'br-,\) W\ ma,' n rtÃ,·V/..-d
§,= 36'5 t{ --; ?=bI3 N~5'3f
(6) Z "'~o.,ho •...sCi.. Plt..h:. Fefi .•li, c.o"" ••.f-r4..;",~db. Re,,~h'o""\ olà.'''''''~,.l-ft •...••..d'1o'1Clfr\,'.c:>
C, No e1u;U,,/u""\ (L. ~ =f O)
(7)3 W .•..•ll,/('o{'("'r rccccl-,,,,,,sC+;,rw:;toD)0... 'PGh- ·lvvo.P"-"P"'"l ~J'\,Ir""~"d Ib. Reacf,'o"'l tlre rI'z;r. ,r•.,{er.,..""" ';O" te..,c. No .('Cjvl\;l.;,r/uw. (2:'I'-1j) 7 o)
(8) Lf (0" l",rn"r r"~o..tf-,'t",( (furuVjh:0)rJ-. F1Jt( i""p-up-'íl'í c..:o",drtl.i'''t'J
p. R.~...or,·"""s ewL stz:..t.ir,J~rcr"';"'Atc::
C, No ~",ilc"'"'''-''''' (:?::. M.D 'lo)
('1) Li ~u,,-c..)I\lVrrcl'\r, MV\-psrdld r~et,O>1.s
(L. PIAre i, co""'rJ<+'/1 wv.tl<o.il'ld::. {ZCC1ci",lMI M~ do.r. i"ÜN((,.,,,h:.c.. ~v:libr;l.J"" i\..1fIilill\ tc..;"J<,t( .
B -=D = 2lf::),N t- -.~(C +.Di'. ::- o) i
ii______________________ '"_tc::".!
A '.é'-=3CON~
BA = 3001\1 = 2.2)0 N
SJf\T.í5.. .8=2230(1),..7.73.
B= 3CúN =Z210N B~2210N""""~t1?7r -
Fn:e.-tod\ J)io.S'-o.YVI. As ir is rv.i~~cl,f"c t<l-n K:"i'" 'Z 3 - rDru: b cdj . Ti,,;5/f-hc {,\,< oF- c:u.r;" •... ,i- 6 '-'It F~"rhr()~" 6 WYl<~ -fh< 1,'"n aF o<r.'o.of- T OY\t\ vJ i",rc0c'-1"",- -
GD O,Sm -o ç- N-:::60'Cch c< = A G ::: --;;:;;- - ../ V\
{} :::± c< ::: 3 o'
~V:::(250-{edXq.Br .,;,6').:.- 2'153 N
FofU' Tr"6~,'\ leT -= vJ ta., ')0" -= (21.f5'3 N) fr..'1 30'
T=!.1f!6kIV ~A::: -i::!..- -= 2lf'i]N = 2832 rY
Co5030' Co<; }<10
A= 2.83l<NL 50" ~
Free- bod~ .D ;DaI"-"'"( 3 • fo("( (: b od '1 )
The I,"'e ar o.e-riDn oF A rnvsrOa.'>'> -K,"'OI)~ h C ".}'n<~< BI -.l)C1nd s"O-lb locul i"dns~,t-.
w( rJ!so r1or.: (-hA.r
flC -= VG2r-OL = lO in.
13
DSOlb~6,~
Sn:e Triú ~o r ~___ -...l-
/lo fi,,!:; f-I,,,f f1,1~ tr,-c.ns I"(S 5 itYi"!{l r to fric""S /~
J1 C.D tJf Ff3 dias(aM:
;1 , B _ SO Ib~:; ~ ---;;;:;;-
(Prob.4.17c.)5'Olb
. 6111.-1]) -'rSino
-B tI
h
Frc:c - bod'1 j} io. 5(11 rY1
~/if)~-;:-;f c. c n'"" ,,' /r,(-'3 fv('~, i...,!«rccf tJ.,f- J),
/Un (Jow! f-J,J
t1 =- 'f 5'0)
B=Pft:= p{i
Ir fDllcw> {I, J...f ti- i chor;~on+,,-I -
. L/ne d c..r.nOh J f r-~c..{-;on
0(- A !Y1u,i p'dS ~hc.) Wh<:r< T C1nJ
15"0- ti loa:! infarcd.
EF Li-bDMMtan ti. = c ~::- 2./).0,. r . fr1"J
0(= 62.115'·
h'1(; == EH = 100M>'.!PI-/ 2 Lfr)",,,,,
(!J -= 22.62"
r<JrT:e Tr,a,,'::S/~
~w d f s,vles:
~;~ J)'O N,.i;';.~
.. ' c/O'-U.'-'~I~El7.J~.
A T 150 HS;" (,7.':0' =- si~ 7..75':;· =- SI'n 85'.07'
",,'~~~~~4.~8 'Fr~e-bodl j)/Ci~~ (3 ·-{iJYce. b04'1)
. L',.,e'oF o.d-,o" 01- r"c,c/-,'ov>é\.f- A Mu<.r PO-'~ /iorucx,:; h ]»
vJher~ Ta,,) BO-Ib loa.d,'r.tcr~ccr ..])(j = -n(AC)-::~(Gl-c)
:: /.'j-ftfel VI (Y -= 120: -= !'s'.f.I: c( :::14..{)li'
A& ·67f)J-. A := DCr _ 1.5ft (1..=36',87/unl_ EG - 2ft I{-
r-6FtBOlb
rurce T"cu1o/e.!.LJ.v.; óf ~ine5 :
11 = T -=5'n5'3.1]' s/n7S.U'
fi = 82.5/b2t J4.0lf; T= 100/6
80 I};;
'S;n So.9J'
.iF;'G1j,(~-"-9~1-(p-G-o-6-, 4--.-'-3 )----r;-0-cc---b-od-j-D-;Ct..-o..r-{>-m-.-
--r-- JOil1.---I (3-force bod'j);,,;~ ri K Ree.ch'onar C fYJusf po-!..<,
"'~{~ fr,rÓ~\Qh k K!~(", F On'/- ~' -.PE
15ô -/6 far"CI!. in fusccr .
faMJ =~ ~ =36.87'3H =- j-CIO,'''')::: /3.33 in.tan C(= CL-::: _G_i~n.__
KL /~.~".JII1.+3i().
c< =1.0,/7'
.;r/Í"~
"",()
f·~"1l).;< ::: 16.70"
lJ~ 15D/b180"-('>
":~'il.3.I3· .~:\~
__~ .DE.::'iit~
PólCC TrlcdJ,,? /e..L.aUJ oF- ~"V1 c-:.:
Fnt: _ c _ 150 110SirI 16.70" - si'I/'!?,!]' - s;" ZO.17'
(Cl) én E = 12 S; O / b ~W
(6) {=26/ /bL 61.8" ~
Fr~e-bod1 ])/<:'3I'11m (3-r-Dr~ ~07he /;,.,< d{ o"d-ioY1 of 1k< n:A~ho'1,J-C IY1v:J p"s> H,n:v:sA D/ IV'Auc
fi an,; I!t::...200-H lcad i",~T-·
AJ)== ~ =- 4Com~ = 693, fJ1"'1
h.~}O· TanjO
PE--:: 6131300 'c: 173m,.,ran IX == Ec ::-.l.5Q. C( = 8.'5'7'
DE qq3
F",,-cc. Tr,c<n3~Lo,>,/ ()f SiY7<'5 ;
A _ C =- 200;-1
Sil] 2'.4/0- 5/",/5'0· SinBS']"
ft::: 1f8,,! /'I C =-66CJ N
~ ~ !,tB) iJ ~ j :: =.- 6(,') N l,BI.'f·
5iVl(C A-C.=- C.J)= 2 OO{1Wj ,
frlc<n S/c ,4-CD tJ iSOy.e/e5:We ;'<1.v(.
u -' "1- C =- 'TO r 3D =/2(;
C01Â 41r = --f: D =:f//BoD-120):::JO·
Ó11hp óJ1,u ho"d,f,.-{f'>Y\ fr,'a~'3 k BCt=: .CF ::-(395'" 30° = />'0 Si.., Ju~ =- 7S m Wf
FD =C D - CF == 2()() '" 75'" =- IZ)'mll-t
rru"1 Tr;aYl'f/~ EFD/ctnr;l 5'''''''(1:' 4J)==.3c/:f=F::: (F])) mn 30~= 12S-fa.., 30°-"", 72./7 tYI"-t
Frd'Yh fr1c."1!j /<.. E FC :tem c<=- CF -= 7Sm,;,
EF 72.,J7"11lt
ft.5 I I (Prob, 4-.f?)
A
400 li rzoO{
H-~"-~ .1),'0.3 r~
(3-fnnc boclj)Read'''on t(j- c ,.,.,,,,1- P"y;.j-1,'UVS" c,wn<.t':: fRJ:>0,-.0{ 'roo-I--! fv(tC.... ;r'ltr(!c'c.t.
F;.D C _ J,tooNS'-n 'I6.1u· - S '0 60" - 5;" 7J.10"
!f;D:::300N) C=-]6/;!
(á) ~= jOO 11 ~
(6) C::- 36/N.::Íl.f6,j" -<@.
B
17DN Y
Frce- bodJJ~jllS~(3- roru bOdj)
The "-coch'oY1 ",r fi mv~r r:~'{iHUUj J-, D wh"'c. f AY1 -<,<:17() - N fu r'~ i fi I-e ($ {'cI- .
f';:tn M =- 160m,.", c(::::28.07~300,.,""
We r1vk 11·""r tr-,""n::)~ A-BDi<. iSr/,u:!..-s (S,r!L(. fie=- ec)
t2rJ. /VI U'C frrrc1:CAD =- c<:::: 28.07"
;fl:;u, $'-"'C( c D J. C.B J
rCo-Lr(L1Y1 {; 17"-""5 A"j/cC;(-= 2.e.o7~ >v;H, het'",·r:oY1ft:.!.
Fõrce Tn'CJ" ,o)c.V/c no/'( {1-, A.t A H-("",~ C< V)I{/e
i c< wl'r~ verf-,ú,/, ThvsA "--"cI C f.rr '" "" ".",(.<.- - ~/50"- (10"_ d.) -2 (1\:: 90~-C(
~
pcme tri,:,nc:k rç /CtL'cey>'lO-ei. C rJ",j tAl< "'Ave
c< - fi ==- /70 JI. C=- 2. {!7Dti)Sin c<=- j60.0t!
.8:/70N~33.1~j f= /bD!YL2!J,Ic ~
4-.52> IH'u. -bod'1 J),4QJOt!j
(3 -6ne bJdj)
fi'71- -II IbOm", ,
7i --rrI 150«lM
JnCI. IÇO""'"
Ls I7DN
lhe r((/c fr'v'n aI f! fY1rr;;- f?D fhr""-'j h D/ 'V~"'" çcw-d /70-fllvrce /11 fus<'c t-.
J... Cí _ /bO«'ln o( ::::-2b'. 07"I tY>1 - XlO rY1W1
W<. /10 ré' f1,a f fílén1:J le /t:D 8 ," i'Dra:!,,!, (sr'J.'" '-'-fie.:- r-,c). íhN<'h..-c. 411 ==- 4- B =- "1()~-0(
If~o ~ Ir])o :::-2 c<róYu: ..Tn'ú"',5H.The a.yH.r: /." b~ rv< e M
;4 ~trd :;;"miJsl- ir<.
-Zc< - c< ::::- c<Thus flffc..e ir ia ~ D/f' /sI ..)
i~tJc;celps. CVY!cl
A: 170/'1
C.:;=-.2 (170N)COS cí ~ 300,0
--'---'-i!7ce - br:::1']) ifl.j rnt<1. .
-,..5 -I I~'" ~j/I~TTt aêJ [~(7r:_~lli
cl ~------lA L ~C
G 3-~~ b~ I
f«(AcJ-,'tJV1 ~rC "MI- f""5~ 1i'r't<f112\
FoIU. f-riIJ.'" ~ /e.S,'m,'/eu fv fr'a.ns/<. 8c 1).'
T _~-=_c_/--;z;;, - '1,"11. /5 (h,
J~4t'.j
ff4~
(7!{(-c;to~(fvC;~) (1:
Th e ró:J, t..-frms ,;>./-,4CU'd.. 13~'~d {H< W~'Sht' ,nuS/:- (fIx:: C-Dn L-U,-r-JY1 t o. r .I). ;,TI, iÇ rn <"" S -j--hce f- r-"'-<.. (1
c,f,'cu3 0'0'1""; C D o f r'V<' G'((:c...~Qk p,- C. B ])ddil1"J 67 !! a.n-!. 8 Gr>1Vsf- b-<. vrr/-ica(. el
li: fol/ü>v~ fi-,At- q: PCB iS ejvC11 f-o C<, _IO" (f,1!. Dfí,"r A",,.,d A !1 C D ,-s ecrvA( lo -&-. t,oA/'~ I r I Ivr<... IV' /I c- ~ ti"-+ li é:]) + --r IX.E =- --r )i-C13 = 90 {t:
e ..t- o: =- 1L/ «E:,II f'i
F:ce - b od'1 'D i 0.'< ra r't1
(3-fDn;b~~
Th~ I'N'''Sh r ~Q"d fí<e ~tJ.ct'·U>1S
§0h1.,.( ~ rnvst beConc.<Jrrenf at .:D.
Trià"St. 8co:IO'M s!~ B c.J) :Tria>15lc GCD:
8c =:(pc) rá.>1éJ
CD::: (8c) r-Clt18
GC::: (CD)tt1l1 rJ
BC =7.-ft1>1-t1
CD = t btnl-éGc -= 2. iMJa
68= GC+&. =-?fZJ.T1~8++"1z:,n eE..j- 68 rs KT1oWY1 7u b~ c;~6.1 fu rad/us
1- fzu13fJ + i. tz,;.. [} -= %
.tJ.,.,.? i3 + tltn f3 = {501v,'''::. '07 tri';(: ftJ;; ();- o.{,B llf
'*' 4-,61LeI- E b: +hc
?o(rJf ~f infrrftt-f/o"1 of ff,~rc tt cf/6f1, 11
ar.d ~,S;'n<~ ,:~ {"'''CS f.-.r0"3h i0/ a.'1,( SiM"" !Ç; I
is f<rp(>1d,'«)lAr .tu frE) fr'A"éJh I
/iCE t's o. r:J},f fr,'ú>1S!c /nseri/H) j" (-l-1c e-;rc/c. ThO/~"'1foin!- E ;.s 0'1 !;'C C_irck 4./1tX fi E=- ZR, nxt"rrcrlYl<f'C /
-4IXJ/7i~ Incccn/rtt! ansle =r«rf0r>dih';; To 1',,< 1(l5Cribuf,-r- onslc !X A , TJ'l<J~ <f J)ori .::: 26 : 11~ -4 EO C=: 2B, I
(a.) rro:..-boi'!]) ~WY~ I
(3 - to•.u: bod~D Frcc-bodj J) t'áBfV.iM (3 -fern:c b4 ) I·61ve.n: ;Te, -:=-' 3 R IThc /111 o( o f ac.f-iolt
! f- ICf) f'1 ui r fc1J:' I/f.,,'UlJsh E I W!,(r~ Tl1r (,"C of Ci.<-h'oY; )1
T atjd vJ i •.•tcrs.(L t oF- !!! ro1VSI- F'H-;48 -
fhn:>v-:;h E.)wh~r!' fi- M'ld ~
; Y\ te n c a·, ThUJfrlid fOIV1r G- Df
nxd l"Y1usf- b<o<ir~cfly k/uw E.'
v/c. V/f''/e Ihaf /fé. anl .46 !lAve lil~ 5'''' J1t'<' nor/'l:on lu!p rOJ cc fioYl :
(!tE)cns 2{) = (4G)~5 {} !2R ces Z 8 =- 3t Coo:,8 1
Lt U/.5 2.e ::::3 .:.os ~ ISdtrn';] Coo. 215= 2~'L8 -{ J ~ n"ve "
-<8rJ 8cos '--o - 3 c.a,s e - fi = [J . . 11,'
SoIv,n:s lhe 7l-1ttdrafrc fDr Cos{):w:,f) = (),c!l101t & - 23 2 ° ~ f
« CoS e = - O.54I.fOCf f) :; 123'.0· (di.sCetrdj'!--I
/---,/
/.J)/
~ '= W fA., 30.8"
7;6 ::-0.596 W
T =-'!:L.c.D QJ S 30. go
7::.D :: I.!b lf W
(4CSinbO'.-IOõCU,(,D')j + (-S8~-t,C)j +-{SBy-IC<J)j.:: oE(ftJ"/-i"::,, {I" c"....{fic.;,,,rJ cr- !~(_ u,,;/-vutv.!. f" <era:
(J) Lf- (5 i~ 'õ--/00 úJ; (,o.= O C -= 11f. lf5lt-11
G) -5 B•.-4 C = O Ele, "'"- 0,B(I'f.43'f) =-11.5"47 jb@ SI!,'f -/00 = O B'I -= 20.0 Ib
2.li-== O: P7 + By -9] = O A7 =- SO - 2v :=" 30.0 IraLV~::0: f+l- rB.:<,.+C=O A •. =/I.')l.I7..,1!{,LtY/:::-2.g27Jb
. .~ = (30.0 Ib)i-(ZJ3 q Ib)! j 3 =- (20.0 Ib)i-(JIS)j~!
- -f = (!lf.Jif/!):.~
Wc Iv'K G U" ç,.,oywrl( ~ 6 c'jS- 01 f.jv,J,.br;v>Y1 - Ore
L [j fi := O : B i: X (8(.i +-!3<, t)+ {J2J + IDj)x (- P1:!)IJk hA 'IC 5 u,,,K,.,own.\ C1/Y1d 6 úJc o f CCjvr'!/"&;UrV1. Me AD -1-(- (,i +- 'f -3:') X (- /50..i ) :::D
ir -fm 1"\1 roft"i( /Âh':wr ;c o.xi( I 6ul--e1u/!, iJ /VlL1lnjC\,'f1d (Z!j:::O). I" •- . 8BJ~-BBll +/2Pj-I00+c;O~1!-I-bOOi:=r)
E1uc:d111S /11c oe:f{ of fhr un/f Vr:'( M {o ,/:-UO:
CD -/01"'-1-600;::' O P::: (.,() (o) P::::60 Ib
.CD·-B~ +12(60):=0 ~ -=10/6
® 6Ej f900 ::::0 3J ::-112.s-Jl,
ZiJ.=o: ~~=o.2") ==D •. f!J -})O -/12,)=0 fly = 262.5 lb
1:. ~ =0; A-<. -601-'/0::::0 p~ = -JcJ!h
(6) 3 :="(2b2.5lhJj- (30 Ib)~
~ -= ~(I12.SlJ,).l+(90/")!!
"'2.[::\/=0: (i gOi)1- (-I çoj) +(300i )x (- no ~)-I' (5'(0 i) x (D~d -1 De t):: O
- 2.7X/D~!! .,. '6/I-1O}' -j S4DI) f;: - )'T04 i = U
E ru~fli;] ÚJ( H. i)f-..i ",,,:f.-!! fo ;!,erlJ"
0) 817/03-5/{0 »2:=- o 4 = 15""0 N
o -Z7"f/oJ+S"l.fOD.y =0 lJ:::' SD i1
L F :: O : !tI' := oxL F::::.o: Ar -rD;;r-f50H:="iJ {j=.!SO-5"O-= IOD";í t;:o : Ar T.D.. - Z7 o ti ;:o À.t': 2 70 - f)l) 7: 120 N
.8=OüONJ/+(i2DN2!!:.; P=(50tlJ.j+(isotlj!..~ ~1
.37
VW =(20'k:61'1,ó'/njS0
= ;16.2 H
V;rY101~/on!:.
in 11lTJ1'
L"H =0: ~n/ X T j. f"-t xl l' + 1: )( (-I'1UH\,'::O-13 '/6 A_ -C./6 c..!.. -G/B '!j
500~X7,;;J.· +(-SoVj+J7S.~)X ~i+(-2sDi';-2SiJ!:)x(-I?'.2j. - =0
. - 500.~!:.'·- 5"ol.J I!-37S[.i. + .lf1.05";</D~ +- lf9. osX /()~. = o
~ 0?d'Y'] _lu :::ro t~<:. =t-fltJC'1tõ. ,f fiM ur.iJ- rnfo.,...,,:
:Je -:'00 I +Jf1.0ÇX/O .:::-0 T =- 1.y.J!'I ~C c.CD -SCO~-375(98'))+If'!.0);(/rf=-() }.=-Zif.S/'f ~
L~-;:::O: 1+~+-r;.-!'J(,.lH=O21j5 +-T8 +-q 8.{- JC;c,. 2....= O
.~- ..:...r'j,@.iJ
._ .• :,í;l ..-2i~;::O: C;<.+D1. +-1;::0) ~"t.:-500-37S'.:::' /2s-f'!- -;,1"
_ .,j.rr:: O: C1
+.J)7 -lf 57J := O; C7 -= J..; 5'0 f-]<X) = 7SO ti---,~ F :=. O:C -::: O- '.- c "'".~~f -= (12. 5Iv)_ L+ (7:;-D NJ)' ~ p':: - (5ÓO tJ)_,' -{3 00 wJ:i <J:JJ~ .' .'-',,0
- I.f{)(j +/80-;- qo:c :::=: ()
.tOO - 120..., 10;1...:::' o-2- =- 2. l/lf ft ~
X -=- O.881..fr~
52 (
(
i
(
~5 =~F-=: I. /21.fh.N
A). + /,570 -I- t(!.7{,)fI.1Z 1) ':: O\f.5 . .4 = -Z.15kN:<. .
z ~=0; f+;j -I.Q[,L-O,'181':"1./77-2(3,30):1.I24) = O,+, ')
!'t(J :: + 5. 77 k t!
'ôD= 3.10'5 rY1
BE=3.'!oS"1
TBD::" -r;D ~ = 78.0 (- Q. ')12j - Q,76B_d +0,38'1 !!)
75", =T R= T-8J-O.SI2.i -Q.7b3j-O,38Y~)~ B~ BE t - _
i ::= Aê. = (3m)wUo'cn,.p i +(3m).s,,,30'J't(3rn)co53c.is'n1'k-C/A - _ -
::: (2.bÓm)eos 1'.:.' + (IS",)/ -;-(2.60m)5"'1 4'!!.
L M = 0:.10 'T. T t'"l- X T -+- ~ I x (- W l' ) ::: Q-A Y/A -eo C/r- -Bé -_cp.:!.. ([) -8J)Sin'J+/6Z0cosc<:::o
3j;.TE.D(-O,5"O-j-O.768j+-O,381f'!5.) CD 8~=o
.t-31·.xl (-O,>ILi-o.768_~-O,3'eY1l) rI\ '" 3 Ib.Q '-' \V -135"Dt-3DJ.)J=O J='IfS.D
-r (2, bO eos r i + f'S_i + 2. bO S;.., +- -1::);< (- Wj)=Df1tlK,M C<=1f5~) i=b5.7'in (I):
l.5j{,To~ R-I-I./S2T i +1.53~T -i:.-/./:aT_L -1J:::- 202.'i';'J~IfÇ'>-=/51,/!u.:J - 8D - BE - Se - :51" ó5.7'
-2.6DW~d:>-k-IZ,bo'l!s;"1 e;bJ. = () 2.:F;,=C: A;z=o&qv,;.hn~ lu .;':<f1J fi,e ~+-h'c;<",ts 6If.,'!: vn,'f v-e,fur-S: p,
, ~ 2lJ =0: ;j-+f57./ljin6S:7"-'10+'f5"=O
1,15"'2 18D - I, I r2.1i, E +- 2.!:D IV S/r) ~ =. O L. ~ := O: R l + í<;7.11 c.os 65.7"=0
/.S-3{, f8D + f,53C,Ts6 -2.60 'rICélS1> = ()ór; 78é-7àD=2.257wslnc? (I)
'SE +T5.D::: í.693WU!sep (Z.)
A-dd;~u(I)(U1d ('1); -: _:: .L ri (2.7. ';;7 SI'Me? + 1,6'"í30S <?)~ "" z- )
Svblic..d·;"'y(i){-r",,(": /e,.p =fW(/.613ws.<f-2,Z>7':,,·n-P
(0.) ff ]3]) ("''''nol- be S/C<'-Ií; «)<1.)(. vaJue of- T;,E ,:5 írodPt!
l'I~O) 1Sl) = o:/.6q) UJS c/> - '2,7-';7 5 I'r, ep -= O
-i-z»,..,dJ=O.7'5" q,::]{"Cfú ~
7/-'( clcrr;ck A~,.( CAbf~ SE t1(( -fi.01 ir>.(I.,p S"'>Yle ?/aY)~,
~?'?,'ti:~.r,;;+f'zl!tlliJi'#)i1êrfS$'l;;;;'''if.j+7I!W_'''1íi'tri''PrNC!) w Ji".,W.i'ieí'Iili1'1:fí"'f ••.• "fah . 'hiW;(j
I
(6) J.f -f1,e Úlble5
~f TU .v;I! IY'
dTsE:_c)d-? -
AJC (c(J/O(f'J b7 riJdç/ 11-.-( f\1fl:Y, vd/Vt::
rcC'ch/j ,yh~n
l.257co'::J ef - 1.013 s,'" c;b =- O
r-,p" eP'= I. j J3 C?.::: 53, / O -<Cl1
n.e p/c.n-<' óf hc' d(rrici( ir f!".fYl f"rp"ndic..J!d r hJ
f~ rcrh'ol f/O'?>! C-o~fC',''';Yl.!f rod B.D,
ê
IÓ~r1~ '_u,'~_ ..?: C 5ir1. A
See o:.olul-1o,., or Prob, lf.78 W FJ3d,'c1.sramo."d dc6vo.r,·ov> of sts.. (I) O\'1c.l (2.):
~ We n ore f+,~I- s h'Li<: C o i5 Cl 1wo -Furc< 1">1' rY\ bu.
Tl1c fun:..:= F ir .(x<.rK. 0>1 f'Y1': -shrrh NI·flC/U.,J-C.Df;,vs cf./,akJ ".fo~~ cc'. ll/, sh,,/I c{c-f-cryn,'V'e
t-hc d,',-ah'Ofl ar C D (-'-0""
Cl s/de Vi<-'w.
Sinc( -/-rit1Yl~/e ACD I"150sce.I,,-'., Tr,'?"',,,,, k ft F.Di~ ()...r/:::/"I r Tr /a ;,"!)(' Ç/ r'"ld w<
h", vI<
5,'n d::: FD ::: -!.. , C(=/1.5'//10 s
~ r, ~yc 6 u"Ií"\Jv,/nSj ~D' A", A7, B).., 87, .8:.., ohd (, Cjul"Jihri"""rlÚYli- OK.
~~Ei:::O: iç/sx.."E::D +-lGIBx(-/5j)+~)ljBX(A:>-{';"Ril)=i)
~Sj +J ~) f. (~.D c"s C< j +- F;.n 5 '''' «j )
~ +(z.5" s,'",2ci i- Z.5'CDS!<i j +-1,5'-!;) X (- 15))
~ + 3 -k X (fJ Z-I- A ")-0- ,- '-- J5!-Jr;: co5w'Íl +- j F c.oS DI .•..- 3 F S"- _I;
-[) - CIJ J C!J'" C( ,
.1) -37.5 :5,'n 2.« ./e .;- 2.2.5 i. +3 A -.; -3 A !. ::: O- - ''x-.E J-
'";:íi<:th'/1~ ru "=:<,,ru !h~' co~fF-r'U<""i-f i,F· +í<~ LM,'/' vC"c /õ~s:
~ ' st;DCOSC< -37.5 sin2 (j == ().
~~ 1;D -= 37.5 (25incXCrJ5cd - IS-Sin rX '-=:/s-( ;-);,~ 5Ú5iX F' := 3.00 /b ~
CD
::;,11 (C b r<'«. S C,4 r?-""d C:S J'Y"'C T""v- Arte: m '-W\ !;<: r; ~ <
force ~ F cwJ F ;-;"c7 0/" f ()n tr-c oIj.-."lf\J./ "fi« t--c:A- -c.e 1
C1 r( d;'-~,hei olol1j C A cv.-.~ICf3, e'~:"%' f-,'~ 17,a =--(I,Zm)j +(U ..m)/-(O,6m)-! CA:/.fJ""c2: =- (I,2m)..! 7- (1.2m)i -(0":")1' c 6:/,B"1
rfÍ ~,''''''vm I. ')- klJ al",c../ WC~I w~ J,,,.;.•.T -= I.)'" k N (- I, 2. ,. T UJ' - lj, 6 -1:) ..
-CA. I, S -, _.,-:o- - (!k N)J + (1k~j -(o, ')kf/)1;
{B -::+ {I k,N)J -I (lkN)j - (o,) k,vHs:J,~~t:
tVc A",-ve,. 7 U f) kY1\lwnS P, J), 1 'D .De) E" :; ~. C1 ~J GJ ,... -71 C. .-1 7' c~
e,ui/;'"ri\.lW1 ejvc;,r,'.Jn5. T~~umpúrl<'Ylf! j)~ t1N<d.E,), aNsf?;.{-'·C~//7 ihc/C famin(1fe; 'o w( ·ShA/) Jf<' Jy)()"".
Zf'! =0: 'y.'~'f-FII+j~/..D'>:.·F +:::~.<--;<PA.'+txE=O-J) ry~ -c -C3 ~/Y - -"'1-0-
J'lj' X (-i +j - 0.51') +(2.ttj + /.2 i)x (i:. +-i. - 0.51:)+(1.2.!-'+-O, 6,i)x P-ie +- 28 ..:";<' (L;..~ + EJ 1...;. E~?) :=: O
1.Z.-.:fr.-O,6_c +2.lfJql.2i-I,Z7-o.6_L-I.2?/-I-O,G.~· .--,-?ur/~-2i.1;=1-; _1"1
, .•..•j '"-v~ ,..:'- "-.c - ..,.I
E..7"''' [,,,':5 'h.:r ~/1) !id ('o' f{,'c •.~ •., /-, .. ti! J-(,,< vn ,'( v(c i-ovs.
Q - 0,6 - o, 6 +- o. 6 ?-::O P == 2 k tJ <~
(j;. l.l-J.l('l)-2.JtE~-=() tj-:::--:?OOl'!"~
%31<'1 f,', ~ rrlL. ,;t;:.,.s" I 01- /1,< ShuC-, wC" "; ,,~o· r,·....(.!
@ I. '1 +-2.1'-1,2 +2.JI C, -:: O EJ :=' - / kJl
2: r;.=-O: ]);.-1 +-1 -/-E .•. ::: q. p". f~=-O
(I!, ~ E' ihPá-r.',>l'·"d• ' • )<
L.Ç==D: ~+/+I+(-J)=O DJ=--/ktf
'2:-T;::-O: ]),,-O . ..,--O,C;-/-Z+{-O.'»)=o -I;, =-5()OH
V/-=(200 kg)(q.8Irn/ç')
:::- (962 rY
\tJe htd~ 6 uf"lKY'owf1» T, A , A B 8~ B, O'1.I>- J' -"-1 v' CI
e.;ut>.r;':!:., OK.CE.:::- -(1,2m}.I: +(1.8m)J -(O.7Z.rn)-tiDE. = - (U..m)j + (1,801 + (I, e 'frnH
T -== T a = lÇ < (_ 1.2 !. +- (. 6 ;. - O.72 +)- Cé C! C E Z .Z Il 12-
-'"T =/ .DE -= T::Jé (-J.2~ T 1.8; +I.e\tk)-De D[ Df. 2,84 - 4 -
"EM ::-0: !C"/nXJc- t"-; XT +1: I ;<'(-I%l1·)+-'1. xA =0-8 _D t: -,[5 -.D:: -G~ ..f. -11/5-
Mi-;Y1:o k,,,/- '!'''I =:-1.Bj +I.G-r: "Moi 'r: =:-D.{,'+I.oY-k-I e - - -C/8 - -
t?rrl V~r·Vl! d~ h."""r"r1"~"o...;+-':-, -~ ht>.ve..
~ 1 -kTet: -;; /.8 I. b
2,2ó -1,"~ 1.5 -0,71.
I ~ ..a -l? .:: ;} ),e
+ Tp1:1 ; 1.8 1.6 -1- Ijbl. 0.10 Õ /.04
l,8'! -1.2 1.8 1,8'1 O -I O
-1- 2,08 ~ 7- U\i + R;jl ) == Õ
~ I) '1 "5""(-'.!..:.1!:- - M..1:.) + 2. o IJ f1 - Ob ' LZ.2B Z.84- ;x -
B".. J / ~ ,...( I. ':L 1.2.) . O"'" S'O . -+,,8'1 z~ - - - ---=• 'L,ZI! 2,13'1
B;<:= ISO· '1 ti
15 + 1f2It, I.f 7 -r- (,8'1. 2'-( ...M..,. 9)_ /162 = OJ 2,28 2,3'tf3., == 557;Y
d
B'l.f-681.25(-9:.73 + (,[],-;)=O B -=-'2l"lN2.:Z:0 2,8'1 2
Q =(/5"0,9 lJ)j '1-(55711)) -(229'rv)!:z
S ubS h'lv!;,,:; in (5');2..,i"'T .j"Z.lb(14<;./)-/f77.2.:::02.2.8 <:~ ' 2,13'1
1:/7 c:: IIU, I NSu6' h·t-0~inc for T owi I jn (7):
. " Cé DE-ill (lI2J5.i)-!.:i?- (11;5.1) 1-2.08 A =0 A ~ (503 i'I)i
2,28 2,81.1 --fl = 5'03.1N (COrJTI NU E.D)
t'~)~ ,,','_11r:~;i~"!Jrt,:i~'6S CoNTIN U ED I Reec.11ins E15. (I) C{MdU) o~ Prub. J.;,BZ:
, . J.. r. -= o: Bx T 50':'.1 - J.,2,... (1126.1) -.i.L (JL,iS:I) -= o,~~ ;J. l.2i) 2.i3't! , , E;r.-= /50,1 N';.,.~ r =0: 13 T..!-.-~ (l12D.I),...!:.!!.- (NO. I) -I"I~Z =- o_~ J .'f 2.2.8 2J)'f '.B == 18I r-J~~ d
';.:: r:-=,D: B - 0,72 (1126.1) j- ~ (145, I) =- o 8 -= 2.[,2. ti:~;;,~ c ~ 2..2tl 2..B'I c-'~~ Q =- (/50, q ti),;, + {981l'I)j +- (2bi'-tlH ~
~;~, 8 Q Se-e "3o/vf,'o.-. Ú ?ro h, lf.80 f,r A~ r'r""""" f, o~ (Jf
a",?/~ o( f:,A.t sh"ck CIJ hn"'~ ,,;/1-1. f1 ••.. iro'1l-n/:
.5in ~:= I0;::: 11.5'('
5ft:
1
~J<:-[;fD,' 3J + ~D 5ino:. - 15':: o••.Gl. BJ + 3 (f) -/5";: o'\-'
- I: ::=0: B~= oI .•• .rt-J.\
;fl~qitlb)j +(1lf, !.fO/},)1;IjB -= -(20.7 Ib. fL-)j -(8,82 Ib'~j.. \.~ •.
, ~ = /IIAD /iJ
5ec S~ivhl>l ar- Prol,. lt,8:) for d",r-a"";",r'o", orQI'I~k c< -rhAr shi:k CD S,rms w,'K, ho(irorj-,,(:
Si,., c<' -= 7' c< ;: li: 57i- 4
Sft-
br-c.=. DC __ ,
(Y= Ji.SV
VJe hAVe S(},.,k,.,ok,/~S, ~D~ ALI A:;lHA)"Jl-fA)J) P.nd. be,v,Fbr,'voYt c:rw..h',p,L Tl.e S..r-.,.•.••. "';",{av fI fr~ lu ,.-no\rC il1
n,e i':,direcf,~. ~, e.;UI'/,hr"VH.1lt YY1a."hi't>.inl',( vnd:-rrn~~/V't"" /Dl!iin~ I Sinc! :z ç::- O,
L,tIA =0: :r::4'1/(-fn-f!:G-//lX(-/~)-r(/'f~~i+(fLf,,~j =0
.-.s-j. X (r GJ~.;(" + F si,., c(J)- (D - C.lJ
+ (2.f;';>12C(j - 2.;'-CMJcj- I. 5"~)x (-15.1) +(11/!,U T(M,J:;} =. O)
5F;D Cc5 c< - 37.5 s.,-,., 2 c: ::::-o
F -:=J7.S(2sino:.casc<) =155/f]cI=/5(~)c:o :?COSC( .
- 72.5' + (/vj~);,= o
l' (Mf'~ =0
F -= 3 00 l.bCD '
(/'1 ) =- 2 L,5 16,ftfi- ;l..
'2 F ::: o: fi -i- F w~::;(= o.2 ;2 , C!)
,4;.:. + 3 c.a, jISlf"=-O
~:=JLr,7oJb
.ê =- (2.q~ Ib)i + (Iif. lfD/b),i j ~ =(22,5Ib·!di ~
w~(200«g ):'1.81 rr/s ~:::-/Q6l..rV
VJ~ Ir.o.ve.
T =/ := TCE J)E
w{ htlv~, 6 Ú"K>-1OWVd, T; B>., Bl, Bb,CN,s).L' (f'IE);)' e;,,..,!f
6 "1vl'II~'Vf~ e7uo fiuV'; - O,i-'(,
CE=-(/,2M).i +(i,Brv,ji-(O,7201)-!!..DÊ :::. -(r'2M); +(/,g"'Ji -l- (i,8lff.,! ~a
T = T CE. -=.I- (- I.2; + /,8;' -(),72 f!)-CE CE Z,W - ~
T -= T:DE = -.I- (_/, 'Li. +1.8)+ /,81f:!)-])1: DE 2.8lJ -
L M-:=,o: 1. x T +- t x T +."l. X (- J<i62;j)'.JMi) Lt{M5) 71-=0
-J) -Ele -Cé -E/e, -PE: -&/e _\'.c ::J-
C E =2,28...,DE,=, 2.J3lfJ1
f.Jo~i"", fI,'.cr~ =/,81+1.6-k Pnd 'Í =O,6L·-I-f.OIf4> ",,..,J. ~ - ~/ E. A - -6/8 - -usins d~f("'r.-.r1"anf-sl \l,Jc hp.ve
é i -/;.1 TI~i~ i~~T O 1:-3 /.b + m D 1.8 I.b +1%2. 0,6 () 1,0'1
2.1.5 -1.2 I,B -{),72 -1.1. /,8 UJ~ o -1 D
.1-(M \ i + (f-'. \ ; - O, " E l;c - \ '81ó i -
_I_: (- 4, J7bi - /,Cil. i ;-'2, I G !::) + ZT (0.1+3 I. i -/.1 I. i +-2.1b -!s)2,21' .SLi - -
+2.040. 'I13i - 1177.2. -:!: +rMô)). + (fv\13\, j = O
'" - o /8 "s( (,8 ' 1.8) /tlbZ-OL (1:::0: v;; + b '1.L. 2.,28 'js'l - 7 -
."" 1:',.;:: O: f< J-ó8925(- 0,72 +!.:!J.!:!.) =0c.. I: Ui;' • 2.28 2,8~
B.J = 181 /'I
B =-ZZ1t1r
E = (65lj/f)j +(981 !'{,~.-(221 N)-/!,) ~t\ = - (883 N.m)j + (/D '1-6 fi, "')1
L~::-O: !JJ + G81,ZS(~ +- E-) -/%2 =0<} 1.,21) l,fJ'i
.., f':=(): ,4 + 681,25(- (),7l + 1,8Lt\ = üL- '-.... 'L,l./l 2,8Y )
0'"Â ;: 13//)J f,l>
fi. =- - 22 q;/ ~:;'l
f3=(6S4N)j +(98JN)j-(227N)~;[:} A ::- ( 1158 I'i' mte - (3 jlf No m) j ~~,
I
(ú:
w = )2 /b ._
Ij!=-wj ::-(l2fb)j
/Í1~ fünes CJ.LNf1"( i.ln roer 48 ""ré8=: Ô.-t! v
F =: E.)- .,;).,UC /l is iJnir wC+or..L ABand(D.::: -:) -[.
i:: :: A,. -; + Fiel.i + 1\ 1:'!::! = - (22,511)1
We. ~'/~ 5 u •.•KroownÇ, S, E J A,..) 1'+11
J1 "') C<nd 6 c7'.):1/-;uY'.í
J r- e1"i/,"'on·urr.. r<Jd /1-6 f1 f-r-,.t! ib sp;n erbvvl' o.Xis. A B,bvr e~uiJ"br;ur'>1 iç f'r1o.i,· rI:< ,-",..J I SI'''Ce ~ f-\.E, =- Q.
-'> .CD ::--(IOin.)j,,+(6;"')..à-(lf.5/!l.~ C,}):IZ,5";V).
""~ T:: T CD = T(-IO; + b)' - lt.N):::- T(-o.8L -i-O.1;Si-{)'~f).::.51\ - C D Il.S - _ -
._2: M = D: -1,;, x. B" + .i,../ x. T + 1. .x (-_w -t ) = o,,,-""..J -A 7)1 - "()1 - -C/A ..'!
"",~/ol;'n5 {',..""f 2fl/k=-(lDin.)i -i-(J2'-n.)j+(tlin.)-}
;"'~ 1C/A =-(IOin.),:' + {6i1'1)j + (4.';'-\01.)1
-i~11-;~ to "b:'('J ih<: CceH,'ci'"h~ !I '2 - -lf o-;,~~.!U - 'T • .) I t::> =
,-.}~'/
.,.,i;;n':.J
:ú~
of ft.,e ~n;r 'Ice for". :
T= /2,::0/6
98 -7.2(12,5D)=0 'f3=/o,olJ,
-/2(10,0)+12.0 =0 (duelo)
® 180 - IS c ""o
/28 -225 + IZ (.':2) -= O
"'~~=o:",:i1.)
fi +13 - 0.8 T= O;..
f1:t. +,10 - 0.8 (12.5'0) = O
A - W + o, 1.f8 T= DJ .Ai! - /Z + o, 1.(8(/2.50) = O
fi - 0.36 T.= O~f1-! -O,3b(/2,:;o)=0
/(,(6.7S)-9(J2.00) -= O (chcek!.)
Thus: tF=E(O.6Ji-O.Bj)= (12.00 ió)((), 6 i. f O.8j) ! -=(7.20 /6)," +(9.60/~} <o1l1W
!!: -= B 1:. P=(6.751b)-&; ~
A",+7.20/b=O li)
!+d + 1. 60 /-6 - 22..5' 16 = O
P,,- + G, 7 5' Ib = O
fiJ = /2.10 /f:,
,4'2, = - 6,7r:; J1:J
4-.93 Sei! Soi"t;oO'\ di- ?,..o'o. Y..'1L f,n F6 J..0~r","'" ,
T~t ftr,IC::' Cith'"q 0'0'\ f'~( Cc,}"""'.(",",<V'" IY"'C', '-'1~CI'( po •.•..•!'; of- e-{'('i,'("r,'ú., M( 0-) [1',)-(0( iY\ r.....-.rÇ' C>\vr.-LM, p\vs f0-( full 00,'",::, :
!!b=-(2iXJX1.81)(=-(IYÚrJ)j) i=G-:::-(O.~",)~
'!lI::: -(SO)(q,BI)_à =--(7BY-.8rJ)j) !/ ::-(rStn)~·i-(1.2",) ~'dI..'" -(6:'-)('i.8I)Jj'-::-(b37.BN).i. h= .'I:..~t-ti
<,The f-cft(S ~ d,'no O" {1.(
v
! r. () fF 'iCCl f, 0'1 CJ"'~" l k
+ -O.b O -1,2O B O
F = (IrC;u N)::' -( bCol!)~
ª=81§ = SiJ2 :::-Di.!} ~-D;2S=25-h
C{nr H<~ we""lnf-! Y1-- vJB
;'J -E,- .ti. )
600 I: "" ri N/o Sa ,'lers. .
!!:p -==-(0. JfBm),!:' -1-(3 M)j -(O.36r.)!1:(3::: -(o'G/II)i r {!'z",)i;. +7-1: = - (o·r,,,,ji -(f,2Mj q.i'.o '" - (o.w...).,g' +(1.2",,) ~j:.~ = -(o,6~}j -(1.2M) t\ ,:; - d.t -(0.6,...,))
'IJ -:: - W .:] W = - v.I]·-, '!j. J -",2 ..
I- .d ~-\- -d. -0.(, O
O 2S
!:. :i -IrO -0.6 -1.2
-D O O
l ~
O -O.S
-D O
(c.j :L.;;::- o:
(b) :L ~:::o:
(2.J'f,j=O:) -ft,Z-2.88+-OtO-I.ip+I.2..Dt2.Sd+o+o:::0
Sd. = 2ZS ;J,"'1-/62-2813 + .2Sd =05.- 300 N, we wrr'tt:..j _ 22.5 IV. r.,- - 3CON
TI-.,) ,'s fí<-e ,-«"vlr Dbt-t\;~,.J "11 Pr"b. 4. q z 67 c{,'rn /-(;wr;t,;.'S 2::fiJ =0. CL>.,-r11'I1S S = 300 rI ;'i tv l-k"
,( {'"h'v" ,Jv:.r cli::: /,p,'",,,,,/ vJc vrril-i t""'- r-a ~ 22<;tI,m -= 0.7'5" rY1
30cl N!'lote: Sn Solv r,'c", oF- Proh. 4.93 fur on
Clltun",iiv~ C<ffíOo.Ch.
,:_4-"~~
I .-'l;;~
, ~;é~Lr. 9 Lf~rl;~ 0=-Mi t""i-";;>
I f=-F_}(';~~ -!;r.i:\-,-=;r§>
I,<IDrc-,-c,~J) -2
I ",.L3;l lfc I d_r ' . .1.._..• ;t!c r.().Vt 6 uI'knvwt1S B;r. B, c C .D D --..~J r"~p~ I J"C) 7' J.., )1.1 11L-1" b
~'1;~vilt'6n'U"" e7v41-,'Oh~ - Ok.
~4~.00;::'O: :f6 x(~+E)+-:?:c X ~ +-.!:'n XP+0 = u
rl ..il.'~oh"3 fi..a.r ::' -'-8<' /f: ;:--2t /( -15,' ?o' JrII 8- -) --- .9 7 -.o -. - - d - -' X
I. ci~", uS ,'n~ de rc,rY\ i .....tJ,., fs - - -L;;.~i j 1: l:.3J ~I)' ~ -;r .f:r. -:1 -9 O O +- O -2 O + {,:; -2. -1'5 ~ 1'1 ~ ::: O
~&.~ B - F. B O C C D D OI .-.;t.;; '1 t L J. A"~ .r :SUl'. f-r'r1~ lo r<:í<J ft.... CtrC".f-+./c (C' •.. + \ o ç: +C-... un:f :Jec fr.rs :l~;..~
r ..:.W o -2C~ +-151) = oí,~id 8 B~+ o - IS' D1- - M := o
r.,~~j.8 F + o +- 1.5"Di + 2. D:r. := or ~c-..•~~ íX =='-0: !3;r. r D;... = O (li)
r~;§ 1=.:1 :=. o : Ci +- !)J - F;:: o (5)
l::1õi5 Pc=0: 'B~ -+ c" =- o (6) --? B,,='-c; ::-7SD;
r ~ '~-r' , ( .) _ J 1")' '. , I Q' • )r·~,·.·r l'/l~ 1"roY>1 I ~ I,;' rM Y,(/Vr:or -'-'l iV'lro (2 :
("'~ 8{-7.5~)- t:;D:;. - ,I--f =0r4!~ /5''D,. .j- bO DJ =c - M
'r.~'êlhil)/'7''''J ,,/1 hr", , in (3) b~ 1f0:
! ""''';.) 80 D:L + (, o D, -= - 320 F (8)Ic:;,h;j) rre-,r''''J (7) f-:-.,rr", (3):
r '.. (; 5' J)x. =- 1'--'1 - ~ 2. o F,.e;z,i[j)r_,.~ve.'" ,D,;;:k: r = ~s Ih, M = Q7,,. 16·fl:-r 'ul,sh'rvh'nS ;,-,1-0 (1):,."",\Th áS']):., ::- Cl7,í-320(b.Ç)l ",-,3'1,'>1~ ;11 ro (7):I :r.;;)' IS(-30,S) -r6o'D)=-17." D,,-=+&'00/1o
rc;~b""" (5): c;; == F-~.:: 6, ')- 6 == 0.5'00 /6t-~"~ (I): C <, -= 7, 5" (b. 00) = J.f ç, o /6r .. i U"'f (lf ).' 8".= - D"..=- +- 30. ') Ihr'~'''''''('G): E!" :=- c~-= - 45,0 /b
í 'c.;:1Z) .§ ~ (30.5/6);" - (45.0 /b)-jJ );'<:<;) c ;:-(o. 51/,) J -I- (LI 5. () li) t. )I ~,~ I? = - (30.5 Ib)i: + (b l.b)j ,I ~,~i .:õ.~
j,"íQ)
~ :r,!~:ft)!
4,95 Scc 5,,(Llh'oV\ or P,.-oS.L[,Q4 hr Fó cJ~'o..<;r[.,_. ;>vcl
du,v"h'oV\ o~ 9" (I) t:"rt.V~!A (~). -
GivU'. D",i-ú.~ F=:o, M:: Cf7,5/b.ft,
SJl:Jsh'tuh'"s i",tu (1): 65'J) :=.17.'; .J) =: 1.5 /b(' (. .r :r.\--c;rr'1i"'~ i"ro lÔ): 80(1.:;) 'i-6oD =0 ]]J -::-2 Ibr;-D~' (5): C"" -2 =0 di C, ==2/6rruY>1 (I): t~= 7.5(-2) = - /)' /b (J
rl"~"I (!t): B;r. = - J)). := -: /, 5" /6Fr<J"\o1 (6 ): B'l ;:-- c == + 15' /b
-r 9::--(I.5'lb)J+(I<;lh)!i; ~c =(Z/6)j:"'(IÇj6)j:', ~D ::- (ISIb)j - (2. /b)} , ~
'iJ,h_V( 6 <JtÍtn...vns,
T T TCO) 80, 8E,
A"" Ri' .4<- I
a"eI 6 c1U,'"Õ(,·Ul«.
qiJc.f ,'oot - OK.
:2M =O;':!:xT +-:i-xT +-'t-xT +1, XvJ==O-fj c. -CD B -Bo -15 -EE IV -
A /oh'n", -(hA.{- ,-s = - i,'?.b t. + 0,16.R 7; ::D,'16rkIV,.J -c - - ) -8 -
~ w' .::- - a i:. + o, '16 --kc;.l1d I):"'",~ eXe./-<:rffl'· •••ATlt!.; !Vc V./,,'re.
~ 1 ~ i:á ~I lii!- If:.j~-/.2b O 0, % ~D + o o o.qbITf"J) + o () (),1f, T]f + -a. Õ 0.%::0
o o.b -0.5 -tu 0.72 -0.%, 1.7'1 o.B 0-0.(, o -2,4 oElvah'rt~ +u 'l:r"rtJ /-lo •• cunfici("!J of f(.,( Urt,'t- v~c.hJ(~:
f:\_: S7' - . Ó 6"Ul,....I.:!:') -o, olc.o-~/b.D+2_30Lf=-é) (I)o -1.008 ~D - I,Z09{, Te]) +o,7b8~E := o (2)
1,7'1 (J)@ -O.75{"T:.n+Z.'fa.=O
R e.c",I/ins f/,,,, ta:: 0.63 iY1 J EJ- (3) 'j ,.ddsT. :=: 2:.:..!!..{.o,H) 7: = 1.00 k. N <::ml
C[) 0,75b Cj)
0-"" (1): - o. ';7(,(2.00)./ Z.3D't == O. (,<]12 T:1 D1.-JLi-rc ".:0.1,101:.['1 ~
SI>
p,'YYl (2): .0,71,8 T" _= 1.008(2. iJo) + I. 2m b (Z,CI ç)De /, 7'1-
T8 Z = 5· 2 'S K;J ~
,:_4-"~~
I.;;;"~~
,~'f.~4-,9 Lr I
f-r,~fi;; tL: - Mi t""~Z;
I F~-F}í~I~~ - B-i AL. __ ;r._
L ".'i§> B
1.<Ivrc-LC'~9 -2
1,~L3) 1Ft: I d_r I . .L~·.,;t!C r.().Vt 6 Ul"kn0Nt1S B;r. B. C- C .D D /'.."J r",,~p~ I J -<.:1 7' J.., )1.1 71 ~" b
~"4;~v"I"6n'UM e7vet fl'oh~ - Ok.
IC4~0o=O: :f6 X(!3+ F) +- 7-CX C +- t. .>\ D+M = Ur I _ - - . - - -n - -
!r-,".,.;ç;Joh"S {i,LJ..r ::!' -'-8<' /I: ::--2 { /, -15,' ?"' }c-.J'.1 8- -) _r .9. 7 -.o -. - - d - -' X
1.~iDJV< u.S/'''~ de rc,1Y\ ,,",o,., fs - - -L;;.~i j ± !:2 ~I)' ~ d- -kr .. ...;.1-8 O O +- O -2 O + I.:; -2. -I, ~ 1"\ j :::O
_•.i:) B - F. B O C C D D OI .-.;r.;; 'I t z. J....,~r :::tu"- {-(Yi~ fo '2:<:í<J .ft.... C<fC" f+,.C(" •••+ \ a ç: +c,(' un:f :Jec n.rs :l~;.~I..:;;W O -2.C.l. +-!5~ = O (I)
r.~id 8B~+O-/S'DL.-M:=O (2.)
r~~~.8:r + O + 1,5'D'( +2. D:r.:= O (3)
r ...:;~ r;. ==--0: 13;r. r D = O (lf)
f 2i<@ 1=.:1 ~ o : C'1 +- D: - F;;:: O ( 5 )
,::;;;..J5 Pc =0: B~ + c" =- O (6 j --? 8" ::c-C;:: -7. "'-D;r ~ I~ -,' , ( .) _ ) 1")' '. , I Q' • )r''',' .r l'rJ~ -rrrP"l I 0-'l;' tt rM '(,(lvr: ar "-'2 i",n, (2 :
!""~ c3 (-7. 5 ~ ) - f:; D2 - ,~:= O
t "41~ IS"D,.. .;.. b O DJ =: - /'--1
'r-E;L'iJ)lhjl)lj'''J f./I hr",( in (3) b~ 1f0:
!"""i) f]o D:L + (, O D, ':' - 320 F (8)r" ,:,J, I're-, 'ri"'~ (7) f-r.,fY'o'l (8):
.",>'1,"" "r "'"'íTh 0 5' ))x. =- 1'--'1- S Z. o F (9 )
l_:~ve.'" J)erk: r=~.s Ib, M = Q7, s- Ib ..f-I:-r 'ul,sh'ruh'nS ;>;/-o (1).o,,:!<~ 65v:.. == Cl7,í-310(b.c:)l "",,~rl"Yl~ ir, lu (7): .I",;). IS(-3D,S) -/-6CJDJ==-17." D,,-=+&.0011o
rc;~bC)'Y) (5): C;;::: F-~.:: 6. ')- 6 == 0.5'00 /6L~"~(I): C <,'= 7, 5" (b. 00) = J.f ç, o 16r .. i. ""'" (lf ).' 8".:: - D"..: +- 30, 'llht'~''''''('G).o BJ.c := - Cl,'= - l.t 5. o /b
í ",:iZ) .§ ~ (30.5/6);' - (45.0 Ib)-fj )j":<;) C == (o. 5 li,) J -I- (LI 5. D li) t. ,I ';,~ j) = - (30.5 Ib)j + (b l.b)j ,I ~,~l .:õ.~
1, ..Q)
~ ;';!~:~)l.
4.95 Scc 5ú{Llr,'oV\ or P.,...o\:'.Lf,Q4 hr Fó cI~'o..'r,. ;Jvcl
du,v",h'oV\ ar- 9" (I) tJ.,rt..V'i,'" ('j). -
GivU'. Do.i-ú..~ F=:o, M:: CJ7,5 Ib.ft.SJl:Jsh'tuh'"S i",tu (1): 65'J) =. 17.'; .J) == 1.5 /b
(' (. .r :>.c.-C;rrJiV':i i"ro lB): 80(1.:;) -I-6oD =:0 .])<'/ -;::-2 Ibr;-D~' (5): CoU -2 :::O di C, == 216FruYo1 (I): t = 7.5(-2) :::- I)' Ib (J
- (' )' ~ /,rl"~\'oj 'I . 13): = -])). -= -: , 5" 16Fr"'" (6 ): B'l ::- - C. == + 15 li:;
-r §=-(I.5'lb),J+(I<;lh)!i; ~f: ~(1./6)j:"(;C;!6):!:·) ~D ::- (fS1b)j - (1.. /b)j. ~
'IJ, h.v, 6 <Jntn •.•••hS,
T T TCO) 80, 8E,
A"" Ri' .4" I
a"eI 6 c1U,'"Õ(I·Ul«.
quc.f '-oot - OK.
:2M =O;'1;:xT +-:i-xT +-~xT +1, XvJ:=O-fi C. -CD B -BO tl -EE IV -
A /oh'n", 1'h"J .-s = -I.'lb t. + 0.16./z 7; -O 16rkIV,.J -c - - J -8- , -
~w'':- - ai:. + O. '16--k
Cil1d IJ:'I'",~ cxe.h:rrn" •.•.A"t", >Jc v.!,,·re..
~ 1 ~ i:á ~I IJi!-llf:.j~- f.2b O O.% ~D + o o o.qbITer; + o () O·1b T]f + -a. i5 0.% =0
o o. b -0.5 -tu 0.12-0.%, 1.7'1 M 0-0.(, o -2,4 D
Eluah''''~ +u ",ai) H-, •• cuni-ic;cY<iJ of f(...( u,.,:/' ';~c.rO(~:
f:\_: S7' - . Ó 6"fll,...\:!:') -O, oICIJ-~'b.D+2_30Lf==;') (I)o -1.008 ~D - I,Z09{, T"en +o.7b8~e =: O (2)1.7'1 (J)
@ -O.75{"Tc.n+Z.'fa.=O
RUA/linS fh",f a:o.63iY1) E;. (3)'I,'ddsT - 2 1; (.Q.D T. - 1. 00 k. N <::%I
Co - --;;:-75b Cj) - .
p;.••" (1): - o. ';7(,(2.00)./ Z.3D't =' O. (,1..12 rq D
/. -JLiT.. ~.2, 101:.['1 ~SD
fr,"M (2): -0,71,8 T,,-= I.008(2.iJO) + 1.2eJ1b (2.1())De j, 7if
T8 Z = 5· 2 ') UJ -<?i:l
4.'77 Çe~ SOiVf,ry, DI- P~u·O. 4.~b ror fB âi,,-sr"rt1 o.....dd(r;vo..h·Ú'1 of- E.rfç. (I], (2.), <1.,,( O):
-0.)76 T __ 0.6'112 Te +7.30'+ ==0Cn /,7'-1 ~
-/.005 Te.o - !..:'l..oq6 15D+O,7b.3~E=O/'74-
-O.7S6lo -{-2.4ct =- o
/ '1 -fhis pro 6' un, foe. 2. 4-/(!'J loe- lij..a"~ CL::- !;2{, m. Grr7i~5 ir:/-u
T =- 2.4 (1.2(,).:: /.r.00CD O.7'ib
rrÔ""(f;: -O,')7{,(J{.Oo)+!-.,O'f::: O.M/Z TSD/,7'1
"From (L): D. 7681E,c:::- I.008(If,OO) t-O
I'r; C!fP Iir"'/ a r c o",d >lo{'
(3 j ond 501viY15 +tlr T0 I
( '2..)
(3)
Vj~ ha!}c 7ü"i('novJ"'~ {j 1'1\ P. B E E E Lh,J (.) ).1 o r "'Ç' ) .). I 11 t)
.e11.J1·r,·I-,("I·~m -eJv" i-,'u;,J , "T~" rCt>c.h·0h( t;.re S-h: fic< 11"ihd.etN~"'''1r.te. !-hw.(N~) f"~( y-arr-,'u" ",I- B rr''1 (o~ fol,)h"b~ wr"h'r~ E "\E = O) whx( A E. i~ /1,(' etl'''~o"'Ai!,,( H,,€ hui :
A-'k :::-(IOin}:.' + (6 "".h - (IÇ iV'.)-!!2'"_ _ loi +-6,;'- 15 1s.
,.. <:: 19
L i'vlO ~ == o: ':71 _. (1- X 8') + ~ . ( k X 6 O i) = àn_ -A::. -13/fi --AE \. -DI:.. - (I)
w he~e /Z, =- (io in.) ~ c<..,d.'" ~ (7, 5 (n.) -k .- E/A - -.J)/E -
M lJ Ih'p 11 iV' S b o H-.. ferll1!: 0+ {1..~ ój L»- r,'o" b'1 19~V1«' (JS""~ ...-ícr-Crml'r1á-n/-s.) W( h(Ál/~
10 6
10 OO .8- f5D B
- 15 lO 6 -15O +, O O 7.5 -= (j
O 60 O O+-27DO-==() B=+-!8!b E =(!Bfb)j~
4.99 Th-c fun~ c:.r.IJ i~ nvLJ -(60/b)j'. 'Ej •. (I)-t>-,-.," (2) of -/-t1~ So!"I-)f.)~ óf fhh. /.f.1B rcNinaJ
L {'-irtE==- o: 2A-E' (i8/1! X.§ ) -I-2A-E • [i.LYEX (- 6Ój~ =0
10 (; -I';) la G -/5lo O o + O o 7.5 =0o B O o -60 O
-1508 + 4'5'00= O B= + )u
l!=- - (100 Ib) !.é? ~(4iJ;nJi -(30inJ-t
CE ~ 50i".
T-:TêÊ- CEI = T ( 0.8 i -Õ. ó ~)
? _ AB _ (24;".)'; :(IOin.Ji-AB - /te - 26 ;n.
2pe, = I~ (12}.- 5~ )
'y{;"a~ ~=/B = ilO} (1n) ~6/,4=121:-5/1 -I- JS-~
U5(n5 deram;",,,,,,!$. ClM rnvli/fJj""S 60ft., TU""l
V'(c wrJ ~ Ef (I) (f!. h Ilo..,;r:12. -5 o ]2 -5 O
o 110 O T + 12 -5 15 -= OO 0.8-0.6 o -100 O
- 28[;T + 18, (;00 == O
"'S a."" c 'o Iv h\J>1 0."+-or Prob. 4.107,c:.)C~rr f'~ now
T = T DE- :DET -= T 2'/J +30';-30~'
- W. 7 it1-
Óf. (I) ir :;ft!J vai/ti,h t/ f E'f.(2) r;ow ro:h
~~ !~I=o-/00 O
T= 60·9/6 ~.
12. -5 O 112u 40 O -..I- + 12.
ZLi 3D -30 lf8.7Y'f O
Ilf)'-/DO T+ /8 OrJD =0liB.71./'-I J
'{OOte( •:::110.%
(o-)~Z: r:: =0:PC.O\ 60· - Tw56o° -= O
T -= P(b) =r-, ~ Me = o:
(T C-O) 30.)(20) - (B 5 i (13 o') tt == O8= 2Tc.o/-30o::: 1Pif3
8==zIf3PL6o'
+) Zl-'15
= o:(/CDSJO·)a. -(CSi;-do")ú ~ ú
C=Tcot30-= pif3f ":::f3 p 760.
TM=o:'" xA +-7.- ;<3 -I-i XC:=ó-o -A - - E> - -c -O-ix (RJi +- '\ 1) + bJ X CBz ~+ Bx.~)
-f Ct x (C", i i- c:Jd') -= O
o.. AJ
1:: - a A~i -I- b 1\ i - b B.>-~ + c C;x....i - c Cf i. :::Oqvc.f,·"~ rJ 'tU-u t"e. c6dfic;(~rJ of r~( vn;r vCc!-J-rs '
CD b B" -cS == O CJ -:.(b/c) E): (I)
G) -al1/: + c C;: ::: O A< :: (c/o) C". (2.)
CD ttAJ
- b 8~ -= O P'J::: ~b/o)3" (3)
L 5 ;:D: RJ + (1- P= O HJ + c.t -= f'
L 'F,. ::: O : It}- t B"/- == O r+ te := - D.
5"vbçrirvf,'",,:o f-,r C)".. tr(T'YI (1.]) iYlfo (2): /'Iz.=-(c/~)!3:<..{YóYfl (I), ({,\ o"d (7)/ v/r ht<ve..:
C-É'B -:::-E.A :::.;.E.f..B;t.. C,=(h}1)!3xJ- c ~ c.;!- C o- cI
H fôllol<JJ -FroW\ (3) t2",d (8) ff".",f C~::-A):; vI:, s f' (' Iv f ,'" S ih lu . (s):
2 A-J
-;:: p flJ = C;j := -i Pl\IiJ/-e .ji,,,/- +1-"'5 r('~v!+ is iY1 c/r f"'>1d,,,~ o-í- ~(
t'1'ii 11(n ",'0'1 S,
(r) :(7) (t):
(2 1.-(8) (It):
F=--k5F=*'í(f-e)
VVc no(-( lkd tr,,,,,S!-<:' 'ti C D ;5
i"Dsc.el~ anel -ií,.d.--8 E -= e c.v~±:
Fl.. - P t co~.P := o2
jE /z. Oi - (j) t - P t Có~ f = o
-;: - 8 = p.e _ (6()Ih )(;5,'n,). ~ ~ .f? t '- - (20 Ib/nXG ill.)'"
7J-8 - /,25Ulft-"-
b'J -tri,;f: -f)= (),3'3J87 ,-"ti
(CUf)'it'\=O:pC\.-(A srn 16')2.0.. ::. o·tA~ ::: P !j=O,707P;{lf.S" ~
+ Xl' .::": Ae-os 'f\""- Ceu~ b~= o~ ~ u -o ~c=-A f -=-O,7D7PYIf) ~
+~'I.~ ;;0: ,A-5j'1l{S-~-c.s;"'íÇ)+D- P.=DSiN~ C:;;A) D-P==o D::. P
D::: pf ~,
+3 ™.B =0: 1(JlD krJ)(8,-n)+(5'Dk,vXif",) I-l2.5"ktJ)(3,r;", )
··+(A..I:n3ct)(6m)
-(ftC<J':. 30·)(12. "") = o. !j-3 2..') - 7. 3 "1 z.. P, -= o
Ft = 5"8,507 k!'lA=S8,SkHtÍW' ~
+ Z~=O; B;>.+Sô's07Sin30°'-25=O B;=-!;.2SJk;J+t L r; ;::.-o: Ec'f + 58.'ÕD7t.o~3'o·-IfO-S-u= o ~ = +J 9.3)/ kH
<J B-;:~1.bkN},.8J,B <ll1\1J
(c"-) ?I'cb. I;.,ID)
+)LfiA =0:e~t)et +(17 T)(IBO) - T(J20)- Pa. ;::.-o
T _ 17 Pa.- ()et-6C{)
Tb<,t"""cI inF-i,"JC. ccnc! "'"Y>-:./-rAinf.sar~ t'm p""Op(r W;' c-; H
15-a- 600 '= o CL=f(.0n1"'1 <íL!J
(b) P '-0 b. 4-. I oBCrY'~ trl);'" rs ar( iW1fTVf""iF /iVlC Jf- ac./-io" o I:fF5~"'5 j1,n»f, ti pin B,(!V.: fi,e" t>J)V~ Xf'-1
B","o)
13vr ~ fV\vrt Ix dr'r~cré't('
c,lavo:] CDJ
S,"Y1(C CDi~ a. t,,·;.)-furiC 01Cl<11 f.::r,-r.
!r/clI'Ó Its 'OED tw.d J)FC CI"'C sim," /c<í:......E::-. = ~ 0...:= 81(. m""
\ II.fD / DI)
(c) Prob, 4-,I 09Con~rrl\l·"ts tire im(!rorcr ;f- w;rr aiA is. f"'tO l/c/ to .p iV'H .E J S'-o(<<
\'/ê hw/<, f7,.rn Z r; j: D.íIJ,s' occ.ur..l whcn .
0(=60" ~- JJP
- ----;-p-f--..o.. - t<-..ic
-Téf, a.
~
D~;p