Mech0110_5-6

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5
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aU61a(JaO~61n tWOtnSO
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(Equilibrium of a Rigid Body)
luundnci11ii~l1<InO11~U~lU'Ia~<llJ"l~'I6~101 ~u"~In~~ O11<1lJ'laiivi'~<llJ'la'l<l~ II1~
(Balance of Forces) IvlaiJa~nU101~'1nm1Ifl~<lU~l~a~~lll1d~ua.<llJ'la'l<l~llJllJu~ (Balance
of Moments) lViaiJa~nu1~qIii..n11l1lJU iflYmm~11l1m1Uli1tlll11lil~U1'lTa~nuJ1mrn
m::vil~tflJlJl ~'jlla:;ffllJl'j()uf)l~(l nl'j~l(JLL'i-3~-3l1lJVlf)'i::YlllJU1'"WQ1U1:::U1U L~£Jl ~-3Jt.J 1uthu
U1nnci111i~<l11'la'll<l~1"qtiJ<l~nm"Vh"lu1=UUU~~<I<l~ijOil1'1<lhn. tnul-'iU1nu (Coplanar or
Two- Dimensional Force System) ~-3~t11Hl11,Jl'j'IJlfltU~hji'lJ9fflti nl'iUni1(J111llUU'Hn~lf
~~m1Jl"~,.u111lhnunll'il~n""r ff111,ulilU,!"'li'lU'l<l~Un~ 5 dncil11i~1" q,ri<l ~nm"vh
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A
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5.1 lGaulmi1l'1SUaufJa51'1C!ulllJlnSIJ (Conditions for Rigid-Body Equilibrium)
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v d";' • • .., ..... t. .., . . . . '-' .., ... . .... ..
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'Iifl ni llll'h fflUll f1v7Vlml L~€I u1l'Uii1m;!1 (1'lJ ~ari""i'urPI QUoU>Jln~.J ~'ill'HU11VI QU-lJ-llfl1~Y1~~U~
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( Internal Forces) <l11Jllm~uu1.nultJ'Ia~
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lJll1lJt'lll v1J Unu1Y1ul11fI UVll~n ill~ tlf I::l~il
LFi+ Lei = 0
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NmllJ~a'''''nlu''an (External Forces) """,'1i' w,Ju LF. ~ LF <llJnl,,J1'''utmmu
L~utthn;Mi1
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attn1 f1l!u~nlJ Tll1tl': 1I1tl'Ui).J nUfJUlUUUllflWlfl{ 1I:;:'lv1'11
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LMo =Lr,xF,=O 15-1)
1~ q U~-lLf)j-J'il ~ o~h!,j~uU illJ"1 i'll'llh r ~i;'I-;nlJ~a~ U'j~j)ltlUDf) (External Forces) rn::l'lll1itl
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~n~~nril1l'hl11l'flJm1l'fIJ"la'iiuuMil
LF+ F'=O
LMo +M'o=O
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=0 (ua: Mo =0) IIH'WlJ'~lJ F' olfl~hil'h1l11~~fl~1ul'flJ"la "~Ull l'flJOl>~ 5-1 iim;o~l'w
ffl1'1fUliaIl1'IJ'IJfl~l'f1J"la
aUfjaluaaoiJPi (Equilibrium in Two Dimensions)
5,2 uTu5lnflaas~ (Free-Body Diagrams)
Ol>tI>:~ n~1'"l'flJn1>l'flJ"lal11fi>ul'f1JPru~:Aa~iim» :1jII>~n1011an~,nlUft1ua:ltil'nlu
fil~nmh~a1,"0 'iiinn~;;~ff" lia nlnlOfr~1'101i1f>:'lJa~1,"0 eT~if,uum>1l'">tI~H'lJa~. . . . ..
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A1S10n 5-1 )l1usaosu<l1I'1Su5AC]llllmnsoi'ius,uullsoaaoiJPins,ri1
(Supports for Rigid Bodies Subjecled 10 Two-Dimensional Force Systems)
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(Types of Connection)
n,.t1!linm
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(Number of Unknowns)
195
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(8)
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,r~~u~ 5-4 (0) !lmn'nJif~:ilu'mIJ'mllA~mlffluuo:nm1l/tl'Ua'mll 1l:iiIlHll1l:1IHlJtI>l
'U(),] ~lH tifllJ-Ji fl,z:vil1JUtllU~~~Yi(H~{)1J~J1t1~ 0-4 (~) 1Ufl'HUt1'Jf}.J"t11JV1 UH1):::Ui'1'~~ lV.!
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197

198
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i'",~ii~flm.nl;'1"'"UUII"lu'"U1U'~01nu (luflnii.i1'1 Illl e ~",UU.1ll1hiim1U~1)
u01.1,nmlJ ftl,mrm:i""l!«fllJru~HIIVlUii'D.'Ullft"VnmOl",n"~1.1 "'U ~.lIlJl1
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m••,UlYlhallDm.«vn' (Resultants of Distributed Surface Loads) D~,""il'lI.ift"!lU
10.'lJllft"oi'UlilulIlJ"11 ~mlvn' (Resultants) il":ml.r1um.viju1i 1",0vi'11tJ1liiim1lJ~1'uu
iI0-3111"01:1 ru::nl 'm n:i1tJ'll u-l'Ull1Ufl f) 'j::yi1~ LlVI11~-3 l~()-l1l1 n~u~ ~1~hl1rfl f)1::';' ij'Uu1~
'~fl1JlflL;jmiiounu'i1uiiihvf'"ll''' (Total Surface Area)
". u,.l1lulwflua:l1lul" (External and Internal Forces) IrtU'"' fli''''~LI;;.'fl'hv,"
flam'lUUIjfl1ft 9j.iiJ'''''flm:n1vf.molllL'ft"fl10UOfl ;'0.m:""fli1'm~oQmolui'",~
":ltiv,1fl!J1u".i''"~iia,: II.iVli' "HillYfl.',n'",11UtiluVi111'1H'"Hnu'li'lll1I0.jj'llUl~,viltlU
9i.vll111~ft«Vltl'lVliliim:vllADi''"~jj~lLi'Ju~u6
1uul.flHUal.H",i''" Qiia'"ffl",m:uU'IIa,i''"Qiiii~ ~~ a'll0.lm.lYr,.~ a,~alJlum'
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nu u'.~m~alJl:wlml.ift:ffl1ILLa"'Jlu.v'mmolu (Internal Forces) 9lJ'hjnlJaQtlU"J1"'~
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nj :vi1;110crIIlJJliilJ01.'1a~l~ n LL~~:fllln1A~:ihr'l1Ufl'ill..,: "1J (jUlIJn~fl11lJ1iilJ01>'UaJ
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11l1.YlU IW fl" n,Tu ,dai'",~jjm1lJ lYJ'lfflJa"1alllu1a~ I;fD'~01 (Homogenous) fJUUflft1.
hrlJril-3il:djvllUl1U.'J~~uUnal.'Jl~.'Jll'Ulflru?l'IJf)"r?lQ (Body's Geometric Center) l-i1uI9fUVl'ie(J~
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r-l-l f.iff1::ffl111Ul~'1ucl~lO~-l111en~lJ1~ CJ~!OW'I )'HU)lthn;:uuL~ll)u'jtuwauvl-Jd
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lviHr~qaoHAi"J ~

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Pl:JBf.hOi'i 5-1
~.".,I1'.r"~1ill':'Jij.mulIJ'lllllD"~lllii 5-5 (0) muii1l1~ 100 kg
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(n)
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,1l~ 5-5
•
~~ .11I)il
11'.1"~1i1l':'Jfl~mUUif.,~hllU~ 5-5 (~) 1~ij~"0!1U:i5~r1Jii A l'Jumr~v.,&i.,miu
iJllHtlfimUTt'I'nmciHf1';j~Yilvi()f11'U~ A tiv A ,A UCl:: M 'UU1~'U{1>lnm~Hrfi1'hjYl'nUfil
... _ ~ ... J ( } , . . • .. •
11~:Yll1VlH~ : QOllll~" UlI1UO'Jij.mtl W =100(9,81) =981 N m:VllInU~"iJUvOWJij~mu
G ~ 3 111 1I1f1 A liir~H1l1nfllujjfll1lJnJ-HtI'lJf)
[99

200
- . ~
G1:lEla1IJn 5-2
~~11'H'~l~~iilm~a~III~nvilLUU!U..raffamil111lJ f;! m'iiD nLfll <l.'li'~ ABC ,r~~u~
5-6 (n)
500 N
/I
('U)
1U~ 5-6
•
~~ .11if11
(0)
fl(1'Ju.Jl1lj91 mzriwi0
(u·ju1a'H::ul J <']
(n)
,;ill n.t:!~'fll;:~;:<U-l
n1::YI1Y1t1111..lYl
r.r,"~nii?f>",r,>u~ 5-6 (,1) ~11JH),1lJl1l.!~ii B ii'»Ilu,.oalJILH B Lm: B lJUIl1~O. . ,
';1LUU!U..rDffD mim1lJ1;! m'iia oLm:l:'li'~ (Bell Crank) IL~ a:fi1'I,llJLLU1OHm: ';lu~
'limllJ~Ul~ ..raoiD~ C iilLl. F n"';11tliiffl'll'~D~..rDAml~:ihJ1n~hivm1l1;1 ii~~D~Il1~n
. c •
,r~ 0on,:!!luN,l~ ~iil'l'l: dlD'~l n..rD12~iiiiu,:10'llti1Un11fllu1011mlJu,r~ 0'Ln, l~ou n ~
iiff1'l1''ij0'm,himllJfilvi',ill1,J~:QnillJIJ~ ih1l'lH~ Qn.ra'.:U110~11iI,.l0uri'ilIJn11illJ'la
1I

'Ul'1))fi~'Ja~I7~1,"Qiil';=~ B 1l<"~~lUlU~ 5-6 (ft) Itia~~lnl1l.l~I'l~milll'Junm~elJ.iu
uui~~~utiuOU mr~ ,hhi'iiI'll ulh1um1uri1il'1))I'l111Ih~ mr~m:,h~UII~a:IIr-IUlal1:UH ~IL .... &I
Julio 8" , B", 110: M". ImuiimUlil~nllil'~~i1iiTi11l'i1t1Un~'JU1~lIadifll'll~lull.ia:II~U
hll:UH~ lila~~lnnl'il'lJlJl""'Jo~lhl1lTnm:l'hlla:~um~1i5~11'111ftrulll hi'<l~In", nn1'l7
11<i'nnnIlH~Vifl""~OU'li'1lJ'IIUllllll'i1t1U ,doiiu,~ B', lIa: B', m:l'iwiulir-lulol1: lIa:l1ljlll '10
"'llh~'ti1'1nufilil'11J11nl11'.1~lni1'lJ01mlJ~"I~Om;U B, lIa: B,
A:JaEi1IJi'i 5-3
l'ionuguvf~ll'fl~ A "0: B 11llolloia: l'iuii1J10 2 kg oQii~':l1il~1:U1UI1iO~.r~lU~
5-7 (0) ~~11",17~1"'q1lil',:lil>frul'ifl A, vie B lIa:J~l'ie A t1U B .11Ut1U
::W~
10-
(0) ('II )
(~)
I' NCI'UfI-lf111lJlu)J(il-l F r'H'I'Ua~yfu~iiil11u'ITu
( tfll1Un) m:::l';,r;ia A m:::riwitJ A
~ ~ .1'6111
fr~""'lii ""li,,.,nJ1i~ A IIff~"UlU~ 5-7 (~) Jilfll)',' Cd W = 29.81) = 19.62 N
liio.Ol0'1n,1ui11<llJ.rll'llUlU ""ulimo1 T, Fila: R m:l'illuViflm,.KNlnUOAt1ULlU1
fflJf-lffiilfHf-h«,HTcr r·rd'';!ot)('I'')!::'U{),nlo 13 lLiX~.Jlw')tJ~ 5-7 (1'1) YfU11 R ;~UVll-HLH'UD,nifl
A fll::riwii.H1D B ~.J~uvi ; -7 (fl) ijrlllYilnuu"::il'i~nu,jllJnU R ejj~Lml-Hll-l'U()"Jvitl B n'l:;nl
"ovio A .r~lU~ 5-7 ('II) I'JUIU""IJOQ'UO'nl'lftgml~'U0~;h.r1l'j'O~ff1lJ
201

202
200 N
A
" ~
~~1..~iil'fwJa~,f~l'ffl~Yiml1JflU (mJu) 1ll'f.nlu~llYi 5-7 (~) UHl'flHll'f R ~nl:lh'
1"l1i1~ A ll~" B Qn~~lnlm'lulll~mulu (Internal Forces) 1l~,~"'lilLl!..~lu~~1..~iil!1: ~,
~.1'IUlll~Yiatilll1LUlLli'llI~Uln1lI'Iu~YiLvi1nUll<>iii~fnn~..H nll'U11] ~~lh1111ncl1~ nUM. .
flmll~~1..oiil!j''IIfl~IL,;~.1~ 0lUlllYi 5 -8 if ""10l1Jlh~111JL'li11~m~Il';~.m,1..ulliu1. . .
,1'1111'n'IIa,1>1q1Jlii..Ti1UlIII unri'1lI~fliinllfhl1u>lllil,ru
-~ ."11i111
(n)
5 k:-.'
u,
tHltJeHUH
fI'i;;vhl'i(l1rn~rl'fl
..
-J kN
!."
L.
500N·m
~H --L
('II)
fl(l'JtH5tll~1JU
~m:: vi1Villlm.Jt1n
(J)
l1lJ1U m{il It'i.Jnl(lh llf)'';'Hhtmd,,m::';,;mhul1rt.Ji/a.JLlHhHlUllall'il'j"l~tl1nuiifi1l1'i1nu u'fiih'1ff
Y'i.JOUll,·lJ <'i,,1linan'iluYiif
jll~ 5-8
•

A":)mi1IJi'i 5-5
ihunm~lilWI~~U~ 5-9 (n) ihJ1~ 100 kg'~~~IJU{rril~ G9l~~fl~r1Jl~ul1lj>l~ C nu D
"~:lmiia AB il~110l~~1~qa"'~:'lJo.ihu"a:lflHmomfl.rU l.w11ii",hl1lrn'UD~lm~mflu
y
(n)
, G b--~
' t ' ~.L- ' ,',
981 N -,--
6m
203
:~~:' ;I j-,
T
- 8 111 - - - - - -
('U)
nl~ 5-9
•
lihil
il)nnlHf.ln ~ lm.mfl1Ji.hulla.,J',l1l'nm:l'ilii<i'nlJlU.fflJlJl~nflm"l.ll1J 1l1.n~. x-y
,,~,ru if!!11l""Qn'llml:111",uh'i,"uu'IJO~"HYiOQ1m.U11JI~UlnU (Coplanar Forces) N~l"'~
on ,<llifv,.lu!uYi ;-9 ('I) W1JiHl~' T 'Ufl>lf)lii~flQlulillJn~mJ ilnmUl!tll'IJV'nl~
m,l'ill",uH>UfIlllJ'Il'UffllJl11EUlJ fl~li'u~.n01J"H C- lIa: C- "l'IU"'~UfimullulIU1~11J"a". , .
"J1~.'Uv.vf'l1~" C Ila: D "llJ~,iu i.Ju l1<i'~.,nmlJ!il~oU'IJD~"mJ~muld nl'IJlUl1
tlHf1~>ll1d<3n'J::vil~ C ml~ft~>ll1d..]n'j:;vil~ D

204
5.3 aUn1saufja (Equations of Equilibrium)
~lm'hua~ 5-[ [~OloUa~nIJ1lIJnl~~~1[ih"ill1fIJ1l1J~,,~a~1~O"~~[n1~ LF = 0u". LM• • 0
o [~alV1q~nm.,h"181'UU'lJ6~u~~~a~UJ~=J1U x-y "~!TJ l'I11J1l0U~nul•.,.nci111J
fflmh=nalJ x ~11l" y ~1l,Jl'IJffll1flJlllJ'l"'Jlla.ijii lie
LF =0
•
(5-2)
[~e LF U"" LF lia ~~nlJvh!mu."mua81Jl[nJ xu'" y 'IJa~ul.,r~l1tJ~m=vi1uJl~Ox '" •
Vl1lHh.,uuo" LM u~J~onlJrh1~w~'IJa.11J[lJmruHrimuull"11J[1JJ.l'IJa.[[Hua8,r.111J",euo •
d t .... , "" , 'I'" ....
Ufl'U.Vl~H'illnfl'U'j ~tn1J x -y ua :-: f.JluVl ::: l!~~ 0 eu-lEll'i1()~ fl ltll'U'l1'l()fllt1'U f)n l<il~
'ti~'lialaef1'Ua.alJflllalJvln (Alternative Sets of Equilibrium Equations) 1hu,j', ,
lllJflll~ 5 - 2 ITn~.H uti'iI!)Jl1111lJ'l"~[~81oUa~nm.uuUH1u,.,,,u[~"1nu "i"oU81/ian'lla~
LF,,=O
LMA= O
LM, =O
(5-3)
[~a"a~flll1'll'i'lJfllld .ra~ii1lJltJ'I.l~" Au". B ~1Iia~1Juu1[i'um~u.;,f.u1nnlJun"
';!~Ul'llJnll~ 5 -3 ,;;al11,iaul'IJff111flJfflJ'l" ';mru1N~1.,qal!~''IIa.l"q~jj,t1~1~1" ~ ,,~,t1
d ' .... . .... .J..i.., ... ,.. d ... 0 ";
'l 5 - [0 (n) Il1l1unm' 'llum"q"""'l"'l"1""""VI~'''01 F" =LF m=m'l~" A Ii""
llJllJu.lUlOrif11IJKmf M = LM "'nJ~ 5- [ 0 ('II) ff1I1fufflJ"" F = 0 u". M = 0 ",!Til.. . RA A ..... • R..I RA
t11 LM = 0 ~ =1.rl1 M = 0 uen~loil F ~=,,'Ju'ltJmlJ LF = 0 ",.hjjj",~ua8mlJlinlJ a
... , "RA R , " ,
".uu uJl01l m=rllI=",~u1nti'IJUnU a ",~t1ii 5- 0 (il) 01L:VI = 0 dia B'llil;i'aulJu"U1
• • •
nlln;"i1'IJa~ F ,,~Ju F = 0 ".1"()~11<I".1U1t1~ 5-[0 (0) ~6u1UfflJ~"~ K ~ .. OJ.
'1!~.,rCH1lDf1iiffil,J'Ua,J i."I'lJnl'H"lJ~ fI ~u
LMA= O
LM,= O
LMc = O
(5-4)
~.~lt'Jti~~~ A, B U~" C ~=1li6QIJ"Ii1I11li'u.m,ilo1f)1I [>im~!~U1Wn1,d[riiJ "Qlu
l'Iil1yjl!IJ~" ,;~"rulNJlv,,~1hll"lU'lHj 5-10 (~) 01 LM = 0 ".Ju lIJ1IJu.l,,~.fifl1IJcl,,6. ... - ..
M = 0 """ LM = 0 01 "Ulnnm"rl1~a~ F r<lU'l""~" B """ill LM = 0 [~iJ CRA B • R , • • c
'lliiJcilu'lu1'ffll~H AB ' ."lliJUV; ~ = 0 u~"l" ul,mJii 5-[0 (11 ) 0.;1"'[,,,"1... /{ ' .. " .

a
~~-.:,>
. ·B.
(n)
F,
a
"
('Il)
~tI~ 5- 10
•
3Sn1Sa1I'1SU3IAS1'1'i (Procedure for· Analysis)
iiinmu'ulYl111'flJ'1~",~lu,:u1ul~0~ nujj,,~if
,
er~l01~;:;al: (Free-Body Diagram) 11~.r~1~q51'f':'lJa~1~~"~~na111tnh"a~ 5. 2
1~0~a~u1'fOl~m~m01.1anu~:llJ IlJ1.1.rUH~Il1mf~l1lJ~iim:~1~ a1~q v.{ alJ'f~':lI'lJU1~II~:
Vi f'('YI1-l'UV-3 n nll'l flfvi'-lnci11 'U1.11 il'U fl-llVI q~-lilliJulu nl1fj ~fllU1rullJtlJ1J~'U fJ-l UH;;}::v'tl,] LlffY'l-l
1ilu.r~1(;)QVim.J10 ri1l1{U<>11utl,'hivlllUri1 1'f1lJ1,O1'flJlJ~'lJtl1 ~111nuU'~l1'allJIlJU.rU;'~ AllJ
iirJ~him1U'lJU1," u~m'UUU1nlln;:~,M
fflJ fll'Hf1J Vla ( Equations of Equilibrium) lun uliHrru.(1'lJlJ ~ x, y He'!::: Z fflJn l1
fflJ,"~ EF = 0, EF = a u~: EM = a (l1,a'li,"'li'al~an'IJaJ1'flJnll~ 5-3 11,a 5 - 4)
' " , ' 0 ~
l~a11~m~O~nllllnl1it;01'flJm,lu'lJtu:I~Olnu Ml'll'fflJnnllJ!lJU.r EMo = a 'flU~," 0 iiaQmJ
~(;)","'IJflJUU1n1,n,:~''JaJm~'1Iim11Jri1,Ya~m~ lui nnm11lJllJ1.1"."a~'" utl,1uvmufl1ii1i1
IiJuf!u£hau 0 u~:j):Mri1,"aul,"o",~ a1l1{U",ulhhil'mtJfl1<>1~viffllJ ,~"''ll'ff1JnliuiJ LF. ,
= 0 u,,: EF = 0 Vifl,"llJl!ntJ x u~: y .,llJm,unuru11,U,JIIUui,Ulwmuaummm1.1 X!!,,: y, "
01fllt'lfJ1J'U 6-l fflJ nl'iC1'lJVlaUftltrw tnfalJ t111f5lJm-lliiflllJllJJ~U'i-l ~f111J~'l-U'YI'nufll LlffVl-l11
iiiiRIm.,,Jn1.1'l!llJ nu~1'I1J1J~1U1'~1," Qii1'1,:
205
a
"

206 i
bOON
..111ul~tl~mu1ciau.nlJllU'l,lUUa"utn~~all1i'UfllUi'UJ1t1Unv1~~tl~ 5-11 (n) lliflY!
11lJJl l1UnUa"fl11lJI1U1~V~fl1U1u011Ii1U11ll
)'
200 N 600 sin 450
N
200N
o.::! III
_ 3 TlI _ _
0
"-2",~ J
~~~~~~~~~"8~B::.,--x
2", J -- Jm--+--21l1
A,.
100 N lOON
(il) ('I)
~u~ 5-11
l1hil
.r~1PlQihn. (Free-Body Diagl'3m) lvivlI11ifflJnmflJ~a.lu;fu Ul~ 600 N ~:1Il'lll
~1ml>~civu x ua: y V<Ui1UH 200 N n>:Yh.iafll1.l~ B Ua"IU1.I"ff>:nue~"1.h:flflUUH B
d ..l~ , "-
lle" B 911ll'lU~a~V1111jyVllJYlVmU ./
y
i;lIJ01'lf1J~a (Equations of Equilibrium) nmnnll>~luVlrrVll1 x ~ :Mi l
~ LF~ :::O; 600 cos 45 N - B, ~ 0
B, ~ -124 N
FhYlvulYlUYl>~~V1 A 111'lYllYluth: unYl1ilflJfll,1lJllJU,[ LM = 0 ,vu~"Y B ffll1i'lJnn
y ' B
ftltl1W ~::tllln~rllUj'l 200 N, 600 cos <t5· N, Bun:: B 'il::nalMlnVl1tJl'JJuvfRw:J~(j·u B
" .
fflJlJ~mmlju.n1Jl-illJ1.nWnn8lJ B ihil,uulJ1n (1uVlrrym ~k) "1iU~ 5-11 (~) ~il.ril
C+J:M,~ O ; 100 N(2 m) +(600 sin 45" N)(5 111)-(600 cDs4S" N)
(0.2 Ill) - AJ7 m) ~ 0
A,~3 19 N PlVU
m>u1fl1ml1.1VlPlvm y 1'liNo A • 319 N ~"1~11y
+ l' J:F ~ Q' 319 N - 600 sin 45' N - lOON - 200 N + B,. ~ ay ,
B, ~ 405 N

207
A~aa1url 5~________________________________________________________~
l;;vn1i'~~ '5-~ (n) 1V~i'1JU1~'IIVJ 100 lb ua:1j'1J1vmvnfl1fuHLi'iu"mu .J111
~niiJlwiianfl C ua.v,fllh.nau'mJlIJJtlBmU1m1JUU111uua.UU1~Jfllllj" A
'l'
t0.5
05 fl
~ Ay
100 lb lOOlb T lOOlb
(n) ('I)
ltl~ 5-12
~~ .l1i1'1'
el.r~q1iil~~ (Free-Body Diagram) thrYl~Dill:'IaJLli'w;;anua:1vn1i'Jltlfi 5-12 ('II)
.1nll11n'llaJnnm.vh Lmtlijinuwi'VJiifl1LYi1 nWL~ijVi ~I'L1J"H nu,j'llJ ,li'wiian.:iifill
n,:.luJ1l11rnm:vj)1tiVn1Ufl1 p mlJlhU'llaJlttL~l1an lu'llru.fi1anihL1JLvhnuLL.ijjYi~"H
nu,j'llJm:vh<'iaLcrwiian <l1l1>u1ilVlud Li'lunni1ufl.:nlJ"Ji'''"1jDlll:'IIaJ,anLLa:,hud'lJ''1l
'lJV-3n1UL~hlfl vr,,,,ru J",nrn f)'l::vil nutJo 'j:: ill £HJ::di~ ill vh!'J:::uu LH'I ::: ~ n'Ui'~ ul nnUl If!n ::t1
"'ltlfi 5- 12 (A)
lllJn11illJ".jil (Equations of Equilibrium) nn1J1nllJL1Jtl"'()U~Yl A Lvia'll;]'Yl A, ua.
A "Jltl~ 5-12 (fl) .:'I.ri1y •
( +LM" = 0; 100 Ib(O.S ft) - TCO.S ft) = 0
T = IOO lb
Vlui1filliiJOJAJ~1",uLcrULiian~lu,an (9l"tJtL.~'<l111>Ul.llJlI'l1 8 ,iLcrwllum;na:
<ll11>U>fliil" 1 r'llBJ1an) 1'Ll'Na<l111i'u T nnUlnlLH~ntl1:qn"Lvia111ILmJ1i mUlriaufilll.1Yl
A
----'--; LF, =0; - A , +100 sin 30' Ib = O
A, = 50.0 Ib
A, - IOO Ib - IOO cos 30
0
Ib = O
A y = 187 Ib
Y
L,
A,
0=30"
T
(fl)

208
_A3aa10n~--------------------------------------------------~~~l1ltt~~UiimVl~!lJ~fl~lU~1i~UUtl~~~ A ri'lMful~HnlflUfUthMll'nmnh"~2U~
5-13 (0)
400 N
400 N
B~lm 1m---l
C
~tm-t-Im---lB __
IT
C
200N
,
2 m
3m
+
2U() N
()
[m
A, A
A ....l.,A MA
~~
I
(0)
A,
('11)
lU~ 5-13
•
44 •
-)tim
"~1{;tQliin~ (Free-Body Diagram) rr~1~q1hneril111Ulm~mDuJmlJ~,,~,t1~ 5-13
('I) ihn"'11!LU11lilm1J';1~~lmfl~fu~u~uumvtU"1V'lUl~'Jfl~ A, ' A, !La: MA
alJ01 1a lJq~ (Equations 01" Equilibrium)
----=........, LF,~ = OJ
+iLF= O;, A, - 400 N -200 N = 0
A :::: 600 N,
M " - 400 N(I 01)- 200 N(2 01) = 0
MA::::::800 N 111
" au
~~ A nml1flnffl111UnllU1nl"tlJUt>l t~fl~~lnUmm",il'Ja~Ul~11ivtllU';1 A u~~ A H1U. .. ~ •.
rl;;;'.!~'idi Yl.Jt.T'U uHvl"JJld I Jd'l~lJ;;Y' J HJ1U111~u)llhHiJu~ 11HjJu;fL~~ .j Qnl1j"ill:;~iltl:l~[rHlf
fln''i!:LU'I:::ll,.l t!~I"'U D-3!1U 'j ()-3 i'uviiiil UUutl1.Ilfi'1.J O'iUU
O.JUlJilU::;loUU1HllJnlH"lJfiJn~il ,n::all1rUlwqU'l'Hn·hl~rr4o.J« IlJ ,rlJ nI'J U~Jl l.ili'ctllTl rjJ'
fflJt1ja~lilY;1) m1~ (flU01,linn!IIn~"'Uutl,:lv'l!"acil~t~ vn.11aril','jj'U nmi1ul!II.,j'" " U~"
Vi'.!lJUlVlUf11J"jllll1Jl1JU~'jmJ ~Ol C

-.
1.
400 N(i!' m)-600 N(2 mj+800 Nm ~O
400 N.m-l200 N.m+800 N.m ~O
fi:J<l'~5-9
Z';lIJ111llJa",luitlYi 5-14 (n) ~nmnh"'011>~lla:hJllJU"llH~mJ «'11l'i~'u~n
>a~rlJ~ A"'0mr~nJ~u lla:Y1 B ll~: C J~ri1UJUll":ri1!Jril~ I.W«lJf.ri'fllJJnJ~!J
~~'nll>~t1iim01Y1~lu>D~'J"~ncil1ii l"o'l.ii"nlJlhmrn~a~lll'i~lu
(n) ('1J)
,t1~ 5-1'
•
Qd •
~fil'll
.r~l"Qi"m (Free-Body Diagram) "~lUYi 5-14 ('U) llmJfim01Yi~nna~jJlf~l1lJ"
~::n'j::vi1~>lUlfltJn&intJlfll~h'Utl-lf1l'HflJN'Hda-l'i)lf)~u~h«lHrf1'51'U~U LL)'J1l.am[Jl~ B un:: C
m:vi11uiiI1Vll~J1 n y' luyjii~: lIlJlJ~ mvmnmllJ "lI';llll·nj~",J ri111ril~'U a~ tni~luyj Qnli'
"h"rl1U!lUl0,rrU
glJfll,glJ~a (Equati,!ns of Equilibrium) l'li',:ulJwn"llln x ,,~: y ,,~l!J,u~ 5-1'
('Ill ~:l"il
~ LF, ~ O; C,. sin 30' + B,. sin 30°- A. ~ O ( I)
+ r LF, ~ 0; - 300 N + C ,. cos 30 + By cos 30' ~ 0 (2)
<:,+LM, ~ O; - B,. (2 m) + 4000 N IlI- C, (6 111) +(300 cos 30' 1')(8 1l) ~ 0 (3)
Lnm;iutHYlJnnllJllJUvll'IU11UU1ld'U'Utl-3nl'Wl::Yil'U().Jf).lrllh::natHll-l 300 s in 30· N
~1t1Y1::;~~il A ;.J,r,t HH;1,.,,,;:1,jft~n'JlufflJnl111JllJtlyf
B,
Cy.
~
~
-1000.0 N
1346.4 N
209

210
I~a~~ln B . d'JUinn~lf~u Yirrl'm~a~ B . ~"iiYifY"'~~nU""lJnU~"ff",~1u"~1"'niiff,"hj
!tI~ 5-14 (~) ',)~Ju ,hu(YlHi'"UU~ B ~.lrlU!lU~a~rUlJlnnilcr1ualHi'ffcil> a~~"fl1D'
l1lJl0aUli11-1rU B . "a.Ul'lu,i1.r~ncil11Ul'rlJn1'~ (1) ~"Mil,
1346.6 sin 30 ' N - 1000.0 sin 30 • N - A, = 0
A, = 173.2 N
~3aa1oft ~----------______________________________________________~
/ fl1u.r~~uvi 5-15 (n) jjml.iDl~fllJ"UUl1lJVlvi A ua.fl~ii,O",nU~llnfl~rU~"U~uvi B
~'111fl~li'u'"nflU~fl~""u5mOlVlllJLl1nllUU~"UU1~,vil1lJ'" A
rjN.
):::.
f '0 A )
/ ~' '::IS.~===I'tp=:©
."--.. -'. ,
0.75 In I 90:'-! · m
'1
1 1m
• 'L' "
A ,. 60 i ...
"" '~~~~)
0.75 III 90 i' In
-~ lm --I---
0-5 III
(n)
'jtJ~ 5- 15
('U )
v
~~ .lfi'tll
"'lOloaa>: (Free-Body Diagram) .lnluvi 5- [5 ('U) UHUumlJl N, ,f~il1nnumu
~ B ()-3filh::fHJU'lJ6-31'j-JJBmul~1)JUUlnUU":::Ul-rl~.JQnuvn.!~ A O.Ju';ll~nt'H}-lftJHUVl1l1~
':Iao~
alJfl1'il>Jq~ (Equations of Equilibrium ) nllnlJ1I.HlJtlollau A • •1,j,h"'flu
l", om~crll1rU N
"
- 90 N 111 - 60 N!I m) +N.(0.75 01 )= 0
N il "",200 N
----'---> IF, = 0: A, - 200 sin 300
N = O
A( - 100 :
A,- 200 cos 300
N - 60 N =O
~ A, = 233 N
'W1J
Olau

fi:Ja~-11 . v "'
. lllJ 150 Ib m"'l11Jutlal"mU.,.~tI'V 5 - 16 (n) ;mn'llU1V11m"iI1'l1...m~lIHtlBm"1
~"'~V1 A ua"m~;i.iUlmiia
C Lx"'I
!.5 ft
I
I: ft
~ [ ,l
8 f. 2,.
150lb
150lb
(n) ('1J)
,tI~ 5-16
•
11hil
.r.r"''liia,. (Free-Body Diagarm) u~.n~",i11Jumui.~tI~ 5- 16 ('II)
i'flJIlUi'flJ"li'f (Equations of Equilibrium) l1lJhHlJtlOf~u1J~" A l;;,,1111"Al"uU
l""V1~"i111'unl~;i.1Ul,,!iia ~.M-il
-(~T)<2 It) - (~T)O Il) + 150 Ib(W Il) = 0
- 3.6T + ISO Ib(lO [t) = O ( I )
T = 416.7 Ib
Hmlll'IJu.nm'i.~lu"" ~"lJu"u.M"h"111.i, T vi c ii~lllJil~llill"1tiutiuumui.
l1Ji'i 5- 16 ('II) iumtiiil11miu"hmU1~' T nl1111lJllJtt,]li'JUljurhulJ A lm:u'IluilJllJu']
"tlD"".UuuhlllU1' llJ (~T) .:ti'Ju 4.5 ft inru LMA= 0 l"'I"alJfll]~ ( 1) i"um, !iiu'~ln
(~T)(45) = 3.6 T
nmllJ1"~~'1vi' A ua: A i,,"H~a'1Ju' T ~.1"il, ,
~ LF~ = 0;
+; 1:1' =0;y
- A , +(*)<4 16.7 Ib) = O
A, = 333.3 Ib (-
G)c416.7 Ib) - 150 Ib -A, = 0
A = 100 Ib J. ., .
211
T
c,0 T
T 1.5 ft
Ii.I A,
A,.

212
6kN
FA ;~(333.3 Ib)' +(100 Ib)'
; 348.0 Ib
e - r 100 Ib
= tan 16.7"
. 333.3 Ib
m Ull'JmrlJfl 10 0 kg i~lU~ 5-17 ( 0) Qmfl~llJ~ A hWl1l~~ uo:~ B Uo: C
1~olfllijo~miifl~9i~lj'lJ1flmflO~Hfil1lJliio~mu~.ilUl1lh D (hllH~~lJ1n~l!~ 8 00 N
1I1lJllmii~1u,mijoriflu~~:"Wl "~I'm:O"lJ1n~l!~"fl~ d ~UH 6 kN 1l'11mOflQuumu
111Jfr~mfl~rfu1"MlJ"tJ~m~uijmol1uUU1nlJlra""U1~~~ A ri6U~lfilijo""'111~ l.W'li1i~11lJ
fil1lJ"Ul'lm~mulunnlilU1Ul
600U N
A
A,
i--- - - - - lOm - ------1 :111 .I. ~'" .1,
A ,.
( 0) ('II )
'iU~ 5-17
•
ifi,ti-)
H~r>l ~6 tf1:: (Free-Body Diagram) ldu-n lflltIl1JftciuL~()-1ll~::tinfH)U'HJn1rfll11J
.. .. t:- .... ~ ..i ..: • ~ OJ t
HHJV'I 'llH lfHUuVl.J'H)JVU.1fW1::l'lWl1t1f1l'iVl..JlJlnVIC!V'l 800 N lti()UH 6 kN 1l'j::YllV1 d Yl-11-ru
@UoiiUH 800 N ~~Vl C Uo: B 1J111l1u1IJViflVllJ'IIa~IAlijil"'~,u~ ;-17 (il)
iflWl~lIIJ 'la (Equalions of Equilibrium) lVl0n1"'lJ11JIlJu,r'll6~1"UU"H5fl1J~ Vl A
'1" ~llJ'j~" , iilVltl1J'IItl,jj ~ d 1VlIVlU~jJ
J
( +M, ;0;
-(6000 N)(d) - 98 IN(5m)+(800sin 6(f N)(Sm) + 800N(IOm); 0
d ; I.+l m
.. -.,- .
u ..,... )
~LF.= O;
+ l' ~F. ; 0;
- A, + SOO cos 60' N; 0
A, ;400 N
A,- 6000 N - 9S1 N+800 sin 60' N+SOO N;O
A , ; 5.-19 kN
.,au
I
I

5.4 BW:I::lUaaIJUa:a1UIlSIJ (Two-and Three-Force Members)
_~ ';,~alJ~a~ifqpn illJ~ft illlJ" 0fl ~iu~tlaVl,.,"01~uri1U~nOJ "Yil","('ffl~111al'fllJ""
'~lUU .
--;: .:;tHiltwa'l!l' (Two-Force Members) ,da~mhu'~ijh"lJu.r~U'''''tifl11Jn'.Yil
,,~fl'~; 2 ,,"m"vhiu'1h'~riltl'W~mlJ1Yi~Ma'~YllYl1 lJU~Uri1U ~uri1uif,~"n-j, iUlhu
l1'a'u" .l,aci"'lJa'l'f01Umlruui!~,lu~t1Yi 5-18 (n) m'Yi~Yl A ,.ft" B l1lJt1uM"fttlv.1l FA
'"
"~ F .lmJYi 5-18 (~) m'M,u""'ncill~.fl'nmfl~flU!r'"l1~mllJYlft"H (LF = 0) ncillliu~I'" 8 .. ... •
F jj~ul~,'ilt1ut1lJ F ,,~jjiifl'l"~Ht1U'UllJ U1ln~lnUlJ illJ~ftml11lJu111allJ'lJu.r (LM =
A. U • • 9
0) 01 F fl~UUl1~"'t1U (Collinear) t1lJ.F, "ft.l'ncinYilMmlU"U1fl11n;.Yil~fl'''''vr,~
, ... , ...
,ilfl'~lmrn~.r-ilUV1"~ A "ft" B .l'uu il"l1l111WWJlllY1UH .l'fl{;"liu~fl,;u,i1u('fa,u"lll
('flJ~",,('f~,lUltlYi 5-19. .
I!J ~uri1lallJ!l1' (Three-Force Members) li'limhll~nm.Yil"l""Hlul.tn1J(~"'t11l
11'1lJ"" ~'~11'JIlYi",,~"iitln1Jrud1lJ~~t1U111fl~Ulllt1lJ (Concurrent or Paraliel) lilillrilll
o"1"''flJ~~ ,viflWil~UW~llruTi'~ohntlYi 5-20 """Ul'('fllJ'ml~"ilO,,,,,,,,nl~ 1 m.Yi,lJll
1~oYiflu~'fl1,m"~,Yi"~t1uYiilYl '0 ;vla1MillJ~ftllJ(lJIl.r'OlJ 0 tTulio LM = 0 u"Yil'fllJil"• • • 0
N1Ul'1:::'l 0 ~vh111'l::1JUllJ.lLn~ fn:d1lJ~V1 (ConcuITcn() 01 ffClJll).3U'ln'UfJ-JLlH('I'llJUH'U'U1Url'U
~~11)J 0 il"QnWil1l0!1l'JU~~1f~fl1J(~~ (Infinity) "". U"Yiffl uil"~tm.iltlt1u""iinl'f1H""
d ........ d J' '" .,,; :::; ~ , .. v
'Wfl~~nU'l~~1l ('flJ'l"m'il" tn~ (LF = 0) 1Ufl""'l]illlJlJ~~1lIH~u1nu
F,
(n)
(~)
"iU~ 5-18v
~t11t 5- 19
213

214
oiui'hulf111U'l.J11lJ1!~
(n)
nl~ 5-20
•
,]ulun ABC ~mV~'1J"1JUl1lj~~ A "a""'m~alJnu'li'voia.ru BD "" tJ~ 5-2 1 (n) 01
Jl11Un'lJa~';;"lhuhjii~ .~11lIm~a""lj"uu,]ulun~ A
•
O.5m
0.2 m
0.2 m
O. lm
(n)
(11)
~t1~ 5-21
11hil
I " B
! /
j ,-'450
I
.; - ' - I
o
F
,,
,,,,
/ {b)
F
('I)
,- -- O.5m - -
"~l"qlhn" (Free-Body Diagrams) lll'f">i"u~kl",qihn:",,tJ~ 5 -2 1 (~) 'li'voia.r"
BD ij€UfflUcHJ.JLL'J-l i .J1.ru u'i.Jclvnf ( Resull.ant Forces) 1~lf'lJ~ 0 lLen: B i'hhn(i1n.m~ijVift

;
,
~~~ nU'U1lJU~diUU1Illl!'~U1t1U 0.LLlr~ U1"~ V~u>.11iVinu ri1 UU1,llWIJV~011m:fi1V1nu
,dU~.,n~lUI'I"~ B Uil: D
flulun ABC L1JWfUrilU"'lJ"l~ (Three-Force Member) ,,.vii.:hf"lJ"l~llJ'lJu.r
LLH'1iti~U'U~~"'lJfmfi"ivflulonvQ~"i1lJt1UYi 0 fl.~tlYi 5-21 (fl) 1"OLilYn:v01~~. WUi1
LL~. F m:fi,.ivri'uloniirilly;,t1uu~iiiiflLlLnnU'.r'lJt1U F YinmhYi B uu'Liv~a 1:0: CO flV
0.5 m ,da~.,nm'ULLtl1LllU~v~num:lil'lJa~ F Im:m~ 400 N
,uJfin""~~ (Equations of Equilibrium) ,dv~,'m:uuLL1.,i'Ju~LlL>llJ'~Olt1uYi 0
,;~tfll 1:Mo 0 0 ljlJ 8 .:ilO1lJ"lllLllll~U~fi11n1:fi1~o~ FA "llJ'l0l11.,n,,11muii~
8 = ,an-,( 0.7 ) =60.3° d" "'OU
0.4
tl1:Qn.r"lJ01~"lJ~aILn "'lJ'Hll11 F U,,: FA
~ LF~ :::: 0;
+iEF = 0;,
"niYunn . :1.1i1
F, = 1075 N
F = ' 320 N
F, cos 60.3° - F cos 45° +400 N = °
F- sin 60.3° - F sin 45° = 0
"'ou
11U10IM~ : iY1lJll0"nift)!l11iilLlLOVI.BtH~ Al"OIL'~OOO1f~"VJ A t1U A IL".lh:qn.r)
LM 0 0 , 1:F 0 0 lL~ : 1:F ~ 0
A x Y
aUfla1ua1uJJ~ (Equilibrium in Three Dimensions)
5.5 wu5f1ooas: (Free-Body Diagrams)
.r"..vumnlunn unilt)!111"lJV)"1llJQ~1M~vu1umill1oJil~ ~a 01,11""~1LlLq0",:~ OJ
1~(! (H1tJ n~}Ji'(;l Qvl!flW1)lHU111htJ~lJU) ritJtl~il~LlC1'l'l~h;L'HU ~lruul'i'{)-l nci110.:J'lfUI'l'U O-lB':i,'J
1.1fimtn~d)Vl;fuTi!l 'U'j eUi'tJl~Uritrw
"'JIJiimol~21"'M1U (Support Reactions) mJGmolL~dlJLlJ1!.r""~mum:1'ilyj
!l"'O,rlJua:nm';flL~mJl" 1 ,rioiuriltmQlultl"'lJiiGiUiY>l,lu~m"~ 5-2 ~'~1!tJ""o,1i
rr~ a flll OlU'YIUUYl" :::2!lU'H)~i''U hHl ~(),J l'J1hifn'Hn vHL:i~uC::hUlJ u vlll7,;J tifl1UhmYl"t~ltt'H) 'l'fu
miit)'wlumrutHJ J ij~ llHil::lf) ~~~llJ'HJ Ji'U~H::~1nYi n"Hft ~tnHhv'U f)~~U,hu~~VI nulH'IJ U!~
~ In 911lJL'lJl!vlU7-J tifl1U lrl 0 011 H'l~U'J f)-l~U rilu~~~ nuQnilu~ n-w uf)~-H)ci l-J1UYll1H~ 5 - 2
!nmnma::llJl (4.) ila~nwlllft~our1HJ1Vl1 · 'J(J-liurilUl'ltHitllJ ~,nru ll1Ji)t fn:::viw;fJ
ilUrilU~."~OL~UlJ u"iiiiIL"ciuo"'tJLLl,~'l~m'lJ'UtnVl F , F ",," F ,rium1lJUHOOO• 1 Y 1
lil-lnal1 ffllJl'J011111U1Vl'Ue-lUH F = /F:! + F2+ F2 LlCl::llffVlH'IHFm"i":) hHJlJ1JViA'VlHoWrlVl. ' ) ~ .
a , f3 um: y ~l UC'lJflll~ 2-7 LtiilJllil~U{hu~ur~f),lJl1lJuf:h'l"H;'HlUUf)'U1Yll ~,;J''jjli1mlJUvl
ILl'~~lu1VlQn"1111.,v'Liu~Dl1ljVI ua:Llh
215

216
L
!lU~a~i'IJllU~~I~Ul (5) U~. (7), l1l.l~I~UUI~Ul (8) Im'UlU~UI~Ul (9) ~U1f,m~u
~ll~i'u,f~II~Iflh:nauII~~U~.llJIlJU,(11H timu ari1~,~iimlJ !lU~a~i'U.1~nci11ifiil'ialitalJfi'J
uu~~, 11l.l~ 111aU1U~u l~fli'mnlO1~l"raQ1flJ'l~u~.'hl"rl~qm~nlum'WTl~Tll1lJU;;~ln~~
l~ajhr,l1rom.'hll":ii!lU~fl~i'ul~alJnUl~q .1~Ju 11~~ufimul (Force Reactions) ~!lU
~a~i'u~:'Wal;;u~rill1i'mlJ~i'ulOiq ,:!OIiinuul1j~illlJllJU.rm~timuItiUli1ulnu (Redundant)
IIa.,]~>f~l,,'1tlri'~101 qihl1: Ill') Na,1~:'ll'V11~Ul1K~~ln1.11I01n.11lJUH ll~~.riHi'11. IlJ.l1.ilJ.rll~i
tiflm:'hili~~~lu~a~i'u.1~ncilll~lJ~~lnnnl1IjU~a~101~~niJfl~nulO1Ull~~uBmUl~lnOl~!lU
lMi'u~Ulla:llJ1'lillJllJl.rm~timu~1ll~i'u
~lS1Ji'i 5-2 :i!lUS<lJsucllV1Su5~CJlli.lJInSJi'ij]S'UUllSJalU[jliins,ri1
(Supports for Rigid Bodies Subjected to Three-Dimensional Force Systems)
Q • ~
'l!U"'Ull~"""lll'l!lllJ
•
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(Reaction)
(1)
( 2)
(3)
(4)
.7.

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tl
-..
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I
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I~,,-
q;
~ f
~~
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;ilU1UollUU~lJjym1Jfh
iil1~',]' uu111.il'lnU ~1 IIHU~ n~ulltlu1I1~~ m: l'h"lllJ
~uli1uluViIll'm~a~IIIIii~
iil1il,vll11Uihi,,;1U~1 ll;JuijmU1IIItill'J mevh,f,U1n'lU
"t'W~h~~V1tY1J~'"
D111mb111hhi"ilUri1 ll~~uij mU1IUW'l>,10,'0aUliHi'f1lJ
LLl-.lhmU1Lln'U x, y LlC1 ~ Z
ii~~·] ~l1.hlllJVlll'Ufll UHtl~f11Ulll}UtJ-J i'1JJ~ rld uUJ-J IftJ..J I!.~..J
~hjl";1IHluUU1l~01 nuIVI ~10 ~lJU~:lW~IlJIlJU.rU~JTj~1U
~f1i:::lll1ltVif(~-3111 nn'UlW"l
1,

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'tiUA,.tl-1'.!~~a l~alJ
(6)
(7)
~
'-. ,
"'--'.-
u1nJ!jmm
(Reaction)
M,_~
Q;'
c:- t F_
';; -;YJ M
M,},Y".-t~~'.¥0 f, ~....:.:.f
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(8)
(9)
(10)
M,.
Q;/....,
)-{-
- -~
f , ~1
f ,
tll~~i1UUL~ (J1 (Single Smooth Pin)
;illlll1~lmh1,jmlllril
217
ii111.11"u~1tjmlll fi1 LLHU~ mUl Lllua~ fi'u~"nall"n,m~
m~~lu1'Ii,,~~1u"u1I>iU1OWvall~Il1~UlJ~~rlHm"<fllJluLIJU,{
UH~f11ll
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un"<fa~luIlJU"II~~ tif11ll~1Iihi1u'Ull,{~l1~U~all unU'Ja~
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f-1~l~OHu';i~ (Free-Bod)' Dia!!,-ams) 1~1~u vt'llt.1~~;:fffl~ r-r,'JlOlOflffj::~(),'Jl~ f1u<J-lLn~,'J~ <.> . '
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ihru1~~hj'V1':illJ ft1Lll'l'~-ln~::vllUH'I-l1Vli.liin~::luVitrUl n lui~il0'lfh~l-n'l~lthHlU 11il::lhu tl fl
i 11.1'i-1 tj fl il n'i~1'l11, (Vifl'V11-lW nA~lth!C'llJ

218
A38U.ufi 5-14 ..--------------------------------------------------------..~
(n)
A
.1'lflcil~~H 1 ~Hl"Q"1)JN~1"Qii<l1:ihm"m'fl~,)~ltl~ 5-22 1ul'lnmru <lrl~!lnU x,
y lm: z U,,:fl~"tl1:nfllJUHtlamul'1il'm1JThluihnm1J1n 1"v'1iiimr1l1un~fl~1"Q
c
c,45 N·m
(
SUO N SOON
IlU~.JU1.llJ Journal [J011.JLLlJlJll1lJl::UlJlt A. B nil:: C Ln.:JtJDm{JltnVll~{JLLu~~jjtYlm'~()rlll1rtJ
IlHua::lflJilallJtlJuYl Luunlni1fl~nJLYt(1
'illnnn~~U1"UlJURa::lLnUth~a~'~
('II )
300 lb
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, ,
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c
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.,
I
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1~()il(),lflUJll'jI14U'H)1HLnll y U('I:: z
•

5.6 aun"1saufla (Equations of Equilibrium)
~10~0 ciTllJlhnhtlfl~ 5 -1 (j()u1~lil11rUlYlJ'l~~ij~10l~U.u~In'~~~m:UUUmfllJiiOi
m::,jl J-3IlHri"vnfu,,:;1lJllJUvlUH tif11Ua'WlflJUl'~ ~ijfh~Yh nUfJ'Uu
alJ"a'IJfl~olJft1111n!,w1 (Vector Equations of Equilibrium) iillfl~L~flU1~lil11rU,
fflJV!1'I'Ufl,rf~ ~ U;J~ If)~,J'uiun fl L~a {Vll-lfl ruVlfll fflwf fl0
LF=O
LMo= O (5·5)
lriV l:F lilufH''jllJnm~wf'Jo-lll'j-lnlu'1VnYinl::yh~t)'rVlmf-3l1lJvHL'':: LM li~lur'HnllJ• 0
IlJIlJU"UHtimuu~"llJIlJU"~fl~UHvf~l1lJVllflU~"i" ~ (0) ~fll~~~uu111flmOUfl0101Q
alJ"a'IJfl~iIlJft11a,"al" (Scalar Equations of Equilibrium) tl'l;juHmOUflnLL~:,
IlJLlJu"~fl~ IL1~ ~ft1um:villuiUl1nLVlil{Vin"ulo l"oul'lu~lulYlJml~ 5-5 ~:;'l"il
H' =LF i + LF j + LF k =0, , ,
LMO= LM i + LM j + LM k = 0~ ) ,
li'ia-31l1nnl·Hn01J«1J1.hdYVl~~fl'H)Hhh::nmJ i, j Ui'I:; k l1Juij~J:::~,Jnuu"::nu fflJn1'5
'li'H"U1fllJl;OI~uu'IVl1u2U
LF, =0
LF =0,
LM, =Q
LM =G-,
LM = 0,
(5-60)
(5-6 ~)
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~nJnl'i~ 5-6 n LnYY1-lNnnWU(),JfJ~rfth:::fHJlJLl'j'1nl(J.wn~fl1::vhll~~m1lJ x, y Llft:: z ~,Jij~l
I'Vhn1J~lHr Ua~illJnl'jvi 5- 6 'U ucrV1~tlf'nlJ'U{l,]{l.Jrllh:;fl fllJhHlJtt~:iUWWU X, y Uft!: z ~,]ihh
Lfilnui,Jwl
55n1SalV1Su5IAS1'vj (Procedure for Analysis)
i finTHUi'U11111CfU~" cl'llJij~ij~,.ni
r-j'-llT1l!eft1~ (Free- Body Diagram) crhHl.r"lYl q a cr'l:::ffllff lJ1C1q ucr~,]UJ.J Lw:::1lJLJJ u~
11 f};J Lll.J~fllU';-ll1lJVll~ n'l!:Vl1~tr)Vl q U'i.J m:::1'1llVltrvr11,jlnVl ll1 ml1'Htrnf) l :::vllfll £l1.W n, u'j,]~N1
ff",r1f~ ()~1~Q1ml10" lJ5mol ~!lma~rU LL~"Jnl1ro~a~1"Q ('unHu~ii~"lJlilrl!llrlfl
liimJnU'U'UH1'IJD-lLlHf)1::l'ilflu '1) (1'11.J~Vll~1J~'U'UD']UflU x, y Uft:: z ~i:'I'~v)ln~ '1Vlllft::iHifl'UOU
ti~u fl n." LLlb'hivnuri1 1.,uvh'luu1l"~,,'j~ci ()o~'himllJrilVrnl1JVl1u0111 n 0 ~1J'''~8'11'1q
~lluurll1111nnl'U L1l'U11I'U i).J llj.J ~;Jvl(l,rn iJ arilur-1.JlVl oihn:::. .
219

220
, <wnUillJ"!" (Equations of Equilibrium) lu'1 nnniiif()j»lilllJUou/i1",'1",uhi'
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. . . x y z ); y 7.
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lt1 lli~"uUYi,"UU unuYila8nli1!1i'un)JUH.r8~,uult1mlJ1"UUununLB8nli1!1i'mllJ11JL)JU.r '
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"f~!101 U llJIlJU';~8~m~ ~,um~~",uuunuil!1~8"H'IlU111t1U llnu~dili1LUUt;!U6 U8 OJ) 1mTu
'10 1 "oucr1lJjj~'ll",1", 1 ~L"8mi1!1i'lJnlnllJUH!1~~1)JLlJu'; om1i8n"ou~1l11J1.crlJj).'Vhl11
lUhnmlJ1lU~lim1ufi11.n",u.m1158Dcimr~Uil1lJ1ma",if()j!1l~lii"'~1nnnuncr)Jnn~9hi8U
ffl!1i'lJilutl,llim1uli1oi" 1 hi'
5.7 dmhrifla1V1Su5~f!1I{jJIns) (Constraints for a Rigid Body)
, ,
vi().Jii,jv~l nVl~ L'HlJl: HlJd1cWill fllltl'l v-3i"'u
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~iill"ri'if()j11 .118U1miu if()j11M~jj~,,~:t1~ 5- 23 (n) !"'"if()j11cr1lJjj~;i'~:t1~ 5-23 ('Il)
uC1~-3vd'DlJ~-1i~~~6fI''l:::...r-l ffil-lVGJll1ij ff n 1V'llthu:::uua'll&LVl u1iJL'U~lllJlJ fffl~ffl ff~{ 1UU.HIl n
Uoi51U1!lU'1l_~"JiilJ1mRumllJ"1l'nll "m;oh'f1l~jj~ ;:;111.1111tlillivLllUfl1 li8 MA
, A" A"
A , B !w" C 1~u'l1j ti)l!""~""!1uilljm1uli1~ffllJllQ11fll'1.rIYil1"ihi; v'ffllJff1Jm'ff1J~'a'. , ' ,
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1~ (J 011 ml'lJ nnfflJVl "v1.:J lti1Y1-11'UfflJ j)1'j~ 5- 6 ~-1~lltltl~fl-1'lli1lJ nl'H~1Jt~hHvit)"t11fll~1Uth
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if(~CJ loUeN O''UfJ ill ffl.j'U~Vll-1n 1801 WU t1,j l'>l CJ~lR{J 1 flU fl"ffl (f~{'U rN n l'Htl ~mmtl (1-1 ~tJ-il-1 l"l1t.1
flflfllffVlf'Utl.J1ffq ( M echanics of M~teri a ls)
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loqiimnl'lllJ ('flJnmllJ~~ m1)J1,jnl~ul (InSlabili,y) ~o~l" q~:'iil'l;jllliio~~ln'lio~l nl'lii
hill1lJl::(flJ (Improper Constraints) ~uJ~lu'JuJfu l'UTl'Hl1i1iY111C111lii~ lVl~lI:::ij,ju~lnVlYi
'I,j,I1lJl" ('[u .h"HuBmU1~1minfumw"nilut",nw~"1nu <!ll'ffuif1)J1l1 ('[a'G~ "nHil',f~~1n
nU':U1U'Jin "",,~:.:un n!l,'JIl~1'I "nTu ldall1,uQ;;jU1'1nm~)J1m:l'hi1)J~" I~U1nil
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Force) ii<i'mJ(U"t1JtUl~'~'lJlmlvf'l1lJi) .J1DciHff1lJ1!~'ffij,jj~Uffi),'ultl~ 5-25 nnnlJU;J
1il11JUnu x iiril11.ilyi1nu~ljti
llJUl,mru 11il~iit!;Ju5 mOllr"oni1fflJn1~fflJliln 11il~ljnmw~n;i,ni)lJ1Jli1lJ (Partially
Constrained) uo.J1m;w'liu t~D'W~nun11il~lu~tI~ 5-26 (0) ~iirr'1i)~~CI,"«"i)fl,i'il';)'lU
,i 5-26 (iJ) 01 0 11Ju~liliilli"ciUlJUlntfflJ AB ('[lJOU LF = 0 U~o LM = 0 il0Il1lJ10('[lJnu• .. , 0
ull"muI Fun. F (,[]Jon Ll' = 0 '1)j(,[11J,~oHa'11rlJl~"jl'lJJl11uomni, .J,tTlJ ;,')j('[IJi)~A B y '
I

,I( n"~ln~~'>1lJm'flJll:olB~,i'Iu1t1"llJ('fB~,i8U1~.iBlt1ii' (1) .,1l1fmnmhJe~'mtlijmU]
hjii~~i;1Jllunlli1l1 IL~: (2) ILHtlijmul~.Jli~lllln1JlLmr~>1lJ~ '~mi11l11lW~UHtlijmUl
~Ii'B~'n~'>1lJl:lI~ Ul)!>11Il:>11rilm~lI~"f!ll1~rt.r ...tTll lIlJm111lJ'l~1I1lJ1Hlhl'>11uHtlijmUl
J,Jl11J~JUlf)~
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•
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U'l.J ~f1 11J Vl1 U'J()U 0'1 ur-iUlJ 1.1 ~Wi f}-3i'uhl'~:::'UlU'IHl-1 LL'UTn1Jl~u~tl L~au~ A, ~nn ftlJ un::: nrl~
B .,~:nl'll!;;Bn~ C l'>11B.rftll"nB1J~fllll11t1iimV1Yi~1l1Blf1J
300N 200 N.m
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2m
8
('I)
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223

224
l1ifll (n11'ilflnnfuuUlIlO~1{)
_H~1~q1lin~ (Free-Budy Diagram) u~~1l5mUl~~111~hhmUfh~nmil~~uli'UU1~
"~~ll~ 5-27 ('II) u.ill:_uHllfimUldQnllllll~ll1nmh'uiillfllown"~d'lumn
1.IlJ011l.lllV!" (Equations of Equilibrium) 1~~o~ln~llmol~on'lllmil,,'u~:llUllllljj~
d'lUUUU~lU 1 'n1~1Iflll:,fuuu,nn1l1{~:111fil"aul.n"u,,~~ul1~li'JUnl~~lu~o:iju nl~nlluHlu
u~ l1:unu ~:Mil
~F, = 0;
~F, = 0;
~F, = 0;
B, =0
B =0,
(I )
IIIIIIU.1'IIao u~o~auunuii~lH11 nu"11 t;!Ill'llao'llU1"U,0Ul1n:u:.fOllln (II'IlUIIIIllU.1)
~1nLLUlL1i'U'IlV~nl~m:Yil'1la~LLJOltltl~unu i'iIlVll0'llv~llJLlJu.1ml"'1,,unJ;Jjj~'1111 ,,~Ju nnnlJ
llJLlJu.1'1la.u~~uu~kr"qiill,:~jjllJLllu.1mnm:YiwnlJllnu x 11;D y ~Li'Juuln ~:Mil
~M, = 0; TC(2 m) - 98 1 N( 1 m) + B,(2 m) = 0 ,- (2)
~M = 0; 300 N(LS m) + 981 N(LS m) - B (3 m) - A (3 111) - 200 N . m = 01 (3)y "l 1.
D•.1th:nDU'llD."'.~ B 1I1lJl~O'll;)"M('lLLnu x', y' Lm" z· QmlllJl1i ":'["11
~M, =0; 981 N( 1 m) + 300 N(2 m) - A,(2 m) =0 (4)
~M,-=O; ·300N(L5m)-981 N(l.5m)-200N.m+Tc(3m)=O (5)
uti'lIlJnl~~ (1) ii, (3) ~:'1"~1 B =0 LLl1: B =0 LLl1:lIlJn1;~ (1), (4) LLll~ (5) ~:1"i1, ,
A,= 790 N B,= -217 N Tc= 707 N VlilU
L~~D~11lJ1Ul1Uti.il11 B nmillui'iff1" "~l 1 ~ _
.'Ui1Ill'"au'lla,urumiI1~"v.linnlllJ'Ila.llJ L1JU.1'ilUllnU z !I~UUl.":O nu,,,UU,.o •
,ilu L~D"ln~luJD,-julliilaonULL~UU1."1Ml;l1ljU;auLLnU z ('1LL~.m<liwivU~U1JHV(jlu
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225
il::lEIti10ri 5-16 - - - - - - - - - - - - - - - - - - - - - - - - - - - -....
IAifl~nl11Jrl~~1l~ 5-28 (n) Qmfl~1mi'1ml1J~~U1J1J Thrusl ~ A U~.II1J~~U1J1J lournal
ntJ~U~ B <t,flQluu1J1~a~lV<al~mlJl"lIlJ ~~111~Ul~~fl~LLHl1Jllln~~ P 9l~m"YilLviflfl~
IIlJ~a~fl~O~ 100 kg ua.u~nJfimOl~U1Ji,
(0)
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16111 (nl'ii lfl'il:::t1111J'lHllnOl{)
"'1",~6ft1" (Free-Body Diagram) Li'ia'~lflU1J5'Vi A ua. B 1Hl~uu1~QnoTfl'
~Lwo,m,tlfimul~fl,umiiV1:iju~~ltllfl"1Jtlrl,.tl~ 5~28 ('IJ)
HlJnl111lJ,!a (Equations of Equilibrium ) nl~11lJhJLlJu,,,atJuflu x ~::'I"filV1fl1J
~U ~Hall1'tJ p fll111lJllJl1Jw',LLtJu ~Ln en! ~HlJmi'a,11l1lJLlJu,,'lJinU~O" U,,~ln N a~(u'lJa,
'J Ul v. Llj,l LlCl :::'i::o:::t.J"lfl" 1fl unu x 'ltJU-lm.r)Lnu'U 8-3 n1'i m"::v1l'U fl -lUH fl )'jhrll.Qiiv~n1LlC'! ::::01'1
lIlJlJ.,IWlJlI"tJ1nm"vhilli'iflvm +i . ::'lvl"il
IM, ~ 0; 98 1 N(O" 1 ml - P(O"3 cos 20· m) ~ 0
p ~ 3-18"0 N
1i~Ja~a'~l P = 348 N U:lllJllJLlJU",OlJl!flIl YUo" z ".Mil
IM ~ 0; -98 I N(0"5 m ) + A (0"8 m ) + (348"0 N)(OA5 m) ~ 0y ,
A, ~ 4 1 AN
IM, ~O; - A, (O"8 m)~ O A, ~ O
IF, =0;
IF = 0:
IF, =0;
A =0,
O+R = O A=fl
4 17A - 9SI +B, - 348"0 = 0 B, = 9I L6N
",1llJ
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226
ol:lm.i10n 5-17 - - - - - - - - - - - - - - - - - - - - - - - - - - - " "
I ~.,;lU,III111U~.~hlUl!1lij~ Be lm: BO
ii~~ AalMrUlfflm:l~.".lunJii 5-29 (0). .
(0)
>tJii 5-29v
('U )
rY~1(;)~alf1: (Free-Body Diagram) ",l,LH·llivmlJ.;luff~.lu".l~ q1iff1:vl.tU~
5-29 ('Il)
lf~ ol,a~"la (Equations of Equilibrium) u('(~.u~a : Ln.lu~tJuulJL1n '~~f~:lJlJw n~
!In 1l::hl'11
F = {- IOOOj }N
1 = A,i +A) + A,k
Tc = 0.707Tci - 0.707Tck
T" =T,,( reD
J=- 0.333T,,; + O.667TDj - 0.667To k ./
'"0
lh: qn"'fflJm lfflJ~ a u,. ~:'hlil
LF = 0; F + FA+ Tc + To = 0
(A , + 0.707Tc - 0.3331'o)i + (-1000 + A, + 0.667To)j
+ (A, - 0.707Te - 0.667T.,)k = 0
LF, = 0; A, + 0.707Tc - 0.3331'0 = 0
LF =0: A + 0.6671'., - 1000 =0
LF, =0; A, - 0.707Tc - 0.667T0 =0
( I )
(2)
(3)

n1111~llJllJu"ha!J~~ A ,.M11
LM" =0; rB.(F+Tc+To) = 0
6k. (-IOOOj + O.707TJ - O.707Tck
-O.333Toi + O.667TJ -O.667TDk) = 0
lh"liiuN~flruu~.nlJIVWmh~ 1 1.1
(-4To + 6000)i+ (4.24Tc - 2TD
)j = 0
LM = O' -4To + 6000 = 0, '
LM, =O; 4.24Tc - 2To =O
!llJnl11lJllJlI.l16!J z (LM = 0) UnfflJnl1~ (I) O~ (5) ,.1.;'11,
To= ISOON
A,. =ON A,= ISOO N
(Inspection)
t
(4)
(5)
..flU
227

P1:mthlln 5-18 ----------------------------....,
mi1l1ii AB "~tU~ 5-30 en) Qnm"l~l.;'lulm 200 N '~mu;~UiimOl~~~~al;jmJ
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228
1fhil (fll11Lfl'n:MUUUnfH~{){)
N~r~,!lill~: (Free- Body Diagram) ,,~~U~ 5-30 ('J) .
lI)JOl~lI)Jq~ (Equations of Equilibrium) ul'lWI~a"U;~U1.l,y~lV1 ~ 1i ll~:'1.l~u n mYiaf
~:U1Jw nmnn ~"1Yi'il
FA:;:: A,I + Ayj + A~k
1'10::::: TEi
To = Toj
F = (-200k) N
U'i:~ mrlIlJ m m lJ ~au"
LF = O; FA+ T,+ To +F=O
(A, + TE)i + (A, + To)j + (A, - 2oo)k = 0
LF, =0; A, + T, =°
LF, = O; A, + To =0
LF, = 0; A -200 = 0,
m~~1lJ1lJLlJmr,a!J ~V1 A .:Mil
IM ... = 0; re x F + rB x (Tc + To) ;::; 0
.. 1 ........
l'tlt)..:]illfl rc = 2" rB ~ ..:] U'U
( Ii +-rj -_O Sk ) x (-2ook) + (2i + 2j - lk) x (T, i + T"j) = °
'JU1U "il:IlV1l!'OlJ~1' 1 hnjM
(To - 200ji + (-TE+ 200)j + (2TD
- 2T,)k = (I
Ltvl =0; 1'0- 200 =0
LM, =0; -1', + 200 =0
LiVI, = O; 21'0 -21', =0
"nffIJO"~ (I) "' (6) ":Mil
A, = A, = -200 N
A = T :; T =200N/ E 0
(I)
(2)
(3)
(4)
(5)
(6)
VliJ'U
'A~a~l1lJ1U amnii' A ua: A iiiiflm~V1'i'ntl,yllJnU~,mV1~lU~I'l",~1Jff'i:"" "JU~
•
5-30 (,,)
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""u1,r,alulU~ 5- 31 (0 ) QmaJfui'i~~ A 1.wuu~JllUU Journal Yi D l~o~~I~VIJ
IIvvaooalma: IlJl lla:Yi~., B l.,olmih BC 1'Il'tWO,lWn11111J"lal1rt,lIlJonl111.i'.h..au
lAuA1,rill1fVn11;i,lwmila BC lllJ~'Yi A 1I.iiVJrfu1"OijV~a,u1,luYifl'l'!1'UOU z U~: y
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•
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fl~rrth:;n tiD ~~'j,JJ,] ,1'1lJ In Yl1l 1f) ~~I1l0 ~~l)lJ U'UU ~n f1 tllJ Un::l'IJ1, 3n ,HI-Hft ~ill f1 UU~J tH'I :-: 0nlf~J
lOl1lhWlRlUi1
CnJnl'H;llJ~g (Equations of Equilibrill~l) t11'j~JH;HUa T u. 'lVl1~uw'l,JhHJnl'jlllJ
1 " - -, ," , ..ULwum OU"mm lUl'l. q~" D U~" A 'I'! flV1 1 '~a 'Jln UlI "U Ul lJ'''0!1 n l''0ll1U'l1U1 U u '1$'
rO->. 1. I .
U = - =----,=:- I ----= J .
'-2 ) frD., ... -
~ -0.707i- 0 707j
,~a H~,'1I~O,1'JIlIU" , 5 lJ unlHuu(lUO 11.'[oi'-j1
n oll o, ~ " _L (I' x f ) ~ 0
..;, r ''''UnOl.,o1'.1.loil''l1tiJl1''"1n~Al.. '1 vWlnu DA 'lu",~..1" 1 uu"ullli'u~a,
n11Ol:vh""'''H F (,)" lIlJn11Yi 4- 11 ) lln'U~ 5- 31 (,,) 5l~i.i'il
229

230
u·(rSxTB+r,xW)~O
(-O.707i - 0.707j)· [(-Ij) x (.Q3.Toi - 0.3 TRj+ 0.6 TSk)+<- S.Oj) x <-98Ik)] ~ 0
0.7 0.7 0.7
(-0.707i -0.707jH(-O.857Ts + 490.5)i + 0.286Tsk] ~ 0
- 0.707(-O.857TR + 49"0.5) +0 +0 ~ 0
T ~ 490.5 .; 572 N
8 0.857
,
th:ia'lfU"fl~nllHnnI~flfl:UU"n?Llllnlill1i'Urh~fluil'ihn n 1unl11'll'iiiUUU <lIna1{.:
vhil1'ri~aln~~'il'ulunnl11l:a:,f~ll1n.lnunu DA 1tJff~llmllf1.L"fl~n1jmnh"fl~ T IvOl:• - 8
l11hiUlnua:1'll'nalulu ~~Ju 1umru~q~ulnL'liuif~~<l1Jft~lun':h1i1111~u1'll'iiil11~nnL~flf
l"U"H~:.lunil
l1lJ1am~ : lu.r,acil~~ 5- [7 ';l"fltJl.,um~ffl11i'tJ A ,'Jul,n~1.,"n"" tJl1JL1J",f
jflU"nw.jluV1:~!lUjfl~i'u~~," elm: D .r~~tJ~ 5-29 (n) 9l~~:V;~"rull';"~11J'lJU.,("fl~"1~
F ua: A "atlniltJ'ltJff~.r,aciH.r~ncil1 VW1"llJtJl:un.,(Ll'1Ailmh~.rulunmmi l A : 1500. ,
N
1

231
f;>nanun:Ju
5-1 ~.'1~r<.1~~1i<l~='Ja.via
«~r<<llluugJ~ A Il~" B
50 kg ~Qmr,!l'J1~u~Jffi . ~ ,-4 ~.'1"'''.1'''~ih'''"'Ja.ll'JJ{fJ;i'J AB ~iiml~m~alJ
llUUl1l~~n A 1l~:la.fmi'lo~JrilJ,ra~a BC
atl~ 5-1
5-2 'il-l11~H.r-31~ t:!Off7::'Ufl-3~L'ill:::LLuuiJmr1J ':;-liianlw::
liJtll1~~~ A U~"'l",alnMUlI;fftl~llmufitl~ B
F== 8 lb
. .
' .5 f[
5-3 'il':)lWlt,rrrW~DU'i::'Ifl.JUl'i':)'ilJl~U'U~ij~~allrfu~ - A,
B ,,~" C
5-5
J",nJn 5000 Ib Ht):;~~fjllU(h,J~ G ~onQflrf15ulV'1Ul1lJ~~
A u~:::l'1j.:)n'j:;'U(Jn1HVI'H)af)~~cH~t)}JUUU111~Vl Be
nJfi 5-5
•

232
• v •
~~f~llYii~1J'U~nn5.:)il B
N
5-7 'Il-llHH,j',rlVl,!fhY'JZ'lJD'Jl1f}YlihJ1C1 100 kg Lla~~Vl
1J"Un"WJ1a~ G ,;:;a~lUja>rD A, B ua< C ,1IUi'DD
'nufh-!
~u~ 5-7
5-8 In'''''>l~QiiCl;:~a>mu~jjnm~mJUDIJI1~~~ A
ua:!llJja>rlJulJlJ~nn1i>Yi B
500;.1
800 N' !l1
,.,
'ju1i 5-8
•
........ .. .J....,; .,;
5- 9 'i)-31 1~N .:) 1~~tl(1''i ~'lJu-3fllU''1lJnllt'b'tllJLlUU'1lJliI'VI A
~Ua~tl~~-3U'U~tHfl[J-l'il1J~U~ B
'JtJ~ 5-9
•
5- 10 ">11~"'1~Q 1l Cl,:~a,%uril" ABC ~iinn';l UU
!~OI1~~~ A ua:'liaoiad,hmHl,l1J BD
~u~ 5-10

OJ '" • .; d
5-11 ~~111'llJl~'lfl~lIHnWfim.l'llYll1l,i~ . A 'lfl~l1l~l.lIlJlJ
lifl~1Jlul~Y1tf'li'e~ 5 - 2
'5-12 ~~111u1~u!lmul~!lme~rlJ A lin: B'1m~U'lu{fu~u
IlJhYlv'li'D~ 5- 4
5-13 ~~111m~ulimU1~!1lJ1fl~rlJciil1rlJmulu!~Y1tf'li'fl~
5-8
5-14 ~"11Lll~ulimUl~l1l~~ Aun";IHllJYI1~n?';1Jfln1amfl
lin'lle~~um~lJ"'llul~Y1tf'li'D~ 5- 5
5-15 ~~111uHu5mUl~!lU1e~rlJlJumulul~Y1v'li'flYi 5 - 9
' 5 - 16 il~111UHU5mUllJuvieYi A, B UM C ltihYlv'li'eYi
5- 7
5 - 17 il~111UHulimUlYi~~ffi"rl'f A, B 'If'" C '1Ja~I,vi~llJ
l~Y1tf'li'DYi 5- 3
5-18 il~l1l'IJU1 ~'l D~m~u5 i1~Ul1JUmll~
l~uhjii"~"'lJl1m'le~~ n'
600N
A LLa t
'15"
~W( tot
AI
.$~fNau
I I
~- 4m +- ~-g",--~
Prob.5-18
~-J'~ 5 -18
B
233
5 -19 m.m"';'';Dl~1D'~lJiu'lIll:Yiil~''1Um1lJ'11fH~'''JU
til F = 110 kip un"1lll1un'le~lft~fl~iij W = 170 kipT ~
~'111 Fun: F nlJl1.1:u:l'll' S IUllu1,crU'lfl.n1lO1:D L
l'll'Ufl-3 LL"J'-3 'Q'ilftl n
4-o:rp~F, = llOk.ip
.,
Juti 5- 19
'0-20 ,iieom1u 5 Ib llJl'flJ~n~~ H l'flJlJ&ii lnlJ5u ,;,hl
,il>lU1.o',.llnunil F un: F vl';U il~111UHvl~nci11ilun:, ("" , A ... ,
Ll'i-l F li",lhh1'lJ(;l fl Li'jt:ni'l4ih~f1'li6mn,J 1J()-JlJ 1"Yl G1:1 ' , ..
1>181,i~"tl,l1U0'11"' ,,'l"
,uti 5- 20
•

234
5-21 ~~l1111mJlimV1viaat~flU B ll~.~nnl'. C ~1lJ,r.vi
mudiJl'llnm:Ulu~uvi A l"ohjii.,mllJ"Ul~iHmU
800 N
~t1~ 5-21
5-22 tJU1~'tla'H~oihrn1rf) 200 Ib Lli:l:;Iili'lu6nennf1(1~
G ~~l11U~~hHftliia CD vi"",nniunnunuu1,, ".Ju ,,~.
tllimulvi B ~:ihiltilllt'!U[r 11lJ,r,fllmrul11fl.flth:nau
tiauluull171U Uq:: IIH1~.J'Ut1,J U,)':]~'l111il A
'nJ~ 5-22
•
5-23 'lflUTlu"ii.;).Jl"un 8 Ib ~U'llu'i'l."ii•.r.1t1 ~"111
UH FH viLo";}lllunl1ii.n1mflvvi B l"uhj1imrl~tl'n~a.
U'IIU'lnUTluJu
8 1b
13 in
')'l1li 5-23
v
5-24 ~mlttHUamUlvi1~Vl A """nl1ii,lutlian BC
ihlill"~l F ~ ,0.kN Ivw'hj/i"flllUHll1'11mmu
;-25 LfftH9ian BC '111,"Lrlanu~.ijril 50 k~V ~.,n
Jl"nrnn"l::lhluutn~.,] F lhJ1n~,!Yl~CfllJ1'Hln'i::~l~(mnt
~ 8 'r:llJvf,J'U10~'Utl"]U'J.,]u~ mtl1'~ A ffl'l1i'uJnn!nfl'J::;yil
ifhw'hjfiVlfllllJ"Ul'11fl.mu
1U~ 5-24/5-25
•

5-26 ihwniilhmrn 250 Ib ,","'.!utfn~l~lJl"~ G.
61,iUunlhuutil~Unn:"vhlJln~i!il ,400 Ib VUii~il G
~.'1llrlMUnoi'luiiuvuiii!il W iil1~ii B ,tiv~V~'nu>i~
vnftlJ
c
1ft
nJ~ 5-26
•
!
6 It
_I
,
8 1"1
I
5-27 ~,jnJ(u1.rf~a".d'1Hllmh"'J~wvf O'lff,j'i.iim llJ
~&'Hlni~ k = 40 Nlin Uft~t..1n5A 0.2 III uJlil f)J~lh :::n tlu
tivUlmUlllU"iI"'ln~~~v~LlHtlBmm~Mllil AnlJ~. ").
"vl1i'iicl6mill B
. [50 mm -- - 1:?:5mm l
~u~ 5 - 27
235
5- 28 191,,,gvUl'lllJilnUUU~"~H~V~~l.{fU,rU O'ltilmrn
rl"Mun,huuhi'iiril 500 Ib ••mu~.luu.i~"ii'm~vulurilu
un
500lb
It.l~ 5-28
5-29 {fu,ruQnrl',uulilouui."uu Journal l1'iv,j~vnuuu
~u~ B ua:::mJ1,HlU1J Thurst ~ A 'il~111a~A'lh:::notJ
tivulU"mll1JUil"UI1~.~V."H~ A nlJ~.uHlu"'n'l1J~
B 0'1 P = 8 kN
5- 30 {f'U~u!mhrr'Ulmmui,] Journal "i5mJ(lf)flu'U1J~1!~
B Lla:::Llu~']UU1J Thrust ~ A olu'li~-3ll1JU Journal
~llJl'H1J1UWl'i'" 12 kN riaw~'il~vr.J i),]111.h mXnn):::vi,
lJln~i!>1 P~ff1lJnO"~lul1'oU.,n{fu,ru "1J~~U1J1J Thrust
~ A ffllJll0l0J~1JIf.v.rf,j,"n01JtivolU"l1'"J"~""Ul
~"''U D.JU7J
6",
,- - - - - - - )Ill - - - - -
I
&)
~
t
~~------------p-
~'J1i 5-29/5-30

236
5-"1 U'lJUlj""li'u~Eu~ni'li1e~fulhmrnm:li1 780 lb ii1
.l1ll'eo T 1I1lJnOe~1:11i1~ 15 ft ::; x ::; 7.5 ft Il~m
'lJU1~lJ1n~l'!~'lJe~LLmJ5m01~!lme~fu A U~: B 1~e1e~
fuLi'Juu~enihll'{f1l4'1I11ljllii1l1:1eUUnU1ULlIJ1~~ uM n~ B
1e~fJLn~luViffU1I1~1111'lJ1U:~ A hi1l1lJl>01el1U
1Uri 5-31
•
20 kN ~O k:-J 20 kN 20 k~
.
~u~ 5 - 32
5-3 3 L1I11rJVl11hUU1I10hhi<'IllJ U';0: <'11o1rJLil",LLHluLlIJ1
~~UllL1I11rJVl1 L~elllml1mrn<'l101rJ.J~:u ll~mmlu5m01
~!lU1e~1U1i~utiwi'u~ D ii,Luu1tJ1.,i,rlll1fualJ""11;0
~ndlu1I1lJ1mli1hi'1110lrJ<llJ1>i' l~111i111101rJ1",u l~eii011
l~~eWIlOil :li1hi'L;;" Iiau1'11,h",fuLIHUBmu11lJIlJlI.r~ D
lJlnVil'!~
gOO lb
I-c;c;-hic--Ht - :
2ft
'.itJ~ 5-3 3
•
5 .:.. 34 lf1"'i~n'H)tJt;! !~'Ju,d"tJhHJqfu ff1 u A B ~(}~ti-3UllvrU
11lJL"iOlJ IJJeQnfUlIH1t1'nm:Yl1 nnm:l10m1lJ.JUlJU A B
.,tJUUlll"JJv1~lU "1I1'lJU1VlI~n;il'!'" d 'lJe~iUl'h1! AS Ll~e
l'hhf1fllJfl'HIU'l~dl~f)THrlJ iilJvr-lFllfl11lJl.ulJ V rl1l"i'U
- - - H<
7 n
WjJJ"- d - -- - -

5-35 nnm~llihJ1n 60 kg Ua"~~fJ1l6nal~)J1aii G
ij~11l~1l1"~ ~~m~11Y<tf~'lflUfllll1 il~ Wi~~m:vhl11u.ia:~.Ii'1J
J~,w~IVi8f~1I1H1I'u1l8Q1ll1rlJ~a . .
O.5m
'nJii 5-35
•
5-36 'iH111U'H ~~ 111 mJfl Wcl'W -fin'i~vh Ol fJ Uvl (l : 'I!Vl"CPU fH
lfl~8~iiJ ij'''ftm"rt~aQ'''nn-nh A Ua.1in'''8~f)1uhl
11~":Un ,B iJmr~(8~ihrl11,rn!~111J" 50 kip lIa"~~lJ6
ch,nncrn G ,h~1~fljil,;)ihtih.ill1Uil 180 kip UCl~"Vl
... ...; W .,: .. r; .J, v ... 1;':"
'iuum~1'1 G, lIa:lma~UU~m(8~9j~8Qfllla:I'llUlJUl11un
l1"'HlJ~ 22 kip LLn::~V1fJuuci1'31ncrVi G
I'
- - 31 n ••._ _ ..l . _
7 ft ::! ft
5 -3 7 lfflhnffVn1~·hj~Vlfl11lJl1.nlnn';j:vhvrlOUl~Ll1l'U(l 80
Ib ij'ifloi'.lU li:n~n,a.ru1"olrH[ja BCD ua: l(l(llJ1'O
ff1JlJ~hthll111WI~~pu A r~mi'>ll11ifJ')V11'HinfrlJl'l1~l~U~~VI
., , ~ ,........4
o 'lW"8 cc Qnu"uUUnUl(11'1n~nal~l(1 h : 15 ft """
... ~ • ... .,. OJ V , ..: .., v
,mUamlllJ>l BC lIa" CD ~nu".,.,nu~8"81'1 C "~I(U
tl,:lultl (i"rilU1mi'i" ~D Qn"lSau61o ) "111nl,ibl"
LflrO" CD' U"::U'j':Hr'l~n A
237
5- 38 l(lhmlvni'~'hjii?lmllJllUl~nm:vilYilUm~ 80 Ib
ijiifl.r~ltl l(l~ma~r1Jl"olmiia· BCD ua:(llJl,OCllJlJii
lilUl1l1"~!lU A lVi81i'~111'lia''lHlhlli'U1'11'I;;U~~11 0
'll8?ia~cl'lJ"ffnU'lla';a~ C U(11,1"'OlHutl,: C{urilulfuiia
CD ~Olfl~auti'lo) olm,~,l11 CD'jj';llilu(ami1~a~
nll~~lu BCD l~111mllJ,!~ h crll1i'umnH'lla';a CE
F :80 1b
~o fl c .==i~1
' ,
: I, 1
, Ii
I
o /2-1,,,_I . I
-!ort-
"jtl~ 5-37/5-38
"
5-39 ~tl!lilhh"n~U~lu~l,f, A, ftm~alj B 11ft: C
Jl1-Hl-lUl..:tmnllin-lfl'i::tltlflnft1-l 0 mJllHluuuKnlJw::
v1,J~tl l-lUllluullnn.!n W llCl!:11l,juluYiff't11>lli,]uon1V1u~Flff'j
'iJ,J 11 'it tl,J -)~q€I"'i~iJtl-31~llMTl.ma::lifflJ n 1i iHJV) ~Yin1lJ l~fflJ
Uff~,J-:i 11..3 HH1Hv1-3 fl ci11JU~lljLOVl nll'HlfU
~u~ 5 - 30

238
5-40 ,i~lD~rtJIW"wfhJVh>iihna 15 kg uadj~~IJHr
.,j .¥ •..: ... ~
na1~lJlal'l G VlUOnD~U~lJlJla 4 kg 11a"~Vlt!UOnaH
ma>i G l!lJ~~i1l!n,I~Ol B 1i"r~,i~lIa.,i'~~nVi~ntJmr~
11tJ~U~ 'A ~~111I1mf>ll1mJn~il~ A lIa"D~,fth:nDtJri8o
1UIIU111tJlIa.UUl~~'118~IIl~t1BmOl'llD~lin,tJu,i'~
ltJ~ 5 - 40
5-41 IInU>D,ftJlr,mrnm:lhluIIU1~~,f~l!8~ l,,"'bjil~
'IIUl"'IID~ua8nli D II". B nlnf,Tl11lJl1U1In,u'UD,U'llU
~~l1lD~,(t1,.natJo""'UIIU1ntJua:llu1~''JD~IIH~l1l1" A
lIa:lmlwmua CB dj8fhl1UVl~' F, = 800 N Ila. F, =
350 N
5-42 lI'UU;D,fu Jmunnm1l1I!IH1~~"f'l!8' F ua" F
OHmUil CB ffllJl1ar"j',mlnm:1'illJln>i'l" 1500 Ib
rlDWmU "':'IllY) j,1111hl1unm:,i,ln~"Ol
"f' 'UIllVl'UiJ;UHUGmOllllnlii!Vl>il111Vl A
c
,t1~ 5 - 4115-42
•
F = 2F ll lJ, ,
5- 43 ~~111I1,~t1limo1t1aDngu A IliD B ItJlJ~nnli~lIa•
CD ItJU;;D~D«U
2.5 kN
,-' - - 4 m- -f---6m---
5- ·1'1 rlll>llUlifiD l~ULfI ~tlt!~-r(1YHnlll flifuun OnCH'UU
tl~luvill;~iJ~-liULl(l::ijJll1Un lO~ Ib :J,Jij~~fJUr1ci1-3~
G ilm''''',''"'nt1n~hi'VI,r'UD',,'~1I0~ti'"tJH;;U A lIa:'UU1", ,
'UD''''JVi''D~nl>Yilj6iltJ B
, ),..-1.5ft
~--'''-i''''' ~'---.~. . 0.) ft
A . ,
')tI~ 5-44
•

5-45 ri'lUU~u~v~{flJ,j'utI~"neUol'lUU'lJU A B ii~eJfu
.rlUl1~Vl~ ~, ~~ul"iU1UJ BC U~"llnJl CD U~~"
~",ii~uun~uVi C O'lJl'H~nm"';l 5 kN Qnu'IJ1ul"u
~ , u ~~
UiUlilaniil1'au 9f~"lu~anii B ~Jm'IJU1"'lJaJIn~~Vj~V1
i~"Lfi"UUIl'IJtI~ A al'Hfuff)J'l~ ~"iinl~~~llJ1ffulu, BC
~~~:nll~~ T lu'fftl,<1lanYil1aU ~~hiii",h'Hrn'IJa~~~'lJu
l. In
~----5 m - - - - -
5 kN
5-46 ~m'iu,j'uiiJll1un 120,000 Ib 1l~"~"i!!uummYi G
.,,; ... ~ .... . . . . . ; I
U~UUU1JU1'HUn 30,000 Ib Lta : ~mltlUn~lJYl G ..m
~lJf1TllOU.:.l~l~n~,!~ e 'U().:.Iu'U'Uiul~tI'.lnf1'illnnl;5~'UtI.l
10 {[U,tll 61Jllni'nnmiTviu'lJ1U fl O W = . 0,000 Ib I""
'l1j~(>lfllllJl1tn'Utl-l5tl~h"ljJ:::iJllJ~ A um: B
5-47 lm'ftl,j'uiiJll1un 120,000 Ib U~:~~iJlIO~l' ~ G
.,j ... r ..., ... , ..,; I
WII'UUtllJ'Ul l1Un 30,000 lb llat~ VlfJUtJ01..1,,1 G ., 0'1
,hl1unnm'ilYiLl~ltlii W ~ 16,000 Ib ~mlL~" uBiBul.,'"
Ulnun~~c1o&iu":~llJYi A LIe" B lunmillJ1ilihi;fo,ii"
fll l)J'HH1'Uu.:.latl~lJ~::'U1U lrimi l'11'UYl 8 = 30·
~t1~ 5-46/5-47
239
5-48 ~tJmof,,~!tJ ffmJiift'l11JU11~ii1J 200 mm ~J'H1
~lJ1,,~a~LI~~"",j~ A LI~:LlH.rJnntln~lJUl1~"~ B ~jjo
LI'lJUO~luoilLll1U~.r~~tJ
,u~ 5-48
•
d '" r .... . . . . ;
5-4.9 "lI'lUfl Ul1U..1lJUll1Un 175 Ib U" ::; ~Vlt!l..wnfl1>3lJl"Yl
G mnf~liuoQlt,oi1Ul1U~.r,ltJ 0'1')(1UftlJlrUola~m ,1.ilJU
IfflIVlj'I,iii0 "'Hl~1llVl'IJ 0 ' 11~"Vl ,j~vf~ffO~.>11ifa,n~:';l
'uwrr~li B !w::m..1hmln11UVi tlQ'tnn-lm11UVi A olJlJ&i
illCnua::chum")'lfl0fluJuijla'Uv.ilUt!lAUfl,n.:JL~tnn'U i -l
,ru ~ll.l,rl.J'Uu.J ,1'1 tJi'Au!:LthmlJu~'lnIlU
'J,j~ 5 - 49
"

240
5- 50 «alfl'iVUOn1i~~OInlJ1m~mVlJ~V~lfl'iuu1~uu,wn~U
Idfl~III n1liiin1~~l1i~~~IWa1'1Ja~«vlI.f~1~uuaD n~~~>111
I~UlJ A, B Ila. C 01thml'nm. li1lJu<i'viii'i1 900 N ,mn
u1~tl5mU1lJUIl1 a1ua.~~~<llJI1'll
30
5-5 1 fll1Hl;j-3lf)~.Jhj fi ~nr1"rf'Un! nH).Ji"'ul~ 0,,.,.11:n.r.J I'I'fl.J
U~tl1lJVl c11ffm>l'lljij fl1:il1~ lrtmJll1trnnl:::vll on lf1~ flUUl 0
j)~1111;j~1tHlI>i a"i'ftJ~~ l~v1>H'lJr111tlnm"li; P "lJ~~
111ln(UHl n11Yll~ ol11ullu1~'~ V~ Ul'1U C 1flJlJ~ i1fl11U
LL9.i~un~,J'U tl.JI'I'm.J k iiflllJ1mWu;JVltll~fnhhrfn1Vl'JYIA)
... J' .. .... 'l':. ..., <=0 •
lOWl9JU1HHI f11U111P-l.'HIU A '1I.Jt.fW nl'H11'11V1'11UC'I'll.JlJfll l lJ
<luvluinl!
p
!''/!!! _m5:t
I
i
.5-52 ~lnuwmn~iH1filJ'lrf) uvhu:au'lYmnl 2.5 ft ua:::
l1tln 3~ Ib/ft owi'lnlJWnll1;i1~ (1liul1u'l1n) ilJ111Un
~ <OJ..: 0 ~ .... ~
40 Ib ua '~~ l!uunal~lJ1aYl G j)~11lj)lU1lJalJ'I1nYl1fllJl; O
~~VVf)lJll.rlla:;:u.'m x ~v~lU'l1m!mhU~lii~nl><i'lJ
f--- 25 ft ----I
~ 15ft 15ft
~tJ~ 5-52
•
5-53yjtl511ariii.JVi:Hr1Jl~nr.J~'IIvHi'lJ~ff A, Bun:: C l).3lil
U'jHjamtJl~~;A-Jf)"11d~~u.J·nl'j·Hl.Ji'ULt1-JluLLln~.J 4 5 Ib
lvl1J'lliii~ml lJlIU l~v~vi v
-'
:w
~ 5 Ib
~tI~ 5-53

5- 54 ~~"m"v" d lill1fUnl111~,rlmrnm"nl P lill1fu
i'I''lIVlful1~'n1H1t1U1tlilUl1U.J- e vl.J2U 1.101ti;;"J'l1tl'o'lla.
l1.1~ 5-54
•
5- 5 5 qtln~ru'lh:::fl8U1l1 nUHUhr..r-lfH)"l LLf-iu1trvlTUilOijV
~,rll1tl'n 10 Ib lLa: i)"fJu6ci..~ G ua:U~U1,r;llU'Jlliifl
~Jll1un 7 Ib ua:'Mu6nalJ~ 'G ~~11lm.~~fl~u"f.... ..¥ .J • .. ~
iW.'O~'JUV1 A, B ua: C
1Uri 5-5 5
•
5-56 llf-il-!nalJihna 20 kg LW::Qn'H).Ji'uu'U~'1.dh~U
V11.n~:uflo~Ul.,ojjflm,~i:imllJL,~.un1. k ~ 400 N/m
uo:m llJ"ll'~lJ = I m «m.rY.fl.fl~ltL1'il"l1ti."Ul
'l1J'~fl.'llmlal" ~ u.,~.,numclm~flu'~n '1 ~'liii.,
Jll1un 'J11lljlJ e al11f1JfflJ~o'llVJclV,iiau
~t1~ 5-56
241
c$ ... ~".
5-57 ~m'JUUlJla m ua:'''TJuvnal~lJlaV1 G .~11111)J
'IIa.nl'iLii".lJln~l'!~ e 1.w1tinll115m.uucllJ
'lJ~ 5-57•
5-58 llYl.J'Jl1H1UDihna m 11.Juuri1ln1~.JiJu'Hht!lfl-3
oJ • ............ • G.... ... ,
m.1JnoUUo:YI.nu ~w ••"fI~.11«111lU «lJVjo~IJUm
sin e = ~(~1 -3 cos' e}(d-l sin e)
r
I
--d--1
,t1~ 5-58
•

242
5- 59 Ji'ui~~lJ1a 60 kg lla"".Vl.nJ.,fu~iiu A 9l.~:
a'" ~, a.iu,ilIII1U.1U llU,~lJ 911Uql1~.aanIn•.1'.III n
11n~lil.~lnfl11lJ~. 2.5 m ~.111fl11lJ"nlJln~,!'" L ~
1l1lJn~~:a",uul",~,a.V{jwll' ~ 1"u~uul,,'lilii"'n1~1iu
l~a~ A
L
/
/
/ ii 2.5 In
~ IA b.L_ _....;/.---""---'--_ _ __
5-60 lI,i. Be ~nrhou1"'Ulfful;;anvf.ffu. IL~""lffU!iun
.4.,. '" ' .... col y 1;' ....
ijfll11JVn a "lI'~tlV1I'1~UUWnUl1lJ~V1 A OTUll1 lW V UC'1:::
2Wi"'II"uHu"~ln11a'"lIfl.1Lvi. ~mll11J effll-d'Jlluil"
l",".r"'~lnll1mltJ ""'1111"'.~""w~ltl!U~U' a """ I j","
'hj~"Jll1rn~u.uvi,
I
IV~
2v~
5-61 lluunalJiima 20 kg ua:fl~ri'Ju~uihl1iU.~lJiu
11a,",),U11~.11fl.lim'Qnli'"~~nJi!u6na1.11fl. IIUUnau
lla::iimhntJ'l1i1-3fJnu~9iVutlun1J~tH~D.I~ A vl-3J.1 ffill~
O'fl'fl~lu,illll1lhIIU,~lJ tiifllluunalJfl~lUlllJ~a o"nu
U111~lJllfl.llm.ii~1 200 mm ~.l1lm1lJ"n~{j"'I~flLl~U
nalJfl ~1UlllJ1)a 1","'liiiL'lIIUl"lIa"If,I1llnilfl."flliiflu
120
k=400N/m
,u~ 5-61
•
5-62 llm.IIJJU"'li.lffuiinmu~"UIIU",!Ul" naniifl
lJJL1J"H;f~f)l'I.J~u'J:::~ nvi' M jj fl11lJ«lJvlH1i'nu n15'l11fu~Hl']
lim, eI1I1·l1i,UI'I?iUlIl.,UlllJn17 M"(20 e)N'm Ollllli.
onU",~",n1JU01u~u.llvi'~I~flu~mLJJl1lJ'" 10 kg ~.111lJlJ. . .
e rl1I1ftJff1J'l"lllli,lliiinl1L1J~"Ulltl",!tI~1.I~U e"O'
'jU~ 5-62
•

, - 63 ~~l11fl~ri'th"nautiflv X, y U~" z ~a~umJ5mu1~
Nlr~li~~~U1jl A U~~ 150 N aQ~lllnUUnl z U~"UH
200 N oli~lllnUUnl y
z
150 N
- - -,--- -"'" N
~tl~ 5-63v
5-64 Ihlun'IJtl~lf)itl~ijl~nn;"lil')lV T = 8 kN ,1n
lfl~tl.J[J'U~Ufl::llHYinl L = 45 kN ,-)'llJ1c1Iu.JUn 2. 1 Mg
H"::~~fJ'Wtfmn~lJl'H)~i!{ G 'i!.nnv.Jflth::oUlJuatJ x, y Ll"::
Z ~""uHtlfimv1~un~na~~~n1Jal""'i'l10'Dl~ A
x
,.
243
, - 65 ~lrltlln1~ihr,111rn 5500 Ib '~l11m~~.llu~~"
1fUU Cl~'if),J i'uU1J1J ~'U'Ultnr.Jil'l lJ ,ri()~~HJnf.Jhn!:"Ul UUU1
11U",~!tl
~tl~ 5-65
•
5-66 Lfliu.JU11J01 III ffC.) II U'J1UMtlU nU'Ha.Jfll'U tl.J (Jlf11'j
1~Ul"ff1lJL~Lii~ (]lLf)~U''''.ncil1ihh111rn 900 Ib LL~:~~. .
TJl6n~HlJl~Vi G flliVi X = 5.5 ft U~: y = 6 ft ••111n11
~.JluUv1 Cl ::LfllUCl I.ll'111UfflJ ~ Cl
5 - 67 Lfli fJ.Jui'u()1n1ffQ fl U'IJ lU,rtl [J nU"rf a.:J fll'U(J.J ()l fl15
1~vHff1lJ'mii~ (]ln1J~.lllmij~ T = 250 Ib T = 300
... A , B
Ib ,,~" T = 200 Ib '.1111h111rn~O~Lfl1o~Lto".il"l11j~
c
(x, y) 'lJtl.~"'.ll6nlmlJ1~ <3
~tJ~ 5 -60 /::;-67

244
5-68 ~m~U)fl"UJ1"l1rnm">il,f'1I1lJ;l'ltl ~'111U;'
tJijmu"l'mntln~uuu.i~:afl,f,1I1lJ
500lb
800 Ib
1.u~ 5-68
•
5-69 "1118' rlJJ;:nflUU amI) J1~m:lfllJU~n nauIlamj'l~
A, "mJaiijulafll~flU B "'l:nl)~,lUlil'UI<iifln CD ~
ftO~n1'Hhl1'rU!"H~(1'H)-3Ur-il!U l-lt U lltU11.J fl (llJ
'lu.;1 5-69
•
5-70- IlIl'lvh'h~nm">il,r,uummua,f'lIfl' 60 lb ul'ia:
uHflQ1umJ1uii~U1uti'm:U1U x-y olnn~hlulllUal'l 'AB'
~fl 80 lb V.'Hlfl,"tl;: nnUUflU x, y ua: Z'Im,uHuijmul
Yi~lUllll 0
,~~-.=~~_ 60lb
...... 45"
A
HO lb
~.J~ 5-70
5-71 n-j'lu,~nm:>il,r:uJnnrnnm11 150 lb ",lf1I!),lu
- • • "" , . ' " . 1 ' _I
UU)')lU P 'VliilfJ-lnl"i,)-3VH)tJ LUPIlln1'U-3~-l~u U(l::: ()-lflu'J::nlllJ
ciUU'Jtl'Hl7-JtJamCJ1~'H)tJtoiu~nn"lJU"::l~1 A ll"::ll1J~.JU1JU
JouIn3l 11UEu B '~fl!!u~,ii B olh!l!m~!l11mi'flma:tii~
lnYjl::mnJ~mUl1J.tn11ti
A
y
x 2 ft
')tJ~ 5-71
•
1

5-12 Ilnm:1I;n~ILil~ILnl~'m~L~UQniholJl~V~DvGifl~nn~lJ -
1I~!IUl~ D lIft~nDmlliift BA 11ft! BC ImjjftQnli~~OlnU
1~11!11U1J~fln~lJ~ B ~OfllJll1liiOlmml.llJ'lJU~llllm!lOl~
lDUlInU z 0'111l1m.10l~f~iluncifl.vijjlJ1ft 200 kg
~~!11n15~blUlmii~LL~:u.l1th"nuuciflV x, Y 11ft: z 'lJfl~115~
!lfimU1vi D
"jtJ~ 5-72
•
5-13 11l1~mhEfu''1 Ull)"f~ lIu~lu.t1 mllU~ I1!l~" nDU
ciUU'IJfl~Uj,t1Qm'Jl1i A ClLJlJ~i1LUlljouGi a~n n(LJ"~'lU1
jllJlf,ri1lJl[UmllH~,11mGiCl.I('lJ'11~ BC u~: ED
20"
'jtl~ 5 - 73
•
245
5-14 ll'IJll AB onf.luCllJOl~1"u,avGiUftnnftlJllft.LtJ1 A
llft:~fln nlJJ.'.U~Ili'lJl;;Uni~,t1 mnD.~th.nuuuav x,. .
y 11ft: Z 'lJu.u,.t1ijmvlvi A Ilft:m~~~iUlflliift DEC 0'1
F = {-1500 k} lb
... & "" ..:
5-15 IfllUft CEO ClllJl5m.m5"~lJ1n1'1l!fl 800 lb nUll
vilfllijft~:'IJ'" ~mlll,.lullU1~~lJlnvi,!fl F vit1'.~n>fnu
U'U1.I J1lJJ-lf11U10111liHrfth:flflUl:imJ x, y mu: z 'JU-1
t1fimv1vi5uvGiD!1~flllft:ltJ1 A
x
5-76 Clluri.ril<i"Qnnmh;'lum,~h 7001b Ol,]lUlll
AB mTn 50 lb 1"uiivfl,!wJnCl1>lnftvi G ~~!1lIJ1J e
Vi ('I')(n1·;11-11K.:)vl1ntlLffl
----.-~~;;,,~~-L___~T' = 171.10 Ib
,t1vi 5-76
•

246
5- 77 H~uonlh5ul~UJou.i0~nmlJlm:l,j'lli A Ii00IllUolrl
~ B O'11h~,rnm:yhlUlmUil' fio 5 !eN llilOflOluJOUllJli
~UllJO'lJlOU1lJ x-z iI'1110"lhh:nalJuau~0"H;"tliimu1li
A ff111i'lJl'flJ,)0
1.5 m
I
x 1m
"
5 kN
nlli 5-77
•
5-78 vi(J'fO,i'uJ'l11,rnn'f.vhIUmJ1~'«"ltl UJ111(J"rllho
nmJuatJ'U()-3uHtJBmUlii'H}U~()anncnJ Ui'!:: tUl A ua::fll'l
~"IUlmuMr15u Be «".BD •
/
J m
/
2 r: I
/ ~ D
/
/ !
/ i
! - ··1.51TI_
1.501_
1m
3 k;i
·H .."
-1 m-i....., ..' l .:l lll ____
3 m-----..:
nlli 5-78
•
2 m
5-79 II~ll'f(J'i'u}iunao"liihr,11lrn 850 Ib iI"1118,rl1.h.
OOlJUcW X, y ua:: z 'Ull.JUHtJfim(Jl~'HHJvio~flmUJLla~LUl
A Iw:n1'f~"IUimiii Be 110: DE
5-80 ITlliio Be 1110 DE <lllJ1'fmo,i'un1J~"lJ1nli<l~
- . .900 Ib riOUITlIUo':~l~ ilmllh111TmJlnYi<lA W ~a,
}ilJnao"li<lllJ1J0II~lUl1aU,lml01U~a.H'IU ;1lJ,r"liltnl!
111fl"rlth: noUUilU x, Y "": Z 'U0"HHuijmu1li'filU.i0
~nn"lJ Ho:l1j'l A
3 fl
2ft
,uli 5-79/5 - 80
•
5-81 Jilnl1"<10" ~ n1i ~ iii~o'UIVIill "il",WOll1~U,y1U~11lJ
'11Iii"~lJfi,li rhK''Io"an A ri"olulu,an B iH111nl'f
>i"lUHtn'flU T hl<llUVllUlJU'filn B IW: il"rlU'f. nilUUflU
x, Y LLa:: z "HJ-lll'i'nlomlJl~UU~.JUU'U Journal ~ CHi'!::
lIu1"HUU ThlUSI li D ill 9 = o· IIui,J'l'Iil'fl~lu.ilUl1ti'
lill1lJ1.<llJU".dlI'IIlW1.U'f,tlBmu1UUIVii1
v
5-82 'HI nl'l-lC'l'f)..J onU Yl~ VI ntJn"la1na:::rwClll1lJU~1Uflll')J
l~ll'ii'~lJfi,li Oli''IJil''On A ri,olu'hhon B iJ,111n1 j
~"'UHtn'f1U T 1111'11UwltJUUlon B 1!i:D~1i'th" nmJuo o
X, y Uft::: z 'UtJ-lm,:jtlnmEll~LLUi-lU1JU Journal ~ C lla~
UU~~UUU ThurS! yj D 0'1 9= 40' L!u1,J~<lOJoQh!!lUl
li111m:fflJ 1m:Iii~Ill"1",",tlamu1UU1" 01
200 m~ - 50N
2)O m~ ..........
~ ...~oomm ~ '~~ H •
~ c , ~"'mm~,-.'
x ~. ~_ ~o mm -~
65 0< l T
801
':itl~ 5-81/5 - 82
•

5-83 ~twnihnCl 3 Mg ua!:~~'!'Utfnal-l'l()-1lj1'HJ~vl G
61ii1Junvn,i'1ofl11lJii1fl~vil,wl'li'LflLilm,f~<fllJ ~~111LLH'U
U~ft:LfHiJfl
5-84 ~uu niilJ1o 2 M g LLO"~"'l'u6nOl'lJ10a2~ G
tll>iu ~ n0 n1..Uhl'Lfl LiloJ, <fllJ ~~l1l Lm1ULL~0"Lfl Lil0
" ,.,. ~ "';'l1rtJLL~ o: LL~~ Il1I'til1W <flJnl ~<flJ'l OllJLlJU~
247
5-86 hloiitlll1un 3500 lb Lm"~"iju6ril'vi G ~'111
v~fi'J~"nvtJrJaolulLul~~'lJa~lL~'YiLL<io:,;aojaJ,<fllJ A, B
LLo: C tJul'l1lo tllhlo~nm:Y]l,hutlll1Unm"Y]la"{'lJa,
<LlJ 250 lb Yim:Y]lluYiflm~"'lJ
, 5 f~
A~~{-~~--.--y
1U~ 0-83 /5 -84
•
5-85 lfl L'U cun ~Hl'J'lU1Herl all u&itJntflu'U1Vl{J'HHJYitl~n n alJ
LLa:nJ1Yi!lUl<fl ~mlfl'lhJi"nauciou'lJD'LLHJgmulvi A
LWvUl' 140 lb <Lo: 75 lb D~lU1"lnulLmHu
75 [b
140 Ib _ _----~l"'O_' .L- _'-_'-=-'=j",kB
~J~ 5 - 85
F = 250 Ib
x
Top view
1uvi 5-86
•
5-87 ~lHil11 AB ~mr,oul"ULmilo BC LLo.Yi A l"VU";'
jJiil11~OlJ~"fcrYiii"A" UDDl101lJ 1 V1:o>nal>nh",fcrvi,,~ ... " .
,J01VHW.1 V 'IJ a,~urilu"'lU .,1118' fi'Uj: naD ciaU'IJ vJ uH
Jgmulvi A uo:n1,(;i,lULflLfjoYi.ra~nl~f~VIl'm:Daf1 800
lb lucrlJVlCL
'nl~ 5-87
•

248
5-88 ~J111U1J~JhlfflD lfi I1j~ U~:DJllth: nflU ciflD~ flJII1J
!lfimDlm:YhUli1J~fln~'ll~ A ~~l,'J'll~O~f~ihu 50 Ib 1'll
ff~~~~~i!lwrci1'~OJihUO~~ G
,.
5-89 II~U AC omo~>IJ~ A 1~U10U~O~nn~UII~"l1J11~u
. ' .'ftlU~li'~ffOJ BDC lIa: CE lmua BDC iifl11lJ.imilin
'la:~lH~ all~11lm~ D ~J HlI11J~J1Hlmjja'IJilJllJli'th.nilU
vvv x, y uC::; 7. 1J(J~Hl,JJomul~ A c11l1Uncitnihillnrn
80 lb
/
E '
.'/ ., ft
.~ ft
c
5-90 Ilvi'JilQmilJrlJ~ A B 110: C 1flUIIJ~'"IJIJ 10umal
~'ll ~J111oJli'th:nlluciilU x, y II~: Z 'IJilJIIHtlllmDlI11J1,
t11I1viJonm:"hIil1UIIH F = 300 Ib II~' F = 250 Ib ,ilo.. I, . 2
F llU1'll1:H1U y-z UIJlJilcilHl'H1iill1lJ1.fflJlI~.liiVlIIH1 .. .., ..
tl!j mU1IJ'llllvi"yi1UH
5-91 IlviJJoQmilJrlJ~ A, B 110: C 1VlUIIIJ~~IIIJIJ 10urnal
EH ~J111'IJH1Vl'IJilJ F. ~l'h1l1'iiVlIIHtliimul C ~IIIJ1~ C
• - . y
ijFlllvi1flUfJutf UU~>3f)~'uuu1iill1lJ l :::trlJ Llu ::: ln~1i1'W l :::u'j,J
tlllmullJ'llllvi~ ,fl1l0111'llfllil F = 300 Ib,
r--__ "
~'
c
atl~ 5-90/5-91
5-92 IlviJ AB Qnn1:YilIil1Dtlailn~Hvi'JlHl' ~ A nllviil
l~ulHthrHltl~ f)~fln"lJUiU;l1rllU'l:::~ B nl1vlOl;t)iJLtJ.tfll~
OVl~~Uti'UU;J,Jlfl~,'] olJll1Unn'i:::vil 50 lb llHf1chl rliJ:W[)lJ
ciao x. y II~" z 'IJilJII'~tliimul~ A 110: B
/l
I/I~...__-:::::::l><!Y--l-
I()fl
I
I
6ft
)Olb
'nJ~ 5-92,

5- 93 m~1",U'ihviio~nm"~1"10n1~ii~ (l{101lJLlJu,)
rimu) 50 N'm ~Jl111lJLlJU,}~fl1UIIlJ"l~~.rOJnn M ' uu
L~~l~~oL.;iom~"L"m"QiULi;'''l1'';J e = 30· LLo: <I> = 60·
"ml 'li"o~o AB ILa: CD .rJlln91JnuLl~:nu LLa:iiiiffl:
. "
1U01111~uii LLu'h"OJ'Ii"0 oj 0
l1Jii 5-93
•
I
/t;
~r~(,
5-9 4 till~ihhH1rn t5 Ib / fl 01uvi-'l~fl JO'l'ru1Y11THH.J~B£n
m'nJ UCI ::UJl ti C B~ ::~W~-1llUU Joulllal l~ 0 ll.'lll1()-1rhh!:"
flV1J ciild X, Yllo: Z'UUJUjJtla iijUl~~lUJilJju"JncinL!a:
llJOJU;:l ~1 1rTi:; ~Il ;;) llHUl u1J()JLn'i,J'uY)H01dJ~-1~lJ
/)
.1 m
,
/'/
1m
~tI~ 5-9 4
249
5-95 ilJ1110"lIh: noucioo X LIn: Z "o'ILHtl5mol~"lIi,
uuu lournal ~ A 11lJ,r'LLH~J1uLiIUL91on BC LL~: BD
~~lLtiUlillii'llIIlJ~iL'llOJLLvio
F = {- SOOk)N
~u~ 5-95
5-96 wnntJnJ1V.ll~uLmi-lu'UlJ Journal ~'.n,f,:nHH A U(lZ
B nlJ,f-l'1J()~fl cfl.l DC 611)JiIJ1!vltifl1'U~f1fl'j:nrjHifm'I (l1
",ltl ~,,.,,"'iftl,. flallci0V"a,'",tlnmOl ~"11"1J LLiL:ILj,
lwuflYia 'lJtl~tltl~h.J'l~ttlU'UUltHi'u'iZUllJ y - z L~(I::: llU~"
oQhHLUlvl111lJ l: fflJU utI>a1
':itl~ 5 - 96
•

250
390lb
800 lb·ft
~"" , ~
I
3f, ..(8ft HI
,,
30"/ B' ~
~tJ~ 5- 97
5-98 ftBiii'flii R iillm~li~Oi.,nUllfiUfi"H I11l1mojj
fi11lJU;j~lIfi~~ k 1I":ft11lJU111~lJ R "~I1",~,i111"lu
Um;llJ F ,ra'nn~~"lnfta'ltJ'Ii'1'11tl'1 lV;al'hMlIm,nlIjU
8 nUllm;1u ~u F = kR (cot 8-cos 8)
"j,j~ 5-98
•
B
- - 1 m - -1--- - 3 m- -"
~,j~ 5-99
~-'~o ~U~1~~~n_;{lO~1"mfl~U" ~C~ II""~ A 1"Utni~lll
1I111"UlJ"~>ff~U"""lIlJlJnlJI'uu 91'U"IIUUI1"1lJ 1 ""ai'!
,n"1"tJlill1~UlJ"<li'II'IJa,tJ"an "'111e,",j,: nalJciau x
~ II""' z 'lJa'''Hufimu1~ A 1I":I"'~,lulmu"~,,a~fil~
f,~u,i1ulu1111OJ"
~
I, "~0.3 m ~ F, = 1-600kIN
x', t~
04m~, _~
~,j~ 5-'00
a.8m B
~
a.3m
F: ={SOOnN ,..- -....
' ~
il l := {-120k t· rn "
5- 101 ;Uri1U AB (lnJlou~ B lV1U1fllij~~la::-~ A 1>HJ
uvi~njam~tllJ1}Y1 i"'ff~iVl ~P1 UUtinu{jUU~-lUVl uutJ11 ft 1lJ .,
""a~ln"1'lU~I~~UlJ""l,a'IJa~,j"an 111 F = 120i-40j- 75k}
Ib "'11la,,,tJ;:neuciau x, y "". z 'lJa'''H,jlimU1~ A
"":"H~hllJlfIIU"
5-l02 .{UiiTU AB ()f)Jlrln~ B hHJlfll1jClUfl~~ A
hwll";-l'IU~l'I1~EllJiI 1P11CI';{~tol~P1Lltiu'jl'Ul~uu91~ti~Ll1 111H(}1)J 1
~'HJVI~~f11.J2U~ll1iUlJ'iI~rff'JD~,jfW n ;)-.1111 LlH~-.1hW'llii"
BC 11111" F = 1- 45 k} Ib
- .----:;::'
~ Rft ~c
/.~

6," y'A~
~" ,
12ft
"" ~- ~'"~F V41'~
,,j~ 5-101/5-102 ~x
•

'(
5- 103 !lUl1nlJn1'll'le~fu~1"nrmff1 12,000 Ib ~m1
1111111'1i')) w, ll~~ w; ~e~!h111rnm:n111uu m:~lvm:l'h
lJUlburiH~O.ll'U71na,,,,1'ulllJ ~a
1-- - - 35;,1. ---- --1
~U~ 5-10 3
•
5-104 ~~"" a~ ilu,: nauuaul1ll1Ull1U"a:IlUl~~~a~ lll~
ri",!!", B ilUVIlU9Ilm:1l<'i'lvm~ ~~ T = 100 N 110:
~1U" 0a",ll~ 0:'0nvi'.('flu
T = 100 N
l,j~ 5-104
25 1
5-105 lll'i~ AB iilJ1~ 5 kg lla:lJme~1'ul",u,a".ia~nn~)J
lla:l1h~ A, ni'lIliion Be lla: mr~"m~vu~ B ~~11l
' . 1 ' _ I '~" ~
a~tllJ':nau"au x, y ll~ : z ~D~"'~lJDn'Ull'l!'U1D~,U
-'
x
5-106 ~~11111Htlamu1~tI'Dl~atl A lla : l1l-l'" B amflJ
ff)J~ a~a~ii'!.Hhu

-
6
O'lS<JlflS'l::111flSoas'lO
(Structural Analysis)
i
lUlmifnci11ii~<llJmlllJ'l"~1'1fllflmI11flm'fh~~lh:namhu{lJrillJ~~fll~alJfllJ.r1Ul1lJ~
(Hinge l1~a Pin) nnilm1:",i1ltJuhl"'llJl1ilnnl'~i1(111m~"'1~a~hn:lJlJ"lJ~0 ,,~JlJ 111';0:
{lJrillJ':fl~llJ"lJ'lO.rlU n1Hh:~n.rfflJnllllJ"l<11lJrillJ';1~ 1 ~a~lm~o", lm,mfllJ l1,a
lf1~tl~;)n'jf)" 'i)~,nlJlJflVl'jl1JU'j-l.J-.1tflJ~~n'J~'til~~V1~()l~mJ ,}1-l'litl1UUVl't1iJfl11lJ fflr1~ li'lU-l
.1 n~"1'l1mliiu~lt1 n1n 1",r,1'",qii",: n1J1i11ilnn1'" fl' n1J01:"'1~ a~ ll',,]5in"1~tl1"
,vi1rltlltlllln'~"1nlJu,;ui1ffVl1~'"HnlJ.,J1lJ 110:nl''],:~ n,,1illlJ"mllJ'l<1
6.1 fASlJliouuUlha (Simple Trusses)
)
lm~on (Truss) ~o lm'lI'1~~,],"nfllJ.r,"{tlri'lJ,']i1,liu,li" rllJVl".r1lJ,]01u"f'lIO,
'';1,of10Hll'" {tlrilt1~1irlu~,'hlltlnmi°lIi'l":,1'IU;fltl1i",'iallli,1",,: nn,;0I~OlJ~"",h'lii
f) 11111-!cr~lFl ~U1111fl l~tllJ~19nJfll(J'U f)-l~urilljflUnNu1fni:::UH~l1Unil m~nHr1Utl'J~FlU (Gusser
Plate) Uff",llJ,,]~ 6-1 (") 11;1lnl,liffilm"1i"'~U1"lm1iI1'fll1lj" 1l01~.1" ~lt1Vl" ~ U~":
~lJ(hu,)~l,]~ 6-[ (~)
A
(0)
~t1~ 6-1
1m,onlm,mu (Planar Trusses) lm'nnlt1J:U1lJO~lt11"tl1lJf~Ul ",,"lyw,]"~.:H
lO'{U11",mU",lI:,m, lm,nn ABCDE "lI",h",]~ 6-2 (n) i"1I11,)11l01,,,o,lm, nn
253

254
)1)~i'ul1Cl~m1)riH~la t1ll1Unm:vil~1)~11cr~m~:~lalt1fr.lm~0'n~~"'1la~m;1llJ (Joints) ~~a
iilltl (Purlins) 'UU'11,jla l,jU DD' dj1l~~10t11l1Uom:vilnlJrlum:villu):ulH~alrlU iia
lrmO'o (Truss) .,~)tI~ 6-2 (~) O1)ilTln:lfm~~lii~lu~urilul,mflmmuUl'f1l~jj~
ull ( Purlins)
lm~onHi'~fl1 (Roof Truss)
(0) ('11)
hm,Ojl'f:Ynuul'fVl~luitl~ 6-3(0) Jll1uomivillJuvtUl'f""'I1U~:~lalJ10~"lvn~ (Stringers)
.., v / v ,
.l nuu1t1 o~mu)1)~Ylu (Floor Beams) ,!mi'101uo~~Vl B, ella: D ~ll~lm~flmlltJ,rl~""~ii
)1l~i'1J 1uvilUll~'~01rlUrlIJ1Tl'~ 0'nl1cl~Tll Jll1Unn,:>illTl" flnl'f:Y<ltJ~:a~1u,:tJ1lJIii01nu
.,~,u~ 6-3 ('I)
l~1ll'f:Vl1ul1~1l1m'O'nl1«'Tlljj,j"':U:Tl11lJU11lh'lJlo 1 !To~:1i(jnn~' (Rocker) 111a
clm~ou (Roller) rill1i'IJ~,a'i'IJ"'l,jU~Vl E iUttl~ 6-2 (0) lI1): 6-3 (n) ~lU'1l,flJ",ocill
d;)~iiaCI')::lUf)l'iU ~u,,::~tn(J ~1'Jf)~~'UriTUdjil~1) 1n~lUl1JJil tW~nl'i f)'J:;";1'U 0-3,h~Hrn
x
fllUl'IU
c , ~
1l"rl'nfl Y'ltH'(::VITW
(Deck)
(Stringer)
( Floor Beam )
(0)
L/' 'II····· i
-.;-=.;_~__ 'i~'__~ ••~A B C f)
l fl'Hclnll':::'fnu
( Rridgc Truss)
mJ1JCi~llHil1t-rtlnl'H13f1!tU'U (Assumptions for Design) fll'itlll f1uutn..r-l;lchl.lUCI :::
nl'l~ f) L~VlJ"t)-31fl1-J ci'n l~lJUln~llllu~u..J111 Ll'jJ~lnY1:iju'ulL~ ,,::iUrilUl~ olfl'lJ cln 'lnthIftrn

: ; ' . . . . . ::. 0 .d •
1. Ul!lUnm~mfl~!llJAnl~mfll!mall.ta (All loading are applied at the joints.)
'''''I'lomu>i%J ,'liu lm~('mr:Ynuua:ml~m 'li'lllllJlJ~!lUii'~09111~ '"oli%Jum1iL~ml1
UHil:hj~AJnnrn'IJIl'~UfflU ,iill'~lnuH~!Jmll,rul"o~ufflUlJn~:ii'IJuw'lJ1n,iia'iiounu
';ll1Un'IJll,iufflwa~ ti'l';ll1Un'IJ1l~~lIffll1~"1llJhm1i 'fln:l1 ~:~",,'IuU1~luulIl~~Uo:
"ti,n~~~lIl"m:yh~u~a:ua1O~Il'~UfflU
"'" • oCt "" " ... <:t
2...'HflUo......oumtJ!I'lA!ltJU (The members are joined together by smooth
pins.) luoH)j~li'omia'~lllJ.rl0nl1'1lUllamOn01!1~fll~alJ 'Ii'alllJlJ~!lUii' Iia UU1'lIUf,lUrJ
naH~a~iufflu~li"Ol..nuiianllU:illJ~",~olnll (Concurrent) ,,~lumru~a~~A A lu!tI~
6- 1 (n)
,iia,illo'Ii'alllJlJ~!lmf,<la, luu~ a.lillffl lI~ a,l~HIi'0~.OJ.vil'l1iiauii'uffllilla'Ul'
(Two Force Member) .",j'u "H~ua1o~a,iufflu~.iiViffm~mlJUU1"OU'IJa,ii'ufflu O'1U1'
ii"Ul1,rlJvi1hiii'ufflU1i""1~:'UlI",,;i, (T) "'!tI~ 6-4 (0) lu'IJu"~O'1UHii,!u11,rlJ,h1M
~Uffll1l1Akua,~:,uu"mr.. (C) "'ltl~ 6-4 ('11) lunnaan"uuil~~~a~lm,('o~l,uu.ra,
'n1UW~~nnlJ~a,IIH111UUII1,;i'11~aIll'tlA 1<')OYj',lu~lIfflII~>u IIl' tlAil:ii~IIIA11l!l011
liufflU~>UII1,?i" iia,~10"a011"..n110~10~I~a011,tI~ouuti0~fll1lJ0l1,ii..ifwiia~ufflU
•
".
T c
T c
ltl~ 6-4
1",..,naUH41o (Simple Truss) ,viaiJll'nuom'ilJll1aOmiio~tI mllulm'('n~•.ra,
,,~"o~, " ",liviall ABCD 1u!tI~ 6-5 .:alJO'11liijyilluVl'w~ AC !l~lJ''lil1tl'lilmUlIlilU1a,rU
maulnHa ciH~l u~ii "m;U:"~"nJmlmj'lI~' fia mau1m,('0!tlll1lJIl1~UlJ (Triangle)
... to ... "i .... , . .. .;. v Jt ~ ' '';O:; .d . ..,.,:
"""" " J rn"lff'l1.l'fl'l'l (lfHltJl' n 1J~ '1,"j"711'J'AI'!.!~11!'tn![fllmih ll,j Cl'11mH'ltl1 J t"!n', .' Be n 1:l1b
6-6 "ft:~m~fllJnUllfl'~lIffll1 (AD ua: BD) ,viall>mtl;)ufflWvilJlOilJ ,,~,fu ••,;hM11
u~ f1::{tHhu~Lvi lJ1JtilJ1nauJ:iuri1lJ'vt11-3 () ~U1J1rn-J on ~1U 1U~(l.J7rH'J~ iH~tJ lJ ,hHi'u 1fl'j,J Or)
. . ..,:.r d ,":
tl til,,],,]1(j 1l::1vnJ'U'U'H lJ.3'HH.I~ tIl'lH)lJ
255

256
p /
1U~ 6-5
•
6.2 5smslll,!flfiEl (The Method 01 Joints)
(hlm~ti'o o~lulllJ,,!" ;l~JU u~ ":~.,~O~ :o~luIllJIi!0""0 i~~"," ojj~U21UA11lJ~1~
l1;ioh,ocilUL1OU1~lllJ"Offl11'1JUl~~0l:vi1I>ial1lJ" (Pin) viu," a:~.,l>io'llo~lm~ ti'o ldo~~ln.. ~ . .
;lJ,hu1flH«mth~;Hh'Uff{)~UH~)jm~nl:;vh'UclmJru::Vll~uu::DQhn::U11J1&1u1nu 'j::'1}UU'j~~
m:vi1viol1lj.,1., 1 jjKn",:,,:~a~lul"U11Jl~"1r1t1ua:0l:vi1il1J~"'~ 01r111 (Coplanar and
Concurrent) ;lotTu 01mljtl1l~al:1JlJIll!'lo'lla~llJllJuof~" ii.,a.,11J1ffivi~.,oja (11~a111-l") ;~
~1Li'luvi l:F ~ 0 !la: l:F ~ 0 lV;O,,riJlllJ.,"mllA~ow;'U15"''flJ.,0~a'':UlJUHl )' • •
l~oli1~~.,~a (Joint Method) '~lJUm~11i'J1I;la~11" N'1",~5 !!l:'Ila.~.,';a riauth:~oof
lii11Jnl·H"l.I~a lLU1'Jfl.:Jfll'Wl::vll (Line of Action) 'lHNU~(1::;uri1uuHnl::yhvlD~V1vi[)vl1lJ
1tll~"'L'i'Ulflru>l'UD.:Jlfl'jlon L~(J.:J'i)1nu'jllu{u,hur-JTW~UJUrn~~fl-l~tl ffl u vrlflciHI'liu l~'Ilnru)
11'-l"'~~" B 'Ila~IA,.ti'olt1ltl~ 6-7 (0) UHvf'!!llJO,:vi11il1l-jVL .run UH 500 N UO""'J~
n,:vi11.,O~u'i1u BA '10: BC NJi'",q5(1,:u(l"'Jlu,tl~ 6-7 ('1) VlU;l Fa, li'ltlnll~J~l1l-l"
l1lJl(JA,)l1rjl~'Uri1l BA (l~lUfll1::nllf'Ull'i.:J~.:J (Tension) ltt'UfU::~ Fftc ~llllnl·'H"H'fl~l111~
~.n.ru ~tHhu Be ()~1Ufll1::n1'ji''UuJ.:)t1~ (Compression) ~1C1Yl-JncillUl~fJtW~ulU'l~iV'll~~
l"onmwnl1l!",i'Ju~urilt1l11n 1 ~a~il'urill1~~81~aJnlJ11l!";l~ltl~ 6-7 (A)
h,"lnmul n1'i'm,",1,.,i~vi~.,';fl~iJIl~J~1uvmuTi1!!aJ lL";l~JtI~ 6-7 ('1) tl,"~0",1'11
l:F ~ 0 U~: LF ~ 0 ~:'1.r(lJJn"vhrAtiilil!!U.crlJnm~a,hullU111ril!!OJ"'illtl1hi1muTi1 l~a, ,
tl"qni(llJO";l~nci11;1 Vi,noN~~O.rU~~UJu,,{urilt1~1um1uTi1!!llJ1101111",1",ohl'ii;lJ<ia
11.1;1
1. ~l'i'f~lJ~U,J~tIrilu~'hjVJ'1miln"vi1~ NJ1'"q1i(1,.'1O.~'" ~00Qlun11: nl'i'lJU' ~
~':]'ll'WHl.J~ 0'nil~l1J.ffll ~ fJl!;1 fll Yl fJ'U tfllft'IJ'IJ tn ff1Jn1'j fflJ ~ ,,~,~~::lift1fflf)" 1fu1 fl dUff'll
~'Wril'.t'Vi5ULL'j-l~-l un~AHHnfn'li1urlll1'j'U;Uffl1t~UU'i-lrl~ t~m'l'jl uUi>liu~ JLI~1u~IJ IIJI'i I
i'f1lJ"oH~1I1,,"~diff1m (T 11~O C) vi~.ra~lu~j'Ji'",qii(l,:~o~~~~ao,,'h.1
2. iii!vn~~~n"a~'IlOJllH%uri1t1hjm-,uti, 'umUi.il~ 1 (l1lJ"01111oi1"'"n"m"~'llJ
;l10a,..,;" F 'u,tl~ 6-7 ('I) "OJ1'll'~""l1lJ" (OllaA) ldOJ~lnt",ciuohllLtn"UBC .. •
F sin 45· ci-l'il~nlJvHlnlJllH 500 N (LF ::: 0) hfrlllW':]l~rnn'U F d"hmH&l~ld().hllf)yja~BC • x BA

crlJ~~ntmHciDvluuU1~~ F cos 45"CEF = 0) lumtiiii9l'u9l'DUIJ10"iilfYll~'IID~m~9lU1hu• Be v y .
1~Y111U~lUllJ110UlJll~M ""ru ,.,cr~~lmh:Q0.,1'll'ulJ0llUll"!a iiIfYll~Vi('(lJlJ~UllJl,ow'!'IU
i,n~a"lm'llM fh"Duiid'JUU1nti~uDoiliiffm~trUQO"D~ lu'llru:iifil"Duiid'Juauti~uDoil
iiffYll~iiDy1u«~101~ii('(mfum~nU'I!llJ "
56n1scl1I'1Su5IAS1:1'i (Procedure for Analysis)
'i~Oll~cil~~lalil,.,funl111~n",.,1m~n01.,vhliii~.,.iD (Joint Method) jj,,~;l'
11Vl«~101 ~ii('(1:'11~~~.,.iaiijjll1~iimlufi,,.,rt~llHlm:llimlufi11lilnucra~U1~ C!h~.,.;ail
a~ii21ll1a~ful., 1 l.,uvi%J1illi'lU"a,,,,,ullm JBmV'nlUUanii!lll1a,fulm,no) l'lliiioll
Il,'''U lYia,."iiffm''IID'U,,'liYl11U~1 nl1~ml'Unu x ua: y ~="D~('(:"lnHuHUU«'1"~
D(,(1:.,vlunlmn1ul11uu1J'tJa,uHciaoluiiffYll' x ua: y ",Ju ('(llJ11oHcra,crlJnl,crlJ,,!a ~a
LF =0 ua: LF =0 utiil(U""U,~9lU1hu1uYlnu<inf'<fa,u~:wu~uiillm,iino.,~,~ y ... ... ..
.;a1111lmm1u.ia:~Vl.i~~u <] i,~lli'lu"a,l~~o~.,.;~iijj<fa,"lu11,1umlUfilua: jjll1,yj
VlllUfillfi1.J LL~.J U7~lu~'Uffl'u~,.nl~til nn171 Ii'l71:a 1't1 fN ~VlIPi()~tJH1 o,j'i-ll~'lh~l1i1~ H" ffl1I1 Hl
Hil.,11:MUH01:';1~~"'; ali011alV'l!l,,.,rt~1., ""lJ,.,cr0'11a, 01101:,;,iiJJrillY;1nuu.;jjiiIf
m:~i1","n'U'ulll
Iii () Ol'i1 lfl n ::Mm.J'UD-l1f1'i.J 0'ntff~'HYlJ!nU 'JUWI'U rl.3~Uri1m":::~Vll<iiauvl () nUll'j ()111'~
1",uHYIqYO'lla~0~III('(OIl'lla' 1"'''!mlJ'I!Dl;!alulJ1m2'UnllDD0UlJU1'l1'1ff1O"lJ -
B
~ "~~" 500N
I1 m
I f,"
_1__" f,1,~F====,,45,;~/=="i~ c
1----2m ----1
Cn)
B
FBA ~
500N
P
;, Fnc In,w"~ (Compression)
LL1>1~-l (Tension)
('U)
B
Fs:
K
500N
~450 F,c """. (Compress;on)
U'H~.J (Tension)
. --(fl)
257

258
A3aalU_~n ~-1 ........................................................__
7-' ~~lilU'lrumu~~lull~~:ilurilu'IJ1Hlrmooi~~uii 6-8 (0) Ufl:U~1JflOililurill1i~
nril l LilUUj~~_ll1~{) m>3tlVl
8
r 500 N
2m
I
(n)
B 500N
F ~FRCBA
('IJ)
~u~ 6-8
Q~ •
L OONA~- -~ FAC "500 N
Ay
(~)
B SOON
500N~707 I 1',1
1
4)0
,~ f T
~r
500+ ""iiJ 45'0.:1°7 1 ,
~=,===<~~C
500 N 500 N 500 N+ 500 t
500 N
(~)
)lim
i11f)nl'l~11'l'C'fDU:pj~ 6-8 (n) iJl'j-l"lrilu~'hjYnl'Ufil C'a_lU'i-l~~Vl B U'i-liu(hu1Jjl'l'nu
fi, ~fl.ll'"11(1" IIHuBiBu11~vll1uri,ii C 11""l",il'l,hu1UVl1lUfil~fl'!" II~'lmuiliBu,11.i
VIl1U1il1fll~llj,ii~", A ~,1,jliiu~a''''lllh l11111~lU"0~u.rIl'llfln"l1ii~'" B M
~Y1 B (Joint B) rr~-j',"nU~"'lJllmlJi'l~ B 1I~",lmuii 6- 3 ('IJ) ll"',f"lllJm">i'~>flJ'"'" . . . . .
m'illUllflO 500 N 1l~:llH1liVl~11Jrilfffl'llH~lii"'1"UiltlrilU BA II"" BC ul:qn,,1"~lH'11
~lJ~~~~"'~flI~lllJ ~:1,;i,
-----'--> LF, =0 500 N - Foe sin 45' =0 Foe =707.1 N (C) Y1a'l'
+ i LF,. =0 FAr cos 45' - FBA =0 1'0.' =500 N (T) ",,)1
l~ll'~'Ollj~lt1o€Uriltl . BC >qM
IImJt]mUliillUla" lI
(
1

~ :EF~ = 0 - FCA + 707. l cos 450
N = 0
+ l' ~F, ~ 0 C, -707. 1 sin 45" N ~ 0
FCA ~ 500 N (T)
C, ~500 N
il~ A (Joint A) O~Iljj'"ilhj~ll'Juvi~"ii~1",oii1~"'~fl (Joint Method) ihmmm1lliH
tJijm~l~!lUlfl~ru1.i 9l~;hIlJlaii~nlliimrlJnmrlJ'l"~fl~vf~l:UuIYifll1lllmlijmOl~!lU10~
11J1" a".tru..rflifd..ni1~"'';fl (Joint Method) IYiflfilu1rul1lllmJijmallfl~rU~~'" A 1.101'11
~"~fl~ F = 500 N no" F = 500 N 'llnN'~1'",o1i<ll".rmJ~ 6-8 (~) ~""'"ilAC AB ~ ..
----'--> ~F. ~ 0
+ l' ~F, ~ 0
500 N - A. ~ O
500 N-A, = 0
A. ~ 500 N
Ay= 500 N
~o~%ualU~';fll~fllJ no: Ill~i11aufl n,f~l1lJ'"~m :vil';fll1lj ~ lu~ru:~N',l'~~1i<l'l:'IJ fl' u';""
-iUtbtHl~Yl-3tl~U-l f.I CI,HH'l1~~t1enun'j:a'h9itl~.lri1U
A:liJthlln 6-2
"Tilu1rul1lnl'm"villu%uri1uvf'"lJ",~o,lm,on.r'ltl~ 6-9 (n)
~/iY'FC() ~
30} x
1.5 kN
(11) (~)
(n)
:l-Ic(
)'
2m
0 (11)
3 k..'' 2m 2m
!.5 ki 1.5 k'
('IJ)
259

260
~ ~ ,
lfiYll
1,wnmm~lYVU iilYV~'i'1111hhimlUfil~~>l A II"" C i~Ju l".rV~YlnUIIH,jBmul
~v~i'uuu1m~onrivu ~lnnllfilu1u ~"1"il A = 3kN iii'!~, A = 1.5 kN iill i !L"" C =
• , II Y . • Y
1.5 kN iiff i 1I11~~m~,jBmUlii~lu~v~i'uii~n"v~lurT~1"~BlI~"1u~,jii 6-9 ('II) 1"Ui5lJ,j'u
1lR,)1~tf~~Vl C
'lYl C (Joint C) ~lnrT~1"~iilY~"iu~u~ 6-9 (fi) ,
~LFx = 0;
+iLF ~O', '
- FeD cos 30
0
+ FCll sin 4,S" =0
1.5 kN + FeD sin 30° - FCB cos 45° =0
(I)
(2)
vril~hnmlJ Iiwwu1"U"'~~l1-1i'ulI~a:II~~1umlufilM"nnl~llnlllJm,~ (1) II": (2)
nhi'l1~v,j~:Qn.rmn1lJIIH"llJII~U~i~lllnnUni'lYl1~'IIv~II~~himlUfilii nm~ un01,vril~l'liU
m'~llJIIHlulIU1l1nu y' 9l•.i'~il1nnUnIlYll.'IIa. F "~'U~ 6-9 (~) ~"M';lOWul>lu"H'lJ1HCD •
FeB
+?' LFy ~0; 1.5cos 30' kN-Feasinl5'~0 .:hi' FeB~5.02kN (C) 'Yl6U
+?' ~Fy" ~ 0; 1.5 cos 45' kN-FeDsin IY= 0 . :1.r FeD= 4.10 kN (T) Yleu
;).. 0 (Joint D) lIUmOi'ml:"oia~." D rT'1",oii1"ml1">l~lulJ~ 6-9 (Il).. l . ..'---
~ LFx = 0; - FDA COS 30' + 4.10 cos 30' kN ~ O
FD
, = 4.10 kN (T) Ylell
+ i LF, =-0;. FDa - 2(~. 10 Sill 30' kN) = 0
( FOR = 4. 10 kN (T) "ell
U]~luilurilul!"ilU BA ~llmOl1l1vi'.,n~" B l1~"~" A luvmu(ju"ii 11"rT~1,,~iJlI"
'U ()'llYl B nlJll'~~l.1VinVll-3VlliHn.n Jlu ~::1~il F = 0 .7 7 6 1u'J (C), u

· ~
A:J8fJ1Un 6-3
~~tilnrul11u1~lulloi~:{Uli1u~a~1m~!ln.r~JiJ~ 6-10 (n) 1i~tJvniiuri1u.r1"illiJu
u1~ii~111VU1~U"
400N 400 N
- - 30>--
c
4m
A ~==========~~~
1___ 6m _ _-I10 600N
3 m--'-- - A.:
(n)
1
~~ IF
DC
---~--x
)'
I
J FAD
AF---~---,
450 N D 600 N
600N
(rt)

1400 N
1I'j,J6'~ 12OO
f
st600 N ~CO~I~ssi~) 600 N, ,I~ +<______=0+ -rr-600 '
_ 250N f OON
~._, I P~
wrrr,;, '1 9'~.c.:;. ~'> 1 3 ..,
, ·~ov ~~
~ Il l~'
' 'i ~
750N " T
L
l(H~.J 250 N , 1200 N
(Tension ) ";j
At ~'f--<o=========n=---o:-" •600 NImN .mN 0
600 N
750 j
(;!)
1U~ 6- 10v
261
--------

~ . ,
262
~~ .,tim
lI~nJilm~l~i!lmV~;1J (Support Reactions) 1liii~>l'>l1l1lJ11()ilml:I1~Unmr~IIH
l1iimUl~!lU1v~i'u~.vi'v~mlurivu Ikr~ Qihn",,()~lm~Gnyf~11lJ"Ull,,~'u~t1~ 6- 10 (,,)
t1,:"n"<1lJnlll!lJ"~ ~.Mll. .
---"--> LF, = 0;
(+ LMc =0;
+iLF = 0', '
600 N - C =0. , C, = 600 N
- A,(6m) + 400 N(3m) + 600 N(4m) = 0 A, = 600 N
600 N -4OU N-C, = 0 C, = 200 N
. . . . ..:' ..: ;,~ . . . . . ~ . 0 ' d .
nl"I~".I1U~ "11lJ"Ul'l~~ A 11JV C IUa~i)lnm~'lfUlllum :m"VI1Ij"m1u11mmlla.
1lil'lnUfh~1U1Ulla,fillULI~a:~""~nci11; .
~>1 A (Joint A) ,,~,t1~ 6- 10 (~) ~ln"~i'",o51'1'. jju"lilUllL1l'llJln~~n,.vil~V11lJ"~ .. ~ ~
vi~" A nm5"~"v~ F I11illn2t1m,6iJ1mil"'''v~lm~Gn )lnl!lJn1ll!lJ~~ ~:1,)'11A6
4
+ i LF, = 0; ~ 600 N - -:cF" =0
)
. 3
F,,, - -c(750 N) = 0 FA" = 450 N (T)
)
I'LlllJ
I'LVIJ
'I" DUoinl D) "~2t1~ 6-10 (. ) 11~"li'Ju~"vilaan~a1t1 L1ja'i)lnl,,"nu"'''i)lIaIJ2t1~
6-10 (0) mlum.1u AD ua"lmviltimlu,h1u DB II". DC ffllJ110111'l" m'nlJ"'~'U
Vif!l'l1'>lllJlltrmU,,~,t1~ 6-10 (~) . ::'1"11
~ LF =0: - ~'N+ ~F + 600 N=O, . ~ _ ou
)
F~n = -250 N
mifl'11lJ1U"lJlj~ifll F m:,hlu~ffll1'Cl)'nmi'llJ""tl~ 6- 10 (,) ,xuRaDB __ ..
Foe = 250 N (T ) I'LlllJ
Ifla11,l Foc ia'ltlfiuuhTViflm,,,", F on,)'a",ti',u><qn" LF "0 11'mJ)"~n"1I1JOuci'OB ..
1,".~~Lflja'11lJ1""1J a'I1i'1J F JuHlViil:nnfi1U101~f,tl'u~Hrr,f", oih'll:ltl(~lJ .ruiiaDB • OJ
i -I _ 'IV+ LF, =0: - Fco -
sl-2)0) = O •• " . Foc = 200 N (C) "alJ
'l" C (Joint C) "~ltl~ 6- 10 (.l
---"--> LF, = 0;
+ i LF =0, '
v v
illl'i1U'1nilmh u
Fcn - 600N=0 il<1,;'
200 N - 200 N = 0
Fen = 600 N (C)
(mllllau)
"ou
6.3 ilua:JufiusumEi1ulf.Ju~utiVlS()fiUcbunllisuusu (Zer'o~liOr&e Members)
rn'illfl'il:::,i1fllH'fl1'lS~1i~~toifl ( Method of Joints) lI::~ltJ{tl tht~lJ~h(Jnl'Hll{u,hu~
'hiiin1l,uJ'11unl", 1 iiulilUII"~li'Ju~u6 (Zero-Force Members) ~.QnHll~an'i1JmllJ
,j'lm,'Ua~lm'«nl111e"'i"n11ria(f{lJu""~eQnhll1n1)i'u(IH~iinllltl~"u"tl,..J,11tlnn':lil

<iJuri'U'JD'lll,~,'Ju~u6'llD.lm.O'nl~aYhhh1l1~an1'~1~fl:m (Inspection) 'llfl.u.ia:
~fl,"fl "'.flU1Wliu Yi~1'1U11m.O'n,j.2t1~ 6-11 (n) t'l«.iflQilffl:'JD'lI~fl~~fl,"fl A ~m1fl
l~jtlli 6-11 ('J) YllJi1%uri.U AB ua: AF ,'Ju%uri.ulil!l.malUluu~u6 lum.nKlJIlu
VI~11l1iillJm":ff1til" t'lYi~llIU1«.i~Q1iil"'Jfl.~.,.ifl FlI~fl B liiD.~lnihh,j.utllhjmllJ
!i1~u';a"~"~D luYi1ufl'l~u.nu r;~lllUl".i~Q1hm'Jfl'~~~fl D ,j.~llli 6- 11 (~) YllJil
DC ua: DE ,Uu%uri.u~Ul.maluluui!u6 ,j.ti'u t'l%uri'Ufffl.9luriflll1'lii~~~.ifllm.O'n
ua:hiiitl'1mTnnj .Yi1111aufl ml~fl u,.tIjjmo1~~1Ul~~i'lJ1'"Yilli~~.ifl 9luri.uti'u~"lUU
9luri.~~uHnlolUluu~u6 tr,mTom:Yi1';fllm.0'01u~tJ~ 6- 11 (n) Q~fl"lJl~a<iJurill"f'l1'l
"'11l>i 6- 11 (,)
D
~===O#===~cB
(0) p
)
I
r"A •
x
F"H
B
(.)
..:t. r Fx = O; F",s=O
+i H~ = O; FM"=O
+ 'iF, =0: Ff)Csin 8=0: rnc =O~inc.:~i n()~O
+I<"'£.F.( =0: Fo£+O= O; Frw =0
(ft)
v;~ljO!llm,O'o,j'ltili 6-t2 (0) ,j"i~Qthm'Jflm~"vi~~~" D lm~,'ultlvi 6-1 2 ('lJ )
.100n.r.llOu y VlllJifUl'hu DC nlJ DE ua: llllU x ~llJifuri.u DA Vluil DA ,uuifuri. u
LLHnlu1wfIHfjwII'HiimJml;'1r1111 1'1 1":i,j~ 6- l2 (ft) 0.nr~t (hf~f;hu~1t.:~lU-1;)111lib~~
.;D1m. 0'09i,iftlri.ulID'ifufl ~1Uutn l~u. nu u". oiu~ffllJ ~ .luu%urilU~ IlHD1V1Ut'Ju'!u6
1~tt;;;iJjihl'J1fllU'Uuf1l{~ulll-3t15m(ll~~1'U'jrHrUfn::'il~~il~u'u~uM 6-L2 (fl ) d' ;it) ~il D
!Tuw. im.O'nulH"'Ulll~ 6 - 12 ( ,) 9i'1l11Jl: lIuri111' lJlill.,fl"lJtl'lmTn P liifl>illnlla~
';U,11uviI",n1alulUU~U6Dflnillnlm,0'n",h
263
p

(0)
+.( EF,,"'O; FDP, =0
+'::.. LFy=O: Foe = FDE
Pl::>€)f.i1un 6-4
p E
/
A
('I)
(n) (~)
x y
+.( r.F~_=O; FC.40 sin (J =0: FCIt =0 LUo,Jill1 ;;in8~O;
+ '!.!.Fy=O: FClJ=Fcu
~~l'1l"iu jVlvi",l1~u<i1l1~ln.f)1"hllth.ji:JU!hf~l1lJVl~fl~lm~t1n1"~'t.I~ 6-13 (n)
_c
( n)
"" i
-,VF:C
_ .
F/{A H FUG
(u)
)'
(n)
I
~t.I~ 6 - 12
•

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