3. analysis of statically determinate trusses

mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa

#> karviPaK truss kMNt;edaysþaTic
Analysis of Statically Determinate Trusses
enAkñúgCMBUkenH eyIgnwgerobrab;BIviFIsMrab;viPaK truss kMNt;edaysþaTickMNt;edayeRbIviFItMN
nigviFImuxkat;. b:uEnþ dMbUgeyIgnwgBN’naBIPaBkMNt; nigsßirPaBrbs; truss. bnÞab;mkeyIgnwgBicarNa
karviPaK truss kñúgbøg;bITMrg;KW³ truss samBaØ/ truss pSM nig truss saMjúaM. cugeRkay eyIgnwgBicarNa
karviPaK truss kñúglMh.

#>!> RbePTTUeTArbs; truss (Common Types of Analysis)
Truss CaeRKOgbgÁúMEdlpSMeLIgedayGgát;Evg²
EdltP¢ab;KñaenAxagcugrbs;va. Ggát;EdleRbICaTUeTA
edIm,IeFVI truss rYmmanr)areQI r)arEdk EdkEkg b¤Edk
GkSr C. CaFmμta tMNRtUv)anbegáIteLIg edayb‘ULúg
b¤edaykarpSarcugGgát;eTAnwgbnÞHEdkFmμta EdleKehA
fa gusset plate dUcbgðajenAkñúg rUbTI 3-1 b¤edayP¢ab;
Ggát;eTAnwgGgát;edayb‘ULúg b¤edayknøas;. Truss kñúgbøg; sßitenAkñúgbøg;eTal ehIyeKeRcIneRbIvaedIm,I
RTdMbUl b¤eRbIvaCas<an.

Truss dMbUl (Roof trusses): CaerOy²eKeRbIdMbUl truss enAkñúgeRKagGKar]sSahkmμ dUcbgðaj
enAkñúgrUbTI 3-2. enATIenH bnÞúkdMbUlRtUv)anbBa¢ÚneTA truss tamry³tMN. eKehAdMbUl truss rYmCa
mYynwgssrEdlCaTMrrbs;vafa bent. CaFmμta dMbUl truss RtUv)anRTedayssrEdleFVIBIeQI Edk
Analysis of Statically Determinate trusses T.Chhay -62

Department of Civil Engineering NPIC

ebtugGarem: b¤RTedayCBa¢aMgdæ. edIm,IrkSa bent eGayrwg nigmanlT§PaBTb;Tl;nwgkMlaMgxül;tam
Tisedk eBlxøHeKRtUveRbIkar knee brace enARtg;ssrEdlCaTM. KMlatrvag bent eKeGayeQμaHfa
bay. sMrab;lkçN³esdækic© eKykKMlat bay RbEhl 4.6m sMrab; bent EdlmanElVg 18m ehIy

RbEhl 6.1m sMrab;ElVg 30m . CaerOy² eKP¢ab; bay edayGgát;BRgwgGgát;RTUgedIm,IrkSaPaBrwgmaM
rbs;eRKagsMNg;.
eKeRCIserIs Truss EdleRbIedIm,IRTdMMbUledayEp¥kelIRbEvgElVg CMral nigsMPar³sMrab;dMeLIg
dMbUl. RbePT truss EdleKniymeRbIRtUv)anbgðajenAkñúgrUbTI 3-3. CaFmμtaeKGaceRbI scissor truss
¬rUbTI 3-3a¦ sMrab;ElVgxøIEdlRtUvkarlMhFM. Howe nig Pratt truss ¬rUbTI 3-3b nig 3-3c¦ RtUv)an

karviPaK truss kMNt;edaysþaTic T.Chhay -63


eRbIsMrab;dMbUlEdlmanElVgmFümKWRbEhl 18m eTA 30m . RbsineKRtUvkarElVgFMedIm,IRTdMbUl eK
GaceRbI fan truss b¤ Fink truss ¬rUbTI 3-3d nig 3-3e¦. eKGacsagsg; truss TaMgenHedayeGay
r)arxageRkamekageLIgelIdUckarbgðajenAkñúgrUbTI 3-3f. RbsinebIeKcg;sg;dMbYlrabesμI b¤esÞIrrab
esμI eKGaceRCIserIs Warren truss enAkñúgrUbTI 3-3g. rUbTI 3-3h Ca truss EdlRtUv)aneKeRbI Ca
erOy²enAeBlNaEdlKMlatrbs;ssrminEmnCabBaðasMxan; ehIyGVIEdlsMxan;KWBnøW. eBlxøHeKeRCIs
erIs truss dUcbgðajenAkñúgrUbTI 3-3i sMrab;cMNtrfynþ XøaMgTukynþehaHFntUc ehIy arched truss
enAkñúgrUbTI 3-3j eTaHbICamantMélsagsg;éføk¾eday k¾eKeRbIvasMrab;sMNg;GKarx<s; nigsMNg;Edl
manElVgFM² dUcCaRKwHsßanGb;rMkay kILasßan>>>.
Truss s<an (Bridge trusses): GgÁt;eRKOgbgÁúMrbs;RbePTs<an truss RtUv)anbgðajenAkñúgrUbTI 3-
4. enATIenH eyIgeXIjfabnÞúkenAelIkMral deck dMbUgRtUv)anepÞreTA stringer bnÞab;mkepÞreTAFñwm
kMral (floor beam) ehIycugeRkaybBa¢ÚneTAtMNén truss xagTaMgBIrEdlRTva. Ggát;xagelI nigGgát;
xageRkamén truss xagTaMgBIrenHRtUv)anP¢ab;KñaedayGgát;BRgwgxagelI (top lateral bracing) nigxag
eRkam EdlvaeFVIkarCaGgát;EdlTb;Tl;kMlaMgxagEdlbgáeLIgedayxül; nigkareyalxag (sidesway)
EdlbgáeLIgedaykarcl½trbs;rfynþenAelIs<an. eKRtUvbEnßmsßirPaBEfmeTotedaytMeLIg portal nig
sway bracing. dUckñúgkrNI truss EdlmanElVgEvg²CaeRcIn eKRtUvdak;TMrkl; (roller) enAcugmçag rbs;

truss s<anedIm,IGnuBaØatkarrIkmaDedaysarkMedA.

RbePTén truss s<anxøHEdlRtUv)aneRbICaElVgeTalRtUv)anbgðajenAkñúgrUbTI 3-5. CaFmμta
eKniymeRbI Pratt, Howe nig Warren truss sMrab;ElVgEdlmanRbEvgrhUtdl; 60m . TMrg; truss
EdlsamBaØCageKKW Warren truss EdlmanGgát;bBaÄr ¬rUbTI 3-5c¦. sMrab;ElVgFMeKeRcIneRbI


Parker truss ¬rUbTI 3-5d¦ edIm,IsnSMsMécsMPar³. eKGacsagsg; Warren truss EdlmanGgát;bBaÄr
tamTMrg; Parker truss sMrab;ElVgrhUtdl; 90m . eKGacTTYl)anlkçN³esdækic©x<s;bMputsMrab;sM-
Par³ enAeBlEdlGgát;Ggát;RTUgmanmuMpÁúMCamYynwgG½kSedkcenøaHBI 45o eTA 60o . RbsinebIeKrkSakar
c,ab;enH enaHsMrab;ElVgEdlFMCag 90m eKRtUvtMeLIgkMBs;rbs; truss ehIyCavi)akeKnwgTTYl)anRb-
EvgEvg. enAkñúgRbB½n§kMral deck EdlmanTMgn;F¶n; nigedIm,IrkSaTMgn;rbs;kMral deck eGayenAkñúg
kMritkMNt;EdlGacTTYlyk)aneKRtUvbegáIt subdivided truss. ]TahrN_sMrab; truss Edlman
subdivided truss rYmman Baltimore nig subdivided Warren truss ¬rUbTI 3-5e nig3-5f¦. cug

eRkay eKk¾GaceRbI K-truss RtUv)anbgðajenAkñúgrUbTI 3-5g edIm,ICMnYseGay subdivided truss,
edaysarvasMercnUveKalbMNgdUcKña.

karsnμt;sMrab;karsikSaKNna³ edIm,IsikSaKNnaGgát; nigtMNrbs; truss/ dMbUgeKcaM)ac;kMNt;kMlaMg
EdlekItmanenAkñúgGgát;nImYy² enAeBl truss rgbnÞúkEdleGay. kñúgkrNIenH eKRtUveFVIkarsnμt;
sMxan;cMnYnedIm,IeFVIKMrUm:UEDl truss.
!> Ggát;TaMgGs;RtUvtP¢ab;Kñaedayknøas;relag ¬snøak;Kμankkit¦. enAkñúgkrNI eKeRbIkartP¢ab;
edayb‘ULúg nigedayTwkbnSar karsnμt;EbbenHGacbMeBjeTA)anluHRtaEtG½kSrbs;Ggát;nImYy²
EdltP¢ab;KñaRtUvkat;KñaRtg;cMnucmYy dUcbgðajenAkñúgrUbTI 3-1. b:uEnþ eKRtUvdwgfa edaysar
tMNCak;EsþgmanPaBrwgmaM (rigidity) xøH dUcenHvanwgeFVIeGayGgát;rgm:Um:g;Bt;;enAeBlEdl truss


rgbnÞúk. kugRtaMgm:Um:g;Bt;EdlekItenAkñúgGgát;RtUv)aneKeGayeQμaHfa kugRtaMgrg (secondary
stress) b:uEnþkugRtaMgenAkñúgGgát;rbs;m:UEDl truss EdlmantMNsnøak;RtUv)aneKeGayeQμaHfa

kugRtaMgem (primary stress). eKkMrnwgeFVIkarviPaKrkkugRtaMgrgrbs; truss Nas; eTaHbIkug
RtaMgenHenAkñúg RbePT truss xøHmantMélFMk¾eday.
@> RKb;bnÞúkTaMgGs;RtUvGnuvtþenARtg;tMN. enAkñúgsßanPaBPaKeRcIn dUcCasMrab;s<an truss nig
dMbUl truss/ karsnμt;enHKWBit. CaerOy² enAkñúgkarviPaKkMlaMg eKecalTMgn;rbs;Ggát;eday
sarGgát;RTkMlaMgFMCagTMgn;rbs;vaxøaMgNas;. RbsinebIeKKitTMgn;rbs;Ggát;eTAkñúgkarviPaK
CaTUeTAeKRtUvKitvaCakMlaMgbBaÄrcMcMnucEdlBak;kNþalénTMhMrbs;vaRtUv)andak;enAcugsgxag
rbs;Ggát;.
edaysarsnμt;TaMgBIrenH Ggát;rbs; truss nImYy²eFVIkarCaGgát;rgkMlaMgtamG½kS (axial force
member) dUcenHkMlaMgEdlmanGMeBIenAxagcugrbs;Ggát;RtUvEtsßitenAelIG½kSrbs;Ggát;. RbsinebIkM-

laMgeFVIeGayGgát;lUt eKehAvafakMlaMgTaj (tensile force T) emIlrUbTI 3-6a. cMENkÉkMlaMgEdl
eFVIeGayGgát;rYjxøI eKeGayeQμaHvafakMlMagsgát; (compressive force C) emIlrUbTI 3-6b. enAkñúg
karsikSaKNna truss Cak;Esþg eKcaM)ac;bgðajfakMlaMgenAkñgGgát;CakMlaMgsgát; b¤kMlaMgTaj eday
ú
sarkarekag (buckling) b¤GsßirPaBPøam²GacekItmanenAkñúgGgát;rgkarsgát; (compression
member).

#>@> karcat;cMNat;fñak;rbs; truss kñúgbøg; (Classification of Coplanar Trusses)
munnwgcab;epþImviPaKrkkMlaMgrbs; truss/ eKcaM)ac;RtUvcat;cMNat;fñak;rbs; truss Ca truss
samBaØ/ truss pSM b¤ truss saMjúaM bnÞab;mkeTotkMNt;rkPaBkMNt; nigsßirPaBrbs;va.
Truss samBaØ (Simple truss): edIm,IkarkardYlrlM rcnasm<½n§rbs; truss RtUvEtrwgmaM. eyIg
eXIjy:agc,as;fa eRKag ABCD enAkñúgrUbTI 3-7 nwgmindYlrlMeT RbsinebIeKEfmGgát;Ggát;RTUg AC.
rcnasm<½n§y:agsamBaØbMputEdlrwgmaM nigsßirPaBKWragRtIekaN. Cavi)ak truss samBaØRtUv)ansagsg;
eLIgedaycab;epþImCamYynwgragRtIekaN dUcCa ABC enAkñúgrUbTI 3-8 ehIytP¢ab;Ggát;BIr ¬AD nig
BD¦ eTot edIm,IbegáItCarcnasm<½n§bEnßm. dUcenH enAeBlEdleKbEnßmGgát;BIreTAelI truss cMnYntMN

nwgekIneLIgmYy.


]TahrN_sMrab; truss samBaØRtUv)anbgðajenAkñúgrUbTI 3-9 Edlrcnasm<½n§EdlmansßirPaB
dMbUgKW ABC. eRkABIrcnasm<½n§dMbUgenH tMNEdlenAsl; D, E nig F RtUv)anerobtamlMdab;GkSr.
b:uEnþ sMrab;viFIsagsg;EbbenH eKRtUvdwgfa truss samBaØTaMgGs;minEmnsuT§EtpSMeLIgedayragRtIekaN
TaMgGs;eT. ]TahrN_RtUv)anbgðajenAkñúgrUbTI 3-10 Edlcab;epþImCamYynwgRtIekaN ABC bnÞab;mk
eKbEnßmr)ar CD nig AD edIm,IbegáIttMN D. cugeRkayeKEfmr)ar BE nig DE edIm,IbegáIttMN E.

Truss pSM (Compound truss): eKbegáIt truss pSMedaykartP¢ab; truss samBaØBIr b¤eRcInbBa©Úl
Kña. CaerOy² eKeRbI truss RbePTenHedIm,IRTbnÞúkEdlmanGMeBIenAelIElVgEvg² edaysarkarcMNay
kñúgkarsagsg; truss pSMEdlmanTMgn;RsalmantMélefakCagkarsagsg; truss samBaØEdlmanTMgn;
F¶n;Cag.
eKmanviFIbIkñúgkartP¢ab; truss samBaØedIm,IpÁúMCa truss pSM.
RbePTTI1³ eKGactP¢ab; truss edaytMNFmμta nigedayr)ar. ]TahrN_RtUv)anbgðaj
enAkñúgrUbTI 3-11a Edl truss EdlmanBN’dit ABC RtUv)antP¢ab;eTAnwg truss Edl
manBN’dit CDE enAkñúgTMrg;dUcbgðajkñúgrUb.
RbePTTI2³ eKtP¢ab; truss edayr)arcMnYnbI dUcenAkñúgkrNIkartP¢ab; truss ABC Edlman
BN’diteTAnwg truss EdlmanTMhMFMCag DEF ¬rUbTI 3-11b¦.



RbePTTI3³ eKGactP¢ab; truss edayCMnYsr)arrbs; truss samBaØFMEdleKeGayeQμaHfa
truss em eday truss samBaØtUcEdleKeGayeQμaHfa truss rgvij. ]TahrN_RtUv)an

bgðajenArUbTI 3-11c EdlbnÞat;dac;rbs; truss em ABCDE RtUv)anCMnYseday truss rg
EdlmanBN’dit. RbsinebI truss enHRTbnÞúkdMbUl kareRbI truss rgGacmanlkçN³esdæ-
kic©Cag edaysarGgát;EdlCabnÞat;dac;CargnUvkarBt;begáagFM É truss rgGacepÞrbnÞúk)an
l¥Cag.

Truss saMjúaM (Complex truss): ral; truss TaMgGs;EdlminRtUv)ancat;cMNat;fñak;cUlkñúg truss
samBaØ nig truss pSM RtUv)aneKeGayeQμaHfa truss saMjúaM EdlmanbgðajenAkñúgrUbTI 3-12.



PaBkMNt; (Determinacy): sMrab;karviPaK truss TaMgGs; eKRtUvdwgcMnYnsrubrbs;GBaØatedayrYm
bBa©ÚlTaMgkMlaMgenAkñúgGgát;rbs; truss EdlmancMnYn b nigcMnYnkMlaMgRbtikmμxageRkAsrub r. eday
sarGgát; truss suT§EtCaGgát;Rtg;rgkMlaMgtamG½kSEdlsßitenAkñúgbøg;EtmYy enaHRbB½n§kMlaMgEdleFVI
GMeBIenARtg;tMNnImYy²KWenAkñúgbøg; nigRbsBVKña. dUcenH smIkarlMnwgsMrab;karrmYl b¤sMrab;m:Um:g; RtUv
)anbMeBjedaysV½yRbvtþenARtg;tMN ¬b¤snøak;¦ ehIyvacaM)ac;RtUvbMeBjsmIkarlMnwg ∑ Fx = 0 nig
∑ Fy = 0 edIm,IFanalMnwgkMlaMg b¤Fanakarcl½t. dUcenH eKGacsrsrsmIkarlMnwgEtBIrsMrab;tMN

nImYy² ehIyRbsinebIeKmantMNcMnYn j enaHcMnYnsmIkarEdlGacmansMrab;dMeNaHRsayKW 2j. eday
eRbobeFobcMnYnGBaØatsrub (b+r) CamYynwgcMnYnsrubrbs;smIkarEdlGacsresr)an dUcenHeKGac
kMNt;PaBkMNt;sMrab; truss TaMgGs;. eyIgman

b+r = 2j kMNt;edaysþaTic
b+r > 2j minkMNt;edaysþaTic (3.1)

dWeRkénPaBminkMNt;RtUv)ankMNt;edayplsgéncMnYn (b + r ) − 2 j .
sßirPaB (Stability): RbsinebI b + r < 2j enaH truss nwgminmansßirPaB ehIyvanwgdYlrlM eday
sarvaminmancMnYnr)arRKb;RKan;edIm,I b¤kMlaMgRbtikmμRKb;RKan;edIm,ITb;tMNTaMgGs;mineGaycl½t)an.
ehIy truss k¾GacGsßirPaBeTaHbIvaCaeRKOgbgÁúMkMNt;edaysþaTic b¤minkMNt;edaysþaTick¾eday.
sMrab;krNIsßirPaB eKRtUvkMNt;edaykarGegát b¤edaykarviPaKkMlaMg.
sßirPaBxageRkA (External stability): dUckarerobrab;enAkñúgkfaxNÐ 2-4 eRKOgbgÁúM b¤ truss
EdlGsßirPaBxageRkARbsinebIkMlaMgRbtikmμTaMgGs;rbs;vaRbsBVKña b¤RsbKña. ]TahrN_ truss BIr
enAkñúgrUbTI 3-13 Ca truss GsßirPaBxageRkA edaysarRbtikmμTMrmanExSskmμRbsBVKña b¤RsbKña.



sßirPaBxagkñúg (Internal stability): eKGacRtYtBinitüsßirPaBxagkñúgrbs; truss edaykarGegát
BIkartMerobGgát;rbs;vaedayRbugRby½tñ. RbsinebIeKGackMNt;fatMNnImYy²RtUv)aneFVIeGayrwg dUcenH
eKminGaccl½t rigid body edayeFobnwgtMNdéT)aneT. cMNaMfa truss samBaØEtgEtmansßirPaB
xagkñúg. edaysarFmμCatiénkarsagsg;rbs;va eKTamTareGaycab;epþImCamYynwgragRtIekaN ehIy
EfmGgát; BIrsMrab;tMNmYyCabnþbnÞab;. Truss enAkñúgrUbTI 3-14 bgðajBIkarsagsg;enH edaycab;
epþImCamYynwg truss ragRtIekaNEdlmanBN’dit ABC ehIytMN D, E, F, G, nig H RtUv)anbEnßm.

RbsinebIeKsg; truss EbbenH tMNrbs;vaminmanTItaMgbgáb;eT dUcenHvaGacnwgGsßirPaB
b¤manTMrg;eRKaHfñak;. ]TahrN_sMrab;krNIenHRtUv)anbgðajenAkñúgrUbTI 3-15 EdleKGaceXIjfaenA
cenøaHtMN C nig F b¤ B nig E minmankarTb;eGayrwgmaMeT dUcenH truss GacnwgdYlrlMeRkamGMeBIrbs;
bnÞúk.

edIm,IkMNt;sßirPaBxagkñúgén truss pSM eKcaM)ac;dwgBIviFIénkartP¢ab;rvag truss
samBaØ. ]TahrN_ truss pSMenAkñúgrUbTI 3-16 KμansßirPaBedaysarkartP¢ab; truss ABC samBaØxag
kñúgeTAnwg truss DEF xageRkAedayr)arbI AD, BE nig CF EdlRbsBVKñaRtg;cMnuc O. dUcenHkMlaMg
xageRkAEdlGnuvtþenARtg;tMN A, B b¤ C GaceFVIeGay truss ABC vil)antictYc.



RbsinebI truss Ca truss saMjúaM eKminGacniyayfavamansßirPaBedaykarGegáteT. ]Ta-
hrN_ eyIgGaceXIjBIkarviPaKEdlmanerobrab;enAkñúgkfaxNÐ 3-7 fa truss saMjúaMenAkñúgrUbTI 3-17
KμansßirPaB b¤manTMrg;eRKaHfñak;RbsinebI d = d’. RbsinebI d ≠ d ' enaHvanwgmansßirPaB.

eyIgGackMNt;BIsßirPaBrbs; truss RKb;TMrg;edayeGaykMuBüÚT½redaHRsayRbB½n§smIkar 2jEdl
sresrsMrab;RKb;tMNTaMgGs;rbs; truss. RbsinebIeyIgminGacTTYllT§pl enaHmann½yfa truss
enaHKμansßirPaB b¤manTMrg;eRKaHfñak;.
RbsinebIeKminGacRbtþibtþikarviPaKtamkMuBüÚT½r eKGaceRbIviFIEdlmanerobrab;BIelIkmunedIm,I
RtYtBinitüsßirPaBrbs; truss. Cakarsegçb RbsinebI truss manr)arcMnYn b/ kMlaMgRbtikmμ r nigtMN
cMnYn j enaHRbsinebI
b+r < 2j KμansßirPaB
b+r ≥ 2j KμansßirPaBRbsinebIkMlaMgRbtikmμRbsBVKña
b¤RsbKña b¤RbsinebIbgÁúM Ggát;rbs; truss
begáIt)anCa collapsible mechanism. (3-2)

RbsinebI truss KμansßirPaB eKmincaM)ac;KitBIkarkMNt;edaysþaTic b¤minkMNt;edaysþaTiceT.
eyIgeXIjy:agc,as;fa eyIgRtUveCosva truss EdlKμansßirPaBenAkñúgkarGnuvtþ.
]TahrN_ 3-1³ cat;cMNat;fñak; truss nImYy²enAkñúgrUbTI 3-18 Ca truss mansßirPaB b¤Kμan sßirPaB
kMNt;edaysþaTic b¤minkMNt;edaysþaTic. Truss rgbnÞúkxageRkAEdleKsnμt;fasÁal; ehIy
GacmanGMeBIenARKb;TItaMgenAelI truss.
dMeNaHRsay³
rUbTI 3-18a³ Truss enHmansßirPaBxageRkA edaysarkMlaMgRbtikmμrbs;vaminRbsBVKña nigminRsb


Kña. eday truss man b = 19 / r = 3 / j = 11 enaH b + r = 2 j b¤ 22 = 22 . dUcenHvaCa truss kMNt;
edaysþaTic. tamkarGegátvaCa truss mansßirPaBxagkñúg.

rUbTI 3-18b³ Truss enHmansßirPaBxageRkA. eday b = 15 / r = 4 / j = 9 enaH b + r > 2 j b¤
19 > 18 . dUcenHvaCa truss minkMNt;edaysþaTic 1 dWeRk. tamkarGegátvaCa truss mansßirPaBxag

kñúg.

rUbTI 3-18c³ Truss enHmansßirPaBxageRkA. eday b = 9 / r = 3 / j = 6 enaH b + r = 2 j b¤
12 = 12 . dUcenHvaCa truss kMNt;edaysþaTic. tamkarGegátvaCa truss mansßirPaBxagkñúg.

rUbTI 3-18d³ Truss enHmansßirPaBxageRkA. eday b = 12 / r =3 / j =8 enaH b+r < 2j b¤
15 < 16 . Truss minmansßirPaBxagkñúg.



#>#> viFItMN (The method of Joint)
RbsinebI truss sßitenAkñúgsßanPaBmanlMnwg enaHtMNrbs;vanImYy²k¾sßitkñúgsßanPaBlMnwgEdr.
dUcenH viFItMNpSMRtUv)anbegáIteLIgedaybMeBjnUvlkçxNÐlMnwg ∑ Fx = 0 nig ∑ Fy = 0 sMrab;kMlaMg
EdlmanGMeBIenAelIsnøak;Rtg;tMNnImYy²rbs; truss.
enAeBleRbIviFItMN eKcaM)ac;RtUvKUrdüaRkamrbs;tMNnImYy²munnwgGnuvtþsmIkarlMnwg. rMlwkfa
ExSskmμénkMlaMgrbs;Ggát;nImYy²EdleFVIGMeBIenAelItMNRtUvykecjBIragFrNImaRtrbs; truss, eday
sarkMlaMgenAkñúgGgát;rt;tamG½kSrbs;Ggát;. ]TahrN_ eKmantMN B én truss enAkñúgrUbTI 3-19a.
BIdüaRkamGgÁesrI ¬rUbTI 3-19b¦ GBaØatCaTMhMrbs;kMlaMgenAkñúgGgát; BA nig BC . dUcbgðajenAkñúg
rUb FBA TajtMN EdlbgðajfaGgát; BA rgkarTaj cMENkÉ FBC rujtMN Ca vi)akGgát; BC rgkar
sgát;. T§iBlenHbgðajy:agc,as;edayeRbIviFImuxkat; nigdak;eGaytMNenAdac;edayELkBIKñaCamYy
nwgkMNat;Ggát;d¾xøIEdlP¢ab;eTAnwgtMNenaH ¬rUbTI 3-19c¦. cMNaMfa karruj nigkarTajenAelIkMNat;
Ggát;d¾xøIbgðajBIT§iBlénGgát;Edlrgkarsgát; b¤karTaj.
enARKb;krNITaMgGs; karviPaKtMNKUrcab;epþImenARtg;tMNNaEdlmankMlaMgEdlsÁal;y:agtic
bMputmYy nigkMlaMgEdlGacGBaØaty:ageRcInbMputBIr dUcbgðajenAkñúgrUbTI 3-19b. tamviFIenH kar
GnuvtþsmIkar ∑ Fx = 0 nig ∑ Fy = 0 pþl;nUvsmIkarBiCKNitcMnYnBIrEdlGaceGayeyIgedaHRsay
rk)ankMlaMgEdlCaGBaØatcMnYnBIr. enAeBlGnuvtþsmIkarTaMgenH eKGackMNt;TisedARtwmRtUvrbs;
GBaØatEdlCakMlaMgedayeRbIviFIBIr.

!> snμt;kMlaMgrbs;Ggát;EdlCaGBaØatEdleFVIGMeBIenAelIdüaRkamGgÁesrIrbs;tMNCakMlaMgTaj.
Rbsin ebIvaEbbnwgEmn enaHdMeNaHRsayCatMélelxénsmIkarlMnwgnwgeGayCatMélviC¢man


sMrab;ral;Ggát;EdlrgkarTaj ehIyeGayCatMélGviC¢mansMrab;ral;Ggát;TaMgLayNaEdlrg
karsgát;. enAeBlEdlkMlaMgenAkñúgGgát;EdlCaGBaØatRtUv)ankMNt;ehIy eRbITMhM nigTisedA
RtwmRtUvrbs;vasMrab;düaRkamGgÁesrIéntMNbnÞab;.
@> enAkñúgkrNICaeRcIn eKGackMNt;TisedAd¾RtwmRtUvrbs;kMlaMgenAkñúgGgát;EdlCaGBaØatedaykar
Gegát. ]TahrN_ FBC enAkñúgrUbTI 3-19b RtUvEtrujtMN ¬sgát;¦ edaysarbgÁúMkMlaMgedk
rbs;va FBC sin 45o RtUvTUTat;CamYynwgkMlaMgGnuvtþn_ 500kN ¬ ∑ Fx = 0 ¦. dUcKña FBA CakM-
laMgTaj edaysarvaTUTat;CamYynwgbgÁúMkMlaMgbBaÄr FBC cos 45o ¬ ∑ Fy = 0 ¦. enAkñúgkrNI
EdlsμúKsμajCagenH eKGacsnμt;TisedAénkMlaMgkñúgrbs;Ggát;EdlCaGBaØat bnÞab;mkeRkayBI
GnuvtþsmIkarlMnwg eKGacEkERbTisedAEdlsnμt;eTAtamlT§plCaelxEdlTTYl)an. cMeLIy
viC¢manbgðajfaTisedAEdlsnμt;KWRtwmRtUv cMENkÉcMeLIyGviC¢manbgðajfaeKRtUvRtLb;Tis
edAEdlbgðajenAelIdüaRkamGgÁesrI. enHCaviFIEdleyIgnwgeRbIenAkñúg]TahrN_xageRkam.

dMeNIrkarkñúgkarviPaK (Procedure for analysis)
CMhanxageRkamenHpþl;nUvmeFüa)aysMrab;karviPaK truss edayeRbIviFItMN.
sg;düaRkamGgÁesrIéntMNEdlmankMlaMgEdlsÁal;y:agticmYy nigGBaØatEdlCakMlaMgy:ag
eRcInBIr. ¬RbsinebItMNenHenARtg;TMrNamYy eKcaM)ac;RtUvKNnaRbtikmμenARtg;TMredayeRbI
düaRkamGgÁesrIrbs; truss TaMgmUl¦.
eRbIviFImYykñúgcMeNamviFITaMgBIrEdlBiBN’naxagelIsMrab;snμt;TisedArbs;GBaØatEdlCakMlaMg.
eKRtUvkMNt;G½kS x nigG½kS y y:agNaedIm,IgayRsYledaHRsaybgÁúMkMlaMgtamG½kS x nigtam
G½kS y enAelIdüaRkamGgÁesrI. GnuvtþsmIkarlMnwgBIr ∑ Fx = 0 nig ∑ Fy = 0 edIm,IkMNt;
kMlaMgkñúgrbs;Ggát;EdlCaGBaØat ehIyepÞógpÞat;TisedAsnμt;rbs;va.
bnþkarviPaKtMNdéTeTot EteKcaM)ac;RtUveRCIserIstMNNaEdlmanGBaØaty:ageRcInBIr nigman
kMlaMgEdlsÁal;y:agticmYy.
eKeRbIkMlaMgenAkñúgGgát;BIkarviPaKtMNRtg;cugmçagrbs;Ggát;BIelIkmunedIm,IviPaKkMlaMgEdl
manGMeBIenAelItMNenAcugmçageTotrbs;va. eKRtUvcgcaMfa Ggát;rgkarsgát;rujtMN ehIyGgát;
rgkarTajTajtMN.



]TahrN_ 3-2³ kMNt;kMlaMgkñúgénGgát;nImYy²rbs; dMbUldUcbgðajenAkñúgrUbTI 3-20a.
truss

bgðajfaGgát;rgkarTaj b¤sgát;. eKeGaykMlaMgRbtikmμenARtg;tMN.

dMeNaHRsay³ eKcaM)ac;kMNt;kMlaMgenAkñúgGgát;EtcMnYnBak;kNþalEtb:ueNÑaH edaysar truss enHman
lkçN³sIuemRTITaMgbnÞúk nigragFrNImaRt.
tMN A / rUbTI 3-20b/ eyIgGaccab;epþImkarviPaKenARtg;tMN A .
ehtuGVI?
düaRkamGgÁesrIRtUv)anbgðajenAkñúgrUbTI 3-20b.
+ ↑ ∑ Fy = 0 / 4 − FAG sin 30 o = 0 FAG = 8kN (C )
+
→ ∑ Fx = 0 / FAB − 8 cos 30 o = 0 FAB = 6.93kN (T )

tMN G / rUbTI 3-20c/ enAkñúgkrNIenH cMNaMBIrebobkMNt;Tisrbs;
G½kS x nig y edIm,IeCosvagRbB½n§smIkar
+ ∑ Fy = 0 FGB − 3 cos 30 o = 0 FGB = 2.60kN (C )

+ ∑ Fx = 0 / 8 − 3 sin 30 o − FGF = 0

FGF = 6.50kN (C )
tMN B / rUbTI 3-20d/
+ ↑ ∑ Fy = 0 / FBF sin 60 o − 2.60 sin 60 o = 0

FBF = 2.60kN (T )
+
→ ∑ Fx = 0 / FBC + 2.60 cos 60 o + 2.6 cos 60 o − 6.93 = 0

FBC = 4.33kN (T )



]TahrN_ 3-3³ kMNt;kMlaMgkñúgénGgát;nImYy²rbs; truss

dMbUldUcbgðajenAkñúgrUbTI 3-21a. bgðajfaGgát; rgkarTaj b¤
sgát;. eKeGaykMlaMgRbtikmμenARtg;tMN.
dMeNaHRsay³
FñwmenHRtUv)anedaHRsaydUcxageRkam.
tMN E / rUbTI 3-21b/ cMNaMfa eKGaceCosvagkaredaHRsay
RbB½n§smIkaredayeRCIserIsTiseGayG½kS x nig y .
+ ∑ Fy = 0 / 764 cos 30 o − FED sin 15o = 0

FED = 2557 N (C )
+ ∑ Fx = 0 / 2557 cos15 o − FEF − 764 sin 30 o = 0

FEF = 2088 N (T )
tMN D / rUbTI 3-21c/
+ ∑ Fx = 0 − FDF sin 75o = 0 FDF = 0
+ ∑ Fy = 0 − FDC + 2557 = 0

FDC = 2557 N (C )
tMN C / rUbTI 3-21d/
+
→ ∑ Fx = 0 FCB sin 45o − 2557 sin 45o = 0

FCB = 2557 N (C )
+ ↑ ∑ Fy = 0 − FCF − 700 + 2(2557 )cos 45o = 0 FCF = 2916 N (T )

tMN B / rUbTI 3-21e/
+ ∑ Fy = 0 FBF sin 75 o − 800 = 0 FBF = 828 N (C )

+ ∑ Fx = 0 2557 + 828 cos 75 o − FBA = 0 FBA = 2771N (C )
tMN A / rUbTI 3-21f/
+
→ ∑ Fx = 0 FAF cos 30 o − 2771cos 45o − 566 = 0 FAF = 2916 N (T )
+ ↑ ∑ Fy = 0 502 − 2771sin 45o + 2916 sin 30 o = 0 epÞógpÞat;
eKGaceFIVkarepÞógpÞat;bEnßmeTotedayeFVIkarviPaKtMN F .



#>$> Ggát;kMlaMgsUnü (Zero-Force Members)
eKGacsMrYlkargarviPaK truss EdleRbIviFItMN RbsinebIeKGackMNt;CaCMhandMbUgral;Ggát;
TaMgLayNaEdlminrgkMlaMg. Ggát;kMlaMgsUnüTaMgGs;enHmansar³sMxan;sMrab;sßirPaBrbs; truss
kñúgGMLúgeBlsagsg; nigpþl;CaTMrRbsinebIbnÞúkGnuvtþn_RtUv)anpøas;bþÚr. CaTUeTA eKGackMNt;Ggát;
kMlaMgsUnürbs; truss edaykarGegáttMN ehIyvaekItmanBIrkrNI.
krNITI1³ BicarNa truss enAkñúgrUbTI 3-22a. Ggát;BIrEkgKñaenARtg;tMN C ehIyminmanbnÞúkxag
eRkAenARtg;tMNenaH. düaRkamGgÁesrIéntMN C ¬rUbTI 3-22b¦ bgðajfakMlaMgenAkñúgGgát;nImYy²
esμIsUnüedIm,IrkSalMnwg. elIsBIenH dUcenAkñúgkrNItMN A ¬rUbTI 3-22c¦ vaBitCaRtwmRtUvedaymin
xVl;BImMu ¬Gacniyyfaθ ¦rvagGgát;EdlpÁúMKña.

krNITI2³ Ggát;kMlaMgsUnük¾ekItmanenARtg;tMNEdlmanlkçN³FrNImaRtdUctMN D enAkñúgrUbTI 3-
23a. enATIenH minmankMlaMgxageRkAeFVIGMeBIelItMN dUcenHplbUkkMlaMgtamTis y ¬rUbTI 3-23b¦
EdlEkgeTAnwgGgát;BIrrt;elIbnÞat;EtmYy TamTareGay FDF = 0 . edayeRbIlT§plenH FC k¾CaGgát;
kMlaMgsUnü dUcbgðajedaykarviPaKkMlaMgéntMN F ¬rUbTI 3-23c¦.

Casegçb RbsinebIGgát;BIrEdlminsßitenAelIbnÞat;EtmYybegáItCatMN truss ehIyminmanrg
GMeBIbnÞúkxageRkA b¤kMlaMgRbtikmμTMr enaHGgát;TaMgBIrenaHCaGgát;kMlaMgsUnü ¬krNITI1¦. ehIy


RbsinebI Ggát;bIbegáIttMN truss mYyEdlkñúgenaHGgát;BIrsßitenAelIbnÞat;EtmYy enaHGgát;TIbICaGgát;
kMlaMgsUnü RbsinebIminmanbnÞúkxageRkA b¤kMlaMgRbtikmμTMrmanGMeBIenARtg;tMNenaH ¬krNITI2¦. eK
RtUvmankarBiinitüemIllkçN³FrNImaRt nigkarrgbnÞúkenARtg;tMN edaysarkarviPaK truss RtUv)an
sMrYly:ageRcInedaysarsÁal;Ggát;kMlaMgsUnü.
]TahrN_ 3-4³ edayeRbIviFItMN bgðajRKb;GgÁt;
TaMgLayNaenAkñúg truss EdlbgðajenAkñúgrUbTI 3-
24a CaGgát;EdlmankMlaMgkñúgesμIsUnü .
dMeNaHRsay³ edayrktMNEdlmanlkçN³Rsedog
nwgtMNEdlbgðajenAkñúgrUbTI 3-22 nig 3-23.
eyIgman
tMN D / rUbTI 3-24b
+ ↑ ∑ Fy = 0 / FDC sin θ = 0 FDC = 0
+
→ ∑ Fx = 0 / FDE + 0 = 0 FDE = 0

tMN E / rUbTI 3-24c
+
← ∑ Fx = 0 / FEF = 0

¬cMNaMfa FEC = P ehIykarviPaKtMN C nwg pþl;nUvkMlaMgenAkñúgGgát; CF ¦
tMN H / rUbTI 3-24d
+ ∑ Fy = 0 / FHB = 0

tMN G / rUbTI 3-24e/ enARtg;TMr rocker G manEtbgÁúMkMlaMgtamG½kS x b:ueNÑaHmanGMeBIenARtg;tMN
enH eBalKW Gx . dUcenH
+ ↑ ∑ Fy = 0 / FGA = 0



#>%> viFImuxkat; (The method of Section)
RbsinebIeKcg;kMNt;EtkMlaMgenAkñúgGgát;xøH CaTUeTAviFImuxkat;pþl;nUvmeFüa)aykñúgkarTTYl
)ankMlaMgTaMgenaHedaypÞal;. viFImuxkat;CaviFIekIteLIgedaykarkat; truss enaHCaBIrcMENk. Rbsin
ebI truss TaMgmUlsßitenAkñúgsßanPaBlMnwg enaHEpñkTaMgBIreRkayeBlEdlkat;k¾sßitenAkñúgsßanPaB
lMnwgEdr ehIyCalT§pl eKRtUvGnuvtþsmIkarlMnwgcMnYnbIeTAelIEpñkNamYyén truss Edlkat;rYc edIm,I
kMNt;rkkMlaMgrbs;Ggát;enARtg;muxkat;enaH.
enAeBlEdleKeRbIviFImuxkat;edIm,IKNnakMlaMgenAkñúgrbs;Ggát; eKRtUveFVIkarsMercBIrebobkat;
truss enaH. edaysareKGacGnuvtþEtsmIkarlMnwgbIEdlÉkraCBIKña ¬ ∑ Fx = 0 / ∑ Fy = 0 nig ∑ M O

= 0 ¦eTAelIEpñkrbs; truss Edlkat;rYc CaTUeTAeKRtUveRCIserIsmuxkat;NaEdlminmankMlaMgkñúgrbs;

Ggát;EdlCaGBaØtelIsBIbI. ]TahrN_ cUrBicarNa truss enAkñúgrUbTI 3-25a. RbsinebIeKRtUvkar
kMNt;kMlaMgenAkñúgGgát; GC karkat;tammuxkat; aa KWsaksmbMput. düaRkamGgÁesrIrbs;EpñkTaMgBIr
RtUv)anbgðajenAkñúgrUbTI 3-25b nig 3-25c. cMNaMfa ExSskmμénkMlaMgnImYy²enAkñúgGgát;Edl
kat;RtUv)ankMNt;BIlkçN³FrNImaRtrbs; truss edaysarkMlaMgenAkñúgGgát;sßitenAelIG½kSrbs;Ggát;.
ehIykMlaMgEdlmanGMeBIenAcugmçagrbs;Ggát; truss mantMélesμIKña EtmanTispÞúyKñanwgkMlaMgEdlman
GMeBIenAelIcugmçageTotrbs;Ggát;dEdlenaH ¬c,ab;TIbIrbs;jÚtun¦. dUckarbgðaj eKsnμt;eGayGgát;
BC nig GC rgkarTaj ÉGgát; GF rgkar sgát;.

eKGacTTYlkMlaMgkñúgrbs;Ggát;EdlCaGBaØat FBC / FGC nig FGF edayGnuvtþsmIkarlMnwgbI
eTAelIdüaRkamGgÁesrIenAkñúgrUbTI 3-25b. b:uEnþ RbsinebIeKBicarNadüaRkamGgÁesrIenAkñúgrUbTI 3-


25c eKRtUvkMNt;kMlaMgRbtikmμTMr Dx / D y nig E x CadMbUgsin. ehtuGVI? ¬eKGackMNt;kMlaMgRbtikmμ
TMrTaMgbIedayBicarNaeTAelIdüaRkamGgÁesrIrbs; truss TaMgmUl¦. enAeBlGnuvtþsmIkarlMnwg eKRtUv
BicarNaBIviFIsresrsmIkary:agNaedIm,ITTYl)andMeNaHRsaysMrab;GBaØatnImYy²edaypÞal; eday
eCosvagkaredaHRsayRbB½n§smIkar. ]TahrN_ plbUkm:Um:g;enARtg;cMnuc C enAkñúgrUbTI 3-25b Gac
eGayeyIgTTYl)andMeNaHRsaysMrab; FGF edaypÞal; edaysar FBC nig FGC begáItm:Um:g;sUnüenARtg;
cMnuc C . dUcKña eKGacTTYl)an FBC edaypÞal;edayeFVIplbUkm:Um:g;Rtg;cMnuc G . cugeRkay eKGayrk
FGC edaypÞal;BIplbUkkMlaMgtamTisQr edaysar FGF nig FBC minmanbgÁúMkMlaMgbBaÄr.

dUcenAkñúgviFItMN eKmanviFIBIrEdleKGackMNt;TisedAd¾RtwmRtUvrbs;kMlaMgkñúgrbs;Ggát;EdlCa
GBaØat.
snμt;kMlaMgkñúgEdlCaGBaØatTaMgGs;enARtg;kEnøgEdlkat;CaGgát;rgkarTaj. edaykarGnuvtþ
EbbenH dMeNaHRsayCaelxénsmIkarlMnwgEdlmantMélviC¢manbgðajfaGgát;rgkarTaj
ehIyRcasmkvijtMélGviC¢manrbs;dMeNaHRsaybgðajfaGgát;rgkarsgát;.
enAkñúgkrNICaeRcIn eKGackMNt;TisedAd¾RtwmRtUvrbs;kMlaMgkñúgEdlCaGBaØatedaykarGegát.
]TahrN_ FBC CakMlaMgTajdUcbgðajenAkñúgrUbTI 3-25b edaysarsmIkarm:Um:g;Rtg;cMnuc G
TamTareGay FGC begáItm:Um:g;EdlpÞúyeTAnwgm:Um:g;EdlbegáItedaykMlaMg 1000 N . ehIy
FGC CakMlaMgTaj edaysarbgÁúMkMlaMgbBaÄrrbs;RtUvEtTUTat;CamYynwgkMlaMg 1000 N . sMrab;

krNIEdlsμúKsμaj eKRtUvsnμt;TisedArbs;kMlaMgEdlCaGBaØat. RbsinebIdMeNaHRsayeGay
CatMélGviC¢man vabgðajfaTisedArbs;kMlaMgpÞúyeTAnwgGIVEdlbgðajenAkñúgdüaRkamGgÁesrI.
vaCaviFIEdleyIgnwgeRbIenAkñúg]TahrN_xageRkam.

xageRkamCaCMhanEdlpþl;CameFüa)aysMrab;GnuvtþviFImuxkat;edIm,IkMNt;kMlaMgenAkñúgGgát;
rbs; truss.
düaRkamGgÁesrI (Free-body diagram)
kat; truss CaBIrcMENkRtg;kEnøgEdlRtUvkarkMNt;lMlaMgrbs;Ggát;.
munnwgpþac;cMEnkrbs; truss Edlkat; dMbUgeyIgcaM)ac;kMNt;kMlaMgRbtikmμrbs; truss dUcenHeK
GaceRbIsmIkarlMnwgEtbIedIm,IkMNt;kMlaMgkñúgrbs;Ggát;enARtg;muxkat;Edlkat;rYc.
KUrdüaRkamGgÁesrIénEpñkrbs; truss Edlkat;rYcEdlmankMlaMgmYycMnYnmanGMeBIelIva.


eRbIviFImYykñúgcMeNamviFITaMgBIrEdlerobrab;xagelIedIm,IedATisedArbs;kMlaMgEdlCaGBaØat.
smIkarlMnwg (Equations of equilibrium)
eKKYreFVIplbUkm:Um:g;enARtg;cMnucNaEdlsßitenARtg;TIRbCMuénExSskmμrbs;kMlaMgEdlCaGBaØat
cMnYnBIr tamviFIenHeKGackMNt;kMlaMgEdlCaGBaØatTIbIedaypÞal;BIrsmIkarenH.
RbsinebIkMlaMgEdlCaGBaØatBIrRsbKña eKRtUveFVIplbUkkMlaMgtamTisEdlEkgeTAnwgkMlaMg
TaMgBIrenaHedIm,ITTYl)ankMlaMgEdlCa GBaØatTIbIedaypÞal;.

]TahrN_ 3-5³ kMNt;kMlaMgenAkñúgGgát; CF
nig GC rbs; truss dMbUlEdlbgðajenAkñúgrUbTI 3-
26a. bgðajfaGgát;rgkMlaMgTaj b¤kMlaMgsgát;.
RbtikmμTMrRtUv)aneKeGay.
dMeNaHRsay³
Ggát; CF
düaRkamGgÁesrI³ eKGacTTYlkMlaMgenAkñúgrbs;Ggát; CF
edayBicarNamuxkat; aa enAkñúgrUbTI 3-26a. düaRkam
GgÁesrIénEpñkxagsþaMrbs;muxkat;enHRtUv)an bgðajenAkñúg
rUbTI 3-26b.
smIkarlMnwg³ eKGacTTYl)andMeNaHRsayedaypÞal;
sMrab; FCF edayGnuvtþ ∑ M E = 0 . ehtuGVI? edIm,Igay
RsYlyl; eyIgnwgrMkil FCF eTAcMnuc C ¬eKalkarN_énPaBGacbBa¢Ún)an¦ rUbTI 3-26b. dUcenH
+ ∑ME = 0 − FCF sin 30o (4 ) + 1.50(2.31) = 0

FCF = 1.73kN (C )
Ggát; GC
düaRkamGgÁesrI³ eKGacTTYlkMlaMgenAkñúgrbs;Ggát; GC
edayBicarNamuxkat; bb enAkñúgrUbTI 3-26a. muxkat;kat;
Ggát;cMnYnbYn b:uEnþkMlaMgenAkñúgGgát; GC RtUv)anKNnarYc.
düaRkamGgÁesrIénEpñkxageqVgrbs;muxkat;enHRtUv)anbgðaj
enAkñúgrUbTI 3-26c.


smIkarlMnwg³ eKeFVIplbUkm:Um:g;enARtg;cMnuc A edIm,Ilb;bM)at;GBaØat FHG nig FCD . edayrMkil FCF
¬1.73kN ¦ eTAcMnuc C eyIg)an
+∑MA = 0 − 1.50(2.31) + FGC (4) − 1.73 sin 30o (4) = 0

FGC = 1.73kN (T )

]TahrN_ 3-6³ kMNt;kMlaMgkñúgrbs;Ggát; GF nig GD rbs; truss EdlbgðajenAkñúgrUbTI 3-27a.
bgðajfaGgát;rgkarTaj b¤rgkarsgát;. eKeGaykMlaMgRbtikmμTMr.

dMeNaHRsay³
düaRkamGgÁesrI³ eKnwgBicarNamuxkat; aa enAkñúgrUbTI 3-27a. ehtuGVI? düaRkamGgÁesrIrbs;mux
kat;xagsþaMRtUv)anbgðajenAkñúgrUbTI 3-27b. eKGackMNt;cMgay EO edayRtIekaNdUc b¤edaydwg
faGgát; GF manRbEvgRbeyalbBaÄresμInwg 4.5 − 3 = 1.5m nigmanRbEvgRbeyaledk 3m ¬rUbTI 3-
27a¦. dUcenH edIm,I)anRbEvg 4.5m edayvas;BIcMnuc G cuHeRkam enaHcMgayBIcMnuc C eTAcMnuc O RtUv
manRbEvg 9m . ehIy mMuEdlpÁúMrvag FGD CamYynwgbnÞat;edkKW tan −1(4.5 / 3) = 56.3o ehIymMuEdlpÁúM
rvag FGF CamYynwgbnÞat;edkKW tan −1(4.9 − 9) = 26.6o .
smIkarlMnwg³ eKGackMNt;kMlaMgkñúgrbs;Ggát; GF edaypÞal;edayGnuvtþsmIkarlMnwg ∑ M D = 0 .
ehtuGVI? sMrab;karKNna eKRtUvrMkilkMlaMg FGF eTAcMnuc O . dUcenH
+ ∑MD = 0 − FGF sin 26.6o (6) + 7(3) = 0

FGF = 7.83kN (C )
eKGackMNt;kMlaMgenAkñúgGgát; GD edaypÞal;edayGnuvtþ ∑ M O = 0 . edIm,IgayRsYlkñúgkarKNna
rMkilkMlaMg FGD eTAcMnuc D . dUcenH
+ ∑ MO = 0 − 7(3) + 2(6) + FGD sin 56.3o (6) = 0

FGD = 1.80kN (C )



]TahrN_ 3-7³ kMNt;kMlaMgkñúgrbs;Ggát; BC nig MC rbs; K-truss EdlbgðajenAkñúgrUbTI 3-
28a. bgðajfaGgát;rgkarTaj b¤rgkarsgát;. eKeGaykMlaMgRbtikmμTMr.

dMeNaHRsay³
düaRkamGgÁesrI³ eTaHbICamuxkat; aa EdlbgðajenAkñúgrUbTI 3-28a
kat;4Ggát;k¾edayk¾eKmanlT§PaBedaHRsayrkkMlaMgenAkñúgGgát;
BC edayeRbImuxkat;enH. düaRkamGgÁesrIénEpñkxageqVgrbs; truss

RtUv)anbgðajenAkñúgrUbTI 3-28b.
smIkarlMnwg³ kareFVIplbUkm:Um:g;Rtg;cMnuc L GaceCosvagGBaØatbI
dUcenH
+ ∑ML = 0 − 14.5(4.5) + FBC (6) = 0

FBC = 10.9kN (T )
düaRkamGgÁesrI³ eKGacTTYl)ankMlaMgenAkñúg MC edayminpÞal;
edaydMbUgeyIgRtUvKNnakMlaMgenAkñúg MB BIsmIkarkMlaMgbBaÄr
enARtg;tMN B ¬rUbTI 3-28c¦enaHeyIgTTYl)an FMB = 6kN (T ) .
bnÞab;mkBIdüaRkamGgÁesrIenAkñúgrUbTI 3-28b eyIg)an
+ ↑ ∑ Fy = 0 14.5 − 6 + 6 − FML = 0

FML = 14.5kN (T )
edayeRbIlT§plTaMgenHdüaRkamGgÁesrIéntMN M RtUv)anbgðajenA
kñúgrUbTI 3-28d.
smIkarlMnwg³
+ ⎛ 3 ⎞ ⎛ 3 ⎞
→ ∑ Fx = 0 ⎜
⎜ ⎟ FMC − ⎜
⎟ ⎜ ⎟ FMK = 0
⎟
⎝ 13 ⎠ ⎝ 13 ⎠
⎛ 2 ⎞ ⎛ 2 ⎞
+ ↑ ∑ Fy = 0 14.5 − 6 − ⎜
⎜ ⎟ FMC − ⎜
⎟ ⎜ ⎟ FMK = 0
⎟
⎝ 13 ⎠ ⎝ 13 ⎠
FMK = 7.66kN (C ) FMC = 7.66kN (T )


eBlxøH ¬dUcenAkñúg]TahrN_enH¦ karGnuvtþTaMgvIFImuxkat; nigTaMgviFItMNeGayeKGacedaHRsay
]TahrN_enHdaypÞal;.
eKk¾GacedaHRsayrkkMlaMgenAkñúgGgát; MC edayeRbIlT§pl FBC pgEdr. enAkñúgkrNienH
kat; truss tamGgát; LK / MK / MC nig BC ¬rUbTI 3-28a¦. pþac;muxkat;xageqVg nigGnuvtþsmIkr
∑MK = 0.

#>^> Truss pSM (Compound Truss)
enAkñúgkfaxNÐ 3.2 eKerobrab;fa truss pSMRtUv)anbegáIteLIgedaytP¢ab; truss samBaØBIr b¤
eRcInedayGgát;r)ar b¤edaytMN. eBlxøH eKRtUvkarviPaK truss EbbenHedayGnuvtþviFITaMgBIrEdl)an
erobrab;xagelI. edIm,IgayRsYl dMbUgeKKYrdwgBIRbePTénkarsagsg; truss pSMenHdUc)anerobrab;enA
kñúgkfaxNÐ 3.2 bnÞab;mkeTIbcab;epþImeFVIkarviPaKedayeRbIdMeNIrkarEdlENnaMxageRkam.
RbePTTI1 truss samBaØEdlRtUv)antP¢ab;bBa©ÚlKñaedaytMNFmμta nigedayGgát;r)ar³ dMbUgeKRtUvkM-
Nt;Rbtikmμrbs; truss nigbnÞab;mk edayeRbIviFImuxkat; kat; truss Rtg;Ggát;EdltP¢ab; truss samBaØ
TaMgBIr dUcenHeKGacTTYl)ankMlaMgkñúgrbs;Ggát;enaHenAeBleKKitdüaRkamGgÁesrIrbs;Epñk truss
Edlkat;enaH. enAeBleKTTYl)ankMlaMgenaHrYcehIy eKGaceFVIkarviPaK truss samBaØedayeRbIviFItMN
¬emIl]TahrN_ 3-8¦.
RbePTTI2 truss samBaØEdlRtUv)antP¢ab;KñaedayeRbIGgát;r)arcMnYnbI³ dMbUgeKRtUvkMNt;kMlaMgRbtikmμ
EdlmanGMeBIelI truss. kat;Ggát;r)arTaMgbIEdltP¢ab; truss samBaØTaMgBIr. BIdüaRkamGgÁesrIénEpñk
Edlkat;NamYy kMNt;kMlaMgkñúgrbs;Ggát;TaMgbIenaH. bnþkarviPaK truss samBaØedayeRbIviFItMN
¬emIl]TahrN_ 3-9¦.
RbePTTI3 truss samBaØEdlRtUv)aneRbICa truss rgsMrab;CMnYsGgát;emrbs; truss em³ eTaHbICaeyIg
GacviPaK truss RbePTenHedayeRbIviFImuxkat; CamYynwgviFItMNk¾eday eyIgnwgeRbIviFIEdlman
lkçN³TUeTACagCMnYsvij. dMbUg eyIgRtUvCMnYs truss rgedayGgát;EdltagedaybnÞat;dac; dUcenH
truss pSMnwgkøayCa truss samBaØ. kMlaMgEdl truss rgGnuvtþeTAelI truss emRtUv)andak;enARtg;tMN

EdltP¢ab;rvag truss rgCamYynwg truss em. kMNt;kMlaMgenAkñúgGgát;bnÞat;dac;edayeRbIviFImuxkat; b¤
viFItMN. bnÞab;mk eyIgGnuvtþkMlaMgEdlrk)aneTAelItMNrbs; truss rg ehIybnÞab;mkedayeRbIviFI
tMN eyIgGackMNt;kMlaMgkñúgrbs; truss rg ¬emIl]TahrN_ 3-10¦.


]TahrN_ 3-8³ bgðajBIrebobviPaK truss pSMEdlbgðajenAkñúgrUbTI 3-29a. eKeGaykMlaMgRbti-
kmμenARtg;tMN.

dMeNaHRsay³ vaCa truss pSMRbePTTI1 edaysar truss samBaØ
ACH nig CEG RtUv)antP¢ab;edaytMNenARtg;tMN C nigr)ar HG .
muxkat; aa enAkñúgrUbTI 3-29a kat;Rtg;r)ar HG nigGgát;
BIrepSgeTotEdlmankMlaMgCaGBaØat. düaRkamGgÁesrIsMrab;Epñk
truss xageqVgEdlbgðajenAkñúgrUbTI 3-29b.

eKkMNt;kMlaMgenAkñúgGgát; HG dUcxageRkam³
+ ∑ MC = 0 − 5(4) + 4(2) + FHG (4 sin 60 o ) = 0

FHG = 3.46kN (C )
eyIgGacbnþkarkMNt;kMlaMgenAkñúgGgát;nImYy²rbs; truss samBaØ
edayeRbIviFItMN. Ca]TahrN_ düaRkamGgÁesrIrbs; truss ACH
RtUv)anbgðajenAkñúgrUbTI 3-29c. eKGacviPaKtMNrbs; truss
tamlMdab;lMedaydUcxageRkam³
tMN A ³ kMNt;kMlaMgkñúg AB nig AI .
tMN H ³ kMNt;kMlaMgkñúg HI nig HJ .
tMN I ³ kMNt;kMlaMgkñúg IJ nig IB .
tMN B ³ kMNt;kMlaMgkñúg BC nig BJ .
tMN J ³ kMNt;kMlaMgkñúg JC .



]TahrN_ 3-9³ bgðajBIrebobviPaK truss pSMEdlbgðajenAkñúgrUbTI 3-30a. eKeGaykMlaMgRbti-
kmμenARtg;tMN.

dMeNaHRsay³ eKcat;cMNat;fñak;xagelIenHCa truss pSMRbePTTI2 edaysar truss samBaØ ABCD
nig FEHG RtUv)antP¢ab;edayGgát;r)arbI CE / BH / DG EdlminRsbKña nigminRbsBVKña.
edayeRbImuxkat; aa enAkñúgrUbTI 3-30a eyIgGackMNt;kMlaMgkñúgGgát;EdltP¢ab;nImYy².
düaRkamGgÁesrIrbs;Epñkénmuxkat; truss RtUv)anbgðajenAkñúgrUbTI 3-30b. dUcenH
+ ∑MB = 0 − 10(2) − FDG (2 sin 45o ) + FCE cos 45o (4)
+ FCE sin 45o (2) = 0 (1)
+ ↑ ∑ Fy = 0 10 − 10 − FBH sin 45o
+ FCE sin 45o = 0 (2)
+
→ ∑ Fx = 0 − FBH cos 45o + FDG
− FCE cos 45o = 0 (3)
BIsmIkar (2)/ FBH = FCE bnÞab;mkedaHRsayRbB½n§smIkar (1) nig
(3) enaHeyIgTTYl)an

FBE = FCE = 8.9kN (C ) FDG = 12.6kN (T )
eKGaceFIVkarviPaK truss samBaØEdltP¢ab;nImYy²edayeRbIviFItMN.
Ca]TahrN_ BIrUbTI 3-30c eKGackMNt;kMlaMgkñúgrbs;Ggát;én truss
pSMtamlMdab;lMedaydUcxageRkam.
tMN A ³ kMNt;kMlaMgkñúg AB nig AD .
tMN D ³ kMNt;kMlaMgkñúg DC nig DB .
tMN C ³ kMNt;kMlaMgkñúg CB .



]TahrN_ 3-10³ bgðajBIrebobviPaK truss pSMsIuemRTIEdlbgðajenAkñúgrUbTI 3-31a. eKeGay
kMlaMgRbtikmμenARtg;TMr.

dMeNaHRsay³
eKcat;cMNat;fñak; truss xagelICa truss pSMRbePT
TI3 Edlman truss AGEF nig truss CHED Ca
truss rg ehIy truss ABCD Ca truss em.

edayyk truss rgTaMgBIrecj ¬rUbTI 3-
31b¦ eKRtUvdak;CMnYsRbtikmμrbs;vaEdlmçag²
esμInwg 1.5kN enARtg;tMNsnøak; A nigtMN E
ehIyenARtg;tMN E nigtMN C . eKGackMNt;
kMlaMgRbtikmμ rbs; truss rgTaMgBIrenH)an eday
sarGnuvtþsmIkarlMnwgeTAelI truss nImYy².
Truss emCamYynwgkardak;bnÞúk 1.5kN RtUv)anbgðajenAkñúgrUbTI 3-31c. eKGackMNt;kMlaMgenAkñúg

Ggát;nImYy²BIviFItMN. Ca]TahrN_ sMrab;tMN A düaRkamGgÁesrIRtUv)anbgðajenAkñúgrUbTI 3-321d.
eyIgman
+ ↑ ∑ Fy = 0 4.62 − 1.5 sin 45o − FAE sin 45o = 0

FAE = 5.03kN (C )
+
→ ∑ Fx = 0 1.5 cos 45o − 5.03 cos 45 o + FAB = 0

FAB = 2.50kN (T )
edaydwgfa FAE = 5.03kN (C ) eyIgGacGnuvtþkMlaMgEdlCatMélelxenHeTAelI truss rg AGEF
enAkñúgrUbTI 3-31b ehIybnÞab;mkbnþkarviPaKkMlaMgenAkñúgGgát;rbs; truss enHedayviFItMN.



cMNaMfa eKk¾GacviPaKkMlaMgenAkñúgGgát;rbs; truss enAkñúgrUbTI 3-31c edaypÞal;edayeRbI
viFImuxkat;k¾)anEdr. Ca]TahrN_ kat; truss Rtg;Ggát; FE / EG nig AB bnÞab;mkkMNt;kMlaMgkñúg
rbs;Ggát;nImYy²edayeRbIviFItMN.
#>&> Truss saMjúaM (Complex Trusses)
eKGackMNt;kMlaMgxagkñúgGgát;rbs; truss saMjúaMedayeRbIviFItMN b:uEnþeKRtUvkarsresrsmIkar
lMnwgBIrsMrab;RKb;tMNEdlmancMnYn j rbs; truss ehIybnÞab;mkedaHRsaysMnMuRbB½n§smIkarcMnYn 2 j . 1

viFIenHBitCaBi)aksMrab;karKNnaedayéd CaBiesssMrab;krNI truss FM². dUcenH viFIEdlmanlkçN³
pÞal;sMrab;viPaK truss saMjúaMKWviFICMnYsGgát; (method of substitute members) ehIyviFIwenHRtUv)an
ykmkerobrab;enATIenH.
eyagtam truss enAkñúgrUbTI 3-32a, xageRkamCaCMhancaM)ac;edIm,IedaHRsayrkkMlaMgkñúg
rbs;Ggát;edayeRbIviFICMnYsGgát;.

kareFVIeGayvaeTACa truss samBaØsßirPaB. kMNt;kMlaMgRbtikmμenARtg;TMr nigcab;epþImviPaKkMlaMgkñúg
rbs;Ggát;edayeRbIviFItMN. eKRtUvCMnYsedayGgát;nimitþcMnYnmYy enARtg;tMNNaEdlmanGBaØatEdl
CakMlaMgcMnYnbI. kareFVIEbbenH KWeKeFVIeGay truss køayCa truss samBaØsßirPaB.
Ca]TahrN_ enAkñúgrUbTI 3-32a eyIgsegÁteXIjfatMNnImYy²mankMlaMgkñúgrbs;Ggát;Ca
GBaØatcMnYnbImanGMeBIelIva. dUcenH eyIgnwgykGgát; AD ecj ehIyCMnYsvaedayGgát;nimitþ EC ¬rUbTI
1
eKGaceRbIviFIenHedaymanCMnYyBIkMuBüÚT½rEdlnwgmanbgðajenAkñúgCMBUkTI14.


3-32b¦. eKGacviPaK truss enaHedayviFItMNsMrab;bnÞúkTaMgBIrRbePTdUcxageRkam.
kMlaMgxageRkAenAelI truss samBaØ³ dak;bnÞúkCak;EsþgenAelI truss samBaØ bnÞab;mkkMNt;kMlaMg S'i
enAkñúgGgát; i . enAkñúgrUbTI 3-32b/ kñúgkrNIEdleKkMNt;kMlaMgRbtikmμrYc eKGaccab;epþImkar viPaK
truss Rtg;tMN AD edIm,IkMNt;kMlaMgenAkñúgGgát; AB nig AF bnÞab;mkviPaKtMN F edIm,IkMNt;kMlaMg

enAkñúgGgát; FE nig FC bnÞab;mkeTotviPaKtMN D edIm,IkMNt;kMlaMgenAkñúgGgát; DE nig DC ¬Ggát;
TaMgBIrenHCaGgát;EdlmankMlaMgsUnü¦ ehIybnÞab;mkeTot viPaKtMN E edIm,IkMNt;kMlaMgrbs;Ggát;
EB nig EC ehIycugeRkay viPaKtMN B edIm,IkMNt;kMlaMgenAkñúgGgát; BC .

ykkMlaMgxageRkAecjBI truss samBaØ³ BicarNa truss samBaØEdlminmankMlaMgxageRkA. dak;bnÞúk
mYyÉktþaenARtg;tMNTaMgBIrEdleyIg)anykGgát;ecj edaybnÞúkÉktþaenaHmanTisedApÞúyKña. Rbsin
ebIbnÞúkÉktþaenHbegáItkMlaMg Si enAkñúgGgát; truss TI i enaHedaysmamaRt kMlaMgEdlCaGBaØat x enA
kñúgGgát;EdlykecjnwgeFVIeGayGgát;TI i rgkMlaMg xsi .
BIrUbTI 3-32c/ bnÞúkÉktþanwgminbegáIteGaymankMlaMgRbtikmμenARtg;TMr A nigTMr C enAeBl
EdlGnuvtþsmIkarlMnwgeTAelI truss TaMgmUl. eKGackMNt;kMlaMg si edayviPaKtMNtamlMdab;lMeday
dUcelIkmun eBalKWcab;epþImBItMN A bnÞab;mktMN F / tMN D / tMN E nigcugeRkaytMN B .
eFVItMrYtpl (superposition)³ RbsinebIeKpÁÜbT§iBlrbs;bnÞúkTaMgBIrxagelI kMlaMgenAkñúgGgát;TI i rbs;
truss nwgkøayCa³
S i = S 'i + xsi (1)
sMrab;kMlaMgenAkñúgGgát;nimitþ EC enAkñúgrUbTI 3-32b KW S EC = S ' EC + xs EC . edaysar enAkñúg truss
Cak;EsþgminmanGgát;nimitþenH dUcenHeyIgRtUveRCIserIstMélrbs; x EbbNaEdlvanwgeFVIeGayGgát;
nimitþCaGgát;kMlaMgsUnü. dUcenH
S ' EC + xs EC = 0 (2)
b¤ x = −S ' EC / s EC . enAeBlEdlkMNt;tMélrbs; x rYcehIy enaHeKGackMNt;kMlaMgenAkñúgGgát;rbs;
truss saMjúaMBIsmIkar (1).

]TahrN_ 3-11³ kMNt;kMlaMgenAkñúgGgát;nImYy²rbs; truss saMjúaMEdlbgðajenAkñúgrUbTI 3-33a.
snμt;tMN B / F nig D sßitenAelIbnÞat;edk. bgðajnUvsßanPaBrgkMlaMgrbs;Ggát;nImYy².
dMeNaHRsay³
eFVIeGay truss køayCa truss samBaØmansßirPaB. edaykarGegát tMNnImYy²mankMlaMgEdlCa
GBaØatcMnYnbI . eKGacGnuvtþviFItMNedayédRbsinebIeKykGgát; CF yk ehIyCMnYsGgát; DB vij


¬rUbTI 3-33b¦. Truss EdlTTYl)anBIkaredaHdUrGgát;mansßirPaB nigmindYlrlM.

KNnakMlaMgkñúgrbs; truss samBaØmansßirPaBeRkamGMeBIkMlaMgxageRkA. dUceXIjenAkñúgrUbTI 3-
33b kMlaMgRbtikmμrbs;TMrRtUv)ankMNt;. edayeRbIviFItMN dMbUgeyIgGacviPaKtMN C edIm,IrkkMlaMg
kñúgrbs;Ggát; CB nig CD . bnÞab;mktMN F EdleyIgeXIjfaGgát; FA nig FE CaGgát;kMlaMgsUnü.
bnÞab;mkeTot viPaKtMN E edIm,IkMNt;kMlaMgenAkñúgGgát; EB nig ED ehIybnÞab;mkeTot viPaKtMN
D edIm,I kMNt;kMlaMgenAkñúgGgát; DA nig DB ehIycugeRkayviPaKtMN B edIm,IkMNt;kMlaMgenAkñúg

Ggát; BA . edaysnμt;fakMlaMgTajviC¢man ehIykMlaMgsgát;GviC¢man enaHkMlaMg S'i RtUv)andak;enAkñúg
CYrQrTI2 éntaragTI 1.
KNnakMlaMgkñúgrbs; truss samBaØsßirPaBedayykkMlaMgxageRkAecj. bnÞúkÉktþaEdlmanGMeBIenA
elIRtUv)anbgðajenAkñúgrUbTI 3-33c. kMlaMgEdldUcKña EtmanTisedApÞúyKñamineFVIeGay truss man
kMlaMgRbtikmμeT. kMNt;kMlaMgkñúgrbs;Ggát;edayeRbIviFItMNtamlMdab;lMedayEdl)anerobrab;xagelI
eBalKWtMN C / F / E / D nig B . lT§plénkarviPaKkMlaMg si RtUv)andak;enAkñúgCYrQrTI3 rbs;tarag
TI1.
eFVItMrYtpl³ eyIgtMrUveGay
S DB = S ' DB + xs DB = 0
edayCMnYstMélrbs; S ' DB nig s DB Edl S ' DB mantMélGviC¢manedaysarvaCakMlaMgsgát; eyIgman
− 10.0 + x(1.167 ) = 0

x = 8.569
tMélrbs; xsi RtUvbgðajenAkñúgCYrQrTI4 éntaragTI1 ehIykMlaMgrbs;Ggát;Cak;Esþg Si = S 'i + xsi
RtUv)andak;enAkñúgCYrQrTI5.


#>*> Truss kñúglMh (Space Trusses)
kñúglMhpSMeLIgedayGgát;EdltP¢ab;Kña
Truss

enARtg;cugrbs;edIm,IbegáItCarcnasm<½n§man sßirPaBbI
TMhM (stable three-dimension structure). enAkñúg
kfaxNÐTI 3-2 )anbgðajBITMrg;d¾samBaØ bMputrbs;
truss mansßirPaBBIrTMhMRtUv)anpSMeLIgedaykartMerob

Ggát;CaragRtIekaN. tamTMrg;dUcKña rUbragsamBaØ
bMputrbs; truss kñúglMhEdlmansßirPaBKWragctut½l
(tetrahedron) EdlbegáIteLIgeday eRbIGgát;r)arcMnYn6

EdltP¢ab;Kña)antMN4 dUcbgðajenAkñúgrUbTI 3-34.
karEfmGgát;bEnßmeTAelIrag mUldæanenHGaceFVIeGayva
manGBaØatelIskñúgkarTb;Tl;kMlaMg P . eKGacbegáIt
truss kñúglMhecjBI ragmUldæanctut½ledayEfmGgát;bI

CamYynwgtMNmYyedIm,ITTYl)anctut½lEfmmYyeTot.
PaBkMNt; nigsßirPaB
edaydwgfaenAkñúgbITMhM eKGacmansmIkarlMnwgcMnYnbIsMrab;Ggát;nImYy² ¬ ∑ Fx = 0 / ∑ Fy = 0 /
∑ Fz = 0 ¦ enaHsMrab; truss kñúglMhEdlmantMNcMnYn j eKGacmansmIkarlMnwgcMnYn 3 j . RbsinebI



truss manr)arcMnYn b nigkMlaMgRbtikmμcMnYn r enaHdUckrNIrbs; truss kñúgbøg; ¬smIkar 3-1 nig 3-2¦
eyIgGacsresr
b+r <3 truss KμansßirPaB

b+r =3j truss kMNt;edaysþaTic RtUvRtYtBinitüsßirPaB
b+r >3j truss minkMNt;edaysþaTic RtUvRtYtBinitüsßirPaB (3-3)
sßirPaBxageRkArbs; truss kñúglMhTamTareGaykMlaMgRbtikmμTMrrkSalMnwgkMlaMg niglMnwgm:Um:g;rbs;
truss RKb;G½kS. eBlxøHeKGacRtYtBinitüvaedaykarGegát. eBlxøH truss KμansßirPaB EtdMeNaHRsay

rbs;smIkarlMnwgnwgeGaylT§plminzitezr.
sßirPaBxagkñúgrbs; truss kñúglMhRtUv)anRtYtBinitüy:agRbugRby½tñedaykarGegátBIkartMerobGgát;.
RbsinebItMNnImYy²manlkçN³bgáb;edayTMr b¤edayGgát;EdltP¢ab; enaHvaminGaccl½t)aneTeFobnw
gtMNepSgeTot ehIy truss enaHRtUv)aneKcat;cMNat;fñak;Ca truss EdlmansßirPaBxagkñúg. ehIy
RbsinebIkareFVIviPaKkMlaMgrbs; truss bgðajlT§plminzitezr enaHmann½yfarUbrag truss enaHminman
sßirPaB b¤k¾manTMrg;eRKaHfñak;.
karsnμt;kñúgkarsikSaKNna³ Ggát;rbs; truss kñúglMhGacCaGgát;rgkMlaMgtamG½kS RbsinebIkMlaMg
xageRkAeFVIGMeBIenARtg;tMN ehIytMNCa ball-and-socket connection. karsnμt;EbbenHBitCaRtwm
RtUv RbsinebIGgát;Edlkat;KñaRtUv)antP¢ab;KñaedaytMNFmμta ehIyeKGacecalTMgn;rbs;Ggát;)an.
enAkñúgkrNIEdleKKitTMgn;rbs;Ggát;kñúgkarviPaK CaTUeTAeKKitTMgn;rbs;CabnÞúkcMcMnucEdlmanTis
bBaÄr edayeKeGayTMhMrbs;vaBak;kNþalmanGMeBIelIcugsgxagrbs;va.
sMrab;karviPaKkMlaMg CaTUeTAeKeRcIneFVIm:UEDleGayTMrCa short link/ plane roller joint,
slotted roller joint b¤ ball-and-socket joint. TMr nigbgÁúMkMlaMgrbs;vanImYy²RtUv)anbgðajenAkñúg

taragTI 3-1.
bgÁúMkMlaMgtamTis x / y / z ³ edaysarkarviPaK truss kñúglMhCakarviPaKtamlkçN³bITMhM eKcaM)ac;
RtUvbMEbkkMlaMg F enAkñúgGgát;CabgÁúMkMlaMgEdleFVIGMeBItamG½kS x / y nig z . Ca]TahrN_ enAkñúgrUbTI
3-35 Ggát; AB manRbEvg l ehIy x / y / z CaRbEvgRbeyalelIG½kSkUGredaenrbs;va. TMnak;TMng
rvagRbEvgRbeyalCamYynwgRbEvgrbs;Ggát;RtUv)ankMNt;edayrUbmnþ
l = x2 + y2 + z 2 (3-4)
edaysarkMlaMg F eFVIGMeBItamG½kSrbs;Ggát; enaHeKGackMNt;bgÁúMrbs;kMlaMg F edaysmamaRtxag
eRkam³

⎛ x⎞ ⎛ y⎞ ⎛z⎞
Fx = F ⎜ ⎟ Fy = F ⎜ ⎟ Fz = F ⎜ ⎟ (3-5)
⎝l⎠ ⎝l⎠ ⎝l⎠
cMNaMfa smamaRtxagelItMrUveGay
F = Fx2 + Fy2 + Fz2 (3-6)

kareRbIR)as;smIkarTaMgenHnwgbgðajenAkñúg]TahrN_ 3-12.

Ggát;kMlaMgsUnü³ enAkñúgkrNIxøH eKGacsMrYlkarviPaKtMNrbs; truss RbsinebIeKGacsÁal;Ggát;Na
mankMlaMgsUn². kardwgGgát;kMlaMgsUnüGaceFVIeTA)anGaRs½ynwgkrNIFmμtaBIrrbs;ragFrNImaRt
rbs;tMN.
krNITI1³ sMrab;Ggát;TaMgGs;EdltP¢ab;KñaRtg;tMNmYy manGgát;mYyminsßitenAkñúgbøg;CamYynwgGgát;
déT ehIytMNenaHminrgbnÞúkxageRkA enaHGgát;enaHCaGgát;kMlaMgsUnü. karbkRsayBIesckþIEcg
enHmanbgðajenAkñúgrUbTI 3-36 EdlGgát; A / B / C sßitenAelIbøg; x − y . edaysarbgÁúMkMlaMgtam
Tis z rbs;kMlaMg FD RtUvEtesμInwgsUnüedIm,IbMeBjlkçxNÐsmIkar ∑ Fz = 0 enaHGgát; D RtUvEtCaGgát;
kMlaMgsUnü. tamkarbkRsaydUcKña Ggát; D nwgrgbnÞúkEdlGackMNt;BIsmIkar ∑ Fz = 0 RbsinebIkM-
laMgxageRkAeFVIGMeBIenAelItMN.



krNITI2³ RbsinebIGgát;BIrkñúgcMeNamGgát;epSgeTotEdltP¢ab;KñaenARtg;tMNmYyCaGgát;kMlaMgsUnü
enaHGgát;EdlenAsl;BIrepSgeTotk¾CaGgát;kMlaMgsUnüEdr kñúgkrNIEdlBYkvaminsßitenAelIbnÞat;Et
mYy. sßanPaBEbbenHRtUv)anbgðajenAkñúgrUbTI 3-37 EdleKdwgfaGgát; A nig C CaGgát;kMlaMgsUnü.
edaysar FD sßitenAelIG½kS y enaHkarGnuvtþén ∑ Fx = 0 b¤ ∑ Fz TamTareGaybgÁúMkMlaMgtamG½kS x
b¤G½kS z rbs; FB RtUvEtesμIsUnü. dUcenH FB = 0 . ehIy FD = 0 edaysar ∑ Fy = 0 .

enAeBleFVIkarviPaK truss kñúglMheKRtUvykcitþTukdak;CamYynwgkrNITaMgBIrEdlerobrab;xag
elI edaysarkardwgBIGgát;kMlaMgsUnüsMrYldl;karviPaK truss kñúglMhy:ageRcIn.

eKGaceRbIviFItMN b¤viFImixkat;edIm,IviPaKkMlaMgkñúgEdlekItmanenAkñúgGgát;rbs; truss kñúglMh.
viFImuxkat;³ RbsinebIeKRtUvkarkMNt;kMlaMgkñúgrbs;Ggát;xøH eKGaceRbIviFImuxkat;. enAeBleKkat; truss
CaBIrcMENk enaHRbB½n§kMlaMgEdleFVIGMeBIenAlIcMENkén truss nImYy²RtUvEtbMeBjsmIkarlMnwg6KW
∑ Fx = 0 / ∑ Fy = 0 / ∑ Fz = 0 / ∑ M x = 0 / ∑ M y = 0 nig ∑ M z = 0 . edaykareRCIserIsmux

kat; nigG½kSd¾RtwmRtUvsMrab;eFVIplbUkkMlaMg nigm:Um:g; enaHeKGackMNt;kMlaMgkñúgrbs;Ggát;EdlCa
GBaØatedaypÞal; edayeRbIlMnwgsmIkarEtmYy. sMrab;krNIEbbenH eyIgRtUvcaMfam:Um:g;énkMlaMgRtg;
cMnucmYyesμIsUnü RbsinebIkMlaMgRsbeTAnwgG½kSEdlcMnucenaHsßitenA.
viFItMN³ CaTUeTA vIFIEdlsaksmbMputsMrab;karkMNt;kMlaMgenAkñúgGgát;TaMgGs;rbs; truss KWviFItMN.
enAeBleKeRbIviFItMN eKcaM)ac;RtUvedaHRsaysmIkarlMnwgbI ∑ Fx = 0 / ∑ Fy = 0 nig ∑ Fz = 0 sMrab;
tMNnImYy². edaysarkarKUrdüaRkamGgÁesrI nigkarGnuvtþsmIkarlMnwgmanlkçN³gayRsYl enaHkar
Gnuvtþrbs;vamanlkçN³zitezr.



]TahrN_ 3-12³ kMNt;kMlaMgenAkñúgGgát;nImYy²rbs; truss kñúglMhEdlbgðajenAkñúgrUbTI 3-
38a. Truss RtUv)anRTeday ball-and-socket enARtg;tMN A / slotted roller enARtg;tMN B nig
edaykabenARtg;tMN C .

dMeNaHRsay³
Truss enHkMNt;edaysþaTic edaysar b + r = 3 j
b¤ 9 + 6 = 3(5) / rUbTI 3-38b.
kMlaMgRbtikmμTMr³
eyIgGacTTYl)ankMlaMgRbtikmμTMrBIdüaRkamGgÁesrIrbs; truss
TaMgmUl ¬rUbTI 3-38b¦ dUcxageRkam³
∑M y = 0 − 4(2) + B x (4) = 0 B x = 2kN

∑Mz = 0 Cy = 0

∑Mx = 0 B y (4) − 4(4) = 0 B y = 4kN

∑ Fx = 0 2 − Ax = 0 Ax = 2kN
∑ Fy = 0 Ay − 4 = 0 Ay = 4kN

∑ Fz = 0 Az − 4 = 0 Az = 4kN
tMN B ³ eyIgGaccab;epþImviFItMNenARtg;tMN B edaysarva
mankMlaMgEdlCaGBaØatcMnYnbIenARtg;tMNenH ¬rUbTI 3-38c¦.
eyIgGacKNnabgÁúMkMlaMgrbs; FBE edaysmamRteTAnwgRbEvg
rbs;Ggát; BE dUcbgðaj edaysmIkar 3-5. eyIgman


⎛4⎞
∑ Fy = 0 − 4 + FBE ⎜ ⎟ = 0 FBE = 6kN (T )
⎝6⎠
⎛2⎞
∑ Fx = 0 2 − FBC − 6⎜ ⎟ = 0 FBC = 0
⎝6⎠
⎛4⎞
∑ Fz = 0 FBA − 6⎜ ⎟ = 0 FBA = 4kN (C )
⎝6⎠
tMN A³ edayeRbIlT§plén FBA = 4kN (C ) . düaRkamGgÁesrIrbs;tMN A RtUv)anbgðajenAkñúgrUbTI
3-38d. eyIgman
∑ Fz = 0 4 − 4 + FAC sin 45o = 0 FAC = 0
⎛ 2 ⎞
∑ Fy = 0 − FAE ⎜
⎜ ⎟+4=0
⎟ FAE = 4.47 kN (C )
⎝ 5⎠
⎛ 1 ⎞
∑ Fx = 0 − 2 + FAD + 4.47⎜
⎜ ⎟=0
⎟ FAD = 0
⎝ 5⎠
tMN D³ edaykarGegát Ggát;enARtg;tMN D ¬rUbTI 3-38a¦ rgbnÞúksUnü
edaysarkartMerobrbs;Ggát;manlkçN³RsedogKñanwgkrNITaMgBIrEdlmanbgðajenAkñúgrUbTI 3-36
nig 3-37. ehIyBIrUbTI 3-38e
∑ Fx = 0 FDE = 0

∑ Fz = 0 FDC = 0
tMN C ³ edaykarGegátdüaRkamGgÁesrIénrUbTI 3-38f
FCE = 0

]TahrN_ 3-13³ kMNt;Ggát;kMlaMgsUnürbs; truss EdlbgðajenAkñúgrUbTI 3-39a. TMrGnuvtþbgÁúM
kMlaMgRbtikmμmkelI truss dUcbgðajenAkñúgrUb.



dMeNaHRsay³
düaRkamGgÁesrI ¬rUbTI 3-39a¦ bgðajfavamankMlaMg
RbtikmμcMnYn8 b:uEnþeKGacmansmIkarlMnwgEtcMnYn6.
eTaHbIy:agenHk¾eday k¾eKGackMNt;kMlaMgRbtikmμ)anEdr
edaysar b + r = 3 j b¤16 + 8 = 3(8) .
edIm,IrkGgát; kMlaMgsUnü eyIgRtUveRbobeFob
lkçxNÐénragFrNImaRt nigkarrgbnÞúkenARtg;tMNeTAnwg
rUbTI 3-36 nig3-37.
BicarNatMN F ¬rUbTI 3-39b¦. edaysarGgát;
FC / FD / FE sßitenAelIbøg; x − y ehIyGgát; FG minsßit

enAelIbøg;enH enaHGgát; FG CaGgát;kMlaMgsUnü. vaRtUvEt
bMeBjlkçxNÐsmIkar ∑ Fz = 0 .
tamrebobdUcKña BItMN E ¬rUbTI 3-39c¦ Ggát;
FE CaGgát;kM;laMgsUnü edaysarvaminsßitenAkñúgbøg; y − z .

vaRtUvEtbMeBjsmIkar ∑ Fx = 0 . edayRtLb;BinitüeTAtMN
F vij ¬rUbTI 3-39b¦ eyIgeXIjfa FFD = FFC = 0 edaysar FFE = FFG = 0 nigKμankMlaMgxag

eRkAeFVIGMeBImkelItMN.
eKGacbnþkarviPaKelItMN G ¬ FGF = 0 ¦ edIm,IkMNt;kMlaMgenAxagkñúgGgát; GH / GB nig
GC . bnÞab;mkviPaKtMN H edIm,IrkkMlaMgenAkñúgGgát; HE / HB / HA . viPaKtMN E sMrab;kMlaMg

enAkñúgGgát; EA / ED . viPaKtMN A sMrab;kMlaMgenAkñúgGgát; AB / AD nig Az . viPaKtMN B edIm,Irk
kMlaMgenAkñúgGgát; BC nig Bx / Bz . viPaKtMN D sMrab;KNnakMlaMgenAkñúgGgát; DC nig D y / Dz .
ehIycugeRkay viPaKtMN C edIm,IkMNt; C x / C y nig C z .



cMeNaT
3>1> cat;cMNat;fñak; truss xageRkamCa truss sßirPaB. RbsinebIminkMNt; cUrbgðajdWeRkrbs;
mansßirPaB KμansßirPaB kMNt;edaysþaTic min va.
kMNt;edaysþaTic. RbsinebIminkMNt;bgðaj
BIdWeRkrbs;va. Ggát;TaMgGs;RtUv)antP¢ab;eday
snøak;enAxagcugrbs;va.

3>3> cat;cMNat;fñak; truss xageRkamCa truss
kMNt;edaysþaTic minkMNt;edaysþaTic b¤Kμan
sßirPaB. RbsinebIminkMNt; cUrbgðajdWeRkrbs;
va.

3>2> cat;cMNat;fñak; truss xageRkamCa truss
kMNt;edaysþaTic minkMNt;edaysþaTic b¤Kμan

cMeNaT T.Chhay -99


elItMNxagelIrbs; truss. kMNt;kMlaMgkñúgGgát;
nImYy²rbs; truss ehIybgðajBIsPaBkMlaMg
EdlGgát;rg. snμt;Ggát;TaMgGs;RtUv)antP¢ab;
edaytMNsnøak;.

3>7> kMNt;kMlaMgenAkñúgGgát;nImYy²rbs; truss.
3>4> kMNt;kMlaMgenAkñúgGgát;nImYy²rbs; truss. bgðajsPaBrgkMlaMgrbs;Ggát;.
bgðajsPaBrgkMlaMgrbs;Ggát;.

bgðajsPaBrgkMlaMgrbs;Ggát;. snμt;Ggát;TaMg
Gs;tP¢ab;Kñaedaysnøak;.
bgðajsPaBrgkMlaMgrbs;Ggát;. yk P = 8kN .

3>9> kMNt;kMlaMgenAkñúgGgát;nImYy²rbs;dMbUl
3>6> Truss EdlbgðajRtUv)aneRbIedIm,IRTkMral truss. bgðajsPaBrgkMlaMgrbs;Ggát;. snμt;
deck. bnÞúkBRgayenAelIkMralKW 30kN / m .
Ggát;TaMgGs;tP¢ab;Kñaedaysnøak;.
bnÞúkenHRtUv)anepÞrBIkMraleTAFñwm EdlQrenA
Problems T.Chhay -100


3>10> Howe truss rgbnÞúkdUcbgðajkñúgrUbxag
eRkam. kMNt;kMlaMgenAkñúgGgát; GF / CD nig
GC . bgðajsPaBrgkMlaMgrbs;Ggát;. 3>14> kMNt;kMlaMgenAkñúgGgát; GH / BC nig
BG rbs; truss s<an. edaHRsayrkGBaØat

nImYy²edayeRbIEtsmIkarlMnwgmYy. bgðaj
sPaBrgkMlaMgrbs;Ggát;. snμt;Ggát;TaMgGs;t
P¢ab;Kñaedaysnøak;.

3>11> kMNt;kMlaMgenAkñúgGgát; GH / BC nig
BG rbs; Howe truss xagelI. bgðajsPaBrg

kMlaMgrbs;Ggát;.
3>12> kMNt;kMlaMgenAkñúgGgát;nImYy²rbs; 3>15> kMNt;kMlaMgenAkñúgGgát;nImYy²rbs;
dMbUl truss. bgðajsPaBrgkMlaMgrbs;Ggát;. dMbUl truss. bgðajsPaBrgkMlaMgrbs;Ggát;.

3>13> kMNt;kMlaMgenAkñúgGgát;nImYy²rbs;
dMbUl truss. bgðajsPaBrgkMlaMgrbs;Ggát;. 3>16> edaHRsaycMeNaT 3>15> eLIgvijeday
snμt;Ggát;TaMgGs;tP¢ab;Kñaedaysnøak;. snμt;famanEtbnÞúk15kN b:ueNÑaHEdleFVIGMeBIelI
tMN I .
cMeNaT T.Chhay -101


3>17> kMNt;kMlaMgenAkñúgGgát; GF / FC nig 3>21> Ggát; AB nig BC GacRTRTg;kMlaMgsgát;
CD rbs; truss kugs‘ul. bgðajsPaBrgkMlaMg Gtibrma 4kN ehIyGgát; AD / DC nig BD
rbs;Ggát;. snμt;Ggát;TaMgGs;tP¢ab;Kñaeday GacRTRTg;kMlaMgTajGtibrma 7.5kN . Rbsin
snøak;. ebI a = 3m kMNt;bnÞúkFMbMputrbs; P Edl truss
GacRT)an. ¬rUbkñúgcMeNaT 3>20¦
3>22> Ggát; AB nig BC GacRTRTg;kMlaMgsgát;
Gtibrma 4kN ehIyGgát; AD / DC nig BD
GacRTRTg;kMlaMgTajGtibrma 10kN . Rbsin
ebI a = 1.8m kMNt;bnÞúkFMbMputrbs; P Edl
3>18> kMNt;kMlaMgenAkñúgGgát; KJ / CD nig truss GacRT)an. ¬rUbkñúgcMeNaT 3>20¦
CJ rbs; truss. bgðajsPaBrgkMlaMgrbs; 3>23> eKeRbI truss Ggát;bIedIm,IRTbnÞúk P .
Ggát;. kMNt;mMu θ edIm,IkMueGaykMlaMgTajGtibrma nig
kMlaMgsgát;GtibrmaFMCag 1.25P nig 0.8P
erogKña.

3>19> kMNt;kMlaMgenAkñúgGgát; JI / JD nig
DE rbs; truss xagelI. bgðajsPaBrgkMlaMg

rbs;Ggát;.
3>20> kMNt;kMlaMgenAkñúgGgát;rbs; truss eday
eRbItYbnÞúk P ehIybgðajsPaBrgkMlaMgrbs; 3>24> kMNt;kMlaMgenAkñúgGgát; GF / FB nig
Ggát;. BC rbs; Fink truss. bgðajsPaBrgkMlaMg

rbs;Ggát;.



3>25> kMNt;kMlaMgenAkñúgGgát; GF / CF nig 3>28> kMNt;RbePTrbs; truss pSM nigkMNt;
CD rbs;dMbUl truss. bgðajsPaBrgkMlaMg kMlaMgenAkñúgGgát; JH / BJ nig BI . bgðaj
rbs;Ggát;. sPaBrgkMlaMg rbs;Ggát;. mMukñúgrbs;Ggát;BIrKW
60 o . Truss enHRtUv)anRTedayTMrsnøak;enA

Rtg;tMN A nigTMrkl;enARtg;tMN F . snμt;

3>26> cat;cMNat;fñak;rbs; truss nwgbgðajfava
mansßirPaBb¤Gt;.

3>29> kMNt;RbePTrbs; truss pSM. eKtP¢ab;
truss ACE nig truss BDF edayGgát;bI CF /

ED nig CD . kMNt;kMlaMgenAkñúgGgát;nImYy²

nigbgðajBIsPaBrgkMlaMgrbs;Ggát;.

truss. bgðajsPaBrgkMlaMgrbs;Ggát;. snμt;


3>30> kMNt;RbePTrbs; truss pSM nigkMNt;
kMlaMgenAkñúgGgát;nImYy² nigbgðajBIsPaBrg
kMlaMgrbs;Ggát;. snμt;Ggát;TaMgGs;tP¢ab;Kña
edaysnøak;.
cMeNaT T.Chhay -103


3>34> kMNt;kMlaMgenAkñúgGgát;TaMgGs;rbs;
truss saMjúaM. bgðajBIsPaBrgkMlaMgrbs;Ggát;.

CMnYy³ CMnYsGgát; JE edayGgát;Edldak;enA
cenøaH K nig F .
3>31> kMNt;kMlaMgenAkñúgGgát; IH / AH nig
BC rbs; truss. bgðajBIsPaBrgkMlaMgrbs;

Ggát;.


3>32> kMNt;kMlaMgenAkñúgGgát;nImYy². bgðaj snμt;Ggát;TaMgGs;tP¢ab;Kñaedaysnøak;.
BIsPaBrgkMlaMgrbs;Ggát;.

3>36> kMNt;kMlaMgenAkñúgGgát; JI / DI nig
3>33> kMNt;kMlaMgenAkñúgGgát;nImYy². bgðaj DE rbs; Pratt truss . bgðajBIsPaBrgkMlaMg
BIsPaBrgkMlaMgrbs;Ggát;. rbs;Ggát;. snμt;Ggát;TaMgGs;tP¢ab;Kñaeday
snøak;.



3>37> eRKag truss mYyrgbnÞúkdUcbgðaj. 3>41> kMNt;kMlaMgenAkñúgGgát; BG / HG nig
kMNt;kMlaMgenAkñúgGgát; JI / JD nig ID . BC rbs; truss nigbgðajBIsPaBrgkMlaMgrbs;
bgðajBIsPaBrgkMlaMgrbs;Ggát;. Ggát;.

3>42> eKeRbI Warren truss edIm,IRTdMbUl
GKar]sSahkmμ. Turss enHRTedayTMrsamBaØ
enAelICBa¢aMgdæenARtg; A nig G dUcenHmanEt
3>38> kMNt;kMlaMgenAkñúgGgát; HI / ED nig kMlaMgRbtikmμtamTisQrb:ueNÑaHekItmanenARtg;
EI enAkñúg truss éncMeNaT 3>37. bgðajBI
TMrTaMgenH. kMNt;kMlaMgenAkñúgGgát; LC / CD
sPaBrgkMlaMgrbs;Ggát;. nig KD . bgðajBIsPaBrgkMlaMgrbs;Ggát;.
3>39> kMNt;kMlaMgenAkñúgGgát; EF / EP nig snμt;Ggát;TaMgGs;tP¢ab;Kñaedaysnøak;.
LK én truss s<an nigbgðajBIsPaBrgkMlaMg

rbs;Ggát;. ehIy bgðajral;Ggát;kMlaMgsUnü.

3>43> kMNt;kMlaMgenAkñúgGgát; KJ / NJ /
ND nig CD én K-truss . bgðajBIsPaBrg

kMlaMgrbs;Ggát;.
3>40> kMNt;kMlaMgenAkñúgGgát; HG / BG nig
BC rbs; truss. bgðajBIsPaBrgkMlaMgrbs;

Ggát;.

3>44> kMNt;kMlaMgenAkñúgGgát; IH / CD nig
LH én K-truss . bgðajBIsPaBrg kMlaMgrbs;

cMeNaT T.Chhay -105


Ggát;. CMnYy³ kat; truss Rtg;Ggát; IH / IL / 3>47> kMNt;kMlaMgenAkñúgGgát;nImYy² nig
LC nig CD edIm,Irk IH nig CD snμt;Ggát; bgðajBIsPaBrgkMlaMgrbs;Ggát;.
TaMgGs;tP¢ab;Kñaedaysnøak;.


CMnYy³ CMnYsGgát; AD edayGgát;enAcenøaH E 3>48> kMNt;kMlaMgRbtikmμ nigkMlaMgenAkñúg
nig C . Ggát; BA / AD nig CD .


CMnYy³ CMnYsGgát; JE edayGgát;enAcenøaH K truss kñúglMh nigbgðajBIsPaBrgkMlaMgrbs;
Ggát;.
nig F .



3>50> kMNt;kMlaMgenAkñúgGgát;nImYy²rbs; 3>53> kMNt;kMlaMgenAkñúgGgát;TaMgGs;rbs;
truss kñúglMh. bgðajBIsPaBrgkMlaMgrbs; truss saMjúaM nigbgðajBIsPaBrgkMlaMgrbs;Ggát;.

Ggát;. CMnYy³ kMlaMgRbtikmμenARtg; E manGMeBItamG½kS
EB . ehtuGVI?

3>51> kMNt;kMlaMgenAkñúgGgát; AB / AD nig
AC rbs; truss kñúglMh. bgðajBIsPaBrg

kMlaMgrbs;Ggát;. 3>54> eKtP¢ab; truss bIdUcKñaedIm,IbegáItCa
rcnasm<½n§dUcbgðaj. RbsinebIrcnasm½<n§sßit
enAelITMrrelag A / C nig E kMNt;kMlaMgenA
kñúgGgát; CD / DH nig CH . bgðajBIsPaBrg
kMlaMgrbs;Ggát;.

3>52> kMNt;kMlaMgRbtikmμ nigkMlaMgenAkñúg
Ggát;nImYy²rbs; truss kñúglMh. bgðajBIsPaB
rgkMlaMgrbs;Ggát;. LaMgmanTMgn; 5kN .

3>55> kMNt;kMlaMgenAkñúgGgát; DF / FH nig
EF rbs; truss enAkñúgcMeNaT 3>54 xagelI.

bgðajBIsPaBrgkMlaMgrbs;Ggát;.
cMeNaT T.Chhay -107


3>56> kMNt;kMlaMgenAkñúgGgát; BE / DF nig KMerag³ dMbUl Pratt truss manKM;latefr 5m .
BC rbs; truss kñúglMh nigbgðajBIsPaBrg kMral sMPar³dMbUl nigédrENgmanTMgn;mFüm
kMlaMgrbs;Ggát;. 0.28kN / m 2 . dMbUlenHrgbnÞúkGefrsrub

1.4kN / m 2 . bnÞúkKitelIépÞRbeyaltamTis

edk. kMNt;kMlaMgkñúgrbs;Ggát;nImYy²Edl
bNþalBIbnÞúkefr nigbnÞúkGefr. TMgn;rbs;Ggát;
truss RtUv)anecal ehIysnμt; A CaTMrsnøak;

nig E CaTMrkl;.
3>57> kMNt;kMlaMgenAkñúgGgát; AB / CD / ED
nig CF rbs; truss kñúglMhéncMeNaT 3>56
xagelI nigbgðajBIsPaBrgkMlaMgrbs;Ggát;.
3>58> eKtP¢ab; truss bYndUcKñaedIm,IbegáItCa
rcnasm<½n§dUcbgðaj. RbsinebIrcnasm½<n§sßit
enAelITMrrelag A / B / C nig G kMNt;kMlaMgenA
kñúgGgát;nImYy²rbs; truss ABCD . bgðajBI
sPaBrgkMlaMgrbs;Ggát;.

3>59> kMNt;kMlaMgenAkñúgGgát;nImYy²én truss
kñúglMh. bgðajBIsPaBrgkMlaMgrbs;Ggát;. TMr
Rtg; A nig B CaTMrkl; ehIyenARtg; C Ca ball-
and-socket. etI truss enHmansßirPaBb¤Gt;?


3. analysis of statically determinate trusses

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