7. approximate analysis of statically indeterminate structures

Department of Civil Engineering NPIC

&> viPaKeRKOgbgÁúMminkMNt;edaysþaTicedayviFIRbEhl
Approximate analysis of statically indeterminate structures

enAkñúgCMBUkenHmanbgðajBIviFIRbEhlxøHEdleRbIedIm,IviPaK trusses nigeRKagminkMNt;eday
sþaTic. viFITaMgenHRtUv)anbegáIteLIgedayQrelIeKalkarN_énkareFVIkarrbs;eRKOgbgÁúM ehIyPaB
suRkitrbs;vaenAkñúgkrNICaeRcInmanlkçN³Rbhak;RbEhlnwgviFIviPaKEdlmanlkçN³Cak;las;Cag.
eTaHCay:agNak¾edayCMBUkenHmin)anelIkykeRKOgbgÁúMRKb;TMrg;mkBiPakSaeT eKalbMNgrbs;CMBUk
enHnwgpþl;nUvsBaØaNRKb;RKan;kñúgkaryl;dwgBIviFITaMgenH dUcenHGñksikSaGacvinicä½yeRCIserIsnUvviFI
EdlRbesIrbMputkñúgkarviPaKkMlaMgéneRKOgbgÁúMminkMNt;edaysþaTicedayviFIRbEhl.
&>!> bMerIbMras;énviFIRbhak;RbEhl (Use of approximate methods)
enAeKeRbIm:UEDledIm,IbgðajeRKOgbgÁúMNamYy karviPaKrbs;vaRtUvbMeBjTaMglkçxNÐlMnwg
(equilibrium) nig TaMglkçxNÐRtUvKña (compatibility) énbMlas;TIenARtg;tMN. lkçxNÐRtUvKñasMrab;

eRKOgbgÁúMminkMNt;edaysþaTicGacTak;TgnwgbnÞúk kñúgkrNIeyIgsÁal;m:UDuleGLasÞicrbs;sMPar³ nig
muxkat; rUbragrbs;Ggát;. b:uEnþ sMrab;karsikSaKNnadMbUg eyIgnwgminsÁal;muxkat;Ggát;eT dUcenHeKmin
GacBicarNakarviPaKeRKOgbgÁúMminkMNt;edaysþaTiceT. sMrab;karviPaK eKRtUvbegáItm:UEDlEdlman
lkçN³samBaØCag dUcCaeRKOgbgÁúMkMNt;edaysþaTic. enAeBleKkMNt;m:UEDleRKOgbgÁúMehIy karviPaK
eRKOgbgÁúMenaHRtUv)aneKeGayeQμaHfa karviPaKRbEhl (approximate analysis). edayGnuvtþkar
viPaKRbEhl eKGaceFVIkarsikSaKNnabzmelIGgátr; bs;eRKOgbgÁúM ehIyenAeBlEdlkarsikSaKNna
bzmenHcb;sBVRKb; eKGaceFVIkarviPaKeRKOgbgÁMminkMNt;edayviFIEdlmanlkçN³Cak;lak; ehIycug
ú
eRkaykarsikSaKNnaRtUv)anEktMrUveGaymanlkçN³l¥RbesIr. karviPaKRbEhlk¾eFVIeGayeyIg)an
dwgBIkareFVIkarrbs;eRKOgbgÁúMeRkamGMeBIrbs;bnÞúk ehIyvapþl;nUvPaBgayRsYlkñúgkarRtYtBinitülT§pl
énviFICak;lak; elIsBIenHeKGaceRbIvasMrab;viPaKeRKOgbgÁúMminkMNt;edaysþaTicenAeBlEdleKminman
eBlevla fvikar niglT§PaB RKb;RKan;kñúgkarGnuvtþkarviPaKEdlmanlkçN³Cak;lak;Cag.
kñúgn½yTUeTA eyIgRtUvdwgfaviFIviPaKeRKOgbgÁúMRbEhlTaMgGs;manlkçN³samBaØ BIeRBaHeKmin
dwglkçxNÐbnÞúkCak;Esþg ragFrNImaRt kareFVIkarrbs;sMPar³ nigersIusþg;rbs;tMNenARtg;tMN. b:uEnþ
enAkñúgCMBUkenH karviPaKminkMNt;edaysþaTicRtUv)aneKsMedAelIkarviPaKCak;lak; ehIykarviPaKkMNt;
edaysþaTicEdlmanlkçN³samBaØCagRtUv)aneKsMedAelIkarviPaKRbEhl.

viPaKeRKOgbgÁúMminkMNt;edaysþaTicedayviFIRbEhl T.Chhay -214

mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa

&>@> Truss
RbePT truss FmμtaEdleKeRcIneRbIsMrab;BRgwgépÞxagrbs;GKar b¤eRbIsMrab;BRgwgGgát;xagelI
nigGgát;xageRkamrbs;s<anEdlbgðajenAkñúgrUbTI 7-1a ¬emIlrUbTI 3-4¦. enAeBleKeRbIvasMrab;
eKalbMNgEbbenH enaHeKminKitvaCaFatusMxan;sMrab;RTRTg;eRKOgbgÁúMeT ehIyCalT§pleKeRcInviPaK
vaedayviFIRbEhl. enAkñúgkrNIEdl)anbgðaj eKRtUvcMNaMfaRbsinebIeKykGgát;Ggát;RTUgecjBI
panel nImYy²én panel TaMgbI vanwgkøayCa truss kMNt;edaysþaTic. dUcenH vaCa truss minkMNt;eday

sþaTicdWeRkTIbI ¬edayeRbIsmIkar 3-1/ b + r > 2 j b¤16 + 3 > 8(2) ¦ dUcenH eyIgRtUveFVIkarsnμt;cMnYnbI
cMeBaHkMlaMgr)aredIm,Ikat;eFIVeGay truss køayCaeRKOgbgÁúMkMNt;edaysþaTic. karsnμt;enHRtUveFVIeLIg
cMeBaHGgát;RTUgEdlExVgKña EdleKdwgfaenAeBlEdlGgát;Ggát;RTUgmYyrbs; panel CaGgát;rgkMlaMg
Taj enaHGgát;Ggát;RTUgmYyeTotCaGgát;rgkMlaMgsgát;. eyIgeXIjy:agCak;EsþgBIrUbTI 7-1b Edl
kMlaMgkat; panel V RtUv)anTb;Tl;edaybgÁúMkMlaMgTajtamTisQenAkñúgGgát; a nigbgÁúMkMlaMgsgát;
tamTisQrenAkñúgGgát; b . CaTUeTAeKmanviFIkñúgkarviPaKcMnYnBIrEdlGacTTYlyk)an.
viFITI 1³ RbsinebIeKmanbMNgcg;sikSaKNnaeGayGgát;Ggát;RTUgEvg nigRsav eKKYrsnμt;favaminGac
Tb;Tl;nwgkMlaMgsgát; ebImindUecñaHeTvanwggayrgkarekag (buckle). dUcenH kMlaMgkat;
panel RtUv)anTb;Tl;edayGgát;Ggát;RTUgrgkMlaMgTaj cMENkÉGgát;Ggát;RTUgrgkarsgát;

RtUv)ansnμt;CaGgát;kMlaMgsUnü.
viFITI 2³ RbsinebIeKcg;sagsg;Ggát;Ggát;RTUgBImuxkat;hUtekþAFM²dUcCaEdkEdlmanmuxkat;Ekg b¤Edk
Edlmanmuxkat;GkSr C enaHvanwgmanlT§PaBesμIKñakñúgkarTb;Tl;kMlaMgsgát; nigkMlaMgTaj.
sMrab;krNIenH eyIgnwgsnμt;faGgát;Ggát;RTUgrgkMlaMgTaj nigGgát;Ggát;RTUgrgkMlaMgsgát;
Tb;Tl;kMlaMgkat; panel Bak;kNþalesμIKña.
viFIviPaKRbEhlTaMgBIrRtUv)anbgðajCatMélelxenAkñúg]TahrN_xageRkam.

Approximate analysis of statically indeterminate structures T.Chhay -215


]TarhN_ 7-1³ kMNt;kMlaMgenAkñúgGgát;rbs; truss dUcbgðajenAkñúgrUbTI 7-2a ¬edaytMél
RbEhl¦. Ggát;Ggát;RTUgRtUv)ansikSaKNnaeGayTb;Tb;TaMgkMlaMgTaj nigkMlaMgsgát; dUcenHva
RtUv)aneKsnμt;eGayTb;Tl;nwgkMlaMgkat; panel Bak;kNþal. kMlaMgRbtikmμTMrRtUv)anKNnaeGay.

dMeNaHRsay³
tamkarGegát truss enHminkMNt;edaysþaTicdWeRkTI2. eKRtUvsnμt;Ggát;RTUgrgkMlaMgTaj nigGgát;
RTUgrgkMlaMgsgát;cMnYnBIredIm,ITb;Tl;kMlaMgesμIKña eBalKW FFB = FAE = F . sMrab;muxkat; panel
xageqVg ¬rUbTI 7-2b¦ eyIgman
⎛ 3⎞
+ ↑ ∑ Fy = 0 20 − 10 − 2⎜ ⎟ F = 0 F = 8.33kN
⎝5⎠
dUcenH FFB = 8.33kN (T )

FAE = 8.33kN (C )
⎛4⎞
+ ∑M A = 0 − 8.33⎜ ⎟3 + FFE (3) = 0 FFE = 6.67 kN (C )
⎝5⎠
⎛4⎞
+ ∑MF = 0 − 8.33⎜ ⎟3 + FAB (3) = 0 FAB = 6.67 kN (T )
⎝5⎠
BItMN A ¬rUbTI 7-2c¦
⎛3⎞
+ ↑ ∑ Fy = 0 FAF − 8.33⎜ ⎟ − 10 = 0 FAF = 15kN (T )
⎝5⎠
muxkat;bBaÄrxagsþaMrbs; panel RtUv)anbgðajenAkñúgrUbTI 7-2d. eyIg)an


FDB = 8.33kN (T ) FED = 6.67 kN (C )
FEC = 8.33kN (C ) FBC = 6.67kN (T )
elIsBIenH edayeRbIdüaRkamGgÁesrIrbs;tMN D nig E ¬rUbTI 7-2e nig 7-2f¦ eyIg)an
FDC = 5kN (C )

FEB = 10kN (T )

]TarhN_ 7-2³ kMNt;kMlaMgenAkñúgGgát;rbs; truss dUcbgðajenAkñúgrUbTI 7-3a ¬edaytMél
RbEhl¦. snμt;faGgát;Ggát;RTUgEvgRsav dUcenHvanwgminTb;Tl;kMlaMgsgát;eT. kMlaMgRbtikmμTMr
RtUv)anKNnaeGay.

dMeNaHRsay³
tamkarGegát truss enHminkMNt;edaysþaTicdWeRkTI4. eKRtUvsnμt;Ggát;RTUgrgkMlaMgsgát;cMnYnbYnCa
Ggát;kMlaMgsUnü. dUcenH BImuxkat; panel xageqVg ¬rUbTI 7-3b¦ eyIgman
FAI = 0
+ ↑ ∑ Fy = 0 40 − 10 − FJB cos 45o = 0 FJB = 42.4kN (T )

+ ∑M A = 0 − 42.4 sin 45o (5) + FJI (5) = 0 FJI = 30kN (C )



+ ∑MJ = 0 − FAB (5) = 0 FAB = 0
BItMN A / rUbTI 7-3c/
FJA = 40kN (C )
muxkat;bBaÄrrbs; truss Rtg;Ggát; IH / IC / BH nig BC RtUv)anbgðajenAkñúgrUbTI 7-3d. kMlaMg
kat; panel KWV = ∑ Fy = 40 − 10 − 20 = 10kN . eyIgman
FBH = 0
+ ↑ ∑ Fy = 0 40 − 10 − 20 − FIC cos 45o = 0 FIC = 14.1kN (T )

+ ∑MB = 0 − 40(5) + 10(5) − 14.1sin 45 o (5) + FIH (5) = 0 FIH = 40kN (C )

+ ∑MI = 0 − 40(5) + 10(5) + FBC (5) = 0 FBC = 30kN (T )
BItMN B ¬rUbTI 7-3e¦
+ ↑ ∑ Fy = 0 42.4 sin 45 o − FBI = 0 FBI = 30kN (C )

eKGackMNt;kMlaMgenAkñúgGgát;déTeTotedaylkçN³sIuemRTI b:uEnþelIkElg FCH . BItMN C ¬rUbTI 7-
3f¦ eyIgman
+ ↑ ∑ Fy = 0 2( .1sin 45o ) − FCH = 0
14 FCH = 20kN (C )

&>#> kMlaMgbBaÄrenAelIeRKagsMNg; (Vertical loads on Building Frames)
CaerOy² eRKagGKarpSMeLIgedayr:tEdltP¢ab;y:agrwgeTAnwgssr dUcenHeRKOgbgÁúMTaMgmUl
manlT§PaBkan;EtRbesIrkñúgkarTb;Tl;nwgT§iBlrbs;kMlaMgxagEdlbNþalBIbnÞúkxül; nigrBa¢ÜydI.
CaerOy²eKehArcnasm<½n§rwgEbbenHfa building bent dUcbgðajenAkñúgrUbTI 7-4.

enAkñúgkarGnuvtþ visVkreRKOgbgÁúMGaceRbIbec©keTsCaeRcInsMrab;GnuvtþkarviPaK building bent
edayviFIRbEhl. viFInImYy²KWQrelIkaryl;dwgBIrebobEdleRKOgbgÁúMeFVIkareRkamGMeBIrbs;bnÞúk.


bec©keTsmYyKitBicarNaEteTAelIGgát;mYyEdlmanTItaMgenAkñúgtMbn;mYyrbs;eRKOgbgÁúM. eKGacpþl;
PaBdabdl;Ggát;enAkñúgtMbn;EdlrMxattictYcdl;Ggát;EdlenAeRkAtMbn;. b:uEnþ PaKeRcIneKeRcInKitExS
ekagPaBdabrbs;eRKOgbgÁúMTaMgmUl. BIkarBicarNaenH eKGackMNt;cMnucrbt;Rbhak;RbEhl ¬cMnuc
EdlGgát;bþÚrkMeNagrbs;va¦. eKGacBicarNacMnucenHCasnøak; edaysarvamanm:Um:g;sUnüenAkñúgGgát;
Rtg;cMnucrbt;enH. eyIgnwgeRbIKMnitenHedIm,IviPaKkMlaMgenAelIeRKagGKarEdlbNþalBIbnÞúkbBaÄr
ehIyenAkñúgkfaxNÐ 7-5 nig 7-6 manbgðajBIviFIviPaKRbEhlsMrab;eRKagEdlrgkMlaMgTTwgG½kS
¬kMlaMgxag¦.
karsnμt;sMrab;karviPaKRbEhl³ eKmanr:tKMrUEdlmanTItaMgenAkñúg building bent ehIyvargbnÞúkbBaÄr
BRgayesμI dUcbgðajenAkñúgrUbTI 7-5a. ssrTMrenARtg;cMnuc A nig B nwgGnuvtþkMlaMgRbtikmμcMnYnbIeTA
elIr:t dUcenHr:tCaeRKOgbgÁúMminkMNt;edaysþaTicdWeRkTI3 ¬RbtikmμcMnYn 6-smIkarlMnwgcMnYn3¦.
edIm,IeFVIeGayr:tenHkøayCaeRKOgbgÁMúkMNt;edaysþaTic dUcenHkarviPaKRbEhlTamTarkarsnμt;cMnYnbI.
RbsinebIssrrwgxøaMg ¬minmanmMurgVilekItmanenARtg;cMnuc A nig B ehIyExSekagPaBdabsMrab;r:tman
ragdUcbgðajenAkñúgrUbTI 7-5b. edayeRbIviFImYykñúgcMeNamviFIepSg²Edlerobrab;enAkñúgCMBUk 9 rhUt
dl;CMBUk 11 karviPakCak;lak;bgðajfasMrab;krNIcMnucrbt;TaMgenH b¤cMnucm:Um:g;sUnü ekItmanenARtg;
0.21L BITMrnImYy²rbs;va. b:uEnþRbsinebItMNssrenARtg;cMnuc A nig B manlkçN³bt;Ebn enaHr:t

manlkçN³dUcr:tTMrsamBaØ enaHm:Um:g;sUnünwgekItenARtg;TMr ¬rUbTI 7-5c¦. b:uEnþ enAkñúgPaBCak;Esþg
ssrnwgpþl;nUvPaBbt;EbnxøHenARtg;TMr dUcenHeyIgsnμt;fam:Um:g;sUnüekItmanenARtg;cMnucmFümcenøaH
EdnkMNt;TaMgBIr eBalKWenARtg; (0.21L + 0) / 2 ≈ 0.1L BITMrnImYy² ¬rUbTI 7-5d¦. elIsBIenH kar
viPaKCak;lak;elIFñwmEdlTb;Tl;nwgkMlaMgbBaÄrbgðajfaeKGacecalkMlaMgtamG½kSEdlmanenAkñúgr:t.
Cakarsegçb eKGaceFVIm:UEDlr:tEdlmanRbEvg L Car:tTMrsamBaØEdlmanRbEvg 0.8L EdlQr
elIcugrbs;Fñwmkugs‘ulBIrEdlmanRbEvg 0.1L ¬rUbTI 7-5e¦. karsnμt;TaMgbIxageRkamenHRtUv)aneFVI
eLIgsMrab;m:UEDleRKOgbgÁúMenH³
1> r:tmanm:Um:g;Bt;esμIsUnüenAcMgay 0.1L BITMrxageqVg.
2> r:tmanm:Um:g;Bt;esμIsUnüenAcMgay 0.1L BITMrxagsþaM.
3> r:tminTb;Tl;nwgkMlaMgtamG½kS
edayeRbIsmIkarsþaTic eKGacTTYl)ankMlaMgkñgrbs;r:t ehIyeKGaceFVIkarsikSaKNnabzm
ú
BImuxkat;tbs;va. ]TahrN_xageRkambgðajBIkarGnuvtþCatMélelx.



]TarhN_ 7-3³ kMNt;m:Um:g;enARtg;tMN E nigtMN C EdlekItBIGgát; EF nig CD rbs; building
bent enAkñúgrUbTI 7-6a.
dMeNaHRsay³
sMrab;karviPaKRbEhl eKeFVIm:UEDleRKagdUcbgðajenAkñúgrUbTI 7-6b. cMNaMfaElVgkugs‘ulEdlRT
cMENkkNþalrbs;r:tmanRbEvg 0.1L = 0.1(5) = 0.5m . sßanPaBlMnwgTamTarkMlaMgRbtikmμenAxag
cugr:tcMENkkNþalesμInwg 32kN ¬rUbTI 7-6c¦. bnÞab;mkElVgkugs‘ulrgm:Um:g;Rbtikmμ
M = 8(0.25) + 32(0.5) = 18kN .m
m:Um:g;RbEhlEdlmanTisedApÞúyKñamanGMeBIenARtg;tMN E nigtMN C ¬rUbTI 7-6a¦.



&>$> Portal frames nig truss
eRKag³ CaerOy² eKeRbI portal frame sMrab;BIelIRckcUlrbs;s<an nigCaFatuEdlrwgmaMenAkñúgkarsikSa
KNnaGKaredIm,IepÞrkMlaMgtamTisedkEdlGnuvtþenAxagelIbMputrbs;eRKageTARKwH. sMrab;s<an eRKag
enHTb;Tl;nwgkMlaMgEdlbNþalBIxül; rBa¢ÜydI nigbnÞúkcracrN_EdlKμantulüPaBenAelIkMrals<an.
Portal frame CamanTMrsnøak; TMrbgáb; b¤RTedayTMrEdlmanPaBrwgmineBjelj. karviPaKRbEhl

énkrNInImYy²nwgerobrab;sMrab; portal frame samBaØEdlmanGgát;bI.
eRKagEdlmanTMrsnøak;³ Portal frame KMrUEdlmanTMrsnøak;RtUv)anbgðajenAkñúgrUbTI 7-7a. eday
sarvamanGBaØatbYnenARtg;TMr EtvamansmIkarlMnwgEtbI dUcenHvaCaeRKOgbgÁúMminkMNt;edaysþaTic
dWeRkTImYy. Cavi)ak eKRtUveFVIkarsnμt;cMnYnmYyedIm,IeFVIeGayeRKagenHkøayCaeRKOgbgÁúMkMNt;eday
sþaTic.



PaBdabeGLasÞicrbs; portal frame RtUv)anbgðajenAkñúgrUbTI 7-7b. düaRkamenHbgðajfa
cMnucrbt;Edlm:Um:g;bþÚrBIviC¢maneTAGviC¢manmanTItaMgenAEk,rcMnuckNþalrbs;r:t ¬edaytMélRbEhl¦.
edaysarm:Um:g;enAkñúgr:tesμIsUnüenARtg;cMnucenH eyIgGacsnμt;famansnøak;enARtg;kEnøgenaH ehIy
bnÞab;mkeyIgkMNt;kMlaMgRbtikmμenARtg;TMredayeRbIsmIkarsþaTic. enAeBlEdleyIgKNnarYcehIy
eyIgeXIjfakMlaMgRbtikmμtamTisedk ¬kMlaMgkat;¦ enARtg;Kl;rbs;ssrnImYy²esμIKña ehIyRbtikmμ
déTeTotRtUv)anbgðajenAkñúgrUbTI 7-7c. elIsBIenH düaRkamm:Um:g;sMrab;eRKagenHRtUv)anbgðajenA
kñúgrUbTI 7-7d.
eRKagEdlmanTMrsnøak;³ Portal frame KMrUEdlmanTMrbgáb;BIr ¬rUbTI 7-8a¦ CaeRKOgbgÁúMminkMNt;
edaysþaTicbIdWeRk edaysarvamanGBaØatcMnYn6 enARtg;TMrrbs;va. RbsinebIGgát;bBaÄrmanRbEvg nig
RkLaépÞmuxkat;esμIKña enaHeRKagnwgxUcRTg;RTaydUcbgðajenAkñúgrUbTI 7-8b. sMrab;krNIenH eyIgnwg
snμt;cMnucrbt;ekItmanenARtg;cMnuckNþalrbs;Ggát;TaMgbI dUcenHeyIgGacdak;snøak;enARtg;cMnucTaMg
enaH. dUcenHeKGackMNt;kMlaMgRbtikmμTMr nigsg;düaRkamm:Um:g;Bt;sMrab;Ggát;nImYy²edaypþac;Ggát;
TaMgenHecjBIeRKagenARtg;snøak; ehIyGnuvtþsmIkarlMnwgeTAelIEpñkTaMgbYnenaH. lT§plRtUv)an
bgðajenAkñúgrUbTI 7-8c. cMNaMfa enAkñúgkrNI portal frame EdlP¢ab;edaysnøak; kMlaMgRbtikmμtam


Tisedk ¬kMlaMgkat;¦ enARtg;Kl;rbs;ssrnImYy²mantMélesμIKña. düaRkamm:Um:g;Bt;sMrab;eRKagenH
RtUv)anbgðajenAkñúgrUbTI 7-8d.

eRKagEdlmanTMrmanPaBrwgmaMmineBjelj³ edaysareKBi)ak ehIycMNayfvikareRcInkñúgkarsag
sg;RKwH b¤TMrbgáb;sMrab; portal frame eKGacsnμt;eGaymanmMurgViltictYcenARtg;TMr ¬rUbTI 7-9a¦.
CalT§pl cMnucrbt;enAelIssrsßitenAcenøaHkrNI portal frame EdlmanTMrsnøak; ¬rUbTI 7-7a¦
EdlcMnucrbt;rbs;vasßitenARtg;TMr ¬Kl;ssr¦ nigkrNI portal frame EdlmanTMrbgáb; ¬rUbTI 7-8a¦
EdlcMnucrbt;sßitenARtg;cMnuckNþalrbs;ssr. visVkrCaeRcIn)ankMNt;TItaMgcMnucrbt;rbs; portal
frame EdlmanTMrmanPaBrwgmaMmineBjeljenARtg;cMgay h / 3 BIKl;ssr ¬rUbTI 7-9b¦ dUcenHeK

RtUvdak;snøak;enARtg;cMnucenaH ehIysMrab;r:tKWsßitenAkNþalElVg.
Truss³ enAeBleKeRbI portal frame sMrab;cMgayElVgEvg eKGaceRbI truss CMnYseGayr:t. eKeRbIrcna

sm<½n§EbbenHsMrab;s<anEdlmanElVgEvg² nigsMrab; bent TTwgénsalshkILa nigGKareragcRk.
]TahrN_KMrURtUv)anbgðajenAkñúgrUbTI 7-10a. enAkñúgkrNITaMgGs; eKsnμt;eGay truss tP¢ab;eTAnwg



ssredaytMNsnøak;. elIsBIenH truss rkSassreGayQrRtg;enAkñúgtMbn;EdltP¢ab; enAeBlEdl
portal truss rgnUv sidesway Δ ¬rUbTI 7-10b¦. Cavi)ak eyIgGacviPaK portal frame EdleRbI truss

edayeRbIkarsnμt;dUcKñanwgkarviPaK portal frame samBaØ. sMrab;ssrEdlmanTMrsnøak; snμt;kMlaMg
RbtikmμtamTisedk ¬kMlaMgkat;¦ esμIKña dUcenAkñúgrUbTI 7-7c. sMrab;ssrEdlmanTMrbgáb; snμt;
kMlaMgRbtikmμtamTisedkesμIKña ehIycMnucrbt; ¬b¤snøak;¦ ekItmanenAelIssrnImYy² EdlsßitenABak;
kNþalssrcenøaHKl;ssreTAcMnucTabCageKéntMNrvagGgát; truss eTAnwgssr ¬emIlrUbTI 7-8c
nig 7-10b¦.
]TahrN_xageRkambgðajBIrebobkMNt;kMlaMgenAkñúgGgát;rbs; portal frame EdleRbI truss
edayeRbIviFIviPaKRbEhlEdl)anerobrab;xagelI.



]TarhN_ 7-4³ kMNt;m:Um:g;enARtg;tMN E nigtMN C EdlekItBIGgát; EF nig CD rbs; building
bent enAkñúgrUbTI 7-6a.



dMeNaHRsay³
Ggát; truss B / C / F / G eFVIkarCaGgát;rwg. edaysarTMrrbs;vaCaTMrbgáb; enaHeKsnμt;facMnucrbt;
sßitenARtg; 7m / 2 = 3.5m BIelIcMnuc A nig I ehIykMlaMgRbtikmμtamTisedk ¬b¤kMlaMgkat;¦eFVIGMeBI
enARtg;Kl;ssrmantMélesμIKña eBalKW ∑ Fx = 0 / V = 40kN / 2 = 20kN . CamYynwgkarsnμt;TaMg
enH eyIgGacpþac;eRKOgbgÁúMenARtg;snøak; J nig K ¬rUbTI 7-11b¦ ehIykMNt;RbtikmμenARtg;Kl;
ssrdUcxageRkam³
Bak;kNþalxageRkamrbs;ssr³
+ ∑MA = 0 M − 3.5(20 ) = 0 M = 70kN .m
EpñkxagelIrbs;ssr³
+ ∑MJ = 0 − 40(5.5) + N (8) = 0 N = 27.5kN
edayeRbIviFImuxkat; ¬rUbTI 7-11c¦ eyIgGacbnþkarviPaKedIm,ITTYl)ankMlaMgenAkñúgGgát; CD / BD
nig BH .
↑ + ∑ Fy = 0 − 27.5 + FBD sin 45o = 0 FBD = 38.9(T )

+ ∑MB = 0 − 20(3.5) − 40(2) + FCD (2) = 0 FCD = 75kN (C )

+ ∑MD = 0 FBH (2 ) − 20(5.5) + 27.5(2 ) = 0 FBH = 27.5kN (T )
tamrebobdUcKña bgðajfaeKTTYllT§pldUcenAkñúgdüaRkamGgÁesrIrbs;ssr FGI enAkñúgrUbTI 7-
11d. edayeRbIlT§plenH eyIgGacrkkMlaMgkñúgrbs;Ggát; truss nImYy²rbs; portal truss eday
eRbIviFItMN.
tMN D rUbTI 7-11e
+ ↑ ∑ Fy = 0 FDH sin 45o − 38.9 sin 45o = 0 FDH = 38.9kN (C )

( )
+
→ ∑ Fx = 0 75 − 2 38.9 cos 45 o − FDE = 0 FDE = 20kN (C )
tMN H rUbTI 7-11f
+ ↑ ∑ Fy = 0 FHE sin 45o − 38.9 sin 45o = 0 FHE = 38.9kN (T )

lT§plTaMgenHRtUv)ansegçbenAkñúgrUbTI 7-11g.



&>%> bnÞúkxagmanGMeBIelIeRKagsMNg;³ Portal method
(Lateral load on building frame: Portal method)
enAkñúgkfaxNÐ 7.4 manerobrab;BIGMeBIrbs;bnÞúkTTwgG½kS b¤kMlaMgxag (lateral load) enAelI
portal frame ehIyeyIgeXIjfaeRKagEdlmanTMrbgáb;mancMnucrbt;enAEk,rBak;kNþalkMBs;rbs;ssr

nigBak;kNþalrbs;FñwmnImYy² ehIyssrrgnUvkMlaMgkat;TTwgesμIKña ¬rUbTI 7-8¦. Building bent xUc
RTg;RTayRsedogKñanwg portal frame Edr ¬rUbTI 7-12a¦ dUcenHeKGacsnμt;facMnucrbt;ekItmanenA
Rtg;cMnuckNþalrbs;ssr nigFñwm. RbsinebIeyIgKitfa bent nImYy²rbs;eRKagpÁúMeLIgeday portal Ca
eRcIn ¬rUbTI 7-12b¦ enaHeKGacsnμt;bnþeTotfassrxagkñúgtMNageGayssrrbs; portal frame
cMnYnBIr dUcenHfaRtUvrgkMlaMgkat;TTwg V BIrdgénssrxageRkA.

Casegçb viFI portal sMrab;karviPaKeRKagGKarEdlmanTMrbgáb;TamTarkarsnμt;dUcxageRkam³
1> snøak;RtUv)andak;enARtg;cMnuckNþalr:t edaysareKsnμt;cMnucenHCacMnucEdlmanm:Um:g;sUnü.
2> snøak;RtUv)andak;enARtg;cMnuckNþalssrnImYy² edaysarvaCacMnucEdlmanm:Um:g;sUnü.
3> enARtg;nIv:UkMral kMlaMgkat;enARtg;snøak;ssrxagkñμúgesμIwnwgBIrdgénsnøak;ssrxageRkA
edaysareKBicarNaeRKagCa portal RtYtelIKña.
karsnμt;TaMgenHpþl;nUvlT§PaBRKb;RKan;kñúgkareFVIeGayeRKagminkMNt;edaysþaTiceTACaeRKag
kMNt;edaysþaTicEdlmansßirPaBeRkamGMeBIénbnÞúk.
edayeRbobeFobCamYynwgkarviPaKeRKagminkMNt;edaysþaTicEdlmanlkçN³Cak;lak; viFI
portal manlkçN³saksmkñúgkareRbIR)as;sMrab;viPaKeRKagEdlmannIv:UTab nigmanElVgeRKagesμIKña.

mUlehtuénkarsnñidæanEbbenH)anBIskmμPaBrbs;rcnasm<½n§eRkamGMeBIrbs;bnÞúk. edIm,IeFVIkarbk
Rsay cUrBicarNaeRKagEdleFVIkardUcFñwmkugs‘ulEdlRtUv)anbgáb;eTAnwgdI. rMlwkBIemkanicénsMPar³
(mechanics of materials) eyIgeXIjfakñúgkarsikSaKNnaFñwmxøI lT§PaBTb;kMlaMgkat;mansar³sMxan;


Cag pÞúymkvijsMrab;karsikSaKNnaFñwmEvglT§PaBTb;nwgm:Um:g;Bt;mansar³sMxan;Cagvijmþg ¬emIl
kfaxNÐ 7.6¦. viFI portal QrelIkarsnμt;EdlTak;TgeTAnwgkMlaMgdUcEdl)anerobrab;enAkñúgcMnucTI3
xagelI.
]TahrN_xageRkambgðajBIrebobénkarGnuvtþviFI portal eTAelIkarviPaK building bent.

]TarhN_ 7-5³ kMNt;kMlaMgRbtikmμenARtg;Kl;ssrrbs;eRKagEdlbgðajenAkñúgrUbTI 7-13a
edaytMélRbEhl. eRbIviFI portal sMrab;viPaKeRKagenH.

dMeNaHRsay³
edayGnuvtþkarsnμt;BIrdMbUgrbs;viFI portal, eyIgdak;snøak;enARtg;kNþalr:t nigssrrbs;eRKag ¬rUbTI
7-13a¦. kat;eRKagtamssrRtg;snøak; I / J / K nig L eyIgnwg)andüaRkamGgÁesrIdUcbgðajenA
kñúgrUbTI 7-13b. enATIenH Gnuvtþkarsnμt;TIbIcMeBaHkMlaMgkat;enAelIssr. enaHeyIg)an
+
→ ∑ Fx = 0 6 − 6V = 0 V = 1kN
edayeRbIlT§plenH eyIgGacbnþkarviPKedaybMEbkeRKagenARtg;snøak;TaMgGs; ehIyKNnakMlaMg
Rbtikmμrbs;va. tamc,ab;TUeTA eKRtUvcab;epþImkarviPaKenHenARtg;tMNcugxagelIeKEdlmanrgGMeBIén
kMlaMgtamTisedk. dUcenH düaRkamGgÁesrIrbs;kMNat; IBM RtUv)anbgðajenAkñúgrUbTI 7-13c. eK


kMNt;bgÁúMkMlaMgRbtikmμTaMgbI I y / M x nig M y enARtg;tMNedayeRbIsmIkar ∑ M M = 0 / ∑ Fx = 0
nig ∑ Fy = 0 erogKña. bnÞab;mk eKRtUveFVIkarviPaKkMNat;EdlenAEk,rKWkMNat; MJN ¬rUbTI 7-13d¦
ehIybnþedaykMNat; NKO ¬rUbTI 7-13e¦ ehIycugeRkayKWkMNat; OGL ¬rUbTI 7-13f¦. eday
eRbIlT§plTaMgenH düaRkamGgÁesrIrbs;ssrCamYynwgkMlaMgRbtikmμTMrrbs;vaRtUv)anbgðajenAkñúg
rUbTI 7-13g.

edaytMélRbEhl. eRbIviFI portal sMrab;viPaKeRKagenH.



dMeNaHRsay³
snøak;TImYyRtUv)andak;enARtg;cMnuckNþalrbs;r:t nigssrrbs;eRKag ¬rUbTI 7-14a¦. eKkat;eRKag
enHtambøg;edkRtg;snøak; O / P / Q nig J / K / L enaHeyIgTTYl)andüaRkamGgÁesrIEdlbgðajenA
kñúgrUbTI 7-14b. eKKNnakMlaMgkat;rbs;ssrdUcxageRkam³
+
→ ∑ Fx = 0 20 − 4V = 0 V = 5kN
+
→ ∑ Fx = 0 20 + 30 − 4V ' = 0 V ' = 12.5kN
edayeRbIlT§plTaMgenH eyIgGacbnþkarviPaKeTAelIEpñknImYy²rbs;eRKag. eKcab;epþImkarviPaK
CamYynwgkMNat;cugEKmxagelIEdlmanrgbnÞúktamTisedk OGR ¬rUbTI 7-14c¦. eKkMNt;GBaØat
O y / R x nig R y edayeRbIsmIkarlMnwg. CamYynwglT§plenH eKbnþkarviPaKeTAelIkMNat; OJM

¬rUbTI 7-14d¦ bnÞab;mkeTotkMNat; JA ¬rUbTI 7-14e¦ kMNat; RPS ¬rUbTI 7-14f¦ kMNat;
PMKN ¬rUbTI 7-14g¦ nigkMNat; KB ¬rUbTI 7-14h¦. ]TahrN_enHbBa©b;edaykarviPaKeTAelI

kMNat; SIQ bnÞab;mkeTAelIkMNat; QNL nigcugeRkay LC ehIyeyIgeXIjfa C x = 12.5kN /
C y = 15.625kN nig M C = 37.5kN .m .

&>^> bnÞúkxagmanGMeBIelIeRKagsMNg;³ Cantilever method
(Lateral load on building frame: Cantilever method)
viFI cantilever QrelIkareFVIkardUcFñwmkugs‘ulEdlrgkMlaMgTTwgG½kS. rMlwkBIemkanicén
sMPar³fabnÞúkbegáItkugRtaMgBt;enAkñúgFñwmEdlERbRbYlCalkçN³bnÞat;BIG½kSNWtrbs;Fñwm ¬rUbTI 7-
15a¦. tamrebobdUcKña bnÞúkxagEdlmanGMeBIelIeRKagcg;eFVIeGayeRKagRkLab; b¤eFVIeGayFñwmvil
CMuvijG½kSNWtEdlsßitenAkñúgbøg;edkEdlkat;tamssrenARtg;nIv:UkMralnImYy². edIm,IRbqaMgnwgkar
RkLab;enH kMlaMg ¬b¤kugRtaMg¦tamG½kSenAkñúgssrCakMlaMgTajenAelIRCugmçagrbs;G½kSNWt ehIy
kMlaMgsgát;enAelIRCugmçageTot ¬rUbTI 7-15b¦. dUcKñanwgFñwmkugs‘ul eKGacsnμt;fakugRtaMgtamG½kS
ERbRbYlCalkçN³bnÞat;BITIRbCMuTMgn;rbs;RkLaépÞssr b¤BIG½kSNWtrbs;ssr. dUcenHviFI cantilever
manlkçN³smRsb RbsinebIeRKagmankMNt;x<s; nigRsav b¤ssrmanRkLaépÞmuxkat;xusKña.
Cakarsegçb edIm,IeRbIviFI cantilever eKRtUvGnuvtþkarsnμt;xageRkameTAelIeRKagEdlmanTMr
bgáb;³
1> eKRtUvdak;snøak;enARtg;Bak;kNþalr:tnImYy² edaysareKRtUvsnμt;vaCacMnucm:Um:g;sUnü.
2> eKRtUvdak;snøak;enARtg;Bak;kNþalssrnImYy² edaysareKRtUvsnμt;vaCacMnucm:Um:g;sUnü.


3> kugRtaMgtamG½kSenAkñúgssrRtUvsmamaRteTAnwgcMgayBITIRbCMuTMgn;rbs;RkLaépÞrbs;ssr
enARtg;nIv:Urbs;kMral. edaysarkugRtaMgesμInwgkMlaMgelIRkLaépÞ enaHsMrab;krNIBiessEdl
manssrmanRkLaépÞmuxkat;dUcKña kMlaMgenAkñúgssrRtUvsmamaRteTAnwgcMgayBITIRbCMuTMgn;
énRkLaépÞmuxkat;ssr.
karsnμt;TaMgbIenHeFVIeGayeRKagkøayCaeRKagEdlmansßirPaB nigkMNt;edaysþaTic. ]TahrN_xag
eRkambgðajBIrebobGnuvtþviFI cantilever kñúgkarviPaK building bent.

edaytMélRbEhl. eKsnμt;fassrmanmuxkat;esμIKña. eRbIviFI cantilever sMrab;viPaKeRKagenH.
dMeNaHRsay³
dMbUgeKdak;snøak;enARtg;Bak;kNþalkMBs;ssr nigBak;kNþalElVgrbs;r:t. TItaMgrbs;cMnucTaMgenH
RtUv)anbgðajBIGkSr G rhUtdl;GkSr L ¬rUbTI 7-16a¦. eKGackMNt;TIRbCMuTMgn;rbs;RkLaépÞssr
TaMgGs;edaykarGegát ¬rUbTI 7-16b¦ b¤edaykarviPaKxageRkam³
∑ ~ A 0( A ) + 6( A )
x
x= = = 3m
∑A A+ A
dUcenHkMlaMgtamG½kSenAkñúgssrnImYy²smamaRteTAnwgcMgayrbs;vaBIcMnucenH. dUcenH muxkat;tam
snøak; H nig K énCan;xagelIRtUv)anbgðajCadüaRkamGgÁesrIenAkñúgrUbTI 7-16c. cMNaMfassrenA
xageqVgcMnucTIRbCMuTMgn;rgkarTaj ÉssrmçageTotrgkarsgát;. karrgkMlaMgEbbenHmansar³sMxan;
Nas;kñúgkarTb;Tl;nwgkarRkLab;EdlbgáeLIgedaykMlaMg 30kN . edayeFVIplbUkm:Um:g;Rtg;G½kSNWt
eyIg)an


+ ∑M = 0 − 30(2) + 3H y + 3K y = 0

GBaØatGacTak;TgeTAnwgRtIekaNdUc ¬rUbTI 7-16c¦ Edl
Hy Ky
3
=
3
b¤ H y = K y
dUcenH H y = K y = 10kN

tamrebobKNnadUcKña edaykat;eRKagtamsnøak; G nig L ¬rUbTI 7-16d¦ eyIgman
+ ∑M = 0 − 30(6) − 15(2) + 3G y + 3L y = 0
Gy Ly
edaysar 3
=
3
b¤ G y = Ly enaH
G y = L y = 35kN

eKGacviPaKkMNat;eRKagnImYy²edayeRbIlT§plxagelI. dUcenAkñúg]TarhN_ 7-5 nig 7-6/ eyIg
cab;epþImCamYynwgkMNat;eRKagcugxagelIeKbMputEdlrgbnÞúkxag eBalKWkMNat;eRKag HCI ¬rUbTI 7-
16a¦. edayGnuvtþsmIkarlMnwgTaMgbI ∑ M I = 0 / ∑ Fx = 0 / ∑ Fy = 0 eyIgnwgTTYl)anlT§pl
sMrab; H x / I x nig I y erogKña EdlbgðajenAelIdüaRkamGgÁesrIenAkñúgrUbTI 7-16e. edayeRbIlT§pl
TaMgenH eKGacviPaKkMNat;eRKag IDK ¬rUbTI 7-16f¦ EdlbnþedaykMNat;eRKag HJG ¬rUbTI 7-
16g¦ bnÞab;mkviPaKkMNat;eRKag KJL ¬rUbTI 7-16h¦ nigcugeRkayviPaKkMNat;eRKagEpñkxageRkam
rbs;ssr ¬rUbTI 7-16i nig 7-16j¦.

]TarhN_ 7-8³ bgðajBIrebobkMNt;kMlaMgRbtikmμenARtg;Kl;ssrrbs;eRKagEdlbgðajenAkñúgrUbTI
7-17a edaytMélRbEhl. ssrmanmuxkat;dUcbgðajenAkñúgrUbTI 7-17b. eRbIviFI cantilever
sMrab;viPaKeRKagenH.
dMeNaHRsay³
dMbUg eKsnμt;famansnøak;enARtg;kNþalElVgrbs;r:t nigBak;kNþalkMBs;rbs;ssr ¬rUbTI 7-17a¦.
eKkMNt;TIRbCMuTMgn;rbs;RkLaépÞmuxkat;ssrTaMgGs;BIrUbTI 7-17b dUcbgðaxageRkam³
∑ ~A 0(6250 ) + 6(5000 ) + 10.5(3750 ) + 18(6250 )
x
x= = = 8.559m
∑A 6250 + 5000 + 3750 + 6250
enATIenH ssrmanmuxkat;xusKña dUcenHkugRtaMgtamG½kSenAkñúgssrRtUvsmamaRteTAnwgcMgayrbs;va
BIG½kSTIRbCMuTMgn;EdlmanTItaMgenARtg; x = 8.56m . dUcenH edaykat;eRKagtambøg;Rtg;snøak; L / M /
N / O eKTTYl)andüaRkamGgÁesrIdUcbgðajenAkññúgrUbTI 7-17c. cMNaMfassrenAxageqVgG½kSTIRbCMu



TMgn;rgkugRtaMgTaj ehIyssrEdlenAxagsþaMrgkugRtaMgsgát;. ehtuGVI? edayeFVIplbUkm:Um:g;Rtg;
G½kSNWteyIg)an
+ ∑M = 0 − 36(1.8) + L y (8.56) + M y (2.56) + N y (1.94) + O y (9.44) = 0 (1)

edaysarssrnImYy²mankugRtaMg σ smamaRteTAnwgcMgayBIG½kSNWt eyIgGaceFVITMnak;TMng
kugRtaMgssredayRtIekaNdUc. edaysMEdgTMnak;TMngTaMgenHeTAnwgkMlaMg L y eyIg)an
2.56 My 2.56 ⎛ L y ⎞
σM = σL = ⎜ ⎟ M y = 0.239 L y (2)
8.56 5000 8.56 ⎜ 6250 ⎟
⎝ ⎠
1.94 Ny 1.94 ⎛ L y ⎞
σN = σL = ⎜ ⎟ N y = 0.136 L y (3)
8.56 3750 8.56 ⎜ 6250 ⎟
⎝ ⎠
9.44 Oy 9.44 ⎛ L y ⎞
σO = σL = ⎜ ⎟ O y = 1.103L y (4)
8.56 6250 8.56 ⎜ 6250 ⎟
⎝ ⎠
edayedaHRsaysmIkar (1)-(4) eyIg)an
L y = 3.26kN M y = 0.78kN N y = 0.44kN O y = 3.60kN



edayeRbIviFIdUcKña bgðajfaeKGacTTYl)anlT§plenAkñúgrUbTI 7-17d sMrab;ssrenARtg;snøak; E /
F / G nig H .

eyIgGacbnþkarviPaKkMNat;eRKagnImYy². dUcenAkñúg]TahrN_elIkmun eyIgcab;epþImCamYynwg
kMNat;eRKagcugxagelIeKKWkMNat;eRKag LP ¬rUbTI 7-17e¦. edayeRbIlT§plEdl)anKNna eKGac
viPaKkMNat;eRKag LEI ¬rUbTI 7-17f¦ EdlbnþedaykMNat;eRKag EA ¬rUbTI 7-17g¦. eKGacbnþ
karviPaKkMNat;eRKagdéTeTottamlMdab;lMeday eBalKW PQM bnÞab;mk MJFI bnÞab;mk FB nigbnþ
bnÞab;.



cMeNaT
7>1> kMNt;kMlaMgenAkñúgGgát;nImYy²rbs; truss
¬edaytMélRbEhl¦. snμt;Ggát;Ggát;RTUgGac
Tb;Tl;TaMgkMlaMgTaj nigkMlaMgsgát;.

éncMeNaT 7>5> ¬edaytMélRbEhl¦. snμt;
Ggát;Ggát;RTUgminGacTb;Tl;nwgkMlaMgTajeT.
7>2> kMNt;kMlaMgenAkñúgGgát;nImYy²rbs; truss ¬edaytMélRbEhl¦. snμt;Ggát;Ggát;RTUgGac
éncMeNaT 7>1> ¬edaytMélRbEhl¦. snμt; Tb;Tl;TaMgkMlaMgTaj b¤kMlaMgsgát;.
Ggát;Ggát;RTUgminGacTb;Tl;nwgkMlaMgTajeT.
Tb;Tl;TaMgkMlaMgTaj b¤kMlaMgsgát;.

7>8> kMNt;m:Um:g;Bt;edaytMélRbEhlenARtg;
cMnuc F nig D rbs;eRKag.

7>4> edaHRsaycMeNaT 7>3 edaysnμt;faGgát;
Ggát;RTUgminGacTb;Tl;nwgkMlaMgsgát;eT.
Tb;Tl;TaMgkMlaMgTaj b¤kMlaMgsgát;.

cMeNaT T.Chhay -236


7>9> kMNt;m:Um:g;Bt;edaytMélRbEhlenARtg;
tMN E nig C EdlekItBIGgát; EF nig CD erog
Kña.

7>12> kMNt;m:Um:g;Bt; nigkMlaMgkat;edaytMél
RbEhlenARtg;xagcugrbs;Ggát;nImYy²rbs;
portal frame. snμt;faTMrenARtg; A nig D CaTMr

bgáb;mineBjelj ehtudUcenHcMnucrbt;manTItaMg
7>10> kMNt;kMlaMgRbtikmμTMrenARtg; A / B enAcMgay h / 3 BIKl;rbs;ssrnImYy².
nig C rbs;eRKag.

7>11> kMNt;m:Um:g;Bt;edaytMélRbEhlenARtg; 7>13> kMNt;m:Um:g;Bt;edaytMélRbEhlenARtg;
tMN I nig L . ehIy kMNt;m:Um:g;Bt;enARtg; tMN D nig C . snμt;TMrenARtg; A nig D CaTMr
tMN H EdlbNþalmkBIGgát; HG . snøak;.

Problems T.Chhay -237


kMNt;kMlaMgenAkñúgGgát;BRgwg CF .

7>16> edaHRsaycMeNaT 7>15 RbsinebIeK
7>14> kMNt;m:Um:g;Bt; nigkMlaMgkat;edaytMél CMnYsTMr A nigTMr B BITMrbgáb;mkCaTMrsnøak;.
RbEhlenARtg;xagcugrbs;Ggát;nImYy²rbs; 7>17> sg;düaRkamm:Um:g;edaytMélRbEhl
portal frame. snμt;faTMrenARtg; A nig D Ca sMrab;ssr ACE rbs; portal frame. snμt;
(a) TMrsnøak; (b) TMrbgáb; nig (c) TMrbgáb;mineBj faGgát;rbs; truss TaMgGs;tP¢ab;eTAnwgssr
eljEdleFVIeGaycMnucrbt;rbs;vasßitenAcMgay edaytMNsnøak;enAxagcugrbs;va. ehIycUr
h / 3 = 2m BIcMnuc A nig D . kMNt;kMlaMgenAkñúgGgát; EG / CG nig EF .

7>18> edaHRsaycMeNaT 7>17 RbsinebIeK
CMnYsTMr A nigTMr B BITMrbgáb;mkCaTMrsnøak;.
7>15> sg;düaRkamm:Um:g;edaytMélRbEhl
7>19> kMNt;kMlaMgkñúgrbs;Ggát; truss nImYy²
sMrab;ssr ACE rbs; portal frame Edlsg;
rbs; portal frame. ehIycUrkMNt;kMlaMgRbti-
edayeRbIr:trwgCamYynwgGgát;BRgwg CF nig DH .
kmμTMrenARtg;TMrbgáb; A nig B . snμt;faGgát;
snμt;fatMNTaMgGs;CatMNsnøak;. ehIycUr
rbs; truss TaMgGs;tP¢ab;KñaedaytMNsnøak;.
cMeNaT T.Chhay -238


kmμTMrenARtg;TMrbgáb; A nig B . snμt;faGgát; 7>22> kMNt;kMlaMgkñúgrbs;Ggát; truss nImYy²
rbs; truss TaMgGs;tP¢ab;KñaedaytMNsnøak;. rbs; portal frame. snμt;faGgát; rbs; truss
TaMgGs;tP¢ab;KñaedaytMNsnøak; ehIyTMr A nig
B CaTMrbgáb;.

7>21> kMNt;kMlaMgkñúgrbs;Ggát; truss nImYy² kmμTMrenARtg;TMrbgáb; A nig B . snμt;faGgát;
rbs; portal frame. ehIycUrkMNt;kMlaMgRbti- rbs; truss TaMgGs;tP¢ab;KñaedaytMNsnøak;.
kmμTMrenARtg;TMrsnøak; A nig B . snμt;faGgát;
rbs; truss TaMgGs;tP¢ab;KñaedaytMNsnøak;.



sMrab;r:t IJKL rbs;eRKagGKaredayeRbI portal
method.

7>24> eRbI portal method cUrkMNt;kMlaMgRbti-
kmμTMrenARtg;TMrbgáb; A / B / C / D nig E 7>28> sg;düaRkamm:Um:g;edaytMélRbEhl
rbs;eRKag edaytMélRbEhl. sMrab;r:t IJKL rbs;eRKagGKarxagelIedayeRbI
cantilever method. ssrTaMgGs;manmuxkat;

dUcKña.
sMrab;r:t IJKL rbs;eRKagGKaredayeRbI portal
method.
7>25> eRbI portal method cUrkMNt;kMlaMgRbti-
kmμTMrenARtg;TMrbgáb; A / B / C nig D rbs;
eRKag edaytMélRbEhl.

7>26> sg;düaRkamm:Um:g;edaytMélRbEhl 7>30> edaHRsaycMeNaT 7>29 edayeRbI
sMrab;r:t EFGH rbs; portal frame xagelI cantilever method. ssrnImYy²manmuxkat;
edayeRbI portal method. dUcbgðaj.

cMeNaT T.Chhay -240


7>31> eRbI portal method cUrkMNt;kMlaMgtam
G½kS kMlaMgkat; nigm:Um:g;Bt;enARtg; A eday
tMélRbEhl.

7>32> edaHRsaycMeNaT 7>31 edayeRbI
cantilever method. ssrnImYy²manmuxkat;

dUcbgðaj.
KMerag 7>1> Building bent EdlbgðajenAkñúg
rUbmanKMlat 3m BIKña ehIyRtUv)ansnμt;favaman
TMrsnøak;TaMgGs;. eRbIm:UEDldUcbgðaj cUrkMNt;
bnÞúkxül;EdlmanGMeBIelI bent. cMNaMfabnÞúk
xül;RtUv)anepÞrBICBa¢aMgeTA purlin TaMgbYn ehIy
bnÞab;mkvaRtUv)anepÞreTAssrEpñkxagsþaM.
edayeRbIkarviPaKRbEhl cUrkMNt;bnÞúktam
G½kSGtibrma nigm:Um:g;Bt;GtibrmaenAkñúgssr
AB . snμt;fassr nigGgát;BRgwgRtUv)antP¢ab;

edaytMNsnøak;enAxagcugrbs;va. GKarenHsßit
enAelITIvalrabesμIenAkñúgrdæ New orleans,
Louisiana Edlman V = 56m / s nig yk

I = 0.87 .


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