Department of Civil Engineering                                                               NPIC




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mhaviTüal½ysMNg;sIuvil                                                     viTüasßanCatiBhubec©keTskm<úCa


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Department of Civil Engineering                                                               NPIC



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mhaviTüal½ysMNg;sIuvil                                                                  viTüasßanCatiBhubec©keTskm<úCa


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Department of Civil Engineering                                                                           NPIC



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mhaviTüal½ysMNg;sIuvil                                                  viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                         NPIC




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mhaviTüal½ysMNg;sIuvil                                                 viTüasßanCatiBhubec©keTskm<úCa




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Department of Civil Engineering                                                            NPIC




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mhaviTüal½ysMNg;sIuvil                                                viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                           NPIC




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mhaviTüal½ysMNg;sIuvil                                            viTüasßanCatiBhubec©keTskm<úCa


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Department of Civil Engineering                                                                            NPIC



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mhaviTüal½ysMNg;sIuvil                                                  viTüasßanCatiBhubec©keTskm<úCa


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Department of Civil Engineering                                                              NPIC



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mhaviTüal½ysMNg;sIuvil                                                viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                             NPIC



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mhaviTüal½ysMNg;sIuvil                                               viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                             NPIC




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mhaviTüal½ysMNg;sIuvil                                                   viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                                                  NPIC




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mhaviTüal½ysMNg;sIuvil                                              viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                          NPIC



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mhaviTüal½ysMNg;sIuvil                                           viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                                 NPIC



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mhaviTüal½ysMNg;sIuvil                                                viTüasßanCatiBhubec©keTskm<úCa




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Department of Civil Engineering                                                          NPIC



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mhaviTüal½ysMNg;sIuvil                            viTüasßanCatiBhubec©keTskm<úCa

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7. approximate analysis of statically indeterminate structures

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7. approximate analysis of statically indeterminate structures

  1. 1. 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
  2. 2. 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
  3. 3. Department of Civil Engineering NPIC ]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 viPaKeRKOgbgÁúMminkMNt;edaysþaTicedayviFIRbEhl T.Chhay -216
  4. 4. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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 ) Approximate analysis of statically indeterminate structures T.Chhay -217
  5. 5. Department of Civil Engineering NPIC + ∑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. viPaKeRKOgbgÁúMminkMNt;edaysþaTicedayviFIRbEhl T.Chhay -218
  6. 6. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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. Approximate analysis of statically indeterminate structures T.Chhay -219
  7. 7. Department of Civil Engineering NPIC ]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¦. viPaKeRKOgbgÁúMminkMNt;edaysþaTicedayviFIRbEhl T.Chhay -220
  8. 8. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa &>$> 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. Approximate analysis of statically indeterminate structures T.Chhay -221
  9. 9. Department of Civil Engineering NPIC 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 viPaKeRKOgbgÁúMminkMNt;edaysþaTicedayviFIRbEhl T.Chhay -222
  10. 10. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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 Approximate analysis of statically indeterminate structures T.Chhay -223
  11. 11. Department of Civil Engineering NPIC 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. viPaKeRKOgbgÁúMminkMNt;edaysþaTicedayviFIRbEhl T.Chhay -224
  12. 12. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa ]TarhN_ 7-4³ kMNt;m:Um:g;enARtg;tMN E nigtMN C EdlekItBIGgát; EF nig CD rbs; building bent enAkñúgrUbTI 7-6a. Approximate analysis of statically indeterminate structures T.Chhay -225
  13. 13. Department of Civil Engineering NPIC 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. viPaKeRKOgbgÁúMminkMNt;edaysþaTicedayviFIRbEhl T.Chhay -226
  14. 14. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa &>%> 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; Approximate analysis of statically indeterminate structures T.Chhay -227
  15. 15. Department of Civil Engineering NPIC 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 viPaKeRKOgbgÁúMminkMNt;edaysþaTicedayviFIRbEhl T.Chhay -228
  16. 16. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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. ]TarhN_ 7-6³ kMNt;kMlaMgRbtikmμenARtg;Kl;ssrrbs;eRKagEdlbgðajenAkñúgrUbTI 7-14a edaytMélRbEhl. eRbIviFI portal sMrab;viPaKeRKagenH. Approximate analysis of statically indeterminate structures T.Chhay -229
  17. 17. Department of Civil Engineering NPIC 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. viPaKeRKOgbgÁúMminkMNt;edaysþaTicedayviFIRbEhl T.Chhay -230
  18. 18. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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. ]TarhN_ 7-7³ kMNt;kMlaMgRbtikmμenARtg;Kl;ssrrbs;eRKagEdlbgðajenAkñúgrUbTI 7-16a 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 Approximate analysis of statically indeterminate structures T.Chhay -231
  19. 19. Department of Civil Engineering NPIC viPaKeRKOgbgÁúMminkMNt;edaysþaTicedayviFIRbEhl T.Chhay -232
  20. 20. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa + ∑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 Approximate analysis of statically indeterminate structures T.Chhay -233
  21. 21. Department of Civil Engineering NPIC 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 viPaKeRKOgbgÁúMminkMNt;edaysþaTicedayviFIRbEhl T.Chhay -234
  22. 22. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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;. Approximate analysis of statically indeterminate structures T.Chhay -235
  23. 23. Department of Civil Engineering NPIC cMeNaT 7>1> kMNt;kMlaMgenAkñúgGgát;nImYy²rbs; truss ¬edaytMélRbEhl¦. snμt;Ggát;Ggát;RTUgGac Tb;Tl;TaMgkMlaMgTaj nigkMlaMgsgát;. 7>6> kMNt;kMlaMgenAkñúgGgát;nImYy²rbs; truss éncMeNaT 7>5> ¬edaytMélRbEhl¦. snμt; Ggát;Ggát;RTUgminGacTb;Tl;nwgkMlaMgTajeT. 7>7> kMNt;kMlaMgenAkñúgGgát;nImYy²rbs; truss 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. 7>3> kMNt;kMlaMgenAkñúgGgát;nImYy²rbs; truss ¬edaytMélRbEhl¦. snμt;Ggát;Ggát;RTUgGac 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. 7>5> kMNt;kMlaMgenAkñúgGgát;nImYy²rbs; truss ¬edaytMélRbEhl¦. snμt;Ggát;Ggát;RTUgGac Tb;Tl;TaMgkMlaMgTaj b¤kMlaMgsgát;. cMeNaT T.Chhay -236
  24. 24. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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
  25. 25. Department of Civil Engineering NPIC 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
  26. 26. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 7>20> kMNt;kMlaMgkñúgrbs;Ggát; truss nImYy² rbs; portal frame. ehIycUrkMNt;kMlaMgRbti- 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>23> kMNt;kMlaMgkñúgrbs;Ggát; truss nImYy² rbs; portal frame. ehIycUrkMNt;kMlaMgRbti- 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;. Problems T.Chhay -239
  27. 27. Department of Civil Engineering NPIC 7>27> sg;düaRkamm:Um:g;edaytMélRbEhl 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. 7>29> sg;düaRkamm:Um:g;edaytMélRbEhl 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
  28. 28. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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 . Problems T.Chhay -241

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