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



Parker truss ¬rUbTI 3-5...
mhaviTüal½ysMNg;sIuvil                                                    viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                             NPIC




          ]TahrN_sMra...
mhaviTüal½ysMNg;sIuvil                                                      viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                                 NPIC



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mhaviTüal½ysMNg;sIuvil                                               viTüasßanCatiBhubec©keTskm<úCa

sßirPaBxagkñúg (Inter...
Department of Civil Engineering                                                               NPIC



         RbsinebI tr...
mhaviTüal½ysMNg;sIuvil                                                        viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                             NPIC



#>#> viFItMN (The meth...
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




#>*> Truss kñúglMh (Sp...
mhaviTüal½ysMNg;sIuvil                                                     viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering             NPIC




karviPaK truss kMNt;edaysþaTic    T.Chhay   -93
mhaviTüal½ysMNg;sIuvil                                                  viTüasßanCatiBhubec©keTskm<úCa
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Department of Civil Engineering                                                                 NPIC



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mhaviTüal½ysMNg;sIuvil                                              viTüasßanCatiBhubec©keTskm<úCa

]TahrN_ 3-12³ kMNt;kMl...
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



3>25> kMNt;kMlaMgenAkñúgGg...
mhaviTüal½ysMNg;sIuvil                                          viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                     NPIC



3>37> eRKag truss mYyrgbnÞúkdU...
mhaviTüal½ysMNg;sIuvil                                         viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                         NPIC



3>50>      kMNt;kMlaMgenAk...
mhaviTüal½ysMNg;sIuvil                                              viTüasßanCatiBhubec©keTskm<úCa

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3. analysis of statically determinate trusses

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Transcript of "3. analysis of statically determinate trusses"

  1. 1. 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
  2. 2. 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
  3. 3. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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 Analysis of Statically Determinate trusses T.Chhay -64
  4. 4. Department of Civil Engineering NPIC 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 karviPaK truss kMNt;edaysþaTic T.Chhay -65
  5. 5. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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. Analysis of Statically Determinate trusses T.Chhay -66
  6. 6. Department of Civil Engineering NPIC ]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¦. karviPaK truss kMNt;edaysþaTic T.Chhay -67
  7. 7. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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. Analysis of Statically Determinate trusses T.Chhay -68
  8. 8. Department of Civil Engineering NPIC 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. karviPaK truss kMNt;edaysþaTic T.Chhay -69
  9. 9. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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. Analysis of Statically Determinate trusses T.Chhay -70
  10. 10. Department of Civil Engineering NPIC 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 karviPaK truss kMNt;edaysþaTic T.Chhay -71
  11. 11. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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. Analysis of Statically Determinate trusses T.Chhay -72
  12. 12. Department of Civil Engineering NPIC #>#> 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 karviPaK truss kMNt;edaysþaTic T.Chhay -73
  13. 13. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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. Analysis of Statically Determinate trusses T.Chhay -74
  14. 14. Department of Civil Engineering NPIC ]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 ) karviPaK truss kMNt;edaysþaTic T.Chhay -75
  15. 15. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa ]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 . Analysis of Statically Determinate trusses T.Chhay -76
  16. 16. Department of Civil Engineering NPIC #>$> 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 karviPaK truss kMNt;edaysþaTic T.Chhay -77
  17. 17. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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 Analysis of Statically Determinate trusses T.Chhay -78
  18. 18. Department of Civil Engineering NPIC #>%> 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- karviPaK truss kMNt;edaysþaTic T.Chhay -79
  19. 19. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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. dMeNIrkarkñúgkarviPaK (Procedure for analysis) 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. Analysis of Statically Determinate trusses T.Chhay -80
  20. 20. Department of Civil Engineering NPIC 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. karviPaK truss kMNt;edaysþaTic T.Chhay -81
  21. 21. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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 ) Analysis of Statically Determinate trusses T.Chhay -82
  22. 22. Department of Civil Engineering NPIC ]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 ) karviPaK truss kMNt;edaysþaTic T.Chhay -83
  23. 23. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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. dMeNIrkarkñúgkarviPaK (Procedure for analysis) 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¦. Analysis of Statically Determinate trusses T.Chhay -84
  24. 24. Department of Civil Engineering NPIC ]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 . karviPaK truss kMNt;edaysþaTic T.Chhay -85
  25. 25. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa ]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 . Analysis of Statically Determinate trusses T.Chhay -86
  26. 26. Department of Civil Engineering NPIC ]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. karviPaK truss kMNt;edaysþaTic T.Chhay -87
  27. 27. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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. dMeNIrkarkñúgkarviPaK (Procedure for analysis) 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. Analysis of Statically Determinate trusses T.Chhay -88
  28. 28. Department of Civil Engineering NPIC 3-32b¦. eKGacviPaK truss enaHedayviFItMNsMrab;bnÞúkTaMgBIrRbePTdUcxageRkam. kMlaMgxageRkAenAelI truss samBaس 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 samBaس 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 karviPaK truss kMNt;edaysþaTic T.Chhay -89
  29. 29. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa ¬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. Analysis of Statically Determinate trusses T.Chhay -90
  30. 30. Department of Civil Engineering NPIC #>*> 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 karviPaK truss kMNt;edaysþaTic T.Chhay -91
  31. 31. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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 Analysis of Statically Determinate trusses T.Chhay -92
  32. 32. Department of Civil Engineering NPIC karviPaK truss kMNt;edaysþaTic T.Chhay -93
  33. 33. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa ⎛ 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. Analysis of Statically Determinate trusses T.Chhay -94
  34. 34. Department of Civil Engineering NPIC 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. dMeNIrkarkñúgkarviPaK (Procedure for analysis) 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. karviPaK truss kMNt;edaysþaTic T.Chhay -95
  35. 35. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa ]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 Analysis of Statically Determinate trusses T.Chhay -96
  36. 36. Department of Civil Engineering NPIC ⎛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. karviPaK truss kMNt;edaysþaTic T.Chhay -97
  37. 37. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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 . Analysis of Statically Determinate trusses T.Chhay -98
  38. 38. Department of Civil Engineering NPIC 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
  39. 39. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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;. 3>8> kMNt;kMlaMgenAkñúgGgát;nImYy²rbs; truss. bgðajsPaBrgkMlaMgrbs;Ggát;. snμt;Ggát;TaMg 3>5> kMNt;kMlaMgenAkñúgGgát;nImYy²rbs; truss. 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
  40. 40. Department of Civil Engineering NPIC 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
  41. 41. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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;. Problems T.Chhay -102
  42. 42. Department of Civil Engineering NPIC 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; Ggát;TaMgGs;tP¢ab;Kñaedaysnøak;. 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;. 3>27> kMNt;kMlaMgenAkñúgGgát;nImYy²rbs; truss. bgðajsPaBrgkMlaMgrbs;Ggát;. snμt; Ggát;TaMgGs;tP¢ab;Kñaedaysnøak;. 3>30> kMNt;RbePTrbs; truss pSM nigkMNt; kMlaMgenAkñúgGgát;nImYy² nigbgðajBIsPaBrg kMlaMgrbs;Ggát;. snμt;Ggát;TaMgGs;tP¢ab;Kña edaysnøak;. cMeNaT T.Chhay -103
  43. 43. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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>35> kMNt;kMlaMgenAkñúgGgát;TaMgGs;rbs; truss saMjúaM. 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;. Problems T.Chhay -104
  44. 44. Department of Civil Engineering NPIC 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
  45. 45. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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;. 3>45> kMNt;kMlaMgenAkñúgGgát;TaMgGs;rbs; truss saMjúaM. bgðajBIsPaBrgkMlaMgrbs;Ggát;. CMnYy³ CMnYsGgát; AD edayGgát;enAcenøaH E 3>48> kMNt;kMlaMgRbtikmμ nigkMlaMgenAkñúg nig C . Ggát; BA / AD nig CD . 3>46> kMNt;kMlaMgenAkñúgGgát;TaMgGs;rbs; 3>49> kMNt;kMlaMgenAkñúgGgát;nImYy²rbs; truss saMjúaM. bgðajBIsPaBrgkMlaMgrbs;Ggát;. CMnYy³ CMnYsGgát; JE edayGgát;enAcenøaH K truss kñúglMh nigbgðajBIsPaBrgkMlaMgrbs; Ggát;. nig F . Problems T.Chhay -106
  46. 46. Department of Civil Engineering NPIC 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
  47. 47. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 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;? Problems T.Chhay -108

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