Viii shear and diagonal tension

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Viii shear and diagonal tension

  1. 1. T.Chhay NPIC VIII. kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg Shear and Diagonal Tension 1> esckþIepþIm enAeBlEdlFñwmTMrsamBaØrgnUvbnÞúk m:Um:g;Bt; nigkMlaMgkat;TTwgnwgekIteLIgelIRbEvgFñwm. edIm,IRT nUvbnÞúkenHedaysuvtßiPaB FñwmRtUv)aneFVIkarKNnaeLIgedIm,ITb;nwgkMlaMgTaMgBIrRbePTenH. karKNnasMrab; karBt;RtUv)aneFVIeLIgdMbUgeK edIm,IkMNt;muxkat;Fñwm nigEdkemcaM)ac; dUcEdl)anENnaMBIemeronmun. bnÞab;mkFñwmRtUv)anKNnaedIm,ITb;nwgkMlaMgkat;TTwg. kñúgkrNIEdlEdkkgminRtUv)andak; enaHFñwm nwg)ak;edaykMlaMgkat;TTwg. kar)ak;edaykMlaMgkat;TTwg ekIteLIgedaymanPaBdabtUc nig)at;bg;nUv lkçN³yWt ehIymin)anRbkasGasnñenAmuneBl)ak;eT. sMrab;kar)ak;edaykarBt;begáag ekIteLIgeday karekIneLIgnUvPaBdabbnþicmþg² nigmansñameRbH dUcenHvamankarpþl;sBaØaRbkasGasnñmuneBl)ak;cug eRkay. karKNnasMrab;kMlaMgkat;TTwg RtUv)aneFVIeLIgedIm,IFananUvkar)ak;edaykMlaMgkat;TTwgekIteLIg eRkaykar)ak;edaykarBt;begáag. 2> kugRtaMgkMlaMgkat;enAkñúgFñwmebtugGarem: rUbmnþTUeTAsMrab;kugRtaMgkMlaMgkat;TTwgenAFñwmrUbFatusac;mYy (homogenous beam) karBRgaykug RtaMg ν= VQ Ib ¬*>!¦ Edl V - kMlaMgkat;srubenAmuxkat;EdlRtUvsikSa Q - m:Um:g;sþaTiceFobGkS½NWténmuxkat;EdlxNÐedaybnÞat;EdlRtUvsikSakugRtaMgkMlaMgkat; kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 125
  2. 2. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa - m:Um:g;niclPaBénmuxkat;eFobGkS½NWt I b - TTwgFñwménmuxkat;EdlRtUvsikSakugRtaMgkMlaMgkat; karBRgaykugRtaMgm:Um:g;Bt; nigkMlaMgkat;TTwgGaRs½yeTAnwgRTwsþIbTeGLasÞicsMrab;muxkat;Fñwm ctuekaN dUcbgðajkñúgrUbTI8>2. kugRtaMgm:Um:g;Bt; Mc f = I Edl kugRtaMgkMlaMgkat;enARKb;cMnucTaMgGs;RtUv)anKNnatamrUbmnþkugRtaMgkMlaMgkat; VQ ν= Ib kugRtaMgkMlaMgkat;GtibrmasßitenAelIGkSNWt nigmantMélesμI 1.5v ¬kMlaMgkat;TTwgmFüm¦ a Edl ν = bh . ExSekagkMlaMgkat;TTwgmanrag):ar:abUl. a V sMrab;FñwmebtugsésEdkrgkarTaj (singly reinforced concrete beam) karBRgaykugRtaMg kMlaMgkat;TTwgenAelIGk½SNWtmanrag):ar:abUl. enAeRkamGk½SNWt kugRtaMgkMlaMgkat;TTwgGtibrmamantMél efr ehIy)anrkSatMélenHRtwmnIv:UEdkrgkarTaj BIeRBaHvaKμankarpøas;bþÚrkMlaMgTajBIcMnucGk½SNWtehIymü:ag eTotkMlaMgTajkñúgebtugRtUv)anecal. kugRtaMgkMlaMgkat;TTwgmantMélesμIsUnü enAeRkamnIv:UEdk ¬rUbTI8> 3¦. sMrab;ebtugsésrEdkEdlmanEdkrgkarsgát; nigmuxkat;GkSret karBRgaykugRtaMgkMlaMg kat;TTwgRtUv)anbgðajkúñgrUbTI8>3. eyIgsegÁteXIjfa kMlaMgkat;TTwgesÞIrEtTaMgGs; RtUv)anTb;edayRT nugEdlsøabTb;nwgPaKrytUcbMput. sMrab;karGnuvtþn_esÞIrTaMgGs; eKecalnUvlT§PaBTb;kMlaMgkat;TTwgrbs; søab. Shear and Diagonal Tension 126
  3. 3. T.Chhay NPIC eyagtamrUbTI8>1 edayykFñwmmYykMNat;tUc dx mkviPaK eyIgeXIjfa m:Um:g;Bt;enAcug sgxagénkMNat; M nig M minmantMélesμIKñaeT. edaysar M < M dUcenHedIm,IrkSalMnwgsMrab;kMNat; 1 2 1 2 dx kMlaMgsgát; C RtUvmantMélFMCag C ¬rUbTI8>4¦. dUcenHkugRtaMgkMlaMgkat;TTwg v ekItmanenAelImux 2 1 kat;edk a − a1 b¤ b − b1 ¬rUbTI8>4 a¦. kugRtaMgkMlaMgEkg (normal stresses) nigkugRtaMgkMlaMgkat;TTwg (shear stresses) enAelIGgát;tUc enAkMritnIv:U a − a1 b¤ b − b1 RtUv)anbgðajenAkñúg¬rUbTI8>4 b¦. cMNaMfa kug RtaMgkM;laMgEkg (normal stresses) enAnIv:UénGkS½NWtKW 0 b:uEnþkMlaMgkat;TTwgmantMélGtibrma. kMlaMgkat; TTwgedkesμInwgkMlaMgkat;TTwgbBaÄr dUcbgðajenAkñúg ¬rUbTI8>4 b¦. enAeBlEdl kugRtaMgkMlaMgEkgmantM élesμIsUnü b¤tUc enaHkrNIkMlaMgkat;TTwgsuT§GacekItman. kñúgkrNIenH kugRtaMgTajGtibrma f t manGMeBI tammMu 45o ¬rUbTI8>4 c¦. kugRtaMgTajsmmUleTAnwgkugRtaMgem dUcbgðajkñúgrUbTI 8>4 d. kugRtaMgemenHRtUv)aneK ehAfakugRtaMgTajGgát;RTUg. enAeBlkugRtaMgTajGgát;RTUgmantMélesμIersIusþg;Tajrbs;ebtug sñameRbH Ggát;RTUgekIteLIg. karviPaKy:agsegçbenHBnül;BIKMniténkMlaMgTajGgát;RTUg nigsñameRbHGgát;RTUg. kar eFVICak;EsþgmanlkçN³sμúKsμajCag ehIyvaTTYlT§iBlBIktþaepSg². sMrab;bnSMénGMeBIénkMlaMgkat;TTwg nigkMlaMgEkgenAcMnucNamYyenAkñúgFñwm kMlaMgTajGgát;RTUg (principal stresses) Gtibrma nigGb,brma f p RtUv)aneGayedaysmIkarxageRkam³ kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 127
  4. 4. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 2 ⎛f ⎞ fp = f 2 ± ⎜ ⎟ + v2 ⎝2⎠ ¬*>@¦ Edl f =GaMgtg;sIueténkugRtaMgEkgEdlbNþalmkBIkarBt; v = kugRtaMgkMlaMgkat; kar)ak;edaykMlaMgkat;TTwgenAkñúgFñwmebtugPaKeRcInTMngCaekIteLIgenAkEnøgEdlkMlaMg kat;TTwgGtibrma CaTUeTAenAEk,rTMrénGgát;. PsþútagTImYykar)ak;EdlKYreGayP½yxøayKWkarekIteLIgnUv sñameRbHGgát;RTUg. Shear and Diagonal Tension 128
  5. 5. T.Chhay NPIC 3> kareFVIkarrbs;FñwmedayKμanEdkkMlaMgkat;TTwg ebtugexSaykñúgkarTaj ehIyFñwmGac)ak;RbsinebImuxkat;EdkminRtwmRtUvRtUv)anpþl;eGay. kugRtaMg TajekItmanenAkñúgFñwmbNþalmkBIkMlaMgTajtamGkS½ kMlaMgBt; kMlaMgkat;TTwg kMlaMgrmYl b¤bnSMénbnÞúk TaMgenH. TItaMgénsñameRbHenAkñúgFñwmebtugGaRs½ynwgTisedAénkugRtaMgem (principal stresses). bnSMénkug RtaMgkMlaMgEkg normal stress nigkugRtaMgkMlaMgkat;TTwg begáIt)ankMlaMgTajtamGgát;RTUg (diagonal tension) GtibrmaEdlsßitenARbEhlcMgay d BImuxénTMr. kareFVIkarrbs;FñwmebtugGarem:edaymanb¤KμanEdkkMlaMgkat;TTwg RtUv)anBiesaFeRkamGMeBIénkarekIn eLIgénbnÞúkdUc)anerobrab;enAkñúgemeronTI3. enAkñúgkarBiesaFn_Fñwm sñameRbHbBaÄrEdlekItBIkarBt;ekIt eLIgenAenAelImuxkat;Edlmanm:Um:g;Bt;Gtibrma enAeBlEdlkugRtaMgTajenAkñúgebtugelIsBIm:UDuldac; (module of rupture) rbs;ebtug b¤ f r = 0.623 f 'c . sñameRbHeRTtenAkñúgRTnugekItmanenAkñúgtMNak;kal bnÞab;enATItaMgEk,rTMr. sñameRbHeRTtEdlekItmanenAkñúgFñwmEdlminTan;)aneRbHBIdMbUg CaTUeTARtUv)aneKeGayeQμaHfa sñameRbHkMlaMgkat;RTnug (web-shear crack). RbsinebIsñameRbHeRTtcab;epþImenABIelIsñameRbHEdlekItBI karBt;EdlmanRsab; ehIyrIksayenAkñúgFñwm enaHsñameRbHRtUv)aneKeGayeQμaHfa sñameRbHkMlaMgkat;rg karBt; (flexural-shear crack) rUbTI8>5. sñameRbH web-shear crack ekItmanenAkñúgFñwmEdlmankMlaMgkat; FM nigm:Um:g;Bt;tUcenAkñúgRTnugesþIg. vaCasñameRbHminFmμtaehIyGacekItmanenAEk,rcMnucrbt;énFñwmCab; b¤ Ek,rTMrénFñwmsamBaØ. sñameRbH flexural-shear crack CaRbePTsñameRbHFmμtaEdleKGaceXIjmanenAelIFñwm. dMbUgsñam eRbH flexural crack ekItmanbBaÄrenAelIFñwm bnÞab;mksñameRbHeRTtcab;epþImekItmanBIelIkMBUlénsñameRbH flexural crack enAeBlEdlkugRtaMgkMlaMgkat;TTwgekItmanenAkñgtMbn;enaH. enAkñugtMbn;EdlmankugRtaMg kMlaMgkat;TTwgFM FñwmRtUvEtBRgwgedayEdkkg stirrup b¤EdkBt; (bent bar) edIm,IeFVIeGayFñwmmanlkçN³sVit (ductile) Edlmin)ak;b¤ dac;. edIm,IeCosvagkar)ak;edaykMlaMgkat; munkar)ak;edaykarBt; emKuNsuvtßiPaB FMRtUv)anpþl;eGayedIm,ITb;nwgkar)ak;edaykMlaMgkat;TTwg. ACI Code kMNt;emKuNkat;bnßyersIusþg; φ = 0.75 sMrab;kMlaMgkat;TTwg. ersIusþg;kMlaMgkat;TTwgenAkñúgGgát;ebtugGarem:RtUv)anekIteLIgedaybnSMénkMlaMgemkanicxageRkam ¬rUbTI8>5¦³ - ersIusþg;kMlaMgkat;TTwgénebtugminTan;eRbH Vz - karepÞrkMlaMgkat;TTwgrvagGnþrépÞ (interface shear transfer) Va EdlbNþalmkBIkarbgçaMKñarvag fμbMEbktambeNþayépÞd¾KRKatrbs;sñameRbH kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 129
  6. 6. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa - GMeBIrbs;FñÚr (arch action) - GMeBIEdkf<k; (dowel action) Vd EdlbNþalmkBIersIusþg;énr)arEdkbeNþayeTAkMlaMgkat;TTwg tamTTwg (transverse shearing force) bEnßmeTAelIkMlaMgTaMgenH EdkkMlaMgkat;TTwg (shear reinforcement) begáInersIusþg;kMlaMgkat;TTwg Vs edayGaRs½yeTAelIGgát;p©it nigKMlatEdkkgEdleRbIenAkñúgGgát;ebtug. RbsinebIEdkkMlaMgkat;TTwg minRtUv)andak;enAkñúgFñwmragctuekaN enaHsmamaRténkMlaMgkat;TTwgEdlTb;edaykMlaMgemkanicepSg²KW³ BI 20% eTA 40% edayVz / BI 35% eTA 50% eday Va / BI 15% eTA 25% eday Vd . 4> T§iBlm:Um:g;eTAelIersIusþg;kMlaMgkat; sMrab;FñwmTMrsamBaØeRkamGMeBIbnÞúkBRgayesμI muxkat;kNþalElVgrgnUvm:Um:g;Bt;FM nigkMlaMgkat;TTwg tUc b¤esμIsUnü EdlpÞúyBImuxkat;enAEk,rTMrEdlm:Um:g;Bt;mantMéltUc ÉkMlaMgkat;TTwgmantMélFM ¬rUbTI8>1¦. kMlaMgkat;TTwg nigm:Um:g;mantMélFMenAEk,rTMrkNþalsMrab;FñwmCab;. enATItaMgEdlkMlaMgkat;TTwgFM nigm:Um:g; Bt;tUc enaHvanwgmankareRbHedaykarBt;tictYc ehIykugRtaMgmFüm v = V / bd . kugRtaMgkMlaMgTajtam Ggát;RTUgCakugRtaMgEdleRTtedaymMuRbEhl 45o ¬rUbTI8>4 c ¦. sñameRbHGgát;RTUgGacrMBwgfanwgekItman enAeBlEdlkugRtaMgkM;laMgTajGgát;RTUgEdlsßitenAEk,rtMbn;GkS½NWtxiteTACit b¤elIsersIusþg;kMlaMgTaj rbs;ebtug. CaTUeTA ersIusþg;kMlaMgkat;TTwgcugeRkay (ultimate shear strength) ERbRbYlcenøaHBI 0.29 f 'c nig 0.42 f 'c . eRkayBIkarBiesaFn_eTAelIFñwmCaeRcInGMBIkMlaMgkat;TTwg nigkMlaMgTajtam Ggát;RTUg eK)anrkeXIjfaenAkñúgtMbn;EdlmankMlaMgkat;TTwgFM nigm:Um:g;Bt;tUc enaHsñameRbHkMlaMgTaj Ggát;RTUgRtUv)anbegáIteLIgenAeBlkMlaMgkat;TTwgmFüm V = 0.29 f ' b d cr c w ¬*>#¦ Edl bw CaTTwgRTnugmuxkat;GkSret b¤TTwgmuxkat;ctuekaN d CakMBs;RbsiT§PaBrbs;Fñwm enATItaMgEdlkMlaMgkat;TTwg nigm:Um:g;Bt;mantMélFM enaHsñameRbHedaykarBt; (flexural crack) RtUv)anekIteLIgdMbUg. enAdMNak;kalTImYy sñameRbHxøHBt;kñúgTisedAGgát;RTUgenAeBlEdlkugRtaMgkMlaMg TajGgát;RTUg EdlsßitenABIcugxagelIénsñameRbHTaMgenaHFMCagkugRtaMgkMlaMgTajrbs;ebtug. RbsinebIeKeGaym:Um:g;FMmanGMeBIelIFñwm sMrab;muxkat;EdlmanbrimaNEdkRKb;RKan; enaHkMlaMg nominal shear force enAeBlEdlsñameRbHekItmanRtUv)aneGaydUcxageRkam Vcr = 0.16 f 'c bw d ¬*>$¦ Shear and Diagonal Tension 130
  7. 7. T.Chhay NPIC tMélenHKWtUcCagtMélEdleGayedaysmIkar ¬*>#¦ eRcInCaBak;kNþalenAeBlEdlm:Um:g;Bt;man tMéltUcNas;. enHmann½yfam:Um:g;Bt;FMkat;bnßytMélrbs;kugRtaMgkM;laMgkat;TTwgenAeBlEdlsñameRbH ekIteLIg. smIkarxageRkamRtUv)anesñIeLIgedIm,ITsSn_TaynUvkugRtaMg nominal shear stress enAeBlEdl sñamGgát;RTUgRtUv)anrMBwgfaekItman³ ⎡ ⎛ V d ⎞⎤ vcr = V = ⎢0.16 f 'c + ⎜17.2 ρ w u ⎟⎥ ≤ 0.29 f 'c ⎜ M ⎟ ¬*>%¦ b d w ⎣ ⎝ u ⎠⎦ ACI Code, Section 11.3.2 )anyksmIkarenHsMrab;KNnakMlaMg nominal ultimate shear force EdlTb;edayebtug Vc = (0.16 f 'c + 17.2 ρ w Vu d Mu )bw d ≤ 0.29 f 'c bw d ¬*>^¦ Edl ρ w = As / bwd / d CakMBs;RbsiT§PaBrbs;muxkat;Fñwm/ bw CaTTwgRTnugsMrab;muxkat;GkSret b¤TTwgénmuxkat;ctuekaN É Vu nig M u CakMlaMgkat;TTwgcugeRkay (ultimate shearing force) nigm:Um:g;Bt; cugeRkay (ultimate bending moment) EdlekIteLIgkñúgeBldMNalKñaenAelImuxkat;sikSa. tMélén Vu d / M u minRtUvFMCag 1.0 sMrab;smIkar ¬*>^¦. RbsinebI M u mantMélFMenAkñúgsmIkar ¬*>^¦ enaHtYrTIBIrnwgmantMéltUcesÞIEtesμIsUnü enaH vc xiteTArk 0.16 f 'c . RbsinebI M u mantMéltUc kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 131
  8. 8. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa enaHtYrTIBIrnwgmantMélFM ehIytMél 0.29 f 'c lub. eRkABIsmIkar ¬*>^¦ ACI Code, Section 11.3.1GnuBaØatieGayKNnaersIusþg;kMlaMgkat;rbs;ebtugdUcxageRkam³ Vc = (0.17 f 'c )bw d ¬*>&¦ 1> kñúgkrNIsMrab;kMlaMgsgát;tamGkS½ N u Vc = (0.16 f 'c + 17.2 ρ w Vu d Mm )bw d ≤ 0.29 f 'c bw d ¬*>*¦ ⎛ 4h − d ⎞ M m = M u − Nu ⎜ ⎟ ⎝ 8 ⎠ Edl ρw = s A bw d h= kMBs;srubrbs;Fñwm Vu d / M u GacFMCag 1.0 b:uEnþ Vc minRtUvFMCag Vc = bw d (0.29 f 'c ) 1 + Nu 3.45 Ag ¬*>(¦ Edl Ag CaRkLaépÞTaMgGs; (gross section) KitCa mm 2 mü:agvijeTot Vc GacRtUv)anKNnaeday Vc = bw d (2 + 0.145 Nu Ag ) f 'c ¬*>!0¦ 2> kñúgkrNIsMrab;kMlaMgTajtamGkS½ N u Vc = bw d (2 + 0.58 Nu Ag ) f 'c ¬*>!!¦ Edl N u mantMélGviC¢mansMrab;kMlaMgTaj RbsinebI Vc GviC¢man enaH Vc RtUv)anykesμIsUnü. 5> FñwmmanEdkkMlaMgkat; EdkEdleRbIedIm,ITb;nwgkMlaMgkat; EdleKeRbIGacmaneRcInRbePTepSg² a. Edkkg EdleKeRbIedaydak;EkgeTAnwgEdkbeNþay ¬Edkem¦ b¤RtUv)aneKdak;eRTt mMuEdl eKniymeRbI 45 . EdkkgEdleKniymeRbImanmuxkat; DB10 nig DB12 . o b. EdkBt; EdlCaEpñkmYyrbs;EdkbeNþayEdleKBt;eLIg ¬enAkEnøgEdleKbBaÄb;¦ edaymMu 30 nig 60 CaTUeTA 45 . o o o c. bnSMrvagEdkkg nigEdkBt; d. sMNaj;Edk CamYynwgsMNaj;EkgeTAnwgGkS½ Shear and Diagonal Tension 132
  9. 9. T.Chhay NPIC e. EdkkgvNÐ EdleKeRbIsMrab;ssr ersIusþg;kMlaMgkat;TTwgrbs;FñwmebtugGarem:RtUv)anbegáIneLIgedaykareRbInUvEdkkMlaMgkat;TTwg. munnwgekItnUvsñameRbHGgát;RTUg EdkkMlaMgkat;TTwgCYyersIusþg;kMlaMgkat;TTwgtictYcbMput. eRkayeBlEdl sñameRbHkMlaMgkat;TTwgekIteLIg EdkkMlaMgkat;TTwgbegáInersIusþg;kMlaMgkat;rbs;Fñwm ehIykMlaMgkñgmþg eTotEdlekIteLIgenAmuxkat;eRbH. enAeBlbrimaNEdkkMlaMgkat;TTwgtUc kar)ak;EdlekIteLIgedaysar EdkenARTnugeFVIkardl; yield GacnwgekIteLIg b:uEnþRbsinebIbrimaNEdkkMlaMgkat;TTwgFM enaHkar)ak;eday shear-compression failure GacnwgekIteLIg TaMgenHCaGVIEdleyIgKYreCosvag. ebtug Edkkg (stirrups) nigEdkdgErk (bent bars) eFVIGMeBIrYmKñaedIm,ITb;nwgkMlaMgkat;TTwg. edaysarersIusþg;rgkarsgát;x<s; ebtugedIrtYCaGgát;rgkarsgát;Ggát;RTUgénRbBn§½Fñwm cMENkÉEdkkgedIrtYCa Ggát;rgkarTajbBaÄr. kMlaMgsgát;Ggát;RTUg k¾dUcCabgÁúMkMlaMgbBaÄrrbs;va mantMélesμInwgkMlaMgTajenAkñúg Edkkg. EdkBt;dgErk (bent-up reinforcement) k¾edIrtYdUcCaGgát;TajenAkñúg truss Edr ¬rUbTI *>^¦. CaTUeTA karcUlrYmrbs;EdkkMlaMgkat;TTwgeTAkñúgersIusþg;kMlaMgkat;TTwgrbs;FñwmebtugGarem: GacRtUv)anBiBN’nadUcxageRkam³ kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 133
  10. 10. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa - vaTb;Tl;EpñkxøHénkMlaMgkat;TTwg/ V s - vabegáInGaMgtg;sIueténkMlaMgkat;rvagGnþrépÞ/ Va ¬rUbTI *>%¦/ edayTb;Tl;nwgkarrIkFMénsñam eRbHeRTt (inclined crack). - vabegáInnUvkMlaMgf<k; (dowel force)/ Vd ¬rUbTI *>%¦/ enAkñúgEdkbeNþay - GMeBITb; (confining action) rbs;EdkkgeTAelIebtugGacbegáInerIusþg;rbs;va - GMeBITb; (confining action) rbs;EdkkgeTAelIebtugbegáInnUvsmtßPaBrgVilénsnøak;)øasÞic (rotation capacity of plastic hinge) EdlekItmanenAkñúgeRKOgbgÁúM indeterminate structure eRkambnÞúkcugeRkay nigbegáInRbEvgEdl yield GacekItmanenAelIva. eday V CaersIusþg;kMlaMgkat;rbs;muxkat;ebtugGarem:enaH n V =V +V n c s ¬*>!@¦ Edl V - ersIusþg;kMlaMgkat;)anBIebtug c V - ersIusþg;kMlaMgkat;)anBIEdk s RbsinebIV kMlaMgkat;Edl)anBIbnÞúkxageRkAenaH u V ≤ φV = φ (V + V ) u n c s ¬*>!#¦ Edl V = 1.2V + 1.6V u nig φ = 0.75 D L V RtUv)anKNnaedaykarviPaK truss ¬rUbTI *>&¦. sMrab;sñameRbH 45 niges‘rIénEdkkg b¤Edk s o dgErk. kMlaMgkat;bBaÄr V esμInwgplbUkbgÁúMkMlaMgbBaÄrénkMlaMgTajEdlekItmanenAkñúgEdkeRTt s V = nA f sin α s v yt ¬*>!$¦ Edl A -muxkat;kat;EdkkMlaMgkat;CamYyKMlat s v f - ersIusþg;EdkkMlaMgkat; yt eday ns = aa + a a 1 1 2 Shear and Diagonal Tension 134
  11. 11. T.Chhay NPIC d = a1a4 = aa1tg 45o ¬BIRtIekaN aa a ¦ 1 4 d = a1a4 = aa2tgα ¬BIRtIekaN aa a ¦ 1 2 ⇒ ns = d (cot 45o + cot α ) = d (1 + cot α ) d ⇒ n = (1 + cot α ) s eKTTYl)an A f d s A f d Vs = v yt sin α (1 + cot α ) = v yt (sin α + cos α ) s ¬*>!%¦ sMrab;krNIEdkkgbBaÄr α = 90 o V = s A f d s v b¤ s = A Vf d yt v yt ¬*>!^¦ s sMrab;krNIEdkkgbBaÄr α = 45 o V = 1.4 s A f d s b¤ s = 1.4 A Vf d v yt v yt ¬*>!&¦ s sMrab;krNIEdkdgErkEtmYy b¤RkumEdkenAmYykEnøg V = A f sin α s v ytb¤ A = f V α sin v s ¬*>!*¦ yt sMrab; α = 45o Av = 1.4 Vs f yt ¬*>!(¦ 6> tMrUvkarrbs; ACI Code sMrab;karKNnakMlaMgkat;TTwg 1> muxkat;eRKaHfñak;sMrab;karKNnaersIusþg;kMlaMgkat;TTwgmFüm Critical section for nominal shear strength calculation ACI Code, Section 11.1.3 GnuBaØateGayykmuxkat;eRKaHfñak;sMrab;karKNnaersIusþg;kMlaMgkat; mFüm enAcMgay d BIépÞmuxénTMr. karENnaMenHQrenAelIPaBCak;EsþgEdlsñameRbHeRTtdMbUgeKTMngCaekIt eLIgenAelIFñwmRtg;cMgay d BITMrEdleRcInelcecjenAeBleFVIBiesaFn_. muxkat;eRKaHfñak;enHRtUv)anGnuBaØat enAkñúglkçxNÐEdlRbtikmμTMrbBa¢ÚnkMlaMgsgát;eTAkñúgtMbn;cug/ bnÞúkRtUv)anGnuvtþenAelI b¤enAEk,rkMBUlén Ggát;ehIyKμanbnÞúkcMcMnucGnuvtþenAcenøaHépÞénTMr nigTItaMgénmuxkat;eRKaHfñak;. bTdæank¾kMNt;Edrfa Edk kMlaMgkat;TTwgRtUv)andak;enAcenøaHépÞénTMr nigcMgay d . 2> muxkat;EdkGb,brmasMrab;EdkkMlaMgkat;TTwg vtþmanrbs;EdkkMlaMgkat;TTwgenAkñúgFñwmebtugTb;Tl;nwgkarrIkraldalénsñameRbHeRTt. mü:agvij eTot PaBsVit (ductility) ekIneLIg ehIyva)anRbkasGasnñmuneBl)ak;. RbsinebIKμanEdkkMlaMgkat;TTwg enaHFñwmmanlkçN³RsYyehIy)ak;edaymin)anR)ab;mun. dUcenH muxkat;EdkkMlaMgkat;TTwgRtUv)ankMNt; kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 135
  12. 12. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa eday Code. ACI Code, Section 11.5.5 tMrUvEdkkgTaMgGs;eGaymanRkLaépÞEdkkMlaMgkat;TTwgGb,br- ma Av esμInwg b s b s Av = 0.062 f 'c w ≥ 0.35 w f f ¬*>@0¦ yt yt Edl bw CaTTwgénRTnug nig s CaKMlatrbs;Edkkg. eKRtUvkarbrimaNEdkkMlaMgkat;TTwgGb,- brmaenAeBlEdl V > 0.5φV elIkElg u c - kMralxNÐ nigeCIgtag - rnUtebtug - FñwmEdlmankMBs;tUcCag max{250mm; 2.5 dgkMras;énsøab; ; 1.5 énTTwgRTnug } RbsinebI 0.062 f 'c = 0.35 enaH f 'c = 31.9MPa . enHman½yfaenAeBlEdl f 'c < 32MPa enaH tMélGb,brma Av = 0.35bw s / f yt manlkçN³lb; EtenAeBlEdl f 'c ≥ 32MPa enaHtMélGb,brma Av = 0.062 f 'c bw s / f yt manlkçN³lub. karekIneLIgnUvRkLaépÞEdkkMlaMgkat;TTwgsMrab; f 'c ≥ 32MPa KWedIm,IkarBarCamunnUvkar)ak;edaykMlaMgkat;TTwg (shear failure )Pøam² enAeBlEdlekIt mansñameRbHeRTt. vaCakarGnuvtþn_mYyd¾FmμtakñúgkardMeLIgkMras;kMralxNÐ kMras;eCIgtag b¤kMBs;Fñwmrak;edIm,IbegáIn lT§PaBTb;Tal;nwgkMlaMgkat;TTwg. EdkkgGacnwgKμanT§BlenAkñúgGgát;rak; edaysartMbn;rgkarsgát; rbs;vamankMBs;tUcEmnETn nigminmanTMBk;RKb;RKan;EdlRtUvkarsMrab;Edkkg. sMrab;FñwmEdlminrak; eKminRtUvkarEdkkMlaMgkat;TTwgenAeBlEdl Vu < 0.5φVc . RkLaépÞEdkkMlaMgkat;TTwgGb,brmaGacnwgRtUv)anTTYledayeRbIEdkkg DB10 dak;enAKMlatGti- brma S max . RbsinebI f yt = 400MPa ehIyEdkkg DB10 manragGkSr U ¬eCIgBIr¦RtUv)aneRbI enaH smIkar ¬*>@0¦køayeTACa Av f yt Av f yt S max = (0.062 f ' )b ≤ 0.35b ¬*>@!¦ c w w sMrab; f 'c < 32MPa / S max = 157 × 400 / 0.35bw = 179400 / bw sMrab; f 'c = 32MPa / S max = 179000 / bw ¬*>@@¦ sMrab; f 'c = 35MPa / S max = 171200 / bw sMrab; f 'c = 42MPa / S max = 156250 / bw RbsinebIeKeRbIEdk DB12 manragGkSr U enaH sMrab; f 'c < 32MPa / S max = 258250 / bw sMrab; f 'c = 32MPa / S max = 25750 / bw ¬*>@#¦ Shear and Diagonal Tension 136
  13. 13. T.Chhay NPIC sMrab; f 'c = 35MPa / S max = 246450 / bw sMrab; f 'c = 42MPa / S max = 224950 / bw RtUvcgcaMfa S max minRtUvFMCag 600mm b¤ d / 2 eT. taragTI 1 pþl;nUv S max edayQrelIsmIkar ¬*>@@¦ nig ¬*>@#¦. KMlatcugeRkayKYrEtRtUvrMkil eTArktMélEdltUc. ]TahrN_ S max = 515mm køayeTACa S max = 500mm . taragTI1> tMélrbs; S max = Av f yt / 0.35bw = 60cm . enAeBlEdl f yt = 400MPa nig f 'c < 32MPa bw (cm) 25 30 35 40 45 50 55 60 bw S max (cm) DB10 60 55 50 40 35 35 30 25 179400 / bw S max (cm) DB12 60 60 60 60 55 50 45 40 258250 / bw 3> kMlaMgkat;TTwgGtibrmaEdlTb;edayEdkkMlaMgkat;TTwg V s edIm,IkarBarkar)ak; shear-compression failure EdlebtugGacEbkedaykugRtaMgkMlaMgkat;TTwgFM nigkugRtaMgkMlaMgsgát;enAkñúgtMbn;eRKaHfñak; enABIelIkMBUlénsñameRbHGgát;RTUg ACI Code, Section 11.5.6.8, tMrUvfa V ≤ 0.67 f ' b d . RbsinebI V > 0.67 f ' b d enaHeKRtUvtMelIgmuxkat;ebtug. s c w s c w edayQrenAelIkarkMNt;enH³ RbsinebI f 'c = 20MPa enaH Vs ≤ 3bwd b¤ Vs / bwd ≤ 3MPa RbsinebI f 'c = 28MPa enaH Vs ≤ 3.5bwd b¤ Vs / bwd ≤ 3.5MPa RbsinebI f 'c = 35MPa enaH Vs ≤ 4bwd b¤ Vs / bwd ≤ 4MPa 4> KMlatEdkkgGtibrma edIm,IFanafasñameRbHGgát;RTUgRtUvkat;Edkkgy:agehacmYy enaH ACI Code, Section 11.5.4 tMrUv fa KMlatrvagEdkkgminKYrelIs d / 2 b¤ 600mm RbsinebI V ≤ 0.33 f ' b d ¬edayQrelIkarsnμt;fa s c w sñameRbHGgát;RTUgekItmantammMu 45o niglatsn§wgtamcMgayedkRbEhlcMgay d . enAkñúgtMbn;kMlaMgkat; TTwgFM Edl Vs > 0.33 f 'c bwd KMlatEdkkgGtibrmacenøaHEdkkgminRtUvFMCag d / 4 . karkMNt;enH caM)ac;edIm,IFanaeGaysñameRbHGgát;RTUgkat;Edkkgy:agehacbI. enAeBlEdl V > 0.67 f ' b d kar s c w kMNt;énKMlatGtibrmaminRtUv)anGnuvtþ ehIyTMhMrbs;muxkat;ebtugKYrRtUv)antMeLIg. karkMNt;TIBIrsMrab;KMlatGtibrmaénEdkkgk¾GacTTYl)anBIlkçxNÐmuxkat;EdkkMlaMgkat;TTwgGb, brma. Av Gb,brma RtUv)anTTYlenAeBlKMlat s Gb,brma ¬smIkar *>@!¦. karkMNt;TIbIsMrab;KMlatGtibrmaesμInwg 600mm enAeBlEdl V ≤ 0.33 f ' b d nigesμInwg s c w 300mm enAeBlEdl 0.33 f 'c bw d < Vs ≤ 0.67 f 'c bw d . tMéltUcCageKénKMlatGtibrmaRtUv)anyk kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 137
  14. 14. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa mkeRbI. tMrUvkarKMlatGtibrmaén ACI Code FanaKMlatCitKñarbs;EdkkgedIm,Icab;EdkrgkarTajbeNþay enAkñúgFñwm edayehtuenHva)anbegáInlT§PaBbgáb;Edkrbs;va Vd ¬rUbTI *>%¦. 5> ersIusþg; yield rbs;EdkkMlaMgkat;TTwg ACI Code, Section 11.5.2. tMrUveGayersIusþg; design yield strength rbs;EdkkMlaMgkat;TTwg minKYrelIs 420MPa . mUlehtuEdlenABIeRkaykarsMercenHKWedIm,IkMNt;TMhMsñameRbHEdlbNþalmkBI kMlaMgTajGgát;RTUg nigedIm,IFanafaEKmrbs;sñameRbHenArkSaépÞb:HCitKñaedIm,IbegáInkMlaMgbBa¢ÚnénkMlaMg kat;rvagGnþrépÞ Va ¬rUbTI *>%¦. sMrab;sésrEdkfñaMgGMeBAsMrab;pSar (welded deformed wire fabric) ersIusþg; design yield strength minKYrelIs 560MPa . 6> TMBk;rbs;Edkkg ACI Code, Section 11.5.2. tMrUvfaEdkkMlaMgkat;TTwgRtUv)andak;enAEk,rseésrrgkarsgát;eRkA bMput nigsésrrgkarTajeRkAbMputtamEtGaceFVIeTA)an CamYynwgtMrUvkarrbs; code sMrab;kMra;karBarEdk edaysarEt enAeBlEdlbnÞúkEdlmanGMeBIenAelIFñwmxiteTACitbnÞúkcugeRkay (ultimate load) sñameRbHkM laMgTaj edaykarBt; (flexural tension crack) bnøayy:ageRCAcUleTAkñúgFñwm. dUcKña edIm,IeGayEdkkg TTYl)annUversIusþg; yield eBj vaRtUvkarnUvTMBk;Edll¥. enAeBlEdlbnÞúkEdlmanGMeBIelIFñwmxiteTACitbnÞúk cugeRkay (ultimate load) kugRtaMgenAkñúgEdkkg)aneTAdl;kugRtaMg yield rbs;va enAcMnucEdlsñameRbH Ggát;RTUgkat;cMEdkkgenaH. tMrUvkarrbs; ACI Code sMrab;TMBk;Edkkg/ Section 12.13 dUcxageRkam³ - karBt;nImYy²enAkñúgEpñkCab;énEdkkgGkSr U Fmμta b¤BhuEdkkgGkSr U KYrBT§½CMuvijEdk beNþay (ACI Code, Section 12.13.3) emIlrUbTI *>*a. - Code GnuBaØateGayeRbInUvTMBk; standard 90o / 135o b¤ 180o CMuvijEdkbeNþysMrab;Edkkg DB16 . RbsinebIEdkkg DB19 / DB 22 nig DB 25 CamYynwg f yt > 280MPa enaH Code, Section 12.13.2 tMrUvTMBk; standard bUknwgRbEvgbgáb; 0.17d b f yt / f 'c cenøaHBak;kNþal kMBs;Fñwm nigEpñkxageRkAénTMBk;. RbsinebIEdkRtUvBt;edaymMu 90o RbEvgBnøÚtminRtUvtUcCag 12d b . sMrab;Edk DB16 b¤EdkkgTMhMtUcCagenH RbEvgBnøÚtKW 6d b (ACI Code, Section 7.1) emIlrUbTI *>*. - RbsinebIEdkkgGkSr U DubRtUv)aneRbIedIm,IpÁúMCaEdkkgbiTCit RbEvgRCYs (lap length) minRtUvtUcCag 1.3ld (ACI Code, Section 12.13.5) emIlrUbTI *>*c . - sésrEdkEdlpSar (welded wire fabric) RtUv)aneRbIsMrab;EdkkMlaMgkat;TTwgenAkñúg]sSahkmμ plitTukmun (precast industry) . TMBk;lMGitRtUv)anpþl;eGayenAkñúg ACI Code, Section 12.13.2.3 nigenAkñúgesckþIBnül; (commentary) rbs;va. Shear and Diagonal Tension 138
  15. 15. T.Chhay NPIC - EdkkgbiTCitRtUv)anpþl;eGaysMrab;FñwmEdlrgnUgkMlaMgrmYl (ACI Code, Section 7.11). - FñwmEdlenABT§½CMuvijeRKOgbgÁúMRtUveRbIEdkkgbiTCitedIm,IrkSa structural integrity rbs;Ggát; (ACI Code, Section 7.13.2.2). 7> EdkkgenAEdlenAEk,rTMr ACI Code, Section 11.1.3 kMNt;faEdkkgkMlaMgkat;TTwgEdlpþl;eGayenAcenøaHépÞTMr nigmuxkat; eRKaHfñak; (critical section) EdlsßitenAcMgay d BITMr KYrRtUv)anKNnasMrab;kMlaMgkat;TTwg Vu dUcKña enAnwg muxkat;eRKaHfñak;. vaCakarGnuvtþn_Fmμtaedaydak;EdkkgTImYyenAcMgay s / 2 BIépÞénTMr Edl s CaKMlat EdlKNnaedaysmIkar ¬*>!^¦ sMrab; Vu enAmuxkat;eRKaHfñak;. kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 139
  16. 16. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 8> RbEvgRbsiT§PaBrbs;EdkdgErk manEtbIPaKbYnRtg;cMnuckNþalénEpñkeRTténEdkbeNþayRtUv)anKitfamanRbsiT§PaBsMrab;EdkkM laMgkat;TTwg. enHmann½yfa KMlatGtibrmarbs;EdkdgErkKW 0.75(d − d ' ) . BIrUbTI *>( RbEvgRbsiT§PaB rbs;EdkdgErkKW 0.75(d − d ' ) / sin 45o = 0.75(1.414)(d − d ' ) = 1.06(d − d ' ) . KMlatGtibrma s esμInwgcM gayedkEdl)anBIkarTMlak;cMeNalEkgénRbEvgRbsiT§PaBEdkdgErk. dUcenH S max = 1.06(d − d ' ) cos 45o b¤ S max = 1.06(d − d ' )0.707 = 0.75(d − d ' ) 7> karKNnaEdkkgbBaÄr eKRtUvkarEdkkg (stirrup) enAeBlEdl Vu > 12 φVc . EdkkgGb,brmaRtUv)aneRbIenAeBlEdl 1 φV < V < φV . kñúgkrNIenHeKeRbIEdkkg DB10 EdlRtUv)andak;nUvKMlatGtibrma. enAeBlEdl 2 c u c Vu > φVc eKRtUvEtdak;EdkkgCamYyKMlattUcCagKMlatGtibrma ehIyGacRtUv)anKNnaedayeRbIsmIkar ¬*>!^¦³ S = Av f yt d / Vs . EdkkgEdlRtUv)aneRbICaTUeTAenAkñúgmuxkat;ebtugCaEdkkg DB10 nig DB12 GkSr U eCIgBIr CamYynwg f yt = 400MPa . RbsinebI DB10 RtUv)aneRbIenaH smIkar¬*>!^¦køayCa³ S Av f yt 157 × 400 62800 d = Vs = Vs = Vs ¬*>@$¦ RbsinebI DB12 RtUv)aneRbIenaH S Av f yt 226 × 400 90400 d = Vs = Vs = Vs ¬*>@%¦ pleFobKMlatEdkkgelIkMBs;RbsiT§PaB d rbs;Fñwm GaRs½ynwg Vs . tMélén S / d sMrab;tMél epSgKñaén Vs enAeBlEdl f yt = 400MPa RtUv)aneGayenAkñúgtaragTI2 nigtaragTI3 sMrab;Edk DB10 nig Edk DB12 erogKña. tMéldUcKñaRtUv)anbgðajCadüaRkamdUcenAkñúgrUbTI 8>10 nigrUbTI 8>11. Shear and Diagonal Tension 140
  17. 17. T.Chhay NPIC taragTI2> pleFob S / d sMrab;tMél V ¬ fs yt / = 400MPa S / d = 62800 / Vs ¦ DB10 Vs (kN ) 125.6 142.7 190.3 237.9 251.2 285.5 330.5 380.6 418.7 475.8 592.5 S /d 0.5 0.44 0.33 0.264 0.25 0.22 0.19 0.165 0.15 0.132 0.106 taragTI3> pleFob S / d sMrab;tMél V ¬ fs yt / = 400MPa S / d = 90400 / Vs ¦ DB12 Vs (kN ) 180.8 225 265 310 361.6 445 490.0 535 665 775 850 S /d 0.5 0.40 0.34 0.29 0.25 0.20 0.18 0.17 0.14 0.12 0.11 kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 141
  18. 18. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa Tamtarag nigdüaRkamxagelIeyIgGacsnñidæan)anfa³ - RbsinebIeKeRbI DB10 / S = d / 2 enAeBlEdl Vs ≤ 125.6kN . enAeBlEdl Vs ekIneLIg S / d fycuHtamExSekageTArktMél 0.132 enAeBl Vs = 475.8kN . RbsinebIKMlatGb,brma RtUv)ankMNt;Rtwm 75mm enaH d ≥ 568mm . enAeBlEdl Vs > 251.2kN enaH S ≤ d / 4 . - RbsinebIeKeRbI DB12 / S = d / 2 enAeBlEdl Vs ≤ 180.8kN . enAeBlEdl Vs ekIneLIg S / d fycuHtamExSekageTArktMél 0.14 enAeBl Vs = 665kN . RbsinebIKMlatGb,brma RtUv)ankMNt;Rtwm 75mm enaH d ≥ 535mm . enAeBlEdl Vs > 361.6kN enaH S ≤ d / 4 . - RbsinebIeKeRbIEdkkgGkSr U f yt = 280MPa enaHeKRtUvKuN S / d edaytMél 7 /10 b¤CaTUeTA f yt / 400 . 8> segçbviFIsaRsþKNnaEdkkgbBaÄr CMhankñúgkarKNnaEdkkgbBaÄrsMrab;kMlaMgkat;TTwg edayeyagtam ACI Code GacRtUv)ansegçb dUcxageRkam³ a. kMNt;kMlaMgkat;KNna V BIbnÞúkEdlGnuvtþn¾mkelIeRKOgbgÁúM. kMlaMgkat;KNnaRKITic u EdlRtUvykmksikSasßitenARbEvg d BImuxénTMr. b. kMNt; φV = φ 0.17 f ' b d b¤ φV = φ (0.16 f ' + 17.2 ρ Vd c c w )b d ≤ φ 0.29 f ' b d c c w u w c w M u bnÞab;mkKNna 1 φV 2 c c. k> RbsinebI V < 1 φV muxkat;minRtUvkarEdkkg 2 u c x> RbsinebI 1 φV < V ≤ φV eRbImuxkat;EdkkgGb,brma 2 c u c K> RbsinebI V > φV muxkat;Edkkg RtUvKNnadUcxageRkam u c d. kMNt;kMlaMgkat;EdlTb;eday Edkkg Vu − φVc Vs = φ e. kMNt; V = 0.33 f ' b d nig V = 0.67 f ' b d = 2V . RbsinebI V > V c1 c w c2 c w c1 s c2 tMeLIgmuxkat;. f. kMNt;KMlatrbs;Edk s = A Vf d 1 v yt s g. kMNt;KMlatEdkGtibrmaEdlGnuBaØatieday ACI Code. KMlatEdkGtibrmaCatMéltUcbMput én s nig s 2 3 Shear and Diagonal Tension 142
  19. 19. T.Chhay NPIC k> s 2 d 2 = ≤ 60cm RbsinebI V ≤ V = 0.33 s c1 f 'c bw d d s2 = ≤ 30cm 4 RbsinebI V < V ≤ V c1 s c2 x> 3A f s3 = v yt ≥ bw 16 Av f yt bw f 'c k> RbsinebI s < s eRbI s h. 1 max 1 x> RbsinebI s > s eRbI s 1 max max i. ACI Code min)ankMNt;nUvKMlatGb,brmaeT. eRkamlkçxNÐFmμta KMlatGb,brma S RtUv)ansnμt;ykesμInwg 75mm sMrab; d ≤ 50cm nigmanKMlatGb,brmaesμInwg 100mm sMrab;FñwmeRCA (deep beam) . RbsinebI S mantMéltUcenaH eKGactMeLIgmuxkat;Edkkg b¤eRbIEdkkgeCIgeRcIn ¬rUbTI 8>8¦. j. sMrab;muxkat;mUl RkLaépÞEdleRbIsMrab;KNna Vc = plKuNGgát;p©itCamYykMBs;RbsiT§PaB d / Edl d = 0.8 énGgát;p©it/ ACI Code, Section11.3.3 . ]TahrN_1³ FñwmTMrsamBaØmanmuxkat;ctuekaN b = 30cm / d = 55cm nig h = 60cm ehIyRtUv)anBRgwg eday 4DB25 . epÞógpÞat;faetImuxkat;enHRKb;RKan;b¤Gt;sMrab;kMlaMgkat;TTwgemKuN (ultimate shear force) xageRkam. RbsinebIva minRKb;RKan; cUrKNnaEdkkMlaMgkat;TTwgkñúgTMrg;CaEdkkgGkSr U . edayeRbI f 'c = 28MPa nig f yt = 400MPa . k> Vu = 50kN x> Vu = 110kN K> Vu = 240kN X> Vu = 345kN g> Vu = 570kN dMeNaHRsay³ CaTUeTA bw = b = 300mm / d = 550mm nig φVc = φ (0.17 f 'c )bd = 0.75(0.17 28 )300 × 550 × 10 −3 = 111.3kN 1 φV = 55.65kN 2 c ( ) ( ) Vc1 = 0.33 f 'c bd = 0.33 28 300 × 550 × 10 −3 = 288kN Vc 2 = (0.67 f 'c )bd = 576kN k> Vu = 50kN < 1 φVc = 55.565kN 2 / muxkat;RKb;RKan; edayminRtUvkarEdkkMlaMgkat;TTwg. x> Vu = 110kN > 1 φVc / b:uEnþvatUcCag φVc = 111.3kN . eday Vs = 0 dUcenH muxkat;RtUvkarEdk 2 kMlaMgkat;TTwgGb,brma. eRbI DB10 CaEdkkgGkSr U enAKMlatGtibrma. π Av = 2 × 10 2 = 157mm 2 4 KMlatGtibrmaCatMéltUcCageKkñúgcMeNam S 2 = d / 2 = 275mm yk 250mm ¬lub¦ kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 143
  20. 20. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa S 3 = Av f yt / 0.35bw = 157 × 400 /(0.35 × 300) = 598mm yk 550mm ¬b¤eRbItaragTI1¦ S 4 = 600mm dUcenHeRbIEdkkg DB10 @ 250mm K> Vu = 240kN > φVc / RtUvkarEdkkMlaMgkat;TTwg. karKNnaGaceFVIeLIgCaCMhanxageRkam³ KNna Vs = (Vu − φVc ) / φ = (240 − 111.3) / 0.75 = 171.6kN edaysar Vs < Vc1 enaH S max = d / 2 ≤ 600mm eRCIserIs DB10 CaEdkkgGkSr U nigKNnaKMlatRtUvkaredayQrelI Vs Av f yt d 157 × 400 × 550 S1 = = = 201mm yk 200mm Vs 171600 KNnaKMlatGtibrma³ S 2 = 250mm / S3 = 550mm nig S 4 = 600mm dUcenH S max = 250mm edaysar S = 200mm < S max = 250mm dUcenHeRbIEdkkg DB10 @ 200mm X> Vu = 345kN > φVc /RtUvkarEdkkMlaMgkat;TTwg. KNna Vs = (Vu − φVc ) / φ = (345 − 111.3) / 0.75 = 311.6kN edaysar Vs > Vc1 enaH S max = d / 4 ≤ 300mm yk 125mm edaysar Vc1 < Vs < Vc2 enaHeKGaceRbIEdkkg edaymincaM)ac;tMeLIgmuxkat;ebtug. eRCIserIs DB10 CaEdkkgGkSr U nigKNnaKMlatRtUvkaredayQrelI Vs Av f yt d 157 × 400 × 550 S1 = = = 110mm yk 100mm Vs 311600 KNnaKMlatGtibrma³ S 2 = d / 4 = 137.5mm yk 125mm / S3 = 550mm nig S 4 = 300mm dUcenH S max = 125mm edaysar S = 100mm < S max = 125mm dUcenHeRbIEdkkg DB10 @100mm g> Vu = 570kN > φVc / RtUvkarEdkkMlaMgkat;TTwg. KNna Vs = (Vu − φVc ) / φ = (570 − 111.3) / 0.75 = 611.6kN edaysar Vs > Vc2 enaHmuxkat;minRKb;RKan;. eKRtUvkartMeLIgTMhMrbs;muxkat;mYy b¤k¾TaMgBIr. cMNaM³ taragTI 2 nigrUbTI 8>10 k¾GacRtUv)aneRbIedIm,IKNnaKMlat S sMrab; K> nig X> )anpgEdr. 1> sMrab; K> Vs = 171.6kN BIrUbTI 8>10 ¬b¤taragTI 2> sMrab;EdkkgGkSr U DB10 ¦ eyIgTTYl)an S / d = 0.37 dUcenH S1 = 203.5mm EdltUcCag d / 2 = 250mm . cgcaMfa S max EdlQrelI Vs KW d / 2 minEmn d / 4 eT. dUcKñaBItaragTI 1> eyIgTTYl)an S3 = Av f yt / 0.35bw = 550mm . Shear and Diagonal Tension 144
  21. 21. T.Chhay NPIC 2> sMrab; X> Vs = 311.6kN / S / d = 0.18 enaH S1 = 100mm / Vs = 311.6kN > 251.2kN enaH S max = d / 4 RtUv)aneRbI. ]TahrN_2³ FñwmTMrsamBaØEdlmanRbEvg 5.2m nigmanRbEvgcenøaHssr (clear span) 4.9m edayRTnUv bnÞúkBRgayesμIefr 65kN / m nigbnÞúkBRgayesμIGefr 55kN / m . TMhMrbs;Fñwm nigsésrEdkRtUv)anbgðaj enAkñúgrUbTI 8>12. epÞógpÞat;muxkat;sMrab;kMlaMgkat;TTwg nigKNnaEdkkMlaMgkat;TTwgcaM)ac;. eKeGay f 'c = 20MPa nig f y = 400MPa . dMeNaHRsay³ eKeGay bw = 350mm / d = 580mm 1> KNnakMlaMgkat;TTwgemKuN (ultimate shear) BIbnÞúkxageRkA³ bnÞúkBRgayesμIemKuN = 1.2 × 65 + 1.6 × 55 = 166kN / m 166 × 4.9 Vu ¬enABImuxépÞTMr¦ = = 406.7 kN 2 KNna Vu ¬enAcMgayBImuxépÞénTMr¦ = 406.7 − 0.58 ×166 = 310.42kN 2> KNna φVc : φVc = φ (0.17 f 'c )bw d = 0.75(0.17 20 )350 × 580 × 10 −3 = 115.75kN 1 φV = 57.87 kN 2 c kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 145
  22. 22. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa KNna Vc1 = 0.33 f 'c bwd = 0.33 20 × 350 × 580 ×10−3 = 299.6kN KNna Vc2 = 2Vc1 = 599.2kN 3> eday Vu > φVc dUcenHmuxkat;RtUvkarEdkkMlaMgkat;TTwg. cMgay x' EdlenARtg;cMgayenHmuxkat; ebtugminRtUvkarEdkkMlaMgkat;TTwg ¬enA 12 φVc ¦KW³ ⎛ 406.7 − 57.87 ⎞ 4.9 x' = ⎜ ⎟ = 2.10m ⎝ 406.7 ⎠ 2 4> KNna Vs = (Vu − φVc ) / φ = (310.42 − 115.75) / 0.75 = 259.56kN . edaysar Vs < Vc1 enaH S max = d / 2 ≤ 600mm RtUv)anBicarNa ¬b¤eyagtamrUbTI 8>10 b¤taragTI2³ Vs > 251.2kN ¦. 5> KNnaEdkkg³ eRCIserIsEdkkgGkSr U DB10 / Av = 157mm 2 . KNna S1 edayQrelI Vs = 259.56kN / S1 = Av f yt d / Vs = 140mm yk 125mm ¬b¤yk S / d = 0.24 BItaragTI2 b¤BIrUbTI 8>10¦ 6> KNnaKMlatGtibrma³ S 2 = d / 2 = 580 / 2 = 290mm yk 250mm / S 3 = Av f yt / 0.35bw = 500mm ¬b¤eRbItaragTI1¦/ S 4 = 600mm . dUcenH S max = 250mm . 7> edaysar S1 = 125mm < S max = 250mm eRbI DB10 @125mm 8> KNna Vs sMrab;KMlatGtibrma 250mm As f yt d 157 × 400 × 580 − 3 Vs = = 10 = 145.7 kN s 250 φVs = 109.3kN φVc + φVs = 115.75 + 109.3 = 225kN cMgay x1 EdlenARtg;cMgayenHmuxkat;GaceRbIKMlat s = 250mm ⎛ 406.7 − 225 ⎞ 4.9 x1 = ⎜ ⎟ = 1.09m ⎝ 406.7 ⎠ 2 edaysar x1 mantMéltUc eRbI s = 125mm sMrab;cMgayFMCag b¤esμI 1.09m . cMNaMfa RbsinebI x1 Evg KMlatenAcenøaH 150mm eTA 250mm GacRtUv)anbEnßm. 9> EdkkgRtUv)anBRgaydUcxageRkam³ dak;EdkkgTI1enAcMgay S / 2 BImuxépÞénTMr EdkkgTImYyenA S / 2 = 125 / 2 = 62.5mm yk 50mm R)aMbYnEdkkgmanKMlat S = 125mm = 1125mm srub 1175mm > 1090mm bYnEdkkgmanKMlat S = 250mm = 1000mm srub 2175mm < 2450mm Shear and Diagonal Tension 146
  23. 23. T.Chhay NPIC cMnYnEdkkgsrubsMrab;FñwmKW 2(1 + 9 + 4) = 28 . karBRgayEdkkgRtUv)anbgðajenAkñúgrUbTI 8>13 ÉkMlaMggkat;TTwgEdl)anKNnaRtUv)anbgðajenAkñúgrUbTI 8>12. 10> dak;Edkkg DB12 cMnYnBIredIm enABIelImuxkat;FñmedIm,IedIrtYrCaEdkkgBüÜr. w 9> kMlaMgkat;TTwgEdlbNþalBIbnÞúkGefr enAkñúg]TahrN_TI2 TaMgbnÞúkefr nigbnÞúkGefrRtUv)ansnμt;faBRgayesμIeBjtambeNþayFñwm Edl begáIt)ankMlaMgkat;TTwgsUnüenAkNþalElVg. CaFmμta bnÞúkefrBitCaBRgayeBjelIbeNþayFñwm EtbnÞúk GefrGacGnuvtþeBj b¤k¾GnuvtþEtEpñkxøHrbs;Fñwm EdltMrUveGaymankMlaMgkat;TTwgGtibrmaekIteLIgenA kNþalElVg b¤muxkat;kMNt;NamYy. rUbTI 8>14 a bgðajBIFñwmTMrsamBaØCamYynwgbnÞúkBRgayesμIGnuvtþeBj beNþayFñwm. kMlaMgkat;TTwgERbRbYlCaragbnÞat;tambeNþayFñwm CamYynwgkMlaMgkat;TTwgGtibrmaenATMr A. kñúgkrNIEdlbnÞúkGefr W2 = 1.6WL kMlaMgkat;TTwgGtibrmamanGMeBIenARtg;TMr A enAeBlEdl W2 GnuvtþeBjElVgFñwm ¬rUbTI 8>14 a ¦. kMlaMgkat;TTwgGtibrmaekItmanenAkNþakElVgRbsinebIbnÞúkGefr RtUv)andak;EtBak;kNþalFñwm BC ¬rUbTI 8>14 b ¦ EdlbegáIt)an Vu enAkNþalElVgesμInwg W2 L / 8 . dUc enH kMlaMgkat;TTwgKNnaRtUv)anbegáIteLIgedaykarbEnßmkMlaMgkat;TTwgGtibrmaEdlbNþalmkBIbnÞúk Gefr ¬EdlRtUv)andak;enAelIRbEvgepSg²énElVg¦ eTAelIkMlaMgkat;TTwgGefr ¬rUbTI 8>14 c ¦. vaCakar Gnuvtþn_FmμtaedayKitkMlaMgkat;TTwgGtibrmaRtg;TMr A esμInwg Wu L / 2 = (1.2WD + 1.6WL ) L / 2 / b:uEnþ Vu enAkNþalElVgesμI W2 L / 8 = (1.6WL ) L / 8 CamYybnÞat;Rtg;ERbRbYltambeNþay AC nig CB dUcbgðajenA kñúg rUbTI 8>14 d. karKNnasMrab;kMlaMgkat;TTwgenAkñúkrNIenHnwgGnutþdUcKñanwgkarBnül;kñúg]TahrN_2. RbsinebI karerobrab;xagelIenHGnuvtþeTAFñwmkñúg]TahrN_2 enaH Vu ¬enATMr A ¦ = 406.7kN nig Vu ¬enA kNþalElVg¦ = (1.6 × 55)4.9 / 8 = 53.9kN . kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 147
  24. 24. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa Shear and Diagonal Tension 148
  25. 25. T.Chhay NPIC ]TahrN_3³ Fñwm cantilever RbEvg 3m manmuxkat;ctuekaNEkg nigRTnUvbnÞúkemKuNBRgayesμI nigcMcMnuc ¬bnÞúkpÞal;xøÜnRtuv)anrab;bBa©ÚlrYc¦ dUcbgðajenAkñgrUb 8>15. edayeRbI f 'c = 28MPa nig f y = 400MPa KNnaEdkkMlaMgkat;TTwgcaM)ac;sMrab;dak;kñúgFñwmTaMgmUl edayeyagtam ACI Code. dMeNaHRsay³ 1> KNnakMlaMgkat;TTwgtambeNþayFñwmEdlbNþalmkBIbnÞúkxageRkA Vu ¬enATMr¦ = 80 × 3 + 89 + 36 = 365kN Vud ¬enAcMgay d ¦ = 365 − 80 510 = 351.4kN 3000 Vu ¬enAcMgay 1.2m xageqVg¦ = 365 − 80 × 1.2 = 269kN Vu ¬enAcMgay 1.2m xagsþaM¦ = 269 − 89 = 180kN Vu ¬enAcugTMenr¦ = 36kN düaRkamkMlaMgkat;TTwgRtUv)anbgðajenAkñúgrUbTI 8>15. 2> KNna φVc ³ φVc = φ (0.17 f 'c bd ) = 0.75(0.17 28 )300 × 510 × 10 −3 = 103.2kN 1 φV = 51.6kN 2 c edaysar Vud > φVc muxkat;ebtugRtUvkarEdkkMlaMgkat;TTwg. KNna Vc1 = 0.33 f 'c bd = (0.33 28 )300 × 510 × 10 −3 = 267.2kN kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 149
  26. 26. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa Vc 2 = 2Vc1 = 534.4kN cMgay x EdlenARtg;enHmuxkat;minRtUvkarEdkkMlaMgkat;TTwg ¬enA 12 φVc = 51.6kN ¦ EdlRtVv)an vas;BITMr A . ⎛ 180 − 51.6 ⎞ x = 1.2 + ⎜ ⎟1.8 = 2.8m ⎝ 180 − 36 ⎠ ¬ 200mm BIcugTMenr¦. dUcKña x1 sMrab; φVc KW 2.16m BI A ¬ 840mm BIcugTMenr¦ 3> Epñk AC ³ kMlaMgkat;TTwgKNna Vu = Vud = 351.4kN . KNna Vs = (Vu − φVc ) / φ = (351.4 − 103.2) / 0.75 = 330.9kN . edaysarEt Vc1 < Vs < Vc 2 enaH S max ≤ d / 4 RtUv)an BicarNa ¬b¤epÞógpÞat;edayeRbIrUbTI 8>10¦. 4> KNnaEdkkg³ eRCIserIsEdkkgGkSr U DB10 / Av = 157mm 2 . KNna S1 ¬QrelI Vs ¦ Av f yt d 157 × 400 × 510 S1 = = = 100mm Vs 330900 eRbI 100mm ¬b¤TTYl s / d = 0.19 BIrUb 8>10¦. 5> KNnaKMlatGtibrma³ S 2 = d / 4 = 510 / 4 = 127.5mm yk 125mm Av f yt 157 × 400 S3 = = = 550mm ¬BItaragTI1 sMrab; b = 300mm ¦ 0.35b w 0.35 × 300 S 4 = 300mm dUcenH S max = 125mm 6> eday S = 100mm < S max = 125mm dUcenHeRbIEdkkg DB10 @100mm 7> enAcMnuc C / kMlaMgkat;TTwgKNna Vu = 269kN > φVc enaH Vs = (269 − 103.2) / 0.75 = 221kN . S1 = Av f yt d / Vs = 145mm Vs = 221kN < Vc1 = 267.2kN S 2 = d / 2 = 255mm ¬b¤ 250mm ¦ enaH S1 = 145mm b¤ 125mm S1 = 145mm < S 2 8> edaysarKMlat 125mm nig 100mm mantMélEk,rKña eRbIEdkkg DB10 @100mm sMrab;Epñk AC . 9> Epñk BC A. Vu = 180kN > φVc Vs = (180 − 103.2) / 0.75 = 102.4kN < Vc1 = 267.2kN B. S1 = Av f yt d / Vs = 157 × 400 × 510 / 102400 = 313mm C. S 2 = d / 2 = 510 / 2 = 255mm¬b¤tUcCag S3 = 550mm nig S 4 = 600mm ¦. yk S max = 250mm . eRbIEdkkg DB10 @ 250mm sMrab;Epñk BC . Shear and Diagonal Tension 150
  27. 27. T.Chhay NPIC 10> karBRgayEdkkgedayvas;ecjBITMr A ³ dak;EdkkgTImYyenA S = 50mm 2 12 × 100 = 1200mm 7 × 250 = 1750mm srub 3000mm karBRgayEdkkgRtUv)anbgðajenAkñúgrUbTI 8>16. EdkkgsrubmancMnYn 20 . 10> kugRtaMgkMlaMgkat;TTwgenAkñúgGgát;EdlmankMBs;ERbRbYl edaysarEtkugRtaMgkMlaMgkat;TTwg v CaGnuKmn_énkMBs;RbsiT§PaB d dUcenHkugRtaMgkat;TTwgERbRbYl tambeNþayFñwmebtugBRgwgedayEdkCamYynwgkBs;ERbRbYl. enAkñúgFñwmEbbenH ¬rUbTI 8>17¦ eKBicarNa elIGgÁGnnþtUc dx . kMlaMgsgát; C enAelImuxkat;NamYyesμInwgm:Um:g;EckeGayédXñas; b¤ C = M / y . edrIevTImYyén C KW³ ydM − Mdy dC = y2 RbsinebI C1 FMCag C2 enaH C1 − C2 = dC = vbdx ydM − Mdy dM M vbdx = 2 = − 2 dy y y y 1 ⎛ dM ⎞ M ⎛ dy ⎞ v= ⎜ ⎟− ⎜ ⎟ yb ⎝ dx ⎠ by 2 ⎝ dx ⎠ edaysar y = jd / dM / dx esμInwgkMlaMgkat;TTwg V nig d ( jd ) / dx CaCMral (slope)/ M ⎡d ⎤ ( jd )⎥ nig v = ¬*>@^¦ V V M v= − 2 ⎢ dx ± tan α bjd b( jd ) ⎣ ⎦ bjd b( jd ) 2 Edl V nig M CakMlaMgkat;TTwg nigm:Um:g;xageRkA ehIy α CamMuCMralénépÞmYyrbs;FñwmeTAnwgépÞmYy eTotrbs;Fñwm. sBaØabUkRtUv)aneRbIenAeBlEdlkMBs;fycuHÉm:Um:g;ekIneLIg b:uEnþsBaØadkRtUv)aneRbIenAeBl kMBs;ekIneLIgehIym:Um:g;k¾ekIneLIg. rUbmnþenHRtUv)aneRbIenAeBlEdlmMuCMraltUc EdlmMu α ≤ 30o . kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 151
  28. 28. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa TMrg;samBaØénsmIkar ¬*>@^¦GacRtUvbegáIteLIgedaysMrYl j enaHeyIgTTYl)an v= V M ± 2 tan α bd bd ¬*>@&¦ sMrab;viFIKNnaersIusþg; smIkarxageRkamGacRtUv)aneRbI vu = Vu ± M φbd φbd 2 tan α ¬*>@*¦ sMrab;kMlaMgkat;TTwg φVn = Vu ± Mu d tan α ¬*>@(¦ Shear and Diagonal Tension 152
  29. 29. T.Chhay NPIC rUbTI 8>18 bgðajBIFñwm cantilever CamYynwgbnÞúkcMcMnucenAcugTMenr. m:Um:g;nigkMBs; d ekInelIgkñúg TisedAeTArkTMr. kñúgkrNIenH sBaØadkRtUv)aneRbIenAsmIkar ¬*>@&¦ ¬*>@*¦ nig¬*>@(¦. dUcKña sBaØadk RtUv)aneRbIsMrab;muxkat; t enAkñúgFñwmTMrsamBaØdUcbgðaj ehIysBaØabUkRtUv)aneRbIsMrab;muxkat; Z Edlm:U m:g;ekIneLIgenAeBlEdlkMBs;fycuH. enAkñúgkrNICaeRcIn karERbRbYlkMBs;rbs;FñwmekItmanenAeLIEpñkrbs;FñwmEdlenAEk,rTMr ¬rUbTI 8>18¦. karBesaFn_eTAelIFñwmCamYykMBs;ERbRbYlbgðajfa FñwmEdlmankMBs;FMenATMrCaTUeTA)ak;edaysar kMlaMgkat;TTwgsgát;. ÉFñwmEdlmankMBs;tUcenATMrCaTUeTA)ak;edaysarPaBKμanesßrPaB EdlbNþalmkBI karraldalénsñameRbHemenAkñúgFñwmeLIgelI ehIybnÞab;mksñameRbHenaHraldaltamTisedkenAelImuxkat; FñwmEpñkxagelI. karBiesaFn_k¾)anbgðajEdrfa sMrab;FñwmEdlmankMBs;ERbRbYl ¬rUbTI 8>18¦ CamYynwgmMu eRTt α RbEhl 10o nigrgnUvkMlaMgkat;TTwg nigkMlaMgBt; ersIusþg;kMlaMgkat;TTwgrbs;ebtug VCV Gac RtUv)anKNnaeday VCV = Vc (1 + tan α ) ¬*>#0¦ Edl VCV = ersIusþg;kMlaMgkat;TTwgrbs;FñwmCamYynwgkMBs;ERbRbYl Vc = ⎢0.16 f 'c + ⎜17.2 ρ w u ⎟⎥bw d ≤ (0.29 f 'c )bw d ⎡ ⎛ V d ⎞⎤ ⎜ ACI Code Eq.11.6 ⎣ ⎝ M ⎟ u ⎠⎦ mMuEdlbegáIteLIgedayTisrbs;Edk. vaRtUv)anKitfaviC¢mansMrab;FñwmEdlmankMBs;tUc α= enATMr nigGviC¢mansMrab;FñwmEdlmankMBs;FMenATMr ¬rUbTI 8>18¦ d s = kMBs;RbsiT§PaBrbs;FñwmenATMr ACI Code Eq.11.3 CasmIkarRtUv)ansMrYl nigGaceRbIedIm,IKNna Vc ³ Vc = (0.17 f 'c )bw d ¬*>#!¦ ]TahrN_4³ KNnaFñwm cantilever dUcbgðajenAkñúgrUbTI 8>19 eRkamGMeBIbnÞúkemKuN. FñwmenHkMBs;srub enAcugTMenr 300mm ehIyekIneLIgeTArkTMr. edayeRbIPaKryEdk ρ = 1.5% / f 'c = 28MPa / f y = 400MPa nig b = 250mm . dMeNaHRsay³ 1> M u ¬TMr¦ = 36.5 × 2.52 / 2 + 62 × 2.5 = 269kN.m 2> sMrab; ρ = 1.5% / Ru = 4.72MPa M 269 ⋅ 10 6 d= = = 477.5mm Ru b 4.72 × 250 kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 153
  30. 30. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa As = 0.015 × 250 × 477.5 = 1790mm 2 ¬eRbIEdk 3DB28 ¦ yk d = 490mm / h = 550mm . 3> KNnasMrab;kMlaMgkat;TTwg³ kMlaMgkat;TTwgGtibrmaenATMrKW 62 + 36.5 × 2.5 = 153.25kN . Eday sarmuxkat;FñwmERbRbYl m:Um:g;RtUv)anBicarNakñúgkarKNnakMlaMgkat;TTwg. edaysarkMBs;FñwmekIn eLIgCamYym:Um:g;ekIneLIg sBaØadkRtUv)aneRbIenAkñúgsmIkar ¬*>@*¦ Vu Mu vu = − (tan α ) φbd φbd 2 edIm,Irk tan α / yk d enAcugTMenresμI 490mm nig d enAKl;TMresμI 240mm 490 − 240 tan α = = 0.1 2500 269 ⋅10 6 vu¬TMr¦ = 153250 − 0.75 × 250 × 490 0.75 × 250 × 490 2 0.1 = 1.07 MPa 4> kugRtaMgkMlaMgTTwgenAcugTMenrKW Vu / φbd ¬ M u = 0 ¦ 62000 vu = = 1.38MPa 0.75 × 250 × 240 5> enAcMgay d = 490mm BImuxépÞénTMr kMBs;RbsiT§PaBKW 441mm ¬BIrUbFrNImaRt¦ Vu = 153.25 − 36.5 × 0.49 = 135.4kN 2.012 Mu ¬enAcMgay 490mm BITMr¦= 62 × 2.01 + 36.5 × 2 = 198.4kN.m 135.4 ⋅10 3 198.4 ⋅10 6 × 0.1 vu = − = 1.09MPa 0.75 × 250 × 441 0.75 × 250 × 4412 Shear and Diagonal Tension 154
  31. 31. T.Chhay NPIC 6> enAkNþalElVg ¬1.25m BITMr¦ d = 365mm Vu = 153.25 − 36.5 × 1.25 = 107.6kN 1.25 2 M u = 62 × 1.25 + 36.5 = 106kN .m 2 107.6 ⋅10 3 106 ⋅10 6 × 0.1 vu = − = 1.15MPa 0.75 × 250 × 365 0.75 × 250 × 365 2 dUcKña enAcMgay 1.9m BITMr ¬ 0.6m BIcugTMenr¦ d = 300mm Vu = 83.9kN M u = 43.8kN vu = 1.23kN enAcMgay 2.2m BITMr ¬ 0.3m BIcugTMenr¦ d = 270mm Vu = 73kN M u = 20.2kN vu = 1.29kN tMélTaMgGs;enHRtUv)anbgðajenAkñúgrUbTI 8>20 7> kugRtaMgkMlaMgkat;TTwgedayebtugKW 0.17 28 = 0.9MPa kugRtaMgkMlaMgkat;TTwgGb,brmaEdlRtUvTb;edayEdkkMlaMgkat;TTwg vus = 1.38 − 0.9 = 0.48MPa ¬ vu nig vus RtUv)anekIneLIgedaypleFob 1/ φ kñúgsmIkar 8>28¦ 8> eRCIserIsEdkkg DB10 EdlmanEdkBIr Av = 2 × 78.5 = 157mm 2 Av f yt 157 × 400 S ¬caM)ac;¦ = = v s bw 0.48 × 250 = 523mm ¬sMrab; ¦ S max d 2 eTA = 245mm 120mm enAcugTMr Av f yt 157 × 400 ¬sMrab;Gb,brma ¦ S max Av = = 0.35bw 0.35 × 250 = 718mm 9> epÞógpÞat;KMlatGtibrma (d / 2) : vus ≤ 0.33 f 'c 0.33 f 'c = 0.33 28 = 1.74MPa > 0.48MPa 10> karBRgayEdkkg ¬cMgayBIcugTMenr¦ EdkkgcMnYnmYymancMgay 50mm = 50mm EdkkgcMnYndb;mancMgay120mm = 1200mm EdkkgcMnYnbImancMgay175mm = 525mm EdkkgcMnYnbI;mancMgay 200mm = 600mm kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 155
  32. 32. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa srub = 2375mm dUcenHenAsl;cMgay 125mm BIépÞémmuxTMr. Shear and Diagonal Tension 156
  33. 33. T.Chhay NPIC 11> Ggát;rgkarBt;eRCA Ggát;rgkarBt;KYrRtUv)anKNnaCaFñwmeRCARbsinebIpleFobén clear span ln ¬Edlvas;BIépÞmuxTl;Kña rbs;TMr rUbTI 8>21¦ elIkMBs;srub h mantMéltUcCag 4 (ACI Code, Section 11.8) . Ggát;KYrrgnUvbnÞúk enAelIépÞEdlQmnwgépÞénTMr EdlGaceFVIeGay strut rgkarsgát;GacbegáIteLIgenAcenøaHbnÞúk nigTMr ¬rUbTI 8>22¦. RbsinebIbnÞúkGnuvtþenA)at b¤épÞxagrbs;FñwmeRCA smIkarKNnakMlaMgkat;TTwgsMrab;FñwmFmμta Edl)aneGayBIxagmuxKYrRtUv)aneRbI. Ca]TahrN_ FñwmeRCAKWCaFñwmElVgxøIEdlRTbnþúkF¶n;/ CBa¢aMgbBaÄreRkam bnÞúkTMnajEpndI (gravity load), shear wall, nigkMralxNнrgnUvbnÞúkedk. niymn½yrbs;Ggát;rgkarBt;eRCAk¾RtUv)anbgðajenAkñúg ACI Code, Section 10.7.1. vabgðajfa Ggát;rgkarBt;EdlmanpleFob ln / h < 4 nigtMbn;rgbnÞúkcMcMnucsßitenAcMgayBIrdgénkMBs;rbs;Ggát;BIépÞén TMrRtUv)ancat;TukCaGgát;rgkarBt;eRCA. FñwmEbbenHKYrRtUv)anKNnaedayKitnUvkarBRgay nonlinear énkug RtaMg nigkarPøat;xag (lateral buckling) rUbTI 8>22 a. rUbTI 8>22 a bgðajBIkarBRgaykugRtaMgeGLasÞic enARtg;muxkat;kNþalElVgénFñwmeRCA nigrUbTI 8>22 b bgðajBIExSekagkugRtaMgemenAkñúgFñwmeRCAEdlrgbnÞúkenAépÞxagelI (top-load deep beam). ExS Cab;bgðajBI karBRgaykugRtaMgTaj ÉExSdac;²bgðajBIkarBRgaykugRtaMgsgát;. eRkambnÞúkF¶n; sñameRbH bBaÄreRTtekItmanenAkñgebtugkúñgTisedAEkgnwgkugRtaMgTajem ehIyesÞIrEtRsbeTAnwgExSKnøgdac; ¬rUbTI 8>22 c ¦. dUcenH eKRtUvkarTaMgEdkedk nigEdkbBaÄredIm,ITb;nwgkugRtaMgem. elIsBIenH EdkrgkarBt; edaykarTaj (tensile flexural reinforcement) RtUv)andak;enARbEhlmYyPaKR)aMenA)atrbs;FñwmtamKnøg kugRtaMgTaj ¬rUbTI 8>22b ¦. CaTUeTA karviPaKFñwmeRCAmanlkçN³sμúKsμaj nigGacGnuvtþedayeRbIKMrU truss b¤edIm,ITTYl)anlT§plkan;EtsuRkiteKeRbIviFI finite element b¤viFIRsedogKña. edIm,IgayRsYlkñúgkarKNna kMlaMgkat;TTwgénFñwmeRCA eKGacGnuvtþtamCMhanEdl)anerobrab;xageRkam³ kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 157
  34. 34. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 1> muxkat;eRKaHfñak; (critical section) ³ RbsinebImuxkat;eRKaHfñak;sMrab;KNnakMlaMgkat;TTwg enAkñúgFñwmeRCAEdlRTbnÞúkbBaÄrGnuvtþenAépÞxagelIrbs;Fñwm sßitenAcMgay X BIépÞénTMr enaHcM gay X GacRtUv)ankMNt;dUcxageRkam ¬rUbTI 8>23¦³ Shear and Diagonal Tension 158
  35. 35. T.Chhay NPIC a. sMrab;FñwmeRCAEdlRTbnÞúkBRgayesμI X = 0.15ln / Edl ln = clear span . b. sMrab;bnÞúkcMcMnuc X 1 = 0.5a1 ¬TMrxageqVg¦ b¤ X 2 = 0.5a2 ¬TMrxagsþaM¦ rUbTI 8>23/ Edl a1 nig a2 esμInwg shear span Ek,rTMrnImYy². Shear span CacMgayBIbnÞúkcMcMnuc eTAépÞénTMr. enAkñúgRKb;krNITaMgGs; cMgay X / X 1 nig X 2 dac;xatminRtUvFMCagkMBs;RbsiT§PaB d . 2> ersIusþg;kMlaMgkat;TTwgGtibrma φVn ³ ersIusþg;kMlaMgkat;TTwgGtibrma φVn sMrab;Ggát;rgkar Bt;eRCAminKYrmantMélFMCagtMélxageRkam ¬ φ = 0.75 ¦³ sMrab; ldn < 2 / φVn = φ 0.67 f 'c bwd ¬*>#@ a ¦ sMrab; 2 ≤ ldn ≤ 5 / φVn = φ 0.055⎛10 + ldn ⎞ f 'c bwd ⎜ ⎟ ¬*>#@ a ¦ ⎝ ⎠ b¤yk φVn = φ 0.83 f 'c bwd ¬*>## ¦ krNITaMgBIr manEcgenAkñúg ACI Code, Section 11.8.3. RbsinebI Vu > φVn enaHeKRtUvtMeLIg muxkat;ebtug. 3> a. ersIusþg;kMlaMgkat;TTwgrbs;ebtug Vc ³ ersIusþg;kMlaMgkat;Fmμta (nominal shear strength) Vc rbs;ebtugGacRtUv)anKNnadUcxageRkam³ Vc = 0.17 f 'c bw d ¬*>#$ ¦ kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 159
  36. 36. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa Vc enHRsedogKñanwgersIusþg;kMlaMgkat;TTwgebtugsMrab;FñwmFmμta dUcenAkñúgEpñkxagmuxénem eronenH. b. mü:agvijeTot eKGaceRbIsmIkarmYyepSgeTotEdlmanTak;Tgnwgm:Um:g;emKuN nigkMlaMgkat;TTwgemKuNenAmuxkat;eRKaHfñak; ⎛ 2.5M u ⎞ ⎡ ⎛ V d ⎞⎤ Vc = ⎜ 3.5 − ⎜ V d ⎟ ⎟ ⎢0.16 f 'c + ⎜17.2 ρ w u ⎟⎥bw d ⎜ M ⎟ ¬*>#% ¦ ⎝ u ⎠⎣ ⎝ u ⎠⎦ b:uEnþ Vc minKYrelIsBI 0.5 f 'c bwd tMél (3.5 − 2.5M u / Vu d ) minKYrFMCag 2.5 nigminKYrtUcCag 1. tMélén M u nig Vu RtUv)anykenARtg;muxkat;KNnaeRKaHfñak;. ersIusþg;kMlaMgkat;FMénsmIkar ¬*>#$ ¦ RtUv)aneRbICamYyKMnitfa sñameRbHEdltUcesÞIrEtemIlmineXIjGacekItmanenAkñúgFñwmeRCA nigGacGueRKaH)an. sñameRbHGaccab;epþIm ekItmanenARbEhlmYyPaKbIénbnÞúkemKuN. 4> EdkkMlaMgkat;TTwg³ enAeBlkMlaMgkat;TTwgemKuN Vu > φVc eKRtUvdak;EdkkMlaMgkat;TTwg Edlcat;Tukfa Vu = φ (Vc + Vs ) b¤ Vs = (Vu − φVc ) / φ . CMhanénkarKNnamandUcxageRkam³ a. kMNt; Vs ³ kMlaMgTb;edayEdkkMlaMgkat;TTwg Vs RtUv)ankMNt;BIsmIkarxageRkam³ ⎡ A ⎛ 1 + l n / d ⎞ Avh ⎛ 11 − l n / d ⎞⎤ Vs = ⎢ v ⎜ ⎟+ ⎜ ⎟⎥ f y d ¬*>#^ ¦ S⎣ v ⎝ 12 ⎠ S h ⎝ 12 ⎠⎦ Edl Av = RkLaépÞsrubénEdkkMlaMgkat;TTwgbBaÄrEdlmanKMlat S v ehIyEkgeTAnwgEdk emrgkarTajedaykarBt;énépÞxagTaMgBIrrbs;Fñwm Avh = RkLaépÞsrubénEdkkMlaMgkat;TTwgedkEdlmanKMlat S h RsbnwgEdkemrgkar TajedaykarBt;énépÞxagTaMgBIrrbs;Fñwm b. KMlatEdkkMlaMgkat;TTwgKW³ KMlatQrGtibrma S v ≤ d ≤ 300mm 5 KMlatedkGtibrma S h ≤ d ≤ 300mm 5 c. EdkkMlaMgkat;TTwgGb,brma³ RkLaépÞEdkkMlaMgkat;TTwgbBaÄrKW Av = 0.0025bw S v . RkLaépÞEdkkMlaMgkat;TTwgedkKW Avh = 0.0015bw S h . d. EdkkMlaMgkat;TTwgRtUvkarenARtg;muxkat;eRKaHfñak;KYrRtUv)anlatsn§wgeBjRbEvg nigkMBs; rbs;FñwmeRCA. e. sMrab;FñwmeRCACab; EdkkMlaMgkat;TTwgdUcKñaKYrRtUv)aneRbIenARKb;ElVg RbsinebIElVgTaMgenaH manRbEvgesμIKñaCamYybnÞúkRsedogKña. Shear and Diagonal Tension 160
  37. 37. T.Chhay NPIC 5> EdkrgkarBt;énFñwmeRCA³ dMeNIrRbRBwtþeTAénkarBt;rbs;FñwmeRCAKWmanlkçN³sμúKsμaj nigTam TarkarviPaKkugRtaMg nigbMErbMrYlrageFobtamlkçN³ nonlinear tamkMBs;rbs;Fñwm. sMrab;kar KNnadMbUg viFId¾sMrYlxageRkamGacRtUv)aneRbI³ φM n = φAs f y ( y ) Edl y = édXñas; = (d − a / 2) . edaysartMél (d − a / 2) mankarBI)akkñgkarKNna/ éd Xñas; y GacRtUv)anKNnaRbEhlykesμInwg 0.6h sMrab; ln / h = 1 nigmantMél esμInwg 0.8h sMrab; ln / h = 2 . viFanéRtzan (Linear interpolation) GacRtUv)an eRbIedIm,IKNna y enAeBl ln / h ERbRbYlcenøaH 1.0 nig 2.0 . dUcenH³ M As = u φyf ¬*>#&¦ y tMélén As minGactUcCagEdkrgkarBt;Gb,brmaEdlRtUvkarsMrab;FñwmFmμtaEdlnwgeGayenA eBlbnÞab; edaysnμt; d = 0.9h . As ¬Gb,brma¦ = ¬*>#*¦ 0.25 f 'c 1.38 bw d ≥ bw d f y f y GgÁTIBIrlub enAeBlEdl f 'c < 30MPa . cMNaMfa f y nig f 'c KitCa MPa . EdkrgkarTajedaykarBt; (flexural tension reinforcement) KYrdak;enA h / 4 eTA h / 5 én Fñwm nigKYrmanKMlatRKb;RKan;tambeNþay)attMbn;Taj. EdkrgkarTajKYrEtf<k;eTAkñúgTMr eGay)anl¥. sMrab;karviPaK nigkarKNnaEdlmanlkçN³suRkwt nigsMrab;FñwmeRCACab; viFI nonlinear Edl manlkçN³hμt;ct;GacRtUv)aneRbIedIm,IbrimaNd¾RtwmRtUv nigkarBRgayénEdkrgkarTaj. ]TahrN_5³ FñwmeRCATMrsamBaØmanElVgRbEvg 4.2m man clear span RbEvg ln = 3.6m kMBs;srub h = 2.5m nigTTwg b = 0.4mm . FñwmeRCARTedaybnÞúkeFVIkarefBRgayesμI 600kN / m ¬rYmbBa©ÚlbnÞúkpÞal; xøÜn¦ nigbnÞúkGefr 320kN / m enAelIEpñkxagelIénFñwm. KNnasésrEdkrgkarBt; nigEdkkMlaMgkat;TTwg sMrab;FñwmenH edayeRbI f 'c = 28MPa nig f y = 400MPa ¬rUbTI8>24¦. dMeNaHRsay³ 1> KNnasMrab;EdkTb;nwgm:Um:g; Wu = 1.2WD + 1.6WL = 1.2 × 600 + 1.6 × 320 = 1232kN / m Wu L2 1232 × 4.2 2 Mu = = = 2716.56kN .m 8 8 l n 3 .6 = = 1.44 h 2 .5 kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 161
  38. 38. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa kMNt;édXñas;/ y . sMrab; ln / h = 1 / y = 0.6d nigsMrab; ln / h = 2 / y = 0.8d dUcenHsMrab; l n / h = 1.44 / y = 0.688d ¬eday interpolation ¦ = 0.688 × 0.9 × 2.5 = 1.55m ¬edaysnμt; d = 0 .9 h ¦ Mu 2716.56 ⋅10 6 As = = = 4868mm 2 φyf y 0.9 × 1550 × 400 edaysar f 'c < 30MPa As ¬Gb,brma¦ = 1.38 1.38 bw d = 400 × 2250 = 3105mm 2 f y 400 dUcenH As = 4868mm 2 lb;. eRbI 10DB25 ¬ 4909mm 2 ¦EdlmanR)aMedImenAépÞmYy² edayBRgay kñúgkMBs; h / 5 = 500mm EdlCatMbn;TajénFñwm. KMlatrbs;Edk = 500 / 5 = 100mm . EdkTaMgenH KYrbgáb;cUleTAkñúgTMreGay)anl¥. 2> KNnasMrab;kMlaMgkat;TTwg k> KNna Vu nig M u enAcMgay x = 0.15ln = d BImuxépÞénTMr 0.15l n = 0.15 × 3.6 = 0.54m < 2.25m KNna Vu = 1232 × 3.6 2 − 1232 × 0.54 = 1552.3kN 0.54 2 M u = 1232 × 3.6 × 0.54 − 1232 × = 1017.9kN .m 2 Mu 1017.9 = = 0.29 Vu d 1552.3 × 2.25 x> KNna Vc ³ Mu 3 .5 − 2 .5 = 3.5 − 2.5(0.29 ) = 2.775 > 2.5 Vu d dUcenH eRbI 2.5 . enAkñúgkrNIenH KNna M u / Vu d edIm,IeRbIkñgkarKNna Vc ³ 2.5 = 3.5 − 2.5M u /(Vu d ) Mu Vu d = 0 .4 b¤ Vu Mud = 2 .5 A 4909 ρw = s = = 0.00545 bw d 400 × 2250 [ ] Vc = 2.5 0.16 28 + (17.2 × 0.00545 × 2.5) 400 × 2250 × 10 −3 = 2432.2kN Vc ≤ 0.5 f 'c bw d = 0.5 28 × 400 × 2250 = 2381.2kN dUcenH Vc = 2381.2kN lb;. φVc = 1785.9kN Shear and Diagonal Tension 162
  39. 39. T.Chhay NPIC K> KNna Vs = (Vu − φVc ) / φ edaysar φVc = 1785.9kN > 1552.3kN enaH Vs = 0 dUcenHeKRtUvkarEdkkMlaMgkat;TTwgGb,brma. X> KNnaEdkkMlaMgkat;TTwg³ edaysnμt;eRbIEdk DB12 sMrab;dak;enAépÞsgçagTaMgtamTisedAedk nigTisedAQrenaH π Av = Avh = 2 × 12 2 = 226mm 2 4 KMlatGtibrmaGnuBaØatrbs;EdkQr nigEdkedk S v = S vh = d 2250 5 = 5 = 450mm > 300mm yk Sv = S nh = 300mm EdkQrGb,brma Av ¬Gb,brma¦= 0.0025 × 400 × 300 = 300mm 2 > 226mm 2 bBa©úHKMlatEdkkgbBaÄr Sv = 400 × 0.0025 = 226mm 226 EdkedkGb,brma Avh ¬Gb,brma¦= 0.0015 × 400 × 300 = 180mm 2 < 226mm 2 dUcenH eRbI DB12 @ 200 sMrab;TisbBaÄr nig DB12 @ 300 sMrab;Tisedk 3> RbsinebIeyIgeRbI Vc = 0.17 f 'c bwd enaH Vc = 0.17 28 × 400 × 2250 ×10 −3 = 809.6kN nig φVc = 607.2kN < 1552.3kN . dUcenH eKRtUvkarEdkkMlaMgkat;TTwg. 1552.3 − 607.2 Vs = = 1260.1kN 0.75 edaysnμt;eRbIEdk DB12 sMrab;dak;enAépÞsgçagTaMgtamTisedAedk nigTisedAQrenaH π Av = Avh = 2 × 12 2 = 226mm 2 4 edaysnμt;faKMlatrbs;EdkTaMgBIrTisedAesμInwg Sv = S h = S nig ln / d = 3.6 / 2.25 = 1.6 ⎡A ⎛ 1 + l n / d ⎞ Avh ⎛ 11 − l n / d ⎞⎤ Vs = ⎢ v ⎜ ⎟+ ⎜ ⎟⎥ f y d ⎣ Sv ⎝ 12 ⎠ S h ⎝ 12 ⎠⎦ ⎡ 226 ⎛ 1 + 1.6 ⎞ 226 ⎛ 11 − 1.6 ⎞⎤ 1260100 = ⎢ ⎜ ⎟+ ⎜ ⎟⎥ 400 × 2250 ⎣ S ⎝ 12 ⎠ S ⎝ 12 ⎠⎦ S = 161mm yk S = 150mm EdltUcCag Sv ¬Gtibrma¦ nig S h ¬Gtibrma¦. eRbI S = 150mm sM rab;TaMgKMlatedk nigKMlatQr. Av ¬Gb,brma¦= 0.0025 × 400 × 150 = 150mm 2 < 226mm 2 Avh ¬Gb,brma¦= 0.0015 × 400 × 150 = 90mm 2 < 226mm 2 kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 163
  40. 40. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa dUcenH eRbI DB12 @150mm enAelIépÞTaMgBIrTaMgTisedAedk nigTisedAQr. sMNaj;EdkpSarGac RtUv)aneRbIedIm,ICMnYskarBRgayEdkEdlCadMeNaHRsaymYyEdlmanlkçN³snSMsMécCag. kar BRgayEdkenAkñúgmuxkat;ebtugRtUv)anbgðajenAkñúgrUbTI 8>24. ]TahrN_6³ FñwmeRCA strut and tie FñwmeRCATMrsamBaØEdlman clear span = 3.6m kMBs;srub = 1.8m nigTTwg = 450mm . FñwmenHRT ssrkaerEdlmanRCug = 450mm enAkNþalElVgEdlRTnUvbnÞúkefr = 1335kN nigbnÞúkGefr = 1070kN . KNnaFñwmenHedayeRbIviFI strut and tie. eKeGay f 'c = 28MPa nig f y = 400MPa ¬rUbTI8>25¦. Shear and Diagonal Tension 164
  41. 41. T.Chhay NPIC dMeNaHRsay³ 1> KNnabnÞúkemKuN ¬rUbTI 8>25¦ TMgn;Fñwm = 4.5 ×1.8 × 0.45 × 25 = 91.1kN edaysarTMgn;pÞal;rbs;FñwmmantMéltUcebIeFobCamYybnÞúkcMcMnucenAkNþalElVg dUcenHbEnßmvaeTA kñúgbnÞúkGefrcMcMnucEdlmanGMeBIrenAkNþalElVg Pu = 1.2 D + 1.6 L = 1.2(1335 + 91.1) + 1.6 × 1070 = 3423.32kN R A = RB = 1711.66kN 2> epÞógpÞat;faetIFñwmenHeRCAtamkarEcgrbs; ACI Code, Section 11.8: clear span ln = 3.6m nig h = 1.8m ehIy l n / d = 2 < 4 dUcenH FñwmenHCaFñwmeRCA. 3> KNnaersIusþg;kMlaMgkat;TTwgGtibrmaénmuxkat;Fñwm³ yk Vu enARtg; A = R A = 1771.66kN nigsnμt;yk d = 0.9h = 0.9 ×1.8 = 1.62m Vn = 0.83 f 'c bw d = 0.83 28 × 450 × 1620 × 10 −3 = 2743.1kN φVn = 0.75 × 2743.1 = 2057.3kN > Vu ¬OK¦ 4> eRCIserIsKMrU truss eRCIserIsKMrU truss RtIekaN. snμt;facMnuc node eFVIGMeBIsßitenAGkS½TMr nigenAcMgay 150mm BI EKm)at b¤EKmkMBUlFñwm ¬rUbTI8>26¦. KMrU strut and tie pÁúMeLIgedayGgát; tie AB mYynigGgát; strut BIr AD nig DB . dUcKña RbtikmμenARtg;cMnuc A nigcMnuc B nigbnÞúk Pu Rtg;cMnuc D tMNagCa strut bBaÄr. RbEvg strut Ggát;RTUg AD = 1.52 + 2.0252 = 2.52m yk θ CamMurvagGgát; strut nigGgát; tie enaH tan θ = 1.5 2.025 = 0.7407 enaH θ = 36.5o > 26o ¬OK¦ 5> KNnakMlaMgenAkñúgGgát; truss ³ kMlaMgsgát;enAkñúgGgát; strut AD = FAD = FBD = 1711.66 21..52 = 2875.6kN 5 kMlaMgTajenAkñgGgát; tie AB = FAB = 2875.6 22..025 = 2311kN 52 6> KNnaersIusþg;RbsiT§PaB f ce . snμt;EdkTb; (confining reinforcement) RtUv)andak;edIm,IkarBar kMlaMgbMEbk (splitting force). Ggát; strut AD nig DB tMNageGayGgát;rgkarsgát;ragdb (bottle-shape compression member) dUcenH β s = 0.75 . f ce = 0.85β s f 'c = 0.85 × 0.75 × 28 = 17.85MPa kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 165
  42. 42. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa Ggát; strut bBaÄrenAcMnuc A / B nig D manmuxkat;esμI (uniform section) dUcenH β s = 1.0 f ce = 0.85β s f 'c = 0.85 × 1× 28 = 23.8MPa tMbn;cMnuc (nodal zone) D mankMlaMg C − C − C dUcenH β s = 1.0 . ersIusþg;RbsiT§PaBenA nodal zone D KW f ce = 0.85β s f 'c = 0.85 × 1× 28 = 23.8MPa edaysarEtGgát; strut AD nig DB P¢ab;eTAcMnucepSgeTot enaH f ce = 17.85MPa lb;elI nodal zone TaMgGs;. 7> KNna nodal zone k> KNna nodal zone enAcMnuc A ³ snμt;fakMlaMgén nodal zone mankugRtaMgdUcKñaKW 17.85MPa ehIyépÞEkgeTAnwgkMlaMgEdlRtUvKña φFn ≥ Fu b¤ φf ce Acs ≥ Fu Edl φ = 0.75 sMrab; strut, tie nig node. RbEvgénépÞedk ab ¬rUbTI8>27 a¦ esμInwg Fu /(φf ce b) = 1711.66 ⋅10 3 /(0.75 × 17.85 × 450) = 284mm BIFrNImaRt RbEvg ac = 284 2311 1711.66 = 383mm dUcKña RbEvg bc = 284 2875.6 1711.66 = 477mm Shear and Diagonal Tension 166
  43. 43. T.Chhay NPIC TIRbCMuTMgn;rbs; nodal zone sßitenA 383 / 2 = 191.5mm BI)aténFñwm ¬eyIg)ansnμt; 150mm ¦ x> KNna nodal zone enAcMnuc D ¬rUbTI8>27 b¦³ RbEvgénépÞedk de = 3423.32 ⋅103 /(0.75 ×17.85 × 450) = 568mm RbEvgén df = ef = 568 3423.32 = 477mm 2875.6 RbEvgrbs; fg = 477 2 − ( 568 ) 2 = 383mm 2 dUcenH TIRbCMuTMgn;én nodal zone sßitenA 383 / 3 = 128mm BIépÞxagelIrbs;Fñwm¬eyIg)ansnμt; 150mm ¦ 8> KNnaEdkQr nigEdkedk³ k> EdkQr³ mMurvagEdkQr nigGgát; strut KW 53.5o BIrUbTI 8>27 a. eRbIEdk DB16 EdlmanKMlat π 300mm / As = 2 × 16 2 = 402mm 2 ¬eCIgBIr¦/ sin 53.5o = 0.804 4 ( Asi / bs S ) sin γ i = 402 /(450 × 300) × 0.804 = 0.0024 x> Edkedk³ mMurvagEdkedk nigGgát; strut KW 36.5o BIrUbTI 8>27 a. eRbIEdk DB16 EdlmanKMlat π 300mm / As = 2 × 16 2 = 402mm 2 ¬eCIgBIr¦/ sin 36.5o = 0.595 4 ( Asi / bs S ) sin γ i = 402 /(450 × 300) × 0.595 = 0.0018 K> ( Asi / bs S ) sin γ i ¬srub¦ = 0.0024 + 0.0018 = 0.0042 > 0.003 ¬OK¦ 9> KNnaGgát; tie edk AB ³ k> KNna As ³ Fu = φAs f y As = 2311 ⋅10 3 / (0.75 × 400) = 7703mm 2 eRbI 12DB30 ¬ As = 8482mm 2 ¦ dak;CabIbICYrdUcbgðajkñúgrUbTI 8>27 c. x> KNnaRbEvgf<k; (anchorage length)³ RbEvgf<k;RtUv)anvas;BIcMnuccab;BI nodal zone ¬rUbTI8>28¦. tan 36.5o = 190 / x x = 257 mm RbEvgTMBk;Edlman = 257 + 142 + 225 − 35 ¬kMras;ebtugkarBarEdk¦ = 589mm RbEvgTMBk;caM)ac;sMrab;Edk DB30 KW 47.5 × 30 = 1425mm > 589mm dUcenHeRbITMBk; 90o cgP¢ab;CamYyEdkssr ( ) l dh = 0.02ψ e λf y d b / f 'c kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 167
  44. 44. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa ψ e = λ = 1.0 d b = 30 l dh = (0.24 × 400 )30 / 28 = 544mm < 589mm Shear and Diagonal Tension 168
  45. 45. T.Chhay NPIC ]TahrN_7³ eKmanFñwmTMrsamBaØmYyEdlmanRbEvg 6m ¬ clear span ¦ rgnUvbnÞúkBRgayefr 47.5kN / m nigbnÞúkBRgayGefr 25kN / m . FñwmenHmanmuxkat; b = 35cm nig d = 55cm . FñwmenHBRgwgedayEdk 4DB25 BRgaymYyCYr. cUrkMNt;nUvmuxkat;caM)ac;sMrab;kMlaMgkat;TTwg. smμtikmμ³ f ' = 28MPa nig f = 280MPa . c yt kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 169
  46. 46. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa dMeNaHRsay³ k> bnÞúkemKuN ¬bnÞúkKNna¦ 1.2 D + 1.6 L = 1.2 × 47.5 + 1.6 × 25 = 97 kN / m x> kMlaMgkat;TTwgKNnaenARtg;muxxagssr 6 Vu = 97 × = 291kN 2 K> kMlaMgkat;TTwgKNnaenAcMgay d BIépÞxagssr Vud = 291 − (0.55 × 97) = 237.65kN X> ersIusþg;kMlaMgkat;TTwgEdlTb;edayebtug Vc = 0.17 f 'c bd = 0.17 28 × 350 × 550 = 173.2kN φVc = 130kN 1 φVc = 65kN 2 g> kMlaMgkat;TTwgEdlEdkRtUvTb; Vu − φVc 237.65 − (0.75 × 173.2) Vs = = = 143.5kN φ 0.75 c> cMgayBImuxépÞssrmk 1 2 φVc = 65kN 291 − 65 x' = × 3 = 2.33m 291 q> KNnaEdkkg 1> eRCIserIsEdk RB10 ¬EdkkgmaneCIgBIr¦ ⇒ Av = 2 × 78.5mm 2 = 157 mm 2 A f d 157 × 280 × 550 ⇒ s1 = v yt = = 168.5mm < 600mmm Vs 143.5 × 103 dUcenHykKMlat 160mm RtYtBinitüKMlatGtibrma d 550 s2 = = = 275mm 2 2 3A f 3 × 157 × 280 s3 = v yt = = 376.8mm b 350 s1 < s2 < s3 2> RtYtBinitüKMlatGtibrmaesμI d 4 Vc1 = 0.33 f 'c bd = 0.33 × 28 × 350 × 550 = 336.1kN Vc 2 = 2Vc1 = 2 × 336.1kN = 672.2kN Shear and Diagonal Tension 170
  47. 47. T.Chhay NPIC eday V < V dUcenHKMlatEdkGtibrmakMritRtwm s = d = 275mm s c1 2 max C> kMlaMgkat;TTwgEdlTb;edayEdksMrab;KMlat s = 2 = 275mm d max Av f yt d 157 × 280 × 550 Vs ( for smax = 275mm) = = = 87.9kN smax 275 φVs = 0.75 × 87.9kN = 65.94kN cMgayBImuxTMr eTAdl;EdkkgEdlmanKMlat s max = 275mm 291 − (130 + 65.94) x1 = × 3 = 0.98m 291 dUcenH sMrab; 0.98m BImuxénTMr eRbIEdkkg RB10 KMlat 160mm nigsMrab;EpñkenAsl; eRbIEdkkg Gb,brma ¬KMlatGtibrma¦ Q> karBRgayEdkkg Edkkg1 manKMlat 2 = 80mm s Edkkg6 manKMlat 160mm = 960mm srub 1040mm = 1.04m > 0.98m Edkkg6 manKMlat 270mm = 1620mm srub 2660mm = 2.66m < 3m nigEdkkgcugeRkay (3 − 2.66) = 0.34m srubEdkkgTaMgGs;EdlRtUveRbIsMrab;RbEvgFñwm 6m man 28kg. kMlaMgkat;TTwg nigkMlaMgTajGgát;RTUg 171
  48. 48. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa Shear and Diagonal Tension 172

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