Xvii design of two way slab

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Xvii design of two way slab

  1. 1. T.Chhay NPIC XVII. karKNnakMralxNнBIrTis Design of Two-Way Slabs 1> esckþIepþIm Introduction kMralxNнGacRtUv)anBicarNaCaGgát;eRKOgbgÁúMEdlmankMras; h tUcCagRbEvg L nigTTwg S . TMrg;d¾samBaØrbs;kMralxNнKWkMralxNнEdlRtUv)anRTedayTMrQmKña Edlvapþl;nUvPaBdabcMbgkñúg TismYy EdleKeGayeQμaHfa kMralxNнmYyTis (one-way slab). karKNnakMralxNнmYyTisman niyayenAkñúgemeronTI 9. enAeBlkMralxNнRtUv)anRTedayRCugTaMgbYn nigmanpleFobbeNþay L elITTwg S tUcCag BIr ehIykMralxNнdabBIrTis elIsBIenHbnÞúkenAelIkMralxNнRtUv)anbBa¢ÚneTATMrTaMgbYnRCug. kMral xNнEbenHRtUv)aneKeGayeQμaHfa kMralxNнBIrTis (two-way slab). m:Um:g;Bt; nigPaBdabenAkñúgkM ralxNнEbbenHtUcCagenAkñúgkMralxNнmYyTis kMralxNнdUcKñaGacRTbnÞúk)aneRcInCagenAeBlEdl vamanTMrTaMgbYnRCug. bnÞúkenAkñúgkrNIenHRtUv)anRTBIrTis ehIym:Um:g;Bt;kñúgTisnImYy²tUcCagm:Um:g; Bt;enAkñúgkMralxNнRbsinebIbnÞúkrbs;vaRtUv)anRTkñúgTisEtmYy. kartMerob rt-Fñwm-kMralxNн (slab- beam-girder) KMrUénkMralxNнmYyTis nigBIrTisRtUv)anbgðajenAkñúgrUbTI 17>1. 2> RbePTkMralxNнBIrTis Types of Two-Way Slabs kMralxNнebtugBIrTisGacRtUv)ancat;cMNat;fñak;dUcxageRkam³ karKNnakMralxNнBIrTis 438
  2. 2. T.Chhay NPIC karKNnakMralxNнBIrTis 439
  3. 3. T.Chhay NPIC a. kMralxNнBIrTisenAelIFñwm (two-way slab on beam)³ krNIenHekItmanenAeBlEdlkMral xNнBIrTisRtUv)anRTedayFñwmenAelIRCugTaMgGs;rbs;va ¬rUbTI17>1¦. bnÞúkBIkMralxNнRtUv bBa¢ÚneTATMrFñwmTaMgbYnrbs;va EdlnwgbBa¢ÚnbnÞúkbnþeTAssr. b. Flat slab³ CakMralxNнBIrTisEdlRtUv)anBRgwgBIrTisedayKñanFñwmRT ehIybnÞúkRtUv)anbBa¢Ún pÞal;eTAssrTMr. ssrcg;TMluHkMralxNн EdlRtUv)ankarBaredaybIviFIxageRkam ¬rUbTI 17>2 nig 17>3¦³ - edayeRbI drop panel CamYynwg column capital. - edayeRbI drop panel EdlKμan column capital. ebtugEdlBT§½CMuvij column capital KYr EtRkas;RKb;RKan;edIm,ITb;Tl;nwgkugRtaMgTajGgát;RTUgEdlekItBIkMlaMgkat; punching shear. - edayeRbI column capital edayKμan drop panel EdlCaviFImYyminFmμta. c. Flat-Plate floor³ CaRbBn§½kMralxNнBIrTisEdlmankMras;kMralxNнesμI nigsßitenABIelIssr edaypÞal;edayKμanFñwm b¤ column capital ¬rUbTI 17>2 a¦. kñúgkrNIenHssrcg;TMluHkMral xNнedaykugRtaMgTajGgát;RTUg. dUcenH CaTUeTAeKRtUvkarbegáInkMras;kMralxNн b¤dak;Edk Biess. d. Two-way ribbed slabs nig waffle slab system³ kMralxNнRbePTenHekItBIkMralxNнEdl manpleFobbeNþayelITTwgtUcCag 2. CaTUeTAkMras;rbs;kMralxNнsßitenAcenøaH 5cm eTA 10cm nigRtUv)anRTedayrnUt (rib or joist) TaMgBIrTis. rnUtRtUv)antMerobkñúgTisnImYy²Ca mYyKMlatRbEhlBI 50cm − 75cm EdlbegáItragkaer b¤ctuekaNEkg ¬rUbTI 17>2 c¦. rnUt k¾GacRtUv)antMerobedaymMu 45o b¤ 60o BIGkS½rbs;kMralxNн EdlbegáInesaPNнPaBsßabtü- kmμ. sMrab; two-way ribbed slabs RbBn§½epSg²GacRtUv)anTTYlyk³ - RbBn§½rnUtBIrTisCamYynwgRbehagcenøaHrnUtEdlTTYledayeRbIBum<Biess EdlCaTUeTA manragkaer. rnUtRtUv)anRTedayrtTaMgbYnRCugEdlsßitenABIelIssr. kMralxNнRbePT enHRtUv)aneKeGayeQμaHfa two-way ribbed (joist) slab system . - RbBn§½rnUtBIrTisCamYyeRKOgbMeBj (filler) enAcenøaHrnUtEdleFVIeGayBidanerobesμI. eKOgbMeBj (filler) CagRbehag nigeFVIBIebtugTMgn;Rsal b¤TMgn;Fmμta b¤BIsMPar³TMgn; RsalepSgeTot. rnUtRtUv)anRTedayrtenARCugTaMgbYnEdlRtUv)anRTbnþedayssr. karKNnakMralxNнBIrTis 440
  4. 4. T.Chhay NPIC kMralxNнRbePTenHk¾RtUv)aneKeGayeQμaHfa two-way ribbed slab system b¤ hollow- block two-way ribbed system . - RbBn§½rnUtBIrTisCamYyRbehagcenøaHrnUt nigKμanrt b¤FñwmRTrnUt. vaQrenAelIssreday pÞal;CamYynwgbnÞHebtugtan;. kMralxNнRbePTenHRtUv)anehAfa waffle slab. karKNnakMralxNнBIrTis 441
  5. 5. T.Chhay NPIC 3> kareRCIserIsRbBn§½kMralxNнebtugEdlmanlkçN³esdækic© Economical Choice of Concrete Floor Systems RbBn§½kMralxNнCaeRcInRbePTRtUv)aneRbIsMrab;GKarTUeTA dUcCa eKhdæan kariyal½y nigGKar rdæ)alepSg². kareRCIserIsRbBn§½kMralxNнEdlmanlkçN³kMralxNн nigRKb;RKan;GaRs½yelIRbePT GKar/ rUbragsßabtükmμ/ esaPNн nigRbEvgElVgEdlenAcenøaHssr. CaTUeTA bnÞúkGefrenAelIGKar ERbRbYlcenøaHBI 3.8kN / m 2 − 7.2kN / m 2 . karENnaMTUeTAsMrab;kareRbIR)as;RbBn§½kMralxNнEdl manlkçN³esdækic©RtUv)ansegçbdUcxageRkam³ - Flat plate ³ saksmbMputsMrab;ElVgEdlmanRbEvgcenøaHBI 6m − 7.5m nigbnÞúkGefrERb RbYlBI 2.9kN / m 2 − 4.8kN / m 2 . GtßRbeyaCn_énkarTTYlyk flat plate rYmmankarcM NayelIBum<Gs;éføefak TTYl)anBidanrabesμI nigkarsagsg;qab;. Flat plate manlT§PaB Tb;kMlaMgkat;TTWgTab nigPaBrwgRkajtUc EdleFIVeGaymanPaBdabFM;. Flat plate RtUv)an eRbIy:agTUlMTUlayenAkñúgGKarCakMralxNнBRgwgedayEdk b¤k¾ebtugeRbkugRtaMg. - Flat slab ³ saksmbMputsMrab;ElVgEdlmanRbEvgBI 6m − 9m nigsMrab;bnÞúkGefrERbRbYlBI 3.8kN / m 2 − 7.2kN / m 2 . vaRtUvkarBum<eRcInCag flat plate CaBiesssMrab; column capital. kñúgkrNICaeRcIn eKeRbIEt drop panel edayKμan column capital . - Waffle slab ³ saksmsMrab;ElVgEdlmanRbEvgBI 9m − 14.5m nigsMrab;bnÞúkGefrERbRbYl BI 3.8kN / m 2 − 7.2kN / m 2 . vaRTbnÞúk)aneRcInCag flat plate nigmanBidanKYreGayTak; TajEtBum<mantMéléfø. - kMralxNнelIFñwm (slab on beam)³ salsmbMputsMrab;ElVgcenøaH 6m − 9m nigbnÞúkGefrBI 2.9kN / m 2 − 5.7 kN / m 2 . FñwmbegáInPaBrwgRkajrbs;kMralxNнEdleFVIeGaymanPaBdab tUc. eKRtUvkarBum<bEnßmsMrab;Fñwm. - kMralxNнmYyTisenAelIFñwm (one-way slab on beam)³saksmbMputsMrab;ElVgEdlmanRb EvgBI 3m − 6m nigbnÞúkGefrcenøaHBI 2.9kN / m 2 − 4.8kN / m 2 . vaGacRtUv)aneRbIsMrab; ElVgFMCagenHCamYynwgtMéléføCag elIsBIenHeKnwgTTYl)anPaBdabFM. eKRtUvkarBum<bEnßm sMrab;Fñwm. karKNnakMralxNнBIrTis 442
  6. 6. T.Chhay NPIC - One-way joist floor system ³ saksmbMputsMrab;ElVgEdlmanRbEvgBI 6m − 9m nigman bnÞúkGefrcenøaH 3.8kN / m 2 − 5.7kN / m 2 . edaysarEtrnUteRCA brimaNebtug nigEdkKWtic EtkarcMNayelIBum<Gs;eRcIn. Bidanrbs;kMralxNнGacnwgemIleTAKYreGayTak;Taj. 4> eKalKMnitkñúgkarKNna Design Concept karviPaKd¾suRkitsMrab;kMlaMg nigbMlas;TIenAkñúgkMralxNнBIrTisKWsμúKsμaj edaysarEtPaB minkMNt;x<s;. vaBitCasμúKsμajebIeTaHbICaT§iBl creep nig nonlinear behavior rbs;ebtugRtUv)an ecalk¾eday. viFI numerical method dUcCa finite element k¾GacRtUv)aneRbI b:uEnþviFId¾samBaØdUcEdl GVI)anbgðajeday ACI Code saksmbMputsMrab;karKNnasMrab;karGnuvtþn_. ACI Code, Chapter 13 snμt;fakMralxNнeFVIkarCaFñwmTUlay Etrak;begáItCaeRKagrwg (rigid frame) CamYynwgssrEdlenA BIeRkam nigBIelIva. karsnμt;énkarEckeRKagCaeRKagsmmUlRtUv)anepÞógpÞat;eLIgvijedaykarsikSa RsavRCavCalkçN³viPaK nigBiesaFn_ (analytical and experimental research). va)anbgðajfa lT§- PaBRTbnÞúkcugeRkay (ultimate load capacity) énkMralxNнBIrTisCamYynwgkarTb;tamRCug ¬restrained boundary) KWesμI RbEhlBIdgénlT§PaBRTbnÞúkcugeRkayEdlKNnaedaykarviPaKtam RTwsþI edaysarkarEbgEckm:U- m:g;eLIgvijd¾FMEdlekIteLIgenAkñúgkMralxNнmunnwg)ak;. enAeBlbnÞúk FM bMlas;TI nigPaBdabFMRtUv)anrMBwgTuk dUcenHeKRtUvkarkMras;kMralxNнGb,brmaedIm,IrkSaPaBdab niglkçxNÐeRbHRKb;RKan; eRkambnÞúkeFVIkar. ACI Code kMNt;viFIsaRsþBIrsMrab;KNnakMralxNнBIrTis³ - viFIKNnaedaypÞal; (direct design method DDM, ACI Code, Section 13.6) CaviFIRbhak; RbEhl (approximate procedure) sMrab;karviPaK nigkarKNnakMralxNнBIrTis. RtUv)ankM Nt;sMrab;RbBn§½kMralxNнEdlrgnUvbnÞúkBRgayesμI nigssrmanKMlatesμIKña b¤esÞIresμIKña. viFI enHeRbInUvsMnuMemKuNedIm,IkMNt;m:Um:g;KNnaenARtg;muxkat;eRKaHfñak;. RbBn§½kMralxNнEdlmin RtUvKñanwgkarkMNt;rbs; ACI Code, Section 13.6.1 RtUv)anviPaKedayviFIsaRsþKNnaEdl manlkçN³suRkitCag. - viFIeRKagsmmUl (equivalent frame method EFM, ACI Code, Section 13.7) CaviFImYy EdlGKarbITMhM (3D) RtUv)anEckecjCaesrIéneRKagsmmUlBIrTMhM (2D) edaykat;GKar karKNnakMralxNнBIrTis 443
  7. 7. T.Chhay NPIC tamExSrcenøaHssr. lT§plrbs;eRKagRtUv)anBicarNadac;edayELkBIKñatamTisbeNþay nigTisTTwgrbs;GKar nigRtUv)anKitBImYyCan;eTAmYyCan; dUcEdlbgðajenAkñúgrUbTI 17>4. viFIsaRsþKNnatam ACI Code BIrKWQrelIelIlT§plénkarviPaKeGLasÞic (elastic analysis) én eRKOgbgÁúMTaMgmUledayeRbIbnÞúkemKuN. viFIEdlEktMrUv (modified approach) viFI direct design method RtUv)anbgðajenAkñúg commentary én code qñaM 1989 CaviFIPaBrwgRkajEktMrUv (modified stiffness method MSM). vaQrkarbBa©ÚlemKuNEbgEckd¾kMNt;mYyCaGnuKmn_énpleFobPaB rwgRkaj α ec sMrab;KuNnwgm:Um:g;sþaTicsrubenAkñúgElVgxagcug. viFIenHRtUv)anBnül;enAeBleRkay. bEnßmBIelI viFIrbs; ACI Code eKenAmanviFIepSg²CaeRcIneTotsMrab;KNna nigviPaKkMralxNн. CalT§pl kMralxNнnwgmanbrimaNEdkticCag b¤eRcInCag. viFIviPaK (analytical method) GacRtUv cat;cMNat;fñak;kñúgRkuménTMnak;TMngeKalrvagbnÞúk nigbMlas;TI CaeGLasÞic/ )aøsÞic nig nonlinear . - enAkñúgkarviPaKeGLasÞic (elastic analysis) kMralxNнebtugRtUv)anKitCakMraleGLasÞic. karBt;kMlaMgkat;TTwg nigPaBdabRtUv)anKNnaedaysmIkarDIepr:g;EsülTI4 (fourth differential equation) EdlTak;TgbnÞúkeTAnwgPaBdabsMrab;kMralesþIgCamYynwgbMlas;TItUc dUcEdl)anbgðaj eday Timoshenko. dMeNaHRsay finite difference solution k¾dUcCadM eNaHRsay finite element solution RtUv)anesñIeLIgedIm,IviPaKkMralxNн. enAkñúgviFI finite element method kMralxNнRtUv)an EbgEckCasMNaj;ragRtIekaN b¤ragkaer (mesh of triangles or quadrilateral). GnuKmn_bMlas;TIén cMnuc (node) Edlkat;KñaedaycMnucsMNaj; (intersecting mesh point) RtUv)anbegáIteLIgCaTUeTA ehIym:aRTicénPaBrwgRkaj (stiffness matrices) RtUv)anbegáItsMrab;karviPaKedaykMuBüÚTr½. - sMrab;karviPaK)aøsÞic eKmanbIviFI. viFI yield line method RtUv)anbegáIteLIgeday Johansen edIm,IkMNt;sßanPaB (limit state) énkMralxNнedayBicarNafa yield line EdlekItmanenA kñúgkMralxNнCaemkanicénkar)ak; (collapse mechanism). viFIcMerok (strip method) RtUv)an begáIteday Hillerborg. kMralxNнRtUv)anEckecjCacMerok (strip) ehIybnÞúkenAelIkMral xNнRtUv)anEbgEckTisedABIrEkgKña. cMerokRtUv)anviPaKCaFñwmsamBaØ. viFITIbICaviFI optimal analysis method sMrab;eFVIeGaybrimaNEdlTTYl)anmantMélGb,brmaedayQrelIkarvi PaK)aøsÞic. dMeNaHRsay optimal solution KWsμúKsμajkñúgkarviPaK nigTTYl)ankarBRgay srésEdlmYyd¾sμúKsμaj. karKNnakMralxNнBIrTis 444
  8. 8. T.Chhay NPIC karKNnakMralxNнBIrTis 445
  9. 9. T.Chhay NPIC - karviPaK nonlinear analysis KitlkçN³bMlas;TIeRkambnÞúkBiténkMralxNнebtugGarem: enA eBlEdlviFI finite element method KitBicarNaEpñk nonlinear énTMnak;TMngkugRtaMg-bMEr bMrYlrageFob (stress-strain relationship) énGgát;mYy²dac;edayELkBIKña. kñúgkrNIenH dMeNaHRsaykøayCasμúKsμaj RbsinebITMnak;TMngEdl)anBIkarBiesaFn_edayTTYl)ankar sMrYlminRtUv)ansnμt;eTenaH. viFIEdl)anerobrab;xagelI RtUv)anbgðajedIm,IENnaMGñksikSanUvviFIepSg²énkarviPaKkMralxNн. kargarBiesaFn_elIkMralxNнminRtUv)anGPivDÄeTkñúgb:unμanqñaMcugeRkayenH b:uEnþkarsikSaCaeRcInRb- EhlCaRtUvkaredIm,IsMrYldMeNIrkarKNnabc©úb,nñCamYysuvtßiPaB karbMerIkargar niglkçN³esdækic¢. 5> cMerokelIssr nigcMerokkNþal Column and Middle Strips rUbTI 17>5 bgðajkMralxagkñúgénkMralxNнBIrTisEdlRtUv)anRTenAelIssr A / B / C nig D . RbsinebIkMralRTbnÞúkBRgayesμI kMralxNнnwgdabBIrTis CamYyPaBdabGtibrmarnAtMbn;kNþal O . cMnucx<s;bMputsßitenAelIssr A / B / C nig D dUcenHEpñkénkMralxNнEdlenACMuvijssrnwg manrage)a:g (convex shape). karpøas;bþÚrrUbragrbs;kMralxNнbnþicmþg² ¬BIPaBe)a:genAelIssreTA rkPaBptenAkNþalkMral¦ eFVIeGayExSkaMnImYy²kat;Rtg;cMnucrbt;. muxkat;Rtg; O / E / F / G nig H nwgmanm:Um:g;Bt;viC¢man b:uEnþenAmþúMbrievNssrnwgmanm:Um:g;Bt;GviC¢manGtibrma. edayBicarNacM eroktambeNþay AFB cMeroknwgekagdUcFñwmCab; ¬rUbTI 17>5 b¦ edaymanm:Um:g;GviC¢manenARtg; A nig B nigmanm:Um:g;Bt;viC¢manRtg; F . cMerokenHlatsn§wgenAcenøaHssrBIr A nig B nigCab;enAelI RCugTaMgsgçagénkMral EdlbegáIt)anCacMErokelIssr (column strip). dUcKñasMrab;cMeroktambeNþay EOG nwgmanm:Um:g;Bt;GviC¢manenARtg; E nig G ehIym:Um:g; viC¢manenARtg; O EdlbegáItCacMerokkNþal. cMerokTIbItambeNþay DHC nwgeFVIkarRsedogKñanwgcM erok AFB . dUcenH bnÞHkMralGacnwgRtUv)anEbgEckbIcMerokKW 1enAkNþaltambeNþay EOG Edl eKeGayeQμaHfacMerokkNþal nigBIreTotsgçagtambeNþay AFB nig DHC EdleKeGayeQμaHfa cMerokelIssr ¬rUbTI 17>5 a¦. cMeroknImYy²eFVIkarCaFñwmCab;. tamviFIdUcKña bnÞHkMralk¾RtUv)anEbg EckCabIcMroksMrab;TisedAmYyeTotKW cMerokkNþalmYytambeNþay FOH nigcMerokelIssrBIreTot tambeNþay AED nig BGC erogKña ¬rUbTI 17>5 e¦. karKNnakMralxNнBIrTis 446
  10. 10. T.Chhay NPIC tamry³rUbTI 17>5 a eyIgeXIjfacMerokkNþalRtUv)anRTedaycMerokelIssr EdlbBa¢Ún bnÞúkbnþeTAssr A / B / C nig D enAkñúgbnÞHkMralenH. dUcenHcMerokssrRTbnÞúkeRcInCagcMerok kNþal. dUcenH m:Um:g;Bt;viC¢manenAkñúgcMerokelIssrnImYy² ¬enARtg; E / F / G nig H ¦ mantMél FMCagm:Um:g;Bt;viC¢manenARtg; O EdlsßitenAcMerokkNþal. dUcKña m:Um:g;GviC¢manenAelIssr A / B / C nig D enAkñúgcMerokelIssrmantMélFMCagm:Um:g;GviC¢manenARtg; E / F / G nig H enAkñúgcMerok kNþal. Epñkénm:Um:g;KNnaEdlRtUv)ankMNt;enAmuxkat;eRKaHfñak;nImYy²éncMerokssr nigcMerok kNþalRtUv)anbgðajenAkñúgEpñkTI 8. TMhMéncMerokelIssr nigcMerokkNþslnImYy²enAkñúgbnÞHkMralRtUv)ankMNt;eday ACI Code, Section 13.2. cMerokelIssr x EdlRtUv)ankMNt;edayTTwgkMralxNнenAelIRCugnImYy²énGkS½ karKNnakMralxNнBIrTis 447
  11. 11. T.Chhay NPIC ssr esμInwgmYyPaKbYnénTMhMbnÞHkMral ¬ l1 nig l2 ¦ mYyNaEdltUcCageK rYmbBa©ÚlTaMgFñwmRbsinebI man. l1 = RbEvgElVg KitBIGkS½eTAGkS½ kñúgTisedAEdlm:Um:g;nwgRtUv)ankMNt; l 2 = RbEvlElVg KitBIGkS½eTAGkS½ kñúgTisedAEkgnwg l1 EpñkénbnÞHkMralcenøaHcMerokelIssrkMNt;cMerokkNþal. 6> kMras;kMralGb,brmaedIm,IkMritPaBdab Minimum Slab Thickness to Control Deflection ACI Code, Section 9.5.3 kMNt;kMras;kMralxNнsMrab;kMralxNнBIrTisedIm,IkMritPaBdab. TMhMénPaBdabrbs;kMralxNнGaRs½ynwgGefrCaeRcInEdlrYmbBa©ÚlTaMgPaBrwgRkajTb;karBt; (flexural stiffness) rbs;kMralxNнEdlbBa©ÚlCaGnuKmn_énkMras;kMralxNн h . enAeBlbegáInkMras; kMralxNн enaHPaBrwgRkajTb;karBt;rbs;kMralxNÐk¾ekIneLIg ehIyPaBdabrbs;kMralxNнnwgRtUv ½ kat;bnßy. edaysarkarKNnaPaBdabsMrab;kMralxNнBIrTismanPaBsμúKsμaj nigedIm,IeCosvagPaB dabFM ACI Code kMNt;kMras;kMralxNнTaMgenHedayTTYlykkarkMNt;Edl)anBIkarBiesaFn_bI. Rb sinebIkarkMNt;rbs;eyIgminsßitenAkñúgEdnkMNt;TaMgbIenHeT eKcaM)ac;RtUvKNnaPaBdab. a. sMrab; 0.2 ≤ α fm ≤ 2 / ⎛ fy ⎞ l n ⎜ 0.8 + ⎜ ⎟ ⎝ 1400 ⎟ ⎠ h= 36 + 5β (α fm − 0.2) ¬!&>!¦ b:uEnþminRtUvtUcCag 125mm b. sMrab; α fm > 2 ⎛ fy ⎞ l n ⎜ 0.8 + ⎜ ⎟ 1400 ⎟ h= ⎝ ⎠ ¬!&>@¦ 36 + 9β b:uEnþminRtUvtUcCag 90mm c. sMrab; α fm < 0.2 h = kMras;kMralxNнGb,brmaedayKμanFñwmxagkñúg ¬tarag 17>1¦ ¬!&>#¦ Edl ln = clear span sMrab;TisEvgEdlvas;BIépÞQmKñarbs;ssr β = pleFobén clear span EvgelI clear span xøI karKNnakMralxNнBIrTis 448
  12. 12. T.Chhay NPIC α fm = tMélmFümén α f sMrab;RKb;FñwménRCugTaMgGs;rbs;bnÞHkMral α f = CapleFobénPaBrwgRkajTb;karBt;énmuxkat;Fñwm Ecb I b lIPaBrwgRkajTb; karBt;énkMralxNн Ecs I s EdlBT§½CMuvijedayGkS½bnÞHkMralenABIelIFñwmRCug nImYy². E I α f = cb b E cs I s ¬!&>$¦ Edl Ecb nig Ecs Cam:UDuleGLasÞicrbs;ebtugenAkñúgFñwm nigkMralxNн erogKña. I b = m:Um:g;niclPaBTaMgmUlénmuxkat;FñwmeFobGkS½TIRbCMuTMgn; ¬muxkat;FñwmrYmTaMg beNþaykMralxNнenAelIRCugTaMgsgçagrbs;FñwmEdlesμInwgkMBs;FñwmBIelI b¤BI eRkamkMralxNн ykmYyNaEdlFMCageK b:uEnþminRtUvFMCagbYndgkMras;kMral xNн¦. I s = m:Um:g;niclPaBénmuxkat;kMralxNнTaMgmUl. b:uEnþ kMras;kMralxNнminKYrtUcCagtMélxageRkam³ - sMrab;kMralxNнEdlman α fm < 2.0 ³ 125mm - sMrab;kMralxNнEdlman α fm > 2 ³ 90mm tarag 17>1 kMras;kMralxNнGb,brmaedayKμanFñwmxagkñúg edayKμan Drop Panel** man Drop Panel*** Yield bnÞHkMralxageRkA bnÞHkMralxageRkA Stress bnÞHkMralxagkñúg bnÞHkMralxagkñúg fy * KμanFñwmxag manFñwmxag KμanFñwmxag manFñwmxag ln ln ln ln ln ln 280 33 36 36 36 40 40 ln ln ln ln ln ln 420 30 33 33 33 36 36 * sMrab;EdkEdlman Yield Stress cenøaH 280 nig 420 kMras;Gb,brmaTTYl)anBI linear interpolation. ** Drop panel RtUv)ankMNt;enAkñúg ACI Sections 13.3.7.7 nig 13.3.7.2 *** kMralxNнEdlmanFñwmcenøaHssrtambeNþayxagkñúg. tMélén α f sMrab;FñwmminKYrmantMéltUcCag 0.8 . RbsinebIFñwmminRtUv)aneRbI dUckñúgkrNI flat plate enaH α f = 0 nig α fm = 0 . smIkar ACI Code sMrab;KNnakMras;kMralxNн h )anKitT§iBlrbs;RbEvgElVg/ TMrg;bnÞHkMral/ yield stress rbs; karKNnakMralxNнBIrTis 449
  13. 13. T.Chhay NPIC Edk f y nigPaBrwgRkajTb;karBt;rbs;Fñwm. enAeBlFñwmEdlmanlkçN³rwgxøaMgRtUv)aneRbI smIkar !&>! Gacpþl;nUvkMras;kMralxNнtUc ehIysmIkar !&>@ Gaclub. sMrab; flat plate nig flat slab enAeBl EdlFñwmxagkñúgminRtUv)aneRbI kMras;kMralxNнGb,brmaGacRtUv)ankMNt;edaypÞal;BItarag 9>5 c én ACI Code EdlRtUv)anbgðajenATIenHKWtarag 17>1. karkMNt;rbs; ACI Code epSgeTotRtUv)ansegçbdUcxageRkam³ - sMrab;bnÞHkMralEdlmanxagminCab;; FñwmxagcugEdlman α = 0.8 RtUv)aneRbI ebImindUcenHeT kMras;kMralxNнGb,brmaRtUv)anKNnatamsmIkar !&>! nig !&>@ RtUv)anbegáIn 10% y:ag tic ¬ ACI Code, Section 9.5.3 ¦. - enAeBl drop panel RtUv)aneRbIedayKμanFñwm kMras;kMralxNнGb,brmaKYrRtUv)anbnßyeday 10% . drop panel KYrRtUv)anlatsn§wgRKb;TisBIGkS½rbs;TMredaycMgayminticCagRbEvg ElVgelI 6 RKb;TiscenøaHGkS½eTAGkS½énTMr nigTMlak;cuHeRkamkMralxNнy:agtic h / 4 . kar bnßyenH)anrYmbBa©ÚleTAkñúgtaragTI 17>1. - edayminKittMélEdlTTYl)anBIsmIkar !&>! nig !&>@ kMras;kMralxNнBIrTisminRtUvtUcCagkrNIdUcteTA³ ¬!¦ 125mm sMrab;kMralxNнEdlKμanFñwm b¤ drop panel. ¬@¦ 100mm sMrab;kMralxNнKμanFñwmEtman drop panel. ¬#¦ 90mm sMrab; kMralxNнmanFñwmenAelIRCUgTaMgbYnCamYynwg α fm ≥ 2 nig 125mm sMrab; α fm ≤ 2 ¬ ACI Code, Section 9.5.3¦. CMhanxageRkamsegçbBIkarKNnaTaMgenH³ !> sMrab;kMralxNнEdlKμanFwñmxagkñúg ¬ flat plate nig flat slab¦ a. KNnakMras;kMralxNнedaypÞal;BItarag 17>1. b:uEnþsmIkar !&>! nig !&>@ k¾GacRtUv)aneRbI ehIyCaTUeTA smIkar !&>! lub. kMras;kMralxNнGb,brmaKYrFMCag b¤esμInwg 125mm sMrab;kMralxNнEdlKμan drop panel nigFMCagb¤esμI 100mm sMrab;kMralxNнEdlman drop panel. b. enAxagEdlminCab; FñwmxagEdlman α f ≥ 0.8 KYrRtUv)aneRbI. ebImindUecñaHeT kMras;kMral xNнGb,brmaRtUv)anKNnaedaysmIkar !&>! nig !&>@ KYrRtUv)anbegáIneday 10% . kar begáIn 10% RtUv)anbBa©ÚleTAkñúgCYrQrTI 2 kñúgtaragTI 17>1 rYcehIy. karKNnakMralxNнBIrTis 450
  14. 14. T.Chhay NPIC c. RbsinebI drop panel RtUv)aneRbIenAkñúg flat slab kMras;kMralxNнGb,brmaRtUv)anbnßyeday 10% enAkñúgkrNIEdl drop panel latsn§wgenARKb;TisBIGkS½énTMrCamYycMgaymintUcCag 1 / 6 RbEvgElVg nigTMlak;eRkamkMralxNнy:agtic h / 4 . karbnßyenH)anbBa¢ÚleTAkñúgem KuNéntarag 17>1. @> sMrab;kMralxNнEdlmanFñwmenARKb;RCug ¬ α fm > 0 ¦ a. KNna α fm nigbnÞab;mkKNnakMras;kMralxNнGb,brmaBIsmIkar !&>! nig !&>@. kñúgkrNI CaeRcInsmIkar !&>@ lub. b. kMras;kMralxNнKYrFMCag b¤esμInwg 125mm sMrab;kMralxNнEdlman α fm < 2.0 nigKYrFMCag b¤esμInwg 90mm sMrab;kMralxNнEdlman α fm ≥ 2.0 . #> sMrab;RKb;kMralxNн³ kMrs;kMralxNнEdltUcCagkMras;Gb,brmaEdleGayenAkñúgCMhan !> nig @> GacRtUv)aneRbI RbsinkarKNnabgðajfaPaBdabminFMCagkarkMNt;rbs; ACI Code, Table 9.5 b EdlBnül;enAkñúgemeronTI 6. ]TahrN_17>1³ RbBn§½kMral flat plate EdlmanTMhM 7.5 × 6m RtUv)anRTenAelIssrkaer 500mm . edayeRbIsmIkar ACI Code kMNt;kMras;kMralxNнGb,brmacaM)ac;sMrab;bnÞHkMralxagkñúg nigbnÞHkM ralkac;RCug dUcbgðajenAkñúgrUbTI 17>6. FñwmxagminRtUv)aneRbI. eKeGay f 'c = 28MPa nig f y = 420MPa . dMeNaHRsay³ 1> sMrab;bnÞHkMralxNнkac;RCugelx ! kMras;Gb,brmaKW 30 ¬ f y = 420MPa ln nigKμanFñwmxagRtUv)aneRbI ¬emIltarag 17>1¦. l n1 = 7500 − 500 = 7000mm hmin = 7000 30 yk = 233mm 250mm müa:gvijeTot smIkar !&>! nig !&>@ GacRtUv)aneRbIedIm,IKNnakMras;Gb,brmaCamYy α f = α fm = 0 . 2> sMrab;bnÞHkMralxagkñúgelx #> CamYy f y = 420MPa kMras;kMralxNнGb,brmaKW hmin = n = 212mm yk 220mm l 33 müa:gvijeTot smIkar !&>! nig !&>@ GacRtUv)aneRbI. karKNnakMralxNнBIrTis 451
  15. 15. T.Chhay NPIC RbsinebIRKb;bnÞHkMralxNнTaMgGs;eRbIkMras;dUcKña enaHeKGacyk hmin = 250mm . ]TahrN_17>2³ RbBn§½kMralxNнdUcbgðajenAkñúgrUbTI 17>7 EdlpSMeLIgedaykMraltan; nigFñwmenA elITaMgBIrTisEdlRTedayssrkaerEdlmanRCug 500mm . edayeRbIsmIkar ACI Code kMNt;kMras; kMralxNнGb,brmacaM)ac;sMrab;bnÞHkMralxagkñúg. eKeGay f 'c = 21MPa nig f y = 420MPa . dMeNaHRsay³ 1> edIm,IeRbIsmIkar !&>! α fm RtUv)anKNnamun. dUcenH eKcaM)ac;kMNt; I b / I s nig α f sMrab; Fñwm nigkMralxNнtamTisEvg nigTisxøI. 2> m:Um:g;niclPaBrbs;FñwmTaMgmUl I b RtUv)anKNnasMrab;muxkat;dUcbgðajenAkñúgrUbTI 17>7 b EdlRtUv)anbegáIteLIgedayFñwm nigEpñksgçagxøHrbs;kMralxNн x = y b:uEnþminRtUvFMCag 4 bYndgkMras;kMralxNн. snμt; h = 18cm ehIyvaRtUv)anepÞógpÞat;enAeBleRkay enaH x = y = 56 − 18 = 38cm < 18 × 4 = 72cm . dUcenH be = 40 + 38 × 2 = 116cm nigmuxkat; karKNnakMralxNнBIrTis 452
  16. 16. T.Chhay NPIC GkSr T RtUv)anbgðajenAkñúgrUbTI 17>7 c . kMNt;TIRbCMuTMgn;rbs;muxkat;edayKitm:Um:g;eFob kMBUlrbs;søab³ RkLaépÞsøab = 18 × 116 = 2088cm 2 RkLaépÞRTnug = 40 × 38 = 1520cm 2 RkLaépÞsrub 3608cm 2 2088 × 9 + 1520 × 37 = 3608 y y = 20.8cm ⎡116 Ib = ⎢ (18)3 + 2088(11.8)2 ⎤ + ⎡ 40 383 + 1520(19 − 2.8)2 ⎤ = 928924.6cm 4 ⎣ 12 ⎦ ⎢ 12 ⎥ ⎣ ⎥ ⎦ 3> m:Um:g;niclPaBénkMralxNнtamTisedAEvgKW bh 3 Il = 12 Edl b = 600cm nig h = 18cm 600 3 Il = 18 = 291600cm 4 12 karKNnakMralxNнBIrTis 453
  17. 17. T.Chhay NPIC ¬tamTisedAEvg¦ = EI b = 928924.6 = 3.19 α fl EI s 291600 4> m:Um:g;niclPaBénkMralxNнtamTisedAxøIKW 760 3 Is = 18 = 369360cm 4 12 ¬tamTisedAxøI¦ α fs EI = b = EI s 928924.6 369360 = 2.51 5> α fm CatMélmFümén α fs nig α fl 3.19 + 2.51 α fm = = 2.85 2 7.6 − 0.5 6> β= 6 − 0.5 = 1.29 7> kMNt; hmin edayeRbIsmIkar !&>@ ¬ ln = 7.1m ¦³ ⎛ 420 ⎞ 7.1⎜ 0.8 + ⎟ hmin = ⎝ 1400 ⎠ = 0.148m 36 + 5 × 1.29(2.82 − 0.2) b:uEnþ tMélenHminRtUvtUcCag h EdleGayedaysmIkar !&>@ ¬ α fm > 2.0 ¦ 7.81 h= = 0.164m 36 + 9 × 1.29 müa:geTot hmin = 90cm . dUcenH h = 16.4cm lub. eKGacTTYlykkMras;kMralxNнEdl)ansnμt; h = 18cm . cMNaMfa enAkñúgkrNIGnuvtþn_CaeRcIn smIkar !&>@ manlkçN³lub. 7> ersIusþg;kMlaMgkat;TTwgrbs;kMralxNн Shear Strength of Slabs sMrab;RbBn§½kMralxNнBIrTis bnÞHkMralRtUvEtmankMras;RKb;RKan;edIm,ITb;nwgm:Um:g;Bt;TaMgBIr nigkMlaMgkat;TTwgenARtg;muxkat;eRKaHfñak;. edIm,IGegátlT§PaBTb;kMlaMgkat;TTwgénkMralxNнBIrTis krNIxageRkamRtUv)anBicarNa. 7>1> kMralxNнBIrTisEdlRTedayFñwm Two-Way Slabs Supported on Beams muxkat;eRKaHfñak;rbs;kMralxNнBIrTisEdlRTedayFñwmKWsßitenAcMgay d BIépÞénFñwmTMr ehIy lT§PaBTb;kMlaMgkat;TTwgénmuxkat;nImYy²KW φVc = φ f 'c bd / 6 . enAeBlEdlFñwmmanlkçN³rwg nigGacbBa¢ÚnbnÞúkkMraleTAssr vaRtUv)ansnμt;eGayRTbnÞúkEdleFVIGMeBImkelIépÞkMralxNнEdlBT§½ karKNnakMralxNнBIrTis 454
  18. 18. T.Chhay NPIC edaybnÞat; 45o EdlKUsecjBIRCugEkg dUcbgðajenAkñúgrUbTI 17>8. bnÞúkenAelIépÞctuekaNBñaynwg RtUv)anRTedayFñwmEvg AB nig CD b:uEnþbnÞúkenAelIépÞRtIekaNnwgRtUv)anRTedayFñwmxøI AC nig BD . kMlaMgkat;TTwgkñúgmYyÉktþaTTwgrbs;kMralmantMélx<s;bMputenAcenøaH E nig F tamTis TaMgBIr ehIy Vu = wu (l2 / 2) Edl wu CabnÞúkemKuNBRgayesμIkñúgmYyÉktþaépÞ. RbsinebIEdkTb;kMlaMgkat;TTwgminRtUv)andak; kMlaMgkat;TTwgenAcMgay d BIépÞénFñwm Vud RtUvEtesμInwg φ f 'c bd Vud ≤ φVc ≤ 6 Edl Vud = wu ⎛ l22 − d ⎞ ⎜ ⎟ ⎝ ⎠ 7>2> kMralxNнBIrTisEdlKμanFñwm Two-Way Slabs Without Beams nig flat slab KμanFñwmeT dUcenHkMralxNнRtUv)anRTedayssredaypÞal;. sMrab;kM Flat plate ralxNнEbbenHkugRtaMgkMlaMgkat;TTwgBIrRtUv)aneFVIkarGegát TImYyKWkMlaMgkat;TTwgmYyTis b¤kMlaMg kat;TTwgFñwm (one-way shear or beam shear). muxkat;eRKaHfñak;RtUv)anykenAcMgay d BIépÞén ssr ehIykMralxNнRtUv)anBicarNadUcFñwmEdlmanTTwgFMsßitenAcenøaHTMr dUckñúgkrNIFñwmmYyTis karKNnakMralxNнBIrTis 455
  19. 19. T.Chhay NPIC (one-way beam) . lT§PaBTb;kMlaMgkat;TTwgénmuxkat;ebtugKW φVc = φ f 'c bd / 6 . RbePTTIBIrén kMlaMgkat;TTwgEdlRtUvsikSaKWkMlaMgkat;TTwgBIrTis b¤kMlaMgkat;pug (two-way shear or punching shear) dUcEdl)anerobrab;enAkñúgkarKNnaeCIgtag. Kar)ak;edaykMlaMgkat;ekItmantambeNþaykM Nat;ekaN b¤kMNat;BIra:mIt (truncated cone or pyramid) CMuvijssr. muxkat;eRKaHfñak;sßitenAcM gay d / 2 BIépÞssr/ column capital/ b¤ drop panel ¬rUbTI 17>9 a¦. RbsinebIEdkkMlaMgkat;TTwg minRtUv)andak; ersIusþg;kMlaMgkat;TTwgrbs;ebtugKWtMélEdltUcCageKkñúgcMeNamsmIkar !&>% nig !&>^³ ⎛1 1 ⎞ φ f 'c bo d φVc = ⎜ + ⎜ 6 3β ⎟ ⎟ f ' c bo d ≤ ¬!&>%¦ ⎝ ⎠ 3 Edl bo = brimaRténmuxkat;eRKaHfñak; β = pleFobénRCugEvgrbs;ssrelIRCugxøI ¬b¤RkLaépÞbnÞúk¦ φ ⎛α d ⎞ φVc = ⎜ s + 2 ⎟ f 'c bo d ⎜ b ⎟ ¬!&>^¦ ⎝ 12 o ⎠ Edl α s esμI 40 sMrab;ssrxagkñúg/ esμI 30 sMrab;;ssrxag nigesμI 20 sMrab;ssrkac;RCug. enAeBlEdlEdkkMlaMgkat;TTwgRtUv)andak; ersIusþg;kMlaMgkat;TTwgminKYrelIs φ φVc ≤ 2 f 'c bo d ¬!&>&¦ 7>3> EdkkMlaMgkat;TTWgenAkñúgkMralxNнBIrTisEdlKμanFñwm Shear Reinforcement in Two-Way Slabs Without Beams enAkñúgRbBn§½kMralxNн flat plate nig flat slab kMras;kMralxNнEdl)aneRCIserIsGacnwgmin RKb;RKan;edIm,ITb;nwgkugRtaMgkMlaMgkat;TTwgEdlGnuvtþeT. kñúgkrNIenH eKGacbegáInkMras;kMralxNн b¤dak;EdkTb;kMlaMgkat;TTwg. ACI Code GnuBaØatkareRbIEdkTb;kMlaMgkat;TTwgCa shearhead nig anchored bar b¤ wire. Shearhead pSMeLIgedayEdkragGkSr I b¤GkSr C EdlpSarExVgCabYn nigRtUv)andak;enAkñúgkM ralxNнBIelIssr ¬rUbTI 17>9 c, d ¦. karKNna Shearhead minGnuvtþsMrab;ssrxageRkA Edlm:U m:g;Bt; nigm:Um:g;rmYlmantMélFMEdlRtUv)anbMElgcenøaHkMralxNн nigssr. ACI Code, Section 11.12.4 bgðajfaenARtg;muxkat;eRKaHfñak; ersIusþg;kMlaMgkat; nominal Vn minKYelIs f 'c bo d / 3 b:uEnþRbsin ebIEdk shearhead RtUv)andak; Vn minKYrelIs 7 f 'c bo d / 12 . edIm,IkMNt;TMhMrbs; shearhead, ACI Code, Section 11.12.4 pþl;nUvkarkMNt;dUcteTA³ karKNnakMralxNнBIrTis 456
  20. 20. T.Chhay NPIC karKNnakMralxNнBIrTis 457
  21. 21. T.Chhay NPIC karKNnakMralxNнBIrTis 458
  22. 22. T.Chhay NPIC !> pleFob α v rvagPaBrwgRkaj Es I rbs;éd shearhead nigPaBrwgRkajénmuxkat;EdleRbH smasEdlmanTTWg c2 + d minRtUvtUcCag 0.15 . @> søabrgkarsgát;énEdkragminRtUvmanTItaMgenAmþúM 0.13d énépÞrgkarsgát;rbs;kMralxNн. #> kMBs;rbs;EdkragminRtUvFMCag 70 énkMras;RTnug. $> lT§PaBTb;m:Um:g;)aøsÞic M P énédnImYy²rbs; shearhead RtUv)anKNnaeday V ⎡ ⎛ c ⎞⎤ φM P = u ⎢hv + α v ⎜ l v + 1 ⎟⎥ ¬ACI Code, Eq. 11.37 ¦ ¬!&>*¦ 2n ⎣ ⎝ ⎠⎦ 2 Edl φ = 0.9 Vu = kMlaMgkat;TTwgemKuNCMuvijbrievNénépÞssr n = cMnYnéd hv = kMBs;rbs; shearhead l v = RbEvg shearhead Edlvas;BIGkS½ssr %> muxkat;kMralxNнeRKaHfñak;sMrab;kMlaMgkat;TTWgRtUvEtkat;éd shearhead enAcMgayesμInwg (3 / 4)(l v − c1 / 2) BIépÞssreTcugénédrbs; shearhead dUcbgðajenAkñúgrUbTI 17>9 c. muxkat;eRKaHfñak;RtUvEtmanbrimaRtGb,brma bo b:uEnþvaminRtUvenACitCag d / 2 BIépÞrbs;sse. ^> Shearhead RtUv)anBicarNaeGaycUlrYmkñúgkarEbgEckm:Um:g;eLIgvij M v eTAcMerokkMralxNнelIssrnImYy²dUcxageRkam³ φ ⎛ c ⎞ Mv = α vVu ⎜ l v 1 ⎟ ¬ACI Code, Eq. 11.38¦ ¬!&>(¦ 2n ⎝ 2⎠ b:uEnþvaminRtUvtUcCagtMéltUcCageKkñúgcMeNam 30% énm:Um:g;emKuNEdlcaM)ac;enAkñúgcMerok elIssr/ karpøas;bþÚrm:Um:g;cMerokelIssrelIRbEvg lv b¤ M p EdleGayenAkñúgsmIkar !&>*. kareRbI anchored bent bar b¤ wire k¾RtUv)anGnuBaØateday ACI Code, Section 11.12.3. Edk Edldak;enAxagEpñkxagelIrbs;ssr niglT§PaBékartMerobEdkRtUv)anbgðajenAkñúgrUbTI 17>9 e. enAeBlEdl bar b¤ wire RtUv)aneRbICaEdkTb;kMlaMgkat;TTwg enaHersIusþg;kMlaMgkat;TTWg nominal KW³ f ' c bo d Av f y d V n = Vc + V s = 6 + s ¬!&>!0¦ Edl Av CaRkLaépÞEdkkgsrub nig bo CaRbEvgénmuxkat;eRKaHfñak;énkMlaMgkat;BIrTisenA cMgay d / 2 BIépÞssr. ersIusþg;kMlaMgkat; nominal Vn minRtUvFMCag f 'c bo d / 2 . karKNnakMralxNнBIrTis 459
  23. 23. T.Chhay NPIC kareRbIEdkkMlaMgkat;enAkñúg flat plate kat;bnßykMras;kMralxNн nigenAEtrkSaPaBrabesμI rbs;BidanedIm,Ikat;bnßyéføBum<. TMrg; stirrup cage sMrab;EdkkMlaMgkat;TTwgRtUv)anbgðajenAkñúgrUbTI 17>9 f . RbePTmü:ageToténEdkkMlaMgkat;pSMeLIgeday studded steel strip ¬rUbTI 17>9 g¦. Steel strip RtUv)andak;CamYy bar chair nigRtUv)anP¢ab;eTAnwgBum< edayCMnYs stirrup gage . ersIusþg; yalrbs;Edk stud RtUv)ankMNt;enAcenøaH 280MPa nig 420MPa edIm,ITTYl)an anchorage eBj eljenAeBlbnÞúkemKuN. 8> karviPaK³nkMralxNнBIrTisedayviFIKNnaedaypÞal; Analysis of Two-Way Slabs by the Direct Design Method Direct design method CaviFIRbhak;RbEhl (approximate method) RtUv)anbegáIteLIgeday ACI Code edIm,IKNnam:Um:g;KNnaenAkñúgkMralxNнBIrTisEdlRTbnÞúkBRgayesμI. edIm,IeRbIviFIenH kar kMNt;xøHRtUv)anelIkeLIgeday ACI Code, Section 13.6.1. 8>1> karkMNt; Limitations !> vaRtUvmankMralxNнCab;Kñay:agticbIkñúgTismYy² @> kMralxNнRtUvEtkaer b¤ctuekaNEkg. pleFobElVgEvgelIElVgxøIrbs;kMralminRtUvFMCagBIr #> ElVgEdlenAEk,rkñúgTisnImYy²minRtUvxusKñaedayFMCagmYyPaKbIénElVgEvgCag. $> ssrminRtUvlyecjBIGkS½ssrd¾éTCaeRcIneTotedaytMélGtibrma 10% énRbEvgElVg enAkñúgTislyecj. %> bnÞúkTaMgGs;RtUvEtBRgayesμI ehIypleFobénbnÞúkGefrelIbnÞúkefrminRtUvFMCag 2 . ^> RbsinebImanFñwmenARKb;RCug pleFobénPaBrwgRkajEdlTak;TgkñúgTisEkgTaMgBI α f 1l 2 / α f 2 l12 minRtUvtUcCag 0.2 nigFMCag 5.0 . 2 8>2> m:Um:g;sþaTicemKuNsrub Total Factored Static Moment RbsinFñwmTMrsamBaØRTbnÞúkBRgayesμI w ¬ kN / m ¦ enaHm:Um:g;Bt;viC¢manGtibrmaekItmanenA kNþalElVgnigesμInwg M o = wl12 / 8 Edl l1 CaRbEvgElVg. RbsinebIRtUv)anbgáb;cugTaMgsgçag b¤ Cab;CamYynwg m:Um:g;GviC¢manesμIKñaenAcugTaMgsgçag enaHm:Um:g;srub M o = M p ¬m:Um:g;viC¢manenAkNþalElVg¦ + M n ¬m:Um:g;GviC¢manenAelITMr¦ = wl12 / 8 ¬rUbTI 17>10¦. karKNnakMralxNнBIrTis 460
  24. 24. T.Chhay NPIC LÚvRbsinebIFñwm AB RTbnÞúk W BIkMralxNнEdlmanTTwg l2 Ekgnwg l1 enaH W = wu l2 ehIy m:Um:g;srubKW M o = (wl2 )l12 / 8 Edl wu = GaMgtg;sIuetbnÞúkKitCa kN / m 2 . kñúgsmIkarenH m:Um:g;BitR)akdEdlekItmanenAeBl l1 esμInwg clear span cenøaHTMr A nig B . RbsinebI clear span RtUv)ankMNt;eday ln enaH 2 ln M o = (wu l 2 ) (ACI Code, Eq. 13.3) 8 Clear span l n RtUv)anvas;BIépÞeTAépÞTMrkñúgTisedAEdlm:Um:g;RtUv)anBicarNa b:uEnþminRtUvticCag 0.65 dgRbEvgElVgBIGkS½eTAGkS½TMr. épÞénTMrEdlmanm:Um:g;GviC¢manKYrRtUv)anKNna RtUv)anbgðaj enAkñúgrUbTI 17>11. RbEvg l2 RtUv)anvas;kñúgTisedAEkgnwg ln ehIyesμITisedAcenøaHGkS½eTAGkS½ rbs;TMr ¬TTwgkMralxNн¦. m:Um:g;srub M o EdlKNnakñúgTisedAEvgRtUv)anKitCa M ol nigkñúgTisedA xøIRtuv)anKitCa M os . enAeBlm:Um:gsrub M o RtUv)anKNnakñúgTisedAmYy vaRtUvEbgEckCam:Um:g;viC¢man M p nigm:U m:g;GviC¢man M n GBa¢wgehIyeTIb M o = M p + M n ¬rUbTI 17>10¦. enaHm:Um:g;nImYy² M p nig M n RtUv)anEbgEckqøgkat;TTwgkMralxNнcenøaHcMerokssr nigcMerokkNþal dUcEdl)anBnül;y:agxøI. 8>3> karEbgEckm:Um:g;tambeNþaykñúgkMralxNн Longitudinal Distribution of Moment in Slabs enAkñúgkMralxagkñúg m:Um:g;sþaTicsrub M o RtUv)anEbgEckenAkñúgm:Um:g;BIr m:Um:g;viC¢man M p enA kNþalElVgesμInwg 0.35M o nigm:Um:g;GviC¢man M n enATMrnImYy²esμInwg 0.65M o dUcbgðajenAkñúgrUbTI 17>12. tMélm:Um:g;TaMgenHQrelIkarsnμt;fakMralxagkñúgCab;kñúgTisTaMgBIr ehIymanRbEvgElVg karKNnakMralxNнBIrTis 461
  25. 25. T.Chhay NPIC nigbnÞúkRbhak;RbEhlesμIKña dUcenHtMNxagkñúgKμanmMurgVilFMeT. elIsBIenHeTot m:Um:g;mantMél RbEhlnwgm:Um:g;rbs;Fñwmbgáb;cugTaMgBIrEdlrgbnÞúkBRgayesμI Edlm:Um:g;GviC¢manenAelITMresμIBIrdg m:Um:g;GviC¢manenAkNþalElVg. enAkñúgrUbTI 17>12 RbsinebI l1 > l2 / enaHkarEbgEckm:Um:g;enAkñúg TisedAEvg nigTisedAxøIKW³ 2 l n1 M ol = (wu l 2 ) M pl = 0.35M ol M n1 = 0.65M ol 8 l2 M os = (wu l1 ) n 2 M ps = 0.35M os M ns = 0.65M os 8 RbsinebITMhMénm:Um:g;GviC¢manenAelITMrxagkñúgmantMélxusKñaedaysarRbEvgElVgminesμIKña ACI Code kMNt;eGayeRbIm:Um:g;EdlFMCagsMrab;KNnasrésEdk. enAkñúgbnÞHkMralxageRkA bnÞúkkMralxNнEdlGnuvtþelIssrxageRkA)anmkEtBIRCugmçag bNþaleGayekItmanm:Um:g;minesμI (unbalanced moment) nigmMurgVilenAtMNxageRkA. dUcenH m:Um:g; viC¢manenAkNþalElVg nigm:Um:g;GviC¢manenAelITMrxagkñúgTImYynwgekIneLIg.TMhMénmMurgViléntMNxag eRkAkMNt;nUvkarelIneLIgnUvm:Um:g;kNþalElVg nigm:m:g;enAelITMrxagkñúg. ]TahrN_ RbsinebIRCugxag U karKNnakMralxNнBIrTis 462
  26. 26. T.Chhay NPIC eRkACaTmrsamBaØ dUckñúgkrNIkMralxNнenAelICBa¢aMg ¬rUbTI 17>13¦ m:Um:g;kMralenARtg;épÞCBa¢aMgesμI 0 m:Um:g;viC¢manenAkNþalElVgGacykesμInwg M p = 0.63M o nigm:Um:g;GviC¢manenATMrxagkñúgKW M s = 0.75M o . tMélTaMgenHbMeBjlkçxNÐsmIkarsþaTic M o = M p + 1 M n = 0.63M o + 2 1 2 (0.75M o ) sMrab;RbBn§½kMral-ssr (slab-column floor system) tMNxageRkAmankarTb; (restraint) xøH Edlpþl;edayPaBrwgRkaJTb;karBt;énkMralxNн nigedayPaBrwgRkajTb;karBt;énssrxageRkA. eyagtam ACI Code, Section 13.6.3 m:Um:g;sþaTicsrub M o enAkñúgElVgcugRtUv)anEbgEckeday pleFobepSgKñaedayeyagtamtarag 17>2 nigrUbTI 17>14. emKuNm:Um:g;enAkñúgCYrQrTI 1 sMrab; RCugEdlminmankarTb;KWQrelIkarsnμt;fa pleFobénPaBrwgRkajTb;karBt;rbs;ssrelIPaBrwg RkajTb;karBt;smasrvagkMralxNн nigFñwmenARtg;tMN α ec KWesμIsUnü. emKuNénCYrQrTI 2 KWQr karKNnakMralxNнBIrTis 463
  27. 27. T.Chhay NPIC elIkarsnμt;fapleFob α ec esμInwgGnnþ. emKuNm:Um:g;enAkñúgCYrQrTI 3/ TI4 nigTI5 RtUv)anbegáIt eLIgedaykarviPaKRbBn§½kMralCamYynwglkçxNÐragFrNImaRt niglkçxNÐTMrepSgKña. karKNnakMralxNнBIrTis 464
  28. 28. T.Chhay NPIC taragTI 17>2 karEbgEckm:Um:g;enAkñúgbnÞHkMralxagcug kMralxNн kMralxNнEdlKμan RCugxageRkA EdlmanFñwm FñwmenAcenøaHTMrxagkñúg minRtUv enAcenøaHRKb; manFñwm KμanFñwm )anTb; Tb;eBj TMr xageRkA xageRkA ¬!¦ ¬@¦ ¬#¦ ¬$¦ ¬%¦ m:Um:g;emKuNGviC¢manxageRkA 0 0.65 0.16 0.30 0.26 m:Um:g;emKuNviC¢man 0.63 0.35 0.57 0.50 0.52 m:Um:g;emKuNGviC¢manxageRkA 0.75 0.65 0.70 0.70 0.70 8>4> karEbgEckm:Um:g;tamTTwgkñúgkMralxNн Transverse Distribution of Moment in Slabs m:Um:g;tambeNþayEdl)anBnül;xagelIKWsMrab;TTwgTaMgmUlrbs;eRKagGKarsmmUl. TTwgeRKag enHCaplbUkénTTwgcMerokelIssrBIr CamYynwgTTwgcMerokkNþalBIrénbnÞHkMralBIrEk,rKña dUcbgðaj enAkñúgrUbTI 17>15. karEbgEcktamTTwgénm:Um:g;tambeNþayeTAcMerokkNþal nigcMerokelIssrKW CaGnuKmn_énpleFob l2 / l1 E I α f = cb b = E I beam stiffness slab stiffness ¬!&>!@¦ cs s E C torsional rigidity of edge beam section β t = cb = 2 E cs I s flexural rigidity of a slab of width equal to beam span length ¬!&>!#¦ Edl C = torsional constant = ∑ ⎛1 − 0.63x ⎞⎛ x3y ⎞ 3 ⎜ ⎜ y ⎟⎜ ⎟⎜ ⎟ ⎟ ¬!&>!$¦ ⎝ ⎠⎝ ⎠ Edl x nig y CaTTwg nigbeNþayrbs;muxkat;ctuekaN. PaKryénm:Um:g;KNnanImYy²Edl nwgRtUvEbgEckeTAcMerokelIssr nigcMerokkNþalsMrab;bnÞHkMralxagkñúg nigbnÞHkMralxageRkA RtUv)aneGayenAkñúgtarag 17>3 dl; 17>6. enAkñúgbnÞHkMralKMrUxagkñg EpñkxøHénm:Um:g;KNna ú EdlminRtUv)andak;eTAkñúgcMerokelIssr ¬tarag 17>3¦ RtUv)anTb;edaycMerokkNþalBak; kNþalEdlRtUvKña. kareFVI linear interpolation sMrab;tMél l2 / l1 EdlenAcenøaH 0.5 nig 2.0 nigsMrab;tMél α f 1l2 / l1 EdlenAcenøaH 0 nig 1 RtUv)anGnuBaØateday ACI Code. BItarag karKNnakMralxNнBIrTis 465
  29. 29. T.Chhay NPIC 17>3 eyIgGacemIleXIjfa enAeBlFñwmminRtUv)aneRbI dUckñúgkrNI flat plate nig flat slab α f 1 = 0 . PaKrycugeRkayénm:Um:g;enAkñúgcMerokelIssr nigcM erokkNþalCaGnuKmn_én M o RtUv)aneGayenAkñúgtaragTI 17>4. sMrab;kMralxageRkA Epñkénm:Um:g;KNnaEdlminRtUv)andak;enAkñúgcMerokelIssr ¬tarag 17>5¦ RtUv)anTb;edaycMerokkNþalBak;kNþalEdlRtUvKña. mþgeTot kareFVI linear interpolation cenøaHtM élEdlbgðajenAkñúgtarag 17>5 RtUv)anGnuBaØateday ACI Code, Section 13.6.4.2. enAeBlEdl FñwmminRtUv)aneRbIenAkMralxageRkA dUckrNI flat plate nig flat slab edayKμanFñwmxag (spandrel beam) α f 1 = 0 / C = 0 nig β t = 0 . enHmann½yfacugssr pþl;nUvkarTb;sMrab;cugkMralxageRkA. tMélGnuvtþn_éntarag 17>5 sMrab;krNIBiessenHRtUv)an bgðajenAkñúgtarag 17>6 nigrUbTI 17>15. karKNnakMralxNнBIrTis 466
  30. 30. T.Chhay NPIC tarag 17>3 PaKryénm:Um:g;tambeNþayenAkñúgcMerokelIssr sMrab;bnÞHkMralxagkñúg (ACI Code, Section 13.6.4) α f 1l 2 / l1 pleFob l2 / l1 0 .5 1 .0 2 .0 m:Um:g;GviC¢manenAelITMrxagkñúg 0 75 75 75 ≥ 1 .0 90 75 45 m:Um:g;viC¢manenAEk,rkNþalElVg 0 60 60 60 ≥ 1 .0 90 75 45 tarag 17>4 PaKryénm:Um:g;enAkñúgkMralxNнxagkñúgBIrTisEdlKμanFñwm ( α 1 = 0) ⎛ l n1 ⎞ 2 m:Um:g;KNnasrub M o = (wu l 2 )⎜ ⎟ n! ⎜ 8 ⎟ r!(n − r )! ⎝ ⎠ m:Um:g;GviC¢man m:Um:g;viC¢man m:Um:g;tambeNþayenAkñúgkMralmYy − 0.65M o ± 0.35M o cMerokelIssr 0.75(− 0.65M o ) = −0.49 M o 0.60(0.35M o ) = 0.21M o cMerokkNþal 0.25(− 0.65M o ) = −0.16 M o 0.40(0.35M o ) = 0.14 M o tarag 17>5> PaKryénm:Um:g;tambeNþayenAkñúgcMerokelIssr sMrab;bnÞHkMralxageRkA (ACI Code, Section 13.6.4) α f 1l 2 / l1 βt pleFob l2 / l1 0 .5 1 .0 2 .0 m:Um:g;GviC¢manenAelITMrxageRkA 0 0 75 75 75 ≥ 2 .5 90 75 45 ≥ 1 .0 0 60 60 60 ≥ 2 .5 90 75 45 m:Um:g;viC¢manenAEk,rkNþalElVg 0 60 60 60 ≥ 1 .0 90 75 45 m:Um:g;GviC¢manenAelITMrxagkúñg 0 75 75 75 ≥ 1 .0 90 75 45 karKNnakMralxNнBIrTis 467
  31. 31. T.Chhay NPIC tarag 17>6> PaKryénm:Um:g;tambeNþayenAkñúgcMerokelIssr nigcMerokkNþal ¬sMrab;pleFob l / l ¦ edayeGay α = β = 0 2 1 f1 t m:Um:g;cugeRkayCaGnuKmn_én % cMerokelIssr cMerokkNþal M o nig α ec ¬cMerokelIssr¦ ⎡ 0.65 ⎤ m:Um:g;GviC¢manenAelITMrxageRkA 100 0.26M o 0 ⎢ ⎥M o ⎣ (1 + 1 α ec ) ⎦ ⎡ 0.28 ⎤ m:Um:g;viC¢man¬ 0.6 × 0.52M o ¦ 60 0.312M o 0.208M o ⎢0.63 − ⎣ (1 + 1 α ec )⎥ o ⎦ M m:Um:g;GviC¢manenAelIMTMrxagkñúg ⎡ 0.10 ⎤ 0.75 − ⎢ ⎥M o ⎣ (1 + 1 α ec ) ⎦ 0.52M o 0.175M o ¬ 0.75 × 0.70M o ¦ 75 BItarag 17>6 eyIgeXIjfaenAeBlEdlFñwmxagminRtUv)aneRbIsMrab;kMralxageRkA β t = 0 nig m:Um:g;KNna 100% RtUv)anTb;edaycMerokelIssr. cMerokkNþalnwgminTb;m:Um:g;NamYyeT dUcenHbrimaNEdkGb,brmaRtUv)andak;. ACI Code, Section 13.6.4.3 kMNt;faenAeBlTMrxag eRkACassr b¤CBa¢aMgEdlRtUv)anBnøÚtsMrab;cMgayesμInwgbIPaKbYnRbEvgElVgTTwg l2 EdleRbIedIm,I kMNt; M o m:Um:g;GviC¢manxageRkAEdlRtUv)anEbgEckesμIkat;tam l2 . enAeBlEdlFñwmRtUV)andak; tam beNþayGkS½ssr ACI Code, Section 13.6.5 tMrUvfam:Um:g;RtUvEtsmamaRtedIm,IkarBarm:Um:g; 85% enAkñúgcMerokelIssr RbsinebI α f 1 (l 2 / l1 ) ≥ 1.0 . sMrab;tMél α f 1 (l 2 / l1 ) enAcenøaH 1.0 nig 0 m:U m:g;EdlmankñúgFñwmRtUv)ankMNt;edayeRbI linear interpolation . m:Um:g;k¾RtUVEtsmamaRt edIm,IkarBar m:Um:g;bEnßmEdlekItedaybnÞúkTaMgGs;EdlGnuvtþedaypÞal;eTAelIFñwm edaybBa©Ül TaMgTMgn;rbs;tYrFñwm EdlKitBIeRkamkMral. Epñkénm:Um:g;Edlmin)andak;eTAkñúgFñwmRtUv)anTb;eday kMralxNнenAkñμúgcMerok elIssr. 8>5> karpþl;rbs; ACI sMrab;T§iBlrbs;KMrUénkardak;bnÞúk ACI Provisions for Effects of Pattern Loading enAkñúgrcnasm<n§½Cab; m:Um:g;Bt;FGtibrma nigGb,brmaenARtg;muxkat;eRKaHfñak;RtUv)anTTYl eday kardak;bnÞúkGefrtamKMrUkMNt;mYyedIm,IbegáIttMélx<s;bMput. kardak;bnÞúkGefrenARKb;ElVg karKNnakMralxNнBIrTis 468
  32. 32. T.Chhay NPIC TaMgGs; nwgminbegáItm:Um:g;Bt;viC¢man b¤m:Um:g;Bt;viC¢manGtibrmaeT.m:Um:g;Gtibrma nigGb,brma GaRs½yCacMbg nwgkrNIxageRkam³ !> pleFobénbnÞúkGefrelIbnÞúkefr. pleFobx<s;nwgbegáInT§iBlrbs;KMrUénkardak;bnÞúk (patter loading). @> pleFobPaBrwgRkajssrelIFñwm. pleFobtUcnwgbegáInT§iBlrbs;KMrUénkardak;bnÞúk. #> KMrUénkardak;bnÞúk. m:Um:g;viC¢manGtibrmaenAkñúgElVgrgT§iBltictYcBIKMrUénkardak;bnÞúk. edIm,IkMNt;m:Um:g;emKuNKNnaenAkñúgrcnasm<n§½Cab; ACI Code, Section 13.7.6 kMNt;dUc xageRkam³ !> enAeBlKMrUénkardak;bnÞúkRtUv)ansÁal; eRKagsmmUlKYrRtUv)anviPaKsMrab;bnÞúkenaH. @> enAeBlbnÞúkGefrERbRbYl b:uEnþminFMCagbIPaKbYnénbnÞúkefr wL ≤ 0.75wD b¤enAeBl EdlRKb;kMralTaMgGs;RtUv)andak;bnÞúkGefrkñúgtMNalKña karviPaKeRKagEdlmandak;bnÞúk GefremKuNeBjeRKagRtUv)anGnuBaØat. #> sMrab;lkçxNÐénkardak;bnÞúkepSgeTot eKGnuBaØateGaysnμt;fa m:Um:g;emKuNviC¢man Gtibrma enAEk,rkNþalElVgekItmanCamYynwg 0.75 énbnÞúkGefremKuNeBjenAelIkMral nigenAelIkM ralqøas;. sMrab;m:Um:g;emKuNGviC¢manGtibrmaenAkñúgkMralxNнelITMr RtUv)an eKGnuBaØateGay snμt;fa 0.75 énbnÞúkGefremKuNGnuvtþEtenAelIkMralEk,r. $> m:Um:g;emKuNminKYryktUcCagm:Um:g;EdlekIteLIgCamYybnÞúkGefremKuNeBjenAelIkMral EdlCab;TaMgGs;eT. 8>6> karlMGitsrésEdk Reinforcement Details eRkayeBlPaKryTaMgGs;énm:Um:g;sþaTicenAkñúgcMerokelIssr nigcMerokkNþalRtUv)ankMNt; brimaNsrésEdkk¾GacRtUv)anKNnasMrab;m:Um:g;viC¢man nigGviC¢manenAkñúgcMeroknImYy² dUc Edl)aneFVIsMrab;FñwmenAkñúgemeronTI4 ⎛ a⎞ M u = φAs f y ⎜ d − ⎟ = Ru bd 2 ⎝ 2⎠ ¬!&>!%¦ KNna Ru nigkMNt;PaKryEdk ρ edayeRbItarag]bsm<n§½ B b¤eRbIsmIkarxageRkam³ ⎛ ρf y ⎞ Ru = φρf y ⎜1 − ⎜ 1.7 f ' ⎟ ⎟ ¬!&>!^¦ ⎝ c ⎠ karKNnakMralxNнBIrTis 469
  33. 33. T.Chhay NPIC Edl φ = 0.9 . RkLaépÞmuxkat;EdkKW As = ρbd . enAeBlEdlkMras;kMralxNнRtUvnwgkarkMNt; kMras;kMralxNнEdl)anerobrab;kñúgEpñkTI 4> enaHeK minRtUvkarEdkrgkarsgát;eT. rUbTI 13>3>8 én ACI Code bgðajRbEvgGb,brmaénEdk nigkar lMGitsrésEdksMrab;kMralEdlKμanFñwm ehIy vak¾RtUvbgðajenATIenHEdr ¬rUbTI 17>16¦. KMlatEdkenAkñúgkMralxNнminRtUvFMCaglImIt Gtibrmarbs; ACI EdlmanKMlat 450mm b¤BIrdgkMras; kMralykmYyNaEdltUcCageK. karKNnakMralxNнBIrTis 470
  34. 34. T.Chhay NPIC 8>7> viFIPaBrwgRkajEdlRtUv)anEktMrUvsMrab;ElVgcug Modified Stiffness Method for End Spans enAkñúgviFIenH PaBrwgRkajrbs;FñwmxagcugkMral nigrbs;ssrxageRkARtUv)anCMnYsedayPaB rwgRkajénssrsmmUl K ec . PaBrwgRkajTb;karBt;énssrsmmUl K ec GacRtUv)anKNnaBI smIkarxageRkam³ 1 = 1 + 1 ∑K b¤ K ec = 1 + ∑ K c/ K ¬!&>!&¦ K ec ∑ K c K t c t Edl K ec = PaBrwgRkajTb;nwgkarBt;rbs;ssrsmmUl K c = PaBrwgRkajTb;nwgkarBt;rbs;ssrBitR)akd K t = PaBrwgRkajTb;karrmYlrbs;Fñwmxag plbUkénPaBrwgRkajrbs;ssrxagelI nigxageRkamkMralxNнGacRtUv)anykdUcxag eRkam³ ⎛I I ⎞ ∑ K c = 4 E ⎜ c1 + c 2 ⎟ ⎜L L ⎟ ¬!&>!*¦ ⎝ c1 c2 ⎠ Edl I c1 nig Lc1 Cam:Um:g;niclPaB nigRbEvgrbs;ssrxagelInIv:UkMralxNн nig I c2 nig Lc 2 Cam:Um:g;niclPaB nigRbEvgrbs;ssrxageRkamnIv:UkMralxNн. PaBrwgRkajTb;nwgkarrmYl rbs;Fñwmcug K t GacRtUv)ankMNt;dUcxageRkam³ Kt = ∑ 9 E cs C 3 ¬!&>!(¦ ⎛ c ⎞ l 2 ⎜1 − 2 ⎟ ⎜ ⎝ l2 ⎟ ⎠ Edl TMhMrbs;ssrctuekaNEkg b¤ctuekaNEkgsmmUl/ capital column b¤ c2 = bracket Edlvas;enAelIElVgTTwgénRCugnImYy²rbs;ssr. Ecs = m:UDuleGLasÞicrbs;ebtugkMral C = efrrmYl (torsion constant) EdlkMNt;BIsmIkarxageRkam³ ⎛ x ⎞⎛ x 3 y ⎞ C = ∑ ⎜1 − 0.63 ⎟⎜ ⎜ y ⎟⎜ 3 ⎟ ⎟ ¬!&>@0¦ ⎝ ⎠⎝ ⎠ Edl x CaTMhMTTwgrbs;ctuekaN nig y CabeNþayrbs;ctuekaN. kñúgkarKNna C vimaRt rbs;muxkat;ctuekaNRtUv)aneRCIserIsy:agNaedIm,IeFVIeGay)antMél C FMCageK. karKNnakMralxNнBIrTis 471
  35. 35. T.Chhay NPIC smIkarxagedImEdl)anENnaMenATIenH nwgRtUv)anykmkeRbIenAkñúgEpñk 12 “Equivalent Frame Method” . RbsinebIkMralmanFñwmRsbKñanwgm:Um:g;EdlRtuvKNna enaHPaBrwgRkajTb;karrmYl K t EdleGaykñúgsmIkar !&>!( RtUv)anCMnYseday K ta EdlmantMélFMCag ehIy K ta RtUv)an KNnadUcxag eRkam³ I sb K ta = K t × Is l2 h 3 Edl Is = 12 m:Um:g;niclPaBrbs;kMralxNнEdlmanTTwgesμInwgTTwgeBjcenøaHGkS½ = kMral ¬edayminrYmbBa©ÚlEpñkrbs;tYrFñwmEdlbnøayeTAelI b¤eTAeRkamkMralxNн¦. I sb = I s / edaybBa©ÚlTaMgtYrFñwmEdlbnøayeTAelI b¤eTAeRkamkMralxNн. muxkat;énGgát;rgkarrmYlxøHEdlmanP¢ab;mkCamYyRtUv)anbgðajenAkúñgrUbTI 17>17. enAeBlEdl K ta RtUv)anKNna enaHpleFobPaBrwgRkaj α ec RtUv)anTTYldUcxageRkam³ α ec = K ec ∑ (K + K ) ¬!&>@!¦ s b Edl Ks = 4 Ecs I s l1 =PaBrwgRkajTb;karBt;rbs;kMralxNн Kb = =PaBrwgRkajTb;karBt;rbs;Fñwm 4 Ecb I b l1 I b = m:Um:g;niclPaBTaMgmUlrbs;muxkat;FñwmbeNþay karEbgEckénm:Um:g;sþaTicsrub M o enAkñúgkMralxageRkARtUv)aneGayCaGnuKmn_én α ec dUcxageRkam³ ⎡ 0 .1 ⎤ Interior negative factored moment = ⎢0.75 − (1 + 1 / α ec )⎥ o M ⎣ ⎦ ⎡ 0.28 ⎤ Positive factored moment = ⎢0.63 − (1 + 1 / α ec )⎥ o M ⎣ ⎦ ⎡ 0.65 ⎤ Exterior negative factored moment = ⎢ ⎥M o ⎣ (1 + 1 / α ec ) ⎦ tMélTaMgenHRtUv)anbgðajenAkñúgkMralxageRkAKMrUkñúgrUbTI 17>18. emKuNTaMgenHRtUv)an BicarNaBIT§iBlrbs;PaBrwgRkajrbs;ssrxageRkAk¾dUcCaT§iBlrbs;PaBrwgRkajrbs;FñwmcugkM ral EdleFVIeGaykarEbgEckm:Um:g;manlkçN³RKb;RKan;. karKNnakMralxNнBIrTis 472
  36. 36. T.Chhay NPIC karKNnakMralxNнBIrTis 473
  37. 37. T.Chhay NPIC 8>8> segçbviFIKNnaedaypÞal; Summary of the Direct Design Method (DDM) krNITI1 kMralKμanFñwm !> RtYtBinitütMrUvkarénkarkMNt;Edl)anBnül;enAkñúgEpñk 8>1. RbsinebIvaminRtUvnwgkar kMNt;eT eKminGaceRbIviFI DDM )aneT. karKNnakMralxNнBIrTis 474
  38. 38. T.Chhay NPIC @> kMNt;kMralxNнGb,brma hmin edIm,IRKb;RKgPaBdabedayeRbItMélenAkñúgtarag 17>1. kM ralxageRkAEdlKμanFñwmxageGay hmin x<s;bMput ¬ ln / 30 sMrab; f y = 420MPa ¦. vaCa karGnuvtþFmμtaEdleRbIkMras;kMralxNнesμIKñasMrab;RKb;kMralxageRkAnigxagkñúg. #> KNnabnÞúkemKuN Wu = 1.2WD. + 1.6WL $> epÞógpÞat;kMras;kMralxNн h edIm,IkarBarkMlaMgkat;TTwgmYyTis nigkMlaMgkat;TTwgBIr Tis. RbsinebIkMras;kMralxNн h minRKb;RKan; eKRtUvbegáInkMras; h b¤dak;EdkTb; kMlaMgkat;TTWg. %> KNnam:Um:g;sþaTicsrub M o sMrab;TisedATaMgBIr ¬smIkar !&>!!¦ ^> kMNt;emKuNEbgEcksMrab;m:Um:g;viC¢man nigm:Um:g;GviC¢manenAkñúgTisedAbeNþay nigTisedA TTwgsMrab;cMerokelIssr nigcMerokkNþalnImYy²TaMgenAkñúgkMralxagkñúg nigkMralxageRkA dUcxageRkam³ a. sMrab;kMralxagkñúg eRbIemKuNm:Um:g;EdleGayenAkñúgtarag 17>4 b¤rUbTI 17>15 b. sMrab;kMralxageRkAEdlKμanFñwmxag emKuNm:Um:g;kMralRtUv)aneGayenAkñúgtarag 17>2 b¤rUbTI 17>14 ¬krNITI5¦. sMrab;karEbgEckm:Um:g;enAkñúgTisedATTwg eRbIta rag 17>6 b¤rUbTI 17>15 sMrab;GRtacMerokelIssr. cMerokkNþalnwgTb;Epñkénm:Um:g; EdlminRtUv)andak;eTAkñμúgcMerokssr. c. sMrab;kMralxageRkAEdlmanFñwmxag emKuNm:Um:g;kMralRtUv)aneGayenAkñúgtarag 17>2 b¤rUbTI 17>14 ¬krNITI4¦. sMrab;karEbgEckm:Um:g;enAkñúgTisedATTwg eRbIta rag 17>5 sMrab;cMerokelIssr. cMerokkNþalnwgTb;lMnwgénm:Um:g;kMral. &> kMNt;brimaNEdksMrab;RKb;muxkat;eRKaHfñak;;éncMerokelIssr nigcMerokkNþalTaMgGs; nigBnøÚtsrésEdkeBjkMralxNн ¬rUbTI 17>16¦ *> KNna unbalanced moment nigRtYtBinitüemIlfaetIkarbMElgm:Um:g; unbalanced moment edaykarBt;RKb;RKan;b¤Gt;. RbsinebIGt;RKb;RKan;eT kMNt;brimaNEdk bEnßmEdlcaM)ac;enAkñúgTTwgeRKaHfñak; ¬eyagtamEpñkTI 10¦. (> RtYtBinitüemIlfaetIkarbMElgm:Um:g; unbalanced moment edaykMlaMgkat;TTwgRKb; RKan; b¤Gt;. RbsinebIGt;eT begáIn h b¤dak;EdkTb;kMlaMgkat;TTwg. ¬eyagtamEpñkTI 10¦ karKNnakMralxNнBIrTis 475
  39. 39. T.Chhay NPIC krNITI2 kMralEdlmanFñwmxagkñúg nigFñwmxageRkA !> RtYtBinitütMrUvkarénkarkMNt;Edl)anBnül;enAkñúgEpñk 8>1. @> kMNt;kMralxNнGb,brma hmin edIm,IRKb;RKgPaBdabedayeRbItMélenAkñúgsmIkar TI !&>! Dl; !&>#. kñúgkrNICaeRcIn smIkarTI !&>@ lub. smIkarTI !&>! KYrRtUv)an KNnadMbUgdUcbgðajenAkñúg]TahrN_TI 17>1. #> KNnabnÞúkemKuN Wu = 1.2WD. + 1.6WL $> epÞógpÞat;kMras;kMralxNн h tamry³kMlaMgkat;TTwgmYyTis nigkMlaMgkat;TTwgBIrTis. CaTUeTA kMlaMgkat;TTWgminmanlkçN³eRKaHfñak;sMrab;kMralxNнEdlRTedayFñwmeT. %> KNnam:Um:g;sþaTicsrub M o sMrab;TisedATaMgBIr ¬smIkar !&>!!¦ ^> kMNt;emKuNEbgEcksMrab;m:Um:g;viC¢man nigm:Um:g;GviC¢manenAkñúgTisedAbeNþay nigTis edA TTwgsMrab;cMerokelIssr nigcMerokkNþalnImYy²TaMgenAkñúgkMralxagkñúg nigkMral xageRkA dUcxageRkam³ a. sMrab;kMralxagkñúg eRbIemKuNm:Um:g;kñúgrUbTI 17>14 ¬krNITI 3¦ b¤rUbTI 17>12. sMrab;karEbgEckm:Um:g;kñúgTisedATTwg eRbItaragTI 17>3 sMrab;cMerokelIssr. cM erokkNþalnwgTb;Epñkénm:Um:g;Edlmin)andak;eTAkñúgcMerokelIssr. KNna α1 BI smIkar !&>!@. b. sMrab;kMralxageRkA eRbIemKuNm:Um:g;kMralenAkñúgtarag 17>2 b¤rUbTI 17>14 ¬krNI TI3¦. sMrab;karEbgEckm:Um:g;enAkñúgTisedATTwg eRbItarag 17>5 sMrab;cM erokelIssr. cMerokkNþalnwgTb;lMnwgénm:Um:g;kMral. c. kñúgkrNITaMgBIr (a) nig (b) FñwmRtUvTb; 85% énm:Um:g;enAkñúgcMerokssr enAeBl Edl α f 1 (l2 / l1 ) ≥ 1.0 b:uEnþGRtaERbRbYlcenøaH 85% nig 0% enAeBl α f 1 (l 2 / l1 ) ERbRbYlcemøaHBI 1.0 nig 0 . &> kMNt;brimaNEdksMrab;RKb;muxkat;eRKaHfñak;;éncMerokelIssr/ Fñwm nigcMerokkNþal TaMgGs; bnÞab;mkBnøÚtsrésEdkeBjkMralxNн ¬rUbTI 17>16¦ *> KNna unbalanced moment nigbnÞab;mkRtYtBinitüemIlkarbMElgénm:Um:g; edaykar Bt; nigkMlaMgkat;TTwg ¬eyagtamEpñkTI 10¦. karKNnakMralxNнBIrTis 476
  40. 40. T.Chhay NPIC ]TahrN_TI17>3³ edayeRbIvIFI direct design method KNnakMral flat plate xagkñúgKMrU dUcEdl)anbgðajenAkñúgrUb TI 17>6 nig 17>19. RbBn§½kMralpSMeLIgeday kMralbYnenARKb;Tis EdlkMralmYy²manTMhM 7.5 × 6m . kMralTaMgGs;RtUv)anRTedayssrTMhM 50 × 50cm manRbEvg 3.6m . kMralxNнRT bnÞúkGefreFVIkar BRgayesμI 4.8kN / m 2 nigbnÞúkefreFVIkarEdlrYmman kMralkargarbegðIy (floor finish) 1.5kN / m 2 rYmTaMgbnÞúkpÞal;rbs;kMral. eKeGay f 'c = 28MPa nig f y = 420MPa . karKNnakMralxNнBIrTis 477
  41. 41. T.Chhay NPIC dMeNaHRsay³ 1> kMNt;kMras;kMralxNнGb,brmaedayeRbItarag 17>1 sMrab; flat plate. BI]TahrN_TI 17>1 kMras;kMralxNнKW 25cm . 2> KNnabnÞúkemKuN³ wD = 1.5 + weight of slab = 1.5 + 0.25 × 25 = 7.75kN / m 2 wu = 1.2 × 7.75 + 1.6 × 4.8 = 17kN / m 2 3> RtYtBinitükMlaMgkat;TTwgmYyTis nigkMlaMgkat;TTwgBIrTis³ a. RtYtBinitükMlaMgkat;pugenAcMgay d / 2 BIépÞssr ¬GMeBIBIrTis¦. Edaysnμt;kMras;ebtugkarBarEdk 2cm nigeRbIEdk DB16 . enaH d mFümKW 25 − 2 − 1.6 = 21.4cm nig bo = 4(50 + 21.4) = 285.6cm ¬emIlrUbTI 17>19 c¦ Vu = [l1l 2 − (71.4 × 71.4)]× wu = (750 × 600 − 5098) × 17 ⋅ 10 −4 = 756.3kN φ 0.75 φVc = f 'c bo d = 28 × 2.856 × 0.214 × 10 3 = 808.5kN 3 3 EdlFMCag Vu b. KNnakMlaMgTTwgFñwmenAcMgay d BIépÞssr. d mFümKW 21.4cm . BicarNacMerok 1m ¬rUbTI 17>19 d¦ CamYyRbEvgcMerokKW³ x = 3.75 − 0.25 − 0.214 = 3.286m Vu = wu (1 × 3.286) = 17 × 3.286 = 55.862kN φ 0.75 φVc = f 'c bd = 28 × 1 × 0.214 × 10 3 = 141.5kN 6 6 EdlFMCag Vu . Kñugkardak;bnÞúkFmμta kMlaMgkat;TTwgmYyTisGt;lub. 4> KNnam:Um:g;sþaTicsrubenAkñúgTisedAEvg nigTisedAxøI 2 kñúgTisedAEvg M ol = 8 = 8 6 × 7 2 = 624.75kN .m wu l 2 l n1 17 2 kñúgTisedAxøI M os = wu l81ln2 = 17 7.5 × 5.52 = 482.11kN .m 8 edaysarEt l2 < l1 TTwgénBak;kNþalcMerokelIssrenAkñúgTisedAEvgKW 0.25 × 6m = 1.5m ehIyTTwgéncMerokkNþalKW 6 − 2 × 1.5 = 3m . TTwgénBak;kNþal cMerokelIssrkñúgTisedAxøI KW 1.5m ehIyTTwgéncMerokkNþalKW 7.5 − 2 × 1.5 = 4.5m . edIm,IKNnakMBs;RbsiT§PaB d kñúgTisedAnImYy² snμt;faEdkenA kñúgTisedAxøIRtUvBIelIEdk karKNnakMralxNнBIrTis 478
  42. 42. T.Chhay NPIC enAkñúgTisedAEvg. dUcenH d (long direction) = 25 − 2 − 0.8 = 22.2cm nig d (short direction ) = 25 − 2 − 1.6 − 0.8 = 20.6cm . sMrab;karGnuvtþn_ d (average) = 25 − 3.5 = 21.5cm GacRtUv)aneRbIsMrab;Tis edATaMgBIr. dMeNIrkarKNnaGacRtUv)anerobcMCaTMrg;tarag dUcbgðajenAkñúgtarag 17>7 nig 17>8. karlMGitsMrab;kareRCIserIssrésEdkRtUv)anbgðajenAkñúgrUbTI 17>20 edayeRbIRbBn§½ EdkRtg;. eKRtUveKarBkardak;RbEvgGb,brmarbs;EdkdUcEdl)anbgðajenAkñúgrUbTI 17>16. Gñksagsg;cUlcitþeRbIEdkRtg; nigEdkEdlmanersIusþg; f ' y = 420MPa . KMlatGtibrma = widthof bars = 3000 = 375mm no. of panel 8 taragTI17>7 karKNnabnÞHkMral flat platexagkñúg ¬kñúgTisEvg¦ M o = 624.75kN .m M n = −0.65M o = −406.1kN .m TisEvg M p = +0.35M o = 218.66kN .m cMerokelIssr cMerokkNþal GviC¢man viC¢man GviC¢man viC¢man karEbgEckm:Um:g; % 75 60 25 40 M u (kN .m) 0.75M n = −304.6 0.6 M p = ±131.2 0.25 M n = −101.5 0.6 M p = ±87.5 TTwgcMerok b(mm) 3000 3000 3000 3000 kMBs;RbsiT§PaB d (mm) 222 222 222 222 Mu Ru = ( MPa) bd 2 2.06 0.89 0.69 0.59 PaKryEdk ρ (%) 0.57 0.24 0.19 0.16 As = ρbd (mm 2 ) 3796.2 1598.4 1265.4 1065.6 As (min) = 0.0018bhs (mm 2 ) 1350 1350 1350 1350 EdkEdleRCIserIs ¬Rtg;¦ 20 DB16 8DB16 12DB12 12DB12 KMlat ≤ 2h = 500mm s 150 375 250 250 karKNnakMralxNнBIrTis 479
  43. 43. T.Chhay NPIC taragTI17>8 karKNnabnÞHkMral flat platexagkñúg ¬kñúgTisxøI¦ M o = 482.11kN .m M n = −0.65M o = −313.4kN .m TisEvg M p = +0.35M o = 168.7kN .m cMerokelIssr cMerokkNþal GviC¢man viC¢man GviC¢man viC¢man karEbgEckm:Um:g; % 75 60 25 40 M u (kN .m) 0.75 M n = −235.05 0.6 M p = ±101.2 0.25 M n = −78.35 0.6 M p = ±67.5 TTwgcMerok b(mm) 3000 3000 4500 4500 kMBs;RbsiT§PaB d (mm) 206 206 206 206 Mu Ru = ( MPa) bd 2 1.85 0.79 0.41 0.35 PaKryEdk ρ (%) 0.51 0.21 0.11 0.09 As = ρbd (mm 2 ) 3151.8 1297.8 1019.7 834.3 As (min) = 0.0018bhs (mm 2 ) 1350 1350 2025 2025 EdkEdleRCIserIs ¬Rtg;¦ 16 DB16 8DB16 18 DB12 18 DB12 KMlat ≤ 2h = 500mm s 187.5 375 250 250 KMlatEdkenAkñúgcMerokelIssrkñúgTisxøIKW 250mm . vamanlkçN³RKb;RKan; edaysarva tUcCag 2hs = 500mm nigtUcCag 450mm EdlkMNt;eday ACI Code. cMNaMfa PaKryEdkTaMgGs;KWticCag ρ max = 0.0182 . dUcenH φ = 0.9 . ]TahrN_TI17>4³ edayeRbIviFI direct design method KNnakMral flat plate xageRkAEdlmanTMhM bnÞúk ersIusþg;ebtug nigersIusþg;EdkdUcKñanwgGVIEdl)aneGayenAkñúg]TahrN_TI 17>3. FñwmminRtUv)aneRbI ¬rUbTI 17>21¦. dMeNaHRsay³ 1> kMNt;kMras;kMralxNнGb,bramedayeRbItarag 17>1 sMrab; flat plate. BI]TahrN_TI 17>1 kMras;kMralxNнKW 25cm . karKNnakMralxNнBIrTis 480
  44. 44. T.Chhay NPIC 2> KNnabnÞúkemKuN³ wu = 17kN / m 2 3> RtYtBinitükMlaMgkat;TTwgmYyTis nigkMlaMgkat;TTwgBIrTis ¬eyagtam]TahrN_TI 17>3 nigrUbTI 17>9¦. a. RtYtBinitükMlaMgkat;pugenAssrxagkñúg Vu = 756.3kN < φVc = 808.5kN b. RtYtBinitükMlaMgkat;TTwgmYyTis³ Vu = 55.862kN < φVc = 141.5kN c. RtYtBinitükMlaMt;pugenAssrxageRkA³ d = 21.4cm 21.4 x = 50 + = 60.7cm 2 karKNnakMralxNнBIrTis 481
  45. 45. T.Chhay NPIC y = 50 + 21.4 = 71.4cm karKNnakMralxNнBIrTis 482
  46. 46. T.Chhay NPIC bo = 2 x + y = 192.8cm ⎡ ⎛ 750 ⎞ ⎤ Vu = ⎢600⎜ + 25 ⎟ − 60.7 × 71.4⎥10 −4 × 17 = 400.6kN ⎣ ⎝ 2 ⎠ ⎦ φ φVc = f ' c bo d = 545.8kN > 400.6kN 3 d. RtYtBinitükMlaMgkat;pugenAssrkac;RCug³ d = 21.4cm 21.4 x = y = 50 + = 60.7cm 2 bo = x + y = 121.4cm ⎡⎛ 600 ⎞⎛ 750 ⎞ ⎤ Vu = ⎢⎜ + 25 ⎟⎜ + 25 ⎟ − 60.7 × 60.7 ⎥10 −4 × 17 = 214.7 kN ⎣⎝ 2 ⎠⎝ 2 ⎠ ⎦ φ φVc = f ' c bo d = 343.7 kN > 214.7 kN 3 4> KNnam:Um:g;sþaTicsrub ¬BI]TahrN_TI 17>3¦ M ol (long direction ) = 624.7 kN .m d = 22.2cm M os (short direction) = 482.11kN .m d = 20.6cm TTwgrbs;cMerokelIssrKW 300cm nigTTwgcMerokkNþalKW 450cm 5> KNnam:Um:g;KNnaenAkñúgTisedAEvg³ l1 = 7.5m ¬eyagtamtarag 17>5 b¤rUb 17>15¦. karEbgEckm:Um:g;srub M ol enAkñúgcMerokelIssr nigcMerokkNþalKWRtUv)anKNnadUcxag eRkam³ a. cMerokelIssr³ m:Um:g;GviC¢manxagkñúg = −0.525M o = −0.525(624.75) = −328kN .m m:Um:g;viC¢manenAkñúgElVg = 0.312M o = 0.312(624.75) = 195kN .m m:Um:g;GviC¢manxageRkA = −0.26M o = −0.26(624.75) = 162.4kN.m b. cMerokkNþal³ m:Um:g;GviC¢manxagkñúg = −0.175M o = −0.175(624.75) = −109.3kN .m m:Um:g;viC¢manenAkñúgElVg = 0.208M o = 0.208(624.75) = 129.9kN .m m:Um:g;GviC¢manxageRkA = 0 karKNnakMralxNнBIrTis 483
  47. 47. T.Chhay NPIC 6> KNnam:Um:g;KNnaenAkñúgTisedAxøI³ ls = 6m . vaRtUv)anKitdUckMralxagkñúgEdr BIeRBaHva Cab;TaMgsgçag. eyagtamtarag 17>4 b¤rUbTI 17>15 karEbgEckm:Um:g;srub M os enA kñúgcMerokelIssr nigcMerokkNþalRtUv)anKNnadUcxageRkam³ a. cMerokelIssr³ m:Um:g;GviC¢man = −0.49M o = −0.49(482.11) = −236.2kN.m m:Um:g;viC¢man = 0.21M o = 0.21(482.11) = 101.2kN .m b. cMerokkNþal³ m:Um:g;GviC¢man = −0.16M o = −0.16(482.11) = −77.1kN.m m:Um:g;viC¢man = 0.14M o = 0.14(482.11) = 67.5kN .m dMeNIrkarKNnaRtUv)antMeroby:aggayRsYlenAkñúgtarag 17>9. karlMGitsMrab;kar eRCIserIssrésEdkRtUv)anbgðajenAkñúgrUbTI 17>22 edayeRbIRbBn§½EdkRtg;;enAkñúgTis Evg. karlMGitsrésEdkenAkñúgTisxøImanlkçN³RsedogKñanwgkarBRgaysrésEdkenA kñúgrUbTI 17>20 edayeRbIkareRCIserIssrésEdkenAkñúgtarag 17>9. cMNaMfa RKb;PaKryEdkTaMgGs;tUcCag ρ max = 0.0182 . dUcenH φ = 0.9 . karKNnakMralxNнBIrTis 484
  48. 48. T.Chhay NPIC tarag 17>9 karKNnakMral flat platexageRkAsMrab;]TahrN_TI 17>4 ¬ d = 22.2cm ¦ cMerokelIssr cMerokkNþal TisEvg xageRkA viC¢man xagkñúg xageRkA viC¢man xagkñúg M u (kN .m) − 162.4 195 − 328 0 129.9 − 109.3 TTwgcMerok b(mm) 3000 3000 3000 3000 3000 3000 Mu Ru = ( MPa) bd 2 1.10 1.32 2.22 0 0.88 0.74 PaKryEdk ρ (%) 0.30 0.36 0.62 0 0.24 0.20 As = ρbd (mm 2 ) 1998 2398 4129 0 1598 1332 As (min) = 0.0018bhs (mm 2 ) 1350 1350 1350 1350 1350 1350 EdkEdleRCIserIs ¬Rtg;¦ 10DB16 12DB16 22DB16 12DB12 18DB12 12DB12 KMlat ≤ 2h = 500mm s 300 250 136 250 167 250 TisxøI cMerokelIssr cMerokkNþal M u (kN .m) − 236.2 101.2 − 77.1 67.5 TTwgcMerok b(mm) 3000 3000 4500 4500 kMBs;RbsiT§PaB d (mm) 206 206 206 206 Mu Ru = ( MPa) bd 2 1.86 0.79 0.40 0.35 PaKryEdk ρ (%) 0.52 0.21 0.11 0.09 As = ρbd (mm 2 ) 3214 1298 1020 834.3 As (min) = 0.0018bhs (mm 2 ) 1350 1350 2025 2025 EdkEdleRCIserIs ¬Rtg;¦ 16DB16 8DB16 18DB12 18DB12 KMlat ≤ 2h = 500mm s 187.5 375 250 250 ]TahrN_TI17>5³ eFVI]TahrN_TI 17>4 elIgvij edayeRbIviFI modified stiffness method. ¬eKRtUvkarKNnaRsedogKña sMrab;viFI equivalent frame method, EpñkTI 12¦. karKNnakMralxNнBIrTis 485
  49. 49. T.Chhay NPIC dMeNaHRsay³ 1> GnuvtþRsedogKñasMrab;CMhanTI 1 dl; 4 dUckñúg]TahrN_TI 17>4 2> KNnaPaBrwgRkajssrsmmUl/ K ec ³ 1 1 1 = + K ec ∑ K c K t eyIgGacsnμt;faEpñkéncMerokkMralEdlenAcenøaHssrxageRkAeFVIkarCassrTb;nwgkarrmYl. muxkat;rbs;kMralxNн-ssrKW 50cm ¬TTWgrbs;ssr¦ × 25cm ¬kMras;kMralxNн¦ dUcEdl bgðajkñúgrUb. a. kMNt;PaBrwgRkajTb;karrmYl K t BIsmIkar !&>@0³ ⎛ x ⎞ x3 y C = ⎜1 − 0.63 ⎟ ⎜ x = 250mm y = 500mm ⎝ y⎟ 3 ⎠ ⎛ 250 ⎞ 250 3 × 500 C = ⎜1 − 0.63 ⎟ = 17.84 ⋅ 10 8 mm 4 ⎝ 500 ⎠ 3 9Ec C 9 E c 17.84 ⋅ 10 8 Kt = 3 = 3 = 3.47 E c ⋅ 10 6 ⎛ c ⎞ ⎛ 500 ⎞ l 2 ⎜1 − 2 ⎟ 6000⎜1 − ⎟ ⎜ ⎟ ⎝ 6000 ⎠ ⎝ l2 ⎠ sMrab;kMralxNнEk,rKñaBIr ¬enAelIRCugTaMgsgçagrbs;ssr¦ EdleFVIkarCaFñwmTTwg K t = 2 × 3.47 E c ⋅ 10 6 = 6.94 E c ⋅ 10 6 b. KNnaPaBrwgRkajrbs;ssr K c / kMBs;ssr Lc = 3.6m 4 Ec I c 4 E c 500 4 Kc = = × = 5.79 E c ⋅ 10 6 Lc 3600 12 sMrab;ssrBIrenABIelI niBIeRkamkMralxNн K c = 2 × 5.79 E c ⋅ 10 6 = 11.58 E c ⋅ 10 6 c. KNna K ec ³ 1 1 1 = + K ec 11.58 E c ⋅ 10 6 6.94 E c ⋅ 10 6 K ec = 4.34 E c ⋅ 10 6 3> KNnaPaBrwgRkajrbs;kMralxNн nigemKuN α ec 3 4Ec I s l 2 hs Ks = hs = 250mm l 2 = 6000mm Is = l1 12 karKNnakMralxNнBIrTis 486
  50. 50. T.Chhay NPIC 4 E c 6000 × 250 3 Ks = × = 4.17 E c ⋅ 10 6 7500 12 K ec α ec = ∑ (K s + K b ) Kb = 0 ¬edaysarKμanFñwm¦ 4.34 Ec ⋅ 10 6 dUcenH α ec = = 1.04 4.17 E c ⋅ 10 6 yk Q = 1+ 1 α ec = 1.96 4> KNnam:Um:g;KNnaenAkñúgTisedAEvg³ ll = 7.5m . karEbgEckm:Um:g;enAkñúgkMralmYyRtUv)anbgðajenAkñúgrUbTI 17>18. m:Um:g;GviC¢manxagkñúgKW ⎡ 0.10 ⎤ ⎛ 0.10 ⎞ M ni = ⎢0.75 − ⎥ M ol = ⎜ 0.75 − 1.96 ⎟(624.7) = −436.6kN .m ⎣ Q ⎦ ⎝ ⎠ m:Um:g;viC¢manKW ⎡ 0.28 ⎤ ⎛ 0.28 ⎞ M p = ⎢0.63 − ⎥ M ol = ⎜ 0.63 − 1.96 ⎟(624.7) = 304.3kN .m ⎣ Q ⎦ ⎝ ⎠ m:Um:g;GviC¢manKW M ne = 0.65 ( M ol ) = 0.65 (624.7 ) = 207.2kN .m Q 1.96 5> KNnakarEbgEckm:Um:g;kMralenAkñúgTisxøIeTAcMerokelIssr nigcMerokkNþal. m:Um:g; M ni / M p nig M ne RtUv)anEbgEckdUcxageRkam ¬eyagtamtarag 17>6¦³ a. m:Um:g;xagkñúg M nl = −436.6kN .m RtUv)anEbgEck 75% sMrab;cMerokelIssr nig 25% sMrab;cMerokkNþal column strip = 0.75(− 436.6 ) = −327.5kN.m Middle strip = 0.25(− 436.6 ) = −109.1kN.m b. m:Um:g;viC¢man M p = 304.3kN .m RtUv)anEbgEck 60% sMrab;cMerokelIssr nig 40% sMrab;cMerokkNþal column strip = 0.60(304.3) = 182.6kN.m Middle strip = 0.40(304.3) = 121.7 kN.m c. m:Um:g;GviC¢manxageRkA M ne = −207.2kN .m RtUv)anEbgEckGaRs½ytamtarag 17>5³ karKNnakMralxNнBIrTis 487
  51. 51. T.Chhay NPIC βt = Ecb C = C 2 Ecs I s 2 I s ¬ebtugkMralxNн nigebtugssrmanm:UDuleGLasÞicdUcKña¦ 250 3 I s = 6000 = 78.125 ⋅ 108 mm 4 12 17.84 ⋅ 10 8 β= = 0.114 2 × 78.125 ⋅ 108 E I l l2 α f 1 = cb b = 0 α f1 2 = 0 = 0 .8 Ecs I s l1 l1 BItarag 17>5 nigedayeFVviFanmUlvacar (interpolation) cenøaH β t = 0 ¬PaKry I =100% ¦ nig β t = 2.5 ¬PaKry = 75% ¦ sMrab; β t = 0.114 PaKryKW 98.9% . m:Um:g;GviC¢manxageRkAenAkñúgcMerokelIssrKW 0.989 × (− 207.2) = −204.92kN.m nigenAkñúgcMerokkNþalKW − 2.28kN.m . kñúgkrNIenHeKGacKitfacMerokelIssrRTm:Um:g; M ne 100% KWesμInwg − 207.2kN.m 6> kMNt;srésEdkEdlcaM)ac;enAkñúgTisedAEvgkñúgtaragEdlmanlkçN³RsedogKñanwg]TahrN_ TI 17>4. lT§plEdlTTYl)anmanlkçN³ERbRbYlticbMputxusBItarag 17>9. 7> eRbobeFoblT§plrvag]TahrN_TI 17>4 nig 17>5 eyIgeXijfam:Um:g;xageRkAenAkñúgcMerok elIssr ¬ − 207.2kN.m ¦FMCagcMelIyEdlTTYl)ankñúg]TahrN_TI 17>4 ¬ − 162.4kN.m ¦ eday 27.6% b:uEnþm:Um:g;viC¢man ¬182.6kN.m ¦ RtUv)ankat;bnßyeday 6.8% ¬eFobnwg 195kN.m ¦ ÉtMéld¾éTeTotesÞIrEtRtUvKña. ]TahrN_TI17>6³ KNnakMralxagkñúgénRbBn§½kMralBIrTisEdl)anbgðajenAkñúgrUbTI 17>7. kMralpSMeLIgedaykMral EdlmanTMhM 7.6 × 6m cMnYn 6 kñúgTisnImYy². kMralTaMgGs;RtUv)anRTedayssrEdlmanTMhM 50 × 50cm RbEvg 3.6m . kMralRtUv)anRTedayFñwmtambeNþayGkS½ssrEdlmanmuxkat;dUcbgðaj kñúgrUb. bnÞúkGefreFVIkarRtUv)anyk 4.8kN / m 2 nigbnÞúkefreFVIkarpSMeLIgeday 1kN / m 2 sMrab;kar garbegðIybEnßmBIelITMgn;pÞal;rbs;kMral. cUreRbI f 'c = 21MPa / f y = 420MPa nigviFI direct design method. dMeNaHRsay³ 1> eKRtUveFVItamkarkMNt;rbs; ACI Code. kMNt;kMras;kMralxNнGb,brmaedayeRbIsmIkar 17>1 nig 17>2. kMras;kMralxNнRtUv)anKNnarYcCaeRscenAkñúg]TahrN_TI 17>2 ehIy karKNnakMralxNнBIrTis 488
  52. 52. T.Chhay NPIC eyIgTTYlykkMras; 18cm . CaTUeTA kMras;kMralxNнenAkñúgRbBn§½kMralRtUv)anRKb;RKgeday kMralkac;RCugdUcCakarKNna hmin kMralxageRkApþl;nUvkMras;kMralFMCagsMrab;kMralxagkñúg. 2> KNnabnÞúkemKuN wD = 1 + 0.18 × 25 = 5.5kN / m 2 wu = 1.2 × 5.5 + 1.6 × 4.8 = 14.28kN / m 2 3> kugRtaMgkMlaMgenAkñúgkMralxNнminmanlkçN³eRKaHfñak;eT. muxkat;eRKaHfñak;mancMgay d BI épÞFñwm. sMrab;TTwg 1m ³ ⎛ 1 ⎞ ⎛ 0.4 ⎞ Vu = wu ⎜ 3 − beam width − d ⎟ = 14.28⎜ 3 − − 0.15 ⎟ = 37.84kN ⎝ 2 ⎠ ⎝ 2 ⎠ φ 0.75 21 φVc = f 'c bd = 1000 × 150 ⋅ 10 −3 = 85.9kN 6 6 4> KNnam:Um:g;sþaTicsrubenAkñúgTisEvg nigTisxøI³ wu l 2 (l n1 )2 = 6(7.1)2 = 539.9kN .m 14.28 M ol = 8 8 w = u l1 (l n 2 )2 = 7.6(5.5)2 = 410.4kN .m 14.28 M os 8 8 5> KNnam:Um:g;KNnaenAkñúgTisEvg³ ll = 7.6m a. karEbgEckm:Um:g;enAkñúgkMral m:Um:g;GviC¢man M n = 0.65M ol = 0.65 × 539.9 = −350.9kN .m m:Um:g;viC¢man M p = 0.35M ol = 0.35 × 539.9 = 189kN .m b. karEbgEckm:Um:g;kMralkñúgTisTTwgeTAFñwm/ cMerokelIssr nigcMerokkNþal α f 1 = α s = b = 3.19 ¬BI]TahrN_TI 17>2¦ l2 6 EI = = 0.79 l 17 .6 EI s l2 α f1 = 3.19 × 0.79 = 2.52 > 1 l1 c. karEbgEckm:Um:g;GviC¢man M n . Epñkénm:Um:g;GviC¢manxagkñúgedIm,IkarBaredaycMerokelI ssrRtUv)anTTYlBItarag 17>3 edayeFVI interpolation nigesμInwg 81.3% ¬sMrab; l 2 / l1 = 0.79 nig α f 1 (l 2 / l1 ) > 1.0 ¦. cMerokelIssr = 0.813M n = 0.813 × 350.9 = −285.3kN .m cMerokkNþal = 0.187M n = 0.187 × 350.9 = −65.6kN .m karKNnakMralxNнBIrTis 489
  53. 53. T.Chhay NPIC edaysarEt α f 1 (l2 / l1 ) > 1/ ACI Code, Section 13.6.5 bgðajfa 85% énm:Um:g; kñúgcMerokelIssrRtUv)anEckeGayeTAFñwm nigenAsl; 15% RtUv)anEckeGayeTAkM ralcMerokelIssr. Fñwm = 0.85 × 285.3 = −242.5kN.m cMerokelIssr = 0.15 × 285.3 = −42.8kN.m cMerokkNþal = −65.6kN.m d. karEbgEckm:Um:g;viC¢man M p . Epñkénm:Um:g;viC¢manxagkñúgEdlRtUv)anTb;edaycMerokelIssrRtUv)anTTYlBItarag 17>3 edayeFVI interpolation nigesμInwg 81.3% ¬sMrab; l2 / l1 = 0.79 nig α f 1 (l2 / l1 ) > 1.0 ¦. cMerokelIssr = 0.813M n = 0.813 × 189 = 153.7kN .m cMerokkNþal = 0.187M n = 0.187 × 189 = 35.3kN .m edaysarEt α f 1 (l2 / l1 ) > 1/ ACI Code, Section 13.6.5 bgðajfa 85% énm:Um:g; kñúgcMerokelIssrRtUv)anEckeGayeTAFñwm nigenAsl; 15% RtUv)anEckeGayeTAkM ralcMerokelIssr. Fñwm = 0.85 × 153.7 = 130.6kN.m cMerokelIssr = 0.15 × 153.7 = 23.1kN.m cMerokkNþal = 35.3kN.m karlMGitm:Um:g;RtUv)anbgðajenAkñúgrUbTI 17>23. 6> KNnam:Um:g;KNnaenAkñúgTisxøI³ ElVg = 6m . viFIKNnaRsedogKñanwgCMhanTI5> m:Um:g;GviC¢man M n = 0.65M os = 0.65 × 410.4 = −266.8kN .m m:Um:g;viC¢man M p = 0.35M os = 0.35 × 410.4 = 143.6kN .m EbgEck M n / M p eTAFñwm/ cMerokelIssr nigcMerokkNþal α f 1 = α s = b = 2.51 ¬BI]TahrN_TI 17>2¦ l 2 7 .6 EI = = 1.27 l 1 6 EI s l2 α f1 = 2.51 × 1.27 = 3.19 > 1 l1 PaKryénm:Um:g;GviC¢man nigGviC¢manenAkñúgcMerokelIssrRtUv)anTTYlBItarag 17>3 eday kareFVI interpolation. ¬sMrab; l2 / l1 = 1.27 nig α f 1 (l2 / l1 ) > 1.0 PaKryEbgKW 67% ¦. karKNnakMralxNнBIrTis 490
  54. 54. T.Chhay NPIC m:Um:g;GviC¢mancMerokelIssr = 0.67M n = 0.69 × 266.8 = −178.8kN .m m:Um:g;GviC¢mancMerokkNþal = 0.33M n = 0.33 × 266.8 = −88kN .m eday α f 1 (l2 / l1 ) > 1.0 / 85% én − 178.8kN.m RtUv)andak;eTAkñúgFñwm. dUcenH m:Um:g;GviC¢manelIFñwm = 0.85 × 178.8 = −152kN.m m:Um:g;GviC¢mancMerokelIssr = 0.15 × 178.8 = −26.8kN.m m:Um:g;viC¢manelIFñwm = 0.85 × 0.67 × 143.6 = 81.8kN.m m:Um:g;viC¢mancMerokelIssr = 0.15 × 0.67 × 143.6 = 14.4kN.m m:Um:g;viC¢mancMerokkNþal = 0.33 × 143.6 = 47.4kN.m 7> brimaNEdkcaM)ac; nigcMnYnEdkRtUv)anbgðajenAkñúgtarag 17>10. cMNaMfaPaKryEdkTaMgGs;tUcCag ρ max = 0.00137 . dUcenH φ = 0.9 . karKNnakMralxNнBIrTis 491

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