T.Chhay                                                                                        NPIC


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Department of Civil Engineering                                              viTüasßanCatiBhubec©keTskm<úCa




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T.Chhay                                                                                        NPIC

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Department of Civil Engineering                                                  viTüasßanCatiBhubec©keTskm<úCa
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T.Chhay                                                                                      NPIC

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Department of Civil Engineering                                              viTüasßanCatiBhubec©keTskm<úCa
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T.Chhay                                                                                            NPIC

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Department of Civil Engineering                                           viTüasßanCatiBhubec©keTskm<úCa
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T.Chhay                                                                                                NPIC

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Department of Civil Engineering                                                  viTüasßanCatiBhubec©keTskm<úCa
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T.Chhay                                                                                           NPIC

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Department of Civil Engineering                                          viTüasßanCatiBhubec©keTskm<úCa
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T.Chhay                                                                                     NPIC

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Department of Civil Engineering                                                viTüasßanCatiBhubec©keTskm<úCa
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T.Chhay                                                                                                NPIC

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Department of Civil Engineering                                                viTüasßanCatiBhubec©keTskm<úCa
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Ix one way slab

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Transcript of "Ix one way slab"

  1. 1. T.Chhay NPIC IX. kMralxNÐmYyTis 1> RbePTkMralxNÐ eRKOgbgÁúMkMralxNÐebtugRtUv)ansagsg;eLIgedIm,Ipþl;nUvépÞrabesμI CaTUeTAmanTisedAedk. kMral xNÐGacRTedayCBa¢aMg b¤edayFñwmebtugsésrEdkEdlCaTUeTARtUv)ancak;kñúgeBldMNalKñaCamYykMralxNÐ (cast monolithically with the slab) b¤edayFñwmEdk b¤edayssr b¤edaydI. CaTUeTAkMras;kMralxNÐman tMéltUcebIeRbobeFobCamYynwgRbEvgElVg ¬rUbTI 9>1¦. kMralxNÐebtugenAkñgGaKarGacEbgEckdUcxageRkam³ a. kMralxNÐmYyTis (one-way slab)³ RbsinebIkMralxNÐEdlRTedayRCugBIrQmKña enaHvanwgekag b¤ dabkñúgTisedAEkgnwgRCugénTMr. GMeBIrbs;rcnasm<næ½KWmanEtmYyTis ehIybnÞúkEdlRTedaykMral xNÐenAkñúgTisedAEdldabtUc. kMralxNÐRbePTenHRtUv)aneKeGayeQμaHfa kMralxNÐmYyTis ¬rUb TI 9>1a¦. RbsinebIkMralxNÐRtUv)anRTedayRCugbYn ehIypleFobRCugEvgelIRCugxøIFMCag b¤esμInwg 2 enaHbnÞúkPaKeRcIn ¬RbEhl 95% b¤eRcInCagenH¦ RtUv)anRTenAkñúgTisedAxøI ehIyGMeBImYyTis RtUv)anBicarNasMrab;karGnuvtþn_TaMgGs; ¬rUb TI 9>1b¦. RbsinebIkMralxNÐRtUv)aneFVIeLIgedayeb tugBRgwgedayEdkedayKμanrnæxül; (no void) enaHeKeGayeQμaHfa kMralxNÐmYyTistan; (one- way solid slab) . rUb TI 9>1 c, d nig e bgðajBIbøg;BuH nigkarBRgayEdk. b. RbBnæ½kMralxNÐrnUtmYyTis (one-way joist floor slab)³ kMralxNÐRbePTenHeKk¾eGayeQμaHfa ribbed slab. vapSMeLIgedaykMralxNÐEdlCaTUeTAmankMras;BI 50mm eTA 100mm RTedayrnUteb tugGarem: (ribs or joist). CaTUeTArnUtmanragsþÜc nigmanKMlatesμI²KñaminelIs 750mm . rnUt RtUv)anRTedayFñwmEdlsßitenAelIssr. KMlatrvagrnUtGacbegáIt)anedaykareRbIBum<Edk b¤Bum<eFVIBI fiberglass rUbTI9>2. enAkñúgkMralxNÐrnUtxøH KMlatrvagrnUtGacRtUv)anbMeBjeday filler edIm,IeFVI eGaykMralxNÐEpñkxageRkamrabesμI. c. RbBnæ½kMralxNÐBIrTis (two-way floor system)³ enAeBlEdlkMralxNÐRTedayRCugbYn ehIypl eFobénRCugEvgelIRCugxøItUcCag 2 enaHkMralnwgdabedaykMeNagDubelITisedATaMgBIr. bnÞúkkMral xNÐRtUv)anbBa¢ÚnkñúgTisedABIreTAFñwmTaMgbYnEdlBTæ½CMuvijkMralxNÐ ¬eyagtamemeronTI17¦. Rb ePTepSgeTotrbs;RbBnæ½kMralxNÐBIrTisman flat plate floor, flat slab nig waffle slab EdlkMral xNÐTaMgenHnwgBnül;kñúgemeronTI17. kñúgemeronenHeyIgniyayEtBIRbBnæ½kMralxNÐmYyTis. kMralxNÐmYyTis 173
  2. 2. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 2> karKNnaénkMralxNÐtan;mYyTis RbsinebIkMralebtugcak;kñúgkMras;esμIedayKμanRbehag eKGacehAva)anfa kMraltan;. enAkñúgkMral xNÐmYyTis (one-way slab) pleFobénRbEvgEvgrbs;kMralxNÐelIRbEvgsøIrbs;vaFMCag 2. bnÞúkrbs;kM ralesÞIrEtTaMgGs;RtUv)anbBa¢ÚneTATisedAxøI ehIykMralxNÐGaccat;TukdUcCaFñwm. cMerokkMralxNÐÉktþa Ca TUeTAmanRbEvg 1m RtUv)ancat;TukCaFñwmctuekaN. FñwmenHmanTTwg1m CamYynwgkMBs;esμInwgkMras;kMral One-Way Slab 174
  3. 3. T.Chhay NPIC xNÐ nigRbEvgElVgesμInwgcMgayrvagTMr. dUcenHkMralxNÐmYyTispSMeLIgedayFñwmctuekaNCaeRcInCab;²Kña ¬rUbTI9>1¦. RbsinebIkMralxNÐmanEtmYyElVg ehIyvasßitenAelITMredayesrI enaHm:Um:g;viC¢manGtibrma M sM rab;bnÞúkBRgayesμI w KW M = (wL2 ) / 8 Edl L KWCaRbEvgElVgrvagTMr. RbsinebIkMralxNÐRtUv)ansag sg;eLIgkñúgeBldMNalKñaCamYy b¤Cab;enAelITMrCaeRcIn enaHm:Um:g;viC¢man nigGviC¢manRtUv)anKNnaedaykar viPaKeRKOgbgÁúM (structural analysis) b¤edayviFIemKuNm:Um:g; (moment coefficient) sMrab;FñwmCab;. ACI Code, Section 8.3 GnuBaØateGayeRbInUvemKuNm:Um:g; nigemKuNkMlaMgkat;enAkñúgkrNIkMralxNÐmaneRcIn ElVgesÞIresμIKña ¬rUbTI 9>3¦. krNIenHGaceRbI)ansMrab;ElVgBIrEdlenACab; b¤enAsgçagEvgCag ElVgEdlenA kNþal b¤ElVgCab;enaHticCag 20% . sMrab;bnÞúkBRgayesμI bnÞúkGefrÉktþaminKYrFMCagbnÞúkefrÉktþa 3bI eT. RbsinebIlkçxNÐTaMgenHminRtUv)anbMeBjeTenaH eKRtUvkarkarviPaKeRKOgbgÁúM (structural analysis). enAkñúgkarviPaKeRKOgbgÁúM m:Um:g;Bt;GviC¢manenARtg;GkS½rbs;TMrRtUv)anKNna. tMélEdlRtUvBicarNaenAkñúg karKNnaKWm:Um:g;GviC¢manenABImuxépÞénTMr. edIm,ITTYl)antMélenH eKRtUvdktMélm:Um:g;GtibrmaenAGkS½TMr eday Vb / 3 Edl V CakMlaMgkat;TTwgEdl)anBIkarviPaKeRKOgpÁúM nig b KWCaTTwgrbs;TMr. M f ¬enABImuxépÞénTMr¦ = M c ¬enARtg;GkS½énTMr¦ − ¬(>!¦ Vb 3 bEnßmBIelIm:Um:g; kMlaMgTajGgát;RTUg nigRbEvgf<k;énEdk KYrEtRtUv)anepÞógpÞat;sMrab;karKNnad¾ RtwmRtUv. kMralxNÐmYyTis 175
  4. 4. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa lkçxNÐEdlemKuNm:Um:g;sMrab;FñwmCab; nigkMralCab;EdleGayenAkñúgrUbTI 9>3 KYrRtUv)aneRbIGacRtUv segçbdUcxageRkam³ a. ElVgmanRbEvgesÞIesμIKña³ ElVgEvg ≤ 1.2 ¬ElVgxøI¦ b. bnÞúkRtUvBRgayesμI c. pleFob ¬bnÞúkGefr / bnÞúkefr¦ RtUvtUcCagb¤esμInwg 3 . d. sMrab;kMralxNÐEdlmanElVgtUcCagb¤esμI 3m m:Um:g;Bt;GviC¢manenABImuxépÞénTMresμInwg 12 wu l n . 1 2 e. sMrab;TMr A EdlminCab; nigmanPaBTMenr enaHemKuNm:Um:g;enARtg;cMnuc A KWesμIsUnü nigRtg;cMnuc B = + 11 1 f. kMlaMgkat;TTwgenARtg;cMnuc C = 1.15wu lu / 2 nigenABImuxépÞTMrdéTeTotTaMgGs;esμInwg 12 wu lu g. M u = ¬emKuN¦ wu lu / Edl l n = clear span. 2 3> EdnkMNt;kñúgkarKNnaEdlGnuelameTAtam ACI CODE EdnkMNt;xageRkamRtUv)ankMNt;eday ACI Code³ a. cMerokkMralxNÐEdlmanTTwg 1m RtUv)ansnμt;. One-Way Slab 176
  5. 5. T.Chhay NPIC b. kMras;Gb,brmaénkMralxNÐmYyTisEdleRbIEdk 400MPa Gnuelamtam ACI Code, Table 9.5a sMrab;kMralxN½Ðtan;mYyTis nigsMrab;kMralxNÐrnUtmYyTisKYresμInwgtMéldUcxageRkam³ - sMrab;TMrsamBaس kMralxNÐtan; (solid slab)/ h = L / 20 ¬kMralxNÐrnUt (ribbed slab), h = L / 16 ¦ - sMrab;kMralxNÐEdlCab;mçag³ kMralxNÐtan;/ h = L / 24 ¬kMralxNÐrnUt , h = L / 18.5 ¦ - sMrab;kMralxNÐEdlCab;sgçag³ kMralxNÐtan; / h = L / 28 ¬kMralxNÐrnUt , h = L / 21 ¦ - sMrab;kMralxNÐ cantilever: kMralxNÐtan; / h = L / 10 ¬kMralxNÐrnUt , h = L / 8 ¦ - sMrab; f y xusBI 400 MPa enaHtMélTaMgGs;xagelIRtUvKuNnwg 0.4 + 1.5 ⋅ 10 −3 f y Edl f y Kit Ca MPa . kMras;Gb,brmaenHRtUv)aneRbITal;EtkarKNnaPaBdabbgðajfakMras;tUcCagenHGac eRbIedayKμanplb:HBal;Rtlb;mkvij. c. eKRtUvepÞógpÞat;PaBdabenAeBlTMrkMralxNÐEdlP¢ab;eTAnwgsMNg;TMngCargeRKaHfñak;xøaMgedayPaB dabFM. PaBdabkMNt;RtUv)ankMNt;eday ACI Code, Table 9.5b . d. eKcUlcitþeRCIserIskMras;kMralxNÐedaytMeLIg b¤bnßymþg 10mm . e. eKRtUvepÞógpÞat;kMlaMgkat;TTwg ebIeTaHbIvaminmantMélFMk¾eday. f. kMras;ebtugkarBarEdk (concrete cover) enAkñúgkMralxNÐebtugminRtUvtUcCag 20mm sMrab;épÞkM ralxNÐEdlRbQmnwgkarsik b¤b:HpÞal;nwgdI. kñúgkrNIenH d = h − 20mm − d b / 2 eyagtamrUbTI 9>1 d . g. sMrab;eRKagkMralxNÐEdlmankMras;esμI enaHbrimaNEdkGb,brmaenAkñúgTisedArbs;kMralxNÐminRtUv tUcCagbrimaNEdktMrUvkarsMrab;karrYmmaD nigTb;nwgsItuNðPaB (shrinkage and temperature reinforcement) eT (ACI Code, Section 7.12). h. EdkemminRtUvmanKMlatFMCagkMras;kMralxNÐbIdg 3h b¤FMCag 450mm eLIy (ACI Code, Section 7.6.5). i. eKRtUveRbIRbBnæ½EdkRtg;TaMgenAEpñkxagelI nigEpñkxageRkamrbs;kMralxNÐCab;. eBlxøHeKk¾GaceRbI RbBnæ½EdkcMruH ¬EdkRtg; nigEdkBt;¦pgEdr. j. bEnßmBIelIEdkem eKk¾RtUvdak;EdkEdlEkgnwgEdkemEdr. EdkbEnßmenHeKehAfa Edkrg (secondary, distribution) EdkrYmmaD b¤EdksItuNðPaB (shrinkage or temperature reinforcement). kMralxNÐmYyTis 177
  6. 6. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 4> EdksItuNðPaB nigEdkrYmmaD CaTUeTAebtugrYmmaDenAeBlEdlTwkkMe)arsIum:g;t¾rwg ehIyeK)anKitTunCamunnUvbrimaNBitR)akdén karrYmmaD. RbsinebIkMralxNÐRtUv)aneKdak;eGaycl½tedayesrIenAelITMrrbs;va enaHvanwgrYjedIm,ITTYlnUv karrYmmaD. b:uEnþkMralxNÐ b¤Ggát;epSgeTotRtUv)anP¢ab;y:agrwgeTAnwgGgát;déTeToténeRKOgbgÁúM EdlbegáIt nUvkMriténkarTb;y:agBitR)akdenAcug. CalTæpleKTTYl)ankugRtaMgTajEdleKsÁal;faCakugRtaMgrYmmaD. karfycuHnUvkugRtMgEdlekItBIsItuNðPaB nigkugRtaMgEdlekItBIkarrYmmaD)aneFVIeGayekItmansñameRbHb:un sésrsk; (hairline crack). sésrEdkEdkdak;enAkñúgkMralxNÐKWedIm,ITb;Tl;nwgkarrYjxøI nigkarraldalén sñameRbH. edaysarEtebtugrYmmaD sésrEdkrgnUvkarsgát;. EdksMrab;karkugRtaMgrYmmaD nigkugRtaMgsItuNðPaBEdlEkgnwgEdkem RtUvdak;enAkñúgkMralxNÐEdl EdlemRtUv)andak;EtmYyTis. ACI Code, Section 7.12.2 kMNt;nUvGRtaEdkGb,brmadUcxageRkam³ - sMrab;kMralxNÐEdleRbIEdk 280MPa b¤ 350MPa enaH ρ = 0.2% - sMrab;kMralxNÐEdleRbIEdk 400MPa b¤EdkpSar b¤EdksMNaj;pSar enaH ρ = 0.18% KμankrNIEdlEdkRtUv)andak;manKMlatFMCag 5dgkMras;kMralxNÐ b¤FMCag 450mm eT. sMrab;EdkrYmmaD nigEdksItuNðPaB kMras;ebtugTaMgmUl h EdlRbQmnwgkarrYmmaDRtUveRbIedIm,I KNnaRkLaépÞEdk. ]TahrN_ RbsinebIkMralxNÐmankMras;srub h = 150mm nig f y = 400MPa enaHRk LaépÞEdkEdlRtUvkarsMrab;TTwgkMralxNÐ 1m KW As = 1000 × 150 × 0.0018 = 270mm 2 . KMlatEdk S GacKNnadUcxageRkam³ S= 1000 Ab As ¬(>@¦ Edl Ab = RkLaépÞEdkeRCIserIs As = RkLaépÞEdkKNna ]TahrN_ RbsinebIeKeRbIEdk DB10 ¬ Ab = 78.5mm 2 ¦ enaH S = 1000 × 78.5 / 270 = 290mm yk 250mm . RbsinebIeKeRCIserIsEdk DB12 ¬ Ab = 113mm 2 ¦ enaH S = 1000 × 113 / 270 = 418mm yk 400mm . EdkenHmantYrnaTICaEdkrgEdlRtUv)andak;EkgnwgEdkemEdlRtUv)anKNnaedaykarviPaK edaykarBt; (flexural analysis). 5> lMGitsésrEdk enAkñúgkMralxNÐmYyTisCab; RkLaépÞEdkemRtUv)anKNnaBIRKb;eRKaHfñak;TaMgGs; TaMgenAkNþalElVg nigenATMr. kareRCIserIssésrEdk niglMGitsésrEdkGaRs½yeTAnwgRkLaépÞEdk KMlatRtUvkar nigRbEvg TMBk;. eKmanRbBnæ½rayEdkBIrRbePT. One-Way Slab 178
  7. 7. T.Chhay NPIC enAkñúgRbBnæ½EdkRtg; ¬rUbTI9>4¦ EdkRtg;RtUv)aneRbIsMrab;dak;enAEpñkxagelI nigEpñkxageRkaménRKb;kM ralxNÐTaMgGs;. karcMNayelIfvikar nigeBlevlasMrab;pltiEdkRtg; RtUvkarticCagkñúgkarplitEdkBt; dUcenHRbBnæ½EdkRtg;RtUv)anTUlMTUlayCagenAkñúgsMNg;. enAkñúgRbBnæ½EdkBt; b¤ trussed EdkRtg; nigEdkBt;RtUv)andak;qøas;KñaenAkñgkMralxNÐ. TItaMgBt; RtUv)anepÞógpÞat;sMrab;karBt; kMlaMgkat;TTwg nigtMrUvkarRbEvgf<k;. sMrab;bnÞúkFmμtaenAkñúgsMNg; bøg;lMGit sésrEdksMrab;ElVgxag nigElVgkNþalénkMralxNÐtan;mYyTisRtUv)anbgðajenAkñúgrUbTI 9>4. 6> karEbgEckbnÞúkBIkMralxNÐmYyTiseTAFñwmTMr enAkñúgRbBnæ½kMralxNÐmYyTis bnÞúkBIkMralxNÐRtUv)anbBa¢ÚneTAFñwmTMrtamcugEvgénkMralxNÐ. Fñwm bBa¢ÚnbnÞúkrbs;vaeTAssrTMr. BIrUbTI 9>5 eyIgeXIjfa Fñwm B2 RTbnÞúkBIkMralxNÐEk,rBIr. edaycat;TukCaFñwmRbEvg 1m bnÞúkbBa¢Ún eTAFñwmesμInwgRkLaépÞéncMerokTTwg 1m nigbeNþay S KuNnwgGaMgtg;sIuetbnÞúkEdlmanGMeBIelIkMralxNÐ. bnÞúkenHbegáItCabnÞúkBRgayesμIenAelIFñwm UB = US ⋅ S kMralxNÐmYyTis 179
  8. 8. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa bnÞúkBRgayesμIenAelIFñwmxag B1 esμInwgBak;kNþalbnÞúkenAelIFñwm B2 edaysarEtvaRTkMralxNÐEtmçag. bnÞúkenAelIssr C4 esμInwgRbtikmμBIFñwm B2 Ek,rBIr bnÞúkenAelIssr C4 = U B L = U S LS bnÞúkenAelIssr C3 esμInwgBak;kNþalbnÞúkenAelIssr C4 edaysarEtvaRTkMralxNÐEtmçag. dUcKñacM eBaHbnÞúkenAelIssr C2 nig C1 KW³ bnÞúkenAelIssr C2 = U S L S = bnÞúkenAelIssr C3 2 bnÞúkenAelIssr C1 = U S 2 2 LS BIkarviPaKenH eyIgeXIjfassrnImYy²RTbnÞúkBIkMralxNÐEdlenACMuvijssrenaH edayKitrhUtdl;GkS½ énkMralxNÐEk,r ¬ L / 2 sMrab;TisEvg nig S / 2 sMrab;TisxøI¦. karBRgaybnÞúkBIkMralxNÐBIrTiseTAFñwmTMr nigssrnwgBnül;enAkñúgemeronTI17. One-Way Slab 180
  9. 9. T.Chhay NPIC ]TahrN_TI1³ KNnaersIusþg;m:Um:g;KNnarbs;kMralxNÐEdlmankMBs;srub h = 175mm nigBRgwgedayEdk DB 20 EdlmanKMlat S = 175mm . eRbI f 'c = 20MPa nig f y = 400MPa . dMeNaHRsay³ 1> KNnakMBs;RbsiTæPaB d ³ d = h − 20mm − b ¬emIlrUb9>1 d¦ d 2 20 d = 175 − 20mm − = 145mm 2 2> KNna As mFümEdlpþl;sMrab;TTwgkMralxNÐ 1m . RkLaépÞénEdk DB20 KW Ab = 314mm 2 1000 × 314 As = = 1794mm 2 / m 175 3> eRbobeFobPaKryEdkEdleRbICamYynwg ρ max nig ρ min . sMrab; f 'c = 20MPa nig f y = 400MPa enaH ρ max = 0.01374 nig ρ min = 0.00333 . ρ ¬eRbIR)as;¦ = 1794 /(1000 × 140) = 0.0128 EdlRKb;RKan; ¬ φ = 0.9 ¦. 4> KNna φM n = φAs f y (d − a / 2) a = As f y /(0.85 f 'c b) = 1794 × 400 /(0.85 × 20 × 1000) = 42.2mm φM n = 0.9 × 1794 × 400 × (140 − 42.2 / 2 ) = 76.79kN .m ]TahrN_TI2³ kMNt;bnÞúkGefrBRgayesμIGnuBaØatEdlGacGnuvtþenAelIkMralxNÐén]TahrN_TI1 RbsinebI ElVgkMralxNÐmanRbEvg 4.9m sßitenAcenøaHTMrsamBaØ nigRTnUvbnÞúkefrBRgayesμI ¬KμanbBa©ÚlbnÞúkpÞal;xøÜn¦ 4.8kN / m 2 . dMeNaHRsay³ 1> ersIusþg;m:Um:g;KNnaénkMralxNÐKW 76.79kN .m elIkMralxNÐTTwg 1m Wu L2 Wu (4.9) 2 M u = φM n = 76.79 = = 8 8 bnÞúkBRgayesμIemKuNKW Wu = 25.6kN / m 2 2> Wu = 1.2D + 1.6L D = 4.8 + 0.175 × 1 × 25 = 9.2kN / m 2 L = 9.1kN / m 2 ]TahrN_TI3³ KNnakMralxNÐTMrsamBaØRbEvg 3.6m edIm,IRTbnÞúkefrBRgayesμI ¬minrab;bBa©ÚlbnÞúkpÞal; xøÜn¦ 5.75kN / m 2 nigbnÞúkGefrBRgayesμI 4.8kN / m 2 . eRbI f 'c = 20MPa / f y = 400MPa nigkar kMNt;rbs; ACI Code. dMeNaHRsay³ kMralxNÐmYyTis 181
  10. 10. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 1> snμt;kMras;kMralxNÐ. sMrab; f y = 400MPa kMras;Gb,brmaedIm,IRKb;RKgPaBdabKW L / 20 = 180mm . snμt;kMrs;srub h = 175mm nigsnμt; d = 150mm ¬RtUvepÞógpÞat;enAeBleRkay¦. 2> KNnabnÞúkemKuN³ bnÞúkkMralxNÐ = 0.175 × 25 = 4.4kN / m 2 Wu = 1.2 D + 1.6 L = 1.2 × (4.4 + 5.75) + 1.6 × 4.8 = 19.86kN / m 2 sMrab;kMralxNÐTTwg 1m / M u = Wu L2 / 8 19.86 × 3.6 2 Mu = = 32.2kN .m 8 3> KNna As ³ sMrab; M u = 32.2kN .m / b = 1m nig d = 0.15m / Ru = M u / bd 2 = 1.43MPa / ρ = 0.0042 < ρ max = 0.01374 / φ = 0.9 . As = ρbd = 0.0042 × 1000 × 150 = 630mm 2 eRCIserIsEdk DB12 ¬ As = 113mm 2 ¦/ nig S = 1000 × 113 / 630 = 179mm epÞógpÞat; d BitR)akd/ d = 175 − 20 − 6 = 149mm GacTTYlyk)an. dUcenH S = 175mm nig As = 645mm 2 4> epÞógpÞat;ersIusþg;m:Um:g;énmuxkat;cugeRkay As f y 645 × 400 a= = = 15.2mm 0.85 f 'c b 0.85 × 20 × 1000 ⎛ a⎞ ⎛ 15.2 ⎞ φM n = φAs f y ⎜ d − ⎟ = 0.9 × 645 × 400⎜150 − ⎟ = 33kN .m > M u = 32.2kN .m ⎝ 2⎠ ⎝ 2 ⎠ 5> KNnaEdkrgEdlEkgnwgEdkem. sMrab; f y = 400MPa ρ min = 0.0018 Ash = 0.0018 × 1000 × 175 = 315mm 2 eRCIserIsEdk DB12 / Ab = 113mm 2 / S = 1000 × 113 / 315 = 358.7mm dUcenHeRbI DB12 @ 350mm sMeab;Edkrg. 6> epÞógpÞat;kMlaMgkat;TTwgcaM)ac;³ Vu enAcMgay d BITMrKW 19.86(1.8 − 0.15) = 32.8kN φVc = φ 0.17 f 'c bd = 0.75 × 0.17 20 × 1000 × 150 × 10 −3 = 85.5kN 1 2 φVc = 42.75kN > Vu = 32.8kN dUcenHmuxkat;RKb;RKan;. 7> muxkat;cugeRkay h = 175mm / Edkem DB12 @175mm nigEdkrg DB12 @ 350mm . ]TahrN_TI4³ muxkat;kMralxNÐtan;mYyTisCab;RtUv)anbgðajkñúgrUbTI 9>6. kMralxNÐenHRTedayFñwmEdl manRbEvg 7.2m . bnÞúkGefrmanGMeBIelIkMralxNÐ)anmkBIbnÞúkpÞal;xøÜnbUknwg 3.7kN / m 2 ehIybnÞúkGefrKW One-Way Slab 182
  11. 11. T.Chhay NPIC 6.2kN / m 2cenøaHTMrsamBaØ. KNnakMralxNÐCab; nigKUrnUvbøg;lMGitsésrEdk. eKeGay f 'c = 20MPa / f y = 280MPa . dMeNaHRsay³ 1> kMras;Gb,brmaénkMralxNÐTI1KW L / 30 edaysarcugmçagCab; nigcugmçageTotGt;Cab;. cMgayrvagGkS½FñwmGaccat;TukCaElVg L = 3.6m . sMrab; f y = 280MPa kMras;srubGb,brma 30 = 3600 = 120mm L 30 kMras;srubGb,brmasMrab;ElVgkNþal 35 = 3600 = 103mm L 35 snμt;kMras;rbs;kMralxNÐesμIKñaRKb;ElVg h = 125mm EdlFMCag 120mm . dUcenH eKmincaM)ac;epÞóg pÞat;PaBdab. 2> KNnabnÞúk nigm:Um:g;enAelIcMerokÉktþa bnÞúkGefr=bnÞúkpÞal;xøÜn + 3.7 = 0.125 × 25 + 3.7 = 6.8kN / m 2 bnÞúkemKuN U = 1.2D + 1.6L = 1.2 × 6.8 + 1.6 × 6.2 = 18.1kN / m 2 RbEvg clear span KW 3.35m . m:Um:g;caM)ac;sMrab;ElVgTImYyenAelITMrEdlmanElVgCab;esIμnwg UL2 / 10 U (3.35)2 Mu = = 20.3kN .m 10 3> snμt; ρ = 1.4% enaH Ru = 3.12MPa tMélenHtUcCag ρ max = 0.0169 nigFMCag ρ min = 0.005 ¬ φ = 0.9 ¦ Mu 20.3 ⋅ 10 6 d= = = 81mm Ru b 3.12 × 1000 As = ρbd = 0.014 × 1000 × 81 = 1134mm 2 eRCIserIs DB16 kMras;srub = d + 16 + 20 = 109mm 2 eRbIkMras;kMralxNÐ 125mm dUckarsnμt;xagelI kMBs; d EdleRbIBitR)akd = 125 − 20 − 8 = 97mm 4> m:Um:g; nigsésrEdkRtUvkarenARtg;muxkat;déTeTot edayeRbI d = 97mm mandUcxageRkam³ TItaMg emKuNm:Um:g; M u (kN .m) Ru = M u / bd 2 (MPa) ρ (%) As (mm 2 ) Edk nigKMlat A − 241 8.46 tUc 0.00500 485 DB12@200 kMralxNÐmYyTis 183
  12. 12. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa B + 14 1 14.51 1.54 0.00646 627 DB16@300 C − 10 1 20.31 2.16 0.00928 900 DB16@200 D − 11 1 18.47 1.96 0.00836 811 DB16@200 E + 16 1 12.70 1.35 0.00561 545 DB16@200 karBRgaysésrEdkRtUv)anbgðajenAkñúgrUbTI 9>7. 5> kMlaMgkat;TTwgekItmanenAkMralxNÐxageRkAénTMrTI2/ muxkat; C 6> Vu ¬Rtg; C ¦ = 1.15ULn / 2 = 1.15 × 182.1× 3.55 = 36.95kN 7> φVc = φ 0.17 f 'c bd = 0.75 × 0.17 20 × 1000 × 97 × 103 = 55.3 lTæplenHGacTTYlyk)an. cMNaMfa kardak;sésrEdkkMlaMgkat;TTwgGb,brmaenAeBlEdl Vu > 12 φVc minRtUv)anGnuvtþsMrab;kMralxNÐeT ¬ ACI Code, Section 11.5.5¦. ]TahrN_TI5³ kMNt;bnÞúkemKuNBRgayesμIenAelIFñwmkNþalEdlRTkMralxNÐén]TahrN_TI 4. dUcKña KNnabnÞúkcMGkS½enAelIssrkNþal eyagtambøg;TUeTAénrUbTI9>5. dMeNaHRsay³ 1> bnÞúkemKuNBRgayesμIkñúgmYyEm:RtRbEvgenAelIFñwmkNþalesμInwgbnÞúkemKuNBRgayesμIenAlIkMral xNÐKuNnwg S EdlCaRCugxIørbs;kMralxNÐ. dUcenH U ¬Fñwm¦= U ¬kMralxNЦ × S = 18.1 × 3.8 = 68.8kN / m bnÞúkrbs;FñwmKYrRtUv)anKitbBa©Úl. RbEvgrbs;FñwmKW 7.2m kMNt;kMBs;srub h= L 20 × 0.8 = 7.2 20 × 0.8 = 0.288m yk 300mm kMras;kMralxNÐKW 125mm dUcenHkMBs;énRTnugrbs;FñwmKW 300 − 125 = 175mm bnÞúkemKuNénRTnugFñwm = 0.175 × 0.25 × 25 × 1.2 = 1.3kN / m bnÞúkBRgayesμIsrubelIFñwm = 68.8 + 1.3 = 70.1kN / m One-Way Slab 184
  13. 13. T.Chhay NPIC 2> bnÞúkenAleIFñwmkNþal Pu = 70.1 × 7.2 = 504.72kN / m 7> RbBnæ½kMralxNÐrnUtmYyTis One-Way joist Floor System RbBnæ½kMralxNÐrnUtmYyTispSMeLIgedaykMralxNÐRbehag (hollow slab) CamYykMBs;srubFMCagkMras; rbs;kMralxNÐtan;mYyTis. kMralxNÐenHmanlkçN³snSMsMécsMrab;GKarEdlmanbnÞúktUc nigmanElVgEvg dUcCa salaeron mnÞIreBTü nigsNæaKar. bnÞúkenAkñúgtMbn;TajKμanTæiBldUcenH tMbn;enHRtUv)anTukeGayRb ehagrvagrnUt b¤RtUv)anbMeBjCamYysMPar³EdlmanTMgn;Rsal edIm,Ikat;bnßyTMgn;pÞal;rbs;kMralxNÐ. viFIsaRsþkñúgkarKNna nigtMrUvkarénkMralxNÐrnUt (ribbed slab) GnuvtþdUckarKNnaFñwmmuxkat;ctu ekaN nigFñwmmuxkat;GkSret EdlmanenAkñúgemeronTI3. cMnucxageRkamRtUv)anGnuvtþsMrab;KNnakMralxNÐ rnUtmYyTis. 1 rnUt (rib) manragsþÜcxageRkam nigmanKMlatdUc²KñaRbEhl 400mm eTA 750mm . Rbehag RtUv)anbegáItrUbragedayeRbIBum<EdlmanTTwg 500mm nigCMerA 150mm eTA 500mm GaRs½y eTAelItMrUvkarénkarKNna. kMeNInbTdæanrbs;kMBs;KWmþg 50mm . 2 rnUtminRtUvmanTTwgtUcCag100mm nigminRtUvmanCMerAFMCagTTwg 3.5 dg. KMlat clear spacing rvagrnUtminRtUvFMCag 750mm (ACI Code, Section 8.11). 3 ersIusþg;kMlaMgkat;TTwgEdlpþl;edayebtugsMrab;rnUtGacykesμInwg 10% FMCagersIusþg;kMlaMg kat;TTwgEdlpþl;edayebtugsMrab;Fñwm. mUlehtucMbgKWbNþalmkBIGnþrkmμrvagkMralxNÐ nig rnUtEdlmanKMlatCit²Kña (ACI Code, Section 8.11.8). 4 CaTUeTAkMralxNÐenABIelIrnUtmankMras;BI 50mm eTA 100mm nigmanEdkGb,brma ¬EdkrYm maD¦. kMras;enHminRtUvtUcCag 1 / 12 én clear span rvagrnUt b¤ 50mm (ACI Code, Section 8.11.6). 5 emKuN ACI sMrab;KNnam:Um:g;enAkñúgkMralxNÐCab; GacRtUv)aneRbIsMrab;KNnakMralxNÐrnUt Cab;. 6 eKmanEdnkMNt;bEnßmmYycMnYn EdlRtUv)ansegçbdUcxageRkam³ - TTwgGb,brmarbs;rnUtKW mYyPaKbIénkMBs;srub b¤ 100mm edayykmYyNaEdlFMCag. - EdkrgenAkñúgkMralxNÐenAkñúgTisedAEkgnwgrnUtminKYrtUcCagbrimaNEdkrYmmaD b¤tUcCag 1 / 5 énRkLaépÞEdkemenAkñúgrnUt. kMralxNÐmYyTis 185
  14. 14. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa - EdkrgEdlRsbnwgrnUtKYrdak;enAkñúgkMralxNÐ ehIyKMlatrbs;vaminRtUvmancMgayFMCagBak; kNþalénKMlatrvagrnUt. - RbsinebIbnÞúkGefrenAelIkMralxNÐrnUttUcCag 3kN / m 2 ehIyRbEvgrbs;rnUtFMCag 5m enaH rnUtTTwgrg (secondary transverse rib) RtUv)andak;enAkNþalElVg ¬TisedArbs;vaKWEkgnwg TisedArbs;rnUtem¦ nigBRgwgedayEdkEdlmanbrimaNesμInwgbrimaNEdkenAkñúgrnUtem. EdkxagelIrbs;vaminRtUvtUcCagBak;kNþalEdkemenAkñúgtMbn;Taj. rnUtrgmannaTIBRgwgkM ralxNÐ (floor stiffener) . - RbsinebIbnÞúkGefrFMCag 3kN / m 2 ehIyrnUtemmanRbEvgERbRbYlcenøaHBI 4m eTA 7m eK RtUvdak;rnUtrgmYydUcbgðajxagelI. RbsinebIrnUtemmanRbEvgFMCag 7m y:agehacNas; rnUtrgBIrRtUv)andak;CamYynwgsésrEdkdUckarENnaMxagelI. ]TahrN_TI6³ kMNt;kMralxNÐrnUtmYyTisenAxagkñúgCamYynwgTinñn½yxageRkam³ RbEvgrnUt 6m ¬TMr samBaئ/ bnÞúkefr ¬edaymin)anbBa©ÚlbnÞúkpÞal;¦ 0.75kN / m 2 / bnÞúkGefr 4.1kN / m 2 / f 'c = 28MPa nig f y = 400MPa . dMeNaHRsay³ 1> KNnakMralxNг snμt;kMras;kMralxNÐxagelIesμInwg 50mm EdlP¢ab;CamYynwgrnUtEdlman clear span 500mm . sMPar³edIm,IbMeBj (filler) minRtUv)aneRbI. bnÞúkpÞal;rbs;kMralxNÐKW 0.050 × 25 = 1.25kN / m 2 . bnÞúkefrsrub D = 1.25 + 0.75 = 2.kN / m 2 U = 1.2 D + 1.6 L = 1.2 × 2 + 1.6 × 4.1 = 9kN / m 2 UL2 Mu = 12 ¬kMralxNÐRtUv)ancak;Cab;CamYynwgrnUt¦ 9 × 0.5 2 Mu = = 0.19kN .m 12 edaycat;Tukm:Um:g;enAkñúgkMralxNÐRtUvRTedayebtugsuTæ enaHersIusþg;TajedaykarBt;GnuBaØatrbs;ebtugKW f t = 0.415 f 'c CamYynwgemKuNkat;bnßyersIu sþg; φ = 0.55 / f t = 0.415 28 = 2.2MPa . ersIusþg;TajrgkarBt; = Mc = φf t I bh 3 1000 × 50 3 I= = = 10.42 ⋅ 10 6 mm 4 12 12 h c = = 25mm 2 One-Way Slab 186
  15. 15. T.Chhay NPIC 10.42 ⋅ 10 6 M = φf t I c = 0.55 × 2.2 × 25 ⋅ 10 −6 = 0.5kN .m > M u = 0.19kN .m ¬muxkat;RKb;RKan;¦ EdkrYmmaD As = 0.0018 × 1000 × 50 = 90mm 2 Edk DB10 manKMlat 300mm RtUv)andak;EkgnwgTisedArbs;rnUt. sMNaj;EdkpSar (welded wire fabric) manlkçN³snSMsMécsMrab;krNIbrimaNEdktic. eRbIEdk DB10 manKMlat 300mm sMrab;dak;RsbnwgTisedArnUt edayEdkmYyedImRtUv)andak;enABI elIrnUtnImYy² nigEdkmYyeTotRtUv)andak;enAcenøaHkNþalrnUtBIr. 2> KNnam:Um:g;enAkñúgrnYt kMBs;Gb,brma = 20 = 20 = 0.3m L 6 kMBs;srubrbs;rnUtnigkMralxNÐKW 250 + 50 = 300mm snμt;TTwgrnUtEpñkxageRkamKW 100mm nigEpñkxagelI ¬nIv:U)atkMralxNЦKW 150mm rUbTI9>8. TTwgmFümrbs;rnUtKW 125mm cMNaMfa kMeNInénTTwgrbs;rnUtedayeRbIBum<cl½tEdlmanpleFob 1 / 12 ¬edk 1 nigQr 12 ¦ TMgn;rnUt= 0.125 × 0.25 × 25 = 0.78kN / m rnUtRTnUvbnÞúkmkBIkMralxNÐEdlmanTTwg 600mm bUknwgbnÞúkpÞal;rbs;va U = 9 × 0.6 + 1.2 × 0.78 = 6.35kN / m UL2 6.35 × 6 2 Mu = = = 28.6kN .m 8 8 3> KNnarnUt³ kMBs;srubrbs;rnUtKW 300mm . snμt;eRbIEdk DB16 nigkMras;ebtugkarBarEdk 20mm kMBs;RbsiTæPaB d = 300 − 20 − 8 = 272mm BinitüemIlersIusþg;énsøab ¬snμt;muxkat; tension-controlled section/ φ = 0.9 ¦ ⎛ t⎞ φM n ¬søab¦ = φC ⎜ d − ⎟ Edl C = 0.85 f 'c bt ⎝ 2⎠ ⎛ 50 ⎞ M u = 0.9(0.85 × 28 × 600 × 50 )⎜ 272 − ⎟ ⋅ 10 −6 = 158.7 kN .m ⎝ 2⎠ ersIusþg;m:Um:g;ebs;søabFMCagm:Um:g;Gnuvtþn_ dUcenHrnUtmannaTICamuxkat;ctuekaNEkgEdlmanTTwg b = 600mm nigkMBs;énbøúkrgkarsgát;smmUl a KWtUcCagkMras;kMralxNÐ 50mm . ⎛ a⎞ As f y φM n = φAs f y ⎜ d − ⎟ = φAs f y (d − ) ⎝ 2⎠ 1.7 f 'c b ⎛ As × 400 ⎞ 28.6 ⋅ 10 6 = 0.9 As × 400⎜ 272 − ⎟ ⎝ 1.7 × 28 × 600 ⎠ kMralxNÐmYyTis 187
  16. 16. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa As = 297mm 2 297 × 400 a= = 8.32mm < 50mm 0.85 × 28 × 600 eRbIEdk 2DB16 sMrab;rnUtmYy (402mm 2 ) As min = 0.0033bw d = 0.0033 × 125 × 272 = 112.2mm 2 < 297mm 2 BinitüemIl 297 ρ= = 0.018 < ρ max = 0.019 600 × 272 EdlCamuxkat; tension-controlled section/ φ = 0.9 . 4> KNnakMlaMgkat;TTwgenAkñúgrnUt³ ersIusþg;kMlaMgkat;TTwgGnuBaØaténRTnugrnUtKW φVc = φ (1.1) × 0.17 f 'c bw d = 0.75 × 1.1 × 0.17 × 28 × 125 × 272 × 10 −3 = 25.2kN kMlaMgkat;TTwgemKuNenAcMgay d BITMrKW Vu = 6.35 × (3 − 0.272) = 17.3kN < φVc = 25.2kN dUcenHEdkkgGb,brmaRtUv)aneRbI ehIykrNIenHEdk DB12 RtUv)anbEnßmenAkñúgkMralxNÐEpñkxag elIedIm,ITb;Edkkg. vaCakarRbesIreBsinebIeKbEnßmrnUtrgmYyenAkNþalElVgEkgnwgrnUtem ehIy manbrimaNEdkdUcKñanwgrnUtem edIm,IeFVIeGaykMralxNÐmanlkçN³rwgmaM. One-Way Slab 188

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