Department of Civil Engineering                                                             NPIC




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T.Chhay                                      viTüasßanCatiBhubec©keTskm<úCa




Two-Way Prestressed Concrete Floor Systems...
Department of Civil Engineering                                                             NPIC




eTAnwg lifting collar...
T.Chhay                                                                        viTüasßanCatiBhubec©keTskm<úCa

Ockleston, ...
Department of Civil Engineering                                                              NPIC




GnuBaØateGay lower b...
T.Chhay                                                               viTüasßanCatiBhubec©keTskm<úCa

TMrg;EdleKmincg;)ane...
Department of Civil Engineering                                                              NPIC




       FñwmTMrsamBaØ...
T.Chhay                                                                 viTüasßanCatiBhubec©keTskm<úCa

9.3.viFIeRKagsmmUl...
Department of Civil Engineering                                                             NPIC




9.3.2.    EdnkMNt;rbs...
T.Chhay                                      viTüasßanCatiBhubec©keTskm<úCa




Two-Way Prestressed Concrete Floor Systems...
Department of Civil Engineering                                                             NPIC




EdlmanRkLaépÞmuxkat;e...
T.Chhay                                                                    viTüasßanCatiBhubec©keTskm<úCa

m:Um:g;enAkNþal...
Department of Civil Engineering              NPIC




RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis   565
T.Chhay                                                                viTüasßanCatiBhubec©keTskm<úCa

          ∑ Kc = pl...
Department of Civil Engineering                                                               NPIC




enAeBlEdleKkMNt;PaB...
T.Chhay                                                                  viTüasßanCatiBhubec©keTskm<úCa

9.4.   bnÞúklMnwg...
Department of Civil Engineering                                                              NPIC




        RbsinebIkMra...
T.Chhay                                                                  viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                                  NPIC




EdlekItmanenAkñú...
T.Chhay                                      viTüasßanCatiBhubec©keTskm<úCa




Two-Way Prestressed Concrete Floor Systems...
Department of Civil Engineering              NPIC




RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis   573
T.Chhay                                                                 viTüasßanCatiBhubec©keTskm<úCa

9.6. Banding of Pr...
Department of Civil Engineering                                                          NPIC




        TTwgrbs;knøHcMer...
T.Chhay                                                                     viTüasßanCatiBhubec©keTskm<úCa

       karGegá...
Department of Civil Engineering                                                                    NPIC




Edl N c CakugR...
T.Chhay                                                                 viTüasßanCatiBhubec©keTskm<úCa

9.6.2.3.    kMlaMg...
Department of Civil Engineering                                                            NPIC




smIkar 9.25(a) nig (b)...
T.Chhay                                                                    viTüasßanCatiBhubec©keTskm<úCa

9.7. Load-Balan...
Department of Civil Engineering                                                                      NPIC




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T.Chhay                                                                     viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                                   NPIC




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T.Chhay                                                                           viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                                                   NPIC



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T.Chhay                                                               viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                                  NPIC




      9.9.2. She...
T.Chhay                                      viTüasßanCatiBhubec©keTskm<úCa




Two-Way Prestressed Concrete Floor Systems...
Department of Civil Engineering                                                             NPIC




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T.Chhay                                                                         viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                           NPIC




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T.Chhay                                                                     viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                              NPIC




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T.Chhay                                                                  viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering              NPIC




RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis   595
T.Chhay                                      viTüasßanCatiBhubec©keTskm<úCa




Two-Way Prestressed Concrete Floor Systems...
Department of Civil Engineering                                                            NPIC




9.11.      sikSaKNnaRb...
T.Chhay                                      viTüasßanCatiBhubec©keTskm<úCa




Two-Way Prestressed Concrete Floor Systems...
Department of Civil Engineering                                                                  NPIC




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



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T.Chhay                                                                       viTüasßanCatiBhubec©keTskm<úCa

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Department of Civil Engineering                                                                             NPIC




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T.Chhay                                                                           viTüasßanCatiBhubec©keTskm<úCa




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Department of Civil Engineering                                                                NPIC




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Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
Ix. two way prestressed concrete floor systems
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Ix. two way prestressed concrete floor systems

  1. 1. Department of Civil Engineering NPIC IX. RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis Two-Way Prestressed Concrete Floor Systems 9.1. esckþIepþIm³ rMlwkBIviFIsaRsþ Introduction: Review of Method CaTUeTA RbB½n§kMralEdlmanTMr (supported floor system) RtUv)aneKsg;BIebtugGarem:Edl cak;enAnwgkEnøg. kMralxNÐBIrTisCakMralxNÐEdlmanpleFobbeNþayelITTwgtUcCagBIr. karsikSa viPaK nigkarsikSaKNnaRbB½n§kMralxNÐEdlbgðajenAkñúgrUbTI 9>1 rYmbBa©ÚlTMrg;kMralxNÐeRcInCag mYyRbePT. enAkñúgemeronenH nwgbgðajBIrebobkMNt; (1) moment capacity, (2) slab-column shear capacity nig (3) serviceability behavior EdlmandUcCakarRKb;RKgPaBdab nigsñameRbH. cMNaMfa flat plate CakMralxNÐEdlRTEdlQrelIssredaypÞal;edayminmanFñwm dUcEdlbgðajenAkñúgrUbRtg; cMnuc (a) cMENkkMralxNÐQrelIFñwmRtUv)anbgðajenAkñúgcMnuc (b) ÉcMnuc (c) bgðajBI waffle slab floor. eKeRbIeKalkarN_dUcKñakñúgkarsikSaviPaKRbB½n§ flat plate ebtugGarem: edIm,IsikSaviPaK flat plate ebtugeRbkugRtaMgCab;BIrTis. b:uEnþ bec©keTskñúgkarsagsg;manlkçN³xusKña . CaerOy² lkçN³esdækic©EtmYyminTMngGacbgðajBIlkçN³smehtuplkñúgkareRbIRbePTRbB½n§kMralxNÐBIrTisE dlbgðajenAkñúgrUbTI 9.1(b) nig (c) eT. CaTUeTA eKniymeRbIRbB½n§ post-tensioned sMrab;RbB½n§ two- way plate Edlcak;ehIy. eBlxøH eKeRbIkMralxNÐBIrTisEdlcak;Rsab;enAkardæan EdleKehAfa lift slabs CaRbB½n§eRKOgbgÁúMdac;edayELkBIKñaEdleFVIeGaykarsagsg;manel,ÓnelOn nigmanlkçN³ esdækic©CagkMralxNÐBIrTiseRbkugRtaMgcak;enAnwgkEnøg. b:uEnþ karxVHbec©keTskñúgkarsagsg; lift slab nigGvitþmanénGñkCMnajÉkeTsxagkargarsagsg;EbbenHGacbegáItnUvlkçxNÐeRKaHfñak;Edl GaceFVIeGay)at;bg;nUvesßrPaB nigeFVIeGayeRKOgbgÁúMdYlrlM. bec©keTssMrab;plit lift slab rYmmankarcak; ground-level slab EdlmantYnaTIBIrKW casting bed EdlenABIelIvaeKGaccak;kMralxNÐepSg²TaMgGs; nigdak;KelIKña EdlEckdac;BIKñaeday mem- brane b¤ sprayed parting agent. ssr EdlGacCaEdk b¤ebtugRtUv)ansg;rhUtdl;kMBs;rbs;GKar munnwgcak; basic bottom slab. kMralxNÐdéTeTotTaMgGs;RtUv)aneKcak;CMuvijssr edayman steel collar pþl;nUvKMlatRKb;RKan;edIm,IGnuBaØat listing (jacking) kMralxNÐdl;kMritnIv:Usmrmürbs;kMral xNÐ dUcbgðajenAkñúgrUbTI 9>1 (d). eKsMerc)ankargar lifting tamry³kareRbI jack Edldak;enAelI kMBUlrbs;ssr nigP¢ab;eTAnwgr)arEdkEdlmaneFμj (threaded rod) EdlbgðÚtcuHeRkamelIépÞrbs;ssr RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 553
  2. 2. T.Chhay viTüasßanCatiBhubec©keTskm<úCa Two-Way Prestressed Concrete Floor Systems 554
  3. 3. Department of Civil Engineering NPIC eTAnwg lifting collar Edlbgáb;enAkñúgkMral. skmμPaBénkar jack TaMgGs;RtUvrkSaPaBedkrbs;kMral edIm,IeCosvagkar)at;bg;lMnwg. karsikSaviPaKkareFVIkarrbs;kMralxNÐeRkamkarBt;begáagrhUtdl;TsvtSr× 1940 nigedImTs- vtSr× 1950 eFVIeLIgedayGnuvtþtamRTwsþIeGLasÞic (classical theory of elasticity). RTwsþIPaBdabtUc rbs; plate (small-deflection of plates) Edlsnμt;sMPar³manlkçN³sac;mYy (homogeneous) nig esμIsac; (isotropic) EdlbegáItCaeKalkarN_én ACI Code recommendation CamYynwgtaragemKuN m:Um:g;. enAqñaM 1943, Johansen )anbgðajRTwsþI yield-line sMrab;kMNt;lT§PaBTb;Tl;kardYlrlMrbs; kMralxNÐ. cab;taMgBIeBlenaHmk kargarsikSaRsavRCavCaeRcInRtUv)aneFVIeLIg EdlkargarTaMgenHTak; TgnwgkareFVIkarrbs;kMralebtugGarem:eRkamGMeBI ultimate. karsikSaedayGñkRsavRCavCaeRcIndUcCa RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 555
  4. 4. T.Chhay viTüasßanCatiBhubec©keTskm<úCa Ockleston, Mansfield, Rzhanitsyn, Powell, Wood, Sawcczuk, Gamble-Sozwn-Siess nig Park )ancUlrYmd¾mhimasMrab;karyl;dwgBI limit-state behavior rbs;kMralxNÐ nig plate enAeBl)ak; k¾dUc enAeBlrgbnÞúkesvakmμ. eKmanviFICaeRcInEdlRutUv)aneRbIsMrab;sikSaviPaK nigsikSaKNnakMralxNÐ nig plate BIrTis RtUv)ansegçbdUcxageRkam³ 9.1.1. viFI ACI Code Bak;kNþaleGLasÞic The Semielastic ACI Code Approach viFI ACI pþl;nUvCMerIsBIrsMrab;sikSaviPaK nigsikSaKNnaRbB½n§ plate b¤kMralxNÐBIrTisKW³ viFI sikSaKNnaedaypÞal; (direct design method) nigviFIeRKagsmmUl (equivalent frame method). viFITaMgBIrnwgRtUv)anykmkBiPakSaenAkñúgcMnuc 9.3.. eKeRbI equivalent frame method enAkñúgkar sikSaKNna nigsikSaviPaK plate nigkMralxNÐeRbkugRtaMg. 9.1.2. The Yield-Line Method eKGnuvtþ semielastic code approach sMrab;krNI nigragsþg;dar ehIyvamanemKuNsuvtßiPaB sMrab;lT§PaBRTRTg;FMNas; cMENkÉ yield-line theory CaRTwsþI)aøsÞicEdlgayRsYlGnuvtþeTAelIlkç- xNÐRBMEdn nigrUbragminRbRktI. RbsinebIeKGnuvtþ serviceability constraints, yield-line theory rbs; Johansen bgðajnUvkareFVIkarBItR)akdrbs; plate nigkMralxNÐebtug EdlGnuBaØatdl;karkMNt; m:Um:g;begáagBI collapse mechanism Edl)ansnμt;EdlGnuKn_eTAnwgRbePTénbnÞúkxageRkA nigrUbrag rbs; floor panel. eyIgnwgBiPakSaRTwsþIenHkan;EtlMGitenAkñúgcMnuc 9.14.. 9.1.3. The Limit Theory of Plates cMNab;GarmμN_kñúgkarbegáIt limit solution køayCacaM)ac;edaysarlT§PaBkñúgkarkMNt; collapse field CaeRcIn EdlGaceGayeKkMNt;)annUv lower failure load. dUcenH upper bound solution EdlTamTarnUv valid mechanism enAeBlEdkrksmIkarkmμnþ (work equation) k¾dUc lower bound solution EdlTamTareGayEdnkugRtaMg (stress field) bMeBjlkçxNÐsmIkarlMnwgDIepr:g;Esül RKb;TIkEnøg (differential equation of equilibrium) Edl ∂2M x ∂ 2 M xy ∂2M y −2 + = −w (9.1) ∂x 2 ∂x∂y ∂y 2 Edl M x / M y nig M xy Cam:Um:g;Bt; nig w CaGaMgtg;sIueténbnÞúkÉktþa. brimaNEdkEdlERbRbYl Two-Way Prestressed Concrete Floor Systems 556
  5. 5. Department of Civil Engineering NPIC GnuBaØateGay lower bound solution enAEtmann½y. Wood, Park nigGñkRsavRCavdéTeTot)anpþl; nUv semiexact prediction EdlsuRkitrbs; collaps load. sMrab; limit-state solution eKsnμt;fakMralxNÐmanlkçN³rwgdac;xatrhUtdl;eBldYlrlM. eRkaymk Nawy )anbBa©ÚlT§iBlénPaBdabeRkamGMeBIbnÞúkFM k¾dUcT§iBlkMlaMg membrane rgkar sgát;eTAkñúgkar)a:n;sμan collapse load. 9.1.4. viFIcMerok The Stripe Method viFIenHRtUv)anesñIeLIgeday Hillerborg kñúgkic©RbwgERbgedIm,ItMerobEdkenAkñúgEdncMerok (stripe field). edaysarkarKitkñúgkarGnuvtþenAkardæanCak;EsþgTamTarnUvkardak;EdkkñúgTisEkgKña (orthogonal direction), Hillerborge kMNt;eGaym:Um:g;rmYl (twisting moment) esμIsUnü ehIybMElg kMralxNÐeGayeTACacMerokFñwmEdlkat;Kña (intersection beam stripe) dUcenHeTIbeKeGayeQμaHfa stripe method. elIkElg yield-line theory rbs; Johansen ecj dMeNaHRsayPaKeRcInCa lower bound. Upper-bound solution rbs; Johansen Gacpþl;nUv collaps load FMbMput kñúgkrNIeKeRbI valid failure mechanism kñúgkar)a:n;RbmaN collapse load. 9.1.5. esckþIsegçb Summary viFIeRKagsmmUlCaviFIcMbgEdlnwgRtUvBiPakSa edaysareRbIR)as;én direct design method enAkñúgkarGnuvtþrbs;vasMrab;RbB½n§kMralebtugeRbkugRtaMgBIrTismanEdnkMNt; nigtMrUvkarnUvkarkMNt; stiffness enARtg;tMNrvagssr nigkMralxNÐenAkñúgdMeNIrkarénkarsikSaKNna. RTwsþI yield-line sMrab;sikSakMralxNÐ nig plate eRkamsßanPaBkMNt;enAeBl)ak;k¾RtUv)anbgðajy:agsegçb. 9.2. kareFVIkarrbs;kMralxNÐBIrTiseRkamkarBt;begáag Flexural Behavior of Two-Way Slabs and Plates 9.2.1. GMeBIBIrTis Two-Way Action eKmankMralctuekaNeTalEdlRCugTaMgbYnrbs;vaRtUv)anRTeday unyielding support dUcCa shear wall b¤ stiff beam. eyIgBinitükareFVIkarrbs;kMraleRkamGMeBI gravity load. kMralnwgdabkñúg RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 557
  6. 6. T.Chhay viTüasßanCatiBhubec©keTskm<úCa TMrg;EdleKmincg;)aneRkamGMeBIbnÞúkxageRkA ehIykac;RCugrbs;vanwgehIbeLIgRbsinebIvaminRtUv)an cak;ebtugCamYynwgTMrkñúgeBlEtmYyeTenaH. ExSvNÐ (contour) EdleXIjenAkñúgrUbTI 9>2 (a) bgðaj faExSekagm:Um:g;enARtg;cMnuckNþal C maneRKaHfñak;enAelIRCugxøItamTis y CagenAelIRCugEvgtamTis x. karkMNt;m:Um:g;tamTis x nigtamTis y BitCamanlkçN³sμúKsμaj edaysarvaeFVIkarCaeRKOg bgÁúMsþaTicminkMNt;dWeRkx<s;. eKbriyaykMralenAkñúgEpñk (a) énrUbTI 9>2 CakrNIsamBaØedayykcM- erok AB nig DE EdlenAkNþalElVg ¬dUckñúgEpñk (b)¦ EdlPaBdabrbs;cMerokTaMgBIrenAcMnuckNþal C mantMélesμIKña. Two-Way Prestressed Concrete Floor Systems 558
  7. 7. Department of Civil Engineering NPIC FñwmTMrsamBaØEdlrgbnÞúkBRgayesμImanPaBdab 5wl 4 / 384EI b¤ Δ = kwl 4 Edl k cMnYnefr. RbsinebIkMras;rbs;cMerokTaMgBIrdUcKña enaHPaBdabrbs;cMerok AB KW kwAB L4 ehIyPaBdabrbs;cMerok DE KW kwDE S 4 Edl w AB nig wDE CacMENkénGaMgtg;sIuetbnÞúksrub w EdlepÞreTAcMerok AB nig cMerok DE erogKña Edl w = wAB + wDE . dak;eGayPaBdabRtg;cMnuckNþal C éncMerokTaMgBIresμI Kña enaHeyIg)an wS 4 w AB = (9.2a) L4 + S 4 wL4 nig wDE = 4 L + S4 (9.2b) BIsmIkarTaMgBIrxagelIenH eyIgeXIjfaElVgEdlxøI S rbs;cMerok DE RTnUvcMENkénbnÞúkFMCag. dUc enH ElVgxøIrbs;kMralEdlenAelI unyielding support KWrgnUvm:Um:g;FMCag EdlRTnUvExSekagEdlman lkçN³ecatenAkñúgrUbTI 9>2 (a). 9.2.2. Relative Stiffness Effects eKmankMralxNÐmYyEdlRTeday flexible support dUcCaFñwm nigssr b¤ flat plate EdlRT edayssr. enAkñúgkrNImYyNak¾eday karEbgEckm:Um:g;enAkñúgTisxøI nigTisEvgmanlkçN³sμúKsμaj Nas;. PaBsμúKsμajenHekIteLIgBIdWeRkén stiffness rbs; yielding support EdlkMNt;PaBecatén ExS contour enAkñúgrUbTI 9>2 (a) enAkñúgTis x nigTis y nigkMNt;nUvkarEbgEckm:Um:g;eLIgvij. pleFob stiffness rbs;FñwmTMrelI stiffness rbs;kMralxNÐGaceFVIeGayExSekag nigm:Um:g; enA elITisEvgFMCagExSekag nigm:Um:g;enAelITisxøI edaysarkMralsrubeFVIkardUc orthotropic plate Edl QrelIssrEdlKμanFñwm. RbsinebIElVgEvg L enAkñúgRbB½n§kMralenHFMCagElVgxøI S xøaMg enaHm:Um:g;Gti- brmaenAcMnuckNþalrbs;kMralnwgmantMélRbhak;RbEhlnwgm:Um:g;Rtg;kNþalElVgrbs;cMerokElVg L EdlrgbnÞúkBRgayesμI ehIyEdlcugrbs;vaRtUv)anTb;mineGayvil. Casegçb edaysarkMralmanlkçN³rlas; (flexible) nigmanbrimaNEdkticEmnETn enaHkar EbgEckm:Um:g;eLIgvijenAkñúgTisTaMgBIrGaRs½ynwg relative stiffness rbs;TMr nigrbs;kMral. kugRtaMg EdlFMRCulenAkñúgtMbn;mYyRtUv)ankat;bnßyedaykarEbgEckm:Um:g;eLIgvijenHeTAkan;tMbn;Edlmankug RtaMgtUc. RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 559
  8. 8. T.Chhay viTüasßanCatiBhubec©keTskm<úCa 9.3.viFIeRKagsmmUl The Equivalent Frame Method 9.3.1. esckþIepþIm Introduction xageRkamCakarerobrab;BIviFI equivalent frame sMrab;karviPaKkMralxNÐBIrTisEdlsegçb ACI Code approach edIm,IkMNt; nigEbgEckm:Um:g;srubenAkñúgkMralBIrTis. kUdsnμt;kat;tambøg;GKar ragctuekaNeRcInCan;tamTisbBaÄrtambeNþayExS AB nig CD enAkñúgrUbTI 9>3 cenøaHkNþalElVg. eKTTYl)an rigid frame enAkñúgTis x . dUcKña bøg;kat;bBaÄr EF nig HG pþl;nUv rigid frame enAkñúg Tis y . Idealized frame EdlpSMeLIgedayFñwmedk b¤kMralxNÐsmmUl nigssrEdlCaTMrGaceGay eKKNnakMralxNÐedaycat;TukvadUcCaFñwm. dUcenH viFI equivalent frame cat;Tuk idealized frame eFVIkarRsedogKñanwgeRKagBitR)akd ehIyvamanEdnkMNt; nigpþl;nUvlT§plsuRkitCag direct design method. viFIenHRtUvkarEbgEckm:Um:g;eLIgvijeRcIndg cMENkÉ direct design method RtUvkarkarEbg Eckm:Um:g;eLIgvijEtmþgKt;. Two-Way Prestressed Concrete Floor Systems 560
  9. 9. Department of Civil Engineering NPIC 9.3.2. EdnkMNt;rbs;viFIKNnaedaypÞal; Limitations of the Direct Design Method xageRkamCaEdnkMNt;rbs; direct design method: !> enAkñúgTisnImYy²RtUvmanbIElVgCab;Kñay:agtic. @> pleFobElVgEvg elIElVgxøIminRtUvFMCag 2.0. #> ElVgkñúgTisnImYy²minRtUvxusKñaedaytMélFMCagmYyPaKbIénElVgEdlEvg. $> ssrGacsßitenAxusBIG½kSedaytMélGtibrma 10% énElVgenAkñúgTisEdlvasßitenA. %> bnÞúkTaMgGs;KYrEtCabnÞúkTMnaj nigCabnÞúkBRgayesμIelIkMralTaMgmUl. bnÞúkGefrminRtUvFM CagbnÞúkefrbIdgeT. ^> RbsinebI kMralRtUv)anRTedayFñwmRKb;Tis/ relative stiffness rbs;FñwmkñúgTisBIEkgKñamin RtUvtUcCag 0.2 b¤FMCag 5.0. edayeKeGayEdnkMNt;TaMgenHsMrab;karviPaKkMralxNÐebtugeRbkugRtaMg eKcaM)ac;eRbI equiva-lent frame method RbesIrCag. 9.3.3. karkMNt;m:Um:g;sþaTic M o Determination of the Statical Moment M o eKmanCMhankñúgkarKNnakMralxNÐsMxan;cMnUn 4dUcxageRkam³ !> kMNt;m:Um:g;sþaTicsrubenAkñúgTisnImYy². @> EbgEckm:Um:g;srubsMrab;karKNnamuxkat;sMrab;m:Um:g;viC¢man nigGviC¢man. #> EbgEckm:Um:g;GviC¢man nigm:Um:g;viC¢maneTAcMerokelIssr nigcMerokkNþalElVg nigeTAFñwmRb sinebIvaman. cMerokelIssr (column strip) CacMerokEdlmanTTwgesμInwg 25%énTTwgeRKag smmUlenAelIRCugnImYy²énG½kSssr ehIyTTwgrbs;cMerokkNþalElVgCaRbEvgEdlenA sl;. $> kMNt;TMhM nigkarEbgEckEdkenAkñúgTisnImYy². tamGVIEdleGaydUcxagelI eKRtUveFVIkarEksMrYltMélrbs;m:Um:g;Edl)anEbgEckehIy. eKman kMralxNÐxagkñúgEdlmanTMhM l1 KitBIG½kSenAkñúgTisénm:Um:g;EdlRtUvBicarNa nigTMhM l2 enAkñúgTis Ekgnwg l1 dUceXIjenAkñúgrUbTI 9>4. Clear span ln CaTMhMEdlKitBIépÞeTAépÞrbs;ssr b¤ capital b¤CBa¢aMg. tMélrbs;vaminRtUvtUcCag 0.65l1 ehIysMrab;TMrEdlmanmuxkat;mUl eKRtUvKitCamuxkat;kaer: RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 561
  10. 10. T.Chhay viTüasßanCatiBhubec©keTskm<úCa Two-Way Prestressed Concrete Floor Systems 562
  11. 11. Department of Civil Engineering NPIC EdlmanRkLaépÞmuxkat;esμIKña. m:Um:g;sþaTicsrubrbs;FñwmTMrsamBaØrgbnÞúkBRgayesμIEdlCa one- dimensional member KW M o = wl 2 / 8 . enAkñúgkMralxNÐBIrTisEdlCa two-dimensional member, eKbMElgeRKOgbgÁúMeGayeTACaeRKagsmmUlEdlGaceGayeKKNna M o mþgenAkñúgTis x nigmþgenA kñúgTis y . RbsinebIeKKitkMralxagkñúgenHCadüaRkamGgÁesrIdUcbgðajenAkñúgrUbTI 9>5 (a) PaBsIuemRTI kat;bnßykMlaMgkat; nigm:Um:g;rmYl (twisting moment) rhUtdl;sUnütambeNþayRCugénkMNat;Edlrg karkat;. RbsinebIenAxagcugcMnuc A nigcMnuc B minmankarTb;nwgkarvil (restraint) enaHeKKitkMral CakMralTMrsamBaØenAkñúgTisénElVg ln . RbsinebIeKkat;enARtg;kNþalElVg dUcenAkñúgrUbTI 9>5 (b) ehIyKitkMralBak;kNþalCadüaRkamGgÁesrI enaHm:Um:g; M o enAkNþalElVgKW wl 2 l n1 l n1 wl 2 l n1 l n1 Mo = − 2 2 2 4 wl (l ) 2 b¤ M o = 2 n1 8 (9.3) edaysarman restraint enARtg;TMr/ eKEbgEck M o enAkñúgTis x eTATMr nigeTAkNþalElVgdUcxag eRkam Mo = MC + 1 (M A + M B ) (9.4a) 2 karEbgEckenHGaRs½ynwgdWeRkénPaBrwgRkajrbs;TMr. enAkñúgrebobdUcKña M o enAkñúgTis y CaplbUk RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 563
  12. 12. T.Chhay viTüasßanCatiBhubec©keTskm<úCa m:Um:g;enAkNþalElVg nigtMélmFüménm:Um:g;elITMrenAkñúgTisenaH. enAkñúgTisEdlEkg smIkar 9.4a køayCa M ' o = M 'C + 1 (M A + M B ) (9.4b) 2 Edl M 'o / M ' A / M 'B nig M 'C Cam:Um:g;enAelIG½kSEdlEkgKñanwg M o / M A / M B nig M C erogKña. dUcKña enAkñúgrebobRsedogKñanwgsmIkar 9.3 eyIg)an wl1 (l n 2 )2 M 'o = (9.5) 8 GaMgtg;sIuetbnÞúk w eRkambnÞúkesvakmμenAkñúgkMralebtugeRbkugRtaMgGacCa Ww kñúgmYyÉktþaépÞ. 9.3.4. viPaKeRKagsmmUl Equivalent Frame Analysis eRKOgbgÁúM ¬EdlEckecjCaeRKagCab;dUcbgðajenAkñúgrUbTI 9>6 sMrab;eRKagkñúgTisTaMgBIrEkg Kña¦ manssrmYyCUr nigFñwm ¬kMralxNЦCab; ABCDE sMrab;bnÞúkTMnaj. kMralnImYy²RtUv)anviPaK dac;edayELkBIKña EdlssrRtUv)ansnμt;fa fixed enARtg;kMralxagelI nigxageRkam. edIm,IbMeBj lkçxNÐsþaTic niglkçxNÐlMnwg eRKagsmmUlnImYy²RtUvRTbnÞúkGnuvtþn_srub. kardak;bnÞúkelIElVg qøas;RtUv)aneRbIsMrab;rklkçxNÐbnÞúkGefrGaRkk;bMput. eKcM)ac;KitBIersIusþg;Tb;mMurgVil (rotational resistance) rbs;ssrenARtg;tMN enAeBlKitBI moment relaxation b¤karEbgEckm:Um:g; elIkElgenAeBlssrmanlkçN³EvgEdleFVIeGayvaman PaBrwg (rigidity) tUceFobeTAnwg rigidity rbs;kMralenARtg;tMN. enAkñúgkarsagsg; lift slab eKcaM )ac;KitEtFñwmCab;Etb:ueNÑaH. rUbTI 9>7 bgðajBIbNþaGgát;éneRKagsmmUl. cMerokkMralRtUv)ansnμt; RTedaykMralTTwg (transverse slab). ssrpþl;nUversIusþg;Tb;m:Um:g;rmYl M T EdlsmmUleTAnwgGaMg tg;sIuetm:Um:g;rmYlGnuvtþn_ mt . muxkat;cugxageRkArbs;cMerokkMralvilFMCagmuxkat;Rtg;kNþaleday sarkMhUcRTg;RTayedaykarrmYl. edIm,IKitBImMurgVil nigkMhUcRTg;RTayenH eKRtUvCMnYsssrCak;Esþg nig transverse slab strip edayssrsmmUlEdl flexibility rbs;ssrsmmUlesμInwgplbUk flexibi- lity énssrCak;Esþg nigcMerokkMral. karsnμt;enHsMEdgedaysmIkarxageRkam³ 1 1 1 = + (9.6) K ec ∑ K c K t Edl K ec = PaBrwgRkajTb;karBt; (flexural stiffness) rbs;ssrsmmUl ¬m:Um:g;kñúgmYyÉktþa mMurgVil¦. Two-Way Prestressed Concrete Floor Systems 564
  13. 13. Department of Civil Engineering NPIC RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 565
  14. 14. T.Chhay viTüasßanCatiBhubec©keTskm<úCa ∑ Kc = plbUk flexural stiffness rbs;ssrxagelI nigxageRkamenARtg;tMN K t = flexural stiffness rbs;FñwmEdlrmYl müa:gvijeTot eKGacsresrsmIkar 9>6 CasmIkar stiffness ∑ Kc K ec = (9.7) ∑ Kc 1+ Kt ehIyeKGackMNt;PaBrwgRkajrbs;ssrsMrab;eRKagsmmUlCa EI ⎡ ⎛L⎞ ⎤ 2 Kc = ⎢1 + 3⎜ ⎟ ⎥ (9.8) l' ⎢ ⎣ ⎝ L' ⎠ ⎥⎦ Edl I Cam:Um:g;niclPaBrbs;ssr/ L CaRbEvgElVgKitBIG½kS/ L' CaRbEvgElVgrbs;FñwmsmmUlEdl KitBIépÞssr. eKykemKuN carryover RbEhlnwg − 12 (1 + 3h / L ) . eKGacKNnaemKuN carry- over )anCak;Elkeday column-analogy method edayeRbIkMralxNÐCa analogous column. smIkarsMrYlsMrab; K c eGaylT§plxusBItMélEdl)anBIsmIkar 9.8 RbEhl 5%. 4 EI Kc = (9.9) Ln − 2h Edl h CakMras;kMralxNÐ. PaBrwgRkajkñúgkarrmYl (torsional stiffness) rbs;kMralxNÐenAkñúgCYr ssr 9 Ecs C Kt = ∑ 3 (9.10a) ⎛ c ⎞ L2 ⎜1 − 2 ⎟ ⎜ L ⎟ ⎝ 2⎠ Edl L2 = TTwg band Ln = ElVg c2 = TMhMrbs;ssrkñúgTisRsbnwgFñwgrgkarrmYl ehIyefrrmYl (torsional constant) KW ⎛ x⎞ ⎜1 − 0.63 ⎟ x 3 y ⎜ y⎟ C =∑⎝ ⎠ (9.10b) 3 Edl x= TMhMxøIénEpñkctuekaNrbs;muxkat;enARtg;TIRbsBVrbs;ssr ¬dUcCakMBs;kMral¦ y = TMhMEvgénEpñkctuekaNrbs;muxkat;enARtg;TIRbsBVrbs;ssr ¬dUcCaTTwgssr¦ PaBrwgRkajrbs;kMralxNÐRtUv)aneGayedaysmIkar 4 Ecs I s Ks = (9.11) Ln − c1 / 2 Two-Way Prestressed Concrete Floor Systems 566
  15. 15. Department of Civil Engineering NPIC enAeBlEdleKkMNt;PaBrwgRkajRbsiT§PaB (effective stiffness) K ec rbs;ssr nigPaBrwgRkajrbs; kMralxNÐ K s eKGacviPaKeRKagsmmUledayviFINamYyk¾)an dUcCa relaxation method b¤ moment distribution method. emKuNEbgEck (distribution) sMrab;m:Um:g;bgáb;cug (fixed-end moment) x = KW Ks DF = (9.12) ∑K Edl ∑ K = K ec + K s(left ) + K s(right ) . eKGaceRbIemKuN carryover COF ≅ 1/ 2 edayminman)at; bg;PaBsuRkit edaysar nonprismatic section bgáT§iBlticNas;eTAelI fixed-end moment nigeTA elIemKuN carryover. m:Um:g;bgáb;cug FEM sMrab;m:Um:g;BRgayesμIKW wl2 (ln )2 /12 enARtg;TMr EdlenA eRkayeBlkarEbgEckm:Um:g;eLIgvij plbUkm:Um:g;EdlEbgEckGviC¢manenARtg;TMr nigm:Um:g;enAkNþal ElVgEtgEtesμInwgm:Um:g;sþaTic M o = wl2 (ln )2 / 8 . 9.3.5. KMrUénkardak;bnÞúkenAelIElVg Pattern Loading of Spans eKmincaM)ac;eFVIkarBRgaybnÞúkelIElVgTaMgGs;kúgeBlEtmYyeT eRBaHvamin)anbegáItkugRtaMg ñ Bt;begáagGviC¢man nigviC¢manGtibrmaeT. dUcenH eKENnaMeGayviPaKeRKageRcInCan;edayeRbIKMrUénkar BRgaybnÞúkqøas;sMrab;bnÞúkGefr. sMrab;eRKagbIElVg KMrUénkardak;bnÞúkEdlesñIeLIgsMrab;bnÞúkGefr RtUv)anbgðajenAkñúgrUbTI 9>8. RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 567
  16. 16. T.Chhay viTüasßanCatiBhubec©keTskm<úCa 9.4. bnÞúklMnwgBIrTis Two-Directional Load Balancing dUcEdl)anerobrab;enAkñúgCMBUkTI 1 bnÞúklMnwg (load balancing) CakMlaMgRbqaMgnwgbnÞúkTMnaj xageRkA. bnÞúkenHRtUv)anbegáIteLIgedaybgÁúMTTwg (transverse component) énkMlaMgeRbkugRtaMgtam beNþayenAkñúg parabolic b¤ harped tendon. bnÞúk w enAkñúgsmIkar 9.3 eTAdl; 9.5 CabnÞúkTTwgG½kS xageRkAEdlmanTiscuHeRkam (downward external transverse load) EdlGacCabnÞúkeFVIkar ww b¤Ca bnÞúkemKuN wu . bnÞúkEdlmanTiseLIgelI (upward load) enAkñúgkMralxNÐEdlbNþalBI transver component énkMlaMgeRbkugRtaMg ¬Edlmanerobrab;enAkñúgCMBUk 1¦ kat;bnßyT§iBlrbs; ww ehIy eKGaceRCIserIsvaCabnÞúklMnwgBitR)akdEdlmanTisedAcuHeRkam. eRkamlkçxNÐEbbenH kMralxNÐBIr Tisminrgm:Um:g;begáag ehIyk¾minrgm:Um:g;rmYl ehIykarviPaKRtUv)ansMrYly:ageRcIn. bnÞúklMnwgBIrTisenAkñúgkMralxNÐBIrTisxusBIbnÞúklMnwgmYyTisenAkñúgFñwm. bnÞúklMnwgEdl begáIteday tendon enAkñúgTismYyGacbegáIn b¤kat;bnßybnÞúklMnwgEdlbegáIteday tendon kñúgTis Ekg. dUcenH kMlaMgeRbkugRtaMg nig tendon profile enAkñúgTisBIrEkgKñaKWmanTMnak;TMngKñaeTAvijeTA mk edayrkSanUveKalkarN_sþaTic. plRbeyaCn_d¾FMCageKrbs;bnÞúklMnwgKWkarKNnakMraleRbkug RtaMgEdlbgÁúMeLIgelIrbs;kMlaMgeRbkugRtaMgpþl;nUvkarBRgaybnÞúkenAkñúgTisnImYy²smmUleTAnwgbnÞú kxageRkAEdlmanTisedAcuHeRkam. karsikSaKNnaEbbenHRtUv)aneKeGayeQμaHfa pure balanced design. eKRtUvviPaKral;kargakecjBIlkçxNÐlMnwg (balanced condition) dUcbnÞúkEdlmanGMeBIelI kMralEdlminrgT§iBlBI bgÁúMeLIgelIrbs;kMlaMgeRbkugRtaMg. Two-Way Prestressed Concrete Floor Systems 568
  17. 17. Department of Civil Engineering NPIC RbsinebIkMralxNÐBIrTisEdlmanTMrrwgdUcCaCBa¢aMgrgeRbkugRtaMgBIrTisEkgKñaEdlmanElVg LS nig LL kñúgTisxøI nigTisEvg erogKña dUcbgðajenAkñgrUbTI 9>9 enaHeKTTYlbnÞúklMnwgEdlmanTis ú eLIgelIEdlRtUvkaredIm,IbegáIt balanced design load Edl)anBIsmIkar 1.15a edaysmIkar 8PS eS Wbal (S ) = (9.13a) L2S nig Wbal (L ) = 8 PL eL L2 (9.13b) L Edl PS nig PL CakMlaMgeRbkugRtaMgRbsiT§PaBeRkaykMhatbg;kñúgmYyÉktþaTTwgrbs;kMralxNÐenA kñúgTisxøI LS nigTisEvg LL erogKña/ eS nig eL CacMNakp©itGtibrmarbs;EdkeRbkugRtaMg. bnÞúklMnwg srubkñúgmYyÉktþaTTwgnwgkøayCa 8PS eS 8PL eL Wbal = Wbal (S ) + Wbal (L ) = + (9.14) L2 S L2 L GñksikSaKNnaKYreRCIserIs Wbal ehIykMNt;tMélrbs;kMlaMgeRbkugRtaMg PS nig PL . bnSMén PS nig PL GacbMeBjsmIkarsßaTic 9.14. RbsinebIkMralxNÐQrelIFñwm b¤RbsinebIkMralxNÐsamBaØ QrelICBa¢aMg enaHkarKNnaEdlmanlkçN³esdækic©CageKGacRTbnÞúk W EtkñúgTisxøI b¤RT W / 2 kñúg TisnImYy²sMrab;krNIkMralxNÐragkaer:. kMralxNÐEdlrgedaybnÞúk Wbal nigrgkugRtaMgedaykMlaMg eRbkugRtaMg PS nig PL nwgRbQmnwgkarBRgaykugRtaMgesμI PS / h nig PL / h enAkñúgTisnImYy² Edl kñúgenaH h CakMras;kMralxNÐ. kMralxNÐRtUvEtrabesμI edayminmanPaBdab nig camber. KMlatén bnÞúkGnuvtþn_BI Wbal nwgTamTarnUvkareRbIRTwsþIeGLasÞicFmμtasMrab;viPaK two-way plate. CaTUeTA edaysarkMralxN§ÐBIrTisebtugeRbkugRtaMgrgkarTajCaeRkay (prestressed post- tensioned two-way slab) Ca flat plate EdlRTedayssredaypÞal; enaHbnÞúkTaMgGs;RtUv)anRTkñúg TisTaMgBIredayeRbIEdkeRbkugRtaMgBRgayesμI b¤ banded tendon CamYynwgkarRbmUlpþúMEdkeRbkugRtaMg enAmþúMcMerokssrrbs;kMralBIrTis. karEbgEckkugRtaMgesμI nigPaBdab b¤ camber sUnüminmansar³sMxan;sMrab;karkMNt;sma- maRtmuxkat;RbB½n§kMraleT. RbsinebImindUecñaHeT bnÞúklMnwgminEmnCaviFIEdlmanlkçN³esdækic© CageKkñúgkarkMNt;kMlaMgeRbkugRtaMgeT. müa:gvijeTot CaerOy²GñksikSaKNnaEtgeRbIbnÞúklMnwg edayEpñk (partial balancing load) Wbal < WD + WL sMrab;RbB½n§kMraleRcIn dUcbgðajenAkñúgrUbTI 9>2. RbsinebIbnÞúk Ww = WD + WL FMCagbnÞúklMnwg Wbal Edl)anBIsmIkar 9.14 enaHm:Um:g;Éktþa M S nig M L nigekItmanenAkñúgTis S nigTis L erogKña. RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 569
  18. 18. T.Chhay viTüasßanCatiBhubec©keTskm<úCa kugRtaMgÉktþaenAkñúgebtugenAkñúgTisxøI nigTisEvgEdlbNþalBIbnÞúkKμanlMnwg (unbalanced loading) RtUv)anTTYledaykardak;bEnßmkMlaMgsgát;esμIEdlbNþalBIbnÞúklMnwgeTAelIkugRtaMgbegáag enAkñúgebtugEdlbgáeLIgedaym:Um:g;Bt;begáag M S nig M L EdlekItBI unbalanced load Ww − Wbal . kugRtaMgebtugenAsrésxagelI nigsrésxageRkamkñúgTisnImYy²RtUv)aneGaydUcxageRkam³ TisxøI PS M S c ft =− − (9.15a) bh IL P M c fb = − S + S (9.15b) bh IL TisEvg PL M L c ft =− − (9.16a) bh IL P M c fb = − L + L (9.16b) bh IL enAkñúgsmIkarTaMgenH GkSr t tMNageGaysrésxagelIbMputrbs;kMral ehIyGkSr b tMNageGay srésxageRkambMputrbs;ebtug/ c = h / 2 / TTwg b = 12in. ehIy PS total PS = L ehIy P total PL = L S CakMlaMgeRbkugRtaMgÉktþa. emKuNm:Um:g;bnÞúkesvakmμ (service-load moment coefficient) sMrab;kM Nt; M S nig M L GacTTYl)anBI chart enAkñúgrUbTI 9>10 sMrab;lkçxNÐRBMEdnTaMgGs;. eKmanem KuNm:Um:g;Bt;sMrab;m:Um:g;Bt;viC¢man nigGviC¢manGtibrma Edl βx2 nig βx'2 GnuvtþeTAelI + M nig − M enAelIElVgxøI Lx erogKña. dUcKña βy2 nig βy'2 GnuvtþeTAelIm:Um:g;Bt;viC¢man nigGviC¢manGtibrmaenA elIElVgEvg Ly erogKña. tamrebobdUcKña chart enAkñúgrUbTI 9>11 pþl;nUvviFIy:asrh½skñúgkarkMNt; ultimate bending moment coefficient enAkñúg plate ebtugeRbkugRtaMgBIrTisCab;. 9.5.ersIusþg;begáagrbs;kMraleRbkugRtaMg Flexural Strength of Prestressed Plates 9.5.1. m:Um:g;KNna M uDesign Moments M u eKkMNt; design moment sMrab; bonded member eRbkugRtaMgsþaTicminkMNt;edaybnSMrvag m:Um:g; M u EdlbNþalBIbnÞúkemKuNefrbUknwgbnÞúkemKuNGefr CamYynwg secondary moment M s Two-Way Prestressed Concrete Floor Systems 570
  19. 19. Department of Civil Engineering NPIC EdlekItmanenAkñúgeRKagedaysar tendon. m:Um:g;em (primary moment) M1 nig secondary moment M s k¾manerobrab;enAkñúgviFIbnÞúklMnwgEdr. dUcenH sMrab;tMélbnÞúkesvakmμ eKcaM)ac;BicarNa Etm:Um:g; net load M net enAkñúgkarKNnam:Um:g;bgáb;cugemKuN xN³EdleKRtUvKit Wbal sMrab;karviPaKersIusþg; begáag. m:Um:g;bgáb;cug M sMrab;karEbgEckm:Um:g; u RbsinebI M1 = Pee = Fe Ca primary moment/ M net Cam:Um:g;lMnwgEdlbNþalmkBI Wbal / M S = M bal − M 1 Ca secondary moment/ ehIy M u Cam:Um:g;bgáb;cugemKuNEdlbNþalBIbnÞúkemKuN Wu enaHy:agehacNas;k¾ design ultimate moment Mu = M u − Ms (9.17) ehIyersIusþg;m:Um:g;EdlGacekItmanKW Mu Mn = (9.18) φ eKGnuvtþkarEbgEckm:Um:g;eLIgvijCa enlastic EdlbNþalBIPaBCab;eTAelIersIusþg;m:Um:g;EdlGacekIt man M n enARtg;TMreTAkan;ersIusþg;m:Um:g;tMrUvkar M n enAkNþalElVg. enAeBlEdleKdak; bonded reinforcement enARtg;TMr ehIyEdkminrgeRbkugRtaMgGb,brma RtUv)andak;edayGnuelamtamsmIkar 9.19 nig 9.20 enaHm:Um:g;GviC¢manEdlKNnaedayRTwsþIeGLasÞic sMrab;kardak;bnÞúksnμt;GacnwgekIneLIg b¤fycuHedayPaKryEdlminFMCagPaKryEdleGayedayem KuNEbgEckm:Um:g;eLIgvij inelastic Edlerobrab;enAkñúgCMBUk 4 nigCMBUk 6. eKKYreRbIm:Um:g;GviC¢manEkERb (modified negative moment) sMrab;KNnam:Um:g;vIC¢manenARtg; muxkat;enAkñúgElVg sMrab;kardak;bnÞúkdUcKña. eKGaceFVIkarEbgEckm:Um:g;eLIgvij inelastic sMrab;m:Um:g; GviC¢manEtenAeBlNaEdlm:Um:g;enARtg;muxkat;enaHRtUv)ankat;bnßy ehIyvaRtUv)aneKsikSaKNna edaymineGay ω p b¤ ω p + (d / d p )(ω / ω ') FMCag 0.24β1 eT ehIymüa:gvijeTotemKuNEbgEckm:Um:g; eLIgvijminRtUvFMCag 1000ε t eT. ]TahrN_ 9>2 bgðajy:aglMGitBIviFIsaRsþviPaKeRKagsmmUlTaMgsMrab;lkçxNÐ service load nig ultimate load nigkarEbgEckm:Um:g;eLIgvij enealsic EdlbNþalBIPaBCab;EdlRtUv)aneRbIenAkñúg karviPaKersIusþg;. RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 571
  20. 20. T.Chhay viTüasßanCatiBhubec©keTskm<úCa Two-Way Prestressed Concrete Floor Systems 572
  21. 21. Department of Civil Engineering NPIC RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 573
  22. 22. T.Chhay viTüasßanCatiBhubec©keTskm<úCa 9.6. Banding of Prestressing Tendons and Limiting Concrete Stresses 9.6.1. karBRgayEdkeRbkugRtaMg Distribution of Prestressing Tendons eKsnμt;fakMral plate nImYy²manTMrCab;tambeNþayTTwgG½kSssr. karsnμt;RtUv)aneFVIeLIg dUckarerobrab;BIelIkmuxfakMralxNÐeFVIkardUckMralFñwmBIrEkgKñaEdlTTwgrbs;vaesμInwgTTwgrbs;kMral EdlRtUv)anRTtambeNþayG½kSssr. dUcenH eKKitfabnÞúk 100% EdlRtUveFVIeGaymanlMnwgRtUv)an RTedaykMralFñwmkñúgTisedABIrEkgKña. eKk¾dwgfakarEbgEckm:Um:g;minmanlkçN³esμItamTTwgrbs;kMral b:uEnþvaeRcInEtRbmUlpþúMenAelI cMerokelIssr. Cavi)ak eKminmanehtuplkñúgkarRbmUlpþúMPaKryy:ageRcInén tendon enAkñúgcMerok elIssreT dUckarkMNt;enAkñúgrUbTI 9>4 ehIyeKRtUvBRgay tendon EdlenAsl;enAkñúgcMerokkNþal ElVg. sMrab;ElVgCab; m:Um:g;BI65 eTA75% kñúgTisnImYy²RtUv)anRTedaycMerokssr xN³EdleKRtUv rkSaRkLaépÞsrub nigcMnYnrbs; tendon EdlTamTaredaym:Um:g;Gnuvtþn_srub. Two-Way Prestressed Concrete Floor Systems 574
  23. 23. Department of Civil Engineering NPIC TTwgrbs;knøHcMerokelIssresμInwgmYyPaKbYnénTMhMEdltUcCageKrbs;kMralxNÐ. cMerok kNþalElVgCa slab band EdlenAGmedaycMerokelIssrBIr. dUcenH karEbgEck b¤ banding rbs; EdkeRbkugRtaMgRtUveFVIeLIgeTAtamPaKryénkarEbgEckm:Um:g;rvagcMerokelIssr nigcMerokkNþal ElVg. Cavi)ak RbsinebI 70%énEdkeRbkugRtaMgRtUv)anRbmUlpþúMenAkñúgcMerokelIssr enaHeKrMBwgfa cMerokelIssrnwgRT 70%énm:Um:g;srub ehIycMerokkNþalElVgRTnUv 30%énm:Um:g;srubEdlenAsl;. rUbTI 9>12 bgðajBIkarEbgEckEdkeRbkugRtaMgenAkñúgTisBIrEkgKña. tameKalkarN_ENnaM TUeTA EdkeRbkugRtaMgkñúgcMerolelIssrRtUvmanKMlatesμInwg3 eTA4dgénkMras;kMralxNÐ ehIyKMlat Gtibrmarbs;kabeRbkugRtaMgenAkñúgcMerokkNþalElVgminRtUvFMCag 6dgénkMras;kMralxNÐeT. kug RtaMgsgát;mFümenAkúñgebtugkñúgTisnImYy²KYrmantMély:agticbMputesμInwg 125 psi(0.90MPa ) . RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 575
  24. 24. T.Chhay viTüasßanCatiBhubec©keTskm<úCa karGegát)anepÞógpÞat;tamry³karBiesaF plate eRbkugRtaMgbYndUcbgðajenAkñúgrUbTI 9>13 bgðajfakarERbRbYlénkarBRgay tendon eRbkugRtaMgEdlmanbrimaNdUcKñaminmanT§iBleTAelIPaB dabeT. Banding rbs;kabeRbkugRtaMgdUcbgðajenAkñúgEpñk (b) énrUb EdlmanEdkeRbkugRtaMg 65% eTA75% enAkñúgcMerokelIssr hak;manRbsiT§PaBCageK CaBiessbegáInlT§PaBepÞr shear-moment enARtg;muxkat;TMrssrrbs;kMralxNÐBIrTis. 9.6.2. kugRtaMgTajkMNt;rbs;ebtugeRkamlkçxNÐbnÞúkesvakmμ Limiting Concrete Tensile Stresses at Service Load 9.6.2.1. karBt;begáag Flexure ACI 318 Code kMNt;kugRtaMgTajkñúgebtugsMrab;Ggát;eRbkugRtaMgedIm,IRKb;RKgkarekItman sñamedaykarBt;begáag (flexural crack). xageRkamCatMélkugRtaMgGnuBaØatGtibrmaenAkñúgGgát;eRb kugRtaMgsMrab;tMbn;m:Um:g;epSg²³ !> RkLaépÞm:Um:g;GviC¢manCamYynwgkarbEnßmEdkminrgeRbkugRtaMg 6 f 'c psi(0.5 f 'c MPa) @> RkLaépÞm:Um:g;GviC¢manEdlKμankarbEnßmEdlminrgeRbkugRtaMg 0 #> RkLaépÞm:Um:g;viC¢manCamYynwgkarbEnßmEdkminrgeRbkugRtaMg 2 f 'c psi(0.166 f 'c MPa) $> RkLaépÞm:Um;g;viC¢manEdlKμankarbEnßmEdkminrgeRbkugRtaMg 0 %> kugRtaMgsgát;enAkñúgebtug ¬eRkamlkçxNÐCak;Elk/ 0.60 f 'c ¦ f c = 0.45 f 'c 9.6.2.2. EdkBRgwg Reinforcement RkLaépÞGb,brmarbs; bonded reinforcement edayelIkElgGIVEdlTamTaredaysmIkar 9.20 xageRkam KW As = 0.004 A (9.19a) Edl A CaRkLaépÞrbs;Epñkénmuxkat;cenøaHépÞrgkarTajedaykarBt;begáagCamYynwgTIRbCMuTMgn;rbs; gross section. sMrab;RkLaépÞm:Um:g;viC¢manEdlkugRtaMgTajenAkñúgebtugeRkamlkçxNÐbnÞúkesvakmμFM Cag 2 f 'c psi(0.166 f 'c MPa) enaHeKKNnaRkLaépÞGb,brmarbs; bonded reinforcement BI Nc As = (9.19b) 0.5 f y Two-Way Prestressed Concrete Floor Systems 576
  25. 25. Department of Civil Engineering NPIC Edl N c CakugRtaMgTajenAkñúgebtugEdlbNþalBIplbUkbnÞúkefr nigbnÞúkGefrKμanemKuN ehIy f y = 60,000 psi (414MPa ) . sMrab;RkLaépÞm:Um:g;GviC¢manenARtg;ssrTMr RkLaépÞGb,brmarbs; bonded reinforcement enAkñúgTisnImYy²RtUv)ankMNt;BI As = 0.00075hL (9.20) Edl RbEvgElVgenAkñúgTisRsbeTAnwgEdkBRgwgEdlRtUv)ankMNt; L= h = kMras;kMralxNÐ eKRtUvBRgayEdkBRgwgEdlTTYl)anBIsmIkar 9.20 kñúg slab band width cenøaHExSEdlmanRbEvg 1.5h BIxageRkAépÞQmrbs;ssr. y:agehacNas;eKRtUvdak; bar b¤ wire 4 kñúgTisTaMgBIr. RbEvgGb,brmarbs; bonded reinforcement enAkñúgRkLaépÞviC¢manKYresμInwgmYyPaKbIén clear span ehIyvaRtUv)aneKdak;enARtg;kNþalRkLaépÞm:Um:g;viC¢man. RbEvgGviC¢manrbs; bonded reinforcement enAkñúgRkLaépÞGviC¢manKYrRtUv)andak;bgðÚt 1/6 én clear span enAelIRCugnImYy²rbs; TMr ehIyeKdak;vaenAsrésxagelI. kugRtaMg f ps enAkñúgEdkeRbkugRtaMgeRkam nominal strength EdlTamTareday ACI 318 Code RtUv)anpþl;eGaydUcxageRkam sMrab; Bonded Tendon ⎛ γp ⎡ f pu ⎤⎞ f ps = f pu ⎜1 − ⎜ β1 ⎢ρ p + d (ω − ω ')⎥ ⎟ (9.21) ⎝ ⎢ ⎣ f 'c d p ⎥⎟ ⎦⎠ Edl ω ' = ρ ' = f y / f 'c nig γ p = 0.40 sMrab; f py / f pu ≥ 0.85 = 0.28 sMrab; f py / f pu ≥ 0.90 RbsinebIeKKitEdkrgkarsgát; enaHtY [ρ p f pu / f 'c +(d / d p )(ω − ω ')] enAkñúgsmIkar 9.21 RtUv)aneK ykmineGaytUcCag 0.17/ ehIy d ' minRtUvFMCag 0.15d p . sMrab; Unbonded Tendon EdlmanpleFobElVgelIkMras;kMralxNÐ ≤ 35 f 'c f ps = f pe + 10,000 + (9.22) 100 ρ p Edl f ps ≤ f py ≤ f pe + 60,000 sMrab; Unbonded Tendon EdlmanpleFobElVgelIkMras;kMralxNÐ > 35 f 'c f ps = f pe + 10,000 + (9.23) 300 ρ p Edl f ps ≤ f py ≤ f pe + 30,000 RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 577
  26. 26. T.Chhay viTüasßanCatiBhubec©keTskm<úCa 9.6.2.3. kMlaMgkat; Shear muxkat;TMrssrenAkñúg flat plate: nominal shear strength Edlpþl;edayebtugenARtg;TIRbsBVrbs; ssrénkMralebtugeRbkugRtaMgRtUv)aneGayeday Vc = (β ρ f 'c + 0.3 f c )bo d + V p (9.24a) b¤ nominal unit shearing strength KW Vp vc = β ρ f 'c + 0.3 f c + (9.24b) bo d Edl bo = brimaRtrbs;muxkat;rgkMlaMgkat;eRKaHfñak;enAcMgay d / 2 BIépÞrbs;TMr f c = tMélmFümrbs;kugRtaMgrgkarsgát;RbsiT§PaBenAkñúgebtugEdlbNþalBIbnÞúkGnuvtþn_xag eRkAsMrab;TisBIrEkgKñaEdlKNnaenARtg;TIRbCMuTMgn;rbs;muxkat;eRkaykMhatbg;eRbkug RtaMg ¬enAkñúg ACI Code eKeRbI f pc ¦ V p = bgÁúMbBaÄrénkMlaMgeRbkugRtaMgRbsiT§PaBTaMgGs;Edlkat;tammuxkat;eRKaHfñak; β ρ = tMéltUcCageKkñúgcMeNam 3.5 nig (α s d / bo + 1.5) Edl α s esμInwg 40 sMrab;ssrxag kñúg nig 30 sMrab;ssrxag nig 20 sMrab;ssrkac;RCug. enAkñúgkMralxNÐEdlmankarBRgaykabeRbkugRtaMg eKminKittY V p eT ebImindUecñaHeTvakøayCacMa)ac; kñúgkareRbIragFrNImaRtkMeNagkabeRbkugRtaMgbRBa©asenAkñúgkarKNnaedIm,I)a:n;RbmaNkMlaMgkat; EdlRTeday tendon Edlkat;tammuxkat;eRKaHfñak;. eyagtam ACI 318 Code/ KμancMENkNarbs; muxkat;ssrKYrenAEk,rcugEdlminCab;FMCagbYndgkMras;kMralxNÐ/ f 'c enAkñúgsmIkar 9.24 minKYrFM Cag 5,000 psi ehIy f c enAkñúgTisnImYy²minRtUvtUcCag 125 psi b¤FMCag 500 psi eT. RbsinebIeKminGacbMeBjlkçxNÐTaMgenHeT eKKYryktMél Vc CatMélEdltUcCageKkñúgcMeNam smIkarxageRkam³ ⎛ 4 ⎞ (i) Vc = ⎜ 2 + ⎜ ⎟ f 'c bo d (9.25a) ⎝ βc ⎟ ⎠ ⎛α d ⎞ (ii) Vc = ⎜ s + 2 ⎟ f 'c bo d ⎜ b ⎟ (9.25b) ⎝ o ⎠ (iii) Vc = 4 f 'c bo d (6.25c) Edl β c = pleFobRCugEvgelIRCugxøIrbs;ssr b¤RkLaépÞbnÞúkRbmUlpþúM. Two-Way Prestressed Concrete Floor Systems 578
  27. 27. Department of Civil Engineering NPIC smIkar 9.25(a) nig (b) CalT§plrbs;karBiesaFEdlbgðajfa enAeBlpleFob bo / d ekIneLIg enaH nominal shear strength Vc EdlGacekItmanfycuH dUcenHenAkñúgsßanPaBEbbenH smIkar 9.25(c) nwgminlubedaysarvakøayCaKμansuvtßiPaB. TMrcugCab; (Continuous Edge Support): sMrab;bnÞúkBRgay nigTMrcugCab;dUcCaFñwm nigCBa¢aMg/ Rbsin ebIkMlaMgeRbkugRtaMgRbsiT§PaBmintUcCag 40%énkugRtaMgTajrbs;EdkBRgwg enaHkugRtaMgkat;GnuBaØat GtibrmaKW ⎡ V d⎤ Vc = ⎢0.60 f 'c + 700 u ⎥bw d p ≥ 2 f 'c bw d ⎣ Mu ⎦ < 5 f 'c bw d ¬xñat US¦ (9.26) ⎡ f 'c V d⎤ Vc = ⎢ + 5 u ⎥bw d p ≥ 0.166 f 'c bw d ⎢ 20 ⎣ Mu ⎥ ⎦ < 0.415 f 'c bw d ¬xñat SI¦ Edl bw RtUv)anykCaTTwgcMerok ehIy Vu d / M u enAcMgay d p / 2 BIépÞrbs;TMr/ d p ≥ 0.80h . tMél f 'c enAkñúgRKb;smIkarxagelITaMgGs;RtUvKuNnwgemKuN λ = 1.0 sMrab;ebtugTMgn;Fmμta/ λ = 0.85 sMrab; sand-lightweight concrete nig λ = 0.75 sMrab; all-lightweight concrete. emKuNkMlaMgkat; (Shear Force Coefficients): eKGackMNt;tMélRbhak;RbEhlrbs;kMlaMgkat; GtibrmaenARtg;cugrbs;kMralxNÐBIrTisEdlRTbnÞúkBRgayesμI ehIyvaRtUv)anRTtambeNþayRbEvg brimaRtrbs;vadUcxageRkam³ 1 V = wLS 3 ¬RCugxøI¦ (9.27a) V = kwLS / (2k + 1) ¬RCugEvg¦ (9.27b) Edl k CapleFobElVgEvg LL elIElVgxøI LS . eKGaceRbItMéldUcKñasMrab;kMralEdlRtUv)anbgáb; b¤ Cab;tambeNþayRCugTaMgbYn. sMrab;krNIdéTeTot eKRtUvEktMrUvkarEbgEckkMlaMgkat; nigkarEbgEck kugRtaMgEdlbNþalBIGVIEdlsUveRKaHfñak;edayQrelIeKalkarN_kMlaMgkat;enAelIRCugCab;FMCagkMlaMg kat;enAelIRCugsamBaØbnþicbnþÜc. ACI Code GnuBaØateGaybegáInkMlaMgkat; 15%enARtg;TMrCab;xagkñúgTImYysMrab; one-way action. RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 579
  28. 28. T.Chhay viTüasßanCatiBhubec©keTskm<úCa 9.7. Load-Balancing Design of a Single-Panel Two-way Floor Slab ]TahrN_ 9>1³ Two-way single-panel prestressed warehouse lift slab 20 ft × 24 ft (6.10m × 7.32m ) manbøg;dUc bgðajenAkñúgrUbTI 9>14. vaRtUv)anRTenAelICBa¢aMgdæTaMgbYnRCug edayminKit rotational restraint enA Rtg;RBMEdnTaMgenH b:uEnþkac;RCugRtUv)anTb;nwgkarrmYl (torsional restraint) . kMralxNÐRtUvRTnUv superimposed service dead load 15 psf (0.72kPa ) bEnßmBIelIbnÞúkpÞal;rbs;va nigRTnUv service live load 75 psf (3.59kPa ) . eKminGnuBaØaeGaymanPaBdabeRkamGMeBI full dead load. sikSaKNnakMralxNÐCa post-tensioned nonbonded prestressed two-way floor edayeRbI kabeRbkugRtaMg 7-wire 270-K Ggát;p©it 1 / 2in.(12.7mm) . eKeGayTinñn½ydUcxageRkam³ f 'c = 5,000 psi (34.5MPa ) ebtugTMgn;Fmμta f 'ci = 3,750 psi(25.9MPa ) fc GtibrmakñúgTis E-W EdlbNþalBI net prestress eRkaykMhatbg; = 200 psi Two-Way Prestressed Concrete Floor Systems 580
  29. 29. Department of Civil Engineering NPIC fc GtibrmakñúgTis N-S EdlbNþalBI net prestress eRkaykMhatbg;minRtUvFMCag 350 psi ¬ACI GnuBaØatrhUtdl; 500 psi ¦ f c GtibrmaEdlbNþalBIkugRtaMgpÁÜb (combined stress) = 0.45 f 'c Ec = 57,000 f 'c = 4.03 ⋅ 106 psi (27.8 ⋅ 106 MPa ) f ps ≤ 0.70 f pu = 189,000 psi(1,303MPa ) dUckarTamTareday ACI Code f py = 240,000 psi(1,655MPa ) f pe = 159,000 psi(1,096MPa ) ( E ps = 29 ⋅ 10 6 psi 200 ⋅ 103 MPa ) f y = 60,000 psi (414MPa ) ( E s = 29 ⋅ 10 6 psi 200 ⋅ 103 MPa ) dMeNaHRsay³ − 1 = 2.0in.(51mm ) 6 eS = e L = 2 eRCIserIskMras;kMralxNÐsakl,gedayQrelIpleFobElVgelIkMras; (span-to-depth ratio) ≅ 45 h= (20 + 24) × 12 × 1 = 5.87in. 2 45 dUcenH sakl,gkMras;kMralxNÐ 6in.(153mm) edaysnμt;Ggát;p©itbMBg; (duct) ≅ 0.5in. ehIykMBs; RbsiT§PaB d p = 6.0 − (0.5 / 2 + 3 4 ) = 5.0in.(127mm) . bnÞúklMnwg (Balancing Load) × 150 = 90 psf (4.31kPa ) 6 WD = 15 psf + 12 edaysar balancing load RtUv)antMrUvsMrab;PaBdab b¤ camber EdlbNþalBIbnÞúkefresμIsUnü enaH snμt; Wbal = WD = 90 psf (4.31kPa) . ehIyedaysar f c EdlbNþalBIkMlaMgeRbkugRtaMg = 200 psi ¬smμtikmμ¦ snμt;vaCakugRtaMgenAkñúgTis E-W. bnÞab;mkkMlaMgeRbkugRtaMgRbsiT§PaBenAkñúgTis E-W KW PL = 200 × 6 × 12 = 14,400lb kñúgmYycMerok nigBIsmIkar 9.13b eyIg)an 8 ×14,400 × 2 ≅ 33 psf (1.58kPa ) 8 PL eL Wbal (L ) = = L2 L (24)2 ×12 Uplift EdlRtUvpþl;eday tendon enAkñúgTisxøI ¬bnÞúkTMngRtUvRTedayElVgenAelITisxøI¦ køayCa Wbal (S ) = WD − Wbal (L ) = 90 − 33 = 57 psf (2.73kPa ) . BIsmIkar 9.13a Wbal (S ) L2 57 × (20)2 × 12 = 17,100lb / ft (249.7kN / m ) bnÞab;BIkMhatbg; S PS = = 8e S 8× 2 RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 581
  30. 30. T.Chhay viTüasßanCatiBhubec©keTskm<úCa kugRtaMgsgát;enAkñúgebtugeRkaykMhatbg;enAkñúgkabeRbkugRtaMgkñúgTis N-S KW PS 17,100 fc = = = 238 psi < 350 psi bh 12 × 6 EdlvabMeBjlkçxNÐ. dUcenH eRbIkabeRbkugRtaMg 7-wire 270-K Ggát;p©it 1/ 2in. EdlmankMlaMgeRb kugRtaMgRbsiT§PaB Pe = 159,000 × 0.153 = 24,327lb(108.2kN ) . KMlattMrUvkarenAkñúgTis N-S KW = 1.42 ft = 17in.(432mm ) 24,327 sS = 17,100 KMlattMrUvkarenAkñúgTis E-W KW = 1.69 ft ≅ 20in.(508mm ) 24,327 sL = 14,400 cMNaMfa KMlatTaMgBIrRtUvKñanwgKMlatEdl)anENnaM ¬3eTA 5dgénkMras;kMral¦. edIm,IkarBarkarEbkebtugenARtg;tMbn; anchorage enAmþúMCBa¢aMg bEnßmEdkFmμtaminrgeRbkugRtaMg 2#4 ¬12.7mm cMnYnBIr¦ tambeNþay anchorage line enAelIbrimaRtkMral. kugRtaMgbnÞúkesvakmμ (Service-load Stresses) bnÞúkGefresvakmμ WL = 75 psf (3.59kPa ) aspect ratio L 24 k= L = = 1.20 LS 20 BIrUbTI 9>10/ emKuNm:Um:g;sMrab;m:Um:g;kNþalElVgGtibrmaenAkñúgTisxøI nigTisEvgKW α N − S = 0.062 nig α E −W = 0.035 erogKña edaysnμt;fakac;RCugrbs;kMralxNÐBIrTisRtUv)anTb;nwgkarrmYl (torsionally restrained). eyIgsnμt;faRbEvgRbsiT§PaBtamTisxøI nigTisEvg LS = 19.5 ft nig LL = 23.5 ft m:Um:g;bnÞúkGefr (Live-load Moment) KW M S = 0.062 × 75 × (19.5)2 × 12 = 21,218in. − lb / ft nig M L = 0.035 × 75 × (23.5)2 × 12 = 17,396in. − lb / ft m:Um:g;niclPaBKW 12(6 )3 Is = = 216in.3 12 Two-Way Prestressed Concrete Floor Systems 582
  31. 31. Department of Civil Engineering NPIC kugRtaMgebtugEdlbNþalBIbnÞúkGefr³ kugRtaMgebtugEdlbNþalBIbnÞúkGefrenAkñúgTisxøUIKW M S c 21,218 × 3 f = = = 295 psi (2.03MPa ) Is 216 kugRtaMgebtugEdlbNþalBIbnÞúkGefrenAkñúgTisEvgKW M L c 17,396 × 3 f = = = 242 psi (1.67 MPa ) Is 216 kugRtaMgtamG½kSpÁÜb (combined axial stresses) EdlbNþalBIbnÞúklMnwg nigkugRtaMgBt;begáagpÁÜb (combined flexural stresses) EdlbNþalBIbnÞúkGefr ¬BIsmIkar 9.15 nig 9.16¦ enAkñúgTisxøI (N-S) køayCa = −238 − 295 = −533 psi (C )(3.68MPa ) PS M S c ft =− − bh Is nig f b = −238 + 295 = +57 psi (T ) ¬edayvamantMéltUc eKGacecal)an¦ ehIyenAkñúgTisEvg (E-W) f t = −200 − 242 = −442 psi (C )(3.05MPa ) nig f b = −200 + 242 = +42 psi (T ) ¬Gacecal)an¦ kugRtaMgsgát;GnuBaØat ACI KW f c = 0.45 × 5,000 = 2,250 psi EdlvamantMélFMCagkugRtaMgCak;Esþg dUcenH vabMeBjlkçxNÐ. CamYynwgkugRtaMgtUcTaMgenH eKGacEksMrYlkMras;kMralxNÐeGayesþIgCag 6in. kñúgkrNIEdlPaBdabedaysarbnÞúkGefrGacTTYl)an. cMNaMfa kMralxNÐbegáItPaBdab nig camber eRkamGMeBIbnÞúkGefrsUnüenAkñúg]TahrN_enH bNþalmkBIbnÞúklMnwg. RtYtBinitüPaBdab (Deflection Check)³ eyIgRtYtBinitüEtPaBdabedaysarbnÞúkGefrEtb:ueNÑaH. BIeKalkarN_emkanic eyIgman 5 ML2 Δ= 48 Ec I s I s = 216in.4 Ec = 4.03 ⋅10 6 psi 5 17,396(24 × 12)2 Δ E −W = = 0.17in. 48 4.03 ⋅10 6 × 216 5 21,218(20 × 12)2 Δ N −S = = 0.15in. 48 4.03 ⋅10 6 × 216 0.17 + 0.15 PaBdabkNþalElVgmFüm Δ= 2 = 0.16in.(4.1mm ) RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 583
  32. 32. T.Chhay viTüasßanCatiBhubec©keTskm<úCa PaBdabEdlGacTTYlyk)an = 360 = 20 ×12 = 0.67in.(17mm) >> 0.16in. LS 360 dUcenH eyIgGaceFVIkarKNnaCMuTIBIrCamYynwgkMras;kMralxNÐ 5.5in. kñúgkrNIEdlersIusþg;m:Um:g; nominal rbs;kMralmanlkçN³RKb;RKan;edIm,IRTbnÞúk. kñúgkrNIenH h = 5.5in. minmanlkçN³RKb; RKan;sMrab;ersIusþg;m:Um:g; nominal dUckarbgðajxageRkam. ersIusþg;m:Um:g; nominal Wu = 1.2 × 90 + 1.6 × 75 = 228 psf (11.0kPa ) dUcKña ElVgRbsiT§PaBtamTisxøI LS = 19.5 ft ElVgRbsiT§PaBtamTisEvg LL = 23.5 ft BIrUbTI 9>11 emKuNm:Um:g;sMrab;m:Um:g;emKuNGtibrmaKW α N − S = 0.072 nig α E −W = 0.038 enAkñúgTis N-S eyIgman M u = 0.072 × 228(19.5)2 × 12 = 74,906in. − lb / ft Mu 74,906 Mn = = = 83,229in. − lb / ft φ 0.9 cMNaMfa kMlaMgeRbkugRtaMgenAkñúgeRKOgbgÁúMenHmin)anbegáIt secondary moment M s edaysarvamin manPaBCab;enARtg;RBMEdnkMralxNÐ. eyIgman Aps = 0.153in.2 enAelI 1.42 ft BIG½kSeTAG½kS ¬Edl )anBIelIkmun¦ nig Aps / f = 0.153 /1.42 = 0.11in.2 / ftt . dUcKña kMlaMgeRbkugRtaMgRbsiT§PaB f pe = 159,000 psi . dUcenH kñúgkrNIEdl A ps EdleRbIFMCag Pe / initial A ps eKRtUvkat;bnßy f pe ; eyIgman 0.11 ρN −S = = 0.0018 12 × 5 20 × 12 pleFobElVgelIkMras;kMral = 6 = 40 BIsmIkar 9.23b f 'c f ps = f pe + 10,000 + ≤ f py ≤ f pe + 30,000 300 ρ p 5,000 f ps = 159,000 + 10,000 + = 178,259 psi 300 + 0.0018 < f py = 240,000 psi < f pe + 30,000 = 189,000 psi < f ps lImIt = 189,000 psi O.K. Two-Way Prestressed Concrete Floor Systems 584
  33. 33. Department of Civil Engineering NPIC A ps f ps 0.11× 178,259 a= = = 0.38in. 0.85 f 'c b 0.85 × 5,000 × 12 m:Um:g; nominal EdlGacman M n = Aps f ps ⎛ d − a ⎞ = 0.11×178,259⎛ 5 − 0.2 ⎞ ⎜ ⎝ 2⎠ ⎟ ⎜ ⎝ 38 ⎟ ⎠ = 94,316in. − lb / ft > M n tMrUvkar = 83,229in. − lb O.K. enAkñúgTis E-W eyIgman M u = 0.038 × 228(23.5)2 × 12 = 57,417in. − lb / ft Mu 57,417 Mn = = = 63,797in. − lb / ft φ 0.9 A ps = 0.153in.2 kñúg 1.69 ft. EdlKitBIG½kSeTAG½kS ¬BIelIkmun¦ 0.153 A ps / ft = = 0.09in.2 / ft 1.69 0.09 ρ E −W = = 0.0015 12 × 5 5,000 f ps = 159,000 + 10,000 + = 180,111 psi O.K. 300 × 0.0015 0.09 × 180,111 a= = 0.32in. 0.85 × 5,000 × 12 ⎛ 0.32 ⎞ m:Um:g; nominal EdlGacman = 0.09 × 180,111⎜ 5 − ⎝ 2 ⎠ ⎟ = 78,456in. − lb / ft > M n tMrUvkar = 63,797in. − lb / ft O.K. (29.1kN .m / m > 23.6kN .m / m ) ersIusþg;kMlaMgkat; BIelIkmun/ aspect ratio k = 1.2 nigBIsmIkar 9.27 1 1 Vu = wu LS = × 228 × 19.5 = 1482lb / ft (N-S) 3 3 kw L Vu = u S (E-W) 2k + 1 = 1,569lb / ft (22.9kN / m ) 19.5 = 1.2 × 228 × 2 × 1.2 + 1 BIsmIkar 9.26 ⎛ V d⎞ 2 f 'c bw d p ≤ Vc = ⎜ 0.6 f 'c + 700 u ⎟bw d p ≤ 5 f 'c bw d p ⎜ ⎝ Mu ⎟ ⎠ eKman 700(Vu d ) / M u = 0 enARtg;RBMEdnén single-panel wall-support slab enAkñúg]TahrN_enH. enAkñúgkrNIEbbenH Vc = 0.6 5,000 × 12 × 5 = 2,546lb / ft (37.2kN / m ) >> 1,569lb / ft RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 585
  34. 34. T.Chhay viTüasßanCatiBhubec©keTskm<úCa EdlvabMeBjlkçxNÐ. dUcenH TTYlykkarsikSaKNnaenH h = 6in.(152mm ) d p = 5in.(127mm ) eRbIkabeRbkugRtaMg 7-wire 270-K Ggát;p©it 1/ 2in. EdlmanKMlat 17in.(432mm) KitBIG½kSeTAG½kS kñúgTis N-S nig 20in.(508mm) G½kSeTAG½kS kñúgTis E-W. dUcKña eRbIEdk 2#4 ¬Ggát;p©it 12.7mm ¦ tambeNþay anchorage zone EdlB½T§CMuvijbrimaRtkMralTaMgGs;. 9.8. RbB½n§kMralmYyTis One-Way Slab Systems kMralxNÐebtugeRbkugRtaMgmYyTiseFVIkarRsedogKñaeTAnwgFñwmedayminKitfavaCakMralTMr samBaØ b¤kMralTMrCab;KñaeRcIneT. dUcenH eKsikSaKNnakMralmYyTisCaFñwmEdlmanTTwg 12in. . eK dak;kabeRbkugRtaMgemenAkñúgTisénbeNþayrbs;kMral Edltamsn§wgtamElVgCab;. pleFobElVgelI TTwgrbs; slab band RtUvman tMélFMCag 2 edIm,IeGayeKKitkMralxNÐCakMralxNÐmYyTis. eyIgGaceRbIdMeNIrkarsikSaKNna nigkarsikSaviPaK nigeRbI]TahrN_enAkñúgCMBUkTI 6 sMrab; karsikSaviPaK nigkarsikSaKNnaRbB½n§kMralxNÐeRbkugRtaMgmYyTisCab;. 9.9. karepÞr Shear-Moment eTAssrEdlRT Flat Plate Shear-Moment Transfer to Column Supporting Flat Plates 9.9.1. ersIusþg;kMlaMgkat; Shear Strength kMlaMgkat;rbs; plate nigkMralxNÐBIrTisKWCa three-dimensional stress problem. bøg;Edl )ak;edaykMlaMgkat;eRKaHfñak;RbRBwtþtambrimaRtrbs;RkLaépÞrgbnÞúk nigmanTItaMgenARtg;cMgayEdl pþl;eGayedaybrimaRtkMlaMgkat;Gb,brma bo . edayEp¥kelIkarepÞógpÞat;tamkarBiesaF nigkarviPaK CaeRcIn bøg;kMlaMgkat;minKYrenAEk,rcMgay d / 2 BIRkLaépÞRbtikmμ b¤RkLaépÞbnÞúkRbmUlpþúM. RbsinebIeKmindak;EdkBRgwgkMlaMgkat;Biess ersIusþg;kMlaMgkat; nominal Vc dUckarTamTar eday ACI RtUv)ankMNt;enAkñúgsmIkar 9.24, 9.25 nig 9.26. eKGaceRbIsmIkar 9.27 sMrab;kMNt;tMél Rbhak;RbEhlrbs;emKuNsMrab;KNnakMlaMgkat;emKuNxageRkA Vu enAkñúgkMralxNÐCab;BIrTisEdl brimaRtrbs;manTMrB½T§CMuvij. Two-Way Prestressed Concrete Floor Systems 586
  35. 35. Department of Civil Engineering NPIC 9.9.2. Shear-Moment Transfer m:Um:g;KμanlMnwg (unbalanced moment) enARtg;épÞssrEdlCaTMrrbs;kMralminmanFñwmCakrNI mYyénkarsikSaKNnaEdleRKaHfñak;CageKenAkñúgkarkMNt;smamaRtmuxkat; flat plate b¤ flat slab. edIm,IFanaPaBRKb;RKan;rbs;ersIusþg;kMlaMgkat; eKTamTareGaymanepÞrm:Um:g;eTAssredaykarBt;begáag Edlkat;tambrimaRtrbs;ssr nigedaykugRtaMgkat;cakp©it EdlRbEhl 60%RtUv)anepÞrdaykarBt; begáag nig 40%RtUv)anepÞredaykMlaMgkat;. cMENk γν énm:Um:g;EdlepÞredaycMNakp©iténkugRtaMgkMlaMgkat;fycuH enAeBlEdlTTwgrbs; épÞénmuxkat;eRKaHfñak;EdlTb;Tl;m:Um:g;ekIneLIg 1 γv = 1− (9.28) 2 b1 1+ 3 b2 Edl b2 = c2 + d CaTTwgénépÞrbs;muxkat;eRKaHfñak;EdlTb;Tl;m:Um:g; ehIy b1 = c1 + d CaTTwgénépÞ EdlEkgeTAnwg b2 . cMENkEdlenAsl; γ f énm:Um:g;KμanlMnwgEdlepÞredaykarBt;begáag nigEdlGMeBIelITTwgkMral xNÐRbsiT§PaBcenøaHExSEdlesμInwg 1.5 dgénkMras;kMralsrub h enAelIRCugTaMgBIrrbs;ssr. 1 γf = = 1− γv (9.29) 2 b1 1+ 3 b2 sMrab;ssrxageRkA b1 = c1 + d / 2 . tMélrbs; γ f GacekIneLIgrhUtdl; 1.0 RbsinebI Vu tUcCag 0.75φVc . enARtg;TMrxagkñúg eKGacbegáIn γ f 25% RbsinebI Vu ≤ 0.4φVc nig ρ ≤ 0.375 ρ b . karEbgEckkugRtaMgkMlaMgkat;CMviujEKmssrRtUv)anbgðajenAkñúgrUbTI 9>15. vaERbRbYlCa lkçN³bnÞat;CMuvijTIRbCMuTMgn;rbs;muxkat;eRKaHfñak;. kMlaMgkat;emKuN Vu nigm:Um:g;emKuNKμanlMnwg M u EdlRtUv)aneKsnμt;favamanGMeBIenARtg;épÞssrRtuv)anepÞreTAkat;G½kSTIRbCMuTMgn; c − c rbs;mux kat;eRKaHfñak;. dUcenH G½kSRtUv)ankMNt;TItaMgedayTTYl)anBIédXñas;kMlaMgkat; g ¬cMgayBIépÞssr eTAbøg;G½kSTIRbCMuTMgn;¦ énmuxkat;eRKaHfñak; c − c sMrab;karepÞr shear-moment. sMrab;karkMNt;kugRtaMgkMlaMgkat;GtibrmaEdlRtUvRTRTg;eday plate enAkñúgtMbn;RCugssr/ ACI Code TamTarkareRbIR)as; full nominal moment strength M n RtUv)anpþl;eGayedaycMerok ssrenAkñúgsmIkar 9.30 edIm,IeFVItamdUcCam:Um:g;KμanlMnwgEdlRtUv)anKuNedayemKuNcMENkepÞr (tran- sfer fraction factor) γ v . m:Um:g;KμanlMnwg M n ≥ M ue / φ RtUv)anpÁúMeLIgedayBIrEpñk³ m:Um:g;cugkMral GviC¢man (negative end panel moment) M ne = M e / φ enARtg;épÞrbs;ssr nigm:Um:g; (Vu / φ )g Edl RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 587
  36. 36. T.Chhay viTüasßanCatiBhubec©keTskm<úCa Two-Way Prestressed Concrete Floor Systems 588
  37. 37. Department of Civil Engineering NPIC bNþalBIkMlaMgkat;brimaRtemKuNcakp©it (eccentric factored perimetric shear factor) Vu . tMél kMNt;rbs;kugRtaMgkat;RtUv)ankMNt;edaysmIkarxageRkam³ vu ( AB ) Vu γ v M ue c AB = + (9.30a) φ φAc φJ c vu (CD ) Vu γ v M ue cCD = − (9.30b) φ φAc φJ c EdlersIusþg;kMlaMgkat; nominal KW vu Vn = (9.30c) φ Edl RkLaépÞrbs;ebtugénmuxkat;eRKaHfñak;snμt; Ac = = 2d (c1 + c2 + 2d ) sMrab;ssrxagkñúg J c = lkçN³énmuxkat;eRKaHfñak;snμt;EdlRsedogKñanwgm:Um:g;niclPaBb:UElrénmuxkat; tMél J c sMrab;ssrxagkúñgKW Jc = 1 (c + d / 2)(d )3 + 2(d ) (c 3 + c 3 )+ (c + d )dc 2 AB CD 2 AB 6 3 BIeKalkarN_eKalénemkanicsMPar³ ersIusþg;kMlaMgkat;KW Vu Mc vu = +γv Ac J EdltYTIBIrenAGgÁxagsþaMCakugRtaMgkMlaMgkat;EdlekItBIm:Um:g;rmYlenARtg;épÞssr. RbsinebIersIusþg;m:Um:g; nominal M n éntMbn;epÞrm:Um:g;-kMlaMgkat;eRkayBIkarKNnaénEdk BRgwgmantMélFMCag M ue / φ enaHeKKYreRbI M n enAkñúgsmIkar 9.30a nig b CMnYseGay M ue / φ . enA eBlEdlersIusþg;m:Um:g; M n = M ne + (Vu / φ )g mankarekIneLIgedaysarkareRbIEdkrgkarBt;begáag eRcInCagtMrUvkarsMrab;Tb;Tl;nwg M ue / φ enaHPaBrwgRkajrbs;kMralmankarekIneLIg dUcenHkarekIn eLIgkugRtaMgkMlaMgkat;EdlepÞr vu EdlKNnaBIsmIkar 9.30a nig b sMrab;begáIt full moment transfer. dUcenH eKENnaM eGayrkSa design moment M ue EdlmantMélEk,rnwgtMélm:Um:g;emKuN M ue Rbsin ebIeKcg;eCosvagkarekIneLIgkugRtaMgkMlaMgkat;EdlbNþalBIkarepÞrm:Um:g;bEnßm nigkarBarkarekIneLIg bEnßmeTotén kMras;kMralxNÐ. ]TahrN_ 9>2 bgðajBIviFIsaRsþsMrab;KNnakugRtaMgkMlaMgkat;brimaRtkMNt;enAkñúg plate Rtg; tMbn;EKmssr. kñúgkrNIssrxagkñúg kugRtaMgkMlaMgkat;brimaRt vu GacmantMélFMCag kugRtaMgkMlaMgkat;Edl RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 589
  38. 38. T.Chhay viTüasßanCatiBhubec©keTskm<úCa KNnaedaysmIkar 9.30a nig b enAeBlEdlElVgEdlenAEk,rminmanTMhMesμIKña b¤minrgbnÞúkesμIKña. sM rab;muxkat;kMralxNÐEdlCab;Tak;Tgnwgm:Um:g;emKuNenAkñúgssr nigCBa¢aMg/ ACI Code kMNt;faGgát; EdlCaTMrdUcCassr b¤CBa¢aMgRtUvTb;Tl;nwgm:Um:g;KμanlMnwg [ M ' = 0.07 (wnd + 0.5wnl )l2ln 2 − w'nd l '2 (l 'n )2 ] (9.31) Edl w'nd / l '2 nig l'n sMedAdl;ElVgxøI. dUcenH eKRtUvEfmtYbEnßmeTAkñúgsmIkar 9.30a b¤ b Vu γ v M u c AB γ v M ' c vu = + + (9.32) Ac Jc J 'c Edl J 'c Cam:Um:g;niclPaBb:UElrEdlmanRkLaépÞm:Um:g;EdlRtUv)anykkñúgTisedAEkgnwgTisEdleRbI sMrab; J c . 9.9.3. tMrUvkarPaBdabsMrab;kMras;Gb,brma³ viFIminpÞal; Deflection Requirements for Minimum Thickness: An Indirect Approach sMrab;kar)a:n;RbmaNkMras;kMralxNÐBIrTisdMbUg eKcaM)ac;eRbInUveKalkarN_ENnaMsMrab;tMélRb hak;RbEhledIm,IeRCIserIskMras;sakl,gelOn nigmanRbsiT§PaB. eKrMBwgfapleFobElVgelIkMras; kMralxNÐsMrab;kMralxNÐebtugeRbkugRtaMgnwgmantMélFMCagpleFobElVgelIkrM as;kMralxNÐsMrab;kM ralxNÐebtugGarem: RbsinebIminmankar)at;bg;KuNsm,tþ×énGgát;eRbkugRtaMg. eKniymeRbI service live load CaplbUksrubénbnÞúkefr nigbnÞúkGefredIm,IkMNt;PaBdab. eKeRbIbnÞúklMnwgEdl)anBIbgÁúMTTwgrbs;kMlaMgeRbkugRtaMgedIm,IeFVIeGayPaBdabEdlekItBI dead load NWt b¤begáIteGayman camber RbsinebIbnÞúkGefrmantMélFMEmnETn. eKeRbIeKalkarN_ENnaMsMrab; tMélRbhak;RbEhlénpleFobElVgelIkMras;kMralxNÐ 16 eTA 25 sMrab; solid cantilever slabs nig 40 eTA 50 sMrab;kMralxNÐCab;BIrTis. sMrab; waffle slab eKENnaMeGayeRbItMél 35 eTA 40. sMrab; ElVgTMrsamBaØ nigsMrab; single-T nig double-T eRbI 90%éntMélTaMgenHsMrab;karsakl,gelIkTImYy. ACI tMrUvfapleFobElVgelIPaBdabGb,brmaRtUv)ankMNt;y:agtwgrwgEdlGaRs½ynwgRbePT énkardak;bnÞúk niglkçxNÐénkareRbIR)as;. karkMNt;enHminRtUv)aneRbIsMrab;karkarBarsñameRbHénkar- garbegðIyenAelIBIdan nigsñameRbHelI partition nigkardk;TwkenAelIdMbUl. taragTI 9>1 eGaynUvtMél ENnaMénpleFobElVgelIPaBdabsMrab;karRKb;RKgPaBdab. karkMNt;PaBdab b¤ camber rbs; plate nigkMralxNÐBIrTisebtugeRbkugRtaMg nigebtugeRbkug RtaMgEdlmanlkçN³suRkitCagRtUv)anbgðajenAkñúgcMnuc 9.12. viFIenHeRbIPaBrwgRkajénGgát;EdlRb- sBVKñaedayeRbIviFIeRKagsmmUlkñúgkarsikSaviPaKPaBdab. viFIenHmanlkçN³gayRsYl nigsmehtu Two-Way Prestressed Concrete Floor Systems 590
  39. 39. Department of Civil Engineering NPIC pledaysaremKuNPaBrwgRkajrbs;Ggát;epSg²RtUv)anKNnarYcehIyenAkñúgkarviPaKkarBt;begáag (flexural analysis) éneRKagCab;smmUl. 9.10. Step-By-Step Trial-and-Adjustment Procedure for the Design of a Two-Way Prestressed Slab and Plate System xageRkamenHCaCMhanbnþbnÞab;EdlRtUv)anesñIreLIgsMrab;kargarsikSaKNna nigsMrab;kargar viPaKkMralxNÐebtugeRbkugRtaMgBIrTis³ !> kMNt;faetIragFrNImaRtrbs;kMralxNÐ nigkardak;bnÞúktMrUvrviPaKtamlkçN³BIrTiseday viFIeRKagsmmUlb¤Gt;. @> eRCIserIskMras;kMralxNÐsakl,gsMrab;beNþayGtibrma h = L / 45 b¤TTwgGtibrma h = L / 45 . KNnabnÞúkefresvakmμsrub bnÞúkGefresvakmμsrub nigbnÞúkemKuN. #> snμt; tendon profile kat;tamElVgCab;kñúgTis E-W nigTis N-S ehIykMNt;kMlaMgeRbkug RtaMg F / kugRtaMgebtug f c = F / Ac / nigcMnYn strand kñúgmYyElVg. KNna balancing load intensity Wbal = 8Fa / L2 nigKNna net load Wnet ↓ = Ww↓ − Wbal ↓ . $> kMNt;lkçN³eRKagsmmUl (equivalent frame characteristics) tamviFIeRKagsmmUl nigkMNt;PaBrwgRkajTb;karBt; nigPaBrwgRkajTb;karrmYlrbs;kMralEdleGayeday 4 EI Kc ≅ Ln − 2h RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 591
  40. 40. T.Chhay viTüasßanCatiBhubec©keTskm<úCa nig Kt = ∑ 9 Ecs C 3 ⎛ c ⎞ L2 ⎜1 − 2 ⎟ ⎜ ⎝ L2 ⎟ ⎠ Edl C = ∑(1 − 0.63x / y )x3 y / 3 . nigbnÞab;mkKNna −1 ⎛ 1 1 ⎞ K ec =⎜ ⎜K + K ⎟⎟ ⎝ c t ⎠ sMrab;ssrxageRkA nigxagkñúg ehIyPaBrwgRkajrbs;kMralxNÐ 4 EI Ks ≅ L1 − c1 / 2 Edl L1 CaElVgEdlKitBIG½kS nig c1 CakMras;ssrsMrab;tMNrvagssr nigkMralxNÐnImYy². %> KNnaemKuNEbgEckm:Um:g;sMrab;kMralBItMél K ec nig K s EdlTTYl)anenARtg;tMNnImYy² Ks DF = ∑K Edl ∑ K = K ec + K S (left ) + K S (rkght ) . bnÞab;mkKNna fixed-end moment FEM enA Rtg;tMNsMrab; net load EdleGayeday FEM = WL2 / 12 sMrab;bnÞúkBRgay. ^> GnuvtþkarEbgEckm:Um:g;sMrab; net load moment M net nigEktMrUvm:Um:g;EdlEbgEckeLIgvij edIm,ITTYl)antMél net moment enARtg;épÞrbs;TMr. smIkarKW M n = M n(centerline) − Vc / 3 . bnÞab;mkepÞógpÞat;fakugRtaMgebtug P M net ft = − + A S EdlTTYl)anm:Um:g;TaMgBIrtUcCagkugRtaMgGnuBaØatGtibrma ft = 6 f 'c psi(0.5 f 'c MPa) sMrab;muxkat;TMr nig ft = 2 f 'c psi(0.166 f 'c MPa ) sMrab;muxkat;kNþalElVg. &> KNna balanced service-load fixed-end moment Wbal L2 FEM bal = 12 nigGnuvtþkarEbgEckm:Um:g;énm:Um:g;bnÞúklMnwg M bal . bnÞab;mkkMNt; primary moment M 1 = Pe e nig secondary moment M s = (M bal − M 1 ) . *> KNna fixed-end factored load moment FEM u− = (Wu L2 )/ 12 ehIyGnuvtþkarEbgEck m:Um:g;én factored moment. bnÞab;mkKNna required design moment M u = M u− − M s sMrab;kMralxNÐenARtg;RKb;tMN nigenARtg;m:Um:g;viC¢manGtibrma M u tambeNþayElVg. Two-Way Prestressed Concrete Floor Systems 592
  41. 41. Department of Civil Engineering NPIC (> kMNt; required nominal moment strength M n = M u / φ sMrab;m:Um:g;TMrGviC¢man − M u nigm:Um:g;ElVgviC¢man + M u . bnÞab;mkRtYtBinitüemIlfa − M n nig + M n EdlGacman sMrab;kMralxNÐ nigsMrab;EdkeRbkugRtaMgRKb;RKan;b¤Gt;. bnÞab;mkeTot kMNt; inelastic moment redistribution ΔM R BIdMeNIrkarEdlmanerobrab;enAkñúgcMnuc 4.12.4 nig 6.7.2. Edl ΔM R = ρ D (support M u ) . bEnßmEdkFmμtaenARtg;TMr nigkNþalElVgRbsinebI caM)ac; edayrMlwkfaEdkminrgeRbkugRtaMgGb,brma As = 0.00075hL . !0> RtYtBinitü nominal shear strength rbs;kMralxNÐenARtg;TMrxageRkA nigTMrxagkñúg rYcKNna karepÞr shear-moment nigkarepÞr flexure-moment eTAssr. emKuNkMlaMgkat;m:Um:g; (moment shear factor) KW 1 γ v = 1− 2 1+ b1 / b2 3 ehIyemKuNkarBt;begáagm:Um:g; (moment flexure factor) KW 1 γf = 2 1+ b1 / b2 3 Edl b1 = c1 + d / 2 sMrab;ssrxageRkA b1 = c1 + d sMrab;ssrxagkñúg b2 = c2 + d eKGacbegáIntMél γ f 25%enARtg;TMrxagkñúg nigbegáInrhUtdl;esμInwg 1.0 enARtg;TMrepSg eTotdUcbgðajenAkñúgsmIkar 9.29. bnÞab;mkKNna c AB nig cCD sMrab;ssrxageRkA k¾dUc total nominal unbalanced moment strength M n = M ue + Ve g . !!> KNna shear ultimate stress EdlbNþalBIkMlaMgkat;brimaRt nigT§iBlrbs; γν M n ³ γ c M vn = u + ν AB n ≤ vc GnuBaØatGtibrma V φ A J v c c V Edl kugRtaMgGnuBaØatGtibrma vc = β p f 'c + 0.3 f c + b pd o β p = tMélEdltUcCageKkñúgcMeNam 3.5 nig (α s d / bo + 1.5) φ = 0.75 sMrab;kugRtaMgkat; nigkugRtaMgrmYl Edl α s = 40 sMrab;ssrxagkñúg/ 30 sMrab;ssrxag nig 20 sMrab;ssrkac;RCug. RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 593
  42. 42. T.Chhay viTüasßanCatiBhubec©keTskm<úCa ssrRtUvmanmuxkat;y:agticbMput 4in. BIépÞénRCugGt;Cab; ehIy f 'c minKYrFMCag 5,000 psi nig f RtUvmantMélGb,brmaesμInwg 125 psi nigGtibrmaesμInwg 500 psi ebImin dUecñaHeT eKKYrKNna vc BItMélEdltUcCageKEdlTTYl)anBIsmIkarxageRkam ⎛ 4 ⎞ ⎛α d ⎞ vc = ⎜ 2 + ⎜ ⎟ f 'c b¤ vc = ⎜ s + 2 ⎟ f ' c b¤ vc = 4 f 'c ⎝ β ⎟ c ⎠ ⎝ ⎜ b o ⎠ ⎟ !@> KNnatMélm:Um:g;emKuN γ f M n nigRtYtBinitüersIusþg;EdlGacekItman M n énmuxkat; EdlRbmUlpþúMEdkenAkñúg column band [c + 2(1.5h)] . !#> RtYtBinitüPaBdab nig camber rbs;kMralxNÐ !$> TTYlykkarsikSaKNnaRbsinebIvabMeBjRKb;lkçxNÐEdl)anerobrab;xagelI. bnÞab;mk GnuvtþkarKNnasMrab;Tis E-W nigTis N-S rbs;RbB½n§kMralxNÐ. rUbTI 9>16 bgðajBI flowchart sMrab;karsikSaKNna nigkarsikSaviPaK plate nigkMralxNÐeb tugeRbkugRtaMgBIrTis Two-Way Prestressed Concrete Floor Systems 594
  43. 43. Department of Civil Engineering NPIC RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 595
  44. 44. T.Chhay viTüasßanCatiBhubec©keTskm<úCa Two-Way Prestressed Concrete Floor Systems 596
  45. 45. Department of Civil Engineering NPIC 9.11. sikSaKNnaRbB½n§kMral Flat-Plate ebtugeRbkugRtaMgTajCaeRkay Design of Prestressed Post-Tensioned Flat-Plate Floor System ]TahrN_ 9>2³ RbB½n§kMral post-tensioned prestressed nonbonded flat-plate sMrab;GKarsñak;enA RtUv)anbgðajenAkñúgrUbTI 9>17. kMralxagmanTMhM 17 ft 6in. × 20 ft (5.33m × 6.10m) EdlKitBIG½kS eTAG½kS ehIykMralxagkñúgmanTMhM 24 ft × 20 ft (7.32m × 6.10m) . kMBs; lu rbs;Can;KW 8 ft 9in. (2.67m ) . sikSaKNnakMralxNÐenHedIm,IRTnUv working live load WL = 40 psf (1.92kPa ) nig superimposed dead load WSD = 20 psf (0.96kPa ) EdlbNþalBI partition nig flooring. snμt;enA kñúgdMeNaHRsayenHfaRKb;kMralTaMgGs;TTYlbnÞúkGefrkñúgeBlCamYyKña nigepÞógpÞat;lT§PaBkarepÞr kMlaMgkat;-m:Um:g; (shear-moment transfer capacity) rbs;kMralenARtg;ssr. eRbIkabeRbkugRtaMg 7- wire 270-K Ggát;p©it 1 / 2in. ehIyeRbIviFIeRKagsmmUl (equivalent frame method) kñúgkarsikSa KNnaenH. xageRkamenHCaTinñn½yEdleKeGay³ f 'c = 4,000 psi (27.6MPa ) ebtugTMgn;Fmμta f 'ct = 3,000 psi (20.7 MPa ) enARtg;TMr f t = 6 f 'c = 380 psi(2.62MPa) enARtg;kNþalElVg f t = 2 f 'c = 127 psi(0.88MPa) kugRtaMgkMlaMgkat;rbs;ebtugGtibrma vc RtUv)anTamTareday ACI Code f pu = 270,000 psi (1,862MPa ) f ps minRtUvFMCag 185,000 psi(1,276MPa ) f py = 243,000 psi (1,675MPa ) f pe = 159,000 psi (1,096MPa ) ( E ps = 29 ⋅10 6 psi 200 ⋅10 3 MPa ) f y = 60,000 psi (414MPa ) dMeNaHRsay Tis N-S I. Service Load analysis !> bnÞúk edIm,IRKb;RKgPaBdab snμt;fakMras;kMralxNÐ h ≅ L / 45 . TisbeNþay 20 ×12 / 45 = 5.33in. ehIy h = 24 ×12 / 45 = 6.40in. . dUcenHsakl,g h = 6 12 in.(165mm) TMgn;pÞal;rbs;kMral = 81 psf . RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 597
  46. 46. T.Chhay viTüasßanCatiBhubec©keTskm<úCa Two-Way Prestressed Concrete Floor Systems 598
  47. 47. Department of Civil Engineering NPIC bnÞúkGefrEdldak;bEnßmBIelI = 20 psf dUcenHeyIg)an bnÞúkGefrsrub WD = 101 psf WL = 40 psf bnÞúkesvakmμ Ww = WD + L = 141 psf (6.75kPa ) Wu = 1.2WD + 1.6WL = 1.2 × 101 + 1.6 × 40 ≅ 186 psf (8.9kPa ) sMrab;EpñkéndMeNaHRsayenH) Ln = bay span (N-S L2 = band width (Tis E-W) @> bnÞúklMnwg nig tendon profile edIm,IeFVIkar)a:n;RbmaNelIkdMbUgsMrab;bnÞúklMnwg snμt;tMélkugRtaMgsgát;enAelIebtugmFüm EdlbNþalBIbnÞúklMnwgKW f c = 170 psi(1.17MPa) . kMlaMgÉktþa F = 170 × 6.5 ×12 = 13,260lb / ft (193.6kN / m ) . dUcenH sakl,gEdkeRbkugRtaMg 7-wire 270-K Ggát;p©it 1 / 2in. . eyIgeXIjfakM- laMgRbsiT§PaB Pe kñúgkabeRbkugRtaMgmYy = Aps f pe = 0.153 ×159,000 = 24,327lb . sMrab; L = 20 ft tamTisbeNþayrbs;eRKOgbgÁúM kMlaMgsrubKW Fe = FL = 13,260 × 20 = 265,200lb(1,180kN ) . cMnYnrbs; strand kñúgmYy bay KW Fe / Pe = 265,200 / 24,327 ≅ 11 ehIykMlaMgeRbkugRtaMgRb siT§PaBsrub Pe = Fe = 24,327 ×11 = 267,597lb . kMlaMgÉktþaCak;Esþg F = 267,597 / 20 = 13,380lb / ft (195.3kN / m ) ehIykugRtaMgsgát;enAkñúgebtugCak;Esþg f c = F / A = 13,380 / (6.5 × 12 ) ≅ 172 psi ≅ 170 psi KWbMeBjlkçxNÐ. dUcenH yk f c = 172 psi EdlbNþalBIbnÞúklMnwg ehIysnμt; parabolic tendon profile dUcbgðajenAkñúgrUbTI 9>18. ElVgxageRkA AB b¤ CD enARtg;kNþalElVg 3.25 + 5.50 a1 = a3 = − 1.75 = 2.625in. 2 BIsmIkar 1.16 sMrab; parabolic tendon RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 599
  48. 48. T.Chhay viTüasßanCatiBhubec©keTskm<úCa 8Fa W= L2n 8 × 13,380 × 2.625 / 12 Wbal = ≅ 72 psf (18)2 Net load EdlbegáItm:Um:g;Bt;KW Wnet = Ww − Wbal = 141 − 72 = 69 psf (3.30 KPa ) ElVgxagkñúg BC a 2 = 6.5 − 1 − 1 = 4.5in. 8Fa 8 × 13,380 × 4.5 / 12 Wbal = 2 = ≅ 70 psf Ln (24)2 Wnet = 141 − 70 = 71 psf (3.40kPa ) #> lkçN³rbs;eRKagsmmUl (Equivalent Frame Characteristics) ykeRKagsmmUlenAkñúgTis N-S Edlbøg;RtUv)anbgðajedaykarqUtenAkñúgrUbTI 9>17. PaBrwg RkajTb;nwgkarBt;Rbhak;RbEhlrbs;ssrxagelI nigxageRkamtMNkMralxNÐ ¬m:Um:g;kñúgmYyÉktþa mMurgVil¦ nigBIsmIkar 9>9 KW 4 Ec I c Kc = Ln − 2h Edl Ln = Lu = 8 ft 9in. = 105in. (a) PaBrwgRkajssrxageRkA (14in.×12in. ) sMrab;ssrxageRkA b = 14in. dUcenH I c = 14(12)3 /12 = 2,016in.4 . snμt;fa Ecol / Eslab = Ecc / Ecs = 1.0 nigeRbI Ecc = Ecs = 1.0 enAkñúgkarKNna eday Ecs minRtUv)anKitenAkñúgsmIkar sMrab; K c . bnÞab;mk eyIgTTYl)an 4 × 1× 2,016 K c srub = × 2 ¬sMrab;cug nigKl;ssr¦ 105 − (2 × 6.5) = 175.3in. − lb / rad / Ecc BIsmIkar 9.10b efrkMlaMgrmYlKW ⎛ x ⎞ x3 y C = ∑⎜1 − 0.63 ⎟ ⎜ ⎝ y⎟ 3 ⎠ ⎛ 6.5 ⎞ 3 12 = ⎜1 − 0.63 × ⎟6.5 × = 724 ⎝ 12 ⎠ 3 PaBrwgRkajTb;karrmYlrbs;kMralenARtg;G½kSssrKW Two-Way Prestressed Concrete Floor Systems 600
  49. 49. Department of Civil Engineering NPIC 9 Ecs C Kt = ∑ 3 ⎛ c ⎞ L2 ⎜1 − 2 ⎟ ⎜ L ⎟ ⎝ 2⎠ 9 × 1 × 724 9 × 1 × 724 = 3 + 3 ⎛ 14 ⎞ ⎛ 14 ⎞ 20 × 12⎜1 − ⎟ 20 × 12⎜1 ⎟ ⎝ 12 × 20 ⎠ ⎝ 12 × 20 ⎠ = 65.0in. − lb / rad / Ecs BIsmIkar 9.7/ PaBrwgRkajsmmUlrbs;ssrKW −1 −1 ⎛ 1 1 ⎞ ⎛ 1 1 ⎞ K ec =⎜ ⎜K + ⎟ =⎜ + ⎟ = 47in. − lb / rad / Ecc ⎝ c Kt ⎟ ⎠ ⎝ 175.3 65 ⎠ (b) PaBrwgRkajssrxagkñúg (14in.× 20in. ) sMrab;ssrxagkñúg b = 14in. / dUcenH I = 14(20)3 /12 = 9,333in.4 . dUcenH eyIgman 4 × 1× 9,333 K c srub = × 2 = 812in. − lb / rad / Ecc 105 − 2 × 6.5 ⎛ 6.5 ⎞ ⎟ × (6.5) × 3 20 C = ⎜1 − 0.63 × = 1,456 ⎝ 20 ⎠ 3 9 × 1,456 9 × 1,456 Kt = 3 + 3 = 131in. − lb / rad / Ecs ⎛ 14 ⎞ ⎛ 14 ⎞ 20 × 12⎜1 − ⎟ 20 × 12⎜1 − ⎟ ⎝ 12 × 20 ⎠ ⎝ 12 × 20 ⎠ −1 ⎛ 1 1 ⎞ K ec = ⎜ + ⎟ = 113in. − lb / rad / Ecc ⎝ 812 131 ⎠ (c) PaBrwgRkajrbs;kMralxNÐ BIsmIkar 9.9 4 Ecs I s Ks = c Ln − 1 2 Edl Ln CaRbEvgElVgEdlKitBIG½kSeTAG½kS nig c1 CakMras;ssr. TTwg slab band enAkñúgTis E-W KW 20 / 2 + 20 / 2 = 20 ft . dUcenH I s = 20 × 12(6.5)3 / 12 = 5,493in.4 ehIysMrab;kMralenA xagsþaMssrxageRkA A 4 × 1× 20(6.5)3 Ks = = 108in. − lb / rad / Ecs 12 × 17.5 − 12 / 2 sMrab;kMralxNÐenAxageqVgssrxagkñúg B 4 × 1× 20(6.5)3 Ks = = 110in. − lb / rad / Ecs 12 × 17.5 − 20 / 2 ehIy sMrab;kMralenAxagsþaMssrxagkñúg B RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 601
  50. 50. T.Chhay viTüasßanCatiBhubec©keTskm<úCa 4 × 1× 20(6.5)3 Ks = = 79in. − lb / rad / Ecs 12 × 24 − 20 / 2 BIsmIkar 9.12/ emKuNEbgEckm:Um:g;enAelIkMralxNÐRtg;tMNKW DF = K s / ∑ K Edl ∑ K = K ec + K s (left ) + K s (right ) . dUcenHsMrab;tMNkMralxNÐxageRkA A / DF = 108 / (47 + 108) = 0.697 sMrab;tMNkMralxNÐxageqVg B / DF = 110 / (113 + 110 + 79 ) = 0.364 nigsMrab;tMN kMralxNÐxagsþaM B / DF = 79 /(113 + 110 + 79) = 0.262 . $> Design Service-Load Moment and Stresses Design net load moment sMrab;ElVgxageRkA AB nig CD / Wnet = 69 psf . dUcenHm:Um:gbgáb;cug (fixed-end moment) KW WL2 69 × (17.5)2 FEM = n = × 12 = 21.1 ⋅10 3 in. − lb 12 12 dUcKña sMrab;ElVgxagkñúg BC / Wnet = 71 psf . dUcenHm:Um:g;bgáb;cugKW 71(24 )2 FEM = × 12 = 40.9 ⋅10 3 in. − lb 12 edayGnuvtþkarviPaKkarEbgEckm:Um:g;dUcbgðajkñúgtarag 9>2/ eKGaceRbIemKuN carryover COF = 1 / 2 sMrab;RKb;ElVgTaMgGs;. eKRtUveFVIkarEksMrYlkarsnμt;EbbenH edaysareKecalT§iBlén nonprismatic section eTAelI fixed-end moment nigemKuN carryover. enAkñúgeRKageRcInElVg eKGacsnμt;faeRKagenARtg;tMNénElVgBIrEdlKitBIxageqVgtMN C RtUv)anKitfaCaTMrbgáb;kñúg karEbgEckm:Um:g;. Two-Way Prestressed Concrete Floor Systems 602
  51. 51. Department of Civil Engineering NPIC kugRtaMgTajrbs;ebtugkMralenARtg;TMr Net moment enARtg;épÞxagkñúgrbs;ssr B Caplsgénm:Um:g;Rtg; centerline CamYynwg Vc / 3 Edl 20 ⎛ 71× 24 ⎞ M net , max = 39.56 ⋅10 3 − ⎜ ⎟ = 33,880in. − lb / ft 3 ⎝ 2 ⎠ m:UDulmuxkat;rbs;kMralxNÐ S = bh 2 / 6 = 12(6.5)2 / 6 = 84.5in.3 ehIyeyIgmankugRtaMg ebtugsMrab;TMr = +229 psi (1.63MPa )(T ) ] P M 33,880 ft = − + = −172 + A S 84.5 dUcenH kugRtaMgGnuBaØat f t = 6 f 'c = 380 psi > 229 psi RKb;RKan;. kugRtaMgTajrbs;ebtugkMralenARtg;kNþalElVg Net moment GtibrmakNþalElVgKW WL2 / 8 − 39.56 ⋅103 b¤ 71(24 )2 M net , max = × 12 − 39.56 ⋅ 10 3 = 21,784in. − lb / ft (7.85kN / m ) 8 ehIy f t Rtg;kNþalElVg =− + P M A S = −172 + 21,784 84.5 = +86 psi (0.545MPa )(T ) dUcenH kugRtaMgGnuBaØati ft = 2 f 'c = 127 psi > 86 psi RKb;RKan;. RbsinebI f t > kugRtaMgGnuBaØat f t / kMlaMgTajTaMgmUlRtUv)anykedayEdkBRgwgFmμtaCamYy kugRtaMg f s = f y / 2 . Ultimate Flexural Strength Analysis II. Design Moment M u !> Balanced moments M bal Secondary moment RtUv)aneGayeday M s = M bal − M 1 / Edl M bal Ca balanced moment nig M 1 Ca primary moment = Pe e = Fe . sMrab;ElVg AB b¤ CD 72(17.5)2 FEM bal = × 12 = 22,050in. − lb / ft 12 nigsMrab;kMral BC 70(24 )2 FEM bal = × 12 = 40,320in. − lb / ft 12 karGnuvtþkarEbgEckm:Um:g;dUcenAkñúgtarag 9>3 nwgkMNt;m:Um:g; M bal GtibrmasMrab;tMNssr xageRkA. RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 603
  52. 52. T.Chhay viTüasßanCatiBhubec©keTskm<úCa @> Secondary moments M s nigm:Um:g;bnÞúkemKuN M u ElVg AB BI tendon profile énrUbTI 9>18/ e = 0 . dUcenHeyIgman³ Primary moment M 1 / ft enARtg;TMr A = Pe e = 0 M bal = 5,670in. − lb / ft ¬BItarag 9>3¦ M s = M bal − M 1 = 5,670 − 0 = 5.67 ⋅10 3 in. − lb / ft Wu l 2 186(17.5)2 m:Um:g;bgáb;cugbnÞúkemKuN FEM u = 12 = 12 × 12 = 56,963in. − lb / ft ElVg BA BI tendon profile enAkñúgrUbTI 9>18/ e = 6.5 / 2 − 1 = 2.25in. . dUcenHeyIgman³ M 1 = 13,380 × 2.25 = 30,105in.lb / ft (11.16kN .m ) M bal = 34,460in. − lb / ft ¬BItarag 9>3¦ M s = 34,460 − 30,105 = 4,355in. − lb / ft (1.61kN .m / m ) m:Um:g;bgáb;cugbnÞúkemKuN FEM u = 56,963in. − lb / ft (21.1kN .m / m) ElVg BC e = 2.25in. M 1 = 30,105in. − lb / ft M bal = 39,320in. − lb / ft ¬BItarag 9>3¦ Two-Way Prestressed Concrete Floor Systems 604
  53. 53. Department of Civil Engineering NPIC M s = 39,320 − 30,105 = 9,215in. − lb / ft (3.4kN .m / m ) m:Um:g;bgáb;cugbnÞúkemKuN FEM u = 18612 ) ×12 = 107,136in. − lb / ft (39.7kN .m / m) (24 2 GnuvtþkarEbgEckm:Um:g;sMrab;m:Um:g;emKuNdUcenAkñúgtarag 9>4. sikSaviPaKKMrUénkardak;bnÞúkelI ElVgqøas;edIm,ITTYllkçxNÐGaRkk;bMputsMrab;m:Um:g;esvakmμ nigm:Um:g;bnÞúkemKuN. #> Design moments M u m:Um:g;KNna (design moment) M u Caplsgénm:Um:g;bnÞúkemKuN M u− nig secondary moment M s b¤ M u = M u − M s ¬BIsmIkar 9.17¦. − m:Um:g; − M u Rtg;tMN A ¬ElVg AB ¦ sMrab;m:Um:g;Rtg;tMN A ¬ElVg AB ¦/ M s = 5,670in. − lb / ft ¬)anBIelIkmun¦ ehIym:Um:g;Rtg; centerline M u = 12,310 − 5,670 = 6,640in. − lb / ft . karkat;bnßym:Um:g;BIssr A = Vc / 3 . dUcenH − − Wu L M u @ B − M u @ A 186 × 17.5 103 (89.88 − 12.31) V AB = − = − 2 Ln 2 17.5 × 12 = 1627.5 − 369.4 = 1231.1lb / ft c = 12in. m:Um:g;Rtg; centerline M u = 12,310 − 5,670 = 6,640in. − lb / ft m:Um:g;Rtg;épÞssrtMrUvkar M u = 6,640 − 123131×12 . RbB½n§kMralxNÐebtugeRbkugRtaMgBIrTis 605

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