More Related Content Similar to Ix. two way prestressed concrete floor systems Similar to Ix. two way prestressed concrete floor systems (12) More from Chhay Teng (20) Ix. two way prestressed concrete floor systems1. 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. T.Chhay viTüasßanCatiBhubec©keTskm<úCa
Two-Way Prestressed Concrete Floor Systems 554
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. 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. 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. 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. 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. 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. 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. T.Chhay viTüasßanCatiBhubec©keTskm<úCa
Two-Way Prestressed Concrete Floor Systems 562
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. 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
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. 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. 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. 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. 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. 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. T.Chhay viTüasßanCatiBhubec©keTskm<úCa
Two-Way Prestressed Concrete Floor Systems 572
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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. T.Chhay viTüasßanCatiBhubec©keTskm<úCa
Two-Way Prestressed Concrete Floor Systems 588
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. 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. 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. 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. 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. 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
44. T.Chhay viTüasßanCatiBhubec©keTskm<úCa
Two-Way Prestressed Concrete Floor Systems 596
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. T.Chhay viTüasßanCatiBhubec©keTskm<úCa
Two-Way Prestressed Concrete Floor Systems 598
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. 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. 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. 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. 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. 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. 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