Xvii design of two way slab

T.Chhay NPIC

XVII. karKNnakMralxNÐ½BIrTis
Design of Two-Way Slabs

1> esckþIepþIm Introduction
kMralxNÐ½GacRtUv)anBicarNaCaGgát;eRKOgbgÁúMEdlmankMras; h tUcCagRbEvg L nigTTwg S .
TMrg;d¾samBaØrbs;kMralxNÐ½KWkMralxNÐ½EdlRtUv)anRTedayTMrQmKña Edlvapþl;nUvPaBdabcMbgkñúg
TismYy EdleKeGayeQμaHfa kMralxNÐ½mYyTis (one-way slab). karKNnakMralxNÐ½mYyTisman
niyayenAkñúgemeronTI 9.
enAeBlkMralxNÐ½RtUv)anRTedayRCugTaMgbYn nigmanpleFobbeNþay L elITTwg S tUcCag
BIr ehIykMralxNÐ½dabBIrTis elIsBIenHbnÞúkenAelIkMralxNÐ½RtUv)anbBa¢ÚneTATMrTaMgbYnRCug. kMral
xNÐ½EbenHRtUv)aneKeGayeQμaHfa kMralxNÐ½BIrTis (two-way slab). m:Um:g;Bt; nigPaBdabenAkñúgkM
ralxNÐ½EbbenHtUcCagenAkñúgkMralxNÐ½mYyTis kMralxNÐ½dUcKñaGacRTbnÞúk)aneRcInCagenAeBlEdl
vamanTMrTaMgbYnRCug. bnÞúkenAkñúgkrNIenHRtUv)anRTBIrTis ehIym:Um:g;Bt;kñúgTisnImYy²tUcCagm:Um:g;
Bt;enAkñúgkMralxNÐ½RbsinebIbnÞúkrbs;vaRtUv)anRTkñúgTisEtmYy. kartMerob rt-Fñwm-kMralxNÐ½ (slab-
beam-girder) KMrUénkMralxNÐ½mYyTis nigBIrTisRtUv)anbgðajenAkñúgrUbTI 17>1.

2> RbePTkMralxNÐ½BIrTis Types of Two-Way Slabs

kMralxNÐ½ebtugBIrTisGacRtUv)ancat;cMNat;fñak;dUcxageRkam³

karKNnakMralxNÐ½BIrTis 438

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a. kMralxNÐ½BIrTisenAelIFñwm (two-way slab on beam)³ krNIenHekItmanenAeBlEdlkMral
xNÐ½BIrTisRtUv)anRTedayFñwmenAelIRCugTaMgGs;rbs;va ¬rUbTI17>1¦. bnÞúkBIkMralxNÐ½RtUv
bBa¢ÚneTATMrFñwmTaMgbYnrbs;va EdlnwgbBa¢ÚnbnÞúkbnþeTAssr.
b. Flat slab³ CakMralxNÐ½BIrTisEdlRtUv)anBRgwgBIrTisedayKñanFñwmRT ehIybnÞúkRtUv)anbBa¢Ún

pÞal;eTAssrTMr. ssrcg;TMluHkMralxNÐ½ EdlRtUv)ankarBaredaybIviFIxageRkam ¬rUbTI
17>2 nig 17>3¦³
- edayeRbI drop panel CamYynwg column capital.
- edayeRbI drop panel EdlKμan column capital. ebtugEdlBT§½CMuvij column capital KYr
EtRkas;RKb;RKan;edIm,ITb;Tl;nwgkugRtaMgTajGgát;RTUgEdlekItBIkMlaMgkat; punching
shear.

- edayeRbI column capital edayKμan drop panel EdlCaviFImYyminFmμta.
c. Flat-Plate floor³ CaRbBn§½kMralxNÐ½BIrTisEdlmankMras;kMralxNÐ½esμI nigsßitenABIelIssr

edaypÞal;edayKμanFñwm b¤ column capital ¬rUbTI 17>2 a¦. kñúgkrNIenHssrcg;TMluHkMral
xNÐ½edaykugRtaMgTajGgát;RTUg. dUcenH CaTUeTAeKRtUvkarbegáInkMras;kMralxNÐ½ b¤dak;Edk
Biess.
d. Two-way ribbed slabs nig waffle slab system³ kMralxNÐ½RbePTenHekItBIkMralxNÐ½Edl

manpleFobbeNþayelITTwgtUcCag 2. CaTUeTAkMras;rbs;kMralxNÐ½sßitenAcenøaH 5cm eTA
10cm nigRtUv)anRTedayrnUt (rib or joist) TaMgBIrTis. rnUtRtUv)antMerobkñúgTisnImYy²Ca

mYyKMlatRbEhlBI 50cm − 75cm EdlbegáItragkaer b¤ctuekaNEkg ¬rUbTI 17>2 c¦. rnUt
k¾GacRtUv)antMerobedaymMu 45o b¤ 60o BIGkS½rbs;kMralxNÐ½ EdlbegáInesaPNÐ½PaBsßabtü-
kmμ. sMrab; two-way ribbed slabs RbBn§½epSg²GacRtUv)anTTYlyk³
- RbBn§½rnUtBIrTisCamYynwgRbehagcenøaHrnUtEdlTTYledayeRbIBum<Biess EdlCaTUeTA
manragkaer. rnUtRtUv)anRTedayrtTaMgbYnRCugEdlsßitenABIelIssr. kMralxNÐ½RbePT
enHRtUv)aneKeGayeQμaHfa two-way ribbed (joist) slab system .
- RbBn§½rnUtBIrTisCamYyeRKOgbMeBj (filler) enAcenøaHrnUtEdleFVIeGayBidanerobesμI.
eKOgbMeBj (filler) CagRbehag nigeFVIBIebtugTMgn;Rsal b¤TMgn;Fmμta b¤BIsMPar³TMgn;
RsalepSgeTot. rnUtRtUv)anRTedayrtenARCugTaMgbYnEdlRtUv)anRTbnþedayssr.


T.Chhay NPIC

kMralxNÐ½RbePTenHk¾RtUv)aneKeGayeQμaHfa two-way ribbed slab system b¤ hollow-
block two-way ribbed system .

- RbBn§½rnUtBIrTisCamYyRbehagcenøaHrnUt nigKμanrt b¤FñwmRTrnUt. vaQrenAelIssreday
pÞal;CamYynwgbnÞHebtugtan;. kMralxNÐ½RbePTenHRtUv)anehAfa waffle slab.


T.Chhay NPIC

3> kareRCIserIsRbBn§½kMralxNÐ½ebtugEdlmanlkçN³esdækic© Economical
Choice of Concrete Floor Systems
RbBn§½kMralxNÐ½CaeRcInRbePTRtUv)aneRbIsMrab;GKarTUeTA dUcCa eKhdæan kariyal½y nigGKar
rdæ)alepSg². kareRCIserIsRbBn§½kMralxNÐ½EdlmanlkçN³kMralxNÐ½ nigRKb;RKan;GaRs½yelIRbePT
GKar/ rUbragsßabtükmμ/ esaPNÐ½ nigRbEvgElVgEdlenAcenøaHssr. CaTUeTA bnÞúkGefrenAelIGKar
ERbRbYlcenøaHBI 3.8kN / m 2 − 7.2kN / m 2 . karENnaMTUeTAsMrab;kareRbIR)as;RbBn§½kMralxNÐ½Edl
manlkçN³esdækic©RtUv)ansegçbdUcxageRkam³
- Flat plate ³ saksmbMputsMrab;ElVgEdlmanRbEvgcenøaHBI 6m − 7.5m nigbnÞúkGefrERb
RbYlBI 2.9kN / m 2 − 4.8kN / m 2 . GtßRbeyaCn_énkarTTYlyk flat plate rYmmankarcM
NayelIBum<Gs;éføefak TTYl)anBidanrabesμI nigkarsagsg;qab;. Flat plate manlT§PaB
Tb;kMlaMgkat;TTWgTab nigPaBrwgRkajtUc EdleFIVeGaymanPaBdabFM;. Flat plate RtUv)an
eRbIy:agTUlMTUlayenAkñúgGKarCakMralxNÐ½BRgwgedayEdk b¤k¾ebtugeRbkugRtaMg.
- Flat slab ³ saksmbMputsMrab;ElVgEdlmanRbEvgBI 6m − 9m nigsMrab;bnÞúkGefrERbRbYlBI
3.8kN / m 2 − 7.2kN / m 2 . vaRtUvkarBum<eRcInCag flat plate CaBiesssMrab; column capital.

kñúgkrNICaeRcIn eKeRbIEt drop panel edayKμan column capital .
- Waffle slab ³ saksmsMrab;ElVgEdlmanRbEvgBI 9m − 14.5m nigsMrab;bnÞúkGefrERbRbYl
BI 3.8kN / m 2 − 7.2kN / m 2 . vaRTbnÞúk)aneRcInCag flat plate nigmanBidanKYreGayTak;
TajEtBum<mantMéléfø.
- kMralxNÐ½elIFñwm (slab on beam)³ salsmbMputsMrab;ElVgcenøaH 6m − 9m nigbnÞúkGefrBI
2.9kN / m 2 − 5.7 kN / m 2 . FñwmbegáInPaBrwgRkajrbs;kMralxNÐ½EdleFVIeGaymanPaBdab

tUc. eKRtUvkarBum<bEnßmsMrab;Fñwm.
- kMralxNÐ½mYyTisenAelIFñwm (one-way slab on beam)³saksmbMputsMrab;ElVgEdlmanRb
EvgBI 3m − 6m nigbnÞúkGefrcenøaHBI 2.9kN / m 2 − 4.8kN / m 2 . vaGacRtUv)aneRbIsMrab;
ElVgFMCagenHCamYynwgtMéléføCag elIsBIenHeKnwgTTYl)anPaBdabFM. eKRtUvkarBum<bEnßm
sMrab;Fñwm.


T.Chhay NPIC

- One-way joist floor system ³ saksmbMputsMrab;ElVgEdlmanRbEvgBI 6m − 9m nigman
bnÞúkGefrcenøaH 3.8kN / m 2 − 5.7kN / m 2 . edaysarEtrnUteRCA brimaNebtug nigEdkKWtic
EtkarcMNayelIBum<Gs;eRcIn. Bidanrbs;kMralxNÐ½GacnwgemIleTAKYreGayTak;Taj.
4> eKalKMnitkñúgkarKNna Design Concept
karviPaKd¾suRkitsMrab;kMlaMg nigbMlas;TIenAkñúgkMralxNÐ½BIrTisKWsμúKsμaj edaysarEtPaB
minkMNt;x<s;. vaBitCasμúKsμajebIeTaHbICaT§iBl creep nig nonlinear behavior rbs;ebtugRtUv)an
ecalk¾eday. viFI numerical method dUcCa finite element k¾GacRtUv)aneRbI b:uEnþviFId¾samBaØdUcEdl
GVI)anbgðajeday ACI Code saksmbMputsMrab;karKNnasMrab;karGnuvtþn_. ACI Code, Chapter
13 snμt;fakMralxNÐ½eFVIkarCaFñwmTUlay Etrak;begáItCaeRKagrwg (rigid frame) CamYynwgssrEdlenA

BIeRkam nigBIelIva. karsnμt;énkarEckeRKagCaeRKagsmmUlRtUv)anepÞógpÞat;eLIgvijedaykarsikSa
RsavRCavCalkçN³viPaK nigBiesaFn_ (analytical and experimental research). va)anbgðajfa lT§-
PaBRTbnÞúkcugeRkay (ultimate load capacity) énkMralxNÐ½BIrTisCamYynwgkarTb;tamRCug
¬restrained boundary) KWesμI RbEhlBIdgénlT§PaBRTbnÞúkcugeRkayEdlKNnaedaykarviPaKtam
RTwsþI edaysarkarEbgEckm:U- m:g;eLIgvijd¾FMEdlekIteLIgenAkñúgkMralxNÐ½munnwg)ak;. enAeBlbnÞúk
FM bMlas;TI nigPaBdabFMRtUv)anrMBwgTuk dUcenHeKRtUvkarkMras;kMralxNÐ½Gb,brmaedIm,IrkSaPaBdab
niglkçxNÐeRbHRKb;RKan; eRkambnÞúkeFVIkar.
ACI Code kMNt;viFIsaRsþBIrsMrab;KNnakMralxNÐ½BIrTis³

- viFIKNnaedaypÞal; (direct design method DDM, ACI Code, Section 13.6) CaviFIRbhak;
RbEhl (approximate procedure) sMrab;karviPaK nigkarKNnakMralxNÐ½BIrTis. RtUv)ankM
Nt;sMrab;RbBn§½kMralxNÐ½EdlrgnUvbnÞúkBRgayesμI nigssrmanKMlatesμIKña b¤esÞIresμIKña. viFI
enHeRbInUvsMnuMemKuNedIm,IkMNt;m:Um:g;KNnaenARtg;muxkat;eRKaHfñak;. RbBn§½kMralxNÐ½Edlmin
RtUvKñanwgkarkMNt;rbs; ACI Code, Section 13.6.1 RtUv)anviPaKedayviFIsaRsþKNnaEdl
manlkçN³suRkitCag.
- viFIeRKagsmmUl (equivalent frame method EFM, ACI Code, Section 13.7) CaviFImYy
EdlGKarbITMhM (3D) RtUv)anEckecjCaesrIéneRKagsmmUlBIrTMhM (2D) edaykat;GKar


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tamExSrcenøaHssr. lT§plrbs;eRKagRtUv)anBicarNadac;edayELkBIKñatamTisbeNþay
nigTisTTwgrbs;GKar nigRtUv)anKitBImYyCan;eTAmYyCan; dUcEdlbgðajenAkñúgrUbTI 17>4.
viFIsaRsþKNnatam ACI Code BIrKWQrelIelIlT§plénkarviPaKeGLasÞic (elastic analysis) én
eRKOgbgÁúMTaMgmUledayeRbIbnÞúkemKuN. viFIEdlEktMrUv (modified approach) viFI direct design
method RtUv)anbgðajenAkñúg commentary én code qñaM 1989 CaviFIPaBrwgRkajEktMrUv (modified

stiffness method MSM). vaQrkarbBa©ÚlemKuNEbgEckd¾kMNt;mYyCaGnuKmn_énpleFobPaB

rwgRkaj α ec sMrab;KuNnwgm:Um:g;sþaTicsrubenAkñúgElVgxagcug. viFIenHRtUv)anBnül;enAeBleRkay.
bEnßmBIelI viFIrbs; ACI Code eKenAmanviFIepSg²CaeRcIneTotsMrab;KNna nigviPaKkMralxNÐ½.
CalT§pl kMralxNÐ½nwgmanbrimaNEdkticCag b¤eRcInCag. viFIviPaK (analytical method) GacRtUv
cat;cMNat;fñak;kñúgRkuménTMnak;TMngeKalrvagbnÞúk nigbMlas;TI CaeGLasÞic/ )aøsÞic nig nonlinear .
- enAkñúgkarviPaKeGLasÞic (elastic analysis) kMralxNÐ½ebtugRtUv)anKitCakMraleGLasÞic.
karBt;kMlaMgkat;TTwg nigPaBdabRtUv)anKNnaedaysmIkarDIepr:g;EsülTI4 (fourth
differential equation) EdlTak;TgbnÞúkeTAnwgPaBdabsMrab;kMralesþIgCamYynwgbMlas;TItUc

dUcEdl)anbgðaj eday Timoshenko. dMeNaHRsay finite difference solution k¾dUcCadM
eNaHRsay finite element solution RtUv)anesñIeLIgedIm,IviPaKkMralxNÐ½. enAkñúgviFI finite
element method kMralxNÐ½RtUv)an EbgEckCasMNaj;ragRtIekaN b¤ragkaer (mesh of

triangles or quadrilateral). GnuKmn_bMlas;TIén cMnuc (node) Edlkat;KñaedaycMnucsMNaj;

(intersecting mesh point) RtUv)anbegáIteLIgCaTUeTA ehIym:aRTicénPaBrwgRkaj (stiffness

matrices) RtUv)anbegáItsMrab;karviPaKedaykMuBüÚTr½.

- sMrab;karviPaK)aøsÞic eKmanbIviFI. viFI yield line method RtUv)anbegáIteLIgeday Johansen
edIm,IkMNt;sßanPaB (limit state) énkMralxNÐ½edayBicarNafa yield line EdlekItmanenA
kñúgkMralxNÐ½Caemkanicénkar)ak; (collapse mechanism). viFIcMerok (strip method) RtUv)an
begáIteday Hillerborg. kMralxNÐ½RtUv)anEckecjCacMerok (strip) ehIybnÞúkenAelIkMral
xNÐ½RtUv)anEbgEckTisedABIrEkgKña. cMerokRtUv)anviPaKCaFñwmsamBaØ. viFITIbICaviFI optimal
analysis method sMrab;eFVIeGaybrimaNEdlTTYl)anmantMélGb,brmaedayQrelIkarvi

PaK)aøsÞic. dMeNaHRsay optimal solution KWsμúKsμajkñúgkarviPaK nigTTYl)ankarBRgay
srésEdlmYyd¾sμúKsμaj.


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T.Chhay NPIC

- karviPaK nonlinear analysis KitlkçN³bMlas;TIeRkambnÞúkBiténkMralxNÐ½ebtugGarem: enA
eBlEdlviFI finite element method KitBicarNaEpñk nonlinear énTMnak;TMngkugRtaMg-bMEr
bMrYlrageFob (stress-strain relationship) énGgát;mYy²dac;edayELkBIKña. kñúgkrNIenH
dMeNaHRsaykøayCasμúKsμaj RbsinebITMnak;TMngEdl)anBIkarBiesaFn_edayTTYl)ankar
sMrYlminRtUv)ansnμt;eTenaH.
viFIEdl)anerobrab;xagelI RtUv)anbgðajedIm,IENnaMGñksikSanUvviFIepSg²énkarviPaKkMralxNÐ½.
kargarBiesaFn_elIkMralxNÐ½minRtUv)anGPivDÄeTkñúgb:unμanqñaMcugeRkayenH b:uEnþkarsikSaCaeRcInRb-
EhlCaRtUvkaredIm,IsMrYldMeNIrkarKNnabc©úb,nñCamYysuvtßiPaB karbMerIkargar niglkçN³esdækic¢.
5> cMerokelIssr nigcMerokkNþal Column and Middle Strips
rUbTI 17>5 bgðajkMralxagkñúgénkMralxNÐ½BIrTisEdlRtUv)anRTenAelIssr A / B / C nig
D . RbsinebIkMralRTbnÞúkBRgayesμI kMralxNÐ½nwgdabBIrTis CamYyPaBdabGtibrmarnAtMbn;kNþal

O . cMnucx<s;bMputsßitenAelIssr A / B / C nig D dUcenHEpñkénkMralxNÐ½EdlenACMuvijssrnwg

manrage)a:g (convex shape). karpøas;bþÚrrUbragrbs;kMralxNÐ½bnþicmþg² ¬BIPaBe)a:genAelIssreTA
rkPaBptenAkNþalkMral¦ eFVIeGayExSkaMnImYy²kat;Rtg;cMnucrbt;. muxkat;Rtg; O / E / F / G nig
H nwgmanm:Um:g;Bt;viC¢man b:uEnþenAmþúMbrievNssrnwgmanm:Um:g;Bt;GviC¢manGtibrma. edayBicarNacM

eroktambeNþay AFB cMeroknwgekagdUcFñwmCab; ¬rUbTI 17>5 b¦ edaymanm:Um:g;GviC¢manenARtg; A
nig B nigmanm:Um:g;Bt;viC¢manRtg; F . cMerokenHlatsn§wgenAcenøaHssrBIr A nig B nigCab;enAelI
RCugTaMgsgçagénkMral EdlbegáIt)anCacMErokelIssr (column strip).
dUcKñasMrab;cMeroktambeNþay EOG nwgmanm:Um:g;Bt;GviC¢manenARtg; E nig G ehIym:Um:g;
viC¢manenARtg; O EdlbegáItCacMerokkNþal. cMerokTIbItambeNþay DHC nwgeFVIkarRsedogKñanwgcM
erok AFB . dUcenH bnÞHkMralGacnwgRtUv)anEbgEckbIcMerokKW 1enAkNþaltambeNþay EOG Edl
eKeGayeQμaHfacMerokkNþal nigBIreTotsgçagtambeNþay AFB nig DHC EdleKeGayeQμaHfa
cMerokelIssr ¬rUbTI 17>5 a¦. cMeroknImYy²eFVIkarCaFñwmCab;. tamviFIdUcKña bnÞHkMralk¾RtUv)anEbg
EckCabIcMroksMrab;TisedAmYyeTotKW cMerokkNþalmYytambeNþay FOH nigcMerokelIssrBIreTot
tambeNþay AED nig BGC erogKña ¬rUbTI 17>5 e¦.


T.Chhay NPIC

tamry³rUbTI 17>5 a eyIgeXIjfacMerokkNþalRtUv)anRTedaycMerokelIssr EdlbBa¢Ún
bnÞúkbnþeTAssr A / B / C nig D enAkñúgbnÞHkMralenH. dUcenHcMerokssrRTbnÞúkeRcInCagcMerok
kNþal. dUcenH m:Um:g;Bt;viC¢manenAkñúgcMerokelIssrnImYy² ¬enARtg; E / F / G nig H ¦ mantMél
FMCagm:Um:g;Bt;viC¢manenARtg; O EdlsßitenAcMerokkNþal. dUcKña m:Um:g;GviC¢manenAelIssr A / B /
C nig D enAkñúgcMerokelIssrmantMélFMCagm:Um:g;GviC¢manenARtg; E / F / G nig H enAkñúgcMerok

kNþal. Epñkénm:Um:g;KNnaEdlRtUv)ankMNt;enAmuxkat;eRKaHfñak;nImYy²éncMerokssr nigcMerok
kNþalRtUv)anbgðajenAkñúgEpñkTI 8.

TMhMéncMerokelIssr nigcMerokkNþslnImYy²enAkñúgbnÞHkMralRtUv)ankMNt;eday ACI Code,
Section 13.2. cMerokelIssr x EdlRtUv)ankMNt;edayTTwgkMralxNÐ½enAelIRCugnImYy²énGkS½


T.Chhay NPIC

ssr esμInwgmYyPaKbYnénTMhMbnÞHkMral ¬ l1 nig l2 ¦ mYyNaEdltUcCageK rYmbBa©ÚlTaMgFñwmRbsinebI
man.
l1 = RbEvgElVg KitBIGkS½eTAGkS½ kñúgTisedAEdlm:Um:g;nwgRtUv)ankMNt;

l 2 = RbEvlElVg KitBIGkS½eTAGkS½ kñúgTisedAEkgnwg l1

EpñkénbnÞHkMralcenøaHcMerokelIssrkMNt;cMerokkNþal.
6> kMras;kMralGb,brmaedIm,IkMritPaBdab Minimum Slab Thickness to
Control Deflection
ACI Code, Section 9.5.3 kMNt;kMras;kMralxNÐ½sMrab;kMralxNÐ½BIrTisedIm,IkMritPaBdab.
TMhMénPaBdabrbs;kMralxNÐ½GaRs½ynwgGefrCaeRcInEdlrYmbBa©ÚlTaMgPaBrwgRkajTb;karBt;
(flexural stiffness) rbs;kMralxNÐ½EdlbBa©ÚlCaGnuKmn_énkMras;kMralxNÐ½ h . enAeBlbegáInkMras;

kMralxNÐ½ enaHPaBrwgRkajTb;karBt;rbs;kMralxNÐk¾ekIneLIg ehIyPaBdabrbs;kMralxNÐ½nwgRtUv
½
kat;bnßy. edaysarkarKNnaPaBdabsMrab;kMralxNÐ½BIrTismanPaBsμúKsμaj nigedIm,IeCosvagPaB
dabFM ACI Code kMNt;kMras;kMralxNÐ½TaMgenHedayTTYlykkarkMNt;Edl)anBIkarBiesaFn_bI. Rb
sinebIkarkMNt;rbs;eyIgminsßitenAkñúgEdnkMNt;TaMgbIenHeT eKcaM)ac;RtUvKNnaPaBdab.
a. sMrab; 0.2 ≤ α fm ≤ 2 /
⎛ fy ⎞
l n ⎜ 0.8 +
⎜
⎟
⎝ 1400 ⎟
⎠
h=
36 + 5β (α fm − 0.2)
¬!&>!¦
b:uEnþminRtUvtUcCag 125mm
b. sMrab; α fm > 2
⎛ fy ⎞
l n ⎜ 0.8 +
⎜
⎟
1400 ⎟
h= ⎝ ⎠ ¬!&>@¦
36 + 9β
b:uEnþminRtUvtUcCag 90mm
c. sMrab; α fm < 0.2
h = kMras;kMralxNÐ½Gb,brmaedayKμanFñwmxagkñúg ¬tarag 17>1¦ ¬!&>#¦
Edl ln = clear span sMrab;TisEvgEdlvas;BIépÞQmKñarbs;ssr
β = pleFobén clear span EvgelI clear span xøI


T.Chhay NPIC

α fm = tMélmFümén α f sMrab;RKb;FñwménRCugTaMgGs;rbs;bnÞHkMral
α f = CapleFobénPaBrwgRkajTb;karBt;énmuxkat;Fñwm Ecb I b lIPaBrwgRkajTb;
karBt;énkMralxNÐ½ Ecs I s EdlBT§½CMuvijedayGkS½bnÞHkMralenABIelIFñwmRCug
nImYy².
E I
α f = cb b
E cs I s
¬!&>$¦
Edl Ecb nig Ecs Cam:UDuleGLasÞicrbs;ebtugenAkñúgFñwm nigkMralxNÐ½ erogKña.
I b = m:Um:g;niclPaBTaMgmUlénmuxkat;FñwmeFobGkS½TIRbCMuTMgn; ¬muxkat;FñwmrYmTaMg

beNþaykMralxNÐ½enAelIRCugTaMgsgçagrbs;FñwmEdlesμInwgkMBs;FñwmBIelI b¤BI
eRkamkMralxNÐ½ ykmYyNaEdlFMCageK b:uEnþminRtUvFMCagbYndgkMras;kMral
xNÐ½¦.
I s = m:Um:g;niclPaBénmuxkat;kMralxNÐ½TaMgmUl.

b:uEnþ kMras;kMralxNÐ½minKYrtUcCagtMélxageRkam³
- sMrab;kMralxNÐ½Edlman α fm < 2.0 ³ 125mm
- sMrab;kMralxNÐ½Edlman α fm > 2 ³ 90mm
tarag 17>1 kMras;kMralxNÐ½Gb,brmaedayKμanFñwmxagkñúg
edayKμan Drop Panel** man Drop Panel***
Yield
bnÞHkMralxageRkA bnÞHkMralxageRkA
Stress
bnÞHkMralxagkñúg bnÞHkMralxagkñúg
fy * KμanFñwmxag manFñwmxag KμanFñwmxag manFñwmxag
ln ln ln ln ln ln
280
33 36 36 36 40 40
ln ln ln ln ln ln
420
30 33 33 33 36 36
* sMrab;EdkEdlman Yield Stress cenøaH 280 nig 420 kMras;Gb,brmaTTYl)anBI linear interpolation.
** Drop panel RtUv)ankMNt;enAkñúg ACI Sections 13.3.7.7 nig 13.3.7.2

*** kMralxNÐ½EdlmanFñwmcenøaHssrtambeNþayxagkñúg. tMélén α f sMrab;FñwmminKYrmantMéltUcCag 0.8 .

RbsinebIFñwmminRtUv)aneRbI dUckñúgkrNI flat plate enaH α f = 0 nig α fm = 0 . smIkar ACI
Code sMrab;KNnakMras;kMralxNÐ½ h )anKitT§iBlrbs;RbEvgElVg/ TMrg;bnÞHkMral/ yield stress rbs;


T.Chhay NPIC

Edk f y nigPaBrwgRkajTb;karBt;rbs;Fñwm. enAeBlFñwmEdlmanlkçN³rwgxøaMgRtUv)aneRbI smIkar !&>!
Gacpþl;nUvkMras;kMralxNÐ½tUc ehIysmIkar !&>@ Gaclub. sMrab; flat plate nig flat slab enAeBl
EdlFñwmxagkñúgminRtUv)aneRbI kMras;kMralxNÐ½Gb,brmaGacRtUv)ankMNt;edaypÞal;BItarag 9>5 c én
ACI Code EdlRtUv)anbgðajenATIenHKWtarag 17>1.

karkMNt;rbs; ACI Code epSgeTotRtUv)ansegçbdUcxageRkam³
- sMrab;bnÞHkMralEdlmanxagminCab;; FñwmxagcugEdlman α = 0.8 RtUv)aneRbI ebImindUcenHeT
kMras;kMralxNÐ½Gb,brmaRtUv)anKNnatamsmIkar !&>! nig !&>@ RtUv)anbegáIn 10% y:ag
tic ¬ ACI Code, Section 9.5.3 ¦.
- enAeBl drop panel RtUv)aneRbIedayKμanFñwm kMras;kMralxNÐ½Gb,brmaKYrRtUv)anbnßyeday
10% . drop panel KYrRtUv)anlatsn§wgRKb;TisBIGkS½rbs;TMredaycMgayminticCagRbEvg

ElVgelI 6 RKb;TiscenøaHGkS½eTAGkS½énTMr nigTMlak;cuHeRkamkMralxNÐ½y:agtic h / 4 . kar
bnßyenH)anrYmbBa©ÚleTAkñúgtaragTI 17>1.
- edayminKittMélEdlTTYl)anBIsmIkar !&>! nig !&>@
kMras;kMralxNÐ½BIrTisminRtUvtUcCagkrNIdUcteTA³ ¬!¦ 125mm sMrab;kMralxNÐ½EdlKμanFñwm
b¤ drop panel. ¬@¦ 100mm sMrab;kMralxNÐ½KμanFñwmEtman drop panel. ¬#¦ 90mm sMrab;
kMralxNÐ½manFñwmenAelIRCUgTaMgbYnCamYynwg α fm ≥ 2 nig 125mm sMrab; α fm ≤ 2 ¬ ACI
Code, Section 9.5.3¦.

CMhanxageRkamsegçbBIkarKNnaTaMgenH³
!> sMrab;kMralxNÐ½EdlKμanFwñmxagkñúg ¬ flat plate nig flat slab¦
a. KNnakMras;kMralxNÐ½edaypÞal;BItarag 17>1. b:uEnþsmIkar !&>! nig !&>@ k¾GacRtUv)aneRbI

ehIyCaTUeTA smIkar !&>! lub. kMras;kMralxNÐ½Gb,brmaKYrFMCag b¤esμInwg 125mm
sMrab;kMralxNÐ½EdlKμan drop panel nigFMCagb¤esμI 100mm sMrab;kMralxNÐ½Edlman drop
panel.

b. enAxagEdlminCab; FñwmxagEdlman α f ≥ 0.8 KYrRtUv)aneRbI. ebImindUecñaHeT kMras;kMral

xNÐ½Gb,brmaRtUv)anKNnaedaysmIkar !&>! nig !&>@ KYrRtUv)anbegáIneday 10% . kar
begáIn 10% RtUv)anbBa©ÚleTAkñúgCYrQrTI 2 kñúgtaragTI 17>1 rYcehIy.


T.Chhay NPIC

c. RbsinebI drop panel RtUv)aneRbIenAkñúg flat slab kMras;kMralxNÐ½Gb,brmaRtUv)anbnßyeday
10% enAkñúgkrNIEdl drop panel latsn§wgenARKb;TisBIGkS½énTMrCamYycMgaymintUcCag

1 / 6 RbEvgElVg nigTMlak;eRkamkMralxNÐ½y:agtic h / 4 . karbnßyenH)anbBa¢ÚleTAkñúgem

KuNéntarag 17>1.
@> sMrab;kMralxNÐ½EdlmanFñwmenARKb;RCug ¬ α fm > 0 ¦
a. KNna α fm nigbnÞab;mkKNnakMras;kMralxNÐ½Gb,brmaBIsmIkar !&>! nig !&>@. kñúgkrNI

CaeRcInsmIkar !&>@ lub.
b. kMras;kMralxNÐ½KYrFMCag b¤esμInwg 125mm sMrab;kMralxNÐ½Edlman α fm < 2.0 nigKYrFMCag

b¤esμInwg 90mm sMrab;kMralxNÐ½Edlman α fm ≥ 2.0 .
#> sMrab;RKb;kMralxNÐ½³ kMrs;kMralxNÐ½EdltUcCagkMras;Gb,brmaEdleGayenAkñúgCMhan !> nig @>
GacRtUv)aneRbI RbsinkarKNnabgðajfaPaBdabminFMCagkarkMNt;rbs; ACI Code, Table 9.5
b EdlBnül;enAkñúgemeronTI 6.

]TahrN_17>1³ RbBn§½kMral flat plate EdlmanTMhM 7.5 × 6m RtUv)anRTenAelIssrkaer 500mm .
edayeRbIsmIkar ACI Code kMNt;kMras;kMralxNÐ½Gb,brmacaM)ac;sMrab;bnÞHkMralxagkñúg nigbnÞHkM
ralkac;RCug dUcbgðajenAkñúgrUbTI 17>6. FñwmxagminRtUv)aneRbI. eKeGay f 'c = 28MPa nig
f y = 420MPa .

dMeNaHRsay³
1> sMrab;bnÞHkMralxNÐ½kac;RCugelx ! kMras;Gb,brmaKW 30 ¬ f y = 420MPa
ln

nigKμanFñwmxagRtUv)aneRbI ¬emIltarag 17>1¦.
l n1 = 7500 − 500 = 7000mm

hmin =
7000
30
yk
= 233mm 250mm

müa:gvijeTot smIkar !&>! nig !&>@ GacRtUv)aneRbIedIm,IKNnakMras;Gb,brmaCamYy
α f = α fm = 0 .
2> sMrab;bnÞHkMralxagkñúgelx #> CamYy f y = 420MPa kMras;kMralxNÐ½Gb,brmaKW
hmin = n = 212mm yk 220mm
l
33
müa:gvijeTot smIkar !&>! nig !&>@ GacRtUv)aneRbI.


T.Chhay NPIC

RbsinebIRKb;bnÞHkMralxNÐ½TaMgGs;eRbIkMras;dUcKña enaHeKGacyk hmin = 250mm .

]TahrN_17>2³ RbBn§½kMralxNÐ½dUcbgðajenAkñúgrUbTI 17>7 EdlpSMeLIgedaykMraltan; nigFñwmenA
elITaMgBIrTisEdlRTedayssrkaerEdlmanRCug 500mm . edayeRbIsmIkar ACI Code kMNt;kMras;
kMralxNÐ½Gb,brmacaM)ac;sMrab;bnÞHkMralxagkñúg. eKeGay f 'c = 21MPa nig f y = 420MPa .
dMeNaHRsay³
1> edIm,IeRbIsmIkar !&>! α fm RtUv)anKNnamun. dUcenH eKcaM)ac;kMNt; I b / I s nig α f sMrab;
Fñwm nigkMralxNÐ½tamTisEvg nigTisxøI.
2> m:Um:g;niclPaBrbs;FñwmTaMgmUl I b RtUv)anKNnasMrab;muxkat;dUcbgðajenAkñúgrUbTI 17>7 b
EdlRtUv)anbegáIteLIgedayFñwm nigEpñksgçagxøHrbs;kMralxNÐ½ x = y b:uEnþminRtUvFMCag 4
bYndgkMras;kMralxNÐ½. snμt; h = 18cm ehIyvaRtUv)anepÞógpÞat;enAeBleRkay enaH
x = y = 56 − 18 = 38cm < 18 × 4 = 72cm . dUcenH be = 40 + 38 × 2 = 116cm nigmuxkat;


T.Chhay NPIC

GkSr T RtUv)anbgðajenAkñúgrUbTI 17>7 c . kMNt;TIRbCMuTMgn;rbs;muxkat;edayKitm:Um:g;eFob
kMBUlrbs;søab³
RkLaépÞsøab = 18 × 116 = 2088cm 2
RkLaépÞRTnug = 40 × 38 = 1520cm 2
RkLaépÞsrub 3608cm 2
2088 × 9 + 1520 × 37 = 3608 y

y = 20.8cm
⎡116
Ib = ⎢ (18)3 + 2088(11.8)2 ⎤ + ⎡ 40 383 + 1520(19 − 2.8)2 ⎤ = 928924.6cm 4
⎣ 12 ⎦ ⎢ 12
⎥ ⎣ ⎥
⎦

3> m:Um:g;niclPaBénkMralxNÐ½tamTisedAEvgKW
bh 3
Il =
12
Edl b = 600cm nig h = 18cm
600 3
Il = 18 = 291600cm 4
12


T.Chhay NPIC

¬tamTisedAEvg¦ = EI b = 928924.6 = 3.19
α fl
EI s 291600
4> m:Um:g;niclPaBénkMralxNÐ½tamTisedAxøIKW
760 3
Is = 18 = 369360cm 4
12
¬tamTisedAxøI¦
α fs
EI
= b =
EI s
928924.6
369360
= 2.51

5> α fm CatMélmFümén α fs nig α fl
3.19 + 2.51
α fm = = 2.85
2
7.6 − 0.5
6> β=
6 − 0.5
= 1.29

7> kMNt; hmin edayeRbIsmIkar !&>@ ¬ ln = 7.1m ¦³
⎛ 420 ⎞
7.1⎜ 0.8 + ⎟
hmin = ⎝ 1400 ⎠
= 0.148m
36 + 5 × 1.29(2.82 − 0.2)
b:uEnþ tMélenHminRtUvtUcCag h EdleGayedaysmIkar !&>@ ¬ α fm > 2.0 ¦
7.81
h= = 0.164m
36 + 9 × 1.29
müa:geTot hmin = 90cm .
dUcenH h = 16.4cm lub.
eKGacTTYlykkMras;kMralxNÐ½Edl)ansnμt; h = 18cm .
cMNaMfa enAkñúgkrNIGnuvtþn_CaeRcIn smIkar !&>@ manlkçN³lub.
7> ersIusþg;kMlaMgkat;TTwgrbs;kMralxNÐ½ Shear Strength of Slabs
sMrab;RbBn§½kMralxNÐ½BIrTis bnÞHkMralRtUvEtmankMras;RKb;RKan;edIm,ITb;nwgm:Um:g;Bt;TaMgBIr
nigkMlaMgkat;TTwgenARtg;muxkat;eRKaHfñak;. edIm,IGegátlT§PaBTb;kMlaMgkat;TTwgénkMralxNÐ½BIrTis
krNIxageRkamRtUv)anBicarNa.
7>1> kMralxNÐ½BIrTisEdlRTedayFñwm Two-Way Slabs Supported on Beams

muxkat;eRKaHfñak;rbs;kMralxNÐ½BIrTisEdlRTedayFñwmKWsßitenAcMgay d BIépÞénFñwmTMr ehIy
lT§PaBTb;kMlaMgkat;TTwgénmuxkat;nImYy²KW φVc = φ f 'c bd / 6 . enAeBlEdlFñwmmanlkçN³rwg
nigGacbBa¢ÚnbnÞúkkMraleTAssr vaRtUv)ansnμt;eGayRTbnÞúkEdleFVIGMeBImkelIépÞkMralxNÐ½EdlBT§½


T.Chhay NPIC

edaybnÞat; 45o EdlKUsecjBIRCugEkg dUcbgðajenAkñúgrUbTI 17>8. bnÞúkenAelIépÞctuekaNBñaynwg
RtUv)anRTedayFñwmEvg AB nig CD b:uEnþbnÞúkenAelIépÞRtIekaNnwgRtUv)anRTedayFñwmxøI AC nig
BD .

kMlaMgkat;TTwgkñúgmYyÉktþaTTwgrbs;kMralmantMélx<s;bMputenAcenøaH E nig F tamTis
TaMgBIr ehIy Vu = wu (l2 / 2) Edl wu CabnÞúkemKuNBRgayesμIkñúgmYyÉktþaépÞ.
RbsinebIEdkTb;kMlaMgkat;TTwgminRtUv)andak; kMlaMgkat;TTwgenAcMgay d BIépÞénFñwm
Vud RtUvEtesμInwg
φ f 'c bd
Vud ≤ φVc ≤
6
Edl Vud = wu ⎛ l22 − d ⎞
⎜ ⎟
⎝ ⎠
7>2> kMralxNÐ½BIrTisEdlKμanFñwm Two-Way Slabs Without Beams

nig flat slab KμanFñwmeT dUcenHkMralxNÐ½RtUv)anRTedayssredaypÞal;. sMrab;kM
Flat plate

ralxNÐ½EbbenHkugRtaMgkMlaMgkat;TTwgBIrRtUv)aneFVIkarGegát TImYyKWkMlaMgkat;TTwgmYyTis b¤kMlaMg
kat;TTwgFñwm (one-way shear or beam shear). muxkat;eRKaHfñak;RtUv)anykenAcMgay d BIépÞén
ssr ehIykMralxNÐ½RtUv)anBicarNadUcFñwmEdlmanTTwgFMsßitenAcenøaHTMr dUckñúgkrNIFñwmmYyTis


T.Chhay NPIC

(one-way beam) . lT§PaBTb;kMlaMgkat;TTwgénmuxkat;ebtugKW φVc = φ f 'c bd / 6 . RbePTTIBIrén
kMlaMgkat;TTwgEdlRtUvsikSaKWkMlaMgkat;TTwgBIrTis b¤kMlaMgkat;pug (two-way shear or punching
shear) dUcEdl)anerobrab;enAkñúgkarKNnaeCIgtag. Kar)ak;edaykMlaMgkat;ekItmantambeNþaykM

Nat;ekaN b¤kMNat;BIra:mIt (truncated cone or pyramid) CMuvijssr. muxkat;eRKaHfñak;sßitenAcM
gay d / 2 BIépÞssr/ column capital/ b¤ drop panel ¬rUbTI 17>9 a¦. RbsinebIEdkkMlaMgkat;TTwg
minRtUv)andak; ersIusþg;kMlaMgkat;TTwgrbs;ebtugKWtMélEdltUcCageKkñúgcMeNamsmIkar !&>%
nig !&>^³
⎛1 1 ⎞ φ f 'c bo d
φVc = ⎜ +
⎜ 6 3β ⎟ ⎟ f ' c bo d ≤ ¬!&>%¦
⎝ ⎠ 3
Edl bo = brimaRténmuxkat;eRKaHfñak;
β = pleFobénRCugEvgrbs;ssrelIRCugxøI ¬b¤RkLaépÞbnÞúk¦
φ ⎛α d ⎞
φVc = ⎜ s + 2 ⎟ f 'c bo d
⎜ b ⎟ ¬!&>^¦
⎝
12 o ⎠
Edl α s esμI 40 sMrab;ssrxagkñúg/ esμI 30 sMrab;;ssrxag nigesμI 20 sMrab;ssrkac;RCug.
enAeBlEdlEdkkMlaMgkat;TTwgRtUv)andak; ersIusþg;kMlaMgkat;TTwgminKYrelIs
φ
φVc ≤
2
f 'c bo d ¬!&>&¦
7>3> EdkkMlaMgkat;TTWgenAkñúgkMralxNÐ½BIrTisEdlKμanFñwm Shear Reinforcement in
Two-Way Slabs Without Beams
enAkñúgRbBn§½kMralxNÐ½ flat plate nig flat slab kMras;kMralxNÐ½Edl)aneRCIserIsGacnwgmin
RKb;RKan;edIm,ITb;nwgkugRtaMgkMlaMgkat;TTwgEdlGnuvtþeT. kñúgkrNIenH eKGacbegáInkMras;kMralxNÐ½
b¤dak;EdkTb;kMlaMgkat;TTwg. ACI Code GnuBaØatkareRbIEdkTb;kMlaMgkat;TTwgCa shearhead nig
anchored bar b¤ wire.

Shearhead pSMeLIgedayEdkragGkSr I b¤GkSr C EdlpSarExVgCabYn nigRtUv)andak;enAkñúgkM

ralxNÐ½BIelIssr ¬rUbTI 17>9 c, d ¦. karKNna Shearhead minGnuvtþsMrab;ssrxageRkA Edlm:U
m:g;Bt; nigm:Um:g;rmYlmantMélFMEdlRtUv)anbMElgcenøaHkMralxNÐ½ nigssr. ACI Code, Section
11.12.4 bgðajfaenARtg;muxkat;eRKaHfñak; ersIusþg;kMlaMgkat; nominal Vn minKYelIs f 'c bo d / 3

b:uEnþRbsin ebIEdk shearhead RtUv)andak; Vn minKYrelIs 7 f 'c bo d / 12 . edIm,IkMNt;TMhMrbs;
shearhead, ACI Code, Section 11.12.4 pþl;nUvkarkMNt;dUcteTA³


T.Chhay NPIC


T.Chhay NPIC

!> pleFob α v rvagPaBrwgRkaj Es I rbs;éd shearhead nigPaBrwgRkajénmuxkat;EdleRbH
smasEdlmanTTWg c2 + d minRtUvtUcCag 0.15 .
@> søabrgkarsgát;énEdkragminRtUvmanTItaMgenAmþúM 0.13d énépÞrgkarsgát;rbs;kMralxNÐ½.
#> kMBs;rbs;EdkragminRtUvFMCag 70 énkMras;RTnug.
$> lT§PaBTb;m:Um:g;)aøsÞic M P énédnImYy²rbs; shearhead RtUv)anKNnaeday
V ⎡ ⎛ c ⎞⎤
φM P = u ⎢hv + α v ⎜ l v + 1 ⎟⎥ ¬ACI Code, Eq. 11.37 ¦ ¬!&>*¦
2n ⎣ ⎝ ⎠⎦
2

Edl φ = 0.9
Vu = kMlaMgkat;TTwgemKuNCMuvijbrievNénépÞssr
n = cMnYnéd

hv = kMBs;rbs; shearhead

l v = RbEvg shearhead Edlvas;BIGkS½ssr

%> muxkat;kMralxNÐ½eRKaHfñak;sMrab;kMlaMgkat;TTWgRtUvEtkat;éd shearhead enAcMgayesμInwg
(3 / 4)(l v − c1 / 2) BIépÞssreTcugénédrbs; shearhead dUcbgðajenAkñúgrUbTI 17>9 c.

muxkat;eRKaHfñak;RtUvEtmanbrimaRtGb,brma bo b:uEnþvaminRtUvenACitCag d / 2 BIépÞrbs;sse.
^> Shearhead RtUv)anBicarNaeGaycUlrYmkñúgkarEbgEckm:Um:g;eLIgvij
M v eTAcMerokkMralxNÐ½elIssrnImYy²dUcxageRkam³
φ ⎛ c ⎞
Mv = α vVu ⎜ l v 1 ⎟ ¬ACI Code, Eq. 11.38¦ ¬!&>(¦
2n ⎝ 2⎠
b:uEnþvaminRtUvtUcCagtMéltUcCageKkñúgcMeNam 30% énm:Um:g;emKuNEdlcaM)ac;enAkñúgcMerok
elIssr/ karpøas;bþÚrm:Um:g;cMerokelIssrelIRbEvg lv b¤ M p EdleGayenAkñúgsmIkar !&>*.
kareRbI anchored bent bar b¤ wire k¾RtUv)anGnuBaØateday ACI Code, Section 11.12.3. Edk
Edldak;enAxagEpñkxagelIrbs;ssr niglT§PaBékartMerobEdkRtUv)anbgðajenAkñúgrUbTI 17>9 e.
enAeBlEdl bar b¤ wire RtUv)aneRbICaEdkTb;kMlaMgkat;TTwg enaHersIusþg;kMlaMgkat;TTWg nominal
KW³
f ' c bo d Av f y d
V n = Vc + V s =
6
+
s
¬!&>!0¦
Edl Av CaRkLaépÞEdkkgsrub nig bo CaRbEvgénmuxkat;eRKaHfñak;énkMlaMgkat;BIrTisenA
cMgay d / 2 BIépÞssr. ersIusþg;kMlaMgkat; nominal Vn minRtUvFMCag f 'c bo d / 2 .

T.Chhay NPIC

kareRbIEdkkMlaMgkat;enAkñúg flat plate kat;bnßykMras;kMralxNÐ½ nigenAEtrkSaPaBrabesμI
rbs;BidanedIm,Ikat;bnßyéføBum<. TMrg; stirrup cage sMrab;EdkkMlaMgkat;TTwgRtUv)anbgðajenAkñúgrUbTI
17>9 f . RbePTmü:ageToténEdkkMlaMgkat;pSMeLIgeday studded steel strip ¬rUbTI 17>9 g¦.
Steel strip RtUv)andak;CamYy bar chair nigRtUv)anP¢ab;eTAnwgBum< edayCMnYs stirrup gage . ersIusþg;

yalrbs;Edk stud RtUv)ankMNt;enAcenøaH 280MPa nig 420MPa edIm,ITTYl)an anchorage eBj
eljenAeBlbnÞúkemKuN.
8> karviPaK³nkMralxNÐ½BIrTisedayviFIKNnaedaypÞal; Analysis of Two-Way
Slabs by the Direct Design Method
Direct design method CaviFIRbhak;RbEhl (approximate method) RtUv)anbegáIteLIgeday
ACI Code edIm,IKNnam:Um:g;KNnaenAkñúgkMralxNÐ½BIrTisEdlRTbnÞúkBRgayesμI. edIm,IeRbIviFIenH kar

kMNt;xøHRtUv)anelIkeLIgeday ACI Code, Section 13.6.1.
8>1> karkMNt; Limitations

!> vaRtUvmankMralxNÐ½Cab;Kñay:agticbIkñúgTismYy²
@> kMralxNÐ½RtUvEtkaer b¤ctuekaNEkg. pleFobElVgEvgelIElVgxøIrbs;kMralminRtUvFMCagBIr
#> ElVgEdlenAEk,rkñúgTisnImYy²minRtUvxusKñaedayFMCagmYyPaKbIénElVgEvgCag.
$> ssrminRtUvlyecjBIGkS½ssrd¾éTCaeRcIneTotedaytMélGtibrma 10% énRbEvgElVg
enAkñúgTislyecj.
%> bnÞúkTaMgGs;RtUvEtBRgayesμI ehIypleFobénbnÞúkGefrelIbnÞúkefrminRtUvFMCag 2 .
^> RbsinebImanFñwmenARKb;RCug pleFobénPaBrwgRkajEdlTak;TgkñúgTisEkgTaMgBI
α f 1l 2 / α f 2 l12 minRtUvtUcCag 0.2 nigFMCag 5.0 .
2

8>2> m:Um:g;sþaTicemKuNsrub Total Factored Static Moment

RbsinFñwmTMrsamBaØRTbnÞúkBRgayesμI w ¬ kN / m ¦ enaHm:Um:g;Bt;viC¢manGtibrmaekItmanenA
kNþalElVgnigesμInwg M o = wl12 / 8 Edl l1 CaRbEvgElVg. RbsinebIRtUv)anbgáb;cugTaMgsgçag b¤
Cab;CamYynwg m:Um:g;GviC¢manesμIKñaenAcugTaMgsgçag enaHm:Um:g;srub
M o = M p ¬m:Um:g;viC¢manenAkNþalElVg¦ + M n ¬m:Um:g;GviC¢manenAelITMr¦ = wl12 / 8 ¬rUbTI 17>10¦.


T.Chhay NPIC

LÚvRbsinebIFñwm AB RTbnÞúk W BIkMralxNÐ½EdlmanTTwg l2 Ekgnwg l1 enaH W = wu l2
ehIy m:Um:g;srubKW M o = (wl2 )l12 / 8 Edl wu = GaMgtg;sIuetbnÞúkKitCa kN / m 2 . kñúgsmIkarenH
m:Um:g;BitR)akdEdlekItmanenAeBl l1 esμInwg clear span cenøaHTMr A nig B . RbsinebI clear span
RtUv)ankMNt;eday ln enaH
2
ln
M o = (wu l 2 ) (ACI Code, Eq. 13.3)
8

Clear span l n RtUv)anvas;BIépÞeTAépÞTMrkñúgTisedAEdlm:Um:g;RtUv)anBicarNa b:uEnþminRtUvticCag
0.65 dgRbEvgElVgBIGkS½eTAGkS½TMr. épÞénTMrEdlmanm:Um:g;GviC¢manKYrRtUv)anKNna RtUv)anbgðaj

enAkñúgrUbTI 17>11. RbEvg l2 RtUv)anvas;kñúgTisedAEkgnwg ln ehIyesμITisedAcenøaHGkS½eTAGkS½
rbs;TMr ¬TTwgkMralxNÐ½¦. m:Um:g;srub M o EdlKNnakñúgTisedAEvgRtUv)anKitCa M ol nigkñúgTisedA
xøIRtuv)anKitCa M os .
enAeBlm:Um:gsrub M o RtUv)anKNnakñúgTisedAmYy vaRtUvEbgEckCam:Um:g;viC¢man M p nigm:U
m:g;GviC¢man M n GBa¢wgehIyeTIb M o = M p + M n ¬rUbTI 17>10¦. enaHm:Um:g;nImYy² M p nig
M n RtUv)anEbgEckqøgkat;TTwgkMralxNÐ½cenøaHcMerokssr nigcMerokkNþal dUcEdl)anBnül;y:agxøI.

8>3> karEbgEckm:Um:g;tambeNþaykñúgkMralxNÐ½ Longitudinal Distribution of
Moment in Slabs
enAkñúgkMralxagkñúg m:Um:g;sþaTicsrub M o RtUv)anEbgEckenAkñúgm:Um:g;BIr m:Um:g;viC¢man M p enA
kNþalElVgesμInwg 0.35M o nigm:Um:g;GviC¢man M n enATMrnImYy²esμInwg 0.65M o dUcbgðajenAkñúgrUbTI
17>12. tMélm:Um:g;TaMgenHQrelIkarsnμt;fakMralxagkñúgCab;kñúgTisTaMgBIr ehIymanRbEvgElVg


T.Chhay NPIC

nigbnÞúkRbhak;RbEhlesμIKña dUcenHtMNxagkñúgKμanmMurgVilFMeT. elIsBIenHeTot m:Um:g;mantMél
RbEhlnwgm:Um:g;rbs;Fñwmbgáb;cugTaMgBIrEdlrgbnÞúkBRgayesμI Edlm:Um:g;GviC¢manenAelITMresμIBIrdg
m:Um:g;GviC¢manenAkNþalElVg. enAkñúgrUbTI 17>12 RbsinebI l1 > l2 / enaHkarEbgEckm:Um:g;enAkñúg
TisedAEvg nigTisedAxøIKW³

2
l n1
M ol = (wu l 2 ) M pl = 0.35M ol M n1 = 0.65M ol
8
l2
M os = (wu l1 ) n 2 M ps = 0.35M os M ns = 0.65M os
8
RbsinebITMhMénm:Um:g;GviC¢manenAelITMrxagkñúgmantMélxusKñaedaysarRbEvgElVgminesμIKña
ACI Code kMNt;eGayeRbIm:Um:g;EdlFMCagsMrab;KNnasrésEdk.

enAkñúgbnÞHkMralxageRkA bnÞúkkMralxNÐ½EdlGnuvtþelIssrxageRkA)anmkEtBIRCugmçag
bNþaleGayekItmanm:Um:g;minesμI (unbalanced moment) nigmMurgVilenAtMNxageRkA. dUcenH m:Um:g;
viC¢manenAkNþalElVg nigm:Um:g;GviC¢manenAelITMrxagkñúgTImYynwgekIneLIg.TMhMénmMurgViléntMNxag
eRkAkMNt;nUvkarelIneLIgnUvm:Um:g;kNþalElVg nigm:m:g;enAelITMrxagkñúg. ]TahrN_ RbsinebIRCugxag
U

T.Chhay NPIC

eRkACaTmrsamBaØ dUckñúgkrNIkMralxNÐ½enAelICBa¢aMg ¬rUbTI 17>13¦ m:Um:g;kMralenARtg;épÞCBa¢aMgesμI
0 m:Um:g;viC¢manenAkNþalElVgGacykesμInwg M p = 0.63M o nigm:Um:g;GviC¢manenATMrxagkñúgKW

M s = 0.75M o . tMélTaMgenHbMeBjlkçxNÐsmIkarsþaTic

M o = M p + 1 M n = 0.63M o +
2
1
2
(0.75M o )

sMrab;RbBn§½kMral-ssr (slab-column floor system) tMNxageRkAmankarTb; (restraint) xøH
Edlpþl;edayPaBrwgRkaJTb;karBt;énkMralxNÐ½ nigedayPaBrwgRkajTb;karBt;énssrxageRkA.
eyagtam ACI Code, Section 13.6.3 m:Um:g;sþaTicsrub M o enAkñúgElVgcugRtUv)anEbgEckeday
pleFobepSgKñaedayeyagtamtarag 17>2 nigrUbTI 17>14. emKuNm:Um:g;enAkñúgCYrQrTI 1 sMrab;
RCugEdlminmankarTb;KWQrelIkarsnμt;fa pleFobénPaBrwgRkajTb;karBt;rbs;ssrelIPaBrwg
RkajTb;karBt;smasrvagkMralxNÐ½ nigFñwmenARtg;tMN α ec KWesμIsUnü. emKuNénCYrQrTI 2 KWQr


T.Chhay NPIC

elIkarsnμt;fapleFob α ec esμInwgGnnþ. emKuNm:Um:g;enAkñúgCYrQrTI 3/ TI4 nigTI5 RtUv)anbegáIt
eLIgedaykarviPaKRbBn§½kMralCamYynwglkçxNÐragFrNImaRt niglkçxNÐTMrepSgKña.


T.Chhay NPIC

taragTI 17>2 karEbgEckm:Um:g;enAkñúgbnÞHkMralxagcug
kMralxNÐ½ kMralxNÐ½EdlKμan
RCugxageRkA
EdlmanFñwm FñwmenAcenøaHTMrxagkñúg
minRtUv enAcenøaHRKb; manFñwm KμanFñwm
)anTb; Tb;eBj TMr xageRkA xageRkA
¬!¦ ¬@¦ ¬#¦ ¬$¦ ¬%¦
m:Um:g;emKuNGviC¢manxageRkA 0 0.65 0.16 0.30 0.26
m:Um:g;emKuNviC¢man 0.63 0.35 0.57 0.50 0.52

m:Um:g;emKuNGviC¢manxageRkA 0.75 0.65 0.70 0.70 0.70

8>4> karEbgEckm:Um:g;tamTTwgkñúgkMralxNÐ½ Transverse Distribution of Moment
in Slabs
m:Um:g;tambeNþayEdl)anBnül;xagelIKWsMrab;TTwgTaMgmUlrbs;eRKagGKarsmmUl.
TTwgeRKag enHCaplbUkénTTwgcMerokelIssrBIr
CamYynwgTTwgcMerokkNþalBIrénbnÞHkMralBIrEk,rKña dUcbgðaj enAkñúgrUbTI 17>15.
karEbgEcktamTTwgénm:Um:g;tambeNþayeTAcMerokkNþal nigcMerokelIssrKW
CaGnuKmn_énpleFob l2 / l1
E I
α f = cb b =
E I
beam stiffness
slab stiffness
¬!&>!@¦
cs s
E C torsional rigidity of edge beam section
β t = cb =
2 E cs I s flexural rigidity of a slab of width equal to beam span length
¬!&>!#¦
Edl C = torsional constant = ∑ ⎛1 − 0.63x ⎞⎛ x3y ⎞
3
⎜
⎜ y ⎟⎜
⎟⎜ ⎟
⎟
¬!&>!$¦
⎝ ⎠⎝ ⎠
Edl x nig y CaTTwg nigbeNþayrbs;muxkat;ctuekaN. PaKryénm:Um:g;KNnanImYy²Edl
nwgRtUvEbgEckeTAcMerokelIssr nigcMerokkNþalsMrab;bnÞHkMralxagkñúg nigbnÞHkMralxageRkA
RtUv)aneGayenAkñúgtarag 17>3 dl; 17>6. enAkñúgbnÞHkMralKMrUxagkñg EpñkxøHénm:Um:g;KNna
ú
EdlminRtUv)andak;eTAkñúgcMerokelIssr ¬tarag 17>3¦ RtUv)anTb;edaycMerokkNþalBak;
kNþalEdlRtUvKña. kareFVI linear interpolation sMrab;tMél l2 / l1 EdlenAcenøaH 0.5 nig 2.0
nigsMrab;tMél α f 1l2 / l1 EdlenAcenøaH 0 nig 1 RtUv)anGnuBaØateday ACI Code. BItarag

T.Chhay NPIC

17>3 eyIgGacemIleXIjfa enAeBlFñwmminRtUv)aneRbI dUckñúgkrNI flat plate nig flat slab
α f 1 = 0 . PaKrycugeRkayénm:Um:g;enAkñúgcMerokelIssr nigcM erokkNþalCaGnuKmn_én M o
RtUv)aneGayenAkñúgtaragTI 17>4.
sMrab;kMralxageRkA Epñkénm:Um:g;KNnaEdlminRtUv)andak;enAkñúgcMerokelIssr ¬tarag
17>5¦ RtUv)anTb;edaycMerokkNþalBak;kNþalEdlRtUvKña. mþgeTot kareFVI linear
interpolation cenøaHtM élEdlbgðajenAkñúgtarag 17>5 RtUv)anGnuBaØateday ACI Code,

Section 13.6.4.2. enAeBlEdl FñwmminRtUv)aneRbIenAkMralxageRkA dUckrNI flat plate nig flat

slab edayKμanFñwmxag (spandrel beam) α f 1 = 0 / C = 0 nig β t = 0 . enHmann½yfacugssr

pþl;nUvkarTb;sMrab;cugkMralxageRkA. tMélGnuvtþn_éntarag 17>5 sMrab;krNIBiessenHRtUv)an
bgðajenAkñúgtarag 17>6 nigrUbTI 17>15.


T.Chhay NPIC

tarag 17>3 PaKryénm:Um:g;tambeNþayenAkñúgcMerokelIssr sMrab;bnÞHkMralxagkñúg (ACI
Code, Section 13.6.4)

α f 1l 2 / l1
pleFob l2 / l1
0 .5 1 .0 2 .0
m:Um:g;GviC¢manenAelITMrxagkñúg 0 75 75 75
≥ 1 .0 90 75 45

m:Um:g;viC¢manenAEk,rkNþalElVg 0 60 60 60
≥ 1 .0 90 75 45

tarag 17>4 PaKryénm:Um:g;enAkñúgkMralxNÐ½xagkñúgBIrTisEdlKμanFñwm ( α 1 = 0)
⎛ l n1 ⎞
2
m:Um:g;KNnasrub M o = (wu l 2 )⎜ ⎟ n!
⎜ 8 ⎟ r!(n − r )!
⎝ ⎠
m:Um:g;GviC¢man m:Um:g;viC¢man
m:Um:g;tambeNþayenAkñúgkMralmYy − 0.65M o ± 0.35M o

cMerokelIssr 0.75(− 0.65M o ) = −0.49 M o 0.60(0.35M o ) = 0.21M o

cMerokkNþal 0.25(− 0.65M o ) = −0.16 M o 0.40(0.35M o ) = 0.14 M o

tarag 17>5> PaKryénm:Um:g;tambeNþayenAkñúgcMerokelIssr sMrab;bnÞHkMralxageRkA (ACI
Code, Section 13.6.4)

α f 1l 2 / l1 βt
pleFob l2 / l1
0 .5 1 .0 2 .0
m:Um:g;GviC¢manenAelITMrxageRkA 0 0 75 75 75
≥ 2 .5 90 75 45
≥ 1 .0 0 60 60 60

≥ 2 .5 90 75 45

m:Um:g;viC¢manenAEk,rkNþalElVg 0 60 60 60

≥ 1 .0 90 75 45
m:Um:g;GviC¢manenAelITMrxagkúñg 0 75 75 75
≥ 1 .0 90 75 45


T.Chhay NPIC

tarag 17>6> PaKryénm:Um:g;tambeNþayenAkñúgcMerokelIssr nigcMerokkNþal ¬sMrab;pleFob
l / l ¦ edayeGay α = β = 0
2 1 f1 t

m:Um:g;cugeRkayCaGnuKmn_én
% cMerokelIssr cMerokkNþal M o nig α ec

¬cMerokelIssr¦
⎡ 0.65 ⎤
m:Um:g;GviC¢manenAelITMrxageRkA 100 0.26M o 0 ⎢ ⎥M o
⎣ (1 + 1 α ec ) ⎦
⎡ 0.28 ⎤
m:Um:g;viC¢man¬ 0.6 × 0.52M o ¦ 60 0.312M o 0.208M o ⎢0.63 −
⎣ (1 + 1 α ec )⎥ o
⎦
M

m:Um:g;GviC¢manenAelIMTMrxagkñúg ⎡ 0.10 ⎤
0.75 − ⎢ ⎥M o
⎣ (1 + 1 α ec ) ⎦
0.52M o 0.175M o
¬ 0.75 × 0.70M o ¦ 75

BItarag 17>6 eyIgeXIjfaenAeBlEdlFñwmxagminRtUv)aneRbIsMrab;kMralxageRkA β t = 0
nig m:Um:g;KNna 100% RtUv)anTb;edaycMerokelIssr. cMerokkNþalnwgminTb;m:Um:g;NamYyeT
dUcenHbrimaNEdkGb,brmaRtUv)andak;. ACI Code, Section 13.6.4.3 kMNt;faenAeBlTMrxag
eRkACassr b¤CBa¢aMgEdlRtUv)anBnøÚtsMrab;cMgayesμInwgbIPaKbYnRbEvgElVgTTwg l2 EdleRbIedIm,I
kMNt; M o m:Um:g;GviC¢manxageRkAEdlRtUv)anEbgEckesμIkat;tam l2 . enAeBlEdlFñwmRtUV)andak;
tam beNþayGkS½ssr ACI Code, Section 13.6.5 tMrUvfam:Um:g;RtUvEtsmamaRtedIm,IkarBarm:Um:g;
85% enAkñúgcMerokelIssr RbsinebI α f 1 (l 2 / l1 ) ≥ 1.0 . sMrab;tMél α f 1 (l 2 / l1 ) enAcenøaH 1.0

nig 0 m:U m:g;EdlmankñúgFñwmRtUv)ankMNt;edayeRbI linear interpolation . m:Um:g;k¾RtUVEtsmamaRt
edIm,IkarBar m:Um:g;bEnßmEdlekItedaybnÞúkTaMgGs;EdlGnuvtþedaypÞal;eTAelIFñwm edaybBa©Ül
TaMgTMgn;rbs;tYrFñwm EdlKitBIeRkamkMral. Epñkénm:Um:g;Edlmin)andak;eTAkñúgFñwmRtUv)anTb;eday
kMralxNÐ½enAkñμúgcMerok elIssr.
8>5> karpþl;rbs; ACI sMrab;T§iBlrbs;KMrUénkardak;bnÞúk ACI Provisions for Effects
of Pattern Loading
enAkñúgrcnasm<n§½Cab; m:Um:g;Bt;FGtibrma nigGb,brmaenARtg;muxkat;eRKaHfñak;RtUv)anTTYl
eday kardak;bnÞúkGefrtamKMrUkMNt;mYyedIm,IbegáIttMélx<s;bMput. kardak;bnÞúkGefrenARKb;ElVg


T.Chhay NPIC

TaMgGs; nwgminbegáItm:Um:g;Bt;viC¢man b¤m:Um:g;Bt;viC¢manGtibrmaeT.m:Um:g;Gtibrma nigGb,brma
GaRs½yCacMbg nwgkrNIxageRkam³
!> pleFobénbnÞúkGefrelIbnÞúkefr. pleFobx<s;nwgbegáInT§iBlrbs;KMrUénkardak;bnÞúk
(patter loading).

@> pleFobPaBrwgRkajssrelIFñwm. pleFobtUcnwgbegáInT§iBlrbs;KMrUénkardak;bnÞúk.
#> KMrUénkardak;bnÞúk. m:Um:g;viC¢manGtibrmaenAkñúgElVgrgT§iBltictYcBIKMrUénkardak;bnÞúk.
edIm,IkMNt;m:Um:g;emKuNKNnaenAkñúgrcnasm<n§½Cab; ACI Code, Section 13.7.6 kMNt;dUc
xageRkam³
!> enAeBlKMrUénkardak;bnÞúkRtUv)ansÁal; eRKagsmmUlKYrRtUv)anviPaKsMrab;bnÞúkenaH.
@> enAeBlbnÞúkGefrERbRbYl b:uEnþminFMCagbIPaKbYnénbnÞúkefr wL ≤ 0.75wD b¤enAeBl
EdlRKb;kMralTaMgGs;RtUv)andak;bnÞúkGefrkñúgtMNalKña karviPaKeRKagEdlmandak;bnÞúk
GefremKuNeBjeRKagRtUv)anGnuBaØat.
#> sMrab;lkçxNÐénkardak;bnÞúkepSgeTot eKGnuBaØateGaysnμt;fa m:Um:g;emKuNviC¢man
Gtibrma enAEk,rkNþalElVgekItmanCamYynwg 0.75 énbnÞúkGefremKuNeBjenAelIkMral
nigenAelIkM ralqøas;. sMrab;m:Um:g;emKuNGviC¢manGtibrmaenAkñúgkMralxNÐ½elITMr RtUv)an
eKGnuBaØateGay snμt;fa 0.75 énbnÞúkGefremKuNGnuvtþEtenAelIkMralEk,r.
$> m:Um:g;emKuNminKYryktUcCagm:Um:g;EdlekIteLIgCamYybnÞúkGefremKuNeBjenAelIkMral
EdlCab;TaMgGs;eT.
8>6> karlMGitsrésEdk Reinforcement Details

eRkayeBlPaKryTaMgGs;énm:Um:g;sþaTicenAkñúgcMerokelIssr nigcMerokkNþalRtUv)ankMNt;
brimaNsrésEdkk¾GacRtUv)anKNnasMrab;m:Um:g;viC¢man nigGviC¢manenAkñúgcMeroknImYy² dUc
Edl)aneFVIsMrab;FñwmenAkñúgemeronTI4
⎛ a⎞
M u = φAs f y ⎜ d − ⎟ = Ru bd 2
⎝ 2⎠
¬!&>!%¦
KNna Ru nigkMNt;PaKryEdk ρ edayeRbItarag]bsm<n§½ B b¤eRbIsmIkarxageRkam³
⎛ ρf y ⎞
Ru = φρf y ⎜1 −
⎜ 1.7 f ' ⎟
⎟ ¬!&>!^¦
⎝ c ⎠


T.Chhay NPIC

Edl φ = 0.9 . RkLaépÞmuxkat;EdkKW As = ρbd . enAeBlEdlkMras;kMralxNÐ½RtUvnwgkarkMNt;
kMras;kMralxNÐ½Edl)anerobrab;kñúgEpñkTI 4> enaHeK minRtUvkarEdkrgkarsgát;eT. rUbTI 13>3>8
én ACI Code bgðajRbEvgGb,brmaénEdk nigkar lMGitsrésEdksMrab;kMralEdlKμanFñwm ehIy
vak¾RtUvbgðajenATIenHEdr ¬rUbTI 17>16¦. KMlatEdkenAkñúgkMralxNÐ½minRtUvFMCaglImIt
Gtibrmarbs; ACI EdlmanKMlat 450mm b¤BIrdgkMras; kMralykmYyNaEdltUcCageK.


T.Chhay NPIC

8>7> viFIPaBrwgRkajEdlRtUv)anEktMrUvsMrab;ElVgcug Modified Stiffness Method
for End Spans
enAkñúgviFIenH PaBrwgRkajrbs;FñwmxagcugkMral nigrbs;ssrxageRkARtUv)anCMnYsedayPaB
rwgRkajénssrsmmUl K ec . PaBrwgRkajTb;karBt;énssrsmmUl K ec GacRtUv)anKNnaBI
smIkarxageRkam³
1
=
1
+
1 ∑K
b¤ K ec = 1 + ∑ K c/ K ¬!&>!&¦
K ec ∑ K c K t c t

Edl K ec = PaBrwgRkajTb;nwgkarBt;rbs;ssrsmmUl

K c = PaBrwgRkajTb;nwgkarBt;rbs;ssrBitR)akd

K t = PaBrwgRkajTb;karrmYlrbs;Fñwmxag

plbUkénPaBrwgRkajrbs;ssrxagelI nigxageRkamkMralxNÐ½GacRtUv)anykdUcxag
eRkam³
⎛I I ⎞
∑ K c = 4 E ⎜ c1 + c 2 ⎟
⎜L L ⎟
¬!&>!*¦
⎝ c1 c2 ⎠
Edl I c1 nig Lc1 Cam:Um:g;niclPaB nigRbEvgrbs;ssrxagelInIv:UkMralxNÐ½ nig I c2 nig
Lc 2 Cam:Um:g;niclPaB nigRbEvgrbs;ssrxageRkamnIv:UkMralxNÐ½. PaBrwgRkajTb;nwgkarrmYl

rbs;Fñwmcug K t GacRtUv)ankMNt;dUcxageRkam³
Kt = ∑
9 E cs C
3
¬!&>!(¦
⎛ c ⎞
l 2 ⎜1 − 2 ⎟
⎜
⎝ l2 ⎟
⎠
Edl TMhMrbs;ssrctuekaNEkg b¤ctuekaNEkgsmmUl/ capital column b¤
c2 =

bracket Edlvas;enAelIElVgTTwgénRCugnImYy²rbs;ssr.

Ecs = m:UDuleGLasÞicrbs;ebtugkMral

C = efrrmYl (torsion constant) EdlkMNt;BIsmIkarxageRkam³
⎛ x ⎞⎛ x 3 y ⎞
C = ∑ ⎜1 − 0.63 ⎟⎜
⎜ y ⎟⎜ 3 ⎟
⎟ ¬!&>@0¦
⎝ ⎠⎝ ⎠
Edl x CaTMhMTTwgrbs;ctuekaN nig y CabeNþayrbs;ctuekaN. kñúgkarKNna C
vimaRt rbs;muxkat;ctuekaNRtUv)aneRCIserIsy:agNaedIm,IeFVIeGay)antMél C FMCageK.


T.Chhay NPIC

smIkarxagedImEdl)anENnaMenATIenH nwgRtUv)anykmkeRbIenAkñúgEpñk 12 “Equivalent
Frame Method” .

RbsinebIkMralmanFñwmRsbKñanwgm:Um:g;EdlRtuvKNna enaHPaBrwgRkajTb;karrmYl K t
EdleGaykñúgsmIkar !&>!( RtUv)anCMnYseday K ta EdlmantMélFMCag ehIy K ta RtUv)an
KNnadUcxag eRkam³
I sb
K ta = K t ×
Is
l2 h 3
Edl Is =
12
m:Um:g;niclPaBrbs;kMralxNÐ½EdlmanTTwgesμInwgTTwgeBjcenøaHGkS½
=

kMral ¬edayminrYmbBa©ÚlEpñkrbs;tYrFñwmEdlbnøayeTAelI b¤eTAeRkamkMralxNÐ½¦.
I sb = I s / edaybBa©ÚlTaMgtYrFñwmEdlbnøayeTAelI b¤eTAeRkamkMralxNÐ½.

muxkat;énGgát;rgkarrmYlxøHEdlmanP¢ab;mkCamYyRtUv)anbgðajenAkúñgrUbTI 17>17.
enAeBlEdl K ta RtUv)anKNna enaHpleFobPaBrwgRkaj α ec RtUv)anTTYldUcxageRkam³
α ec =
K ec
∑ (K + K )
¬!&>@!¦
s b

Edl Ks =
4 Ecs I s
l1
=PaBrwgRkajTb;karBt;rbs;kMralxNÐ½
Kb = =PaBrwgRkajTb;karBt;rbs;Fñwm
4 Ecb I b
l1
I b = m:Um:g;niclPaBTaMgmUlrbs;muxkat;FñwmbeNþay

karEbgEckénm:Um:g;sþaTicsrub M o enAkñúgkMralxageRkARtUv)aneGayCaGnuKmn_én α ec
dUcxageRkam³
⎡ 0 .1 ⎤
Interior negative factored moment = ⎢0.75 −
(1 + 1 / α ec )⎥ o
M
⎣ ⎦
⎡ 0.28 ⎤
Positive factored moment = ⎢0.63 −
(1 + 1 / α ec )⎥ o
M
⎣ ⎦
⎡ 0.65 ⎤
Exterior negative factored moment = ⎢ ⎥M o
⎣ (1 + 1 / α ec ) ⎦
tMélTaMgenHRtUv)anbgðajenAkñúgkMralxageRkAKMrUkñúgrUbTI 17>18. emKuNTaMgenHRtUv)an
BicarNaBIT§iBlrbs;PaBrwgRkajrbs;ssrxageRkAk¾dUcCaT§iBlrbs;PaBrwgRkajrbs;FñwmcugkM
ral EdleFVIeGaykarEbgEckm:Um:g;manlkçN³RKb;RKan;.


T.Chhay NPIC


T.Chhay NPIC

8>8> segçbviFIKNnaedaypÞal; Summary of the Direct Design Method (DDM)

krNITI1 kMralKμanFñwm
!> RtYtBinitütMrUvkarénkarkMNt;Edl)anBnül;enAkñúgEpñk 8>1. RbsinebIvaminRtUvnwgkar
kMNt;eT eKminGaceRbIviFI DDM )aneT.


T.Chhay NPIC

@> kMNt;kMralxNÐ½Gb,brma hmin edIm,IRKb;RKgPaBdabedayeRbItMélenAkñúgtarag 17>1.
kM ralxageRkAEdlKμanFñwmxageGay hmin x<s;bMput ¬ ln / 30 sMrab; f y = 420MPa ¦.
vaCa karGnuvtþFmμtaEdleRbIkMras;kMralxNÐ½esμIKñasMrab;RKb;kMralxageRkAnigxagkñúg.
#> KNnabnÞúkemKuN Wu = 1.2WD. + 1.6WL
$> epÞógpÞat;kMras;kMralxNÐ½ h edIm,IkarBarkMlaMgkat;TTwgmYyTis nigkMlaMgkat;TTwgBIr
Tis. RbsinebIkMras;kMralxNÐ½ h minRKb;RKan; eKRtUvbegáInkMras; h b¤dak;EdkTb;
kMlaMgkat;TTWg.
%> KNnam:Um:g;sþaTicsrub M o sMrab;TisedATaMgBIr ¬smIkar !&>!!¦
^> kMNt;emKuNEbgEcksMrab;m:Um:g;viC¢man nigm:Um:g;GviC¢manenAkñúgTisedAbeNþay
nigTisedA TTwgsMrab;cMerokelIssr nigcMerokkNþalnImYy²TaMgenAkñúgkMralxagkñúg
nigkMralxageRkA dUcxageRkam³
a. sMrab;kMralxagkñúg eRbIemKuNm:Um:g;EdleGayenAkñúgtarag 17>4 b¤rUbTI 17>15

b. sMrab;kMralxageRkAEdlKμanFñwmxag emKuNm:Um:g;kMralRtUv)aneGayenAkñúgtarag

17>2 b¤rUbTI 17>14 ¬krNITI5¦. sMrab;karEbgEckm:Um:g;enAkñúgTisedATTwg
eRbIta rag 17>6 b¤rUbTI 17>15 sMrab;GRtacMerokelIssr.
cMerokkNþalnwgTb;Epñkénm:Um:g; EdlminRtUv)andak;eTAkñμúgcMerokssr.
c. sMrab;kMralxageRkAEdlmanFñwmxag emKuNm:Um:g;kMralRtUv)aneGayenAkñúgtarag

17>2 b¤rUbTI 17>14 ¬krNITI4¦. sMrab;karEbgEckm:Um:g;enAkñúgTisedATTwg
eRbIta rag 17>5 sMrab;cMerokelIssr. cMerokkNþalnwgTb;lMnwgénm:Um:g;kMral.
&> kMNt;brimaNEdksMrab;RKb;muxkat;eRKaHfñak;;éncMerokelIssr nigcMerokkNþalTaMgGs;
nigBnøÚtsrésEdkeBjkMralxNÐ½ ¬rUbTI 17>16¦
*> KNna unbalanced moment nigRtYtBinitüemIlfaetIkarbMElgm:Um:g; unbalanced
moment edaykarBt;RKb;RKan;b¤Gt;. RbsinebIGt;RKb;RKan;eT kMNt;brimaNEdk

bEnßmEdlcaM)ac;enAkñúgTTwgeRKaHfñak; ¬eyagtamEpñkTI 10¦.
(> RtYtBinitüemIlfaetIkarbMElgm:Um:g; unbalanced moment edaykMlaMgkat;TTwgRKb;
RKan; b¤Gt;. RbsinebIGt;eT begáIn h b¤dak;EdkTb;kMlaMgkat;TTwg. ¬eyagtamEpñkTI
10¦


T.Chhay NPIC

krNITI2 kMralEdlmanFñwmxagkñúg nigFñwmxageRkA
!> RtYtBinitütMrUvkarénkarkMNt;Edl)anBnül;enAkñúgEpñk 8>1.
@> kMNt;kMralxNÐ½Gb,brma hmin edIm,IRKb;RKgPaBdabedayeRbItMélenAkñúgsmIkar
TI !&>! Dl; !&>#. kñúgkrNICaeRcIn smIkarTI !&>@ lub. smIkarTI !&>! KYrRtUv)an
KNnadMbUgdUcbgðajenAkñúg]TahrN_TI 17>1.
#> KNnabnÞúkemKuN Wu = 1.2WD. + 1.6WL
$> epÞógpÞat;kMras;kMralxNÐ½ h tamry³kMlaMgkat;TTwgmYyTis nigkMlaMgkat;TTwgBIrTis.
CaTUeTA kMlaMgkat;TTWgminmanlkçN³eRKaHfñak;sMrab;kMralxNÐ½EdlRTedayFñwmeT.
%> KNnam:Um:g;sþaTicsrub M o sMrab;TisedATaMgBIr ¬smIkar !&>!!¦
^> kMNt;emKuNEbgEcksMrab;m:Um:g;viC¢man nigm:Um:g;GviC¢manenAkñúgTisedAbeNþay nigTis
edA TTwgsMrab;cMerokelIssr nigcMerokkNþalnImYy²TaMgenAkñúgkMralxagkñúg nigkMral
xageRkA dUcxageRkam³
a. sMrab;kMralxagkñúg eRbIemKuNm:Um:g;kñúgrUbTI 17>14 ¬krNITI 3¦ b¤rUbTI 17>12.

sMrab;karEbgEckm:Um:g;kñúgTisedATTwg eRbItaragTI 17>3 sMrab;cMerokelIssr. cM
erokkNþalnwgTb;Epñkénm:Um:g;Edlmin)andak;eTAkñúgcMerokelIssr. KNna α1 BI
smIkar !&>!@.
b. sMrab;kMralxageRkA eRbIemKuNm:Um:g;kMralenAkñúgtarag 17>2 b¤rUbTI 17>14

¬krNI TI3¦. sMrab;karEbgEckm:Um:g;enAkñúgTisedATTwg eRbItarag 17>5 sMrab;cM
erokelIssr. cMerokkNþalnwgTb;lMnwgénm:Um:g;kMral.
c. kñúgkrNITaMgBIr (a) nig (b) FñwmRtUvTb; 85% énm:Um:g;enAkñúgcMerokssr enAeBl

Edl α f 1 (l2 / l1 ) ≥ 1.0 b:uEnþGRtaERbRbYlcenøaH 85% nig 0% enAeBl
α f 1 (l 2 / l1 ) ERbRbYlcemøaHBI 1.0 nig 0 .
&> kMNt;brimaNEdksMrab;RKb;muxkat;eRKaHfñak;;éncMerokelIssr/ Fñwm nigcMerokkNþal
TaMgGs; bnÞab;mkBnøÚtsrésEdkeBjkMralxNÐ½ ¬rUbTI 17>16¦
*> KNna unbalanced moment nigbnÞab;mkRtYtBinitüemIlkarbMElgénm:Um:g; edaykar
Bt; nigkMlaMgkat;TTwg ¬eyagtamEpñkTI 10¦.


T.Chhay NPIC

]TahrN_TI17>3³
edayeRbIvIFI direct design method KNnakMral flat plate xagkñúgKMrU dUcEdl)anbgðajenAkñúgrUb
TI 17>6 nig 17>19. RbBn§½kMralpSMeLIgeday kMralbYnenARKb;Tis EdlkMralmYy²manTMhM
7.5 × 6m . kMralTaMgGs;RtUv)anRTedayssrTMhM 50 × 50cm manRbEvg 3.6m . kMralxNÐ½RT

bnÞúkGefreFVIkar BRgayesμI 4.8kN / m 2 nigbnÞúkefreFVIkarEdlrYmman kMralkargarbegðIy (floor
finish) 1.5kN / m 2 rYmTaMgbnÞúkpÞal;rbs;kMral. eKeGay f 'c = 28MPa nig f y = 420MPa .


T.Chhay NPIC

dMeNaHRsay³
1> kMNt;kMras;kMralxNÐ½Gb,brmaedayeRbItarag 17>1 sMrab; flat plate. BI]TahrN_TI
17>1 kMras;kMralxNÐ½KW 25cm .
2> KNnabnÞúkemKuN³
wD = 1.5 + weight of slab = 1.5 + 0.25 × 25 = 7.75kN / m 2
wu = 1.2 × 7.75 + 1.6 × 4.8 = 17kN / m 2
3> RtYtBinitükMlaMgkat;TTwgmYyTis nigkMlaMgkat;TTwgBIrTis³
a. RtYtBinitükMlaMgkat;pugenAcMgay d / 2 BIépÞssr ¬GMeBIBIrTis¦.

Edaysnμt;kMras;ebtugkarBarEdk 2cm nigeRbIEdk DB16 . enaH d mFümKW
25 − 2 − 1.6 = 21.4cm nig bo = 4(50 + 21.4) = 285.6cm ¬emIlrUbTI 17>19 c¦

Vu = [l1l 2 − (71.4 × 71.4)]× wu = (750 × 600 − 5098) × 17 ⋅ 10 −4 = 756.3kN
φ 0.75
φVc = f 'c bo d = 28 × 2.856 × 0.214 × 10 3 = 808.5kN
3 3
EdlFMCag Vu
b. KNnakMlaMgTTwgFñwmenAcMgay d BIépÞssr. d mFümKW 21.4cm . BicarNacMerok

1m ¬rUbTI 17>19 d¦ CamYyRbEvgcMerokKW³

x = 3.75 − 0.25 − 0.214 = 3.286m
Vu = wu (1 × 3.286) = 17 × 3.286 = 55.862kN
φ 0.75
φVc = f 'c bd = 28 × 1 × 0.214 × 10 3 = 141.5kN
6 6
EdlFMCag Vu . Kñugkardak;bnÞúkFmμta kMlaMgkat;TTwgmYyTisGt;lub.
4> KNnam:Um:g;sþaTicsrubenAkñúgTisedAEvg nigTisedAxøI
2
kñúgTisedAEvg M ol = 8 = 8 6 × 7 2 = 624.75kN .m
wu l 2 l n1 17

2
kñúgTisedAxøI M os = wu l81ln2 = 17 7.5 × 5.52 = 482.11kN .m
8
edaysarEt l2 < l1 TTwgénBak;kNþalcMerokelIssrenAkñúgTisedAEvgKW
0.25 × 6m = 1.5m ehIyTTwgéncMerokkNþalKW 6 − 2 × 1.5 = 3m . TTwgénBak;kNþal

cMerokelIssrkñúgTisedAxøI KW 1.5m ehIyTTwgéncMerokkNþalKW 7.5 − 2 × 1.5 = 4.5m .
edIm,IKNnakMBs;RbsiT§PaB d kñúgTisedAnImYy² snμt;faEdkenA kñúgTisedAxøIRtUvBIelIEdk

T.Chhay NPIC

enAkñúgTisedAEvg. dUcenH d (long direction) = 25 − 2 − 0.8 = 22.2cm nig
d (short direction ) = 25 − 2 − 1.6 − 0.8 = 20.6cm . sMrab;karGnuvtþn_ d (average) =

25 − 3.5 = 21.5cm GacRtUv)aneRbIsMrab;Tis edATaMgBIr.

dMeNIrkarKNnaGacRtUv)anerobcMCaTMrg;tarag dUcbgðajenAkñúgtarag 17>7 nig 17>8.
karlMGitsMrab;kareRCIserIssrésEdkRtUv)anbgðajenAkñúgrUbTI 17>20 edayeRbIRbBn§½
EdkRtg;. eKRtUveKarBkardak;RbEvgGb,brmarbs;EdkdUcEdl)anbgðajenAkñúgrUbTI
17>16.
Gñksagsg;cUlcitþeRbIEdkRtg; nigEdkEdlmanersIusþg; f ' y = 420MPa .
KMlatGtibrma = widthof bars = 3000 = 375mm
no.
of panel
8
taragTI17>7 karKNnabnÞHkMral flat platexagkñúg ¬kñúgTisEvg¦
M o = 624.75kN .m

M n = −0.65M o = −406.1kN .m
TisEvg M p = +0.35M o = 218.66kN .m

cMerokelIssr cMerokkNþal
GviC¢man viC¢man GviC¢man viC¢man
karEbgEckm:Um:g; % 75 60 25 40

M u (kN .m) 0.75M n = −304.6 0.6 M p = ±131.2 0.25 M n = −101.5 0.6 M p = ±87.5

TTwgcMerok b(mm) 3000 3000 3000 3000
kMBs;RbsiT§PaB d (mm) 222 222 222 222
Mu
Ru = ( MPa)
bd 2 2.06 0.89 0.69 0.59

PaKryEdk ρ (%) 0.57 0.24 0.19 0.16
As = ρbd (mm 2 ) 3796.2 1598.4 1265.4 1065.6
As (min) = 0.0018bhs (mm 2 ) 1350 1350 1350 1350
EdkEdleRCIserIs ¬Rtg;¦ 20 DB16 8DB16 12DB12 12DB12
KMlat ≤ 2h = 500mm
s 150 375 250 250


T.Chhay NPIC

taragTI17>8 karKNnabnÞHkMral flat platexagkñúg ¬kñúgTisxøI¦
M o = 482.11kN .m

M n = −0.65M o = −313.4kN .m
TisEvg M p = +0.35M o = 168.7kN .m

GviC¢man viC¢man GviC¢man viC¢man
karEbgEckm:Um:g; % 75 60 25 40

M u (kN .m) 0.75 M n = −235.05 0.6 M p = ±101.2 0.25 M n = −78.35 0.6 M p = ±67.5

TTwgcMerok b(mm) 3000 3000 4500 4500
Mu
Ru = ( MPa)
bd 2 1.85 0.79 0.41 0.35

PaKryEdk ρ (%) 0.51 0.21 0.11 0.09
As = ρbd (mm 2 ) 3151.8 1297.8 1019.7 834.3
As (min) = 0.0018bhs (mm 2 ) 1350 1350 2025 2025
EdkEdleRCIserIs ¬Rtg;¦ 16 DB16 8DB16 18 DB12 18 DB12
s 187.5 375 250 250
KMlatEdkenAkñúgcMerokelIssrkñúgTisxøIKW 250mm . vamanlkçN³RKb;RKan; edaysarva
tUcCag 2hs = 500mm nigtUcCag 450mm EdlkMNt;eday ACI Code.
cMNaMfa PaKryEdkTaMgGs;KWticCag ρ max = 0.0182 . dUcenH φ = 0.9 .

]TahrN_TI17>4³
edayeRbIviFI direct design method KNnakMral flat plate xageRkAEdlmanTMhM bnÞúk ersIusþg;ebtug
nigersIusþg;EdkdUcKñanwgGVIEdl)aneGayenAkñúg]TahrN_TI 17>3. FñwmminRtUv)aneRbI ¬rUbTI 17>21¦.
dMeNaHRsay³
1> kMNt;kMras;kMralxNÐ½Gb,bramedayeRbItarag 17>1 sMrab; flat plate. BI]TahrN_TI
17>1 kMras;kMralxNÐ½KW 25cm .


T.Chhay NPIC

2> KNnabnÞúkemKuN³ wu = 17kN / m 2
3> RtYtBinitükMlaMgkat;TTwgmYyTis nigkMlaMgkat;TTwgBIrTis ¬eyagtam]TahrN_TI 17>3
nigrUbTI 17>9¦.

a. RtYtBinitükMlaMgkat;pugenAssrxagkñúg Vu = 756.3kN < φVc = 808.5kN
b. RtYtBinitükMlaMgkat;TTwgmYyTis³ Vu = 55.862kN < φVc = 141.5kN
c. RtYtBinitükMlaMt;pugenAssrxageRkA³ d = 21.4cm
21.4
x = 50 + = 60.7cm
2


T.Chhay NPIC

y = 50 + 21.4 = 71.4cm


T.Chhay NPIC

bo = 2 x + y = 192.8cm
⎡ ⎛ 750 ⎞ ⎤
Vu = ⎢600⎜ + 25 ⎟ − 60.7 × 71.4⎥10 −4 × 17 = 400.6kN
⎣ ⎝ 2 ⎠ ⎦
φ
φVc = f ' c bo d = 545.8kN > 400.6kN
3
d. RtYtBinitükMlaMgkat;pugenAssrkac;RCug³ d = 21.4cm
21.4
x = y = 50 + = 60.7cm
2
bo = x + y = 121.4cm
⎡⎛ 600 ⎞⎛ 750 ⎞ ⎤
Vu = ⎢⎜ + 25 ⎟⎜ + 25 ⎟ − 60.7 × 60.7 ⎥10 −4 × 17 = 214.7 kN
⎣⎝ 2 ⎠⎝ 2 ⎠ ⎦
φ
φVc = f ' c bo d = 343.7 kN > 214.7 kN
3
4> KNnam:Um:g;sþaTicsrub ¬BI]TahrN_TI 17>3¦
M ol (long direction ) = 624.7 kN .m d = 22.2cm

M os (short direction) = 482.11kN .m d = 20.6cm
TTwgrbs;cMerokelIssrKW 300cm nigTTwgcMerokkNþalKW 450cm
5> KNnam:Um:g;KNnaenAkñúgTisedAEvg³ l1 = 7.5m ¬eyagtamtarag 17>5 b¤rUb 17>15¦.
karEbgEckm:Um:g;srub M ol enAkñúgcMerokelIssr nigcMerokkNþalKWRtUv)anKNnadUcxag
eRkam³
a. cMerokelIssr³

m:Um:g;GviC¢manxagkñúg = −0.525M o = −0.525(624.75) = −328kN .m
m:Um:g;viC¢manenAkñúgElVg = 0.312M o = 0.312(624.75) = 195kN .m
m:Um:g;GviC¢manxageRkA = −0.26M o = −0.26(624.75) = 162.4kN.m
b. cMerokkNþal³

m:Um:g;GviC¢manxagkñúg = −0.175M o = −0.175(624.75) = −109.3kN .m
m:Um:g;viC¢manenAkñúgElVg = 0.208M o = 0.208(624.75) = 129.9kN .m
m:Um:g;GviC¢manxageRkA = 0


T.Chhay NPIC

6> KNnam:Um:g;KNnaenAkñúgTisedAxøI³ ls = 6m . vaRtUv)anKitdUckMralxagkñúgEdr BIeRBaHva
Cab;TaMgsgçag. eyagtamtarag 17>4 b¤rUbTI 17>15 karEbgEckm:Um:g;srub M os enA
kñúgcMerokelIssr nigcMerokkNþalRtUv)anKNnadUcxageRkam³
a. cMerokelIssr³

m:Um:g;GviC¢man = −0.49M o = −0.49(482.11) = −236.2kN.m
m:Um:g;viC¢man = 0.21M o = 0.21(482.11) = 101.2kN .m
b. cMerokkNþal³

m:Um:g;GviC¢man = −0.16M o = −0.16(482.11) = −77.1kN.m
m:Um:g;viC¢man = 0.14M o = 0.14(482.11) = 67.5kN .m
dMeNIrkarKNnaRtUv)antMeroby:aggayRsYlenAkñúgtarag 17>9. karlMGitsMrab;kar
eRCIserIssrésEdkRtUv)anbgðajenAkñúgrUbTI 17>22 edayeRbIRbBn§½EdkRtg;;enAkñúgTis
Evg. karlMGitsrésEdkenAkñúgTisxøImanlkçN³RsedogKñanwgkarBRgaysrésEdkenA
kñúgrUbTI 17>20 edayeRbIkareRCIserIssrésEdkenAkñúgtarag 17>9.
cMNaMfa RKb;PaKryEdkTaMgGs;tUcCag ρ max = 0.0182 . dUcenH φ = 0.9 .


T.Chhay NPIC

tarag 17>9 karKNnakMral flat platexageRkAsMrab;]TahrN_TI 17>4 ¬ d = 22.2cm ¦
TisEvg
xageRkA viC¢man xagkñúg xageRkA viC¢man xagkñúg
M u (kN .m) − 162.4 195 − 328 0 129.9 − 109.3
TTwgcMerok b(mm) 3000 3000 3000 3000 3000 3000
Mu
Ru = ( MPa)
bd 2 1.10 1.32 2.22 0 0.88 0.74

PaKryEdk ρ (%) 0.30 0.36 0.62 0 0.24 0.20
As = ρbd (mm 2 ) 1998 2398 4129 0 1598 1332
As (min) = 0.0018bhs (mm 2 ) 1350 1350 1350 1350 1350 1350
EdkEdleRCIserIs ¬Rtg;¦ 10DB16 12DB16 22DB16 12DB12 18DB12 12DB12
s 300 250 136 250 167 250
TisxøI cMerokelIssr cMerokkNþal
M u (kN .m) − 236.2 101.2 − 77.1 67.5

TTwgcMerok b(mm) 3000 3000 4500 4500
Mu
Ru = ( MPa)
bd 2 1.86 0.79 0.40 0.35

PaKryEdk ρ (%) 0.52 0.21 0.11 0.09

As = ρbd (mm 2 ) 3214 1298 1020 834.3
As (min) = 0.0018bhs (mm 2 ) 1350 1350 2025 2025
EdkEdleRCIserIs ¬Rtg;¦ 16DB16 8DB16 18DB12 18DB12
s 187.5 375 250 250

]TahrN_TI17>5³
eFVI]TahrN_TI 17>4 elIgvij edayeRbIviFI modified stiffness method. ¬eKRtUvkarKNnaRsedogKña
sMrab;viFI equivalent frame method, EpñkTI 12¦.


T.Chhay NPIC

dMeNaHRsay³
1> GnuvtþRsedogKñasMrab;CMhanTI 1 dl; 4 dUckñúg]TahrN_TI 17>4
2> KNnaPaBrwgRkajssrsmmUl/ K ec ³
1 1 1
= +
K ec ∑ K c K t
eyIgGacsnμt;faEpñkéncMerokkMralEdlenAcenøaHssrxageRkAeFVIkarCassrTb;nwgkarrmYl.
muxkat;rbs;kMralxNÐ½-ssrKW 50cm ¬TTWgrbs;ssr¦ × 25cm ¬kMras;kMralxNÐ½¦ dUcEdl
bgðajkñúgrUb.
a. kMNt;PaBrwgRkajTb;karrmYl K t BIsmIkar !&>@0³
⎛ x ⎞ x3 y
C = ⎜1 − 0.63 ⎟
⎜ x = 250mm y = 500mm
⎝ y⎟ 3
⎠
⎛ 250 ⎞ 250 3 × 500
C = ⎜1 − 0.63 ⎟ = 17.84 ⋅ 10 8 mm 4
⎝ 500 ⎠ 3
9Ec C 9 E c 17.84 ⋅ 10 8
Kt = 3
= 3
= 3.47 E c ⋅ 10 6
⎛ c ⎞ ⎛ 500 ⎞
l 2 ⎜1 − 2 ⎟ 6000⎜1 − ⎟
⎜ ⎟ ⎝ 6000 ⎠
⎝ l2 ⎠
sMrab;kMralxNÐ½Ek,rKñaBIr ¬enAelIRCugTaMgsgçagrbs;ssr¦ EdleFVIkarCaFñwmTTwg
K t = 2 × 3.47 E c ⋅ 10 6 = 6.94 E c ⋅ 10 6
b. KNnaPaBrwgRkajrbs;ssr K c / kMBs;ssr Lc = 3.6m
4 Ec I c 4 E c 500 4
Kc = = × = 5.79 E c ⋅ 10 6
Lc 3600 12
sMrab;ssrBIrenABIelI niBIeRkamkMralxNÐ½
K c = 2 × 5.79 E c ⋅ 10 6 = 11.58 E c ⋅ 10 6
c. KNna K ec ³
1 1 1
= +
K ec 11.58 E c ⋅ 10 6
6.94 E c ⋅ 10 6

K ec = 4.34 E c ⋅ 10 6
3> KNnaPaBrwgRkajrbs;kMralxNÐ½ nigemKuN α ec
3
4Ec I s l 2 hs
Ks = hs = 250mm l 2 = 6000mm Is =
l1 12


T.Chhay NPIC

4 E c 6000 × 250 3
Ks = × = 4.17 E c ⋅ 10 6
7500 12
K ec
α ec =
∑ (K s + K b )
Kb = 0 ¬edaysarKμanFñwm¦
4.34 Ec ⋅ 10 6
dUcenH α ec = = 1.04
4.17 E c ⋅ 10 6

yk Q = 1+
1
α ec
= 1.96

4> KNnam:Um:g;KNnaenAkñúgTisedAEvg³ ll = 7.5m .
karEbgEckm:Um:g;enAkñúgkMralmYyRtUv)anbgðajenAkñúgrUbTI 17>18.
m:Um:g;GviC¢manxagkñúgKW
⎡ 0.10 ⎤ ⎛ 0.10 ⎞
M ni = ⎢0.75 − ⎥ M ol = ⎜ 0.75 − 1.96 ⎟(624.7) = −436.6kN .m
⎣ Q ⎦ ⎝ ⎠
m:Um:g;viC¢manKW
⎡ 0.28 ⎤ ⎛ 0.28 ⎞
M p = ⎢0.63 − ⎥ M ol = ⎜ 0.63 − 1.96 ⎟(624.7) = 304.3kN .m
⎣ Q ⎦ ⎝ ⎠
m:Um:g;GviC¢manKW
M ne =
0.65
( M ol ) =
0.65
(624.7 ) = 207.2kN .m
Q 1.96
5> KNnakarEbgEckm:Um:g;kMralenAkñúgTisxøIeTAcMerokelIssr nigcMerokkNþal. m:Um:g; M ni /
M p nig M ne RtUv)anEbgEckdUcxageRkam ¬eyagtamtarag 17>6¦³

a. m:Um:g;xagkñúg M nl = −436.6kN .m RtUv)anEbgEck 75% sMrab;cMerokelIssr nig

25% sMrab;cMerokkNþal

column strip = 0.75(− 436.6 ) = −327.5kN.m

Middle strip = 0.25(− 436.6 ) = −109.1kN.m
b. m:Um:g;viC¢man M p = 304.3kN .m RtUv)anEbgEck 60% sMrab;cMerokelIssr nig 40%
sMrab;cMerokkNþal
column strip = 0.60(304.3) = 182.6kN.m

Middle strip = 0.40(304.3) = 121.7 kN.m
c. m:Um:g;GviC¢manxageRkA M ne = −207.2kN .m RtUv)anEbgEckGaRs½ytamtarag 17>5³


T.Chhay NPIC

βt =
Ecb C
=
C
2 Ecs I s 2 I s
¬ebtugkMralxNÐ½ nigebtugssrmanm:UDuleGLasÞicdUcKña¦
250 3
I s = 6000 = 78.125 ⋅ 108 mm 4
12
17.84 ⋅ 10 8
β= = 0.114
2 × 78.125 ⋅ 108
E I l l2
α f 1 = cb b = 0 α f1 2 = 0 = 0 .8
Ecs I s l1 l1
BItarag 17>5 nigedayeFVviFanmUlvacar (interpolation) cenøaH β t = 0 ¬PaKry
I
=100% ¦ nig β t = 2.5 ¬PaKry = 75% ¦ sMrab; β t = 0.114 PaKryKW 98.9% .
m:Um:g;GviC¢manxageRkAenAkñúgcMerokelIssrKW 0.989 × (− 207.2) = −204.92kN.m
nigenAkñúgcMerokkNþalKW − 2.28kN.m . kñúgkrNIenHeKGacKitfacMerokelIssrRTm:Um:g;
M ne 100% KWesμInwg − 207.2kN.m

6> kMNt;srésEdkEdlcaM)ac;enAkñúgTisedAEvgkñúgtaragEdlmanlkçN³RsedogKñanwg]TahrN_
TI 17>4. lT§plEdlTTYl)anmanlkçN³ERbRbYlticbMputxusBItarag 17>9.
7> eRbobeFoblT§plrvag]TahrN_TI 17>4 nig 17>5 eyIgeXijfam:Um:g;xageRkAenAkñúgcMerok
elIssr ¬ − 207.2kN.m ¦FMCagcMelIyEdlTTYl)ankñúg]TahrN_TI 17>4 ¬ − 162.4kN.m ¦
eday 27.6% b:uEnþm:Um:g;viC¢man ¬182.6kN.m ¦ RtUv)ankat;bnßyeday 6.8% ¬eFobnwg
195kN.m ¦ ÉtMéld¾éTeTotesÞIrEtRtUvKña.

]TahrN_TI17>6³
KNnakMralxagkñúgénRbBn§½kMralBIrTisEdl)anbgðajenAkñúgrUbTI 17>7. kMralpSMeLIgedaykMral
EdlmanTMhM 7.6 × 6m cMnYn 6 kñúgTisnImYy². kMralTaMgGs;RtUv)anRTedayssrEdlmanTMhM
50 × 50cm RbEvg 3.6m . kMralRtUv)anRTedayFñwmtambeNþayGkS½ssrEdlmanmuxkat;dUcbgðaj

kñúgrUb. bnÞúkGefreFVIkarRtUv)anyk 4.8kN / m 2 nigbnÞúkefreFVIkarpSMeLIgeday 1kN / m 2 sMrab;kar
garbegðIybEnßmBIelITMgn;pÞal;rbs;kMral. cUreRbI f 'c = 21MPa / f y = 420MPa nigviFI direct
design method.

dMeNaHRsay³
1> eKRtUveFVItamkarkMNt;rbs; ACI Code. kMNt;kMras;kMralxNÐ½Gb,brmaedayeRbIsmIkar
17>1 nig 17>2. kMras;kMralxNÐ½RtUv)anKNnarYcCaeRscenAkñúg]TahrN_TI 17>2 ehIy


T.Chhay NPIC

eyIgTTYlykkMras; 18cm . CaTUeTA kMras;kMralxNÐ½enAkñúgRbBn§½kMralRtUv)anRKb;RKgeday
kMralkac;RCugdUcCakarKNna hmin kMralxageRkApþl;nUvkMras;kMralFMCagsMrab;kMralxagkñúg.
2> KNnabnÞúkemKuN
wD = 1 + 0.18 × 25 = 5.5kN / m 2

wu = 1.2 × 5.5 + 1.6 × 4.8 = 14.28kN / m 2
3> kugRtaMgkMlaMgenAkñúgkMralxNÐ½minmanlkçN³eRKaHfñak;eT. muxkat;eRKaHfñak;mancMgay d BI
épÞFñwm. sMrab;TTwg 1m ³
⎛ 1 ⎞ ⎛ 0.4 ⎞
Vu = wu ⎜ 3 − beam width − d ⎟ = 14.28⎜ 3 − − 0.15 ⎟ = 37.84kN
⎝ 2 ⎠ ⎝ 2 ⎠
φ 0.75 21
φVc = f 'c bd = 1000 × 150 ⋅ 10 −3 = 85.9kN
6 6
4> KNnam:Um:g;sþaTicsrubenAkñúgTisEvg nigTisxøI³
wu
l 2 (l n1 )2 = 6(7.1)2 = 539.9kN .m
14.28
M ol =
8 8
w
= u l1 (l n 2 )2 = 7.6(5.5)2 = 410.4kN .m
14.28
M os
8 8
5> KNnam:Um:g;KNnaenAkñúgTisEvg³ ll = 7.6m
a. karEbgEckm:Um:g;enAkñúgkMral

m:Um:g;GviC¢man M n = 0.65M ol = 0.65 × 539.9 = −350.9kN .m
m:Um:g;viC¢man M p = 0.35M ol = 0.35 × 539.9 = 189kN .m
b. karEbgEckm:Um:g;kMralkñúgTisTTwgeTAFñwm/ cMerokelIssr nigcMerokkNþal

α f 1 = α s = b = 3.19 ¬BI]TahrN_TI 17>2¦
l2 6 EI
= = 0.79
l 17 .6 EI s
l2
α f1 = 3.19 × 0.79 = 2.52 > 1
l1
c. karEbgEckm:Um:g;GviC¢man M n . Epñkénm:Um:g;GviC¢manxagkñúgedIm,IkarBaredaycMerokelI
ssrRtUv)anTTYlBItarag 17>3 edayeFVI interpolation nigesμInwg 81.3% ¬sMrab;
l 2 / l1 = 0.79 nig α f 1 (l 2 / l1 ) > 1.0 ¦.

cMerokelIssr = 0.813M n = 0.813 × 350.9 = −285.3kN .m
cMerokkNþal = 0.187M n = 0.187 × 350.9 = −65.6kN .m


T.Chhay NPIC

edaysarEt α f 1 (l2 / l1 ) > 1/ ACI Code, Section 13.6.5 bgðajfa 85% énm:Um:g;
kñúgcMerokelIssrRtUv)anEckeGayeTAFñwm nigenAsl; 15% RtUv)anEckeGayeTAkM
ralcMerokelIssr.
Fñwm = 0.85 × 285.3 = −242.5kN.m
cMerokelIssr = 0.15 × 285.3 = −42.8kN.m
cMerokkNþal = −65.6kN.m
d. karEbgEckm:Um:g;viC¢man M p .

Epñkénm:Um:g;viC¢manxagkñúgEdlRtUv)anTb;edaycMerokelIssrRtUv)anTTYlBItarag 17>3
edayeFVI interpolation nigesμInwg 81.3% ¬sMrab; l2 / l1 = 0.79 nig α f 1 (l2 / l1 ) > 1.0 ¦.
cMerokelIssr = 0.813M n = 0.813 × 189 = 153.7kN .m
cMerokkNþal = 0.187M n = 0.187 × 189 = 35.3kN .m
edaysarEt α f 1 (l2 / l1 ) > 1/ ACI Code, Section 13.6.5 bgðajfa 85% énm:Um:g;
kñúgcMerokelIssrRtUv)anEckeGayeTAFñwm nigenAsl; 15% RtUv)anEckeGayeTAkM
ralcMerokelIssr.
Fñwm = 0.85 × 153.7 = 130.6kN.m
cMerokelIssr = 0.15 × 153.7 = 23.1kN.m
cMerokkNþal = 35.3kN.m
karlMGitm:Um:g;RtUv)anbgðajenAkñúgrUbTI 17>23.
6> KNnam:Um:g;KNnaenAkñúgTisxøI³ ElVg = 6m . viFIKNnaRsedogKñanwgCMhanTI5>
m:Um:g;GviC¢man M n = 0.65M os = 0.65 × 410.4 = −266.8kN .m
m:Um:g;viC¢man M p = 0.35M os = 0.35 × 410.4 = 143.6kN .m
EbgEck M n / M p eTAFñwm/ cMerokelIssr nigcMerokkNþal
α f 1 = α s = b = 2.51 ¬BI]TahrN_TI 17>2¦
l 2 7 .6 EI
= = 1.27
l 1 6 EI
s
l2
α f1 = 2.51 × 1.27 = 3.19 > 1
l1
PaKryénm:Um:g;GviC¢man nigGviC¢manenAkñúgcMerokelIssrRtUv)anTTYlBItarag 17>3 eday
kareFVI interpolation. ¬sMrab; l2 / l1 = 1.27 nig α f 1 (l2 / l1 ) > 1.0 PaKryEbgKW 67% ¦.


T.Chhay NPIC

m:Um:g;GviC¢mancMerokelIssr = 0.67M n = 0.69 × 266.8 = −178.8kN .m
m:Um:g;GviC¢mancMerokkNþal = 0.33M n = 0.33 × 266.8 = −88kN .m
eday α f 1 (l2 / l1 ) > 1.0 / 85% én − 178.8kN.m RtUv)andak;eTAkñúgFñwm. dUcenH
m:Um:g;GviC¢manelIFñwm = 0.85 × 178.8 = −152kN.m
m:Um:g;GviC¢mancMerokelIssr = 0.15 × 178.8 = −26.8kN.m
m:Um:g;viC¢manelIFñwm = 0.85 × 0.67 × 143.6 = 81.8kN.m
m:Um:g;viC¢mancMerokelIssr = 0.15 × 0.67 × 143.6 = 14.4kN.m
m:Um:g;viC¢mancMerokkNþal = 0.33 × 143.6 = 47.4kN.m
7> brimaNEdkcaM)ac; nigcMnYnEdkRtUv)anbgðajenAkñúgtarag 17>10.
cMNaMfaPaKryEdkTaMgGs;tUcCag ρ max = 0.00137 . dUcenH φ = 0.9 .


Xvii design of two way slab

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