1. T.Chhay NPIC
IX. kMralxNÐmYyTis
1> RbePTkMralxNÐ
eRKOgbgÁúMkMralxNÐebtugRtUv)ansagsg;eLIgedIm,Ipþl;nUvépÞrabesμI CaTUeTAmanTisedAedk. kMral
xNÐGacRTedayCBa¢aMg b¤edayFñwmebtugsésrEdkEdlCaTUeTARtUv)ancak;kñúgeBldMNalKñaCamYykMralxNÐ
(cast monolithically with the slab) b¤edayFñwmEdk b¤edayssr b¤edaydI. CaTUeTAkMras;kMralxNÐman
tMéltUcebIeRbobeFobCamYynwgRbEvgElVg ¬rUbTI 9>1¦.
kMralxNÐebtugenAkñgGaKarGacEbgEckdUcxageRkam³
a. kMralxNÐmYyTis (one-way slab)³ RbsinebIkMralxNÐEdlRTedayRCugBIrQmKña enaHvanwgekag b¤
dabkñúgTisedAEkgnwgRCugénTMr. GMeBIrbs;rcnasm<næ½KWmanEtmYyTis ehIybnÞúkEdlRTedaykMral
xNÐenAkñúgTisedAEdldabtUc. kMralxNÐRbePTenHRtUv)aneKeGayeQμaHfa kMralxNÐmYyTis ¬rUb
TI 9>1a¦. RbsinebIkMralxNÐRtUv)anRTedayRCugbYn ehIypleFobRCugEvgelIRCugxøIFMCag b¤esμInwg
2 enaHbnÞúkPaKeRcIn ¬RbEhl 95% b¤eRcInCagenH¦ RtUv)anRTenAkñúgTisedAxøI ehIyGMeBImYyTis
RtUv)anBicarNasMrab;karGnuvtþn_TaMgGs; ¬rUb TI 9>1b¦. RbsinebIkMralxNÐRtUv)aneFVIeLIgedayeb
tugBRgwgedayEdkedayKμanrnæxül; (no void) enaHeKeGayeQμaHfa kMralxNÐmYyTistan; (one-
way solid slab) . rUb TI 9>1 c, d nig e bgðajBIbøg;BuH nigkarBRgayEdk.
b. RbBnæ½kMralxNÐrnUtmYyTis (one-way joist floor slab)³ kMralxNÐRbePTenHeKk¾eGayeQμaHfa
ribbed slab. vapSMeLIgedaykMralxNÐEdlCaTUeTAmankMras;BI 50mm eTA 100mm RTedayrnUteb
tugGarem: (ribs or joist). CaTUeTArnUtmanragsþÜc nigmanKMlatesμI²KñaminelIs 750mm . rnUt
RtUv)anRTedayFñwmEdlsßitenAelIssr. KMlatrvagrnUtGacbegáIt)anedaykareRbIBum<Edk b¤Bum<eFVIBI
fiberglass rUbTI9>2. enAkñúgkMralxNÐrnUtxøH KMlatrvagrnUtGacRtUv)anbMeBjeday filler edIm,IeFVI
eGaykMralxNÐEpñkxageRkamrabesμI.
c. RbBnæ½kMralxNÐBIrTis (two-way floor system)³ enAeBlEdlkMralxNÐRTedayRCugbYn ehIypl
eFobénRCugEvgelIRCugxøItUcCag 2 enaHkMralnwgdabedaykMeNagDubelITisedATaMgBIr. bnÞúkkMral
xNÐRtUv)anbBa¢ÚnkñúgTisedABIreTAFñwmTaMgbYnEdlBTæ½CMuvijkMralxNÐ ¬eyagtamemeronTI17¦. Rb
ePTepSgeTotrbs;RbBnæ½kMralxNÐBIrTisman flat plate floor, flat slab nig waffle slab EdlkMral
xNÐTaMgenHnwgBnül;kñúgemeronTI17. kñúgemeronenHeyIgniyayEtBIRbBnæ½kMralxNÐmYyTis.
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2. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa
2> karKNnaénkMralxNÐtan;mYyTis
RbsinebIkMralebtugcak;kñúgkMras;esμIedayKμanRbehag eKGacehAva)anfa kMraltan;. enAkñúgkMral
xNÐmYyTis (one-way slab) pleFobénRbEvgEvgrbs;kMralxNÐelIRbEvgsøIrbs;vaFMCag 2. bnÞúkrbs;kM
ralesÞIrEtTaMgGs;RtUv)anbBa¢ÚneTATisedAxøI ehIykMralxNÐGaccat;TukdUcCaFñwm. cMerokkMralxNÐÉktþa Ca
TUeTAmanRbEvg 1m RtUv)ancat;TukCaFñwmctuekaN. FñwmenHmanTTwg1m CamYynwgkMBs;esμInwgkMras;kMral
One-Way Slab 174

3. T.Chhay NPIC
xNÐ nigRbEvgElVgesμInwgcMgayrvagTMr. dUcenHkMralxNÐmYyTispSMeLIgedayFñwmctuekaNCaeRcInCab;²Kña
¬rUbTI9>1¦.
RbsinebIkMralxNÐmanEtmYyElVg ehIyvasßitenAelITMredayesrI enaHm:Um:g;viC¢manGtibrma M sM
rab;bnÞúkBRgayesμI w KW M = (wL2 ) / 8 Edl L KWCaRbEvgElVgrvagTMr. RbsinebIkMralxNÐRtUv)ansag
sg;eLIgkñúgeBldMNalKñaCamYy b¤Cab;enAelITMrCaeRcIn enaHm:Um:g;viC¢man nigGviC¢manRtUv)anKNnaedaykar
viPaKeRKOgbgÁúM (structural analysis) b¤edayviFIemKuNm:Um:g; (moment coefficient) sMrab;FñwmCab;. ACI
Code, Section 8.3 GnuBaØateGayeRbInUvemKuNm:Um:g; nigemKuNkMlaMgkat;enAkñúgkrNIkMralxNÐmaneRcIn
ElVgesÞIresμIKña ¬rUbTI 9>3¦. krNIenHGaceRbI)ansMrab;ElVgBIrEdlenACab; b¤enAsgçagEvgCag ElVgEdlenA
kNþal b¤ElVgCab;enaHticCag 20% . sMrab;bnÞúkBRgayesμI bnÞúkGefrÉktþaminKYrFMCagbnÞúkefrÉktþa 3bI
eT. RbsinebIlkçxNÐTaMgenHminRtUv)anbMeBjeTenaH eKRtUvkarkarviPaKeRKOgbgÁúM (structural analysis).
enAkñúgkarviPaKeRKOgbgÁúM m:Um:g;Bt;GviC¢manenARtg;GkS½rbs;TMrRtUv)anKNna. tMélEdlRtUvBicarNaenAkñúg
karKNnaKWm:Um:g;GviC¢manenABImuxépÞénTMr. edIm,ITTYl)antMélenH eKRtUvdktMélm:Um:g;GtibrmaenAGkS½TMr
eday Vb / 3 Edl V CakMlaMgkat;TTwgEdl)anBIkarviPaKeRKOgpÁúM nig b KWCaTTwgrbs;TMr.
M f ¬enABImuxépÞénTMr¦ = M c ¬enARtg;GkS½énTMr¦ − ¬(>!¦
Vb
3
bEnßmBIelIm:Um:g; kMlaMgTajGgát;RTUg nigRbEvgf<k;énEdk KYrEtRtUv)anepÞógpÞat;sMrab;karKNnad¾
RtwmRtUv.
kMralxNÐmYyTis 175

4. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa
lkçxNÐEdlemKuNm:Um:g;sMrab;FñwmCab; nigkMralCab;EdleGayenAkñúgrUbTI 9>3 KYrRtUv)aneRbIGacRtUv
segçbdUcxageRkam³
a. ElVgmanRbEvgesÞIesμIKña³ ElVgEvg ≤ 1.2 ¬ElVgxøI¦
b. bnÞúkRtUvBRgayesμI
c. pleFob ¬bnÞúkGefr / bnÞúkefr¦ RtUvtUcCagb¤esμInwg 3 .
d. sMrab;kMralxNÐEdlmanElVgtUcCagb¤esμI 3m m:Um:g;Bt;GviC¢manenABImuxépÞénTMresμInwg 12 wu l n .
1 2
e. sMrab;TMr A EdlminCab; nigmanPaBTMenr enaHemKuNm:Um:g;enARtg;cMnuc A KWesμIsUnü nigRtg;cMnuc
B = + 11
1
f. kMlaMgkat;TTwgenARtg;cMnuc C = 1.15wu lu / 2 nigenABImuxépÞTMrdéTeTotTaMgGs;esμInwg 12 wu lu
g. M u = ¬emKuN¦ wu lu / Edl l n = clear span.
2
3> EdnkMNt;kñúgkarKNnaEdlGnuelameTAtam ACI CODE
EdnkMNt;xageRkamRtUv)ankMNt;eday ACI Code³
a. cMerokkMralxNÐEdlmanTTwg 1m RtUv)ansnμt;.
One-Way Slab 176

5. T.Chhay NPIC
b. kMras;Gb,brmaénkMralxNÐmYyTisEdleRbIEdk 400MPa Gnuelamtam ACI Code, Table 9.5a
sMrab;kMralxN½Ðtan;mYyTis nigsMrab;kMralxNÐrnUtmYyTisKYresμInwgtMéldUcxageRkam³
- sMrab;TMrsamBaس kMralxNÐtan; (solid slab)/ h = L / 20 ¬kMralxNÐrnUt (ribbed slab),
h = L / 16 ¦
- sMrab;kMralxNÐEdlCab;mçag³ kMralxNÐtan;/ h = L / 24 ¬kMralxNÐrnUt , h = L / 18.5 ¦
- sMrab;kMralxNÐEdlCab;sgçag³ kMralxNÐtan; / h = L / 28 ¬kMralxNÐrnUt , h = L / 21 ¦
- sMrab;kMralxNÐ cantilever: kMralxNÐtan; / h = L / 10 ¬kMralxNÐrnUt , h = L / 8 ¦
- sMrab; f y xusBI 400 MPa enaHtMélTaMgGs;xagelIRtUvKuNnwg 0.4 + 1.5 ⋅ 10 −3 f y Edl f y Kit
Ca MPa . kMras;Gb,brmaenHRtUv)aneRbITal;EtkarKNnaPaBdabbgðajfakMras;tUcCagenHGac
eRbIedayKμanplb:HBal;Rtlb;mkvij.
c. eKRtUvepÞógpÞat;PaBdabenAeBlTMrkMralxNÐEdlP¢ab;eTAnwgsMNg;TMngCargeRKaHfñak;xøaMgedayPaB
dabFM. PaBdabkMNt;RtUv)ankMNt;eday ACI Code, Table 9.5b .
d. eKcUlcitþeRCIserIskMras;kMralxNÐedaytMeLIg b¤bnßymþg 10mm .
e. eKRtUvepÞógpÞat;kMlaMgkat;TTwg ebIeTaHbIvaminmantMélFMk¾eday.
f. kMras;ebtugkarBarEdk (concrete cover) enAkñúgkMralxNÐebtugminRtUvtUcCag 20mm sMrab;épÞkM
ralxNÐEdlRbQmnwgkarsik b¤b:HpÞal;nwgdI. kñúgkrNIenH d = h − 20mm − d b / 2 eyagtamrUbTI
9>1 d .
g. sMrab;eRKagkMralxNÐEdlmankMras;esμI enaHbrimaNEdkGb,brmaenAkñúgTisedArbs;kMralxNÐminRtUv
tUcCagbrimaNEdktMrUvkarsMrab;karrYmmaD nigTb;nwgsItuNðPaB (shrinkage and temperature
reinforcement) eT (ACI Code, Section 7.12).
h. EdkemminRtUvmanKMlatFMCagkMras;kMralxNÐbIdg 3h b¤FMCag 450mm eLIy (ACI Code, Section
7.6.5).
i. eKRtUveRbIRbBnæ½EdkRtg;TaMgenAEpñkxagelI nigEpñkxageRkamrbs;kMralxNÐCab;. eBlxøHeKk¾GaceRbI
RbBnæ½EdkcMruH ¬EdkRtg; nigEdkBt;¦pgEdr.
j. bEnßmBIelIEdkem eKk¾RtUvdak;EdkEdlEkgnwgEdkemEdr. EdkbEnßmenHeKehAfa Edkrg (secondary,
distribution) EdkrYmmaD b¤EdksItuNðPaB (shrinkage or temperature reinforcement).
kMralxNÐmYyTis 177

6. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa
4> EdksItuNðPaB nigEdkrYmmaD
CaTUeTAebtugrYmmaDenAeBlEdlTwkkMe)arsIum:g;t¾rwg ehIyeK)anKitTunCamunnUvbrimaNBitR)akdén
karrYmmaD. RbsinebIkMralxNÐRtUv)aneKdak;eGaycl½tedayesrIenAelITMrrbs;va enaHvanwgrYjedIm,ITTYlnUv
karrYmmaD. b:uEnþkMralxNÐ b¤Ggát;epSgeTotRtUv)anP¢ab;y:agrwgeTAnwgGgát;déTeToténeRKOgbgÁúM EdlbegáIt
nUvkMriténkarTb;y:agBitR)akdenAcug. CalTæpleKTTYl)ankugRtaMgTajEdleKsÁal;faCakugRtaMgrYmmaD.
karfycuHnUvkugRtMgEdlekItBIsItuNðPaB nigkugRtaMgEdlekItBIkarrYmmaD)aneFVIeGayekItmansñameRbHb:un
sésrsk; (hairline crack). sésrEdkEdkdak;enAkñúgkMralxNÐKWedIm,ITb;Tl;nwgkarrYjxøI nigkarraldalén
sñameRbH. edaysarEtebtugrYmmaD sésrEdkrgnUvkarsgát;.
EdksMrab;karkugRtaMgrYmmaD nigkugRtaMgsItuNðPaBEdlEkgnwgEdkem RtUvdak;enAkñúgkMralxNÐEdl
EdlemRtUv)andak;EtmYyTis. ACI Code, Section 7.12.2 kMNt;nUvGRtaEdkGb,brmadUcxageRkam³
- sMrab;kMralxNÐEdleRbIEdk 280MPa b¤ 350MPa enaH ρ = 0.2%
- sMrab;kMralxNÐEdleRbIEdk 400MPa b¤EdkpSar b¤EdksMNaj;pSar enaH ρ = 0.18%
KμankrNIEdlEdkRtUv)andak;manKMlatFMCag 5dgkMras;kMralxNÐ b¤FMCag 450mm eT.
sMrab;EdkrYmmaD nigEdksItuNðPaB kMras;ebtugTaMgmUl h EdlRbQmnwgkarrYmmaDRtUveRbIedIm,I
KNnaRkLaépÞEdk. ]TahrN_ RbsinebIkMralxNÐmankMras;srub h = 150mm nig f y = 400MPa enaHRk
LaépÞEdkEdlRtUvkarsMrab;TTwgkMralxNÐ 1m KW As = 1000 × 150 × 0.0018 = 270mm 2 . KMlatEdk S
GacKNnadUcxageRkam³
S=
1000 Ab
As
¬(>@¦
Edl Ab = RkLaépÞEdkeRCIserIs
As = RkLaépÞEdkKNna
]TahrN_ RbsinebIeKeRbIEdk DB10 ¬ Ab = 78.5mm 2 ¦ enaH S = 1000 × 78.5 / 270 = 290mm
yk 250mm . RbsinebIeKeRCIserIsEdk DB12 ¬ Ab = 113mm 2 ¦ enaH S = 1000 × 113 / 270 = 418mm
yk 400mm . EdkenHmantYrnaTICaEdkrgEdlRtUv)andak;EkgnwgEdkemEdlRtUv)anKNnaedaykarviPaK
edaykarBt; (flexural analysis).
5> lMGitsésrEdk
enAkñúgkMralxNÐmYyTisCab; RkLaépÞEdkemRtUv)anKNnaBIRKb;eRKaHfñak;TaMgGs; TaMgenAkNþalElVg
nigenATMr. kareRCIserIssésrEdk niglMGitsésrEdkGaRs½yeTAnwgRkLaépÞEdk KMlatRtUvkar nigRbEvg
TMBk;. eKmanRbBnæ½rayEdkBIrRbePT.
One-Way Slab 178

7. T.Chhay NPIC
enAkñúgRbBnæ½EdkRtg; ¬rUbTI9>4¦ EdkRtg;RtUv)aneRbIsMrab;dak;enAEpñkxagelI nigEpñkxageRkaménRKb;kM
ralxNÐTaMgGs;. karcMNayelIfvikar nigeBlevlasMrab;pltiEdkRtg; RtUvkarticCagkñúgkarplitEdkBt;
dUcenHRbBnæ½EdkRtg;RtUv)anTUlMTUlayCagenAkñúgsMNg;.
enAkñúgRbBnæ½EdkBt; b¤ trussed EdkRtg; nigEdkBt;RtUv)andak;qøas;KñaenAkñgkMralxNÐ. TItaMgBt;
RtUv)anepÞógpÞat;sMrab;karBt; kMlaMgkat;TTwg nigtMrUvkarRbEvgf<k;. sMrab;bnÞúkFmμtaenAkñúgsMNg; bøg;lMGit
sésrEdksMrab;ElVgxag nigElVgkNþalénkMralxNÐtan;mYyTisRtUv)anbgðajenAkñúgrUbTI 9>4.
6> karEbgEckbnÞúkBIkMralxNÐmYyTiseTAFñwmTMr
enAkñúgRbBnæ½kMralxNÐmYyTis bnÞúkBIkMralxNÐRtUv)anbBa¢ÚneTAFñwmTMrtamcugEvgénkMralxNÐ. Fñwm
bBa¢ÚnbnÞúkrbs;vaeTAssrTMr.
BIrUbTI 9>5 eyIgeXIjfa Fñwm B2 RTbnÞúkBIkMralxNÐEk,rBIr. edaycat;TukCaFñwmRbEvg 1m bnÞúkbBa¢Ún
eTAFñwmesμInwgRkLaépÞéncMerokTTwg 1m nigbeNþay S KuNnwgGaMgtg;sIuetbnÞúkEdlmanGMeBIelIkMralxNÐ.
bnÞúkenHbegáItCabnÞúkBRgayesμIenAelIFñwm
UB = US ⋅ S
kMralxNÐmYyTis 179

8. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa
bnÞúkBRgayesμIenAelIFñwmxag B1 esμInwgBak;kNþalbnÞúkenAelIFñwm B2 edaysarEtvaRTkMralxNÐEtmçag.
bnÞúkenAelIssr C4 esμInwgRbtikmμBIFñwm B2 Ek,rBIr
bnÞúkenAelIssr C4 = U B L = U S LS
bnÞúkenAelIssr C3 esμInwgBak;kNþalbnÞúkenAelIssr C4 edaysarEtvaRTkMralxNÐEtmçag. dUcKñacM
eBaHbnÞúkenAelIssr C2 nig C1 KW³
bnÞúkenAelIssr C2 = U S L S = bnÞúkenAelIssr C3
2
bnÞúkenAelIssr C1 = U S 2 2
LS
BIkarviPaKenH eyIgeXIjfassrnImYy²RTbnÞúkBIkMralxNÐEdlenACMuvijssrenaH edayKitrhUtdl;GkS½
énkMralxNÐEk,r ¬ L / 2 sMrab;TisEvg nig S / 2 sMrab;TisxøI¦.
karBRgaybnÞúkBIkMralxNÐBIrTiseTAFñwmTMr nigssrnwgBnül;enAkñúgemeronTI17.
One-Way Slab 180

9. T.Chhay NPIC
]TahrN_TI1³ KNnaersIusþg;m:Um:g;KNnarbs;kMralxNÐEdlmankMBs;srub h = 175mm nigBRgwgedayEdk
DB 20 EdlmanKMlat S = 175mm . eRbI f 'c = 20MPa nig f y = 400MPa .
dMeNaHRsay³
1> KNnakMBs;RbsiTæPaB d ³
d = h − 20mm − b ¬emIlrUb9>1 d¦
d
2
20
d = 175 − 20mm − = 145mm
2
2> KNna As mFümEdlpþl;sMrab;TTwgkMralxNÐ 1m . RkLaépÞénEdk DB20 KW Ab = 314mm 2
1000 × 314
As = = 1794mm 2 / m
175
3> eRbobeFobPaKryEdkEdleRbICamYynwg ρ max nig ρ min . sMrab; f 'c = 20MPa nig
f y = 400MPa enaH ρ max = 0.01374 nig ρ min = 0.00333 .
ρ ¬eRbIR)as;¦ = 1794 /(1000 × 140) = 0.0128 EdlRKb;RKan; ¬ φ = 0.9 ¦.
4> KNna φM n = φAs f y (d − a / 2)
a = As f y /(0.85 f 'c b) = 1794 × 400 /(0.85 × 20 × 1000) = 42.2mm
φM n = 0.9 × 1794 × 400 × (140 − 42.2 / 2 ) = 76.79kN .m
]TahrN_TI2³ kMNt;bnÞúkGefrBRgayesμIGnuBaØatEdlGacGnuvtþenAelIkMralxNÐén]TahrN_TI1 RbsinebI
ElVgkMralxNÐmanRbEvg 4.9m sßitenAcenøaHTMrsamBaØ nigRTnUvbnÞúkefrBRgayesμI ¬KμanbBa©ÚlbnÞúkpÞal;xøÜn¦
4.8kN / m 2 .
dMeNaHRsay³
1> ersIusþg;m:Um:g;KNnaénkMralxNÐKW 76.79kN .m elIkMralxNÐTTwg 1m
Wu L2 Wu (4.9) 2
M u = φM n = 76.79 = =
8 8
bnÞúkBRgayesμIemKuNKW Wu = 25.6kN / m 2
2> Wu = 1.2D + 1.6L
D = 4.8 + 0.175 × 1 × 25 = 9.2kN / m 2
L = 9.1kN / m 2
]TahrN_TI3³ KNnakMralxNÐTMrsamBaØRbEvg 3.6m edIm,IRTbnÞúkefrBRgayesμI ¬minrab;bBa©ÚlbnÞúkpÞal;
xøÜn¦ 5.75kN / m 2 nigbnÞúkGefrBRgayesμI 4.8kN / m 2 . eRbI f 'c = 20MPa / f y = 400MPa nigkar
kMNt;rbs; ACI Code.
dMeNaHRsay³
kMralxNÐmYyTis 181

10. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa
1> snμt;kMras;kMralxNÐ. sMrab; f y = 400MPa kMras;Gb,brmaedIm,IRKb;RKgPaBdabKW L / 20
= 180mm . snμt;kMrs;srub h = 175mm nigsnμt; d = 150mm ¬RtUvepÞógpÞat;enAeBleRkay¦.
2> KNnabnÞúkemKuN³ bnÞúkkMralxNÐ = 0.175 × 25 = 4.4kN / m 2
Wu = 1.2 D + 1.6 L = 1.2 × (4.4 + 5.75) + 1.6 × 4.8 = 19.86kN / m 2
sMrab;kMralxNÐTTwg 1m / M u = Wu L2 / 8
19.86 × 3.6 2
Mu = = 32.2kN .m
8
3> KNna As ³ sMrab; M u = 32.2kN .m / b = 1m nig d = 0.15m / Ru = M u / bd 2 = 1.43MPa /
ρ = 0.0042 < ρ max = 0.01374 / φ = 0.9 .
As = ρbd = 0.0042 × 1000 × 150 = 630mm 2
eRCIserIsEdk DB12 ¬ As = 113mm 2 ¦/ nig S = 1000 × 113 / 630 = 179mm
epÞógpÞat; d BitR)akd/ d = 175 − 20 − 6 = 149mm GacTTYlyk)an.
dUcenH S = 175mm nig As = 645mm 2
4> epÞógpÞat;ersIusþg;m:Um:g;énmuxkat;cugeRkay
As f y 645 × 400
a= = = 15.2mm
0.85 f 'c b 0.85 × 20 × 1000
⎛ a⎞ ⎛ 15.2 ⎞
φM n = φAs f y ⎜ d − ⎟ = 0.9 × 645 × 400⎜150 − ⎟ = 33kN .m > M u = 32.2kN .m
⎝ 2⎠ ⎝ 2 ⎠
5> KNnaEdkrgEdlEkgnwgEdkem. sMrab; f y = 400MPa
ρ min = 0.0018
Ash = 0.0018 × 1000 × 175 = 315mm 2
eRCIserIsEdk DB12 / Ab = 113mm 2 / S = 1000 × 113 / 315 = 358.7mm
dUcenHeRbI DB12 @ 350mm sMeab;Edkrg.
6> epÞógpÞat;kMlaMgkat;TTwgcaM)ac;³ Vu enAcMgay d BITMrKW 19.86(1.8 − 0.15) = 32.8kN
φVc = φ 0.17 f 'c bd = 0.75 × 0.17 20 × 1000 × 150 × 10 −3 = 85.5kN
1
2
φVc = 42.75kN > Vu = 32.8kN dUcenHmuxkat;RKb;RKan;.
7> muxkat;cugeRkay h = 175mm / Edkem DB12 @175mm nigEdkrg DB12 @ 350mm .
]TahrN_TI4³ muxkat;kMralxNÐtan;mYyTisCab;RtUv)anbgðajkñúgrUbTI 9>6. kMralxNÐenHRTedayFñwmEdl
manRbEvg 7.2m . bnÞúkGefrmanGMeBIelIkMralxNÐ)anmkBIbnÞúkpÞal;xøÜnbUknwg 3.7kN / m 2 ehIybnÞúkGefrKW
One-Way Slab 182

11. T.Chhay NPIC
6.2kN / m 2cenøaHTMrsamBaØ. KNnakMralxNÐCab; nigKUrnUvbøg;lMGitsésrEdk. eKeGay f 'c = 20MPa /
f y = 280MPa .
dMeNaHRsay³
1> kMras;Gb,brmaénkMralxNÐTI1KW L / 30 edaysarcugmçagCab; nigcugmçageTotGt;Cab;.
cMgayrvagGkS½FñwmGaccat;TukCaElVg L = 3.6m . sMrab; f y = 280MPa
kMras;srubGb,brma 30 = 3600 = 120mm
L
30
kMras;srubGb,brmasMrab;ElVgkNþal 35 = 3600 = 103mm
L
35
snμt;kMras;rbs;kMralxNÐesμIKñaRKb;ElVg h = 125mm EdlFMCag 120mm . dUcenH
eKmincaM)ac;epÞóg pÞat;PaBdab.
2> KNnabnÞúk nigm:Um:g;enAelIcMerokÉktþa
bnÞúkGefr=bnÞúkpÞal;xøÜn + 3.7 = 0.125 × 25 + 3.7 = 6.8kN / m 2
bnÞúkemKuN U = 1.2D + 1.6L = 1.2 × 6.8 + 1.6 × 6.2 = 18.1kN / m 2
RbEvg clear span KW 3.35m . m:Um:g;caM)ac;sMrab;ElVgTImYyenAelITMrEdlmanElVgCab;esIμnwg
UL2 / 10
U (3.35)2
Mu = = 20.3kN .m
10
3> snμt; ρ = 1.4% enaH Ru = 3.12MPa tMélenHtUcCag ρ max = 0.0169 nigFMCag ρ min = 0.005
¬ φ = 0.9 ¦
Mu 20.3 ⋅ 10 6
d= = = 81mm
Ru b 3.12 × 1000
As = ρbd = 0.014 × 1000 × 81 = 1134mm 2
eRCIserIs DB16
kMras;srub = d + 16 + 20 = 109mm
2
eRbIkMras;kMralxNÐ 125mm dUckarsnμt;xagelI
kMBs; d EdleRbIBitR)akd = 125 − 20 − 8 = 97mm
4> m:Um:g; nigsésrEdkRtUvkarenARtg;muxkat;déTeTot edayeRbI d = 97mm mandUcxageRkam³
TItaMg emKuNm:Um:g; M u (kN .m) Ru = M u / bd 2 (MPa) ρ (%) As (mm 2 ) Edk nigKMlat
A − 241
8.46 tUc 0.00500 485 DB12@200
kMralxNÐmYyTis 183

12. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa
B + 14
1
14.51 1.54 0.00646 627 DB16@300
C − 10
1
20.31 2.16 0.00928 900 DB16@200
D − 11
1
18.47 1.96 0.00836 811 DB16@200
E + 16
1
12.70 1.35 0.00561 545 DB16@200
karBRgaysésrEdkRtUv)anbgðajenAkñúgrUbTI 9>7.
5> kMlaMgkat;TTwgekItmanenAkMralxNÐxageRkAénTMrTI2/ muxkat; C
6> Vu ¬Rtg; C ¦ = 1.15ULn / 2 = 1.15 × 182.1× 3.55 = 36.95kN
7> φVc = φ 0.17 f 'c bd = 0.75 × 0.17 20 × 1000 × 97 × 103 = 55.3
lTæplenHGacTTYlyk)an. cMNaMfa kardak;sésrEdkkMlaMgkat;TTwgGb,brmaenAeBlEdl Vu > 12 φVc
minRtUv)anGnuvtþsMrab;kMralxNÐeT ¬ ACI Code, Section 11.5.5¦.
]TahrN_TI5³ kMNt;bnÞúkemKuNBRgayesμIenAelIFñwmkNþalEdlRTkMralxNÐén]TahrN_TI 4. dUcKña
KNnabnÞúkcMGkS½enAelIssrkNþal eyagtambøg;TUeTAénrUbTI9>5.
dMeNaHRsay³
1> bnÞúkemKuNBRgayesμIkñúgmYyEm:RtRbEvgenAelIFñwmkNþalesμInwgbnÞúkemKuNBRgayesμIenAlIkMral
xNÐKuNnwg S EdlCaRCugxIørbs;kMralxNÐ. dUcenH
U ¬Fñwm¦= U ¬kMralxNЦ × S = 18.1 × 3.8 = 68.8kN / m
bnÞúkrbs;FñwmKYrRtUv)anKitbBa©Úl. RbEvgrbs;FñwmKW 7.2m
kMNt;kMBs;srub h=
L
20
× 0.8 =
7.2
20
× 0.8 = 0.288m yk 300mm
kMras;kMralxNÐKW 125mm dUcenHkMBs;énRTnugrbs;FñwmKW 300 − 125 = 175mm
bnÞúkemKuNénRTnugFñwm = 0.175 × 0.25 × 25 × 1.2 = 1.3kN / m
bnÞúkBRgayesμIsrubelIFñwm = 68.8 + 1.3 = 70.1kN / m
One-Way Slab 184

13. T.Chhay NPIC
2> bnÞúkenAleIFñwmkNþal
Pu = 70.1 × 7.2 = 504.72kN / m
7> RbBnæ½kMralxNÐrnUtmYyTis One-Way joist Floor System
RbBnæ½kMralxNÐrnUtmYyTispSMeLIgedaykMralxNÐRbehag (hollow slab) CamYykMBs;srubFMCagkMras;
rbs;kMralxNÐtan;mYyTis. kMralxNÐenHmanlkçN³snSMsMécsMrab;GKarEdlmanbnÞúktUc nigmanElVgEvg
dUcCa salaeron mnÞIreBTü nigsNæaKar. bnÞúkenAkñúgtMbn;TajKμanTæiBldUcenH tMbn;enHRtUv)anTukeGayRb
ehagrvagrnUt b¤RtUv)anbMeBjCamYysMPar³EdlmanTMgn;Rsal edIm,Ikat;bnßyTMgn;pÞal;rbs;kMralxNÐ.
viFIsaRsþkñúgkarKNna nigtMrUvkarénkMralxNÐrnUt (ribbed slab) GnuvtþdUckarKNnaFñwmmuxkat;ctu
ekaN nigFñwmmuxkat;GkSret EdlmanenAkñúgemeronTI3. cMnucxageRkamRtUv)anGnuvtþsMrab;KNnakMralxNÐ
rnUtmYyTis.
1 rnUt (rib) manragsþÜcxageRkam nigmanKMlatdUc²KñaRbEhl 400mm eTA 750mm . Rbehag
RtUv)anbegáItrUbragedayeRbIBum<EdlmanTTwg 500mm nigCMerA 150mm eTA 500mm GaRs½y
eTAelItMrUvkarénkarKNna. kMeNInbTdæanrbs;kMBs;KWmþg 50mm .
2 rnUtminRtUvmanTTwgtUcCag100mm nigminRtUvmanCMerAFMCagTTwg 3.5 dg. KMlat clear spacing
rvagrnUtminRtUvFMCag 750mm (ACI Code, Section 8.11).
3 ersIusþg;kMlaMgkat;TTwgEdlpþl;edayebtugsMrab;rnUtGacykesμInwg 10% FMCagersIusþg;kMlaMg
kat;TTwgEdlpþl;edayebtugsMrab;Fñwm. mUlehtucMbgKWbNþalmkBIGnþrkmμrvagkMralxNÐ nig
rnUtEdlmanKMlatCit²Kña (ACI Code, Section 8.11.8).
4 CaTUeTAkMralxNÐenABIelIrnUtmankMras;BI 50mm eTA 100mm nigmanEdkGb,brma ¬EdkrYm
maD¦. kMras;enHminRtUvtUcCag 1 / 12 én clear span rvagrnUt b¤ 50mm (ACI Code, Section
8.11.6).
5 emKuN ACI sMrab;KNnam:Um:g;enAkñúgkMralxNÐCab; GacRtUv)aneRbIsMrab;KNnakMralxNÐrnUt
Cab;.
6 eKmanEdnkMNt;bEnßmmYycMnYn EdlRtUv)ansegçbdUcxageRkam³
- TTwgGb,brmarbs;rnUtKW mYyPaKbIénkMBs;srub b¤ 100mm edayykmYyNaEdlFMCag.
- EdkrgenAkñúgkMralxNÐenAkñúgTisedAEkgnwgrnUtminKYrtUcCagbrimaNEdkrYmmaD b¤tUcCag
1 / 5 énRkLaépÞEdkemenAkñúgrnUt.
kMralxNÐmYyTis 185

14. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa
- EdkrgEdlRsbnwgrnUtKYrdak;enAkñúgkMralxNÐ ehIyKMlatrbs;vaminRtUvmancMgayFMCagBak;
kNþalénKMlatrvagrnUt.
- RbsinebIbnÞúkGefrenAelIkMralxNÐrnUttUcCag 3kN / m 2 ehIyRbEvgrbs;rnUtFMCag 5m enaH
rnUtTTwgrg (secondary transverse rib) RtUv)andak;enAkNþalElVg ¬TisedArbs;vaKWEkgnwg
TisedArbs;rnUtem¦ nigBRgwgedayEdkEdlmanbrimaNesμInwgbrimaNEdkenAkñúgrnUtem.
EdkxagelIrbs;vaminRtUvtUcCagBak;kNþalEdkemenAkñúgtMbn;Taj. rnUtrgmannaTIBRgwgkM
ralxNÐ (floor stiffener) .
- RbsinebIbnÞúkGefrFMCag 3kN / m 2 ehIyrnUtemmanRbEvgERbRbYlcenøaHBI 4m eTA 7m eK
RtUvdak;rnUtrgmYydUcbgðajxagelI. RbsinebIrnUtemmanRbEvgFMCag 7m y:agehacNas;
rnUtrgBIrRtUv)andak;CamYynwgsésrEdkdUckarENnaMxagelI.
]TahrN_TI6³ kMNt;kMralxNÐrnUtmYyTisenAxagkñúgCamYynwgTinñn½yxageRkam³ RbEvgrnUt 6m ¬TMr
samBaئ/ bnÞúkefr ¬edaymin)anbBa©ÚlbnÞúkpÞal;¦ 0.75kN / m 2 / bnÞúkGefr 4.1kN / m 2 / f 'c = 28MPa
nig f y = 400MPa .
dMeNaHRsay³
1> KNnakMralxNг snμt;kMras;kMralxNÐxagelIesμInwg 50mm EdlP¢ab;CamYynwgrnUtEdlman clear
span 500mm . sMPar³edIm,IbMeBj (filler) minRtUv)aneRbI. bnÞúkpÞal;rbs;kMralxNÐKW 0.050 × 25
= 1.25kN / m 2 .
bnÞúkefrsrub D = 1.25 + 0.75 = 2.kN / m 2
U = 1.2 D + 1.6 L = 1.2 × 2 + 1.6 × 4.1 = 9kN / m 2
UL2
Mu =
12
¬kMralxNÐRtUv)ancak;Cab;CamYynwgrnUt¦
9 × 0.5 2
Mu = = 0.19kN .m
12
edaycat;Tukm:Um:g;enAkñúgkMralxNÐRtUvRTedayebtugsuTæ
enaHersIusþg;TajedaykarBt;GnuBaØatrbs;ebtugKW f t = 0.415 f 'c CamYynwgemKuNkat;bnßyersIu
sþg; φ = 0.55 / f t = 0.415 28 = 2.2MPa .
ersIusþg;TajrgkarBt; = Mc = φf t
I
bh 3 1000 × 50 3
I= = = 10.42 ⋅ 10 6 mm 4
12 12
h
c = = 25mm
2
One-Way Slab 186

15. T.Chhay NPIC
10.42 ⋅ 10 6
M = φf t
I
c
= 0.55 × 2.2 ×
25
⋅ 10 −6 = 0.5kN .m > M u = 0.19kN .m ¬muxkat;RKb;RKan;¦
EdkrYmmaD As = 0.0018 × 1000 × 50 = 90mm 2
Edk DB10 manKMlat 300mm RtUv)andak;EkgnwgTisedArbs;rnUt. sMNaj;EdkpSar (welded
wire fabric) manlkçN³snSMsMécsMrab;krNIbrimaNEdktic.
eRbIEdk DB10 manKMlat 300mm sMrab;dak;RsbnwgTisedArnUt edayEdkmYyedImRtUv)andak;enABI
elIrnUtnImYy² nigEdkmYyeTotRtUv)andak;enAcenøaHkNþalrnUtBIr.
2> KNnam:Um:g;enAkñúgrnYt
kMBs;Gb,brma = 20 = 20 = 0.3m
L 6
kMBs;srubrbs;rnUtnigkMralxNÐKW 250 + 50 = 300mm
snμt;TTwgrnUtEpñkxageRkamKW 100mm nigEpñkxagelI ¬nIv:U)atkMralxNЦKW 150mm rUbTI9>8.
TTwgmFümrbs;rnUtKW 125mm
cMNaMfa kMeNInénTTwgrbs;rnUtedayeRbIBum<cl½tEdlmanpleFob 1 / 12 ¬edk 1 nigQr 12 ¦
TMgn;rnUt= 0.125 × 0.25 × 25 = 0.78kN / m
rnUtRTnUvbnÞúkmkBIkMralxNÐEdlmanTTwg 600mm bUknwgbnÞúkpÞal;rbs;va
U = 9 × 0.6 + 1.2 × 0.78 = 6.35kN / m
UL2 6.35 × 6 2
Mu = = = 28.6kN .m
8 8
3> KNnarnUt³ kMBs;srubrbs;rnUtKW 300mm .
snμt;eRbIEdk DB16 nigkMras;ebtugkarBarEdk 20mm
kMBs;RbsiTæPaB d = 300 − 20 − 8 = 272mm
BinitüemIlersIusþg;énsøab ¬snμt;muxkat; tension-controlled section/ φ = 0.9 ¦
⎛ t⎞
φM n ¬søab¦ = φC ⎜ d − ⎟ Edl C = 0.85 f 'c bt
⎝ 2⎠
⎛ 50 ⎞
M u = 0.9(0.85 × 28 × 600 × 50 )⎜ 272 − ⎟ ⋅ 10 −6 = 158.7 kN .m
⎝ 2⎠
ersIusþg;m:Um:g;ebs;søabFMCagm:Um:g;Gnuvtþn_ dUcenHrnUtmannaTICamuxkat;ctuekaNEkgEdlmanTTwg
b = 600mm nigkMBs;énbøúkrgkarsgát;smmUl a KWtUcCagkMras;kMralxNÐ 50mm .
⎛ a⎞ As f y
φM n = φAs f y ⎜ d − ⎟ = φAs f y (d − )
⎝ 2⎠ 1.7 f 'c b
⎛ As × 400 ⎞
28.6 ⋅ 10 6 = 0.9 As × 400⎜ 272 − ⎟
⎝ 1.7 × 28 × 600 ⎠
kMralxNÐmYyTis 187

16. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa
As = 297mm 2
297 × 400
a= = 8.32mm < 50mm
0.85 × 28 × 600
eRbIEdk 2DB16 sMrab;rnUtmYy (402mm 2 )
As min = 0.0033bw d = 0.0033 × 125 × 272 = 112.2mm 2 < 297mm 2
BinitüemIl
297
ρ= = 0.018 < ρ max = 0.019
600 × 272
EdlCamuxkat; tension-controlled section/ φ = 0.9 .
4> KNnakMlaMgkat;TTwgenAkñúgrnUt³ ersIusþg;kMlaMgkat;TTwgGnuBaØaténRTnugrnUtKW
φVc = φ (1.1) × 0.17 f 'c bw d = 0.75 × 1.1 × 0.17 × 28 × 125 × 272 × 10 −3 = 25.2kN
kMlaMgkat;TTwgemKuNenAcMgay d BITMrKW
Vu = 6.35 × (3 − 0.272) = 17.3kN < φVc = 25.2kN
dUcenHEdkkgGb,brmaRtUv)aneRbI ehIykrNIenHEdk DB12 RtUv)anbEnßmenAkñúgkMralxNÐEpñkxag
elIedIm,ITb;Edkkg. vaCakarRbesIreBsinebIeKbEnßmrnUtrgmYyenAkNþalElVgEkgnwgrnUtem ehIy
manbrimaNEdkdUcKñanwgrnUtem edIm,IeFVIeGaykMralxNÐmanlkçN³rwgmaM.
One-Way Slab 188