បេតុងពង្រឹងដោយដែក 8 viii-shear-and-diagonal-tension
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Transcript of បេតុងពង្រឹងដោយដែក 8 viii-shear-and-diagonal-tension
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 125
VIII. kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUgShear and Diagonal Tension
1>
esckIepImenAeBlEdlFwmTMrsamBargnUvbnk m:Um:g;Bt; nigkMlaMgkat;TTwgnwgekIteLIgelIRbEvgFwm. edIm,IRT
nUvbnkenHedaysuvtiPaB FwmRtUv)aneFVIkarKNnaeLIgedIm,ITb;nwgkMlaMgTaMgBIrRbePTenH. karKNnasMrab;karBt;RtUv)aneFVIeLIgdMbUgeK edIm,IkMNt;muxkat;Fwm nigEdkemcaM)ac;dUcEdl)anENnaMBIemeronmun.
bnab;mkFwmRtUv)anKNnaedIm,ITb;nwgkMlaMgkat;TTwg. kgkrNIEdlEdkkgminRtUv)andak; enaHFwmnwg)ak;edaykMlaMgkat;TTwg. kar)ak;edaykMlaMgkat;TTwg ekIteLIgedaymanPaBdabtUc nig)at;bg;nUv
lkNyWt ehIymin)anRbkasGasnenAmuneBl)ak;eT. sMrab;kar)ak;edaykarBt;begag ekIteLIgedaykarekIneLIgnUvPaBdabbnicmg nigmansameRbH dUcenHvamankarpl;sBaaRbkasGasnmuneBl)ak;cugeRkay. karKNnasMrab;kMlaMgkat;TTwg RtUv)aneFVIeLIgedIm,IFananUvkar)ak;edaykMlaMgkat;TTwgekIteLIgeRkaykar)ak;edaykarBt;begag.
2>kugRtaMgkMlaMgkat;enAkgFwmebtugGarem:
rUbmnTUeTAsMrab;kugRtaMgkMlaMgkat;TTwgenAFwmrUbFatusac;mYy (homogenous beam) karBRgaykugRtaMg
Ib
VQ= *>!
EdlV
- kMlaMgkat;srubenAmuxkat;EdlRtUvsikSaQ - m:Um:g;saTiceFobGkSNWtnmuxkat;EdlxNedaybnat;EdlRtUvsikSakugRtaMgkMlaMgkat;
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Department of Civil Engineering viTasanCatiBhubeckeTskm2.kugRtaMgm:Um:g;Bt;
I
Mcf =
Edl kugRtaMgkMlaMgkat;enARKb;cMnucTaMgGs;RtUv)anKNnatamrUbmnkugRtaMgkMlaMgkat;
Ib
VQ=
kugRtaMgkMlaMgkat;GtibrmasitenAelIGkSNWt nigmantMlesIav5.1 kMlaMgkat;TTwgmFm
Edlbh
Va = . ExSekagkMlaMgkat;TTwgmanrag):ar:abUl.
sMrab;FwmebtugssEdkrgkarTaj (singly reinforced concrete beam) karBRgaykugRtaMgkMlaMgkat;TTwgenAelIGkSNWtmanrag):ar:abUl. enAeRkamGkSNWt kugRtaMgkMlaMgkat;TTwgGtibrmamantMl
efr ehIy)anrkSatMlenHRtwmnIv:UEdkrgkarTaj BIeRBaHvaK
ankarpas;brkMlaMgTajBIcMnucGkSNWtehIym:ageTotkMlaMgTajkgebtugRtUv)anecal. kugRtaMgkMlaMgkat;TTwgmantMlesIsUn enAeRkamnIv:UEdk rUbTI8>3.
sMrab;ebtugssrEdkEdlmanEdkrgkarsgt;nigmuxkat;GkSret karBRgaykugRtaMgkMlaMgkat;TTwgRtUv)anbgajkgrUbTI8>3. eyIgsegteXIjfa kMlaMgkat;TTwgesIrEtTaMgGs;RtUv)anTb;edayRTnugEdlsabTb;nwgPaKrytUcbMput. sMrab;karGnuvtn_esIrTaMgGs; eKecalnUvlTPaBTb;kMlaMgkat;TTwgrbs;
sab.
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 127
eyagtamrUbTI8>1 edayykFwmmYykMNat;tUc dx mkviPaK eyIgeXIjfa m:Um:g;Bt;enAcugsgxagnkMNat; 1M nig 2M minmantMlesIKaeT. edaysar 21 MM < dUcenHedIm,IrkSalMnwgsMrab;kMNat;dx
kMlaMgsgt; 2C
RtUvmantMlFMCag 1C
rUbTI8>4. dUcenHkugRtaMgkMlaMgkat;TTwgv
ekItmanenAelImuxkat;edk 1aa b 1bb rUbTI8>4 a. kugRtaMgkMlaMgEkg (normal stresses) nigkugRtaMgkMlaMgkat;TTwg(shear stresses) enAelIGgt;tUc enAkMritnIv:U 1aa b 1bb RtUv)anbgajenAkgrUbTI8>4b. cMNaMfa kugRtaMgkM;laMgEkg (normal stresses) enAnIv:UnGkSNWtKW0 b:uEnkMlaMgkat;TTwgmantMlGtibrma. kMlaMgkat;TTwgedkesInwgkMlaMgkat;TTwgbBar dUcbgajenAkg rUbTI8>4b. enAeBlEdl kugRtaMgkMlaMgEkgmantMlesIsUn btUc enaHkrNIkMlaMgkat;TTwgsuTGacekItman. kgkrNIenH kugRtaMgTajGtibrma tf manGMeBI
tammMuo45
rUbTI8>4c
.kugRtaMgTajsmmUleTAnwgkugRtaMgem dUcbgajkgrUbTI 8>4 d. kugRtaMgemenHRtUv)aneKehAfakugRtaMgTajGgt;RTUg. enAeBlkugRtaMgTajGgt;RTUgmantMlesIersIusg;Tajrbs;ebtug sameRbHGgt;RTUgekIteLIg. karviPaKy:agsegbenHBnl;BIKMnitnkMlaMgTajGgt;RTUg nigsameRbHGgt;RTUg. kareFVICak;EsgmanlkNsKsajCag ehIyvaTTYl\TiBlBIktaepSg. sMrab;bnSMnGMeBInkMlaMgkat;TTwgnigkMlaMgEkgenAcMnucNamYyenAkgFwm kMlaMgTajGgt;RTUg (principal stresses) Gtibrma nigGb,brma pf
RtUv)aneGayedaysmIkarxageRkam
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 129
3>kareFVIkarrbs;FwmedayKanEdkkMlaMgkat;TTwg
ebtugexSaykgkarTaj ehIyFwmGac)ak;RbsinebImuxkat;EdkminRtwmRtUvRtUv)anpl;eGay. kugRtaMgTajekItmanenAkgFwmbNalmkBIkMlaMgTajtamGkSkMlaMgBt;kMlaMgkat;TTwg kMlaMgrmYl bbnSMnbnk
TaMgenH. TItaMgnsameRbHenAkgFwmebtugGaRsynwgTisedAnkugRtaMgem (principal stresses). bnSMnkugRtaMgkMlaMgEkg normal stress nigkugRtaMgkMlaMgkat;TTwg begIt)ankMlaMgTajtamGgt;RTUg (diagonaltension) GtibrmaEdlsitenARbEhlcMgay dBImuxnTMr.
kareFVIkarrbs;FwmebtugGarem:edaymanbKanEdkkMlaMgkat;TTwg RtUv)anBiesaFeRkamGMeBInkarekIneLIgnbnkdUc)anerobrab;enAkgemeronTI3. enAkgkarBiesaFn_Fwm sameRbHbBarEdlekItBIkarBt;ekIteLIgenAenAelImuxkat;Edlmanm:Um:g;Bt;Gtibrma enAeBlEdlkugRtaMgTajenAkgebtugelIsBIm:UDuldac;
(module of rupture) rbs;ebtug b cr ff '623.0= . sameRbHeRTtenAkgRTnugekItmanenAkgtMNak;kalbnab;enATItaMgEk,rTMr.
sameRbHeRTtEdlekItmanenAkgFwmEdlminTan;)aneRbHBIdMbUg CaTUeTARtUv)aneKeGayeQaHfasameRbHkMlaMgkat;RTnug (web-shear crack). RbsinebIsameRbHeRTtcab;epImenABIelIsameRbHEdlekItBIkarBt;EdlmanRsab;ehIyrIksayenAkgFwm enaHsameRbHRtUv)aneKeGayeQaHfa sameRbHkMlaMgkat;rgkarBt;(flexural-shear crack)rUbTI8>5. sameRbH web-shear crack ekItmanenAkgFwmEdlmankMlaMgkat;
FMnigm:Um:g;Bt;tUcenAkgRTnugesIg. vaCasameRbHminFm
taehIyGacekItmanenAEk,rcMnucrbt;nFwmCab; bEk,rTMrnFwmsamBa.
sameRbH flexural-shear crackCaRbePTsameRbHFmtaEdleKGaceXIjmanenAelIFwm. dMbUgsameRbH flexural crackekItmanbBarenAelIFwm bnab;mksameRbHeRTtcab;epImekItmanBIelIkMBUlnsameRbHflexural crackenAeBlEdlkugRtaMgkMlaMgkat;TTwgekItmanenAkgtMbn;enaH. enAkugtMbn;EdlmankugRtaMgkMlaMgkat;TTwgFM FwmRtUvEtBRgwgedayEdkkg stirrupbEdkBt;(bent bar)edIm,IeFVIeGayFwmmanlkNsVit(ductile)Edlmin)ak;bdac;. edIm,IeCosvagkar)ak;edaykMlaMgkat;munkar)ak;edaykarBt;emKuNsuvtiPaBFMRtUv)anpl;eGayedIm,ITb;nwgkar)ak;edaykMlaMgkat;TTwg. ACI CodekMNt;emKuNkat;bnyersIusg;
75.0= sMrab;kMlaMgkat;TTwg.ersIusg;kMlaMgkat;TTwgenAkgGgt;ebtugGarem:RtUv)anekIteLIgedaybnSMnkMlaMgemkanicxageRkam
rUbTI8>5- ersIusg;kMlaMgkat;TTwgnebtugminTan;eRbH zV
-
kareprkMlaMgkat;TTwgrvagGnrp(interface shear transfer) aV EdlbNalmkBIkarbgaMKarvagfbMEbktambeNaypdKRKatrbs;sameRbH
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Department of Civil Engineering viTasanCatiBhubeckeTskm1.kMlaMgkat;TTwg nigm:Um:g;mantMlFMenAEk,rTMrkNalsMrab;FwmCab;. enATItaMgEdlkMlaMgkat;TTwgFM nigm:Um:g;Bt;tUc enaHvanwgmankareRbHedaykarBt;tictYc ehIykugRtaMgmFm bdVv /= . kugRtaMgkMlaMgTajtamGgt;RTUgCakugRtaMgEdleRTtedaymMuRbEhl o45 rUbTI8>4 c. sameRbHGgt;RTUgGacrMBwgfanwgekItmanenAeBlEdlkugRtaMgkM;laMgTajGgt;RTUgEdlsitenAEk,rtMbn;GkSNWtxiteTACit belIsersIusg;kMlaMgTaj
rbs;ebtug. CaTUeTA ersIusg;kMlaMgkat;TTwgcugeRkay(ultimate shear strength)
ERbRbYlcenaHBIcf'29.0 nig cf'42.0 . eRkayBIkarBiesaFn_eTAelIFwmCaeRcInGMBIkMlaMgkat;TTwg nigkMlaMgTajtam
Ggt;RTUg eK)anrkeXIjfaenAkgtMbn;EdlmankMlaMgkat;TTwgFM nigm:Um:g;Bt;tUc enaHsameRbHkMlaMgTajGgt;RTUgRtUv)anbegIteLIgenAeBlkMlaMgkat;TTwgmFm
dbfV wccr '29.0= *>#Edl wb CaTTwgRTnugmuxkat;GkSret bTTwgmuxkat;ctuekaN
d
CakMBs;RbsiTPaBrbs;FwmenATItaMgEdlkMlaMgkat;TTwg nigm:Um:g;Bt;mantMlFM enaHsameRbHedaykarBt;(flexural crack)RtUv)anekIteLIgdMbUg. enAdMNak;kalTImYy sameRbHxHBt;kgTisedAGgt;RTUgenAeBlEdlkugRtaMgkMlaMgTajGgt;RTUg EdlsitenABIcugxagelInsameRbHTaMgenaHFMCagkugRtaMgkMlaMgTajrbs;ebtug.RbsinebIeKeGaym:Um:g;FMmanGMeBIelIFwm sMrab;muxkat;EdlmanbrimaNEdkRKb;RKan;enaHkMlaMg nominalshear forceenAeBlEdlsameRbHekItmanRtUv)aneGaydUcxageRkam
dbfVwccr
'16.0=
*>$
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 131
tMlenHKWtUcCagtMlEdleGayedaysmIkar *># eRcInCaBak;kNalenAeBlEdlm:Um:g;Bt;man
tMltUcNas;. enHmannyfam:Um:g;Bt;FMkat;bnytMlrbs;kugRtaMgkM;laMgkat;TTwgenAeBlEdlsameRbHekIteLIg. smIkarxageRkamRtUv)anesIeLIgedIm,ITsSn_TaynUvkugRtaMg nominal shear stressenAeBlEdlsamGgt;RTUgRtUv)anrMBwgfaekItman
cu
uwc
wcr f
M
dVf
db
Vv '29.02.17'16.0
+== *>%
ACI Code, Section 11.3.2 )anyksmIkarenHsMrab;KNnakMlaMg nominal ultimate shear force
EdlTb;edayebtugdbfdb
M
dVfV wcw
u
uwcc '29.0)2.17'16.0( += *>^
Edl dbA wsw /= / dCakMBs;RbsiTPaBrbs;muxkat;Fwm/ wb CaTTwgRTnugsMrab;muxkat;GkSretbTTwgnmuxkat;ctuekaN uV nig uM CakMlaMgkat;TTwgcugeRkay (ultimate shearing force)nigm:Um:g;Bt;cugeRkay (ultimate bending moment)EdlekIteLIgkgeBldMNalKaenAelImuxkat;sikSa.
tMln uu MdV / minRtUvFMCag 0.1 sMrab;smIkar *>^. RbsinebI uM mantMlFMenAkgsmIkar
*>^ enaHtYrTIBIrnwgmantMltUcesIEtes
IsUn enaH cv xiteTArk cf'16.0 . RbsinebI uM mantMltUc
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Department of Civil Engineering viTasanCatiBhubeckeTskm&
1>
kgkrNIsMrab;kMlaMgsgt;tamGkS uN dbfdb
M
dVfV wcw
m
uwcc '29.0)2.17'16.0( += *>*
=
8
4 dhNMM uum
Edldb
A
w
sw =
=h kMBs;srubrbs;Fwm
uu MdV / GacFMCag 0.1 b:uEn cV minRtUvFMCag
g
ucwc
A
NfdbV
45.31)'29.0( += *>(
Edl gA CaRkLapTaMgGs; (gross section)KitCa 2mm m:agvijeTot cV GacRtUv)anKNnaeday
cg
uwc f
A
NdbV ')145.02( += *>!0
2>
kgkrNIsMrab;kMlaMgTajtamGkS uN
cg
uwc f
A
NdbV ')58.02( += *>!!
Edl uN mantMlGviCmansMrab;kMlaMgTajRbsinebI cV GviCman enaH cV RtUv)anykesIsUn.
5>FwmmanEdkkMlaMgkat;
EdkEdleRbIedIm,ITb;nwgkMlaMgkat;EdleKeRbIGacmaneRcInRbePTepSga. Edkkg EdleKeRbIedaydak;EkgeTAnwgEdkbeNay Edkem bRtUv)aneKdak;eRTt mMuEdl
eKniymeRbI o45 . EdkkgEdleKniymeRbImanmuxkat; 10DB nig 12DB .b. EdkBt; EdlCaEpkmYyrbs;EdkbeNayEdleKBt;eLIg enAkEngEdleKbBab; edaymMu
o30 nig o60 CaTUeTA o45 .c. bnSMrvagEdkkg nigEdkBt;d.
sMNaj;Edk CamYynwgsMNaj;EkgeTAnwgGkS
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Department of Civil Engineering viTasanCatiBhubeckeTskm%/ edayTb;Tl;nwgkarrIkFMnsameRbHeRTt (inclined crack).
-
vabegInnUvkMlaMgf%/ enAkgEdkbeNay- GMeBITb; (confining action) rbs;EdkkgeTAelIebtugGacbegInerIusg;rbs;va-
GMeBITb; (confining action) rbs;EdkkgeTAelIebtugbegInnUvsmtPaBrgVilnsnak;)asic(rotation capacity of plastic hinge) EdlekItmanenAkgeRKOgbgMindeterminate structureeRkambnkcugeRkay nigbegInRbEvgEdl yield GacekItmanenAelIva.eday nV CaersIusg;kMlaMgkat;rbs;muxkat;ebtugGarem:enaH
scn VVV += *>!@Edl cV - ersIusg;kMlaMgkat;)anBIebtug
sV - ersIusg;kMlaMgkat;)anBIEdkRbsinebI uV kMlaMgkat;Edl)anBIbnkxageRkAenaH
)( scnu VVVV += *>!#Edl
LDu VVV 6.12.1 += nig 75.0=
sV RtUv)anKNnaedaykarviPaK trussrUbTI*>&. sMrab;sameRbHo
45 nigesrInEdkkg bEdkdgErk. kMlaMgkat;bBar sV esInwgplbUkbgMkMlaMgbBarnkMlaMgTajEdlekItmanenAkgEdkeRTt
sinytvs fnAV = *>!$Edl vA -muxkat;kat;EdkkMlaMgkat;CamYyKMlat s
ytf - ersIusg;EdkkMlaMgkat;
eday 211 aaaans +=
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 135
otgaaaad 45141 == BIRtIekaN 41aaa tgaaaad 241 == BIRtIekaN 21aaa
)cot1()cot45(cot +=+= ddns o
)cot1( += s
d
n eKTTYl)an )cos(sin)cot1(sin +=+=
s
dfA
s
dfAV
ytvytv
s *>!%
sMrab;krNIEdkkgbBar o90=
s
dfAV
ytv
s = bs
ytv
V
dfAs= *>!^
sMrab;krNIEdkkgbBar o45=
s
dfA
V ytv
s 4.1= b sytv
V
dfA
s 4.1= *>!&sMrab;krNIEdkdgErkEtmYy bRkumEdkenAmYykEng
sinytvs fAV = bsin
yt
sv
f
VA = *>!*
sMrab; o45=
yt
sv
f
VA 4.1= *>!(
6>
tMrUvkarrbs; ACI CodesMrab;karKNnakMlaMgkat;TTwg
1> muxkat;eRKaHfak;sMrab;karKNnaersIusg;kMlaMgkat;TTwgmFm
Critical section for nominal shear strength calculation
ACI Code, Section 11.1.3GnuBaateGayykmuxkat;eRKaHfak;sMrab;karKNnaersIusg;kMlaMgkat;mFm enAcMgay dBIpmuxnTMr. karENnaMenHQrenAelIPaBCak;EsgEdlsameRbHeRTtdMbUgeKTMngCaekIteLIgenAelIFwmRtg;cMgay dBITMrEdleRcInelcecjenAeBleFVIBiesaFn_. muxkat;eRKaHfak;enHRtUv)anGnuBaatenAkglkxNEdlRbtikm
TMrbBankMlaMgsgt;eTAkgtMbn;cug/ bnkRtUv)anGnuvtenAelIbenAEk,rkMBUlnGgt;ehIyKanbnkcMcMnucGnuvtenAcenaHpnTMr nigTItaMgnmuxkat;eRKaHfak;. bTdankkMNt;Edrfa EdkkMlaMgkat;TTwgRtUv)andak;enAcenaHpnTMr nigcMgay d.
2>muxkat;EdkGb,brmasMrab;EdkkMlaMgkat;TTwg
vtmanrbs;EdkkMlaMgkat;TTwgenAkgFwmebtugTb;Tl;nwgkarrIkraldalnsameRbHeRTt. m:agvijeTot PaBsVit (ductility)ekIneLIg ehIyva)anRbkasGasnmuneBl)ak;. RbsinebIKanEdkkMlaMgkat;TTwgenaHFwmmanlkNRsYyehIy)ak;edaymin)anR)ab;mun. dUcenH muxkat;EdkkMlaMgkat;TTwgRtUv)ankMNt;
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Department of Civil Engineering viTasanCatiBhubeckeTskm@!sMrab; MPaf c 32' < / ww bbS /17940035.0/400157max == sMrab; MPaf c 32' = / wbS /179000max= *>@@sMrab; MPaf c 35' = / wbS /171200max= sMrab; MPaf c 42' = / wbS /156250max= RbsinebIeKeRbIEdk 12DB manragGkSr UenaH
sMrab; MPaf c 32' < / wbS /258250max= sMrab; MPaf c 32' = / wbS /25750max= *>@#
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 137
sMrab; MPaf c 35' = / wbS /246450max= sMrab; MPaf c 42' = / wbS /224950max= RtUvcgcaMfa maxS minRtUvFMCag mm600 b 2/d eT.
taragTI 1 pl;nUv maxS edayQrelIsmIkar *>@@ nig *>@#. KMlatcugeRkayKYrEtRtUvrMkileTArktMlEdltUc. ]TahrN_ mmS 515max= kayeTACa mmS 500max = .taragTI1> tMlrbs; cmbfAS wytv 6035.0/max == . enAeBlEdl MPafyt 400= nig MPaf c 32' <
wb )(cm 25 30 35 40 45 50 55 60 wb
maxS )(cm 10DB 60 55 50 40 35 35 30 25 wb/179400
maxS )(cm 12DB 60 60 60 60 55 50 45 40 wb/258250
3>
kMlaMgkat;TTwgGtibrmaEdlTb;edayEdkkMlaM gkat;TTwg sVedIm,IkarBarkar)ak;shear-compression failure EdlebtugGacEbkedaykugRtaMgkMlaMgkat;TTwgFM
nigkugRtaMgkMlaMgsgt;enAkgtMbn;eRKaHfak; enABIelIkMBUlnsameRbHGgt;RTUg ACI Code, Section11.5.6.8, tMrUvfa dbfV wcs '67.0 . RbsinebI dbfV wcs '67.0> enaHeKRtUvtMelIgmuxkat;ebtug.edayQrenAelIkarkMNt;enH
RbsinebI MPaf c 20' = enaH dbV ws 3 b MPadbV ws 3/
RbsinebI MPaf c 28' = enaH dbV ws 5.3 b MPadbV ws 5.3/ RbsinebI MPaf c 35' = enaH dbV ws 4 b MPadbV ws 4/ 4>KMlatEdkkgGtibrma
edIm,IFanafasameRbHGgt;RTUgRtUvkat;Edkkgy:agehacmYy enaH ACI Code, Section 11.5.4tMrUvfa KMlatrvagEdkkgminKYrelIs 2/d b mm600 RbsinebI dbfV wcs '33.0 edayQrelIkarsnt;fasameRbHGgt;RTUgekItmantammMu o45 niglatsnwgtamcMgayedkRbEhlcMgay d. enAkgtMbn;kMlaMgkat;
TTwgFMEdl dbfV wcs '33.0> KMlatEdkkgGtibrmacenaHEdkkgminRtUvFMCag 4/d . karkMNt;enHcaM)ac;edIm,IFanaeGaysameRbHGgt;RTUgkat;Edkkgy:agehacbI. enAeBlEdl dbfV wcs '67.0> karkMNt;nKMlatGtibrmaminRtUv)anGnuvtehIyTMhMrbs;muxkat;ebtugKYrRtUv)antMeLIg.
karkMNt;TIBIrsMrab;KMlatGtibrmanEdkkgkGacTTYl)anBIlkxNmuxkat;EdkkMlaMgkat;TTwgGb,brma. vA Gb,brma RtUv)anTTYlenAeBlKMlat s Gb,brma smIkar *>@!.
karkMNt;TIbIsMrab;KMlatGtibrmaesInwg mm600 enAeBlEdl dbfV wcs '33.0 nigesInwgmm300 enAeBlEdl dbfVdbf wcswc '67.0'33.0 < . tMltUcCageKnKMlatGtibrmaRtUv)anyk
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Department of Civil Engineering viTasanCatiBhubeckeTskm%.
5> ersIusg;yield rbs;EdkkMlaM gkat;TTwg
ACI Code, Section 11.5.2. tMrUveGayersIusg;design yield strength rbs;EdkkMlaMgkat;TTwgminKYrelIs MPa420 . mUlehtuEdlenABIeRkaykarsMercenHKWedIm,IkMNt;TMhMsameRbHEdlbNalmkBIkMlaMgTajGgt;RTUg nigedIm,IFanafaEKmrbs;sameRbHenArkSapb:HCitKaedIm,IbegInkMlaMgbBannkMlaMgkat;rvagGnrp aV rUbTI*>%. sMrab;ssrEdkfaMgGMeBAsMrab;pSar (welded deformed wire fabric)ersIusg;design yield strength minKYrelIs MPa560 .
6> TMBk;rbs;Edkkg
ACI Code, Section 11.5.2. tMrUvfaEdkkMlaMgkat;TTwgRtUv)andak;enAEk,rsesrrgkarsgt;eRkAbMput nigssrrgkarTajeRkAbMputtamEtGaceFVIeTA)an CamYynwgtMrUvkarrbs;code sMrab;kMra;karBarEdkedaysarEt enAeBlEdlbnkEdlmanGMeBIenAelIFwmxiteTACitbnkcugeRkay (ultimate load) sameRbHkMlaMgTaj edaykarBt; (flexural tension crack) bnayy:ageRCAcUleTAkgFwm. dUcKa edIm,IeGayEdkkgTTYl)annUversIusg; yield eBj vaRtUvkarnUvTMBk;Edll. enAeBlEdlbnkEdlmanGMeBIelIFwmxiteTACitbnkcugeRkay (ultimate load)kugRtaMgenAkgEdkkg)aneTAdl;kugRtaMg yield rbs;va enAcMnucEdlsameRbH
Ggt;RTUgkat;cMEdkkgenaH. tMrUvkarrbs;ACI Code sMrab;TMBk;Edkkg/ Section 12.13 dUcxageRkam-
karBt;nImYyenAkgEpkCab;nEdkkgGkSr U Fmta bBhuEdkkgGkSr U KYrBTCMuvijEdkbeNay (ACI Code, Section 12.13.3)emIlrUbTI*>*a.
- CodeGnuBaateGayeRbInUvTMBk;standard o90 / o135 b o180 CMuvijEdkbeNysMrab;Edkkg16DB . RbsinebIEdkkg 19DB / 22DB nig 25DB CamYynwg MPafyt 280> enaH Code,
Section 12.13.2 tMrUvTMBk; standard bUknwgRbEvgbgb; cytb ffd '/17.0 cenaHBak;kNal
kMBs;Fwm nigEpkxageRkAnTMBk;. RbsinebIEdkRtUvBt;edaymMuo
90 RbEvgBntminRtUvtUcCagbd12 . sMrab;Edk 16DB bEdkkgTMhMtUcCagenH RbEvgBntKW bd6 (ACI Code, Section 7.1)
emIlrUbTI*>*.-
RbsinebIEdkkgGkSr U DubRtUv)aneRbIedIm,IpMCaEdkkgbiTCit RbEvgRCYs (lap length)minRtUvtUcCag dl3.1 (ACI Code, Section 12.13.5)emIlrUbTI *>*c.
- ssrEdkEdlpSar (welded wire fabric) RtUv)aneRbIsMrab;EdkkMlaMgkat;TTwgenAkg]sSahkm
plitTukmun (precast industry) . TMBk;lMGitRtUv)anpl;eGayenAkg ACI Code, Section12.13.2.3nigenAkgesckIBnl; (commentary) rbs;va.
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 139
- EdkkgbiTCitRtUv)anpl;eGaysMrab;FwmEdlrgnUgkMlaMgrmYl (ACI Code, Section 7.11).- FwmEdlenABTCMuvijeRKOgbgMRtUveRbIEdkkgbiTCitedIm,IrkSa structural integrity rbs;Ggt;
(ACI Code, Section 7.13.2.2).
7>EdkkgenAEdlenAEk,rTMr
ACI Code, Section 11.1.3kMNt;faEdkkgkMlaMgkat;TTwgEdlpl;eGayenAcenaHpTMr nigmuxkat;eRKaHfak; (critical section)EdlsitenAcMgay dBITMr KYrRtUv)anKNnasMrab;kMlaMgkat;TTwg uV dUcKa enAnwg
muxkat;eRKaHfak;. vaCakarGnuvtn_Fm
taedaydak;EdkkgTImYyenAcMgay 2/s BIpnTMr Edl s CaKMlatEdlKNnaedaysmIkar *>!^ sMrab; uV enAmuxkat;eRKaHfak;.
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Department of Civil Engineering viTasanCatiBhubeckeTskmRbEvgRbsiTPaBrbs;EdkdgErk
manEtbIPaKbYnRtg;cMnuckNalnEpkeRTtnEdkbeNayRtUv)anKitfamanRbsiTPaBsMrab;EdkkMlaMgkat;TTwg. enHmannyfa KMlatGtibrmarbs;EdkdgErkKW )'(75.0 dd . BIrUbTI*>( RbEvgRbsiTPaB
rbs;EdkdgErkKW )'(06.1)')(414.1(75.045sin/)'(75.0 dddddd o
== . KMlatGtibrma s es
InwgcMgayedkEdl)anBIkarTMlak;cMeNalEkgnRbEvgRbsiTPaBEdkdgErk. dUcenH
oddS 45cos)'(06.1max = b )'(75.0707.0)'(06.1max ddddS ==
7>karKNnaEdkkgbBar
eKRtUvkarEdkkg (stirrup)enAeBlEdl cu VV 21> . EdkkgGb,brmaRtUv)aneRbIenAeBlEdl
cuc VVV !^ sytv VdfAS /= .
EdkkgEdlRtUv)aneRbICaTUeTAenAkgmuxkat;ebtugCaEdkkg 10DB nig 12DB GkSr UeCIgBIrCamYynwg MPafyt 400= . RbsinebI 10DB RtUv)aneRbIenaH smIkar*>!^kayCa
sss
ytv
VVV
fA
d
S 62800400157=
== *>@$
RbsinebI 12DB RtUv)aneRbIenaH
sss
ytv
VVV
fA
d
S 90400400226=
== *>@%
pleFobKMlatEdkkgelIkMBs;RbsiTPaB drbs;Fwm GaRsynwg sV . tMln dS/ sMrab;tMlepSgKan sV enAeBlEdl MPafyt 400= RtUv)aneGayenAkgtaragTI2 nigtaragTI3 sMrab;Edk 10DB nigEdk 12DB erogKa. tMldUcKaRtUv)anbgajCadaRkamdUcenAkgrUbTI8>10 nigrUbTI8>11.
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 141
taragTI2> pleFob dS/ sMrab;tMl sV MPafyt 400= / sVdS /62800/ = 10DB sV )(kN 125.6 142.7 190.3 237.9 251.2 285.5 330.5 380.6 418.7 475.8 592.5
dS/
0.5 0.44 0.33 0.264 0.25 0.22 0.19 0.165 0.15 0.132 0.106
taragTI3> pleFob dS/ sMrab;tMl sV MPafyt 400= / sVdS /90400/ = 12DB sV )(kN 180.8 225 265 310 361.6 445 490.0 535 665 775 850
dS/
0.5 0.40 0.34 0.29 0.25 0.20 0.18 0.17 0.14 0.12 0.11
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Department of Civil Engineering viTasanCatiBhubeckeTskm enaH 4/dS .- RbsinebIeKeRbI 12DB / 2/dS= enAeBlEdl kNVs 8.180 . enAeBlEdl sV ekIneLIg
dS/ fycuHtamExSekageTArktMl 14.0 enAeBl kNVs 665= . RbsinebIKMlatGb,brmaRtUv)ankMNt;Rtwm mm75 enaH mmd 535 . enAeBlEdl kNVs 6.361> enaH 4/dS .
-
RbsinebIeKeRbIEdkkgGkSr U MPafyt 280= enaHeKRtUvKuN dS/ edaytMl 10/7 bCaTUeTA400/ytf .
8>
segbviFIsaRsKNnaEdkkgbBar
CMhankgkarKNnaEdkkgbBarsMrab;kMlaMgkat;TTwg edayeyagtam ACI CodeGacRtUv)ansegbdUcxageRkam
a. kMNt;kMlaMgkat;KNnauV BIbnkEdlGnuvtnmkelIeRKOgbgM. kMlaMgkat;KNnaRKITic
EdlRtUvykmksikSasitenARbEvg dBImuxnTMr.
b.
kMNt;dbfV wcc '17.0 =
bdbfdb
M
dVfV wcw
u
uwcc
'29.0)2.17'16.0( +=
bnab;mkKNna cV
2
1
c. k> RbsinebI cu VV
2
1< muxkat;minRtUvkarEdkkg
x> RbsinebI cuc VVV RbsinebI cu VV > muxkat;Edkkg RtUvKNnadUcxageRkamd.
kMNt;kMlaMgkat;EdlTb;eday Edkkg
cu
s
VVV
=
e. kMNt; dbfV wcc '33.01= nig 12 2'67.0 cwcc VdbfV == . RbsinebI 2cs VV > tMeLIgmuxkat;.
f. kMNt;KMlatrbs;Edks
ytv
V
dfAs =1
g.
kMNt;KMlatEdkGtibrmaEdlGnuBaatieday ACI Code. KMlatEdkGtibrmaCatMltUcbMputn 2s nig 3s
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 143
k> cmds 602
2 = RbsinebI dbfVV wccs '33.01=
cmd
s 304
2 = RbsinebI 21 csc VVV <
x>cw
ytv
w
ytv
fb
fA
b
fAs
'
1633 =
h.
k> RbsinebI max1 ss < eRbI 1s x> RbsinebI max1 ss > eRbI maxs
i. ACI Codemin)ankMNt;nUvKMlatGb,brmaeT. eRkamlkxNFmta KMlatGb,brma SRtUv)ansnt;ykesInwg mm75 sMrab; cmd 50 nigmanKMlatGb,brmaesInwg mm100 sMrab;FwmeRCA (deep beam). RbsinebI SmantMltUcenaH eKGactMeLIgmuxkat;Edkkg
beRbIEdkkgeCIgeRcIn rUbTI 8>8.j. sMrab;muxkat;mUl RkLapEdleRbIsMrab;KNna =cV plKuNGgt;pitCamYykMBs;RbsiTPaB
d/ Edl 8.0=d nGgt;pit/ ACI Code, Section11.3.3.]TahrN_
FwmTMrsamBamanmuxkat;ctuekaN cmb 30= / cmd 55= nig cmh 60= ehIyRtUv)anBRgwgeday 254DB . epgpat;faetImuxkat;enHRKb;RKan;bGt;sMrab;kMlaMgkat;TTwgemKuN (ultimate shear force)xageRkam. RbsinebIva minRKb;RKan;cUrKNnaEdkkMlaMgkat;TTwgkgTMrg;CaEdkkgGkSr U. edayeRbI
MPaf c 28' = nig MPafyt 400= .k> kNVu 50= x> kNVu 110= K> kNVu 240= X> kNVu 345= g> kNVu 570= dMeNaHRsay
CaTUeTA mmbbw 300== / mmd 550= nig( ) ( ) kNbdfV cc 3.111105503002817.075.0'17.0 3 ===
kNVc 65.5521 =
( ) ( ) kNbdfV cc 288105503002833.0'33.03
1 ===
) kNbdfV cc 576'67.02 ==
k> kNVkNV cu 565.5550 21 = cu VkNV 21110 >= / b:uEnvatUcCag kNVc 3.111= . eday 0=sV dUcenH muxkat;RtUvkarEdk
kMlaMgkat;TTwgGb,brma. eRbI 10DB CaEdkkgGkSr UenAKMlatGtibrma.22 157
4102 mmAv ==
KMlatGtibrmaCatMltUcCageKkgcMeNammmdS 2752/2 == yk mm250 lub
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 145
2>sMrab;X> kNVs 6.311= / 18.0/ =dS enaH mmS 1001= / kNkNVs 2.2516.311 >= enaH4/max dS = RtUv)aneRbI.
]TahrN_2
FwmTMrsamBaEdlmanRbEvg m2.5 nigmanRbEvgcenaHssr (clear span) m9.4 edayRTnUv
bnkBRgayes
Iefr mkN/65 nigbnkBRgayes
IGefr mkN/55 . TMhMrbs;Fwm nigssrEdkRtUv)anbgajenAkgrUbTI 8>12. epgpat;muxkat;sMrab;kMlaMgkat;TTwg nigKNnaEdkkMlaMgkat;TTwgcaM)ac;. eKeGay
MPaf c 20' = nig MPafy 400= .
dMeNaHRsay
eKeGaymmbw 350=
/mmd 580=
1>
KNnakMlaMgkat;TTwgemKuN (ultimate shear)BIbnkxageRkAbnkBRgayesIemKuN mkN/166556.1652.1 =+=
uV enABImuxpTMr kN7.4062
9.4166=
=
KNna uV enAcMgayBImuxpnTMr kN42.31016658.07.406 == 2>KNna :cV
( ) kNdbfV wcc 75.115105803502017.075.0)'17.0(3
===
kNVc 87.572
1 =
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Department of Civil Engineering viTasanCatiBhubeckeTskm
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 147
cMnYnEdkkgsrubsMrab;FwmKW 28)491(2 =++ . karBRgayEdkkgRtUv)anbgajenAkgrUbTI 8>13kMlaMggkat;TTwgEdl)anKNnaRtUv)anbgajenAkgrUbTI8>12.
10> dak;Edkkg 12DB cMnYnBIredIm enABIelImuxkat;FwmedIm,IedIrtYrCaEdkkgBr.
9>
kMlaMgkat;TTwgEdlbNalBIbnkGefrenAkg]TahrN_TI2 TaMgbnkefr nigbnkGefrRtUv)ansnt;faBRgayesIeBjtambeNayFwm Edl
begIt)ankMlaMgkat;TTwgsUnenAkNalElVg. CaFmta bnkefrBitCaBRgayeBjelIbeNayFwm EtbnkGefrGacGnuvteBj bkGnuvtEtEpkxHrbs;Fwm EdltMrUveGaymankMlaMgkat;TTwgGtibrmaekIteLIgenAkNalElVg bmuxkat;kMNt;NamYy. rUbTI8>14 abgajBIFwmTMrsamBaCamYynwgbnkBRgayesIGnuvteBjbeNayFwm. kMlaMgkat;TTwgERbRbYlCaragbnat;tambeNayFwm CamYynwgkMlaMgkat;TTwgGtibrmaenATMrA .
kgkrNIEdlbnkGefr LWW 6.12 = kMlaMgkat;TTwgGtibrmamanGMeBIenARtg;TMr A enAeBlEdl
2W GnuvteBjElVgFwm rUbTI8>14 a. kMlaMgkat;TTwgGtibrmaekItmanenAkNakElVgRbsinebIbnkGefrRtUv)andak;EtBak;kNalFwm BCrUbTI8>14b EdlbegIt)an uV enAkNalElVgesInwg 8/2LW . dUcenH kMlaMgkat;TTwgKNnaRtUv)anbegIteLIgedaykarbEnmkMlaMgkat;TTwgGtibrmaEdlbNalmkBIbnkGefr EdlRtUv)andak;enAelIRbEvgepSgnElVg eTAelIkMlaMgkat;TTwgGefr rUbTI8>14 c. vaCakar
Gnuvtn_Fm
taedayKitkMlaMgkat;TTwgGtibrmaRtg;TMr A es
Inwg 2/)6.12.1(2/ LWWLW LDu += / b:uEn uV enAkNalElVgesI 8/)6.1(8/2 LWLW L= CamYybnat;Rtg;ERbRbYltambeNay ACnig CB dUcbgajenAkg rUbTI 8>14 d. karKNnasMrab;kMlaMgkat;TTwgenAkkrNIenHnwgGnutdUcKanwgkarBnl;kg]TahrN_2.RbsinebI karerobrab;xagelIenHGnuvteTAFwmkg]TahrN_2 enaH uV enATMr A kN7.406= nig uV enAkNalElVg kN9.538/9.4)556.1( == .
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Department of Civil Engineering viTasanCatiBhubeckeTskm
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 149
]TahrN_3
Fwm cantileverRbEvg m3 manmuxkat;ctuekaNEkg nigRTnUvbnkemKuNBRgayesInigcMcMnucbnkpal;xnRtuv)anrab;bBalrYc dUcbgajenAkgrUb 8>15. edayeRbI MPaf c 28' = nig MPafy 400= KNnaEdkkMlaMgkat;TTwgcaM)ac;sMrab;dak;kgFwmTaMgmUl edayeyagtam ACI Code.
dMeNaHRsay1>KNnakMlaMgkat;TTwgtambeNayFwmEdlbNalmkBIbnkxageRkA
uV enATMr kN3653689380 =++=
udV enAcMgay d kN4.3513000
51080365 ==
uV enAcMgay m2.1 xageqVg kN2692.180365 ==
uV
enAcMgaym2.1
xagsaM kN18089269 ==
uV enAcugTMenr kN36=
daRkamkMlaMgkat;TTwgRtUv)anbgajenAkgrUbTI8>15.2>KNna cV
( ) ( ) kNbdfV cc 2.103105103002817.075.0'17.0 3 === kNVc 6.512
1 =
edaysar cud VV >
muxkat;ebtugRtUvkarEdkkMlaMgkat;TTwg. KNnakNbdfV cc 2.26710510300)2833.0('33.0
31 ===
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Department of Civil Engineering viTasanCatiBhubeckeTskmEpk AC kMlaMgkat;TTwgKNna kNVV udu 4.351== . KNna /)( cus VVV = kN9.33075.0/)2.1034.351( == . edaysarEt 21 csc VVV 10.4>KNnaEdkkg eRCIserIsEdkkgGkSr U 10DB / 2157mmAv = . KNna 1S QrelI sV
mmV
dfAS
s
ytv100
330900
5104001571 ===
eRbI mm100 bTTYl 19.0/ =ds BIrUb 8>10.5>KNnaKMlatGtibrma mmdS 5.1274/5104/2 === yk mm125
mmb
fAS
w
ytv550
30035.0
400157
35.03 =
== BItaragTI1 sMrab; mmb 300=
mmS 3004 =
dUcenH mmS 125max= 6>eday mmSmmS 125100 max=
enAcMnuc C/ kMlaMgkat;TTwgKNna cu VkNV >= 269 enaH ( ) kNVs 22175.0/2.103269 == .mmVdfAS sytv 145/1 ==
kNVkNV cs 2.267221 1=Epk BC
A. cu VkNV >=180 kNVkNV cs 2.2674.10275.0/)2.103180( 1=
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 151
10> karBRgayEdkkgedayvas;ecjBITMr A dak;EdkkgTImYyenA mmS 502=
mm120010012 = mm17502507 =
srub mm3000 karBRgayEdkkgRtUv)anbgajenAkgrUbTI8>16. EdkkgsrubmancMnYn 20 .
10> kugRtaMgkMlaMgkat;TTwgenAkgGgt;EdlmankMBs;ERbRbYl
edaysarEtkugRtaMgkMlaMgkat;TTwg v CaGnuKmn_nkMBs;RbsiTPaB ddUcenHkugRtaMgkat;TTwgERbRbYl
tambeNayFwmebtugBRgwgedayEdkCamYynwgkBs;ERbRbYl. enAkgFwmEbbenH rUbTI8>17 eKBicarNaelIGgGnntUc dx . kMlaMgsgt;CenAelImuxkat;NamYyesInwgm:Um:g;EckeGaydXas;b yMC /= .
edrIevTImYyn CKW
2y
MdyydMdC
=
RbsinebI 1C FMCag 2C enaH vbdxdCCC == 21
dyy
M
y
dM
y
MdyydMvbdx
22 =
=
=dx
dy
by
M
dx
dM
ybv
2
1
edaysar jdy= / dxdM/ esInwgkMlaMgkat;TTwg V nig dxjdd /)( CaCMral (slope)/
= )(
)( 2 jd
dx
d
jdb
M
bjd
Vv nig tan
)( 2jdb
M
bjd
Vv = *>@^
Edl Vnig MCakMlaMgkat;TTwg nigm:Um:g;xageRkA ehIy CamMuCMralnpmYyrbs;FwmeTAnwgpmYyeTotrbs;Fwm. sBaabUkRtUv)aneRbIenAeBlEdlkMBs;fycuHm:Um:g;ekIneLIg b:uEnsBaadkRtUv)aneRbIenAeBlkMBs;ekIneLIgehIym:Um:g;kekIneLIg. rUbmnenHRtUv)aneRbIenAeBlEdlmMuCMraltUc EdlmMu o30 .
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Department of Civil Engineering viTasanCatiBhubeckeTskm@^GacRtUvbegIteLIgedaysMrYl j enaHeyIgTTYl)an
tan2
bd
M
bd
Vv = *>@&
sMrab;viFIKNnaersIusg;smIkarxageRkamGacRtUv)aneRbI
tan2
bd
Mbd
Vv uu = *>@*
sMrab;kMlaMgkat;TTwg
tand
MVV uun = *>@(
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 153
rUbTI 8>18 bgajBIFwm cantileverCamYynwgbnkcMcMnucenAcugTMenr. m:Um:g;nigkMBs; dekInelIgkgTisedAeTArkTMr. kgkrNIenH sBaadkRtUv)aneRbIenAsmIkar *>@& *>@* nig*>@(. dUcKa sBaadkRtUv)aneRbIsMrab;muxkat; tenAkgFwmTMrsamBadUcbgaj ehIysBaabUkRtUv)aneRbIsMrab;muxkat;ZEdlm:U
m:g;ekIneLIgenAeBlEdlkMBs;fycuH.enAkgkrNICaeRcIn karERbRbYlkMBs;rbs;FwmekItmanenAeLIEpkrbs;FwmEdlenAEk,rTMr rUbTI
8>18.karBesaFn_eTAelIFwmCamYykMBs;ERbRbYlbgajfa FwmEdlmankMBs;FMenATMrCaTUeTA)ak;edaysar
kMlaMgkat;TTwgsgt;. FwmEdlmankMBs;tUcenATMrCaTUeTA)ak;edaysarPaBKanesrPaB EdlbNalmkBIkarraldalnsameRbHemenAkgFwmeLIgelIehIybnab;mksameRbHenaHraldaltamTisedkenAelImuxkat;
FwmEpkxagelI. karBiesaFn_k)anbgajEdrfa sMrab;FwmEdlmankMBs;ERbRbYl rUbTI8>18 CamYynwgmMueRTt RbEhl o10 nigrgnUvkMlaMgkat;TTwg nigkMlaMgBt;ersIusg;kMlaMgkat;TTwgrbs;ebtug CVV GacRtUv)anKNnaeday
)tan1( += cCV VV *>#0Edl =CVV ersIusg;kMlaMgkat;TTwgrbs;FwmCamYynwgkMBs;ERbRbYl
( ) dbfdbM
dVfV wcw
u
uwcc '29.02.17'16.0
+= ACI Code Eq.11.6
= mMuEdlbegIteLIgedayTisrbs;Edk. vaRtUv)anKitfaviCmansMrab;FwmEdlmankMBs;tUcenATMr nigGviCmansMrab;FwmEdlmankMBs;FMenATMr rUbTI 8>18
=sd kMBs;RbsiTPaBrbs;FwmenATMrACI Code Eq.11.3 CasmIkarRtUv)ansMrYl nigGaceRbIedIm,IKNna cV
) dbfV wcc '17.0= *>#!]TahrN_4
KNnaFwmcantilever
dUcbgajenAkgrUbTI8>19 eRkamGMeBIbnkemKuN. FwmenHkMBs;srubenAcugTMenr mm300 ehIyekIneLIgeTArkTMr. edayeRbIPaKryEdk %5.1= / MPaf c 28' = /MPafy 400= nig mmb 250= .
dMeNaHRsay
1> uM TMr mkN.2695.2622/5.25.36 2 =+=
2>sMrab; %5.1= / MPaRu 72.4=
mmbR
M
du
5.47725072.4
10269 6
=
==
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Department of Civil Engineering viTasanCatiBhubeckeTskm
KNnasMrab;kMlaMgkat;TTwg kMlaMgkat;TTwgGtibrmaenATMrKW kN25.1535.25.3662 =+ . Edaysarmuxkat;FwmERbRbYl m:Um:g;RtUv)anBicarNakgkarKNnakMlaMgkat;TTwg. edaysarkMBs;FwmekIn
eLIgCamYym:Um:g;ekIneLIg sBaadkRtUv)aneRbIenAkgsmIkar *>@*)(tan
2
bd
M
bd
Vv uuu =
edIm,Irk tan / yk denAcugTMenresI mm490 nig denAKl;TMresI mm240
1.02500
240490tan =
=
uv TMr MPa07.11.049025075.0
10269
49025075.0
1532502
6
=
=
4>
kugRtaMgkMlaMgTTwgenAcugTMenrKW bdVu / 0=uM MPavu 38.1
24025075.0
62000=
=
5>enAcMgay mmd 490= BImuxpnTMr kMBs;RbsiTPaBKW mm441 BIrUbFrNImaRt
kNVu 4.13549.05.3625.153 ==
uM enAcMgay mm490 BITMr= mkN.4.1982
01.25.3601.262
2
=+
MPavu 09.144125075.0
1.0104.19844125075.0
104.1352
63
= =
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 155
6>enAkNalElVg m25.1 BITMr
mmd 365= kNVu 6.10725.15.3625.153 ==
mkNMu .1062
25.15.3625.162
2
=+= MPavu 15.1
36525075.0
1.010106
36525075.0
106.1072
63
=
=
dUcKa enAcMgay m9.1 BITMr m6.0 BIcugTMenr
mmd 300= kNVu 9.83= kNMu 8.43= kNvu 23.1= enAcMgay m2.2 BITMr m3.0 BIcugTMenr
mmd 270=
kNVu 73=
kNMu 2.20=
kNvu 29.1=
tMlTaMgGs;enHRtUv)anbgajenAkgrUbTI8>207>
kugRtaMgkMlaMgkat;TTwgedayebtugKW
MPa9.02817.0 = kugRtaMgkMlaMgkat;TTwgGb,brmaEdlRtUvTb;edayEdkkMlaMgkat;TTwg
MPavus 48.09.038.1 ==
uv nig usv RtUv)anekIneLIgedaypleFob /1 kgsmIkar 8>288> eRCIserIsEdkkg 10DB EdlmanEdkBIr21575.782 mmAv ==
ScaM)ac; mmbv
fA
ws
ytv523
25048.0
400157=
==
maxS sMrab;2
d mm245= eTA mm120 enAcugTMr
maxS
sMrab;Gb,brmavA
mm
b
fA
w
ytv718
25035.0
400157
35.0
=
==
9> epgpat;KMlatGtibrma :)2/(d cus fv '33.0
MPaMPaf c 48.074.12833.0'33.0 >== 10>karBRgayEdkkg cMgayBIcugTMenr
EdkkgcMnYnmYymancMgay mm50 mm50= EdkkgcMnYndb;mancMgay mm120 mm1200=
EdkkgcMnYnbImancMgay mm175 mm525= EdkkgcMnYnbI;mancMgay mm200 mm600=
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 157
11> Ggt;rgkarBt;eRCA
Ggt;rgkarBt;KYrRtUv)anKNnaCaFwmeRCARbsinebIpleFobn clear span nl Edlvas;BIpmuxTl;Karbs;TMr rUbTI 8>21 elIkMBs;srub h mantMltUcCag 4 (ACI Code, Section 11.8). Ggt;KYrrgnUvbnk
enAelIpEdlQmnwgpnTMr EdlGaceFVIeGay strut rgkarsgt;GacbegIteLIgenAcenaHbnk nigTMr rUbTI8>22. RbsinebIbnkGnuvtenA)at bpxagrbs;FwmeRCA smIkarKNnakMlaMgkat;TTwgsMrab;FwmFmtaEdl)aneGayBIxagmuxKYrRtUv)aneRbI. Ca]TahrN_FwmeRCAKWCaFwmElVgxIEdlRTbnkFn;/ CBaaMgbBareRkambnkTMnajEpndI (gravity load), shear wall, nigkMralxNrgnUvbnkedk.
niymnyrbs;Ggt;rgkarBt;eRCAkRtUv)anbgajenAkg ACI Code, Section 10.7.1. vabgajfaGgt;rgkarBt;EdlmanpleFob 4/ 22 a.
rUbTI8>22 abgajBIkarBRgaykugRtaMgeGLasic enARtg;muxkat;kNalElVgnFwmeRCA nigrUbTI8>22bbgajBIExSekagkugRtaMgemenAkgFwmeRCAEdlrgbnkenApxagelI(top-load deep beam). ExSCab;bgajBIkarBRgaykugRtaMgTaj ExSdac;bgajBIkarBRgaykugRtaMgsgt;. eRkambnkFn;sameRbH
bBareRTtekItmanenAkgebtugkgTisedAEkgnwgkugRtaMgTajem ehIyesIrEtRsbeTAnwgExSKngdac;rUbTI8>22 c. dUcenH eKRtUvkarTaMgEdkedk nigEdkbBaredIm,ITb;nwgkugRtaMgem. elIsBIenH EdkrgkarBt;edaykarTaj (tensile flexural reinforcement)RtUv)andak;enARbEhlmYyPaKR)aMenA)atrbs;FwmtamKngkugRtaMgTaj rUbTI8>22b . CaTUeTA karviPaKFwmeRCAmanlkNsKsaj nigGacGnuvtedayeRbIKMrUtrussbedIm,ITTYl)anlTplkan;EtsuRkiteKeRbIviFIfinite elementbviFIRsedogKa. edIm,IgayRsYlkgkarKNnakMlaMgkat;TTwgnFwmeRCA eKGacGnuvttamCMhanEdl)anerobrab;xageRkam
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Department of Civil Engineering viTasanCatiBhubeckeTskm muxkat;eRKaHfak; (critical section) RbsinebImuxkat;eRKaHfak;sMrab;KNnakMlaMgkat;TTwgenAkgFwmeRCAEdlRTbnkbBarGnuvtenApxagelIrbs;Fwm sitenAcMgay XBIpnTMr enaHcMgay XGacRtUv)ankMNt;dUcxageRkam rUbTI8>23
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 159
a. sMrab;FwmeRCAEdlRTbnkBRgayesI nlX 15.0= / Edl =nl clear span.b. sMrab;bnkcMcMnuc 11 5.0 aX = TMrxageqVg b 22 5.0 aX = TMrxagsaM rUbTI8>23/
Edl 1a nig 2a esInwg shear spanEk,rTMrnImYy. Shear span CacMgayBIbnkcMcMnuc
eTApnTMr.enAkgRKb;krNITaMgGs; cMgayX/ 1X nig 2X dac;xatminRtUvFMCagkMBs;RbsiTPaB d.
2> ersIusg;kMlaMgkat;TTwgGtibrma nV ersIusg;kMlaMgkat;TTwgGtibrma nV sMrab;Ggt;rgkarBt;eRCAminKYrmantMlFMCagtMlxageRkam 75.0=
sMrab; 2#@ a
byk dbfV wcn '83.0 = *>##krNITaMgBIr manEcgenAkg ACI Code, Section 11.8.3. RbsinebI nu VV > enaHeKRtUvtMeLIg
muxkat;ebtug.3>a.ersIusg;kMlaMgkat;TTwgrbs;ebtug cV ersIusg;kMlaMgkat;Fmta (nominal shear strength)
cV rbs;ebtugGacRtUv)anKNnadUcxageRkamdbfV wcc '17.0= *>#$
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Department of Civil Engineering viTasanCatiBhubeckeTskm#$ RtUv)aneRbICamYyKMnitfasameRbHEdltUcesIrEtemIlmineXIjGacekItmanenAkgFwmeRCA nigGacGueRKaH)an. sameRbHGaccab;epImekItmanenARbEhlmYyPaKbInbnkemKuN.
4>
EdkkMlaMgkat;TTwg enAeBlkMlaMgkat;TTwgemKuN cu VV > eKRtUvdak;EdkkMlaMgkat;TTwgEdlcat;Tukfa )( scu VVV += b /)( cus VVV = . CMhannkarKNnamandUcxageRkam
a. kMNt; sV kMlaMgTb;edayEdkkMlaMgkat;TTwg sV RtUv)ankMNt;BIsmIkarxageRkam
dfdl
S
Adl
S
AV y
n
h
vhn
v
vs
+
+=
12
/11
12
/1 *>#^
Edl =vA RkLapsrubnEdkkMlaMgkat;TTwgbBarEdlmanKMlat vS ehIyEkgeTAnwgEdkemrgkarTajedaykarBt;npxagTaMgBIrrbs;Fwm
=vhA RkLapsrubnEdkkMlaMgkat;TTwgedkEdlmanKMlat hS RsbnwgEdkemrgkarTajedaykarBt;npxagTaMgBIrrbs;Fwm
b. KMlatEdkkMlaMgkat;TTwgKW
KMlatQrGtibrma mmdSv 3005
KMlatedkGtibrma mmdSh 3005
c. EdkkMlaMgkat;TTwgGb,brma RkLapEdkkMlaMgkat;TTwgbBarKW vwv SbA 0025.0= .RkLapEdkkMlaMgkat;TTwgedkKW hwvh SbA 0015.0= .
d. EdkkMlaMgkat;TTwgRtUvkarenARtg;muxkat;eRKaHfak;KYrRtUv)anlatsnwgeBjRbEvg nigkMBs;rbs;FwmeRCA.
e.
sMrab;FwmeRCACab;EdkkMlaMgkat;TTwgdUcKaKYrRtUv)aneRbIenARKb;ElVg RbsinebIElVgTaMgenaHmanRbEvgesIKaCamYybnkRsedogKa.
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 161
5> EdkrgkarBt;nFwmeRCA dMeNIrRbRBwteTAnkarBt;rbs;FwmeRCAKWmanlkNsKsaj nigTamTarkarviPaKkugRtaMg nigbMErbMrYlrageFobtamlkN nonlineartamkMBs;rbs;Fwm. sMrab;karKNnadMbUg viFIdsMrYlxageRkamGacRtUv)aneRbI
)(yfAM ysn = Edl =y dXas; ( )2/ad= . edaysartMl ( )2/ad mankarBI)akkgkarKNna/ d
Xas;y GacRtUv)anKNnaRbEhlykesInwg h6.0 sMrab; 1/ =hln nigmantMlesInwg h8.0 sMrab; 2/ =hln . viFanRtzan(Linear interpolation)GacRtUv)aneRbIedIm,IKNna y enAeBl hln / ERbRbYlcenaH 0.1 nig 0.2 . dUcenH
y
us
yf
MA
= *>#&
tMln sA minGactUcCagEdkrgkarBt;Gb,brmaEdlRtUvkarsMrab;FwmFm
taEdlnwgeGayenAeBlbnab;edaysnt; hd 9.0= .
sA Gb,brma dbf
dbf
fw
yw
y
c 38.1'25.0 = *>#*
GgTIBIrlub enAeBlEdl MPaf c 30' < . cMNaMfa yf nig cf' KitCa MPa .EdkrgkarTajedaykarBt; (flexural tension reinforcement)KYrdak;enA 4/h eTA 5/h n
Fwm nigKYrmanKMlatRKb;RKan;tambeNay)attMbn;Taj. EdkrgkarTajKYrEtf
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Department of Civil Engineering viTasanCatiBhubeckeTskm
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 163
K> KNna /)( cus VVV = edaysar kNkNVc 3.15529.1785 >= enaH 0=sV dUcenHeKRtUvkarEdkkMlaMgkat;TTwgGb,brma.
X> KNnaEdkkMlaMgkat;TTwg
edaysn
t;eRbIEdk 12DB sMrab;dak;enApsgagTaMgtamTisedAedk nigTisedAQrenaH22 226
4122 mmAA vhv ===
KMlatGtibrmaGnuBaatrbs;EdkQr nigEdkedk
mmmmd
SS vhv 3004505
2250
5>==== yk mmSS nhv 300==
EdkQrGb,brma
vA Gb,brma= 22 2263003004000025.0 mmmm >=
bBaHKMlatEdkkgbBar mmSv 2260025.0400
226=
=
EdkedkGb,brma
vhA Gb,brma= 22 2261803004000015.0 mmmm
RbsinebIeyIgeRbIdbfV
wcc
'17.0=
enaHkNV
c
6.8091022504002817.0 3 ==
nigkNkNVc 3.15522.607
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Department of Civil Engineering viTasanCatiBhubeckeTskm24.
]TahrN_6 FmeRCA strut and tie
FwmeRCATMrsamBaEdlman clear span m6.3= kMBs;srub m8.1= nigTTwg mm450= . FwmenHRT
ssrkaerEdlmanRCug mm450=
enAkNalElVgEdlRTnUvbnkefr kN1335=
nigbnkGefr kN1070=
.KNnaFwmenHedayeRbIviFIstrut and tie. eKeGay MPaf c 28' = nig MPafy 400= rUbTI8>25.
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 165
dMeNaHRsay
1>KNnabnkemKuN rUbTI8>25TMgn;Fwm kN1.912545.08.15.4 ==
edaysarTMgn;pal;rbs;FwmmantMltUcebIeFobCamYybnkcMcMnucenAkNalElVg dUcenHbEnmvaeTAkgbnkGefrcMcMnucEdlmanGMeBIrenAkNalElVg
( ) kNLDPu 32.342310706.11.9113352.16.12.1 =++=+= kNRR BA 66.1711==
2>
epgpat;faetIFwmenHeRCAtamkarEcgrbs; ACI Code, Section 11.8: clear span mln 6.3= nigmh 8.1= ehIy 42/
KNnaersIusg;kMlaMgkat;TTwgGtibrmanmuxkat;Fwmyk uV enARtg; kNRA A 66.1771== nigsnt;yk mhd 62.18.19.09.0 ===
kNdbfV wcn 1.27431016204502883.0'83.03 ===
un VkNV >== 3.20571.274375.0 OK4>eRCIserIsKMrUtruss
eRCIserIsKMrUtruss RtIekaN. snt;facMnuc node eFVIGMeBIsitenAGkSTMr nigenAcMgay mm150 BI
EKm)at bEKmkMBUlFwm rUbTI8>26. KMrUstrut and tiepMeLIgedayGgt; tieAB mYynigGgt;strutBIrAD nig DB . dUcKa RbtikmenARtg;cMnuc A nigcMnuc B nigbnk uP Rtg;cMnuc D tMNagCastrutbBar.RbEvg strutGgt;RTUg mAD 52.2025.25.1 22 =+= yk CamMurvagGgt;strut nigGgt;tieenaH
7407.0025.2
5.1tan == enaH oo 265.36 >= OK
5>
KNnakMlaMgenAkgGgt; truss kMlaMgsgt;enAkgGgt;strut kNFFAD BDAD 6.2875
5.1
52.266.1711 ====
kMlaMgTajenAkgGgt; tie kNFAB AB 231152.2
025.26.2875 ===
6>KNnaersIusg;RbsiTPaB cef . snt;EdkTb; (confining reinforcement) RtUv)andak;edIm,IkarBarkMlaMgbMEbk (splitting force). Ggt;strut AD nig DB tMNageGayGgt;rgkarsgt;ragdb
(bottle-shape compression member) dUcenH 75.0=
s .MPaff csce 85.172875.085.0'85.0 ===
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Department of Civil Engineering viTasanCatiBhubeckeTskm
KNna nodal zone
k> KNnanodal zone
enAcMnucA
sn
t;fakMlaMgnnodal zone
mankugRtaMgdUcKaKWMPa85.17
ehIypEkgeTAnwgkMlaMgEdlRtUvKa
un FF b ucsce FAf Edl 75.0= sMrab; strut, tienig node.RbEvgnpedk ab rUbTI8>27 a esInwg
mmbfF ceu 284)45085.1775.0/(1066.1711)/(3 ==
BIFrNImaRt RbEvg mmac 38366.17112311
284 ==
dUcKa RbEvg mmbc 477
66.1711
6.2875284 ==
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 167
TIRbCMuTMgn;rbs; nodal zonesitenA mm5.1912/383 = BI)atnFwm eyIg)ansnt; mm150 x> KNna nodal zoneenAcMnuc D rUbTI8>27bRbEvgnpedk ( ) mmde 56845085.1775.0/1032.3423 3 ==
RbEvgn mmefdf 47732.34236.2875
568 === RbEvgrbs; mmfg 383)
2
568(477 22 ==
dUcenH TIRbCMuTMgn;n nodal zonesitenA mm1283/383 = BIpxagelIrbs;FwmeyIg)ansnt;mm150
8>KNnaEdkQr nigEdkedkk> EdkQr mMurvagEdkQr nigGgt;strutKW o5.53 BIrUbTI 8>27 a. eRbIEdk 16DB EdlmanKMlat
mm300 / 22 4024
162 mmAs == eCIgBIr/ 804.05.53sin =o
0024.0804.0)300450/(402sin)/( ==issi SbA x> Edkedk mMurvagEdkedk nigGgt;strutKW o5.36 BIrUbTI 8>27 a. eRbIEdk 16DB EdlmanKMlat
mm300 / 22 4024
162 mmAs == eCIgBIr/ 595.05.36sin =o
0018.0595.0)300450/(402sin)/( ==issi SbA
K> issi SbA sin)/( srub 003.00042.00018.00024.0 >=+= OK9>KNnaGgt; tie edk AB
k> KNna sA
ysu fAF = ( ) 23 770340075.0/102311 mmAs == eRbI 3012DB 28482mmAs = dak;CabIbICYrdUcbgajkgrUbTI8>27 c.x> KNnaRbEvgf= dUcenHeRbITMBk; o90 cgPab;CamYyEdkssr
( ) cbyedh fdfl '/02.0 =
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Department of Civil Engineering viTasanCatiBhubeckeTskm
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 169
]TahrN_7
eKmanFwmTMrsamBamYyEdlmanRbEvg m6 clear span rgnUvbnkBRgayefrmkN/5.47 nigbnkBRgayGefr mkN/25 . FwmenHmanmuxkat; cmb 35= nig cmd 55= .
FwmenHBRgwgedayEdk 254DB BRgaymYyCYr. cUrkMNt;nUvmuxkat;caM)ac;sMrab;kMlaMgkat;TTwg. smtikmMPaf c 28' = nig MPafyt 280= .
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Department of Civil Engineering viTasanCatiBhubeckeTskm bnkemKuN bnkKNna
mkNLD /97256.15.472.16.12.1 =+=+
x> kMlaMgkat;TTwgKNnaenARtg;muxxagssrkNVu 291
2
697 ==
K> kMlaMgkat;TTwgKNnaenAcMgay dBIpxagssr
kNVud 65.237)9755.0(291 == X> ersIusg;kMlaMgkat;TTwgEdlTb;edayebtug
kNbdfV cc 2.1735503502817.0'17.0 === kNVc 130= kNVc 65
2
1=
g> kMlaMgkat;TTwgEdlEdkRtUvTb;
kNVV
V cus 5.14375.0
)2.17375.0(65.237=
=
=
c> cMgayBImuxpssrmk kNVc 652
1=
mx 33.23291
65291' =
=
q> KNnaEdkkg1>eRCIserIsEdk 10RB EdkkgmaneCIgBIr
22 1575.782 mmmmAv == mmmmm
V
dfAs
s
ytv6005.168
105.143
55028015731
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T.Chhay NPIC
kMlaMgkat;TTwg nigkMlaMgTajGgt;RTUg 171
eday 1cs VV < dUcenHKMlatEdkGtibrmakMritRtwm mmd
s 2752
max ==
C> kMlaMgkat;TTwgEdlTb;edayEdksMrab;KMlat mmds 2752
max ==
kN
s
dfA275mmsforV
ytv
maxs 9.87
275
550280157)(
max
=
===
kNkNVs 94.659.8775.0 == cMgayBImuxTMr eTAdl;EdkkgEdlmanKMlat mms 275max=
mx 98.03291
)94.65130(2911 =
+=
dUcenH sMrab; m98.0 BImuxnTMr eRbIEdkkg 10RB KMlat mm160 nigsMrab;EpkenAsl; eRbIEdkkgGb,brma KMlatGtibrma
Q> karBRgayEdkkgEdkkg1 manKMlat mms 80
2=
Edkkg6 manKMlat mmmm 960160 = srub mmmm 98.004.11040 >= Edkkg6 manKMlat mmmm 1620270 = srub mmmm 366.22660
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