of 20
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T.Chhay NPIC
Flexural Design on Reinforced Concrete Beams 53
IV. karKNnaFwmebtugGarem:rgkarkac;begag
1>kMBs;RbsiTiPaBsMrab;Fwm nigkMralxN
kMBs;rbs;Fwmxmuxkat;ctuekaNEkgCamYyEdkrgkarTaj
xageRkamCarUbmnsMrab;karKNnamuxkat;rgkarTaj)
600
600(
'85.0 1
yy
cb
ff
f
+=
)008.0
003.0
(maxs
y
b
E
f+
=
sMrab; MPafy 400=
b 625.0max = ehIy 85.01= sMrab;ebtugEdlmanersIusg; MPaf c 28' .
)7
28'(05.085.01
= c
f sMrab;ebtugEdlmanersIusg; MPafMPa c 56'28 < .
65.01= sMrab;ebtugEdlmanersIusg; MPaf c 56' > .tMlnsac;lUteFobrbs;Edkkan;EtFMbgajBIPaBsVitrbs;ebtugGarem:kan;EtFM)annyfaenAeBl
muxkat;ebtugkan;EtFMCamYyPaKryEdkticPaBsVitkan;EtFM pymkvijenAeBlmuxkat;ebtugkan;EttUcCamYy
PaKryEdkkan;EtFMenaHPaBsVitrbs;ebtugkan;EttUc. xageRkamCataragbgajBIPaKryEdksMNUmBrGaRsyersIusg;ebtug nigersIusg;Edk.
kMralxNmYyTis
L/24 L/28 L/1L/2
Fwm L/18 5
L/21
L/8
L/16
8/11/2019 4 Flexural Design on Reinforced Concrete Beams
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Department of Civil EngineeringviTasanCatiBhubeckeTskm Ca
karKNnaFwmebtugGarem:rgkarkac;begag 54
taragTI1 PaKryEdksMNUmBrs
)(' MPaf c )(MPafy s% 20 235 1.4
400 1.2
28 400 1.4500 1.2
35 400 1.6
500 1.4
sac;lUteFobEdksuT t edIm,IeGaymuxkat;rgkarTajRtUv)ankMNt;FMCag 005.0 enaH 9.0= .
)3
250)(002.0(65.0 += t sac;lUteFobEdksuT t enAcenaH 005.0004.0 .
smIkarKNnaersIusg;m:Um:g;kgmanTMrg;dUcxageRkam2
bdRMMuun
==
Edln
c
y
yu Rf
ffR
== )
'7.11(
Edl 9.0= sMrab;muxkat;rgkarTajnig 9.0
8/11/2019 4 Flexural Design on Reinforced Concrete Beams
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T.Chhay NPIC
Flexural Design on Reinforced Concrete Beams 55
)'7.1
411(
'85.02bdf
M
f
f
c
u
y
c
=
bdAs = - RbsinebI b RtUv)ansnt;bEnmBIelI enaHeKRtUv
KNna )'7.1
1(c
y
yuf
ffR
=
KNnabR
Md
u
u=
RbsinebI 2=b
d enaH 3 2bR
Md
u
u=
bdAs =
3>
KMlatEdk nigRsTab;karBarEdk
k> KMlatEdk
ssrEdkRtUv)antMerobedaymanKMlaty:agticbMputesInwgGgt;pitEdk b:uEnminRtUvtUcCag mm25 edIm,IeGayeKGacbgab;ebtug)any:aggayRsYlkgeBlcak;ebtug. KMlatEdksMrab;kartMerobEdkbBarEdlmaneRcInCagmYyRsTab; minRtUvmantMltUcCag mm25 Edr. RbsinebIKMlatEdkmanTMhMtUcenaHl,ayeb
tugminGacBTCMuvijEdk)anleT.
x> RsTab;karBarEdk
RsTab;karBarEdk Casac;ebtugEdlenAcenaHpxageRkA nigprbs;Edk. eKcaM)ac;RtUvkarRsTab;karBarEdkeRBaHvamanplRbeyaCn_bYny:ag
8/11/2019 4 Flexural Design on Reinforced Concrete Beams
4/20
Department of Civil EngineeringviTasanCatiBhubeckeTskm Ca
karKNnaFwmebtugGarem:rgkarkac;begag 56
-edIm,IetagsitssrEdkeTAnwgebtugEdleFVIeGaysMParTaMgBIreFVIkarCamYyKa. \TiBlrbs;PaBsitGaRsyeTAnwgkMras;RsTab;karBar.
-edIm,IkarBarssrEdkeTAnwgERcHsIuEdk.
-
edIm,IkarBarkar)at;bg;ersIusg;EdkEdlbNalmkBIkMedA. kMras;RsTab;karBar mm20 GacTb;Tl;nwgePIgeqH)an 1em:ag.
-
sMrab;yandan eragcRk cMNtrfyn RsTab;karBarbEnmRtUv)aneKdak;BIelIkMralxNEfmeTotedIm,IkarBarkarswkercrwlEdlbNalmkBIcracrN_.
kMras;RsTab;karBarEdkGaRsyeTAnwgmCdanEdleRKOgbgMenaHsitenA. xageRkamCataragbgajBIkMras;RsTab;karBarGb,brma
mCdan kMras;karBarEdk )(mm ebtugcak;pal;nwgdI 75 ebtugcak;pal;nwgdIbhalxl;
+ Ggt;pitEdkFMCag mm16 50 + Ggt;pitEdktUcCag mm16 35
ebtugmincak;pal;nwgdI bminhalxl;
- kMralxNCBaaMg+ Ggt;pitEdkFMCag mm36 35 + Ggt;pitEdktUcCag mm36 20
- Fwm ssr 35 - kMralekag
+ Ggt;pitEdkFMCag mm20 20 + Ggt;pitEdktUcCag mm20 15
K> TTwgGb brmarbs;muxkat;ebtug
smIkarTUeTAedIm,IkMNt;TTwgGb,brmarbs;muxkat;ebtugGacsresrdUcxageRkam
)(2)(2)1(min karBarEdkRsTab;Edkkg +++= snnDb Edl n - cMnYnEdkbeNay
D - Ggt;pitEdkEdlFMCageKs - KMlatEdk
8/11/2019 4 Flexural Design on Reinforced Concrete Beams
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T.Chhay NPIC
Flexural Design on Reinforced Concrete Beams 57
X> kMBs;Gb,brmarbs;muxkat;ebtugkMBs;rbs;muxkat;ebtugRtUv)ankMNt;edayGaRsynigRsTab;Edk.
- EdkmYyRsTab; mmDdh 502
11 ++=
-
EdkBIrRsTab; mmDdh 6022 ++= ]TahrN_1kMNt;muxkat;Edk nigmuxkat;ebtugedIm,ITb;Tl;nwgm:Um:g;KNna mkN.490 edayeRbIPaKryEdkGtibrma max sMrab;muxkat;rgkarTaj. smtikm MPaf c 20' = nig MPafy 400= .dMeNaHRsay
eday MPaf c 20' = / MPafy 400= / 85.01= nig 9.0= sMrab;muxkat;rgkarTaj
)600
600(
'85.0 1
yy
cb
ff
f
+=
021675.0)400600
600(
400
2085.0 2 =
+=b
01355.0625.0)008.0
003.0
(max ==
+
= bs
y
b
E
f
MPaf
ffR
c
y
yu 1.4)
207.1
40001355.01(40001355.09.0)
'7.11(
max
max(max) =
==
366
(max)
2 105.119
1.4
10490mm
R
Mbd
u
u =
==
dUcenHsMrab;karsnt; b / kMNt; d nig bdAs = mmb 200= / mmd 773= / 295.20 cmAs = mmb 250= / mmd 5.691= / 242.23 cmAs = mmb 300= / mmd 630= / 261.25 cmAs = 256DB mmb 400= / mmd 5.546= / 262.29 cmAs =
* kareRCIserIskMBs;RbsiTiPaBGaRsynwgktaxageRkam-kMBs;bnb; TTwgrbs;muxkat;tUcpl;nUvkMBs;FwmFM
Edlkat;bnylMhrkMBs;. elIsBIenH FwmeRCA cegtkat;bnyersIusg;m:Um:g;edaykarxUcRTg;RTayxaglateral deformation.
-brimaN nigkarBRgayssrEdk FwmcegtRtUvkarssrEdkeRcInCagmYyRsTab;dUcenHvabegItkMBs;Fwm.
-
kMras;CBaaMg RbsinebIbksIum:g;t_RtUv)aneRbITTwg b RtUv)aneRCIserIses
InwgkMras;CBaaMg. sMrab;GKarCBaaMgxagRkas;CagCBaaMgkg.
8/11/2019 4 Flexural Design on Reinforced Concrete Beams
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Department of Civil EngineeringviTasanCatiBhubeckeTskm Ca
karKNnaFwmebtugGarem:rgkarkac;begag 58
* kareRCIserIsmuxkat;EdkGaRsynwgktaxageRkam-kartMerobEdkRKb;RKan;enAkgmuxkat;CaTUeTA mYyRsTab;bBIrRsTab;nigbMeBjtamlkxN ACI
CodesMrab;KMlatEdkGb,brma.
-
pmuxkat;EdkeRCIserIsRtUvmantMlEk,rbMputpssrEdktMrUvkardUcenHeyIgeRCIserIsyk mmb 300= / mmd 630= / 261.25 cmAs = 25@6 DB RtUvtMerobBIrRsTab;kMNt;kMBs;Fwm mmmmDdh 715602563060 =++=++= dUcenHyk mmh 750= mmd 665= ]TahrN_2
edaHRsay]TahrN_1 edayeRbIRbEhl %1 nig cmb 35= dMeNaHRsay
eday MPaf c 20' = / MPafy 400= / 01355.0max= sMrab;muxkat;rgkarTaj)
'7.11(
c
y
yuf
ffR
= MPaRu 1765.3)
207.1
40001.01(40001.09.0 =
=
36
2 1542578301765.3
10490mm
R
Mbd
u
u =
==
sMrab; cmb 35= mmd 665= 2275.235.663501.0 cmA
s ==
edayeRCIserIs 284DB mYyRsTab;2
62.24 cmAs=
epgpat;TTwg mmsnnDb 95)1(min ++= edayyk Ds= cmmmmmDb 3529195287957min
8/11/2019 4 Flexural Design on Reinforced Concrete Beams
7/20
T.Chhay NPIC
Flexural Design on Reinforced Concrete Beams 59
003.0)005.0
( =b
t
021675.0)400600
600(
400
2085.0 2 =
+=b
452.0
021675.0
0098.0==
b
005.0008.0003.0
452.0
005.0>==t epgpat;
m:ageTot 47.1985.0
55.16
85.0===
ac
375.03.06.65
47.19
8/11/2019 4 Flexural Design on Reinforced Concrete Beams
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Department of Civil EngineeringviTasanCatiBhubeckeTskm Ca
karKNnaFwmebtugGarem:rgkarkac;begag 60
dMeNaHRsay
sMrab; MPaf c 28' = / MPafy 400= / 85.01= 030345.0=b / 019.0max=
sMrab;muxkat;rgkarTaj 9.0= edayeRbI 019.0max=
MPaf
ffR
c
y
yu 75.5)
287.1
400019.01(400019.09.0)
'7.11(
max
max(max) =
==
366
(max)
2 10913.7375.5
10425mm
R
Mbd
u
u =
==
sMrab; cmdcmb 4635 == 2
59.304635019.0 cmAs == edayeRbIEdk 32 4edIm 2154.32324 cmDB = EdkRtUv)antMerobmYyCYr mmsnnDb 95)1(min ++= edayyk sD= mmmmmmDb 35031995327957min =
=
sac;lUteFobEdksuT 004.00046.0003.0)005.0( >==
b
t
muxkat;sitkgtMbn;transition region
9.0867.0)3
250)(002.0(65.0
8/11/2019 4 Flexural Design on Reinforced Concrete Beams
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T.Chhay NPIC
Flexural Design on Reinforced Concrete Beams 61
4>muxkat;ctuekaNEkgCamYyEdkrgkarsgt;
RbsinebIm:Um:g;KNnamantMlFMCagersIusg;m:Um:g;kg enaHmuxkat;RtUv)armuxkat;EdkbEnmsMrab;tMbn;rgkarTaj nigrgkarsgt;. ssrEdkrgkarsgt;pl;nUvkMlaMgsgt;bEnmeTAelIkMlaMgsgt;rbs;ebtug.
k> edaysnt;EdkrgkarTajmanmYyRsTab;
viFIsaRsKNnasMrab;muxkat;ctuekaNEkgCamYyEdkrgkarsgt;enAeBleKsal; uM / cf' / b / d nig 'd mandUcxageRkam
- KNnaPaKryEdkbalanced b nigPaKryEdkGtibrma max edayeRbIsmIkarxageRkam
)600
600(
'85.0 1
yy
cb
ff
f
+= nig )
008.0
003.0
(maxs
y
b
E
f+
=
kMNt;muxkat;EdkGtibrmasMrab;rgkarTaj bdAs max1 = - KNna (max)uR edayeRbI max )9.0( =
)'7.1
1( max
max(max)
c
y
yuf
ffR
=
- KNnaersIusg;m:Um:g;kgEdlekItedaysarmuxkat;EdkrgkarTaj 1uM edayeRbI (max)uR 2
(max)1 bdRM uu = +
RbsinebIuu MM 1 enaHminRtUvkarEdkrgkarsgt;eT. KNnaPaKryEdk tamrUbmn
)'7.1
411(
'85.02bdf
M
f
f
c
u
y
c
= nigKNna bdAs = .
-
KNna 12 uuu MMM = CaersIusg;m:Um:g;EdlekItBIEdkrgkarsgt;- KNna 2sA BI )'(22 ddfAM ysu = nigbnab;mkKNna 21 sss AAA += - KNnakugRtaMgenAkgEdkrgkarsgt;dUcxageRkam
+ KNna ys fc
dcf = )'(600' + bKNna
s' BIdaRkambMErbMrYlrageFob nig
sss Ef '' = . RbsinebI ys =' enaHEdkrgkarsgt;yar ehIy
ys ff =' .+ KNna sA' BI )'('22 ddfAM ssu = .RbsinebI ys ff =' enaH 2' ss AA = . EtebI ys ff ehIy )'
(' 2s
y
ssf
fAA = .
-
eRCIserIsmuxkat;EdksMrab; sA nig sA' edIm,IeGaysml
mnwgTTwg b . CaTUeTA Edk sA eRcIntMerobCaBIrRsTab; sA' eRcIntMerobCamYyRsTab;.
8/11/2019 4 Flexural Design on Reinforced Concrete Beams
10/20
Department of Civil EngineeringviTasanCatiBhubeckeTskm Ca
karKNnaFwmebtugGarem:rgkarkac;begag 62
- KNna mmdh 65+= sMrab;EdkrgkarTajmYyRsTab; nig mmdh 90+= sMrab;Edkrgkar
TajBIrRsTab;. RtYtBinitfa max)]'('[ edaysn t;EdkrgkarTajmanBIrRsTab;
kgkrNIEdkrgkarTajmanBIrRsTab;eKGacsn
t;fa mmhd 90= nigmmdmmhdt 2565 +== . eKmanviFIBIry:agkgkarkMNt;muxkat;ssrEdk
- vIFITI1 edaysnt; sac;lUteFobEdksuTenAnIv:UTIRbCMuTMgn;EdkTajesI 005.0 b 005.0=s enAnIv:U d. kgkrNIenH sac;lUteFobEdksuTsMrab;ssrEdkRsTab;eRkambMputmantMlFMCag
005.0 .
005.0003.0)( >
=c
cdtt . dUcenHeyIgedaHRsaydUckrNIxagelI EdkrgkarTajmanmYyRs
Tab;.- vIFITI2 edaysnt; 005.0=t enAnIv:UEdkRsTab;eRkameK td . kgkrNIenH sac;lUtEdkeFob
enAnIv:UTIRbCMuTMgn;EdkTajmantMltUcCag 005.0 005.0003.0)(
8/11/2019 4 Flexural Design on Reinforced Concrete Beams
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T.Chhay NPIC
Flexural Design on Reinforced Concrete Beams 63
bKNnas' BIdaRkambMErbMrYlrageFob nig
sss Ef '' = . RbsinebI ys =' enaHEdkrgkarsgt;yar ehIy
ys ff =' . KNna
sA' BI )'('22 ddfAM ssu = . RbsinebI ys ff =' enaH 2' ss AA = . EtebI
ys ff ehIy )'(' 2 sy
ssf
f
AA = .]TahrN_5
eKmanFwmmYymanmuxkat; cmb 25= nigkMBs; cmh 55= EdlRtUvRTnUvm:Um:g;Bt;KNnamkNMu .300= . KNnassrEdktMrUvkar. smtikm MPaf c 20' = nig MPafy 345= .
dMeNaHRsay
-kMNt;ersIusg;m:Um:g;EdlekItBIEdkrgkarTajCaeKalsMrab;lkxNmuxkat;rgkarTajsMrab; MPaf c 20' = nig MPafy 345= / 85.01=
0266.0)345600
600(345
2085.0)600
600('85.0 21 =+
=+
=yy
cb
ff
f
0157.0)008.0
200000
345003.0
(0266.0)008.0
003.0
(max =+
=
+
= s
y
b
E
f
MPaf
ffR
c
y
yu 1.4)
207.1
3450157.01(3450157.09.0)
'7.11(
max
max(max) =
==
edaysnt;EdkrgkarTajmanBIrRsTab;
mmmmhd 4609055090 === MPaMmkNmmNbdRM uun 300.89.216.1089.2164602501.4
622
(max) =
8/11/2019 4 Flexural Design on Reinforced Concrete Beams
12/20
Department of Civil EngineeringviTasanCatiBhubeckeTskm Ca
karKNnaFwmebtugGarem:rgkarkac;begag 64
001725.0200000
345
200000=== yy
f
eday mmbf
fAa
c
ys6.146
2502085.0
3451806
'85.0
1=
==
mma
c 47.17285.0
6.146
1
===
ys >=
= 00196.0003.0)
47.172
6047.172(' eFVIkardl;yar
- RtYtBinit t edayeyIgeRbI max nig uR mkeRbIsMrab;edaHRsay edayeGaysac;lUteFobEdksuTenAnIv:UTIRbCMuTMgn;Edk
005.0=s . dUcenHeyIgRtUvkMNt; t sMrab;EdkenARsTab;eRkameKbMput.
mmdt 49060550 == 005.00055.0003.0)
47.17247.172490(003.0)( >===
ccdt
t RtwmRtUv
dUcenH EdktMrUvkarsMrab;karTaj 275.24 cmAs = eRbI 255DB sMrab;karsgt; 269.6' cmA s= eRbI 222DB
]TahrN_6
eKmanFwmmYymanmuxkat;cmb 30=
nigkMBs;cmh 50=
EdlRtUvRTnUvm:Um:g;Bt;KNnamkNMu .400= . KNnassrEdktMrUvkar. smtikm MPaf c 28' = nig MPafy 400= .dMeNaHRsay manBIrviFIsaRsvIFITI1
- kMNt;ersIusg;m:Um:g;Gtibrmanmuxkat;EdlmanEtEdkrgkarTajCaeKalsMrab; MPaf c 28' = / MPafy 400= / 85.01=
030345.0=b
/019.0max=
sMrab;muxkat;rgkarTaj 9.0=
8/11/2019 4 Flexural Design on Reinforced Concrete Beams
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T.Chhay NPIC
Flexural Design on Reinforced Concrete Beams 65
MPaf
ffR
c
y
yu 75.5)
287.1
400019.01(400019.09.0)
'7.11(
max
max(max) =
==
edaysnt; mmhd 4109050090 === EdkmanBIrRsTab;
MPammNbdRM uu 290.1029041030075.5 622
1
8/11/2019 4 Flexural Design on Reinforced Concrete Beams
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8/11/2019 4 Flexural Design on Reinforced Concrete Beams
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T.Chhay NPIC
Flexural Design on Reinforced Concrete Beams 67
mkNMu .75.9325.3064002 == 22
6
22 44.7744
)60410(4009.0
1075.93
)'(9.0cmmm
ddf
MA
y
us ==
=
=
muxkat;EdkrgkarTajsrub 221 47.3244.703.25 cmAAA sss =+=+= eRbIEdk 305DB -
RtYtBinit Edkrgkarsgt;eFVIkardl;yarbGt;00444.0)
400600
600)(
410
60(
400
2885.0 2 =
+=K
K enaH ta> KNnaCaragGkSret T. RbsinebI nfu MM < enaH ta< KNna
CaragctuekaNEkg.
8/11/2019 4 Flexural Design on Reinforced Concrete Beams
16/20
Department of Civil EngineeringviTasanCatiBhubeckeTskm Ca
karKNnaFwmebtugGarem:rgkarkac;begag 68
+ RbsinebI ta< enaHKNna )'7.1
411(
'85.02
bdf
M
f
f
c
u
y
c
= / KNna bdAs = .
epgpat; min w .+ RbsinebI ta> enaHKNna sfA sMrab;Epksabsgxag >>>
ywcsf ftbbfA /)('85.0 = )
2(2
tdfAM ysfu =
m:Um:g;EdlTb;edayRTnugKW
21 uuu MMM = KNna 1 edayeRbI 1uM / wb nig d
)'7.1
4
11(
'85.02
1
1 dbf
M
f
f
wc
u
y
c
= nigKNna dbA ws 11 = muxkat;Edksrub sfss AAA += 1
bnab;mkRtYtBinit maxss AA dUcKa RtUvRtYtBinit min =db
A
w
w
+ RbsinebI ta= enaHy
cs
f
btfA
'85.0=
-
enAeBleKminsal; dnig sA karKNnaRtUveFVItamviFIsaRsxageRkam+ snt; ta= nigKNnabrimaNEdksrub sftA EdlRtUvkarsMrab;Tb;nwgkMlaMgsgt;kgsab
TaMgmUl bt
y
csft
f
btfA
'85.0=
+ kMNt; dBIsftA nig ta= tamrUbmnxageRkam
)
2
( t
dfAM ysftu =
RbsinebIeKyktam d KNnarkeXIjenaHsfts AA = nig mmdh 65+= sMrab;
EdkmanmYyRsTab;b mmdh 90+= sMrab;EdkmanBIrRsTab;. RbsinebIeKyk 1d fIFMCag d KNnaenaHmuxkat;eFVIkarCaragctuekaNEkg.
ehIy )'7.1
411(
'85.02
bdf
M
f
f
c
u
y
c
= / KNna bdAs = .
8/11/2019 4 Flexural Design on Reinforced Concrete Beams
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T.Chhay NPIC
Flexural Design on Reinforced Concrete Beams 69
RbsinebIeKyk 21d fItUcCag d KNnaenaHmuxkat;eFVIkarCaragGkSr T. ehIymuxkat;EdkcugeRkay
sA FMCag sftA . kgkrNIenH eKRtUveFVIdUckrNIxagelI>>> edIm,IkMNt;muxkat;
sA .
]TahrN_7 eKmanFwmmYymanGkSr T EdlmanRTnug cmbw 25= RbEvgsab cmb 100= kMras;sabcmt 10= nigkMBs;RbsiTiPaB cmd 37= . kMNt;muxkat;EdkcaM)ac;edIm,ITb;nwgm:Um:g; mkNMu .375= .
smtikm MPaf c 20' = nig MPafy 400= .dMeNaHRsay
- RtYtBinitGkSNWt edaysnt; cmta 10==
mmNt
dbtfM cn .106.489)2
100370(10010002085.09.0)
2('85.0 6===
eday un MM > muxkat;manlkNCactuekaNEkg- kMNt;muxkat;EdkrgkarTaj
00845.0)3701000209.07.1
10375411(
400
2085.0)
'7.1
411(
'85.02
6
2 =
==
bdf
M
f
f
c
u
y
c
2265.313710000845.0 cmbdAs === edayeRbI 2325.35305 cmDB =
- RtYtBinit 0035.04004.1
0382.03725
325.35min
==>=
== db
A
w
s
w swwe
y
cs
Acmdbtbbf
fA >=+= 21max 41.44]375.0)[(
'85.0
dUcKa cmbf
fAa
c
ys31.8
1002085.0
400325.35
'85.0=
==
cma
c 78.985.0
31.8
1
===
nig 005.000835.0)78.9
78.937(003.0 >=
=s
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8/11/2019 4 Flexural Design on Reinforced Concrete Beams
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Department of Civil EngineeringviTasanCatiBhubeckeTskm Ca
karKNnaFwmebtugGarem:rgkarkac;begag 70
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8/11/2019 4 Flexural Design on Reinforced Concrete Beams
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Flexural Design on Reinforced Concrete Beams 71
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8/11/2019 4 Flexural Design on Reinforced Concrete Beams
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Department of Civil EngineeringviTasanCatiBhubeckeTskm Ca
w : ; 2
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