4 Flexural Design on Reinforced Concrete Beams

8/11/2019 4 Flexural Design on Reinforced Concrete Beams

1/20

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


2/20

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


3/20

T.Chhay NPIC


)'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


4/20



-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


5/20

T.Chhay NPIC


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.


6/20



* 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


7/20

T.Chhay NPIC


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


8/20



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


9/20

T.Chhay NPIC


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;.


10/20



- 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)(


11/20

T.Chhay NPIC


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) =


12/20



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=


13/20

T.Chhay NPIC


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


14/20


15/20

T.Chhay NPIC


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.


16/20



+ 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 = .


17/20

T.Chhay NPIC


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

]TahrN_8 RbBnkMralxNdUcbgajkgrUb EdlpMeLIgedaykMralxNEdlmankMras; cmt 8= EdlRTedayFwmRbEvg cmL 430= EdlmanKMlatBIKa cml 300= KitBIGkSmkGkS. FwmmanRTnug cmbw 35=


18/20



nigkMBs;RbsiTPaB cmd 47= . kMNt;muxkat;EdkcaM)ac;edIm,ITb;nwgm:Um:g;KNna mkNMu .575= .smtikm MPaf c 20' = nig MPafy 400= .

dMeNaHRsay

- kMNt;RbEvgsab

+

=

l

L

bt

bw

e4

16

min

=

=+

=

mm

mmmm

3000

10754

4300 16303508016min

dUcenH mmbe 1075= - RtYtBinitTItaMgGkSNWt edaysnt; ta=

)2

('85.0 t

dbtfM cn =

mkNmkNmmNMn

.575.794.565.794.565)2

80470(8010752085.09.0


19/20

T.Chhay NPIC


-

RtYtBinitt

/ cmbf

fAa

c

ys278.9

5.1072085.0

40039.42

'85.0=

==

cma

c 91.1085.0

278.9

1

===

cmdt

50656 ==

005.00107.0)

91.10

91.1050(003.0 >=

= t

]TahrN_9sMrab;RbBnkMralxNmYy EdlmanTTwgsabRbEvg cmbe 122= TTwgRTnug 40=wb ehIykMralxNmankMras; cmt 10= . KNnamuxkat;GkSr T edIm,IrgnUvm:Um:g;KNna mkNMu .1100= . smtikm

MPaf c 20' = nig MPafy 400= .dMeNaHRsay

-edaysarminsal;kMBs;RbsiTPaB eyIgeGay ta= kMNt;muxkat;Edk sftA sMrab;sabTaMgmUl

285.51400

101222085.0'85.0cmf

btfA

y

csft =

== eGay )

2(

tdfAM ysftu = KNna d

mmt

fA

Md

ysft

u 3.6392

100

40051859.0

101100

2

6

=+

=+=

eyIgeXIjfa RbsinebI cmd 93.63= enaH sfts AA = - RbsinebI cmd 93.63> / eyIgsnt;yk cmd 67= enaH ta< muxkat;manlkNCaragctuekaNEkg

PaKryEdk RtUv)anKNnatamrUbmnxageRkam)

'7.1

411(

'85.02

dbf

M

f

f

wc

u

y

c

=

006.06701220209.07.1

101100411(

400

2085.02

6

=

=

enaHmuxkat;Edk 204.4967122006.0 cmbdAs === - RbsinebI cmd 93.63< / eyIgsnt;yk cmd 60= enaH ta> muxkat;manlkNCaragGkSret T .

285.34400

)40122(102085.0)('85.0 cmf

bbtfAy

wcsf ===


20/20


w : ; 2

mmNt

dfAM ysfu .10690)2

100600(40034859.0)

2( 62 ===

mkNMu .41069011001 ==

sMrab;muxkat;EdkrgkMlaMgTajeKal cmbw 40= / cmd 60= nig mkNMu .4101=

MPadb

M

R mkN

w

u

u 85.22.284760.04.0

410222

1

====

0088.0)209.07.1

85.2411(

400

2085.0)

'7.1

411(

'85.01 =

==

c

u

y

c

f

R

f

f

2

11 12.2160400088.0 cmdbA ws === 2

1 97.5512.2185.34 cmAAA sfss =+=+=

eRbIEdk 227.56327 cmDB = -

RtYtBinitt

cmbf

fAa

wc

ys42.12

402085.0

40012.21

'85.0

1 =

==

cma

c 6.1485.0

42.12

85.0===

cmdt 63=

005.00099.0003.0 >=

=

c

cdtt muxkat;rgkarTaj

- KNnamuxkat;EdksrubGtibrma

)]60040085.0375.0100)4001220[(400

2085.0]375.0)[(

'85.0 1max +=+= dbtbb

f

fA wwe

y

cs

222

max 27.5636.676736 cmcmmmAs >== RtwmRtUv

4 Flexural Design on Reinforced Concrete Beams

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