បេតុងពង្រឹងដោយដែក 15 xv-design-for-torsion

8/11/2019 15 xv-design-for-torsion

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Department of Civil Engineering viTasanCatiBh ubeckeTskm esckIepIm Introduction

kugRtaMgrmYlekItmanenAkgmuxkat;FwmenAeBlEdlm:Um:g;manGMeBIRsbeTAnwgmuxkat;enaH.m:Um:g;rmYleFVIeGayGgt;vil nigmansameRbHenAelIprbs;va CaTUeTAEtgekItmanenAelImuxkat;mUl.edIm,IbgajkugRtaMgrmYl eKGnuvtkMlaMgrmYl T Fwm cantilever muxkat;mUlEdleFVIBIelastichomogenous materialdUcbgajkgrUbTI15>1. kMlaMgrmYlnwgeFVIeGayFwmvil. cMnuc B clteTA

cMnuc 'B enAxagcugrbs;Fwm b:uEncugmageTotrbs;FwmRtUv)anbgb;. mMuRtUv)aneKehAfa mMurmYl(angle of twist). bg; OBAO' nwgdUrrageTACarag ''OBAO . edaysnt;fa Ggt;enArkSaRbEvgrbs;vadEdl enaH shear strainKW

L

r

L

BB ==

'

Edl L CaRbEvgrbs;Fwm nig rCakaMrbs;muxkat;rgVg;.

enAkgeRKOgbgMebtugGarem:Ggt;nwgrgm:Um:g;rmYlenAeBlGgt;enaHekagenAkgbg;/ RTcantilever slab/ mannaTICa spandrel beam (end beam)/ bCaEpkrbs;CeNIrvil.


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T.Chhay NPIC

karKNnasMrab;kMlaMgrmYl 347

Ggt;eRKOgbgMGacrgnUvEtkMlaMgrmYlsuTbenAkgkrNICaeRcIn vargCamYyKakgeBlEtmYynUvkMlaMgkat;TTwg nigm:Um:g;Bt;. ]TahrN_TI15>1 bgajBIkMlaMgepSgEdlGacGnuvtmkelImuxkat;

epSgKanFwm cantilever.]TahrN_TI 5>

KNnakMlaMgEdlmanGMeBIenAmuxkat;!/ @ nig # nFwm cantileverEdlbgajenAkgrUbTI 15>2. FwmrgnUvkMlaMgbBar kNP 671= / kMlaMgedk kNP 5.532 = EdleFVIGMeBIenAcMnuc Cnigbnkedk

kNP 893= EdlGnuvtenAcMnuc B nigEkgeTAnwgTisedArbs;kMlaMg 2P .

dMeNaHRsay

yk =N kMlaMgEkg (normal force)/ =V kMlaMgkat;(shear force)/ =M m:Um:g;Bt;(bendingmoment)/ T=m:Um:g;rmYl (torsional moment). kMlaMgTaMgGs;RtUv)anbgajenAkgtaragxageRkammuxkat; )(kNN ).( mkNMx ).( mkNMy )(kNVx )(kNVy ).( mkNT

! 0 9.180 45.144 5.53 67 0 @ 5.53 sgt; 0 45.144 89 67 9.180 # 5.53 sgt; 2.241 85.464 89 67 9.180


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Department of Civil Engineering viTasanCatiBh ubeckeTskm m:Um:g;rmYlenAkgFwm Torsional Moments in Beams

dUcbgajenAkgrUbTI15>1 kMlaMgGacGnuvtenAelIeRKagsMNg;GKar edayeFVIeGaymanm:Um:g;rmYl. RbsinebIkMlaMgcMcMnuc P GnuvtenARtg;cMnuc CenAelIeRKag ABCdUcbgajenAkgrUb 15>3 avabegItm:Um:g;rmYl PZT= enAkgFwm AB Rtg;cMnuc D. enAeBl D sitenAkNalElVgnFwm AB

enaHm:Um:g;rmYlKNnaenAkgkMNat;AD esInwgm:Um:g;rmYlKNnaenAkgkMNat; DB besInwg T2

1 . Rb

sinebIkMral cantilever slabRtUv)anRTedayFwm AB rUbTI 15>3b enaHkMralxNbegItm:Um:g;rmYlBRgayesI tm tambeNayFwm AB . m:Um:g;rmYlBRgayesIenH KWekItBIbnkenAelIcMerokTTwkmYyktarbs;kMralxN. RbsinebI SCaTTwgn cantilever slabnig w CabnkenAelIkMralxN 2/mkN enaH 2/2wSmt= mmkN /. nFwm AB . m:Um:g;rmYlKNnaGtibrmaenAkgFwm AB KW

2/LmT t= EdlGnuvtenARtg;cMnuc A nig B . krNIbnkepSgeTotRtUv)anbgajenAkgtarag15>1. CaTUeTA daRkamm:Um:g;rmYlenAkgFwmmanrag nigmantMldUcKanwgdaRkamkMlaMgkat;TTWgsM

rab;FwmEdlrgnUvkMlaMg tm nig T.


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T.Chhay NPIC



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Department of Civil Engineering viTasanCatiBh ubeckeTskm kugRtaMgrmYl Torsional Moments in Beams

edayBicarNaelIFwm cantileverEdlmanmuxkat;mUl rUbTI15>1 enAeBlEdlm:Um:g;rmYl T manGMeBIelIFwm vanwgbegIteGaymankMlaMgkat;TTwg dV EkgeTAnwgkaMrbs;muxkat;. BIlkxNl4 enaHGaMgtg;sIuetnkMlaMgrmYlKW

= rdVT

edayykv

CakugRtaMgkMlaMgkat;TTWgenaHvdAdV= nig = rvdAT kMlaMgkat;TTwgeGLasicGtibrmaekItmanenApxageRkArbs;muxkat;rgVg;Rtg;kaM rCamYynwgkM

ras;drenaHkMlaMgrmYlGacRtUv)ankMNt;edayKitm:Um:g;eFobnwgcMnuc 0 sMrab;RkLapkg

( )vrrdrdT 2= Edl rdr2 CaRkLapkg nigv CakugRtaMgkMlaMgkat;TTwgenAkgkg. dUcenH

( ) drrvrrdrTRR

==

0

2

0

22

!%>!sMrab;muxkat;RbehagEdlmankaMxagkg 1R /drrT

R

R= 122 !%>@

sMrab;muxkat;tan;edayeRbIsmIkar !%>! nig Rrvv /max=

=

=

RRdrrv

Rdr

R

rvrT

0

3max

max

0

2 22

3max

4

max

24

2Rv

Rv

R

=

=


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T.Chhay NPIC


3max

2

R

Tv

= !%>#

m:Um:g;niclPaBb:UElrnmuxkat;rgVg;KW 2/4RJ = . dUcenH kugRtaMgkMlaMgkat;GacRtUv)an

sresrCaGnuKmn_nm:Um:g;niclPaBb:UElrdUcxageRkam

J

TRv =max !%>$

4> m:Um:g;rmYlenAkgmuxkat;ctuekaN Torsional Moments in Rectangular Sections

karKNnakugRtaMgenAkgGgt;manmuxkat;minmUlEdlrgbnkrmYlminsamBadUckarKNnasMrab;muxkat;mUleT. b:uEnlTplEdlTTYlBIRTwsIeGLasic (theory of elasticity)bgajfakugRtaMg

kMlaMgkat;TTwgGtibrmasMrab;muxkat;ctuekaNEkgGacRtUv)ankMNt;dUcxageRkam

yx

Tv

2max = !%>%

Edl =T kMlaMgrmYlEdlGnuvt=x RCugxIrbs;muxkat;ctuekaN=y RCugEvgrbs;muxkat;ctuekaN=

emKuNEdlGaRsynwgpleFobnxy /

tMlrbs;vaRtUv)aneGayenAkgtaragxageRkam.

xy / 0.1 2.1 5.1 0.2 0.4 10

208.0 219.0 231.0 246.0 282.0 312.0 kugRtaMgkMlaMgkat;TTwgGtibrmaekItmanenAtamGkSnRCugEvg y rUbTI 15>5.sMrab;Ggt;EdlekItBIkarpMnmuxkat;ctuekaNEkg dUcCamuxkat;GkSr L / T nig I tMl

GacRtUv)ansn

t;faes

Inwg 3/1 ehIymuxkat;GacRtUv)anEckecjCamuxkat;ctuekaNCaeRcInEdlmanRCugEvg iy nigRCugxI ix . kugRtaMgkMlaMgkat;TTwgGacRtUv)anKNnaBI

=

ii yx

Tv

2max

3 !%>^

Edlii

yx 2 CatMlEdl)anBIplbUkmuxkat;ctuekaNEkgtUc. enAeBlEdl 10/ xy eKGaceRbIsmIkarsMrYlxageRkam


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Department of Civil Engineering viTasanCatiBh ubeckeTskm&

5> kMlaMgpbrvagkMlaMgkat; nigkMlaMgrmYl Combined Shear and Torsion

enAkgkrNIGnuvtn_CaeRcIn Ggt;eRKOgbgMGacrgnUvTaMgkMlaMgkat;nigkMlaMgrmYlCamYyKa.kugRtaMgkMlaMgkat;GacnwgekItmanenAkgmuxkat;CamYynwgkugRtaMgkMlaMgkat;mFm 1v= enAkgTis


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T.Chhay NPIC


edAnkMlaMgkat;V rUbTI 15>6 a. kMlaMgrmYl TbegItkugRtaMgrmYlenAelIRKb;RCugrbs;muxkat;ctuekaN ABCD rUbTI15>6 a CamYynig 23 vv > . karBRgaykugRtaMgcugeRkayRtUv)anTTYlBI

karbUkbBalnUv\TiBlnkugRtaMgkMlaMgkat;nigkugRtaMgrmYl edIm,IbegIttMlGtibrmaes

I 31 vv + enAelIRCug CD b:uEnRCug AB nwgmankugRtaMgcugeRkayesI 31 vv . RCug AD nig BCnwgrgEtkugRtaMgrmYl 2v . muxkat;RtUvd)anKNnasMrab;kugRtaMgGtibrma ( )31 vvv += .

6> RTwsIkarrmYlsMrab;Ggt;ebtug Torsion Theories for Concrete Members

eKmanviFICaeRcInsMrab;viPaKGgt;ebtugBRgwgedayEdkEdlrgkarrmYl brgkarrmYl karBt;

nigkarkat;kgeBlEtmYy. CaTUeTAviFIKNnasMGageTAelIRTwsIeKalBIrKWthe skew bending theory

nig space truss analogy.6>1> Skew Bending Theory

viFIeKalrbs;skew bending theoryEdlENnaMeday HsuCaviFIEdlsikSakar)ak;nmuxkat;ctuekaNedaykarrmYlEdlekItedaykarBt;eFobGkSRsbeTAnwgpnmuxkat; y FMCag nigeRTtedaymMu o45 eTAnwgGkSEvgnFwm rUbTI 15>7. QrelIviFIsaRsenH m:Um:g;rmYlGb,brma nT GacRtUv)an

KNnadUcxageRkam

rn fyx

T

=

3

2

!%>*

Edl rf KWm:UDuldac;rbs;ebtug. rf RtUv)ansnt;esInwg 12/'5 cf enAkgkrNIenH Edl

RtUv)aneRbobeFobCamYy 12/'5.7 cf EdlTTYleday ACI CodesMrab;KNnaPaBdabenAkgFwm.


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Department of Civil Engineering viTasanCatiBh ubeckeTskm


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T.Chhay NPIC


=s KMlatEdkkg

1x nig =1y RbEvgxInigRbEvgEvg KitBIGkSeTAGkSnEdkkgbiTCit bBIEdkenARCug.

smIkarmunecalnUvlTPaBTb;karrmYlrbs;ebtug. Mitchellnig CollinsENnaMnUvsmIkarxageRkamedIm,IKNnamMurmYlkgmYyktaRbEvg

( )

+

+

=

sin

2tan

tan2

d

o

hhl

o

o

P

P

A

P

!%>!@Edl =l bMErbMrYlrageFob (strain)enAkgEdkbeNay (longitudinal reinforcing steel)

=h bMErbMrYlrageFobenAkgEdkkg (hoop steel)=d bMErbMrYlrageFobebtugGgt;RTUgenARtg;TItaMgnkMlaMgpbnFarkMlaMgkat;

(shear flow)=hP brimaRtrbs;EdkkgKitRtwmGkSEdk

= mMunkMlaMgsgt;Ggt;RTUg ( )

++=

o

h

hdld P

P

/ =oA RkLapEdlBTCMuvijedaykMlaMgkat;b

q2/torque= Edl =q FarkMlaMgkat;=oP brimaRtnKngFarkMlaMgkat; brimaRtrbs; oA

smIkarmMurmYlxagelImanlkNRsedogKanwgsmIkarmMukMeNagkgkarBt;rUbTI 15>10

d

sc +

== curvature !%>!#


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Department of Civil Engineering viTasanCatiBh ubeckeTskm!$

Edl oA / oP nig s RtUv)anBnl;BIxagelI= sysfA kMlaMg yield nEdkbeNayTaMgGs;

=hyhfA kMlaMg yield nEdkkg

ACI Code )anTTYlykRTwsIenHedIm,IKNnaGgt;eRKOgbgMebtugEdlrgkarrmYl bkarrmYlnigkarkat;enAkgviFIsaRsdsMrYl.

7> ersIusg;rmYlnGgt;ebtugsuT Torsional Strength of Plain Concrete Memgers

Ggt;ebtugrgkarrmYlCaTUeTARtUv)anBRgwgedayEdkTb;nwgkarrmYlBiess. kgkrNIEdlkugRtaMgrmYlmantMltUc nigRtUvkarKNnasMrab;Ggt;ebtugsuT kugRtaMgkMlaMgkat; tcv GacRtUv)ankMNt;edayeRbIsmIkar !%>^

2

'32

ctc

f

yx

Tv =


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T.Chhay NPIC


nigmMurmYlKW yGxTL 3/3= / Edl TCam:Um:g;rmYlEdlGnuvtmkelImuxkat;tUcCagm:Um:g;rmYlEdleFVIeGayeRbH nig G KWCam:UDulkMlaMgkat;nigGacRtUv)ansnt;esInwg 45.0 dgnm:UDuleG-

Lasicrbs;ebtug cE Edl cfG '2135= . kMlaMgkat;TTwgeFVIeGayeRbHedaysarkarrmYl(torsional cracking shear) cv enAkgebtugsuTGacRtUv)ansnt;esI cf'5.0 . dUcenH sMrab;muxkat;ctuekaNebtugsuT

cc fyxT '12

2= !%>!%

nigsMrab;muxkat;EdlpSMeLIgedayctuekaNEkgeRcIn

= yxfT cc2'

12

!%>!^

8> karrmYlenAkgGgt;ebtugBRgwgedayEdk Torsion in Reinforced ConcreteMemebers (ACI Code Procedure)

8>1> sBaaNTUeTA GeneraldMeNIrkarKNnasMrab;karrmYlmanlkNRsedogKaeTAnwgkMlaMgkat;TTwgedaykarBt;. enA

eBlEdlm:Um:g;rmYlemKuNGnuvtenAelImuxkat;FMCaglTPaBTb;m:Um:g;rmYlkgrbs;ebtugGacTb;)an

enaHsameRbHEdlekItedaykarrmYl(torsional crack) ekIteLIg dUcenHEdkTb;karrmYl (torsionalreinforcement) kgTMrg;CaEdkkgbiTCit (closed stirrup or hoop reinforcement) RtUv)andak;.bEnmBIelIEdkkgbiTCit EdkbeNaykRtUv)andak;enAtamRCugrbs;Edkkg nigRtUv)anBRgayy:aglenACMuvijmuxkat;. TaMgEdkkgbiTCit nigEdkbeNaymansarsMxan;Nas;kgkarTb;nwgkMlaMgTajGgt;RTUgEdlbNaymkBIkMlaMgrmYl EdkEtmYyRbePTnwgKanRbsiTPaBeTebIKanEdkmYyRbePTeTot. EdkkgRtUvEtbiTCit edaysarkugRtaMgrmYlekItmanenARKb;RCugrbs;muxkat;.

EdkcaM)ac;sMrab;karrmYlRtUv)anbEnmelIEdkcaM)ac;sMrab;kMlaMgkat;/ sMrab;karBt;nigkMlaMgtamGkS. EdkEdkcaM)ac;sMrab;karrmYlRtUv)andak;edIm,IeFVIeGayersIusg;m:Um:g;rmYlrbs;muxkat; nT FMCagbesInwgm:Um:g;rmYlemKuN uT EdlRtUv)anKNnaBIbnkemKuN.

un TT !%>!&enAeBleKRtUvkarEdkTb;karrmYl ersIusg;m:Um:g;rmYl nT RtUv)anKNnaedaysnt;kMlaMg

rmYl uT TaMgGs; RtUv)anTb;edayEdkkg nigEdkbeNayCamYynwgersIusg;Tb;karrmYlrbs;ebtug


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T.Chhay NPIC


kgbiTCitxageRkAbMput RtUv)ankMNt;eday ohA pqUtenAkgrUbTI15>11. edaysarGgdTeTotRtUv)aneRbIenAkgsmIkarKNna vakRtUv)anENnaMCadMbUgenATIenHedIm,ICYyeGaykaryl;nUvsmIkarman

lkNgayRsYl. BIrUbTI 15>11 GgEdleGayRtUv)ankMNt;dUcxageRkam=cpA RkLapmuxkat;ebtugEdlBTCMuvijedaybrimaRtxageRkAnmuxkat;ebtug=cpP brimaRtnmuxkat;ebtugTaMgmUl cpA =ohA RkLapEdlBTCMuvijedayGkSnEdkrgkarrmYlTTwgbiTCitxageRkAbMput pqUtkgrUbTI

15>11=oA RkLapEdlBTCMuvijedayKngFarkMlaMgkat;TTwg nigGacykesInwg ohA85.0

=hP brimaRtebtugrbs;EdkrgkarrmYlTTwgbiTCitxageRkAbMput= mMunkMlaMgsgt;Ggt;RTUgcenaH o30 eTA o60 bGacykesInwg o45 sMrab;Ggt;ebtugGarem:

sMrab;muxkat;GkSr T nig L TTwgRbsiTPaBnsabmagRtUv)ankMNt;esInwgkMBs;FwmEdlsitenABIelIbBIeRkamkMralxNedayykmYyNaEdlFMCag b:uEnminRtUvFMCag 4 dgkMras;kMralxNeTACI Code, Sections 11.6.1 and 13.2.4.

8>3> m:m:g;rmYleFVeGayeRbH crT Cracking Torsional Moment crT

m:Um:g;eFVIeGayeRbHeRkamm:Um:g;rmYlsuT crT GacRtUv)anTajecjedayCMnYsmuxkat;BitR)akdmunnwgeRbH CamYynwg thin-walled tubesmmUl cpcp PAt /75.0= / CamYynwgRkLapEdlBTCMuvijedayGkSCBaaMg 3/20 cpAA = . enAeBlEdl kugRtaMgTajGtibrma kugRtaMgem mantMlesI

3/'cf sameRbHnwgekItman ehIyCaTUeTAm:Um:g;rmYl TesInwgtAT o2= !%>!*

Edl = kugRtaMgkMlaMgkat;edaykarrmYl 3/'cf= sMrab;sameRbHedaykarrmYl.

CMnYs eday 3/'cf

ncp

cpccr T

P

AfT =

=

2

3

' nig cru TT = !%>!(

edaysnt;fam:Um:g;rmYltUcCagbesInwg 4/crT nwgmineFVIeGaymankarkat;bnyersIusg;Tb;karBt; bTb;kMlaMgkat;enAkgGgt;nrcnasm


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Department of Civil Engineering viTasanCatiBh ubeckeTskm muxkat;!a. mU:m:g;eFVIeGayeRbH crT GacRtUv)anKNnaBIsmIkar !%>!(

=

cp

cpccr

P

AfT

2

3

'


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T.Chhay NPIC


sMrab;muxkat;enH oocp yxA = RkLapmuxkat;TaMgmUl Edl mmxo 400= nigmmyo 610=

2244000610400 mmAcp == =cpP brimaRtnmuxkat;ebtugTaMgmUl

( ) ( ) mmyx oo 202061040022 =+=+=

mkNTcr .392020

244000

3

2875.0

2

=

=

b. nT GnuBaatEdlGacGnuvtedaymineRbI EdkTb;karrmYlRtUv)anKNnaBIsmIkar !%>@0

mkN

T

T

cr

a .75.94

39

4===

2> muxkat;@

a. dMbUgKNna cpA nig cpP sMrab;muxkat;enH nigGnuvtsmIkarTI !%>!( edIm,IKNna crT .edaysnt;sabRtUv)andak;CamYyEdkkgbiTCit enaHsabRbsiTPaBEdlRtUveRbIenARCugmagnRTnugesInwg $dgkMras;sab b ( ) mmhmm w 4004001004 ===

flangeseffectiveofareaareaweb +=cpA

22550004001002350500 mmAcp =+= ( ) ( ) mmhbPcp 3300500400235022 =++=+=

mkNTcr .263300

255000

3

2875.0

2

=

=

cMNaM RbsinebIsabRtUv)anecal ehIyEdkTb;karrmYlRtUv)andak;EtenAkgRTnugenaH

2175000500350 mmAcp ==

( ) mmPcp 17005003502 =+= mkNTcr .8.23=

b. nT GnuBaatEdlGacGnuvtedaymineRbIEdkTb;karrmYl

mkNT

T cra .5.64

26

4===

3> muxkat;3


17/32


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T.Chhay NPIC


nkMhUcRTg;RTay (compatibility of deformation) RtUv)anrkSa enAkgGgt;eRKOgbgM.rUbTI15>14 bgajBI]TahrN_sMrab;krNIenH EdlFwmTTwgBIrmanGMeBIelIFwmEKmbegIt

m:Um:g;rmYl. mMurmYlFMekItman enAeBlsameRbHedaykarrmYlelcecj Edlpl;nUvkarbgEckbnkdFMenAkgeRKOgbgM. vanwgeTAdl;m:Um:g;rmYlEdleFVIeGayeRbH crT eRkamGMeBInbnSMkarBt;karkat;nigkarrmYl enAeBlEdlkugRtaMgem (principle stress) mantMlRbEhl 3/'cf . enAeBlEdl cru TT > m:Um:g;rmYlesInwg crT smIkar !%>!(EdlGacsnt;ekItmanenARtg;muxkat;eRKaHfak;enACitpnTMr.

ACI CodekMNt;m:Um:g;rmYlKNnaesInwgtMltUcCageKn uT Edl)anBIbnkemKuN b crT

BIsmIkar !%>!(.

8>5> karkMNt;nersIsg;m:m:g;rmYl Limitation of Tortional Moment StrengthACI Code,Section 11.6.3kMNt;TMhMmuxkat;edaysmIkarxageRkamBIr!> sMrab;muxkat;tan;


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Department of Civil Engineering viTasanCatiBh ubeckeTskm@@

Edl == 6/' dbfV wcc ersIusg;kMlaMgkat;sMrab;ebtugTMgn;Fmta. GgdTeTotRtUv)ankMNt;enAkgEpk 8>2.

karkMNt;enHKWQrelIPaBCak;EsgEdlfaplbUknkugRtaMgEdlbNalBIkMlaMgkat;nigm:Um:g;

rmYl GgxageqVg minRtUvFMCagkugRtaMgEdleFVIeGayeRbHbUknwg3/'2 cf

. krNIdUcKaRtUv)anGnuvtedIm,IKNnakMlaMgkat;edayK

anm:Um:g;rmYlenAkgemeronTI8. eKRtUvkarkarkMNt; (limitation)edIm,Ikat;bnysameRbH nigedIm,IkarBarEbkpebtugEdlbNalmkBIkugRtaMgkMlaMgkat;TTwgeRTtnigm:Um:g;rmYleRTt.

8>6> muxkat;Rbehag Hollow SectionbnSMnkugRtaMgkMlaMgkat;nigkugRtaMgm:Um:g;rmYlenAkgmuxkat;RbehagRtUv)anbgajenAkgrUb

15>6 EdlkMras;CBaaMgRtUvOansn

t;faefr. enAkgmuxkat;RbehagxH kMras;CBaaMgGacERbRbYlCMuvijbrimaRt. sMrab;krNIenH smIkar !%>@@ RtUv)ankMNt;enATItaMgEdlGgxageqVgmantMlGtibrma. cMNaMfa enAnwgsabxagelI nigsabxageRkam CaTUeTAkugRtaMgkMlaMgkat;RtUv)anecal. CaTUeTA RbsinebIkMras;CBaaMgnmuxkat;Rbehag ttUcCag hoh PA / enaHsmIkar !%>@@ kayCa

+

+

c

w

c

oh

hu

w

u fdb

V

tA

PT

db

V'

3

2

7.1 !%>@#

(ACI Code, Section 11.6.3).

8>7> EdkRTnug Web ReinforcementdUcEdl)anBnl;rYcehIy viFIACI CodesMrab;KNnaGgt;Edlrgm:Um:g;rmYlKWQrelIspace

truss analogyenAkgrUbTI15>8. bnab;BIkareRbHedaykarrmYl eKRtUvkarEdkBIrRbePTedIm,ITb;nwgm:Um:g;rmYlEdlGnuvt uT KWEdkTTwg (transverse reinforcement) tA enAkgTMrg;CaEdkkgbiTCit nigEdkbeNay (longitudinal reinforcement) lA . ACI Code)anbgajnUvsmIkarxageRkamedIm,IKNna tA nig lA

!> EdkkgbiTCit tA EdlGacKNnadUcxageRkam


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T.Chhay NPIC


s

fAAT

ytton

cot2= !%>@$

Edl

un

TT = nig 75.0=

=tA RkLapneCIgmYyrbs;EdkkgbiTCit=ytf ersIusg;yal (yield strength)rbs; tA MPaAt 400

=s KMlatEdkkg

oA nig RtUv)ankMNt;enAkgEpk 8>2. smIkar !%>@$ GacRtUv)ansresrdUcxageRkam

cot2 yto

nt

fA

T

s

A= !%>@%

RbsinebI o45= enaH 0.1cot = nigRbsinebI MPafyt 400= enaHsmIkar !%>@% kayCa

o

nt

A

T

s

A

800= !%>@^

Edl nT KitCa mmN. . KMlatEdkkg sminRtUvFMCagntMltUcCageKkgcMeNam 8/hP nigmm300 . sMrab;muxkat; RbehagrgkarrmYl

cMgayEdlvas;BIGkSnEdkkgeTApxagkgrbs;CBaaMgminRtUvtUcCag hoh PA /5.0 .

@> EdkbeNaybEnm lA

EdlcaM)ac;sMrab;karrmYlminKYrtUcCagtMlxageRkam2cot

=

y

yth

tl

f

fP

s

AA !%>@&

Rbsin o45= nig MPaff yyt 400== sMrab;TaMgEdkkg nigEdkbeNayenaHsmIkar !%>@& kayCa

( )112 yxs

AP

s

AA th

tl +

=

= !%>@*

hP RtUv)ankMNt;enAkgEpk 8>2. cMNaMfa EdkEdlcaM)ac;sMrab;karrmYlKYrRtUv)anbEnmBIelIEdlEdlcaM)ac;sMrab;kMlaMgkat; m:Um:g;Bt;nigkMlaMgtamGkSEdleFVIGMeBIrYmKaCamYykMlaMgrmYl. karkMNt;epSgeTotsMrab;EdkbeNay lA mandUcxageRkam

a. Ggt;pitEdktUcbMputsMrab;EdkbeNayKW 10DB bKMlatEdkkgelI 24 b 24/s edayykmYyNaEdlmantMltUcCageK.

b. EdkbeNayKYrRtUv)anBRgayCMuvijbrimaRtrrbs;EdkkgCamYyKMlatGtibrma mm300 .


21/32

Department of Civil Engineering viTasanCatiBh ubeckeTskm8> EdkTb;karrmYlGb,brma Minimum Torsional Reinforcement

enAkEngNaEdlEdkTb;karrmYlGb,brmaRtUvkar EdkTb;karrmYlGb,brmaRtUv)ankMNt;dUcxageRkam (ACI Code, Section 11.6.5)

!> EdkkgbiTCitGb,brmasMrab;bnSMnkMlaMgkat;TTwg nigkarrmYl emIlEpk 8>6

yt

wtv

f

sbAA

35.02 + sMrab; MPaf c 31' <

+

yt

wctv

f

sbfAA '063.02 sMrab; MPaf c 31' !%>@(

Edl =vA RkLapeCIgTaMgBIrrbs;EdkkgEdlkMNt;)anBIkMlaMgkat;=tA RkLapeCIgEtmYyrbs;EdkkgEdlkMNt;BIm:Um:g;rmYl

=s KMlatEdkkg=ytf ersIusg;yal (yield strength)rbs;Edkkg MPa400

KMlatEdkkg s minKYrFMCagtMltUcCagkgcMeNam 8/hP nig mm300 . KMlatenHRtUvkaredIm,IRKb;RKgsameRbH.

@> RkLapEdksrubGb,brmarbs;EdkbeNayTb;karrmYl

=

y

yth

t

y

cpcl

f

fP

s

A

f

AfA

'5min

!%>#0Edl sAt / minRtUvyktUcCag ytw fb /173 .

lA Gb,brmaenAkgsmIkar !%>#0 RtUv)ankMNt;edIm,Ipl;nUvGRtaGb,brmanmaDEdkTb;kMlaMgrmYlelImaDebtug mantMlRbEhl %1 sMrab;ebtugGarem:EdlrgkMlaMgrmYlsuT.

9> segbviFIsaRsKNnaeday ACI Code Summary of ACI Code Procedures

viFIsaRsKNnasMrab;bnSMkMlaMgkat;TTwg nigkMlaMgrmYlGacRtUv)ansegbdUcxageRkam


22/32

T.Chhay NPIC


!> KNnakMlaMgkat;TTwgemKuN uV nigm:Um:g;rmYlemKuN uT BIkMlaMgEdlGnuvtmkelIeRKOgbgM. tMleRKaHfak;sMrab;kMlaMgkat;TTwg nigkMlaMgrmYlKWsitenARtg;muxkat;EdlmancM

gay d BIprbs;TMr.@> a.eKRtUvkarEdkkMlaMgkat;TTwgenAeBl 2/cu VV > Edl 6/' dbfV wcc = .

b.EdkTb;karrmYlRtUvkarenAeBlEdl

>

cp

cpcu

P

AfT

2

12

' !%>@0

RbsinebIEdkRTnugRtUvkar GnuvtviFIsaRsxageRkam.

#> KNnasMrab;kMlaMgkat;TTwga. KNnaersIuisg;kMlaMgkat;nominalEdlpl;edayebtug cV . kMNt;kMlaMgkat;TTwg

EdlTb;edayEdkRTnug

scu VVV += b

cus

VVV

=

b. eRbobeFob sV Edl)anKNnaCamYynwgtMlGnuBaatGtibrma 3/'2 dbf wc eyagtam ACI Code. RbsinebI sV tUcbnkarKNna EtpymkvijtMeLIgTMhMmuxkat;rbs;

ebtug.c. EdkRTnugkMlaMgkat;TTwgRtUv)anKNnadUcxageRkam

df

sVA

yt

sv =

Edl =vA RkLapneCIgTaMgBIrrbs;Edkkg=s KMlatEdkkg

EdkkMlaMgkat;TTwgkgmYyktaRbEvgKWdf

V

s

A

yt

sv =

d. RtYtBinit sAv / Edl)anKNnaCamYynwg sAv / Gb,brma

=

yt

w

yt

wc

v

f

b

f

bf

s

A35.0'063.0(min)

vA Gb,brma RtUv)ankMNt;edaybTdaneRkambnSMnGMeBIrbs;kMlaMgkat;TTwg nigkM

laMgrmYlRtUv)aneGayenAkgCMhanTI5


23/32

Department of Civil Engineering viTasanCatiBh ubeckeTskm KNnasMrab;karrmYla.

RtYtBinitfaetIm:Um:g;rmYlemKuN uT begItm:Um:g;rmYllMnwg (equilibrium torsion)

bm:Um:g;rmYlRtUvKa (compatibility torsion). sMrab; equilibrium torsion eRbI uT .sMrab;compatibility torsionm:Um:g;rmYlKNnaKWtMltUcCageKn uT BIbnkemKuNnig

=

cp

cpcu

P

AfT

2

23

' !%>!(

b. RtYtBinitfaetITMhMnmuxkat;RKb;RKan;bGt;. vaTTYl)anedayeRbIsmIkar !%>@! sMrab;

muxkat;tan;bsmIkar !%>@@ sMrab;muxkat;Rbehag. RbsinebItMlenAGgxageqVgFMCag ( )3/'2/ cwc fdbV + enaHbegInmuxkat;pymkvijKNnabn. sMrab;muxkat;Rbehag RtYtBinitfaetIkMras;CBaaMg ttUcCag hoh PA / bGt;. RbsinebIvatUcCageRbIsmIkar !%>@# pymkvijeRbIsmIkar !%>@@.

c. kMNt;EdkkgbiTCitcaM)ac;BIsmIkar !%>@%

cot2 yto

nt

fA

T

s

A= !%>@%

sAt / minRtUvtUcCag ytw fb /173 . ehIy mMuGacsn

t;es

I o45 / /un TT = nig75.0= .

snt; ( )1185.085.0 yxAA oho == Edl 1x nig 1y CaTTwg nigkMBs;rbs;muxkat;KitBIGkSeTAGkSEdkkg emIlrUbTI!%>!!. sMrab; o45= nig MPafy 400=

o

nt

A

T

s

A

800

= !%>@^

KMlatGnuBaatGtibrma s KWtMltUcCageKn mm300 b 8/hP .d.

kMNt;EdkbeNaybEnmBIsmIkar !%>@&

2cot

=

y

yth

tl

f

fP

s

AA !%>@& a

EtminRtUvtUcCag

= y

yt

h

t

y

cpc

l f

f

Ps

A

f

Af

A 12

'5

min !%>@&b


24/32

T.Chhay NPIC


sMrab; o45= nig MPafyt 400= enaH ( ) htl PsAA /= !%>@*EdkbeNayTb;karrmYlKYrmanGgt;pity:agticesIKMlatEdkkgelI24 b 24/s b:uEn

minRtUvtUcCag 10DB . EdkbeNayRtUvdak;enAkgEdkkgbiTCitCamYyKMlatGtibrmaesI mm300 . y:agehaceKRtUvdak;EdkmYyedImenARKb;mMurbs;Edkkg. CaTUeTAmYyPaKbIn Edk lA RtUv)anbEnmeTAelIEdkTaj mYyPaKbIenABak;kNalkMBs;rbs;muxkat;nigmYyPaKbIeTotenAEpksgt;.

%> kMNt;RkLapsrubnEdkkgbiTCitEdlbNalBI uV nig uT .

( )yt

wtvvt

f

sbAAA

35.02 += !%>@(

eRCIserIsEdkkgbiTCitsmrmCamYyKMlat s EdlmantMltUcCageKkgcMeNam mm300 nig 8/hP .EdkkgKYrRtUv)andak;enAcMgay )( dbt+ eRkaycMnucEdlRTwsIRtUvkar Edl =tb TTwgnmuxkat;EdlTb;nwgkMlaMgrmYl.

]TahrN_ 5>3

(Equilibrium Torsion)

kMNt;brimaNEdkRTnugcaM)ac;sMrab;muxkat;ctuekaNEkgdUcbgajenAkgrUbTI15>15. muxkat;rgnUvkMlaMgkat;emKuN kNVu 5.213= nigkMlaMgrmYllMnwg (equilibrium torsion) mkNTu .41= enATItaMgEdlmancMgay dBIpnTMr. eKeGay MPaf c 28' = nig MPafy 400= .


25/32


kMlaMgKNnaKW kNVu 5.213= nig mkNTu .41= 2>a. EdkTb;kMlaMgkat;RtUvkarenAeBl 2/cu VV > .

( )( ) kNbdfV cc 6.13710520400286

75.0'

6

3 ===

kNV

kNV cu 8.682

5.213 =>=

eKRtUvkarEdkTb;kMlaMgkat;.b.

eKRtUvkarEdkTb;karrmYlenAeBla

cp

cpcu T

P

AfT =

>

2

12

'

2232000580400 mmyxA oocp === ( ) ( ) mmyxP oocp 184052040022 =+==

( )mkNTa .7.910

184012

2320002875.0 62

=

=

mkNmkNTu .7.9.41 >= EdkTb;kMlaMgrmYlRtUvkarcaM)ac;. cMNaMfa RbsinebI uT tUcCag mkN.7.9 enaHEdkTb;kar

rmYlnwgminRtUvkar b:uEnEdkTb;kMlaMgkat;RtUvkar.3>KNnakMlaMgkat;TTwg

a. scu VVV += / kNVs 2.101= b. ( )( ) scs VkNbdfV >=== 8.73352040028

3

2'

3

2(max)

c. mmmdf

VsA

y

sv /5.0520400102.101 23 =

== eCIgBIr

mmms

Av /25.02

2= eCIgmYy

4>KNnasMrab;karrmYla. kMlaMgrmYlKNna mkNTu .41= . KNnalkNmuxkat;edaysnt;kMras;ebtugkarBar

Edk mm40 nigeRbIEdkkg 12DB

( ) mmx 30864024001 =+=


26/32

T.Chhay NPIC


( ) mmy 48864025801 =+= CakarGnuvtn_eKGacsnt; mmbx 901 = nig mmhy 901 =

211 150304488308 mmyxAoh === 24.12775885.0 mmAA oho ==

( ) ( ) mmyxPh 159248830822 11 =+=+= o45= nig 0.1cot =

b. RtYtBinitPaBRKb;RKan;rbs;muxkat;edayeRbIsmIkar !%>@!

+

+

c

w

c

oh

hu

w

u f

db

V

A

PT

db

V'

3

2

7.1

2

2

2

kNVc 6.137= nig kNVc 5.183=

MPa82.11503047.1

159241000000

520400

137600sidehandLeft

2

2

2

=

+

=

MPaMPa 82.13.3283

2

520400

18350075.0sidehandRight >=

+

=

muxkat;RKb;RKan;c.

kMNt;EdkkgbiTCitcaM)ac;EdlbNalBIkarrmYlBIsmIkar !%>@%

cot2 yto

nt

fA

T

s

A=

mkNT

T un .7.5475.0

41===

0.1cot = 24.127758 mmAo =

mmms

At /535.04004.1277582

107.54 26

=

= eCIgmYy

d. kMNt;EdkbeNaybEnmBIsmIkarTI!%>@&

2cot

=

y

yth

tl

f

fP

s

AA

535.0=s

At mmPh 1592= MPaff yyt 400== 0.1cot = 272.8511592535.0 mmAl ==

=

y

yth

t

y

cpcl

f

fP

s

A

f

AfA

12

'5(min)

2232000mmAcp = 535.0=sAt MPaff yyt 400==


27/32


kMNt;RkLapEdkkgsrub

a. sMrab;eCIgmYyrbs;Edkkgs

A

s

A

s

A vtvt

2+=

EdkkgEdlcaM)ac; mmmAvt /785.025.0535.0 2=+= eCIgmYyeRbIEdk 12DB RkLapmuxkat;rbs;EdkkgsMrab;eCIgmYyKW 2113mm

mm144785.0

113stirrupsofspacing == yk mm140

b. KMlatGtibrma mmPs h 199815928 === b mm300 mYyNaEdltUcCag.KMlatEdleRbIKW mmmm 199140 <

c. sAvt / Gb,brma mmmmmmf

b

yt

w /785.0/35.0400

40035.035.0 22 edIm,IrkkarBRgayEdkbeNay cMNaMfa lA srub 272.851 mm= . eRbImYyPaKbIenAEpkxagelI b 29.2833/72.851 mm= edIm,IbEnmenAkgEdkrgkarsgt; sA' . eRbImYyPaKbIdak;enA

EpkxageRkam edIm,IbEnmBIelIEdkrgkarTaj nigEdkmYyPaKbIeTotdak;enAkMBs;Bak;kNal.a.

RkLapEdksrubenAEpkxagelIesI 29.5099.283226 mm=+ . eRbI 163DB 2603mmAs =

b. RkLapEdksrubenAEpkxageRkamesI 27.33629.2838.3078 mm=+ . eRbI 283DB nig 322DB enARCugmMu sA srub 28.3455 mm=

lA srubEdleRbI ( ) ( ) 27548.30788.3455226603 mm=+=

c.

enAkMBs;Bak;kNal eRbIEdk 122DB 2

226mmAs = bg;srsEdklMGitRtUv)anbgajenAkgrUbTI15>15. KMlatEdkbeNayesInwgmm230 EdltUcCagKMlatEdkGtibrmaEdlRtUvkar 2300mm . Ggt;pitEdkkg 12DB Edl

eRbIFMCagGgt;pitGb,brma 10DB bKMlatEdkkgelI 24 mms 8.524/ = .]TahrN_ 5>4

(Compatibility Torsion)edaHRsay]TahrN_TI 15>3 eLIgvij RbsinebIkMlaMgrmYlemKuNCa compatibility torsion.

dMeNaHRsay


28/32

T.Chhay NPIC


eyagtamdMeNaHRsaykg]TahrNITI 15>3!> kMlaMgKNnaKW kNVu 5.213= nig compatibility torsion mkNTu .41=

@> CMhan (a)nig (b)dUcKaenAkg]TahrN_TI15>3. eKRtUvkarEdkRTnug.#> CMhan (c) KWdUcKa.$> KNnasMrab;kMlaMgrmYl

edaysar compatibility torsion mkNTu .41= enaH uT KNnaRtUvtUvCag mkN.41 b crT RtUv)aneGayenAkgsmIkar !%>!(

mkN

P

AfT

cp

cpccr .7.3810

1840

232000

3

2875.0

3

' 622

=

=

=

edaysarEt ucr TT 3 edayeRbI mkNTu .7.38= edIm,IkMNt;famuxkat;RKb;RKan;.

mmms

At /5.0 2= eCIgmYy279615925.0 mmAl ==

eRbI (min)852 2 ll AmmA >=

%> vtA caM)ac; mmm /75.05.025.0 2=+= eCIgmYy

mms 6.15075.0

113==

eRbI mm150 . eRCIserIsEdkbeNay nigEdkkgdUckg]TahrN_TI15>3.]TahrN_ 5>5

(L-section with Equilibrium Torsion)FwmxagnRbBnkMralxNrbs;GKardUcbgajenAkgrUbTI15>16. muxkat;enAcMgay dBIpnTMrrg

nUvkNV

u235=

nigequilibrium torque mkNT

u.27=

. KNnaEdkRTnugcaM)ac;edayeRbIMPaf c 28' = nig MPafy 400= sMrab;RKb;EdkEdleRbIenAkgFwm.

dMeNaHRsay1>kMlaMgKNnaKW kNVu 235= nig mkNTu .27= 2>a. EdkTb;kMlaMgkat;RtUvkarenAeBl 2/cu VV >

kNdbf

V wc

c 3.105104553506

2875.0

6

' 3 ===

kNVV cu 65.522

=>


29/32


muxkat;RtUvkarEdkTb;karrmYl.3>KNnaEdkTb;kMlaMgkat;TTwg

a. scu VVV +=

sV75.03.105235 += kNVs 173=

b. swcs VkNdbfV >== 8.561'3

2(max)

c. mmmdf

V

s

A

y

sv /95.0455400

173000 2=

== eCIgBIr

mmms

Av /475.02

95.0

2

2==

4>KNnaEdkTb;karrmYl mkNTu .27= a. KNnalkNmuxkat;edaysnt; kMras;ebtugkarBarEdk mm40 nigEdkkg 12DB .

RTnug ( ) mmx 258124023501 == ( ) mmy 438124025301 == sab mmx 3801= EdkkghYscUleTAkgRTnug

mmy 58921501 == ( ) ( ) 213504443825838058 mmAoh =+=

24.11478785.0 mmAA oho == ( ) ( ) mmPh 22684382582380582 =+++= o45=

0.1cot =


30/32

T.Chhay NPIC


b. RtYtBinitPaBRKb;RKan;rbs;muxkat;edayeRbIsmIkarTI!%>@! kNVu 235= /kNVc 3.105= / kNVc 4.140= / mkNTu .27=

MPa47.21350447.1

22681027

455350

235000sidehandLeft2

62=

+

=

MPa3.3283

2

455350

14040075.0sidehandRight =

+

=

muxkat;manlkNRKb;RKan;c. kMNt;EdkkgbiTCitedIm,ITb;karrmYl sAt / BIsmIkar !%>@%

mmm

fA

T

s

A

yto

nt /392.0

4004.114787275.0

1027

cot2

26

=

==

eCIgmYy

d. KNnaEdkbeNaybEnmBIsmIkar !%>@* sMrab; MPaf c 400' = nig 0.1cot = 28892268392.0 mmP

s

AA h

tl ==

=

minlA BIsmIkar !%>#0 KW2

min 7.44788940012

242500285mmAl =

=

karcUlrYmrbs;sabRtUv)anecaledaysarTTYl)anlTplxusKatictYc nigtMlBlkm

ticCag.5>kMNt;RkLapmuxkat;EdkkgbiTCit

a. sMrab;eCIgmYy

s

A

s

A

s

A vtvt

2+=

muxkat;cM)ac; mmmAvt /867.0475.0392.0 2=+= eCIgmYyeRCIserIsEdk 12DB 2113mmAs =

KMlatEdkkg mm130867.0113

== eRbI mm125 b. KMlatEdkGtibrma mmPs h 5.283

8

2268

8max === . eRbI mms 125= dUckarKNna.

c. mmmmmmf

b

s

A

yt

wvt /867.0/31.0400

35035.035.0 22 kMNt;karBRgayrbs;EdkbeNay. lA srubKW 2889mm . eRbImYyPaKbIb

23.2963/889 mm= enAEpkxagelI EpkkNal nigEpkxageRkam.


31/32

Department of Civil Engineering viTasanCatiBh ubeckeTskm16. KMlatEdkbeNayKW mmmm 300190 < . Ggt;pitrbs;EdkkgKWmm12 EdlFMCagGgt;pitEdk 10DB bKMlatEdkkgelI 24 mms 2.524/ = .

bEnmEdkbeNay 12DB enARKb;mMurbs;EdkkgenAkgRTnugFwm nigsabFwm.


32/32

T.Chhay NPIC

បេតុងពង្រឹងដោយដែក 15 xv-design-for-torsion

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