បេតុងពង្រឹងដោយដែក 15 xv-design-for-torsion
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Transcript of បេតុងពង្រឹងដោយដែក 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
karKNnasMrab;kMlaMgrmYl 349
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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
karKNnasMrab;kMlaMgrmYl 351
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
karKNnasMrab;kMlaMgrmYl 353
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
karKNnasMrab;kMlaMgrmYl 355
=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
karKNnasMrab;kMlaMgrmYl 357
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
karKNnasMrab;kMlaMgrmYl 359
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
karKNnasMrab;kMlaMgrmYl 361
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
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T.Chhay NPIC
karKNnasMrab;kMlaMgrmYl 363
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
karKNnasMrab;kMlaMgrmYl 365
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 .
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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
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T.Chhay NPIC
karKNnasMrab;kMlaMgrmYl 367
!> 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
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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
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T.Chhay NPIC
karKNnasMrab;kMlaMgrmYl 369
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= .
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Department of Civil Engineering viTasanCatiBh ubeckeTskm
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 =+=
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T.Chhay NPIC
karKNnasMrab;kMlaMgrmYl 371
( ) 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==
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Department of Civil Engineering viTasanCatiBh ubeckeTskm
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
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T.Chhay NPIC
karKNnasMrab;kMlaMgrmYl 373
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
=>
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Department of Civil Engineering viTasanCatiBh ubeckeTskm
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 =
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T.Chhay NPIC
karKNnasMrab;kMlaMgrmYl 375
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.
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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.
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T.Chhay NPIC