បេតុងពង្រឹងដោយដែក 11 xi-members-in-compression-and-bending

Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa

Members in Compression and Bending 196

XI. eRKOgbgÁúMrgkarsgát; nigrgkarBt;

1> esckþIepþIm eRKOgbgÁúMbBaÄrCaEpñkmYyrbs;eRKagsMNg; EdlrgkMlaMgsgát; nigm:Um:g;. kMlaMgTaMgenH )anBIkMlaMg

xageRkAdUcCa bnÞúkefr bnÞúkGefr nigbnÞúkxül;. kMlaMgRtUv)ankMNt;eday karKNnaedayéd b¤edaykMuBüÚT½r EdlQrelIeKalkarN¾sþaTic nigviPaKeRKOgbgÁMú (structural analysis). Ca]TahrN¾ sMrab;rUb (1) bgðajfa eRKagQrelITMr hinged BIr EdlrgbnÞúkemKuNBRgayesμ I enAelIGgát; BC. düaRkamm:Um:g;Bt;RtUv)anKUrenA EpñkxagTaj. kMNat;ssr AB nig CD rgnUvkMlaMgsgát; nigm:Um:g;Bt;. pleFobrvagm:Um:g;Bt; nigkMlaMg sgát; RtUv)aneGayeQ μaHfa cMgaycakp©it e Edl

n

n

PMe = . e CacMgayBITIRbCMuTMgn;)aøsÞic(plastic centroid)

énmuxkat;eTA cMnucénbnÞúkmanGMeBI. TIRbCMuTMgn;)aøsÞic (plastic centroid) RtUv)anTTYledaykarkMNt;TItaMgkM laMgpÁÜbbegáItedaysésEdk nigebtug edaysnμt;kugRtaMgsgát;sMrab;Edk yf nigkugRtaMgsgát;sMrab;ebtug

cf '85.0 . sMrab;muxkat;sIuemRTI TIRbCMuTMgn;)aøsÞic (plastic centroid) RtYtsIuKñaCamYyTIRbCMuTMgn;rbs;muxkat;. sMrab;muxkat;minsIuemRTI TIRbCMuTMgn;)aøsÞic (plastic centroid) RtUv)ankMNt;edayeRbIm:Um:g; eFobnwgGkS½ arbitrary axis.

]TahrN_1³ kMNt;TIRbCMuTMgn;)aøsÞic (plastic centroid)

énmuxkat;dUcbgðajkñúgrUbTI2. smμtikmμ³ MPaf c 28' = nig MPaf y 400= .

dMeNaHRsay³ !> kugRtaMgsgát;sMrab;ebtugRtUv)ankMNt;yk cf '85.0

=cF kMlaMgkñúgrbs;ebtug gc Af '85.0=

rUbTI1³ eRKagTMr pin BIrCamYynwgdüaRkamm:Um:g;

rUbTI2³ TIRbCuMTMgn;)øasÞic (P.C)énmuxkat;

T.Chhay NPIC

eRKOgbgÁúMrgkarsgát; nigrgkarBt; 197

kN4165500350)2885.0( =×××= cF sßitenAelITIRbCMuTMgn;énmuxkat;ebtug ¬enAcMgay mm250 BIGkS½ AA − ¦

@> kMlaMgenAkñúgsésEdk kNfAF yss 2.985400

4284

2

11 =××

×==π

kNfAF yss 6.4924004282

2

22 =××

×==π

#> kMNt;m:Um:g;eFob AA − mmx 85.233

6.4922.9854165)4356.492()652.985()2504165(=

++×+×+×

= dUcenH TIRbCMuTMgn;)aøsÞic (plastic centroid) RtUvsßitenAelIcMgay mm85.233 BIGkS½ AA− $> RbsinebI 21 ss AA = ¬muxkat;sIuemRTI¦ dUcenH mmx 250= BIGkS½ AA − .

2> karsnμt;sMrab;KNnassr GaRs½ytam ACI Code EdnkMNt;sMrab;karKNnassrkMNt;dUcxageRkam³ !> kMhUcRTg;RTayeFob strain enAkñúgebtug nigEdk RtUvsmamaRteTAnwgcMgayBIGkS½NWt. @> RtUvEtbMeBjlkçxNÐ smIkarlMnwgénkMlaMg nigPaBRtUvKñaénkMhUcRTg;RTayeFob strain

compatibility. #> kMhUcRTg;RTayeFobrbs;ebtugrgkarsgát;EdleRbIR)as;GtibrmaKW 003.0 . $> ersIusþg;rbs;ebtugrgkarTajGacRtUvecal. %> kugRtaMgenAkñúgEdkKW yss fEf ≤= ε . ^> bøúkkugRtaMgGackMNt;manragctuekaNCamYykugRtaMg cf '85.0 BRgayBIRbEvg ca 1β= . Edl c CacMgayBIGkS½NWt nig

⎪⎩

⎪⎨

⎧−

−=

65.0

)7

28'(05.085.085.0

1cfβ sMrab;ebtugEdlmanersIusþg;

MPafMPafMPa

MPaf

c

c

c

56'56'28

28'

>≤<

≤

3> düaRkamGnþrkmμbnÞúk-m:Um:g; Load-moment interaction diagram enAeBlEdlbnÞúktamGkS½RtUv)anGnuvtþmkelIssrxøI krNIdUcxageRkamGacekIteLIg edayGaRs½y

eTAnwgTItaMgGnuvtþbnÞúkedayeFobeTAnwg TIRbCMuTMgn;)aøsÞic (plastic centroid). rUb



kMlaMgsgát;tamGkS½ oP CakMlaMgsgát;tamGkS½EdlmantMélFMGnuvtþenAelITIRbCMuTMgn;)aøsÞic (plastic

centroid) 0=e nig 0=nM . kar)ak;rbs;ssr ekIteLIgedayebtugEbk nigEdkeFVIkardl; yielding. vaRtUv)ansMEdgeday oP enAelIExSekag.

!> Maximum nominal axial load maxnP : CakrNIEdlkMlaMgtamGkS½GnuvtþeTAelImuxkat;CamYy cM

gaycakp©it eccentricity Gb,rma. tam ACI Code, on PP 80.0max = sMrab;ssrEdkkgdac;² tie

column nig on PP 85.0max = sMrab;ssrEdlmanEdkkgdUcrWus½r spirally reinforced column . kar)ak; ekIteLIgedayebtugEbk nigEdkeFVIkardl; yielding.

@> Compression failure: CakrNIEdlbnÞúktamGkS½FMGnuvtþenAcMgaycakp©ittUc. bnÞúktamGkS½kñúg krNIenHmantMélERbRbYlBI tMélGtibrma maxnn PP = eTAtMélGb,rma bn PP = (balanced load). s r)ak;edayebtugEbkenAEpñkrgkarsgát;CamYYynwgbMErbMrYlrageFob strain 003.0= ÉcMEnkkugRtaMgkñúgEdk ¬EpñkrgkarTaj¦ KWtUcCag yield strength ys ff < . kñúgkrNIenH en PP > nig nee < .

#> Balanced condition bP : lkçxNÐenHekItmaneLIgenAeBlEdl bMErbMrYlrageFobrgkarsgát; compression strain enAkñúgebtugmantMélesμ I 003.0 ehIybMErbMrYlrageFobrbs;EdkrgkarTajmantMél

rUbTI3 a³ düaRkamGnþrkm μbnÞúk-m:Um:g;

T.Chhay NPIC


s

yy E

f=ε . kar)ak;rbs;ebtugekIteLIgtMNalKñanwgEdk yield. m:Um:g;EdlekItedaysarbnÞúkenHRtUv)an

eKehAfa balanced moment bM cMgaycakp©itRtUv)aneKehAfa balanced eccentricity b

bb P

Me = .

$> Tension failure: CakrNIekItmanenAxN³Edl bnÞúktamGkS½tUc nigcMNakp©itFM ehIyEdlmanm:U m:g;FM. muneBl)ak; kugRtaMgTajekItmanenAelIEpñkd¾FMénmuxkat; bNþaleGayEdkrgkarTaj yield muneBl

rUbTI3 b³ muxkat;ssrEdlbgðajBITItaMgbnÞúk nP sMrab;lkçxNÐbnÞúkepSg²



ebtugEbk. enAeBl)ak; bMErbMrYlrageFobrbs;EdkrgkarTajmantMélFMCagbMErbMrYlrageFob yield yε ehIybMErbMrYlrageFobenAkñúgebtugesIμ 003.0 . krNIenHekItmanBI Balanced condition eTAdl; pure

flexure bn PP < nig eee > . %> Pure flexure: muxkat;kñúgkrNIenHrgm:Um:g;Bt; nM Edl 0=nP . kar)ak;dUcKñanwg kar)ak;rbs;

FñwmrgkarBt;. cMNakp©itRtUv)ansn μt;fa Gnñn. 4> karpþl;nUvsuvtßiPaB Safety provisions

!> emKuNbnÞúksMrab; bnÞúk gravity nigbnÞúkxül; DU 4.1=

LDU 6.12.1 += WLDU 8.06.12.1 ++= WLDU 6.10.12.1 ++=

WDU 6.19.0 += bnSMbnÞúkemKuNEdlmantMélsFMCageKRtUv)anykmkeRbIR)as;sMrab;karKNna. @> emKuNkat;bnßyersIusþg; φ eRbIsMrab;KNnassrGaRs½yeTAnwgkrNIxageRkam³ k> enAeBl gcnu AfPP '1.0≥= φ eBlenaH 65.0=φ sMrab;ssrEdkkgdac;² tie column

ehIy 7.0=φ sMrab;muxkat;ssr EdlmanEdkkgdUcrWus½r spirally reinforced column . krNIenHssrRtUv )anrMBwg fa)ak;edaykarrsgát;.

rUbTI4³ tMélemKuNφ

T.Chhay NPIC


x> muxkat;EdlbMErbMrYlrageFobrgkarTajsuT§ net tensile strain tε sMrab;ersIusþg;Fm μta nominal strength enAkñúgEdkrgkarTajeRkAeKbMput KWsißtenAcenøaH 005.0 nig 002.0 (transition region)

φ ERbRbYlCalkçN³bnÞat;cenøaH 9.0 nig 67.0 b¤ ¬ 7.0 ¦. sMrab;muxkat;EdlmanEdkkgdUcrWus½r spiral section

)3

200)(002.0(7.0 −+= tεφ b¤ ⎥⎦

⎤⎢⎣

⎡−+=

35

/12.07.0

tdcφ (-1)

sMrab;muxkat;epSgeTot )

3250)(002.0(65.0 −+= tεφ b¤ ⎥

⎦

⎤⎢⎣

⎡−+=

35

/125.065.0

tdcφ (-2)

K> enAeBl 0=uP kñúgkrNIrgkarBt;suT§ 9.0=φ sMrab; muxkat; tension-control section

nig ERbRbYlBI 9.0 nig 65.0 b¤ ¬ 7.0 ¦ enAkñúgtMbn; transion region.

5> Balanced condition – muxkat;ctuekaN

Balanced condition ekItmanenAkñúgmuxkat;ssrenAeBlEdl bnÞúkEdlGnuvtþmkelImuxkat;ssr Edlman nominal strength begáItbMErbMrYlrageFobesμ I 003.0 enAkñúgsésrgkarsgát;rbs;ebtug nigbMEr bMrYlrageFobes μ I

s

yy E

f=ε enAkñúgr)arEdkrgkarTajkñúgeBldMNalKña. enHKWCakrNIBiessEdl GkS½NWt

GacRtUv)ankMNt;BI strain diagram edaysÁal;tMélFMbMput. enAeBlEdlbnÞúkcakp©itmantMél FMCag bP enaHeKehAmuxkat;enaHfa compression control. pÞúymkvijeKehAfa tension control .

karviPaK balanced column section GacRtUv)anBnül;dUcxageRkam³ !> yk bc CacMgayBIsésrgkarsgát;q¶aybMputmkGkS½NWt. BI strain diagram

s

y

b

Efd

c

+=

003.0

003.0)balanced( (-3)



eday MPaEs 200000=

yb f

dC+

=⇒600

600

kMBs;bøúkrgkarsgát;smmUl equivalent compressive block

df

cay

bb 11 600600 ββ ⎟

⎟⎠

⎞⎜⎜⎝

⎛

+== (-4)

Edl ⎪⎩

⎪⎨

⎧−

−=

65.0

)7

28'(05.085.085.0

1cfβ sMrab;ebtugEdlmanersIusþg;

MPafMPafMPa

MPaf

c

c

c

56'56'28

28'

>≤<

≤

@> BIsmIkarlMnwg plbUkkMlaMgtamTisedkesIμsUnü 0=+−− TCCP scb

Edl abfC cc '85.0= nig ys fAT = (-5) )'85.0'(' css ffAC −= ys ff =' enAeBlEdlEdkrgkarsgát;eFVIkardl; yield

ys fc

dcf ≤⎟⎠⎞

⎜⎝⎛ −

='600' pÞúymkvij

yscsscb fAffAabfP −−+=⇒ )'85.0'(''85.0 (-6) #> cMNakp©it be RtUv)anvas;BI plastic centroid nig 'e RtUv)anvas;BITIRbCMuTMgn;énEdkrgkarTaj.

"' dee += ¬sMrab;krNIrnH "' dee b += ¦ Edl "d CacMgayBITIRbCMuTMgn;)øasÞiceTATIRbCMuTMgn;Edkrgkar Taj. be RtUv)anKNnaedayKitm:Um:g;Rtg; plastic centroid

")"'()"2

( TddddCdadCeP scbb +−−+−−= (-7) b¤ ")"')('85.0'(')"

2('85.0 dfAdddffAdadabfeP yscscbb +−−−+−−= (-8)

cMNakp©it balanced eccentricity

b

bb P

Me = (-9)

sMrab;muxkat;minEmnctuekaN eyIgeRbIviFIsaRsþdUcKñakñúgkarviPaK edayKitRkLaépÞBitR)akdrbs;ebtug rgkarsgát;.

emKuNkat;bnßyersIusþg; φ sMrab; balanced condition CamYy MPaf y 400= RtUv)ansnμt;yk 65.0 b¤ 7.0 . enHedaysar 002.0===

s

yts E

fεε .

]TahrN_2³ kMNt;kMlaMgsgát; balanced compressive force bP rYckMNt; be nig bM sMrab;muxkat; bgðajkñúgrUb. eKeGay MPaf c 27' = nig MPaf y 400= .

dMeNaHRsay³

T.Chhay NPIC


!> sMrab; balanced condition bMErbMrYlrageFobenAkñúgebtugKW 003.0 ehIy bMErbMrYlrageFobenAkñúgEdk 002.0

200000400

==yε @> TItaMgGkS½NWt

mmdf

cy

b 3005006.0600

600=×=

+=

mmca bb 25530085.01 =×== β @> RtYtBinitü Edkrgkarsgát;/ BI strain diagram

30050300'

003.0' −

=−

=c

dcsε

ys εε >=⇒ 0025.0' dUcenHEdkrgkarsgát; yield

b¤RtYtBinitütam ys fcdcf ≤⎟⎠⎞

⎜⎝⎛ −

="600'

MPaMPaf s 400500300

50300600' >=⎟⎠⎞

⎜⎝⎛ −

=

dUcenH MPaff ys 400' == $> KNnakMlaMgmanGMeBImkelImuxkat;

kNabfC cc 3.20483502552785.0'85.0 =×××== kNfAT yss 2.985400282 =××== π

kNffAC cyss 7.928)2785.0400(28)'85.0(' 2 =×−=−= π %> KNna eP nig be

kNTCCP scb 8.19912.9857.9283.2048 =−+=−+= ")"'()"

2( TddddCdadCePM scbbb +−−+−−==

rUbTI6³ balanced condition



mkNeM bb .8.7322252.985)22550500(7.928)2252

255500(3.20488.1991 =×+−−+−−== meb 368.0

8.19918.732==⇒

^> sMrab; balanced condition 65.0=φ kNPb 67.12948.199165.0 =×=φ

mkNM b .32.4768.73265.0 =×=φ

6> muxkat;ssreRkamGMeBIbnÞúkcakp©it Column sections under eccentric loading

sMrab;krNIBIr enAeBlEdlmuxkat;ssr)ak;edaykarsgát;b¤karTaj smIkarlMnwgmUldæanBIrGac RtUv)aneRbIsMrab;viPaKssrEdlrgbnÞúkcakp©it.

!> plbUkkMlaMgtamGkS½edk b¤tamGkS½QRtUvesμ IsUnü @> plbUkm:Um:g;eFobnwgGkS½NamYyRtUves μ IsUnü eyagtamrUb eKGacsresrsmIkarTaMgBIrxagelI dYcxageRkam !> 0=+−− TCCP scn (-10) Edl abfC cc '85.0= )'85.0'(' csss ffAC −= ¬RbsinebIEdkrgkarsgát; yield enaH ys ff =' ¦ ss fAT = ¬RbsinebIEdkrgkarTaj yield enaH ys ff = ¦ @> Kitm:Um:g;Rtg;cMnuc sA

0)'()2

(' =−−−− ddCadCeP scn (-11) Edl "' dee += ¬ "d CacMgayBITIRbCMuTMgn;)øasÞiceTATIRbCMuTMgn;rbs;EdkrgkarTaj¦ b¤

2' hdee −+= sMrab;muxkat;ssrEdlmanEdksIuemRTI

rUbTI7³ krNITUeTA muxkat;ctuekaNEkg

T.Chhay NPIC


⎥⎦⎤

⎢⎣⎡ −+−= )'()

2(

'1 ddCadCe

P scn (-12)

Kitm:Um:g;Rtg; cC 0)'

2()

2()

2(' =−−−−⎥⎦

⎤⎢⎣⎡ −− daCadTadeP sn (-13)

)2

'(

)'2

()2

(

dae

daCadTP

s

n

−+

−+−= (-14)

Rbsid\nebI ss AA '= ehIy yss fff == ' enaH

22

)'(

2'

)'(ahe

ddfA

dae

ddfAP ysys

n

+−

−=

−+

−= (-15)

)'(

)22

('

ddf

ahePAA

y

n

ss −

+−== (-16)

7> ersIusþg;rbs;ssrsMrab;kar)ak;edaykarTaj Stregth of columns for tension failure

enAeBlEdlssrrgbnÞúkcakp©itCamYynwgcMNakp©it e FM enaHeKrMBwgfassrnwg)ak;edaykarTaj. ssr)ak;edayEdkeFIVkardl; yield ebtugEbkenAeBlEdl strain rbs;EdkFMCag )(

s

yyy E

f=εε . Kñúg

krNIenH nominal strength nP nwgmantMéltUcCag bP b¤k¾ cMNakp©it n

nP

Me = FMCag balanced

eccentricity be . edaysarkñúgkrNIxøHeKmankarBi)akkñúgkarTsSn_TayfavaCamuxkat; tension control

b¤ compression control enaHeKGacsn μt;fa tension failure GacekIteLIgenAeBl de > . Karsn μt;enH GaceFVIeLIgenAeBleRkay.

smIkarlMnwgTUeTA 0=+−− TCCP scn nig

0)'()2

(' =−−−− ddCadCeP scn GacRtUv)aneRbIR)as;sMrab;KNna nominal strength rbs;ssr. !> sMrab;kar)ak;edaykarTaj EdkrgkarTaj yield ys ff = . sn μt;fakugRtaMgEdkrgkarsgát;

ys ff =' . @> KNna TCCP scn −+= Edl abfC cc '85.0= )'85.0(' cyss ffAC −= ys fAT = #> KNna nP edayKitm:Um:g;Rtg; sA



)'()2

(' ddCadCeP scn −+−= Edl "' dee += b¤

2' hdee −+= enAeBl ss AA '=

$> BICMhan @ nig # eyIg)an

⎥⎦⎤

⎢⎣⎡ −+−=−+ )'()

2(

'1 ddCadCe

TCC scsc

vaCasmIkarTIdWeRkTI2 EdlmanGBaØti a . CMnYstMél cC / sC nig T ehIyedaHRsayrk a . %> eRkayBICMnYs cC / sC nig T smIkardWeRkTI2 Gacsresry:agsMrYldUcxageRkam

02 =++ CBaAa Edl bfA c'425.0= )'(2)'('85.0 deAdebfB c −=−= ')'')('85.0'(' efAddeffAC yscss −+−−=

AACBBa

242 −±−

=⇒ RbsinebI 0'85.0' <− cs ff RtUvykvaes μI 0 .

^> CMnYs a eTAkñúsmIkarCMhan @edIm,ITTYl nP . m:Um:g; nM kMNt;tam ePM nn =

&> RtYtBinitüemIlfaetIEdkrgkarsgát; yield dUckarsn μt;b¤Gt;. RbsinebI ys εε ≥' enaH Edkrgkar sgát; yield . pÞúymkvij sss Ef '' ε= . Gnuvtþn_CMhan @ dl;% mþgeTot. [ ] 003.0/)'(' cdcs −=ε /

s

yy E

f=ε nig 1/ βac = .

*> RtYtBinitüfamuxkat;Ca tension control . Tension control enAeBlNa bee > b¤ bn PP < . (> Net tensile strain tε enAkñúgmuxkat; CaFm μtaFMCag limit strain sMrab;muxkat; compression-

controlled section 002.0 . dUcenHtMélénemKuNkat;bnßyersIusþg; φ ERbRbYlcenøaHBI 65.0 ¬b¤ 70.0 ¦ nig 90.0 . smIkar )

3200)(002.0(7.0 −+= tεφ b¤ ⎥

⎦

⎤⎢⎣

⎡−+=

35

/12.07.0

tdcφ sMrab;muxkat; EdlmanEdk

kgdUcrWus½r spiral section nig )3

250)(002.0(65.0 −+= tεφ b¤ ⎥⎦

⎤⎢⎣

⎡−+=

35

/125.065.0

tdcφ sMrab;muxkat;

epSgeTot RtUv)aneRbIsMrab;KNnark emKuNkat;bnßyersIusþg; φ . ]TahrN_3³ kMNt; nominal compressive strength nP sMrab;muxkat;EdleGaydUckñúgrUbxageRkam Rbsin ebI mme 500= . dMeNaHRsay³

T.Chhay NPIC


!> eday mme 500= mmd 485=> sn μt;famuxkat;)ak;kñúglkçxNÐ tension failure condion controls

¬EdlRtUveFVIkarRtYtBinitüenAeBleRkayeTot¦. Strain rbs;EdkrgkarTaj sε GacFMCag yε dUcenHeyIg ykkugRtaMg yf . edaysn μt;faEdkrgkarsgát; yield ys ff =' EdlRtUvRtYtBinitüenAeBleRkay. @> BIsmIkarlMnwg TCCP scn −+= Edl akNaabfC cc 03.83502785.0'85.0 =××== kNffAC cyss 68.928)2785.0400(

4284)'85.0('

2

=×−=−=π

kNfAT ys 2.985400282 === π 52.5603.82.98568.92803.8 −=−+=⇒ aaPn ¬1¦

#> Kitm:Um:g;Rtg; sA

⎥⎦⎤

⎢⎣⎡ −+−= )'()

2(

'1 ddCadCe

P scn

edayTIRbCMuTMgn;)øasÞic plastic centroid sßitenAelITIRbCMuTMgn;énmuxkat; mmd 210"= . mmdee 710210500"' =+=+=

36.54949.50056.0)65485(68.928)2

485(03.87101 2 ++−=⎥⎦

⎤⎢⎣⎡ −+−= aaaaPn ¬2¦

$> pÁúMsmIkar ¬1¦ nig ¬2¦ eyIg)an 088.60554.20056.0 2 =−+ aa

mma 74.172=⇒ %> kNPn 58.133052.5674.17203.8 =−×=

rUbTI8³ ]TahrN_TI3 kar)ak;edaykarTaj Tension failure



mkNM n .29.6655.058.1330 =×= ^> RtYtBinitüfa Edkrgkarsgát; yield b¤Gt;

mmc 22.20385.074.172

== 002.0

20000040000204.0003.0

22.2036522.203' ==>=

−= ys εε dUcenHEdksgát; yield

RtYtBinitü strain enAkñúgEdkTaj ys εε >=⎟

⎠⎞

⎜⎝⎛ −

= 00416.0003.022.203

22.203485

RbsinebIEdksgát;Gt; yield eRbI sss Ef '' ε= rYceFVIkarKNnaeLIgvij. &> KNna φ ³ eday 00416.0=tε muxkat;sßitenAkñúgtMbn; transition region

( ) 83.03

250002.065.0 =⎟⎠⎞

⎜⎝⎛−+= tεφ

kNPn 38.110458.133083.0 =×=φ mkNM n .19.55229.66583.0 =×=φ

8> ersIusþg;rbs;ssrsMrab;kar)ak;edaykarsgát; Stregth of columns for compression failure

RbsinebIbnÞúkGnuvtþn_sgát; nP FMCagbnÞúk balanced force bP b¤cMNakp©it n

n

PMe = tUcCag be enaH

ssrnwgrMBwgfaRtUv)ak;edaykarsgát;. kñúgkrNI compression controls ehIy strain rbs;ebtugnwgmantMél 003.0 Edl strain rbs;EdkmantMéltUcCag yε . PaKeRcInrbs;muxkat;ssrnwgrgkarsgát;. GkS½Nwtxit

eTArkEdkrgkarTaj edaybegáInmuxkat;sgát; dUcenHcMgayeTAGkS½NWt bcc > .

rUbTI9³ düaRkam strain enAeBl compression controls

T.Chhay NPIC


edaysareKBi)akkñúgkarTsSn_TaynUvmuxkat;ssrfa tension failure b¤ compression failure eK)ansn μt;fa enAeBl

32de < enaHssr)ak;eday compression failure EdlRtUvepÞógpÞat;enAeBleRkay.

edIm,IKNna nominal load strength nP eKeRbIeKalkarN_sþaTic. karviPaKmuxkat;ssrsMrab;kar)ak;eday karsgát; compression failure eKGaceRbIsmIkar 0=+−− TCCP scn nigsmIkar

0)'()2

(' =−−−− ddCadCeP scn nigdMeNaHRsaymYykñúgcMeNamdMeNaHRsayxageRkam. 8>1> dMeNaHRsay Trial solution

dMeNaHRsayenHRtUv)ansegçbdUcCMhanxageRkam³ !> KNnacMgayeTAGkS½NwtsMrab;muxkat; balanced section bc

y

tb f

dc+

=600

600 (-3)

@> kMNt; nP edayeRbIlkçxNÐlMnwg TCCP scn −+= (-10)

#> KNna nP edayKitm:Um:g;Rtg;EdkrgkarTaj sA )'()

2(' ddCadCeP scn −+−= (-11)

Edl "' dee += kñúgkrNITUeTA b¤

2' hdee −+= enAeBl ss AA '=

abfC cc '85.0= )'85.0'(' csss ffAC −= ss fAT = $> edaysnμt;tMél bcc > KNna ca 1β= . sn μt; ys ff =' %> KNna sf

yt

sss fc

cdEf ≤⎟⎠⎞

⎜⎝⎛ −

== 600ε

^> CMnYstMélEdlrkeXIjeTAkñúgsmIkarCMhan @ nigCMhan # edIm,Irk 1nP nig 2nP . RbsinebI 21 nn PP ≈ eRCIsyktMéltUcCageK b¤mFümPaKén 1nP nig 2nP . EtebI 1nP mantMélxusKñaq¶ayBI 2nP eK

RtUvsn μt; c b¤ a fμ I ehIyeFVIkarKNnaeLIgvijcab;epþImBICMhan $ rhUtdl; 21 nn PP ≈ . ¬eKGacTTYlyk)an ebI 1nP nig 2nP xusKña %1 ¦.



&> epÞógpÞat;fa Edkrgkarsgát; yield edayKNna ( )[ ]cdcs /'003.0' −=ε ehIyeRbobeFobCamYy

s

yy E

f=ε . enAeBlEdl ys εε ≥' Edkrgkarsgát; yield RbsinebImindUcenaHeT sss Ef '' ε= b¤

ys fc

dcf ≤⎟⎠⎞

⎜⎝⎛ −

='600

*> epÞógpÞat;fa bee < b¤ bn PP > sMrab; compression failure. (> sMrab;muxkat; compression controlled section CaTUeTA net tensile strain tε enAkñúgmuxkat;tUc

Cag 002.0 . dUcenH emKuNkat;bnßyersIusþg; 65.0=φ ¬b¤ 70.0 sMrab;ssrEdleRbIEdkkgCab;¦. ]TahrN_4³ kMNt; nominal compressive strength nP sMrab;muxkat;EdleGay RbsinebI mme 254= . dMeNaHRsay³ !> edaysar mmdmme 33.333

32254 =<= . sn μt; compression failure. karsn μt;enHRtUvepÞógpÞat;enA

eBleRkay. KNnacMgayeTAGkS½NwtsMrab; balanced section bc :

y

tb f

dc+

=600

600 mm300400600500600

=+×

=

@> BIsmIkarlMnwg TCCP scn −+= (-10)

Edl akNaabfC cc 03.83502785.0'85.0 =×××== kNffAC cyss 68.928)2785.0400(28)'85.0(' 2 =×−=−= π edaysn μt;Edkrgkarsgát; yield ¬karsn μt;enHRtUvepÞógpÞat;enAeBleRkay¦ kNfffAT ssss 46.2282 === π ¬ ys ff < ¦ sn faP 46.268.92803.8 −+= #> Kitm:Um:g;Rtg; sA

rUbTI10³ ]TahrN_TI4 Compression controls

T.Chhay NPIC


⎥⎦⎤

⎢⎣⎡ −+−= )'()

2(

'1 ddCadCe

P scn (-11)

TIRbCMuTMgn;)øasÞicsßitenAelITIRbCMuTMgn;rbs;muxkat; mmd 225"= mmdee 479225254"' =+=+= ( ) 57.8720084.038.8505008.928

250003.8

4791 2 +−=⎥

⎦

⎤⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ −= aaaaPn

$> edaysnμt; mmc 342= EdlmantMélFMCag mmcb 300= mma 7.29034285.0 =×=

CMnYstMél a eTAkñúgsmIkarkñúgCMhanTIBIrxagelIeyIg)an kNPn 78.259857.8727.2900084.07.29038.8 2

1 =+×−×= %> KNna sf BIdüaRkam strain enAeBlEdl mmc 340=

MPafs 19.277600342

342500=

−=

00139.0200000

19.277====

s

sts E

fεε

^> edayCMnYs mma 7.290= nig MPafs 19.277= eTAkñúgsmIkarCMhanTImYyedIm,IKNna 2nP kNPn 11.258119.27746.268.9287.29003.82 =×−+×=

eday 1nP nig 2nP mantMélxusKñamindl; %1 dUcenHeyIgyk kNPn 11.2581= mkNePM nn .6.655254.011.2581 =×==

&> epÞógpÞat;fa Edkrgkarsgát; yield BIdüaRkam strain

002.000256.0003.0342

50342' =>=−

= ys εε

dUcenH Edkrgkarsgát; yield dUckarsn μt;. *> kNPkNP bn 8.199111.2581 =>= ehIy mmemme b 368254 =<= bgðajfavaCamuxkat; compression control dUckarsnμt;. cMNaM³ eKGaceFVIkarsakl,gKNnaedIm,IeGay 1nP nig 2nP mantMél kan;Etes μ Ikña. (> KNna φ

mmddt 500== mmc 342= tε ¬enAnIv:UedkrgkarTaj¦ 002.000139.0

342342500003.0 <=

−= enaH 65.0=φ

kNPn 72.167711.258165.0 =×=φ mkNM n .14.4266.65565.0 =×=φ



8>2> dMeNaHRsayviPaKcMnYn Numerical Analysis Solution

enAeBl compression control karviPaKssrGaceFVIeTA)anedaykat;bnßykarKNnamkRtwmsmIkar dWeRkTI3 EdlmanTMrg; 023 =+++ DCaBaAa rYcedaHRsayrktMél a edayviFIcMnYn numerical method

b¤ a GacTTYl)anBIm:asIunKitelx. BIsmIkarlMnwg TCCP scn −+= sscysc fAffAabf −−+= )'85.0(')'85.0( (-10)

Kitm:Um:g;Rtg;EdkTaj sA

⎥⎦⎤

⎢⎣⎡ −−+−=⎥⎦

⎤⎢⎣⎡ −+−= )')('85.0(')

2('85.0

'1)'()

2(

'1 ddffAadabf

eddCadC

eP cyscscn (-11)

BIdüaRkam strain

003.0)(

003.0

1

1

β

βε a

ad

ccdt

s

−=⎟

⎠⎞

⎜⎝⎛ −

=

kugRtaMgenAkñúgEdkTajKW )(600200000 1 ad

aEf ssss −=== βεε

edayCMnYstMél sf eTAkñúgsmIkar (-10) nigedaHRsaysmIkar (-10) nig (-11) eRkayBIsMrYlrYceyIg TTYl)an

0'600]'600)'')('85.0('[)]'('85.0['85.01

23 =−++−−+−+⎟⎠⎞

⎜⎝⎛ deAaeAddeffAadebfa

cbf

sscyscc β

enHCasmIkardWeRkTI3 EdlmanTMrg; 023 =+++ DCaBaAa Edl

2'85.0 bfA c=

)'('85.0 debfB c −= '600)'')('85.0(' eAddeffAC scys ++−−= deAD s 1'600 β−= enAeBlEdleKKNna)antMél A / B / C nig D enaH a GacRtUv)anKNnaedayviFIsakl,g b¤ TTYl)anedaypÞal;Bim:asIunKitelx. dMeNaHRsaysmIkardWeRkTI3 GacTTYl)anedayeRbIviFI Newton-

Raphson . viFIenHmanRbsiT§PaBkñúgkaredaHRsayrkb¤srbs; ( ) 0=xf . vaTak;Tgnwgbec©keTssamBaØ ehIyeKqab;TTYl)ancMelIyedayeFVItamCMhanxageRkam³ !> eGay DCaBaAaaf +++= 23)( nigKNna A / B / C nig D @> KNnaedrIevTImYyén )(af ³ CBaAaaf ++= 23)(' 2 #> edaysnμt;tMéldMbUg oa KNnatMélbnÞab;

T.Chhay NPIC


)(')(

1o

oo af

afaa −=

$> edayeRbItMél 1a KNna 2a dUcsmIkarxagelI

)(')(

1

112 af

afaa −=

%> Gnuvtþn_nUvviFIenHrhUtdl;)antMélsuRkitmYy 1−≅ nn aa . kñúgkrNIviPaKssrenAeBl compression

control tMél a EtgEtFMCag ba . dUcenH eKcab;epþImCamYy bo aa = ehIyGnuvtþsmIkarxagelIBIrdgedIm,I TTYl)ancMelIy. ]TahrN_5³ eFVI]TahrN_TI4eLIgvijedayeRbIviFI numerical analysis

dMeNaHRsay³ !> KNna A / B / C nig D nigkMNt; )(af

25.40162

3502785.02

'85.0=

××==

bfA c ( ) 5.1686825004793502785.0)'('85.0 −=−××=−= debfB c

08.734800328

47928600)50500479)(2785.0400(28

'600)'')('85.0('22

=××++−×−=

++−−=

CC

eAddeffAC scys

ππ

4.83300844190350085.047928600'600 21 −=××××−=−= πβ deAD s

4.83300844190308.7348003285.16868225.4016)( 23 −+−= aaaaf

@> KNnaedrIevTI1 08.73480032833736575.12048)(' 2 +−= aaaf #> eGay mmaa bo 255== sMrab;muxkat; balanced section mmcb 300= nig mmab 255= 39.295

)255(')255(2551 =−=

ffa

$> nigKNna 2a ³ mm

ffa 4.292

)39.295(')39.295(39.2952 =−=

tMélrbs; a mantMélRsedognwg a enAkñúg]TahrN_TI3. CMnYstMél a eTAkñúgsmIkar (-10) b¤ (-11) eKTTYl)an kNPn 66.2594=

8>3> dMeNaHRsayRbEhl Approximate Solution

smIkar approximate RtUv)anesñIreLIgeday Whitney edIm,IedaHRsayrk nominal compressive

strength sMrab;ssrxøI enAeBl compression control.



5.0

)'(

'

18.13'

2 +−

++

=

dde

fA

dhebhfP ysc

n (-17)

smIkarxagelIenHGaceRbIeTA)ansMrab;EtssrEdlmansésEdksIuemRTItMerobEtmYyRsTab; ehIyRsbeTA nwgGkS½énkarBt;. smIkar approximate TI2 RtUv)anesñIeLIgeday Hsu

0.15.1

=⎟⎟⎠

⎞⎜⎜⎝

⎛+

−−

o

n

bo

bn

MM

PPPP (-18)

Edl nP = nominal axial strength énmuxkat;ssr bb MP , = nominal load nig nominal moment énmuxkat; balanced section nM = nominal bending moment ePn ⋅=

oP = nominal axial load enAeBl e=0 yststgco fAAAfP +−= )('85.0

gA = gross area énmuxkat; bh= stA = muxkat;EdkbeNþayminEmnkugRtaMgsrub ]TahrN_6³ kMNt; nominal compressive strength nP sMrab;muxkat;EdleGaydUckñúg]TahrN_TI4 edaysmIkar ¬*>#>!¦ nig ¬*>#>@¦edayeRbInUvcMNakp©itdUcKña mme 254= rYceRbobeFobcMelIy. dMeNaHRsay³ !> dMeNaHRsaytamsmIkar Whitney k> lkçN³énmuxkat; mmb 350= / mmh 550= / mmd 500= / mmd 50'= / 22463' mmA = nig mmdd 450)'( =− x> GnuvtþsmIkar Whitney

kNPn 15.27455.0

450254

4002463

18.1500

254550327550350

2

=+

×+

+××

××=

kNPn 35.178415.274565.0 =×=φ K> nP EdlKNnaedaysmIkar Whitney CatMélEdlminsnSMsMécenAkñúg]TahrN_enH ehIytMél

kNPn 15.2745= KWFMCagtMélsuRkit kNPn 11.2581= EdlKNnaedaysmIkarsþaTickñúg]TahrN_TI4. @> dMeNaHRsaytamsmIkar Hsu

k> sMrab; balanced condition kNPb 8.1991= nig kNM b 8.732= ¬]TahrN_TI2¦ x> 40024632)24632350550(2785.0)('85.0 ××+×−×××=+−= yststgco fAAAfP kNPo 22.6275=

T.Chhay NPIC


K> 18.732

02548.199122.6275

8.1991 5.1

=⎟⎠⎞

⎜⎝⎛+

−− nn PP

edayKuNnwg 1000 ehIyedaHRsayrk nP 146500654.023346.0 5.1 =+ nn PP

Edaykarsakl,gtMél kNPn 65.2587= EdlmantMélRbEhl kN11.2581 EdlKNnaedaysþa Tic.

9> ]TahrN_sMrab;düaRkamGnþrkmμ Interaction Diagram Example

enAkñúg]TahrN_TI2 bnÞúk balanced load bP , bM nig be RtUv)anKNnasMrab;muxkat;dUckñúgrUbTI6 ¬ mmeb 368= ¦. dUcKña enAkñúg]TahrN_TI3 nigTI4 load capacity sMrab;muxkat;dUcKñaRtUv)anKNnasMrab; krNIenAeBl mme 500= ¬tension failure¦ nigenAeBl mme 254= ¬compression failure¦. tMélTaMg enHnwgRtUvbgðajenAkñúgtaragTI1.

edIm,IKUrdüaRkamGnþrkmμbnÞúk-m:Um:g; tMélepSg²én nPφ nig nMφ RtUv)anKNnasMrab;tMél e epSg² Edl e ERbRbYlBI 0=e eTA =e Gtibrma sMrab;krNIm:Um:g;Bt;suT§ pure moment enAeBl 0=nP . düa Rkamnþr km μbnÞúk-m:Um:g;RtUv)anbgðajkñúgrUbTI11. bnÞÞúk kNPno 90.4078=φ CabnÞúkcMGkS½tamRTwsþI enAeBl

0=e . Et ACI Code GnuBaØatibnÞúkGb,brmaRtwmEt kNPno 12.32638.0 =φ EdlRtUvKñanwg cMNakp©wtGb, brma. cMNaMfa sMrab;kar)ak;edaykarsgát; compression failure bee < nig bn PP > ehIysMrab;kar)ak;

taragTI1³taragKNnasegçb rUbTI11³düaRkamGnþrkm μbnÞúk-m:Um:g;



edaykarTaj tension failure bee > nig bn PP < . krNI =e Gtibrma ssrrgnUvm:Um:g;Bt;suT§dUckrNIFñwm. 10> ssrmuxkat;ctuekaNCamYyEdkxag Rectangular columns with side bars

enAkñúgmuxkat;ssrxøH EdkRtUv)aneKdak;BRgaytamRCugTaMgGs;. EdkxagRtUv)andak;tamkMBs;énmux kat;edaybEnßmeTAelIEdkTaj nigEdksgát; sA nig sA' ehIyRtUv)aneKkMNt;eGayeQ μaH ssA ¬rUbTI12¦. kñúgkrNIenH viFIsaRsþkñúgkarKNnaEdl)anBnül;rYcmkehIyGacRtUv)anGnuvtþ edayKitBicarNabEnßmkar pøas;bþÚr strain tamkMBs;énmuxkat; nigTMnak;TMngkMlaMgenAkñúgEdkxagnImYy²eTAkñúgtMbn;sgát; b¤tMbn;Taj énmuxkat;. kMlaMgTaMgenHRtUv)anbUkbEnßmeTAelI cC sC nig T edIm,IkMNt; nP smIkarmanragdUcxag eRkam³

∑ ∑−+= TCCP scn (-10a) ]TahrN_TI7 Bnül;BIkarKNnaenH. cMNaMfa RbsinebIEdkxagsßitenAEk,rGkS½NWt ¬rUb12 b¦ strain

nigkMlaMg enAkñúgEdkmantMéltUcNas;EdleKGacecal)an. cMENkEdkEdlsßitenAEk,r sA nig sA' mantM élFMKYrsm nigCYybegáInlT§PaBRTRTg;bnÞúkénmuxkat;.

]TahrN_7³ kMNt;bnÞúk bP m:Um:g; bM nigcMNakp©it be sMrab;muxkat;bgðajkñúgrUbTI13. edayeRbI

MPaf c 28' = nig MPaf y 400= . dMeNaHRsay³ muxkat; balanced section RtUv)anKNnadUcKñanwg]TahrN_TI2Edr. eKeGay

mmhb 550== / mmd 485= nig mmd 65'= . 22

24.40214325' mmAA ss ===

π ( )325DB / nigEdkxag 326DB ¬ 323DB sMrab;mçag¦.

1> KNnacMgayeTAGkS½NWt

rUbTI12³ EdkxagenAkñúgmuxkat;ctuekaNEkg

T.Chhay NPIC


mmdf

c ty

b 291485400600

600600

600=⎟

⎠⎞

⎜⎝⎛

+=⎟

⎟⎠

⎞⎜⎜⎝

⎛

+=

mmca bb 35.24729185.085.0 =×== 2> KNnakMlaMgenAkñúgebtug nigEdk tamry³rUb 13 a . enAtMbn;sgát;

kNabfC cc 81.323755035.2472885.0'85.0 =×××== ( )csss ffAC '85.0'' −=

enAnIv:U mm65− MPaMPa

cdcf s 400466

29165291600'600' 1 >=⎟

⎠⎞

⎜⎝⎛ −

=⎟⎠⎞

⎜⎝⎛ −

=

dUcenH MPaf s 400' = ( ) kNCs 79.15122885.040024.40211 =×−=



enAnIv:U mm170− MPa

cdcf s 48.249

291170291600'600' 2 =⎟

⎠⎞

⎜⎝⎛ −

=⎟⎠⎞

⎜⎝⎛ −

=

( ) kNCs 3632885.048.2494322

2

2 =×−×=π

enAnIv:U mm275− MPa

cdcf s 99.32

291275291600'600' 3 =⎟

⎠⎞

⎜⎝⎛ −

=⎟⎠⎞

⎜⎝⎛ −

=

( ) kNCs 78.142885.099.324322

2

3 =×−×=π

enAkñúgtMbn;Taj ¬nIv:U mm380− ¦

T.Chhay NPIC


64 1053.917003.0

291291380 −⋅=×

−=sε

MPafs 5.1831053.917200000 64 =⋅×= −

kNT 16.295)5.183(4322

2

1 =×=π

kNT 5.160840024.40212 =×= 3> KNna ∑∑ −+= TCCP scb

kNPb 72.3224)5.160816.295()78.1436379.1512(81.3237 =+−+++= 4> KNnam:Um:g;Rtg;TIRbCMuTMgn;)øasÞic

2105.160810516.29510536321079.1512325.15181.3237 ×+×+×+×+×=bM mkNMb .54.1214=

mPMe

b

bb 377.0

72.322454.1214

===

5> KNna φ sMrab; balanced section 002.0== yt εε / 65.0=φ kNPn 07.209672.322465.0 =×=φ

niig mkNMb .45.74954.121465.0 =×=φ ]TahrN_8³ edaHRsay]TahrN_TI7 eLIgvijenAeBlEdl mme 152= . dMeNaHRsay³ 1> edaysar mme 152= mmeb 326=< enaHvaCalkçxNÐ)ak;edaykarsgát; compression failure

condition. sn μt; mmc 5.399= ¬edaykarsakl,g¦ nig 85.05.399 ×=a mma 58.339= ¬ rUbTI13 b ¦.

2> KNnakMlaMgenAkñúgebtug nigEdk kNCc 1.444555058.3392885.0 =×××=

dUcKñanwgkrNI balanced MPafs 4001 = nig kNCs 79.15121 = MPafs 68.3442 = nig kNCs 13.5162 = MPafs 98.1863 = nig kNCs 48.2623 =

MPafs 29.294 = nig kNCs 83.84 = MPafs 41.1285 = nig kNT 37.516=

3> KNna ∑ ∑ =−+= kNTCCP scn 96.6228 mkNePM nn .8.94615296.6228 =×=⋅=



4> KNna nP edayKitm:Um:g;Rtg; sA

⎥⎦⎤

⎢⎣⎡ −−+−−+−−+−+−= )3'()2'()'()'()

2(

'1

4321 sddCsddCsddCddCadCe

P sssscn

mmhdee 3622

5504851522

' =−+=−+= mms 105= KMlatrvagEdkxag ¬efr sMrab;]TahrN_enH¦

( ) ( )

( ) ( ) ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

×−−+×−−+

−−+−+⎟⎠⎞

⎜⎝⎛ −

=10536548583.810526548548.262

1056548513.5166548579.15122

58.3394851.44453621

nP

kNPn 6230= 5> KNna φ

mmddt 485== mmc 5.399= tε ¬enAnIv:UEdkTaj¦ ( ) ( ) 00064.05.399/5.39948503.0/03.0 =−=−= ccdt

eday 002.0<tε enaH 65.0=φ kNPn 8.404896.622865.0 =×=φ

mkNM n .42.6158.94665.0 =×=φ cMNaM³ RbsinebIEdkxagminRtUv)anKit enaH

kNPb 1.3142= nP ¬enA mme 152= ¦ kN54.568248.42279.151223.4592 =−+=

RbsinebIeKKitEdkxagenaH bP ekIneLIgRbEhl %6.2 nig nP ekIneLIgRbEhl %6.9 . 11> lT§PaBRTbnÞúkrbs;ssrmuxkat;mUl Load Capacity of Circular Columns

11>1 lkçxNÐ Balanced Condition

tMélénbnÞúk balanced load nP nig m:Um:g; balanced moment nM sMrab;muxkat;mUlGacRtUv)ankM Nt;edayeRbIsmIkarlMnwgdUckrNImuxkat;cuekaNpgEdr. sésrEdkenAkñúgmuxkat;rgVg;EdlRtUv)antMerobeTA tamcMNayBIGkS½TIRbCMuTMgn;)øasÞicERbRbYl KWGaRs½yeTAnwgcMnYnEdkenAkñúgmuxkat;. bBaðacMbgKWrkkMBs;bøúk sgát; a nigkugRtaMgenAkñúgsésrEdk. ]TahrN_xageRkamBnül;BIkarviPaKmuxkat;eRkamlkçxNÐ balanced

condition. nitiviFIdUcKñaGacRtUv)aneRbIedIm,IviPaKmuxkat;sMrab; tension control b¤ compression control. ]TahrN_9³ kMNt;bnÞúk balanced load nP nig m:Um:g; balanced moment nM sMrab;ssrmuxkat;rgVg;Edkkg vNÐGgát;p©it mm400 CamYynig 288DB dUcbgðajkñúgrUbTI14. eKeGay MPaf c 28' = nig MPaFy 400= .

dMeNaHRsay³

T.Chhay NPIC


1> edaysarEtEdksIuemRTInwgGkS½ AA − Edlkat;tamTIRbCMuTMgn;rgVg; enaHTIRbCMuTMgn;)øasÞicsßitenAelI GkS½enaH.

2> kMNt;TItaMgTIRbCMuTMgn;GkS½NWt mmdt 34.329=

s

yy E

f=ε

yyt

bfd

c+

=+

=600

600003.0

003.0ε

mmcb 6.19734.329400600

600=

+=

mmab 96.167= 3> kMNt;lkçN³rbs;cMerokrgVg; circular segment ¬rgVg;TI15¦

RkLaépÞcMerokrgVg; ( )ααα cossin2 −= r (-19) TItaMgTIRbCMuTMgn; x ¬BITIRbCMuTMgn; 0¦

( )ααα

αcossin

sin32 3

−=

rx (-20) xrZ −= (-21) ( )arr −=αcos b¤ ⎟

⎠⎞

⎜⎝⎛ −=

ra1cosα (-22)

16.0200

96.1671cos =⎟⎠⎞

⎜⎝⎛ −=α

o79.80=⇒α / 987.0sin =α nig rad41.1=α RkLaépÞcMerokrgVg; ( )987.016.041.12002 ×−=

22.50083 mm=

( ) mmx 39.10216.0987.041.1

987.020032 3

=×−

×⎟⎠⎞

⎜⎝⎛=

mmZ 61.9739.102200 =−= 4> kMNt;kMlaMgsgát; cC

×= cc fC '85.0 RkLaépÞcMerokrgVg; kN11922.500832885.0 =××=

vaeFVIGMeBIenA mm39.102 BITIRbCMuTMgn;ssr

T.Chhay NPIC


5> KNna strain, stress nig kMlaMgenAkñúgEdkrgkarTaj nigEdkrgkarsgát;.

kMNt;bMErbMrYlrageFob strain BIdüaRkambMErbMrYlrageFob. sMrab; 1T

002.0== yεε MPaff ys 400== kNT 6.492400

4282

2

1 =×=π

sMrab; 2T 4

3 105.874.13198.55 −⋅== ys εε

MPafs 170200000105.8 43 =×⋅= −

kNT 36.2091704282

2

2 =×=π

sMrab; 1sC 3

1 1093.1003.06.19794.126 −⋅=×=sε

MPafs 3862000001093.1 31 =×⋅= − MPa400<

( ) kNCs 05.4462885.03864

2822

1 =×−=π

sMrab; 2sC 4

2 1077.7003.06.197

18.51 −⋅=×=sε MPafs 4.1552000001077.7 4

2 =×⋅= − ( ) kNcs 07.1622885.04.155

4282

2

2 =×−=π

6> kugRtaMgenAkñúgEdkrgkarsgát;RtUv)ankat;bnßy edIm,IKitenAkñúgebtugEdlCMnYsedayEdk.



kMlaMg balanced KW ∑∑ −+= TCCP scb kNPb 16.1098)36.2096.492()07.16205.446(1192 =+−++=

sMrab;muxkat; balanced 002.0=tε nig 65.0=φ kNPb 8.713=φ

7> Kitm:Um:g;Rtg;TIRbCMuTMgn;)øasÞic ¬GkS½ AA − kat;tamGkS½TIRbCMuTMgn;¦ sMrab;kMlaMgTaMgGs; )58.5334.12958.5334.12939.102[ 2121 ×+×+×+×+×== TTCCCePM sscbbb

mkNMb .36.263= mkNMb .18.171=φ

mmeb 8.23916.109836.263

== 11>2 ersIusþg;rbs;muxkat;mUlsMrab;kar)ak;edaykarsgát; Strength of circular column for compression failure

muxkat;ssreRkamkMlaMgcMNakp©it GacRtUv)anviPaKtamCMhandUcmuxkat; balanced Edr. va TTYl)anedaykarsn μt; bCC > b¤ baa > nigKNnakMlaMgenAkñúgebtug nig EdkenATItaMgepSgKñaedIm,I kMNt; ∑ ∑−+= TCCP scn1 . dUcKña nM GacRtUv)anKNnaedayKitm:Um:g;Rtg;TIRbCMuTMgn;)øasÞic ¬TIRbCuMTMgn;rbs; muxkat;¦ ehIykMNt;

eMP n

n =2 . RbsinebItMél 1nP nig 2nP minRbhak;RbEhl KñaeTenaH sn μt; C b¤ a fμ I ehIyeFVIkarKNnaeLIgvij ¬emIlcMnucTI8¦. tMélxusKñarvag 1nP nig 2nP sßit enArgVg; %1 . muxkat; Camuxkat; compression controls enAeBl bee < b¤ bn PP > .

sMrab;]TahrN_ RbsinebIvaTamTarkMNt;ersIusþg;rbs;muxkat;ssrenAkñúg]TahrN_TI9 enAeBlEdl mme 150= nP GacRtUv)anKNnaedayCMhandUcnwg]TahrN_TI 9.

1> eday mme 150= tUcCag mmeb 8.239= lkçxNÐ)ak;edaykarsgát; compression failure

condion ekIteLIg. 2> sn μt; mmc 225= ¬edaykarsμan¦ 6.197=> bC nig mma 25.191= 3> KNna mmx 63.89= / mmZ 37.110= RkLaépÞcMerokrgVg; 297.59332 mm= 4> -5> KNnakMlaMg³ kNCc 125.1412= / kNCs 29.4631 = kNCs 73.2282 = / kNT 66.3421 = /

kNT 84.932 = 6> KNna kNTCCP scn 64.16671 =−+= ∑ ∑ 7> Kitm:Um:g;Rtg;GkS½ssr ¬TIRbCMuTMgn;)øasÞic¦³

mkNM n .1.248=

T.Chhay NPIC


mme

MP n

n 97.16532 == EdlmantMélRbEhl 1nP ¬tMélxusKñaRbEhl %1 ¦. dUcenH kNPn 97.1653=

cMNaM³ RbsinebIEdkkgrbs;ssrCaEdkkgvNÐdUcrWus½renaH 70.0=φ . smIkartMélRbEhl approximate equation sMrab;karKNna nP sMrab;muxkat;mUl enAeBl

compression controls RtUv)anesñIeLIgedayelak Whitney

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+

+

⎥⎥⎦

⎤

⎢⎢⎣

⎡+

+

=

1318.1

67.08.06.9

'

2 s

yst

s

cgn

De

fA

Dhhe

fAP (-23)

Edl =gA RkLaépÞmuxkat; gross area

=h Ggát;p©itmuxkat; =sD Ggát;p©itmuxkat;ssrEdlvas;BITIRbCMuTMgn;EdkmçageTATIRbCMuTMgn;EdkmçageTot =stA RkLaépÞmuxkat;EdkbBaÄr =e cMNakp©itEdlvas;BITIRbCMuTMgn;)øasÞic ]TahrN_10³ KNnaersIusþg;kMlaMgsgát; nominal nP sMrab;muxkat;sMrab;]TahrN_TI9 edayeRbIsmI kar Whitney RbsinebIcMNakp©it mme 150=

dMeNaHRsay³ 1> mme 150= tUcCag mmeb 8.239= . tamkarKNnadUceBlmun bgðajfamuxkat;ssrCamuxkat; compression controls. 2> edayeRbIsmIkar Whitney

mmh 400= 222 7.125663400

44mmhAg ===

ππ / mmDs 280120400 =−=

22

49264288 mmAs =

××=π

( )

kNPn 94.17851

2801503

4004926

18.128067.04008.0

1504006.9

287.125663

2

=⎟⎠⎞

⎜⎝⎛ +

××

+

⎥⎥⎦

⎤

⎢⎢⎣

⎡+

×+×

××

×=

3> mkNePM nn .89.26715.094.1785 =×== tMél nP enAeBlenHFMCagtMél kNPn 97.1653= EdlKNnaenAeBlmunedaysþaTic.



11>3 ersIusþg;rbs;muxkat;mUlsMrab;kar)ak;edaykarTaj Strength of circular column for tension failure

kar)ak;edaykarTajsMrab;ssrmUlenAeBlbnÞúkRtUv)anGnuvtþn_enARtg;cMNakp©it bee > b¤ bn PP < . enAkñúgkrNIenH muxkat;ssrGacRtUv)anviPaKtamCMhandUckarviPaKmuxkat; balanced nigdUc

kñúg]TahrN_TI8. karviPaKRtUv)aneFVIeLIgedaysnμt; bCC < b¤ baa < rYcehIyGnuvtþn_tamCMhanBnül; kñúgEpñkTI11>1. cMNaMfa edaysarEtsésrEdkRtUv)antMerobedaymancenøaHefrtambrimaRtmuxkat;rgVg; enaHEdkTaj sA Edlpþl;eGayGacmantMéltUc ehIylT§PaBRTbnÞúkk¾køayCamantMéltUc. dUcenH eK)anENnaMeGayeCosvagkareRbIR)as;muxkat;mUlsMrab;krNIkar)ak;edaykarTaj tension failure. 12> karviPaK nigkarKNnassredayeRbIdüaRkam Analysis and Design of

Column Using Charts karviPaKmuxkat;ssrEdl)anBnül;BIxagedImKWQrelIeKalkarN_sþaTic. sMrab;karviPaK b¤kar

KNnassrCaCMhandMbUg düaRkamb¤taragBiessGacRtUv)aneRbIedIm,IkMNt; nPφ nig nMφ sMrab;muxkat; EdleGay nigkar KNnamuxkat;EdkcaM)ac;sMrab; uP nig uM EdleGay. düaRkam nigtaragenHRtUv)ane)aH Bum<pSayeday viTüasßanebtugGaemric American Concrete Institute (ACI) viTüasßanebtugBRgwgedayEdk Concrete Reinforcing Steel Institute (CRSI) nigsmaKmsIum:g;t_Br½Eln Porland Cement Association

(PCA). karKNnassrcugeRkayRtUvEteFVIeLIgedayQrelIsmIkarsþaTic edaykarKNnaedayéd b¤eday km μviFIkMuBüÚTr½. kareRbIdüaRkam ACI RtUv)anbgðajenAkñúg]TahrN_xageRkam. düaRkamRtUv)anbgðajkñúgrUb TI16 nigrUbTI17. Tinñn½yTaMgenHRtUv)ankMnt;sMrab;muxkat;ssrdUcbgðajenARCugxagelIEpñkxagsþaMéntarag.

]TahrN_11³ kMnt;sésrEdkcaM)ac;sMrab;ssr short tied column dUcbgðajenAkñúgrUbTI 18 a

edIm,IRTnUvbnÞúkemKuN kN2150 nigm:Um:g;emKuN mkN.440 . ssrmanTTwg mm350 nigbeNþaysrub mmh 500= . eRbI MPaf c 28' = / MPaf y 400= . dMeNaHRsay³

1> cMNakp©it mmP

Me

u

u 65.2042150440

===

yk mmd 44060500 =−= mmh 380120500 =−=γ enaH 76.0

500380

==γ 2> eday de <= 65.204 sn μt;famuxkat;)ak;edaykarsgát; compression-controlled section

CamYynwg 65.0=φ

T.Chhay NPIC


T.Chhay NPIC


kNPn 7.330765.0

2150==

nig mkNM n .9.67665.0

440==

675.050035028

107.3307'

3=

××⋅

==gc

nn Af

PK

276.0500

65.204675.0 =⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛=

heKR nn

3> BItaragkñúgrUbTI16 sMrab; 7.0=γ / 048.0=ρ dUcKñasMrab; 8.0=γ / 043.0=ρ eday interpolation sMrab; 76.0=γ / 045.0=ρ

27875350500045.0 mmAs =××= eRbI 3210DB ( )248.8042 mmAs = / R)aMedImenAtamRCugxøI. eRbIEdkkg mmDB 350@10 ¬rUbTI18 a¦

]TahrN_12³ eRbItaragedIm,IkMNt;bnÞúkersIusþg; nPφ rbs;ssrxøIdUcbgðajkñúgrUbTI 18 b EdlGnuvtþ

enAcMgaycMNakp©it mme 305= . eRbI MPaf c 35' = nig MPaf y 400= . dMeNaHRsay³ A. lkçN³rbs;muxkat;³ mmH 600= / mmh 480120600 =−=γ ¬cMgayrvagEdlTaj

nigEdk sgát;¦. 8.0600480

==γ ehIy 03.03506004

3282

=×

××

=

π

ρ B. eday de < / sn μt;vaCamuxkat; compression-controlled section.



yk 002.0=tε / 0.1=y

sff ehIy 65.0=φ BItaragkñúgrUbTI 17 eKTTYl)an

3506003536.0

××== n

nP

K dUcenH kNPn 2646=

C. EpÞógpÞat;karsn μt;sMrab;muxkat; compression controlled³ sMrab; 36.0=nK

183.0==heKR nn

BIdüaRkameyIgTTYl)an 03.0019.0 <=ρ / dUcenH kNPn 2646> ¬edIm,I)an 03.0=ρ ¦ D. karsakl,gelIkTI2³ yk 0015.0=tε / MPafs 3002000000015.0 =×=

75.0400300

==y

sff 03.0=ρ 43.0=nK

kNPn 5.31603506003543.0 =×××= E. EpÞógpÞat;karsn μt;³ sMrab; 43.0=nK / 219.0==

heKR nn

BItarag 03.0=ρ dUcGVIEdleGay dUcenH kNPn 5.3160=

kNPn 3.20545.316065.0 =×=φ nig mkNM n .6.626=φ tamkarviPaK kNPn 2027=φ ¬mantMélRbEhlKñanwgkarKNnaedayeRbItarag¦.

13> karKNnassreRkambnÞúkcakp©it Design of Columns Under Eccentric Loading karKNnassrmanlkçN³sμ úKsμajCagkarviPaKssr edaysarEtbnÞúkxageRkA uP nigm:Um:g; uM

Casm μtikmμ ehIyeKRtUvkarkMNt;nUvGBaØtiCaeRcIndUcCa b / h / sA / sA' CamYynwgkarkMNt;rbs; ACI Code. vaCakarGnuvtþn_TueTAedaysnμt;dMbUgnUvmuxkat;ssr ehIykMnt;brimaNmuxkat;EdkRtUvkar. RbsinebIGñk KNnaRtUvkardUrmuxkat;EdkKNna enaHmuxkat;ssrk¾RtUv)anEkERbeTAtamenaHEdr. ]TahrN_xageRkam bgðajBIkarKNnassr.

13>1 KNnassrsMrab;kar)ak;edaykarsgát; Design of Column for Compression Failure

sMrab; compression failure eKniymeRbI ss AA '= sMrab;muxkat;ctuekaN. cMNakp©it u

uP

Me = .

edayQrenAelItMélrbs; e eKman2krNIRtUv)anbegáIteLIg 1> enAeBlEdl mme 100≤ krNIcMNakp©itGb,brmaGacekItman EdlGaceKNnaedayeRbIrUbmnþ

T.Chhay NPIC


( )[ ]cystgcnu ffAAfKPP '85.0'85.0 −+== φφ Edl 65.0=φ nig 80.0=K sMrab;ssrEdl man dkkgdac;² nig 70.0=φ nig 85.0=K sMrab;ssrEdlmanEdkvNÐ½ ¬sUmemIl]TahrN_kñúg emeronssrrgkMlaMgcMGkS½¦. sMrab;krNIepSgBIenH GñkKNnaGacGnuvtþtamkrNITI2. krNIbnÞúk enHRbRBwtþeTAsMrab;ssrGKarCan;eRkaménGKareRcInCan; Edlm:Um:g; uM )anmkBIRbBn§½mYyCan; nig

uP )anmkBIbnÞúkRKb;Can;EdlmanGMeBIenABIelIva. 2> tMbn; compression failure KWtMbn;EdlsßitenAcenøaHGkS½QreTAbnÞat; balanced load dUcbgðaj kñúgrUbTI 3 nigrUbTI11. kñúgkrNIenH muxkat; bh GacRtUv)ansn μt; ehIybnÞab;mkmuxkat;EdkRtUv)an KNnasMrab; uP nig uM EdleGay. CMhanénkarKNnaRtUv)ansegçbdUcxageRkam³

k> sn μt;muxkat;kaer b¤ctuekaN bh rYckMNt; d / 'd nig u

uPMe =

x> edaysn μt; ss AA '= KNna sA' BIsmIkar 5.0

)'(

'

18.13'

2 +−

++

=

dde

fA

dhebhfP ysc

n edayeRbI

TMhMmuxkat;Edl)ansn μt; nig 65.0=φ sMrab;ssrEdleRbIEdkkgFmμta. yk ss AA '= rYc eRCIserIsmuxkat;RKb;RKan;. kMNt;muxkat;BitR)akdEdleRbIsMrab; sA nig sA' . mü:agvij eToteKGaceRbIdüaRkam ACI. K> epÞógpÞat;fa %8'%1 ≤

+=≤

bhAA ss

gρ . RbsinebI gρ mantMéltUc kat;bnßymuxkat; sn μt; b:uEnþBRgIkmuxkat;RbsinebIeKcg;)anmuxkat;EdktUc. X> epÞógpÞat;PaBRKb;RKan;rbs;muxkat;cugeRkayedayKNna nPφ BIsmIkarsþaTic dUcBnül;kñúg]TahrN_xagedIm. un PP ≥φ . g> kMNt;EdkkgcaM)ac;.

rUbmnþRbhak;RbEhl approximate formula y:agsamBaØ sMrab;kMNt;muxkat;ssrdMbUg bh b¤PaK ryEdksrub total steel retio gρ KW

2bhKP cn = b¤ 2bhKPP cnu φφ == ¬-24¦ Edl cK mantMéldUcbgðajkñúgtaragTI2 nigbgðajkñúgrUbTI19 sMrab;Edk MPaf y 400= nig ss AA '= . xñatrbs; cK KW 3/ mkN . taragTI2 tMélrbs; cK ¬ MPaf y 400= ¦

cK ( )%gρ )28(' MPaf c )35(' MPaf c )42(' MPaf c 1% 24817 30246 35286 4% 37574 43003 48044



8% 54675 60103 65144

tMél cK RtUv)anbgðajkñúgtaragTI2 CatMélRbhak;RbEhl niggayRsYleRbI edaysar cK ekIn eLIgmþg 5429sMrab;karekIneLIgrbs; cf ' mþg 7 . sMrab;muxkat;dUcKña enAeBlEdlcMNakp©it

u

uPMe =

ekIneLIg nP fycuH dUcenH cK fycuH. dUcenH tMél cK sMEdgbnÞúk nP enAelIdüaRkamGnþrkm μcenøaH noP8.0 nig bP dUcbgðajkñúgrUbTI 3 nigTI 11.

Linear interpolation GacRtUv)aneRbI. ]TahrN_ 5.46124=cK sMrab; %6=gρ nig MPaf c 28' = . CMhankñúgkarKNnamuxkat;ssrGacRtUv)ansegçbdUcxageRkam³

1> sn μt;muxkat;dMbUgsMrab;muxkat;ssr bh 2> KNna ( )2bh

PK uc

φ=

3> kMNt; gρ BItaragTI 2 sMrab; cf ' EdleGay 4> kMNt;

2'

bhAA g

ssρ

== rYceRCIserIsEdkbBaÄr nigEdkkg. 5> kMNt; nPφ énmuxkat;cugeRkaytamsmIkarsþaTic ¬dMeNaHRsayCak;lak;¦. tMélén nPφ KYrEt

mantMélFMCagb¤es μI uP . RbsinebImindUecñaHeT EktMrUv bh b¤ gρ .

24000

29000

34000

39000

44000

49000

54000

59000

64000

69000

1 2 3 4 5 6 7 8ρ g (%)

K c ( kN/m3)

f'c=28MPaf'c=35MPaf'c=42MPa

rUbTI19 tMél cK nig gρ

T.Chhay NPIC


mü:agvijeTot RbsinebIeKcg;)anPaKryEdksrubCak;lak; ]TahrN_ %6=gρ bnÞab;mkGnuvtþdUc xageRkam³

1> sn μt; gρ dUcEdlTamTar nigbnÞab;mkKNna u

uPMe =

2> edayQrelI cf ' nig gρ EdleGay/ kMNt; cK BItaragTI2 3> KNna

c

uKPbhφ

=2 bnÞab;mkeRCIserIs b nig h . GnuvtþCMhan 4 nig 5 eLIgvij.

eKKYrEtepÞógpÞat;fa %8%1 ≤≤ gρ . dUcKña epÞógpÞat;fa c Edl)anmkBIkarKNnatamsþaTicmantMélFMCag

y

tb f

dc+

=600

600 sMrab; compression failure .

]TahrN_13³ kMNt;muxkat;EdkTaj nigmuxkat;Edksgát;sMrab;ssrEdleRbIEdkkgFmμtamanmuxkat; 600400× edIm,IRTbnÞúk kNPu 3470= nig mkNM u .530= . edayeRbI kNf c 28' = nig MPaf y 400= .

dMeNaHRsay³

1> KNna mmPMe

u

u 74.1523470530

=== . eyIgman mmh 600= yk mmd 550= nig mmd 50'=

edaysar mmde 67.36632

=< snμt;fa compression failure. 2> sn μt; ss AA '= . kMNt;tMéldMbUgrbs; sA' tamrUbmnþ

5.0)'(

'

18.13'

2 +−

++

=

dde

fA

dhebhfP ysc

n (-17)

sMrab; kNPP un 5.5338

65.03470

===φ

ss AmmA == 28.4271'



eRbIEdk 32DB 6=⇒ n edIm 25.4825326 mmDB = sMrab; sA nig sA' ¬rUbTI 20¦

3> %4600400

5.48252=

××

=gρ EdlvaRtUvEttUcCag 08.0 nig FMCag 01.0 4> epÞógpÞat;muxkat;edaysmIkarsþaTictamCMhanénkarKNnakñúg]TahrN_TI4 eKTTYl)an mma 18.430= / mmc 09.506= / kNCc 32.4095= kNCs 35.1815)2885.0400(5.4825 =×−= MPa

ccdfs 06.52

09.50609.506550600600 =⎟

⎠⎞

⎜⎝⎛ −

=⎟⎠⎞

⎜⎝⎛ −

=

kNfAT ss 21.25106.525.4825 =×== kNkNTCCP scn 5.53385.5659 >=−+=

cMNaMfa RbsinebI un PP <φ cUrdMeLIg sA nig sA' rYceFVIkarKNnaeLIgvij. 5> epÞógpÞat; nP edayeRbIsmIkar ⎥

⎦

⎤⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ −= )'(

2'1 ddCadCe

P scn Edl 2

' hdee −+=

eyIgTTYl)an kNPn 5659= 6> sMrab; muxkat; balanced section

mmdf

c ty

b 3305501000600

600600

==⎟⎟⎠

⎞⎜⎜⎝

⎛

+=

edaysarEt mmcmmc b 33009.506 =>= vaCakrNI compression failure dUckarsnμt;. 7> edayeRbIEdkkgmanGgát;p©it mm10

KMlatEdkkg

400400512480

min400

32161048

min1648

min =⎪⎩

⎪⎨

⎧=

⎪⎩

⎪⎨

⎧××

=⎪⎩

⎪⎨

⎧

bdφ

dUcenHeRbIEdkkg 400@10DB . ]TahrN_14³ eFVI]TahrN_TI13 eLIgvijedayeRbIsmIkar ¬-24¦ dMeNaHRsay³ 1> muxkat;ssrEdleGay 600400× 2> kMNt; cK BIsmIkar ¬-24¦ 3> 322 37073

6.04.065.03470

mkN

bhPK u

c =××

==φ

T.Chhay NPIC


4> BItaragTI 2 b¤rUbTI19 sMrab; 337073mmkNKc = MPaf c 28' = eday interpolation

eyIgTTYl)an %88.3248173757414)2481737073(1 =

−−

−+=gρ 5> KNna ( )( ) 246562/6004000388.02/' mmbhAA ss ==== ρ

eRbIEdk 32DB 6=⇒ n edIm 6> 25.4825326 mmDB = 7> kMNt; uPφ edayeFVItamCMhan 4-7 sMrab;]TahrN_TI13. kNPkNP nn 5.53385659 =>=

dUcenHmuxkat;EdkRKb;RKan; 8> RbsinebImuxkat;minRKb;RKan; b¤ nn PP <φ tMeLIgmuxkat; sA nig sA' rYceFVIkarepÞógpÞat;eLIgvij

edIm,ITTYl)antMélEk,r. ]TahrN_15³ KNnamuxkat;ssrctuekaNEkgedIm,IRTbnÞúk kNPu 3150= nig mkNM u .630=

CamYynwgPaKryEdksrub gρ RbEhl %4 . eRbI MPaf c 28' = / MPaf y 400= nig mmb 450= . dMeNaHRsay³ 1> KNna m

PMe

u

u 2.03150630

=== . sn μt; compression failure ( 65.0=φ ) ¬RtUvepÞógpÞat;enA

eBleRkay¦ ehIy ss AA '= 2> sMrab; %4=ρ nig MPaf c 28' = enaH 37574=cK ¬taragTI2¦ 3> KNna 2bh BIsmIkar (-24): 2bhKP cu φ= rW ( )( ) 245.03757465.03150 h= dUcenH

mh 535.0= dUcenHyk mmh 550= . KNna ( ) 24950

255045004.0' mmAA ss =

×== . eRCIserIs 365DB

)4.5089( 2mmAs = dUcbgðajkñúgrUbTI 21. eRbIEdkkg 450@12DB . 4> epÞógpÞat; muxkat;cugeRkayedaykarviPaK RsedogKñanwg]TahrN_TI4 eyIgTTYl)an

mma 8.327= / mmc 65.385= / kNabfC cc 7.3510'85.0 == / MPaf s 400' = / kNffAC cyss 6.1914)'85.0(' =−= / MPa

ccdfs 79.146600 =⎟⎠⎞

⎜⎝⎛ −

= / nig kNT 747=

dUcenH kNTCCP scn 3.4678=−+= ehIy kNkNPP nu 31503041 <==φ edaysarmuxkat;minRKb;RKan; eyIgRtUvtMeLIgmuxkat;Edk b¤muxkat;ebtug rYceFVIkarepÞógpÞat;eLIg vij. ¬yk mmh 600= ¦ rUbTI21.

5> sMrab;muxkat; balanced section



mmcmmdc tb 32.436318400600

600=<=⎟

⎠⎞

⎜⎝⎛

+= ¬ mmd 530= ¦

dUcenH vaCa compression failure dUckarsnμt;.

13>2 KNnassrsMrab;kar)ak;edaykarTaj Design of Column for tension Failure

Kar)ak;edaykarTaj tension failure ekItmanenAeBl un PP < b¤k¾cMNakp©it bee > dUckarBnül; enAkñúgEpñkTI7. kñúgkarKNnassr uP nig uM RtUv)aneGay ehIyvaTamTarnUvkarkMNt;muxkat;ssr nigmux kat;Edk. vaGacRtUv)ansn μt; ¬dUckarENnaM¦ favaCa tension control enAeBlNa

⎩⎨⎧

≥<

>mmhmmh

PM

u

u

600600600530

sMrab; sMrab;

. kñúgkrNIenH muxkat;ssrGacRtUv)ansnμt; ehIybnÞab;mk sA nig

sA' RtUv)ankMNt;. düaRkam ACI GacRtUv)aneRbIedIm,IKNna gρ sMrab;muxkat;EdleGayCamYynwg sA = sA' . cMNaMfa φ ERbRbYlcenøaH )7.0(65.0 nig 9.0 dUckarBnül;kñúgEpñkTI 4.

enAeBl tension controls EdkTaj yields b:uEnþEdksgát;Gac yields nigmin yields. karsn μt;dMbUg ys ff =' nig ss AA '= . smIkar (-16) ¬kñúgEpñkTI 6¦ GacRtUv)aneRbIedIm,IKNnatMéldMbUgrbs; sA nig

sA' .

( )'22'

ddf

ahePAA

y

n

ss −

⎟⎠⎞

⎜⎝⎛ +−

== (-16)

edaysar a minRtUv)andwgenAeLIy snμt; da 4.0= nig nu PP φ= bnÞab;mk

)'()2.05.0('

ddfdhePAA

y

uss −

+−==

φ (-25)

muxkat;ssrcugeRkayKYrRtUv)anepÞógpÞat;edaysmIkarsþaTicedIm,Ibgðajfa un PP ≥φ . ]TahrN_ TI16 Bnül;BIviFIsaRsþkñúgkarKNnaenH.

T.Chhay NPIC


enAeBlbnÞúk uP mantMéltUcNas;ebIeRbobeFobCamYynwgm:Um:g; uM TMhMrbs;muxkat;GacRtUv)ankM Nt;edayeRbIEt uM EtmYy)anehIy edaysnμt;fa 0=uP . muxkat;cugeRkayKYrRtUv)anepÞógpÞat;eday smIkarsþaTic. krNIenHekIteLIgsMrab;eRKagGKarmYyCan; b¤BIrCan; EdlGKarenaHRtUv)aneKeRbIsMrab;eFVICa saltaMgBiBN’ b¤k¾GKarTaMgLayNaEdlmanlkçN³dUcKñaenaH. sMrab;krNIenH sA' GacRtUv)ansnμt;eGay mantMéltUcCag sA . karKNnay:aglMGitsMrab;saltaMgBiBN’kMBs;mYyCan;Edlmansnøak;BIrRtUv)anBnül; enAkñúgCMBUkTI 16 FñwmCab; nigeRKag.

]TahrN_16³ kMNt;sésrEdkcaM)ac;sMrab;ssrragctuekaNEkg 560400× EdlmanEdkkg FmμtaRTbnÞúk kNPu 1140= nig mkNM u .850= . eRbI MPaf c 28' = nig MPaf y 400=

dMeNaHRsay³

1> KNna mP

Me

u

u 7456.01140850

=== . yk mmd 50060560 =−= . edaysar

mmmmP

M

u

u 5306.745 >= b¤edaysar de > sn μt;fassrenH)ak;edaykrNI tension failure

enaH 9.0=φ ¬RtUvepÞógpÞat;enAeBleRkay¦. 2> sn μt; ss AA '= nig ys ff =' nigeRbIsmIkar (-25) edIm,IkMnt; sA nig sA' . eday kNPu 1140= /

mme 6.745= / mmh 560= / mmd 500= / nig mmd 60'= ( )

( )2

3

71.4070605004009.0

5002.05605.06.745101140' mmAA ss =−×

×+×−⋅==

eRbI 325DB ( )224.4021 mm sMrab; sA nig sA' . ¬rUbTI22¦ 3> epÞógpÞat; ( ) 0359.0

56040024.40212

=×

=gρ EdltUcCag 08.0 nigFMCag 01.0 .

4> epÞógpÞat;kareRCIserIsmuxkat;edaysmIkarsþaTic EdlkarKNnaRsedogKñanwg]TahrN_TI3



a. kMNt;tMélrbs; a edayeRbIsmIkarTUeTA 02 =++ CBaAa CamYynwg mmhdee 6.965

2' =−+= / 4760'425.0 == bfA c / ( ) 4432512'2 =−= deAB /

( )( ) 758040793''''85.0' −=−+−−= efAddeffAC yscys . eKTTYl)an mma 62.147= nig mmac 67.17385.0/ == .

b. epÞógpÞat; sf ' ³ MPac

dcf s 71.39267.173

6067.173600'600' =⎟⎠⎞

⎜⎝⎛ −

=⎟⎠⎞

⎜⎝⎛ −

=

c. KNna a eLIgvij ( )( ) 3.773454123'''''85.0'' −=−+−−= efAddeffAC sscss

eKTTYl)an mma 25.150= nig mmc 77.176=

d. epÞógpÞat; sf ' ³ MPac

dcf s 34.39677.176

6077.176600'600' =⎟⎠⎞

⎜⎝⎛ −

=⎟⎠⎞

⎜⎝⎛ −

=

KNna kNCc 38.143040025.1502885.0 =×××=

kNffAC csss 07.1498)2885.034.396(24.4021)'85.0'(' =×−=−=

kNfAT ys 5.160840024.4021 =×==

e. kNTCCP scn 95.1319=−+=

5> KNna φ ³ 0055.0003.0 =⎟⎠⎞

⎜⎝⎛ −

=c

cdttε edaysarEt 005.00055.0 >=tε enaH 9.0=φ

6> kNkNPn 114095.118795.13199.0 >=×=φ muxkat;RKb;RKan; 14> karBt;tamBIrTis Biaxial Bending

karviPaK nigkarKNnassreRkamGMeBIbnÞúkcakp©itEdl)anBiPakSaknøgmk CakrNIkarBt;mYyTis. enHmann½yfa nP GnuvtþenAelIGkS½ y ¬rUbTI23¦ begáIt)anbnSMénkMlaMgcMGkS½ nP nigm:Um:g;Bt;CMuvijGkS½ x esμ Inwg ynnx ePM = b¤ nP GnuvtþenAelIGkS½ x ¬rUbTI24¦ CamYynwgcMNakp©it xe begáIt)anbnSMénkMlaMgcM GkS½ nP nigm:Um:g;Bt; xnny ePM = .

T.Chhay NPIC


RbsinebIbnÞúk nP GnuvtþenAkEnøgNamYyEdlmancMgay ye BIGkS½ x nigcMgay xe BIGkS½ y enAeBl enaHmuxkat;ssrnwgrgnUvbnSMbnÞúkEdlman bnÞúkcMp©it nP m:Um:g;Bt;CMuvijGkS½ x KW ynnx ePM = nigm:Um:g;Bt; CMuvijGkS½ y KW xnny ePM = ¬rUbTI25¦.kñúgkrNIenHmuxkat;ssrrgnUvkarBt;tamBIrTis. vaminEmngay RsYleTenAeBlEdleKeRbIeKalkarN_sþaTicedIm,IviPaK nigKNnamuxkat;ssrsMrab;krNIenH. GkS½Nwtsßit enAelIRCugEdlkat;GkS½ x nigGkS½ y ehIyeKRtUvkarkarKNnad¾EvgedIm,IkMNt;TItaMgrbs;GkS½NWt bMErbMrYl rageFob strain RkLaépÞebtugrgkarsgát; nigkMlaMgkñúgrYmTaMgcMnucEdlvaGnuvtþ. dUcenH eKcaM)ac;RtUvbegáIt nUvdMeNaHRsayd¾mansamBaØmYyedIm,IKNnanUvlTæPaBRTRTg;rbs;ssrbnÞúkcMp©itnig m:Um:g;Bt;BIrTis. rUbmnþ Edl)anbegáIteLIgsMrab;ssrrgm:Um:g;BIrTis Tak;TgeTAnwgersIusþg;rbs;vaTb;nwgkarBt;CMuvijGkS½emnImYy².

rUbTI26 bgðajBIExSekagGnþrGMeBIbnÞúk-m:Um:g;kñúglMhr ¬3TMhM¦sMrab;ersIusþg;m:Um:g;BirTisrbs;ssrrg

kMlaMgcMGkS½. es‘rIénExSekagGnþrGMeBIbnÞúk-m:Um:g;mYyTis EdlmankaMKUsBIGkS½ nP )anbegáItCaépÞénExSekag GnþrGMeBIbnÞúk-m:Um:g;BIrTis. ExSekag oxM bgðajnUvExSekagGnþrGMeBIsMrab;m:Umg;mYyTisCMuvijGkS½ x nig ExS



ekag oyM bgðajnUvExSekagGnþrGMeBIsMrab;m:Umg;mYyTisCMuvijGkS½ y . bøg;enARtg;bnÞúkcMGkS½efr nP bgðajBI ExSvNÐ½énm:Um:g;Bt; nM CMuvijGkS½epSg².

ssrEdlmanmuxkat;epSg²RtUv)aneRbIR)as;edIm,ITb;Tl;nwgbnÞúkcMGkS½ nigmU:m:g;Bt;BIrTis. muxkat; ssrmUl kaer b¤ctuekaNEkgGacRtUv)aneKeRbIR)as;CamYynwglTæPaBTb;nwgm:Um:g;CMuvijGkS½ x nigGkS½ y Edl mantMélesμ IKña b¤minesμIKña.

15> ssrmUlCamYynwgkarrayEdkesμIeRkamm:Um:g;Bt;BIrTis Circular Columns With

Uniform reinforcement Under Biaxial Bending ssrmUlCamYynwgkarrayEdkEdlmanlkçN³ÉksNæan manlTæPaBTb;nwgm:Um:g;dUcKñaRKb;Tis. Rb

sinssrmUlRbQmnwgm:Um:g;BIrTisCMuvijGkS½ x nigGkS½ y enaHm:Um:g;mYyTissmmUl uM GacRtUv)anKNna edayeRbIsmIkarxageRkam³

( ) ( ) ePMMM uuyuxu ⋅=+= 22 (-26)

nig ( ) ( )u

uyx P

Meee =+= 22 (-27)

Edl yuux ePM = m:Um:g;emKuNCMuvijGkS½ x xuuy ePM = m:Um:g;emKuNCMuvijGkS½ y

ePM uu = m:Um:g;emKuNmYyTissmmUlénmuxkat;EdlekIteday uxM nig uyM sMrab;ssrmUl eKcaM)ac;eRbIEdky:agtic6edIm ehIyEdkTaMgenaHRtUv)anBRgayesμ IenAkñúgmuxkat;enaH. ]TahrN_17³ ssrmUl

T.Chhay NPIC


kMNt;lTæPaBRTbnÞúk nP rbs;ssrragmUlEdlmanGgát;p©it mm500 CamYyEdk 3210DB enAeBl Edl mmex 100= nig mmey 150= . eRbI MPaf c 28' = nig MPaf y 400= .

dMeNaHRsay³ 1> KNnacMNakp©itEdlsmmUleTAnwgkareFVIGMeBItammYyTisedayeRbIrUbmnþ (-27)

mmeee yx 28.180150100 2222 =+=+=

2> kMNt;lTæPaBRTbnÞúkrbs;ssredayQrelIcMNakp©it mme 28.180= . edaHRsaydUc]TahrN_ TI 9 eKTTYl)an³

mmd 7.430= mma 75.250= mmc 295= ¬edaysakl,g¦

kNCc 49.2345= kNCs 35.1188=∑ kNT 09.662=∑ kNTCCP scn 75.2871∑ ∑ =−+=

3> sMrab;lkçxNÐ balanced condition

mmdc tb 42.2587.4301000600

400600600

==+

=

bcmmc >= 295 EdlCakrNI)ak;edaykarsgát; compression failure

16> ssrmuxkat;kaer nigctuekaNeRkamm:Um:g;Bt;BIrTis Square and Rectangular Columns under Biaxial Bending 16>1 viFI; Bresler Reciprocal Method

ssrkaer b¤ctuekaNrgnUvm:Um:g;Bt;CMuvijGkS½emrbs;vamantMélminesμ IKña RtUvkarbrimaNEdkxusKña sMrab;TisedAmYy². viFIsaRsþRbEhlsMrab;viPaKmuxkat;EbbenHRtUv)anbegáIteLIgedayelak Boris Bresler

ehIyRtUv)aneKeGayeQ μaHfa viFI Bresler Reciprocal Method. tamry³viFIenH lTæPaBRTbnÞúkrbs;ssr eRkamGMeBIm:Um:g;Bt;2TisGacRtUv)anKNnaedayeRbIsmIkarxageRkam³

uouyuxu PPPP1111

−+= (-28)

b¤ nonynxn PPPP1111

−+= (-29)

Edl uP = lTæPaBRTbnÞúkemKuNeRkamGMeBIm:Um:g;BIrTis uxP = lTæPaBRTbnÞúkemKuNtamGkS½mYyenAeBlbnÞúkeFVIGMeBIenAcMNakp©it ye nig 0=xe uyP = lTæPaBRTbnÞúkemKuNtamGkS½mYyenAeBlbnÞúkeFVIGMeBIenAcMNakp©it xe nig 0=ye uoP = bnÞúkcMp©itemKuNenAeBlEdl 0== xy ee

φu

nP

P = φux

nxP

P = φuy

nyP

P = φuo

noP

P =



lTæPaBRTbnÞúktamTismYy nxP / nyP / noP GacRtUv)anKNnaedayeRbIsmIkarnigviFIsaRsþEdl)an ENnaMBIxagmuxkñúgemeronenH. bnÞab;mk vaRtUv)anCMnYseTAkñúgsmIkarTI (-29) edIm,IKNna nP .

smIkar Bresler mann½ysMrab;RKb;krNITaMgGs;enAeBlNaEdl non PP 10.0≥ . enAeBlEdl non PP 10.0< kMlaMgtamGkS½GacRtUvecal ehIymuxkat;GacRtUv)anKNna dUcGgát;rgnUvm:Um:g;Bt;BIrTissuTæ

edayeRbIsmIkarxageRkam³ 0.1≤+

y

uy

x

uxMM

MM (-30)

b¤ 0.1≤+oy

ny

ox

nxMM

MM (-31)

Edl yuux ePM = = m:Um:g;KNnaCMuvijGkS½ x xuuy ePM = = m:Um:g;KNnaCMuvijGkS½ y xM nig yM = lTæPaBTb;m:Um:g;CMuvijGkS½ x nigGkS½ y

φ

uxnx

MM =

φuy

nyM

M = φ

xox

MM =

φy

oyM

M =

smIkar Bresler minRtUv)anENnaMeGayeRbIenAeBlEdlmuxkat;rgnUvbnÞúkTajtamGkS½eT. 16>2 viFExSvNÐ½bnÞúk Bresler Bresler Load Contour Method

sMrab;viFIenH épÞ)ak; failure surface Edl)anbgðajenAkñúgrUbTI 26 RtUv)ankat;edaybøg;éntMélefr nP pþl;nUvtMélénmU:m:g; nxM nig nyM . CaTUeTA rUbmnþsMrab;viFIenHKW³

0.121

=⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛αα

oy

ny

ox

nx

MM

MM ` (-32)

elak Bresler )anbgðajfa niTsSnþ α GacmantMéldUcKñasMrab;tYrTaMgBIrénsmIkarenH ( )21 αα = . mü:agvijeTot Kat;)anbBa¢ak;fatMél α ERbRbYlcenøaH 15.1 nig 55.1 ehIyvaGacRtUv)ansnμt;esμ I 50.1 sMrab; ssrmuxkat;ctuekaNEkg. sMrab;muxkat;kaer α ERbRbYlBI 5.1 eTA 2 ehIytMélmFüm 75.1=α RtUv)aneK eRbIsMrab;karKNnaGnuvtþn_. enAeBlEdsésEdkRtUv)anBRgaymanlkçN³dUcKñasMrab;muxTaMgbYnrbs;ssr kaer enaHeKGacsn μt;yk 5.1=α .

0.15.15.1

=⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛

oy

ny

ox

nx

MM

MM (-33)

bTdæanGg;eKøs British Code )ansn μt; 1.67 1.33; 1.0;=α nig 0.2 enAeBlEdlpleFob uo

u

PP1.1

esμ Inwg 0.6 0.4; 0.2; nig 8.0 erogKña.

T.Chhay NPIC


17> viFIExSvNÐ½bnÞúk Parme Parme Load Contour Method

viFIExSvNÐ½bnÞúk load contour methode EdlesñIeLIgeday smaKmn_sIum:g;Br½ELn Porland Cement

Association (PCA) CaviFImYyEdlbegáIteLIgedayeRbIviFIExSvNÐ½bnÞúk Bresler. enAkñúgviFIenH EdleKGac ehAmü:ageTotfa Parme load contour methode cMnuc B enAelIExSvNÐ½bnÞúk ¬énbøg;edkenARtg;bnÞúkefr nP dUcbgðajenAkñúgrUbTI 26¦ RtUv)ankMNt;y:agdUcenHfa pleFobénlTæPaBTb;m:Um:g;BIrTis nxM nig nyM esμ I nwgpleFobénlTæPaBTb;m:Um:g;mYyTis oxM nig oyM .

oy

ox

ny

nx

MM

MM

= b¤ β==oy

ny

ox

nx

MM

MM

tMél β EdlmanenAkñúgrUbTI 27 bgðajnUvEpñkefrEdllTæPaBTb;m:Um:g;tamTisnImYy²GacRtUv)an GnuBaØatieGayGnuvtþn_mkelImuxkat;ssrkñúgeBltMNalKña.

sMrab;karKNnaGnuvtþn_ ExSvNÐ½bnÞúk load contour Edl)anbgðajenAkñúgrUbTI27 GacRtUveRbIedIm,I

KNnaedaykarRbhak;RbEhledayeRbIbnÞat;Rtg; AB nig BC . CMerl slope rbs;bnÞat; AB KW ββ /)1( − nigCMerl slope rbsbnÞat; BC KW )1/( ββ − . dUcenHenAeBl

ox

nx

oy

ny

MM

MM

> enaH 11=⎟⎟

⎠

⎞⎜⎜⎝

⎛ −+

ββ

ox

nx

oy

ny

MM

MM (-34)

ehIyenAeBl ox

nx

oy

ny

MM

MM

< enaH 11=⎟⎟

⎠

⎞⎜⎜⎝

⎛ −+

ββ

oy

ny

ox

nx

MM

MM (-35)

tMélBitR)akdrbs; β GaRs½yeTAnwgpleFob o

n

PP sMPar³ niglkçN³énmuxkat;. sMrab;ssrEdl

RTnUvbnÞúkRsal β nwgERbRbYlBI 55.0 eTA 7.0 . tMélmFüm 65.0=β GacRtUv)aneRbIsMrab;karKNna.



enAeBlEdlsésEdkRtUv)anBRgaymanlkçN³dUcKñaRKb;épÞTaMgbYnrbs;muxkat;ctuekaN enaHpl eFob

oy

ox

MM mantMélRbhak;RbEhlnwg

hb Edl b nig h CaTTwg nigkMBs;srubrbs;muxkat;ctuekaNerogKña.

edayCMnYspleFobenHeTAkñúgsmIkarTI (-34) nig (-35) eKTTYl)an

oynxny MhbMM ≈⎟⎟

⎠

⎞⎜⎜⎝

⎛ −⎟⎠⎞

⎜⎝⎛+

ββ1 (-36)

oxnynx MbhMM ≈⎟⎟

⎠

⎞⎜⎜⎝

⎛ −⎟⎠⎞

⎜⎝⎛+

ββ1 (-37)

sMrab; 65.0=β nig 5.1=bh nxnyoy MMM 36.0+≈ (-38)

nynxox MMM 8.0+≈ (-39) BIkarbgðajenH eyIgeXIjfasmIkars μúKsμajEdlmanlkçN³pÞal;sMrab;KNnassreRkambnÞúkcM GkS½ nigm:Um:g;BIrTisminGaceFVIeTA)aneLIy. dUcenHGñkKNnaKYrmanbTBiesaFn_RKb;RKan;edIm,IsμannUvmuxkat; dMbUgedayeRbInUvtMél nP / nxM nig nyM CamYynigsmIkarsMrab;mYyTis nigbnÞab;mkepÞógpÞat;PaBRKb;RKan; rbs;muxkat;edayeRbIsmIkarsMrab;m:Um:g;BIrTis b¤edayeRbIkMuBüÚT½r.

]TahrN_18³ ssrxøIEdleRbIEdkkgFm μtamanmuxkat; 600400× CamYynwg 328DB BRgaydUc bgðajkñúgrUbTI 28. kMNt;bnÞúkKNna design load nPφ enAelImuxkat; RbsinebIvaeFVIGMeBIenA mmex 205= nig mmey 305= . eRbI MPaf c 35' = / MPaf y 400= nig smIkar Bresler Reciprocal equation.

dMeNaHRsay³ 1> kMNt;lTæPaBRTbnÞúkmYyTis nxP tamGkS½ x enAeBl mmey 305= . kñúgkrNIenH mmb 400= nig

mmh 600= / mmd 540= / mmd 60'= nig 274.2412' mmAA ss == . dMeNaHRsayGaceFVIeTAtamCMhandUckñúg]TahrN_TI 2 nigTI4sMrab;lkçxNÐmuxkat; balanced

condition nigmuxkat; compression-control condition. a. sMrab; balanced condition

mmdf

cy

b 324540400600

600600

600=⎟

⎠⎞

⎜⎝⎛

+=⎟

⎟⎠

⎞⎜⎜⎝

⎛

+=

mmab 2.2593248.0 =×= ¬ 8.01 =β enAeBl MPaf c 35' = ¦ kNabfC cc 48.3084'85.0 ==

MPaf s 89.488324

60324600' =⎟⎠⎞

⎜⎝⎛ −

= dUcenH MPaff ys 400' ==

kNffAC cyss 32.893)'85.0(' =−= kNfAT ys 1.965== kNTCCP scbx 7.3012=−+=

T.Chhay NPIC


kNPP bxbx 25.19587.301265.065.0 =×==φ ¬ 65.0=φ sMrab; 002.0=tε ¦ b. sMrab; mmdmmey 540305 =<= / sn μt;famuxkat;sßitkñúglkçxNÐ compression failure ehIy

GnuvtþtamCMhankñúg]TahrN_TI4 edIm,ITTYl)an mma 69.265= nig mmac 1.3328.0==

mmcb 324=> . dUcenH muxkat;Camuxkat; compression control. epÞógpÞat; ys fMPa

cdcf >=⎟⎠⎞

⎜⎝⎛ −

= 60.491'600' dUcenH eyIgyk MPaff ys 400' ==

epÞógpÞat; ys fMPac

cdf <=⎟⎠⎞

⎜⎝⎛ −

= 59.375600

KNnakMlaMg kNabfC cc 71.3161'85.0 == kNffAC cyss 32.893)'85.0(' =−= kNfAT ss 2.906=⋅= bxscnx PkNTCCP >=−+= 83.3148 dUcenHvaCakrNI compression

failure dUckarsnñidæan. 002.000188.0003.0 <=⋅⎟

⎠⎞

⎜⎝⎛ −

=c

cdtε 65.0=⇒φ

kNPnx 74.2046=φ c. Kitm:Um:g;Rtg; sA edayeRbIsmIkar (-11)

mmd 240"= mme 545'= ( ) kNddCadC

eP scnx 80.3148'

2'1

=⎥⎦

⎤⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ −=

2> kMNt;lTæPaBRTbnÞúkmYyTis nyP tamGkS½ y enAeBl mmex 205= . kñúgkrNIenH mmh 400= nig mmb 600= / mmd 340= / mmd 60'= nig 274.2412' mmAA ss == .

dMeNaHRsaynwgeFVIeLIgedayeRbIsmIkarsþaTic dUcesckþIBnül;kñúgCMhanxagelI. a. sMrab; balanced condition

mmdf

cy

b 204340400600

600600

600=⎟

⎠⎞

⎜⎝⎛

+=⎟

⎟⎠

⎞⎜⎜⎝

⎛

+=

mmab 2.1632048.0 =×= ¬ 8.01 =β enAeBl MPaf c 35' = ¦ kNabfC cc 12.2913'85.0 ==

MPaf s 5.423204

60204600' =⎟⎠⎞

⎜⎝⎛ −

= dUcenH MPaff ys 400' ==

kNffAC cyss 32.893)'85.0(' =−= kNfAT ys 1.965== kNTCCP scby 34.2841=−+=



kNPP byby 9.184634.284165.065.0 =×==φ ¬ 65.0=φ sMrab; 002.0=tε ¦ b. sMrab; mmdmmex 340205 =<= / sn μt;famuxkat;sßitkñúglkçxNÐ compression failure

ehIy GnuvtþtamCMhankñúg]TahrN_TI4 edIm,ITTYl)an mma 166= nig mmac 5.2078.0==

mmcb 204=> . dUcenH muxkat;Camuxkat; compression control. epÞógpÞat; ys fMPa

cdcf >=⎟⎠⎞

⎜⎝⎛ −

= 5.426'600' dUcenH eyIgyk MPaff ys 400' ==

epÞógpÞat; ys fMPac

cdf <=⎟⎠⎞

⎜⎝⎛ −

= 383600

KNnakMlaMg kNabfC cc 3.2963'85.0 == kNffAC cyss 32.893)'85.0(' =−= kNfAT ss 22.924=⋅= byscny PkNTCCP >=−+= 4.2932 dUcenHvaCakrNI compression

failure dUckarsnñidæan. 002.00019.0003.0 <=⋅⎟

⎠⎞

⎜⎝⎛ −

=c

cdtε 65.0=⇒φ

kNPny 1.1906=φ c. Kitm:Um:g;Rtg; sA edayeRbIsmIkar (-11)

mmd 140"= mme 345'= ( ) kNddCadC

eP scny 5.2932'

2'1

=⎥⎦

⎤⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ −=

T.Chhay NPIC


3> kMNt;bnÞúkcMp©it noP tamRTwsþI

)'85.0('85.0 cystgcno ffAAfP −+= ( ) ( ) kN2.95223585.040064346004003585.0 =×−+×××=

kNPno 4.6189=φ 4> edayeRbIsmIkar Bresler (-28) nigKuNCamYy 1000 eyIg)an

8516.04.6189

10001.1906

100074.2046

10001000=−+=

uP

kNPu 3.1174= nig kNPP un 6.1806

65.0==

cMNaM³ 1> smIkarRbEhl approximate equation b¤taragExSekag ACI GacRtUv)aneRbIedIm,IkMNt; nxP nig

nyP . edaysarEtsmIkar Bresler pþl;cUvdMeNaHRsayEdlmantMélRbhak;RbEhl enaHeKKYr EteRbIviFIsaRsþkñúgkaredaHRsayEdlmanlkçN³suRkitdUcEdl)anGnuvtþkñúg]TahrN_xagelIenH edIm,IkMNt; nxP nig nyP . dMeNaHRsayRbhak;RbEhlCaeRcIn pþl;nUvlTæplminsuRkit. eKGac rk)annUvkmμviFIkMuBÚüTr½EdlQrelIeKalkarN_smIkarsþaTic ehIyeKGaceRbIvaedIm,IepÞógpÞat;nUv lTæplrbs;eyIg.



2> enAkñúg]TahrN_TI 18 xagelI RkLaépÞEdkenARKb;RCugRtUv)aneRbIBIrdg edaymþgeRbIedIm,I KNna nxP nigmþgeToteRbIedIm,IKNna nyP . dMeNaHRsayEdlmanlkçN³snSMsMéc KweRbIEdk EdlsßitenARCugEtBak;kNþalsMrab;TismYy² Edl 25.1608' mmAA ss == enaHvanwgkat;bnßy tMélrbs; nxP nig nyP .

]TahrN_19³ kMNt;bnÞúkKNna nominal design load nP sMrab;ssrmuxkat;dUc]TahrN_TI18 edayeRbIviFIExSvNÐ½bnÞúk Parme. emIlrUbTI29. dMeNaHRsay³ 1> sn μt; 65.0=β . lTæPaBRTbnÞúktammYyTissMrab;TisedA x nig y RtUv)anKNnaenA

kñúg]TahrN_TI18. 2> kNPux 74.2046= kNPuy 1.1906= kNPnx 83.3148= kNPny 4.2932= lTæPaBTb;m:Um:g;rbs;muxkat;CMuvijGkS½ x mkNePM ynxox .4.960305.083.3148 =×== lTæPaBTb;m:Um:g;rbs;muxkat;CMuvijGkS½ x mkNePM xnyoy .14.601205.04.2932 =×== 3> eday nP Ca nominal design load enaH nominal design moment enAelImuxkat;CMuvijGkS½ x KW

nynnx PePM 305.0== ehIy nominal design moment enAelImuxkat;CMuvijGkS½ y KW

nxnny PePM 205.0== 4> RtYtBinitü >

oy

ny

MM

ox

nx

MM

4.960305.0

14.601250.0 nn PP

> b¤ nn PP 44 1017.31041.3 −− ⋅>⋅ dUcenHeRbIsmIkar (-34)

5> 165.0

65.014.960

305.014.601

250.0=⎟

⎠⎞

⎜⎝⎛ −

+ nn PP

eyIgTTYl)an kNPn 125.1953= kNPP nu 5.1269==φ ( )65.0=φ eyIgeXIjfa uP EdlKNnaedaysmIkar Parm FMCag uP EdlKNnaedaysmIkar Bresler

RbEhl %8 .

T.Chhay NPIC


18> smIkarépÞ)ak; Equation of failure surface

smIkarTUeTAsMrab;viPaK nigKNnassrebtugxøIEdkkgFmμtamuxkat;ctuekaNEkgRtUv)anesñIeLIg edayelak Hsu. smIkarRtUv)ansn μt;tMNageGayépÞ)ak; failure surface nigdüaRkamGnþrkm μ interaction

diagram rbs;ssrEdlrgnUvm:Um:g;BirTis nigbnÞúkcMGkS½ dUcbgðajkñúgrUbTI26. bnÞúkcMGkS½GacCakMlaMgsgát; b¤kMlaMgTaj.

0.15.15.1

=⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛−−

by

ny

bx

nx

bo

bn

MM

MM

PPPP (-40)

Edl =nP ersIusþg;Tb;kMlaMgtamGkS½ nominal axial strength ¬viC¢manenAeBlrgkarsgát; nigGviC¢ manenAeBlrgkarTaj¦ sMrab;cMNakp©itEdleGay.

=oP bnÞúktamGkS½ nominal axial load ¬viC¢manenAeBlrgkarsgát; nigGviC¢ manenAeBlrgkar Taj¦ sMrab;cMNakp©itsUnü.

=bP bnÞúksgát;tamGkS½ nominal axial compressive load enAkñúglkçxNÐ balanced strain. =nynx MM , m:Um:g;Bt; nominal bending moment CMuvijGkS½ x nig y erogKña. =bybx MM , m:Um:g;Bt; nominal balanced bending moment CMuvijGkS½ x nig y erogKña enAlkçxNÐ

balanced strain condition.



edIm,IeRbIsmIkar (-40) RKb;tYrTaMgGs;RtUvmansBaØaviC¢man. tMélrbs; oP KW yststgco fAAAfP +−= )('85.0 (-41)

bnÞúk nominal balanced load, bP / nigm:Um:g; nominal balanced moment, bbb ePM = Edl)aneGay enAkñúgsmIkar (-6) nig (-7) erogKña sMrab;muxkat;CamYynwgEdkrgEtkarTaj nigsgát;b:ueNÑaH. sMrab;muxkat; epSgeTot tMélenHGacTTYl)anedayeRbIeKalkarN_smIkarsþaTic.

cMNaMfa smIkarépÞ)ak; failure surface k¾GaceRbIsMrab;m:Um:g;mYyTisEdlbgðajenA kñúgdüaRkamGnþr- kmμ interaction diagram pgEdr. kñúgkrNIenH GgÁTIbInwgRtUvlb;ecalenAeBl 0=xe nigGgÁTIBIrnwgRtUvlb; calenAeBl 0=ye .

enAeBl 0=xe ¬manEtm:Um:g;Bt;CMuvijGkS½ x ¦

0.15.1

=⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛−−

bx

nx

bo

bn

MM

PPPP (-42)

¬vaCasmIkar (-18) EdlmanBIxagedIm¦ enAeBl 0=ye ¬manEtm:Um:g;Bt;CMuvijGkS½ y ¦

0.15.1

=⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛−−

by

ny

bo

bn

MM

PPPP (-43)

Gnuvtþn_smIkar (-42) eTAkñúg]TahrN_TI 2 nigTI 4. kNPb 8.1991= mkNM bx .8.732= mmey 254= nig kNPo 23.6275)4008

428()8

428350550(2785.0

22

=×××

+××

−×××=ππ

18.732

254.08.199123.6275

8.1991 5.1

=⎟⎠⎞

⎜⎝⎛+

−− nn PP

23.627502764.0 5.1 =+ nn PP kNPn 5.2603= EdlvamantMélRbEhlnwg nP EdlKNnaedaykarviPaK.

]TahrN_20³ kMNt;bnÞúkKNna nominal design load nP sMrab;ssrmuxkat;dUc]TahrN_TI18 edayeRbIsmIkarépÞ)ak; failure surface. dMeNaHRsay³ 1> KNna yststgco fAAAfP +−= )('85.0

kNPo 18.95224004328)8

432400600(3585.0

22

=+−××=ππ

2> KNna bP nig bM edayeRbIsmIkar (-8) nig (-9) tamGkS½ x nig y erogKña A. tamGkS½ x mmdt 540=

mmf

dcy

tbx 324

400600540600

600600

=+×

=+

=

mmabx 2.2593248.0 =×=

T.Chhay NPIC


MPac

dcf s 89.488'600' =⎟⎠⎞

⎜⎝⎛ −

= MPaf s 400' =

mmd x 240" = 274.2412' mmAA ss == yscysbxcbx fAffAbafP −−+= )'85.0(''85.0

kN7.301240074.2412)3585.0400(74.24124002.2593585.0 =×−×−+×××= xysxcysx

bxbxcbx dfAdddffAdadbafM ")"')('85.0('"

2'85.0 +−−−+⎟

⎠⎞

⎜⎝⎛ −−=

mkN.28.973= B. tamGkS½ y mmdt 340= mmd y 140" = 274.2412' mmAA ss ==

mmf

dcy

tby 204

400600340600

600600

=+×

=+

=

mmaby 2.1632048.0 =×= MPa

cdcf s 53.423'600' =⎟⎠⎞

⎜⎝⎛ −

= MPaf s 400' = kNPby 34.284140074.2412)3585.0400(74.24216002.1633585.0 =×−×−+×××=

yysycysyby

bycby dfAdddffAda

dhafM ")"')('85.0('"2

'85.0 +−−−+⎟⎟⎠

⎞⎜⎜⎝

⎛−−=

mkN.09.605= 3> KNnabnÞúk nominal balanced load bbP sMrab;m:Um:g;BirTis

672.0305205tan ====

yn

xn

nx

ny

ePeP

MM

α o9.33=α

α−Δ

=−

ob

obybx PPP

9090 oo

bo

P9.339090

34.28417.3012−Δ

=−

kNPb 8.106=Δ kNPPP bbybb 14.29488.10634.2841 =+=Δ+=

4> KNna nP BismIkarépÞ)ak; failure surface³ 0.1

09.605205.0

28.973305.0

14.294818.952214.2948 5.15.1

=⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛

−− nnn PPP

18.95220775.0 5.1 =+ nn PP edaykarsakl,g eyIgTTYl)an kNPn 3.2094= . edaysar bbn PP < vaCakrNI)ak;eday karTaj tension failure sMrab;karBt;BIrTis. dUcenHeyIgyk kNPo 18.9522−= edIm,IrkSaGgÁ TImYyviC¢man.

0.109.605

205.028.973

305.014.294818.9522

14.2948 5.15.1

=⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛

−−− nnn PPP

18.9522147.0 5.1 −=− nn PP



kNPn 5.1811= nig kNPu 5.1177= cMNaM³ ersIusþg;RTbnÞúk nPφ rbs;ssrmuxkat;ctueekaNEdl)anKNnaedayeRbIsmIkar Bresler

reciplocal equation (-18) viFI Parme method (-19) nigviFI Hsu method (20) edIm,I TTYl)an kNPn 3.1174=φ / kN5.1269 nig kN5.1177 erogKña. eyIgeXIjfa viFI Parme method

pþl;nUvtMélFMCageKsMrab;]TahrN_enH.

បេតុងពង្រឹងដោយដែក 11 xi-members-in-compression-and-bending

Documents

Transcript of បេតុងពង្រឹងដោយដែក 11 xi-members-in-compression-and-bending