1. T.Chhay NPIC
X. ssrrgkMlaMgcMG½kS
1> esckþIepþIm
ssrCaeRKOgbgÁúMd¾sMxan;sMrab;RTnUvbnÞúksgát;cG½kS ehIymanpleFobssrelIRCugxagEdltUcCag
M
eK FMCag 3 . sMrab;sMNg;ebtugGarem: Fñwm kMral nigssrRtUv)ancak;kñúgeBlEtmYy (monolithic) EdleFVI
eGaymanm:Um:g;xøH manGMeBIrelIssredaysarkarTb;enAxagcug. elIsBIenHeTot ssrsMrab;GaKareRcInCan;
kartMrg;ssrtamTisQr minGaceFVIeTA)antex©aHenaHeT EdlbegáIteGaymankMlaMgcakp©it edayeFobeTA
nwgG½kSssr. kMlaMgcakp©itbegáIteGaymanm:Um:g;elIssr. dUcenH ssrEdlrgnUvbnÞúktamG½kSsuT§minGac
ekItmanenAkñúgsMNg;ebtugGarem:eT. EteKGacsnμt;fa ssrrgkMlaMgcMG½kS kalNavamancMgaycakp©it e
tUc EdlmantMélRbEhl 0.1h . h CaCMerAsrubrbs;ssr nig e CacMgaycakp©itBIG½kSssr. edayebtug
manersIusþg;sgát;x<s; ehIyvaCasMPar³EdlmantMélminéfø dUcenHvaRtUv)aneKeRbIedIm,IKNnasMrab;eRKOgbgÁúM
rgkMlaMgsgát; edaymanlkçN³esdækic©x<s;.
2> RbePTssr
ssrRtUv)anEbgEckedayQrelIeKalkarN_epSg²dUcxageRkam³
i. QrelIeKalkarN_bnÞúk ssrcat;cMNat;fñak;dUcxageRkam³
+ ssrrgbnÞúkcMG½kS EdlbnÞúkRtUv)ansnμt;manGMeBIenAcMG½kSénmuxkat;ssr
+ ssrrgbnÞúkcakp©it EdlbnÞúkmanGMeBIenAcMgay e BIG½kSénmuxkat;ssr. cMgay e GacsßitenA
tamG½kS x b¤ G½kS y EdlbegáIt)anCam:Um:g;tamG½kS x b¤ G½kS y .
+ ssrrgbnÞúkcakp©itBIrTis EdlbnÞúkRtUv)anGnuvtþn_enAcMNucNamYyénmuxkat;ssr ehIyEdl
begáIt)anCam:Um:g;tamG½kS x nigG½kS y .
ii. QrelIeKalkarN_RbEvgssrcat;cMNat;fñak;dUcxageRkam³
+ ssrxøI Edlssr)ak;edaykarEbkebtug rWEdkeFVIkardl;cMnucyareRkamlT§PaBRTRTg;bnÞúkeBj
rbs;ssr
+ ssrEvg EdlkarPøat; nigPaBrlas;RtUv)anykmkBicarNa dUcenHlT§PaBRTRTg;bnÞúkrbs;ssr
RtUv)ankat;bnßyebIeFobnwgssrxøI
iii. QrelIeKalkarN_rUbragénmuxkat; muxkat;ssrGacmanragCa kaer ctuekaNEkg mUl >>>> b¤rUbrag
cg;)anNamYy.
iv. QrelIeKalkarN_EdkkgTTwg ssrRtUv)anEbgEckCa³
ssrrgkMlaMgcMG½kS 189

2. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa
+ ssrEdlmanEdkkgdac;²BIKña EdlmantYnaTIhMuBT§½EdkbBaÄrem. EdkkgCaTUeTAmanKMlatdUc²
KñaeBjmYykMBs;ssr.
+ ssrEdlmanEdkkgvNÐ EdlmantYnaTIhMuBT§½EdkbBaÄrem ehIyCYybegáInPaByWtrbs;ssrmun
eBl)ak;. CaTUeTA Edkkg nigEdkkgvNÐ RtUv)aneKeRbIedIm,IkarBarPaBrlas;rbs;ssr kugRtaMgEdk
bBaÄrEdlekItBIkarPøat; nigkarpÞúHEbkénebtugkarBarsésEdk.
v. QrelIeKalkarN_viPaKeRKag ssrCaEpñkmYyéneRKagEdlmanCnÞl;RbqaMgnwgkareRTtcMehog nig
CaEpñkmYyéneRKagEdlminmanCnÞl;RbqaMgnwgkareRTtcMehog. CnÞl;Gac)anmkBIkareRbICBa¢aMgeb
tugGarem: b¤CnÞl;BIeRKag. sMrab;eRKagmanCnÞl; ssrCaeRKOgbgÁMúEdleRbIsMrab;Tb;nwgbnÞúkTMnaj
ehIyCBa¢aMgebtugGarem:RtUv)aneKeRbIedIm,ITb;nwgkMlaMgtamTisedk nigbnÞúkxül;. ÉeRKagKμanCnÞl;
ssrCaeRKOgbgÁúMEdleRbIedIm,ITb;nigbnÞúkTMnajpg nigbnÞúkxül;pg dUcenHlT§PaBRTRTg;rbs;ssr
RtUv)ankat;bnßy.
vi. QrelIeKalkarN_sMPar³ ssrGacCassrebtugGarem: ssrebtugeRbkugRtaMg ssrsmas.
ssrebtugGarem:RtUv)aneKeRbICaTUeTAsMrab;sMNg;GKar.
Axial Loaded Column 190

3. T.Chhay NPIC
3> criklkçN³énssrrgbnÞúkcMG½kS
enAeBlEdlbnÞúkmanGMeBIcMG½kSénssrxøIebtugGarem: ebtugRtUv)anBicarNaeGayeFVIkarmanlkçN³
eGLasÞic enAeBlEdlvargnUvkugRtaMgTabEdlmantMélRbEhl f ' . RbsinebIbnÞúkEdlmanGMeBIenAelI
1
3 c
ssrxiteTArkersIusþg;cugeRkayrbs;va enaHebtugxiteTArkersIusþg;cugeRkay ehIyEdkk¾xiteTArkersIusþg;rMhU
f . lT§PaBRTRTg;bnÞúcugeRkaymFümrbs;ssr GacsresrdUcxageRkam³
y
Po = 0.85 f 'c An + Ast f y
Edl A nig A CaRkLaépÞebtugsuT§ nigRkLaépÞEdk
n st
An = Ag − Ast
Camuxkat;rgGMeBI
Ag
kar)ak;rbs;ssr ekIteLIgBIrRbePTepSgKña GaRs½yeTAnwgkareRbIR)as;Edkkg nigEdkkgvNн.
sMrab;ssrEdkkg ebtug)ak;edaypÞúHEbkpÞat;ecjeRkA EdkembBaÄr)ak;edayPøat;ecjcenøaHEdkkg dUcenH
ssr)ak;ekIteLIgPøam². sMrab;ssrEdkkgvNн)ak;edaymankarbgðajnUvrMhUr EdlekItmannUvkMhUcRTg;
RTayEdlGacKit)an munnwgkar)ak;eBjelj.
4> lkçxNÐrbs; ACI Code
ACI Code )anbgðajnUvlkçxNÐmYycMnYndUcxageRkamkñúgkarKNnaeRKOgbgÁúMrgkarsgát;³
- sMrab;ssrrgkarsgát;cMG½kS k¾dUccakp©it ACI Code )ankMNt;ykemKuNkat;bnßyersIusþg;
φ = 0.65 srab;ssrEdlmanEdkkgdac;² nig φ = 0.7 sMrab;ssrEdlmanEdkkgvNн. tMélxusKña 0.05
bgðajGMBIPaBsVitrbs;ssrEdlmanEdkkgvNн. emKuNkat;bnßyersIusþg;sMrab;ssrmantMéltUcCagsMrab;
eRKOgbgÁúMrbkarBt; nigkMlat;TTwg enHedaysarEtersIusþg;rbs;ssrrgkarsgát;cMG½kS GaRs½yCacMbgeTAnwg
ersIusþg;rbs;ebtug EdlpÞúyBIeRKOgbgÁúMrgkarBt;TTYlT§iBlticCagBIersIusþg;ebtug CaBiesskñúgkrNImuxkat;
rgkarTaj. elIsBIenHeTot rgnUvkarbMEbkFatul,ayebtugeRcInCagkrNIFñwm. ssrRtUvcak;bBaÄrx<s;
nigBum<ceg¥ót b:uEnþebtugkñúgFñwmRtUv)ancak;kñúgBum<rak; edk. dUcenHkar)ak;rbs;ssrenAkñúgeRKagRtUv)aneK
BicarNaeRcInCagFñwmkMral.
ssrrgkMlaMgcMG½kS 191

4. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa
- PaKryEdkemGb,brma 1% nigGtibrmaKW 8% énmuxkat;ssr. muxkat;EdkGb,brmaRtUv)an
dak;sMrab;Tb;nwgkarBt;EdlvaGacekItmaneLIg nigCYykat;bnßyT§iBl creep nigkarrYmmaDrbs;ebtugeRkam
GMeBIénkugRtaMgsgát;. sMrab;karGnuvtþn_ vaCakarBi)akbMputkñúgkarBRgayEdkEdlmanmuxkat;eRcInCag 8%
eTAkñúgssr BIeRBaHeKRtUvkarKMlatEdksmrmüedIm,IeGayebtugeRcotcUlcenøaHEdk.
- y:agehacNas;EdkbYnedImRtUv)andak;sMrab;ssrctuekaN nigssrmUlEdlmanEdkkgdac;² nig
EdkR)aMmYyedImsMrab;ssrmUlEdlmanEdkkgvNн. sMrab;muxkat;ssrepSgeTot EdkRtUv)andak;RKb;RCug
TaMgGs;. EdkminRtUv)andak;edaymanKMlatFMCag 15cm . kñúgkrNIEdkmanKMlatFMCag 15cm eKRtUvdak;
EdkkgbEnßm. RsTab;ebtugkarBarEdkGb,brma 40mm .
- PaKryEdkkgvNÐ ρ RtUv)ankMNt;³
s
Ag f'
ρ s = 0.45( − 1) c
Ac f yt
Edl Ag muxkat;ssr
Ac muxkat;ssrKitRtwmEpñkxageRkAEdkkgvNн
f yt ersIusþg;Edkkg
Axial Loaded Column 192

5. T.Chhay NPIC
- muxkat;EdkkgvNÐGb,brma 9.5mm nigmanKMlatcenøaH 2.5cm → 7.5cm . kartEdkeFVIeLIg
edaypSaehIyRbEvgtEdksMrab;fñaMgGMeBA 48d nigFMCag 30cm sMrab;Edkrelag 72φ nigFMCag 30cm .
- Ggát;p©iténEdkkgdac;²Gb,brma 9.5mm RtUv)aneRbIedIm,IrMuBT§½EdkbBaÄrEdlmanGgát;p©ittUcCag
32mm nigsMrab;EdkbBaÄrEdlmanGgát;p©itFMCag 32mm EdkkgRtUvmanGgát;p©it 12mm .
- KMlatEdkkgminRtUvmantMélFMCag
⎧48φ
⎪
min ⎨16d
⎪ b
⎩
Edl φ Ggát;p©itEdkkg/ d Ggát;p©itEdkbBaÄr/ b RCugEdlmanTMhMtUcCageKénmuxkat;ssr.
5> smIkarsMrab;KNna
bnÞúkEdlssrGacRT)anRtUv)ankMNt;edaysmIkar
Po = 0.85 f 'c An + Ast f y
EtCaTUeTA ssrminEdlrgbnÞúkcMG½kSeT vaEtgEtrgbnÞúkcakp©itbnþic dUcenH ACI Code )anKuNnwg
emKuN 0.8 sMrab;ssrEdlmanEdkkgdac;² nig 0.85 sMrab;ssrEdlmanEdkvNÐ.
sMrab;ssrEdlmanEdkkgdac;² bnÞúkemKuNEdlssrGacRT)ankMNt;eday
P = φP = φ 0.8[0.85 f ' ( A − A ) + A f ] nig φ = 0.65
u n c g st st y
sMrab;ssrEdlmanEdkkgvNн mKuNEdlssrGacRT)ankMNt;eday
P = φP = φ 0.85[0.85 f ' ( A − A ) + A f ] nig φ = 0.7
u n c g st st y
smIkarxagelITaMgBIrGacsresry:agsegçbdUcxageRkam³
Pu = φPn = φk[0.85 f 'c Ag + Ast ( f y − 0.85 f 'c )]
Edl φ = 0.65 nig k = 0.8 sMrab;ssrEdlmanEdkkgdac;² nig φ = 0.7 nig k = 0.85 sMrab;ssr
EdlmanEdkkgvNн.
smIkarxagelIRtUv)aneRbIedIm,IKNnalT§PaBRTRTg;rbs;ssrrgbnÞúkcMG½kS.
RbsinebIpleFobEdk ρ = A enaHsmIkarxagelIkøayeTACa
A
g
st
g
Pu = φPn = φkAg [0.85 f 'c + ρ g ( f y − 0.85 f 'c )]
smIkarxagelIenHvij RtUveRbIedIm,IKNnamuxkat;ssr edaysnμt;PaKryEdlenAcenøaH 1% → 8% .
ssrrgkMlaMgcMG½kS 193

6. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa
6> kMlaMgTajcMG½kS
ebtugnwgminmansñameRbHeT ebIvargnUvkugRtaMgEdlmantMélTabCagersIusþg;rgkarTajrbs;va kñúg
krNIenH TaMgebtug nigEdkTb;nigkugRtaMTaj. b:uEnþenAeBlEdl kMlaMgTajmantMélFMCag ersIusþg;rgkar
Tajrbs;va ¬RbEhl 10 énersIusþg;rgkarsgát;rbs;ebtug¦ sñameRbH)anekItmanenAelImuxkat;ebtug ehIy
1
kMlaMgTajTaMgGs; RtUvTb;Tl;edayEdk. bnÞúkFmμtaEdlGgát;TTYl)anKWCaersIusþg;Tajrbs;Edk³
Tn = Ast f y
Tu = φAst f y
φ = 0.9 sMrab;karTajcMG½kS
Ggát;EdlrgkarTaj ebtugeRbH ehIyr)arEdkrgnUvbnÞúkTajTaMgGs; ebtugmantYnaTICaGñkkarBar
ePøIg nigERcHsIuEdk. sMrab;GagsþúkTwk eKRtUvykcitþTukdak;eTAelIebtug edaymineGayvamansñameRbHeRkam
GMeBIénkMlaMgTaj EdlbNþalmkBIsMBaFTwk.
]TahrN_³ KNnassrxøImuxkat;ctuekaNEdlmanEdkkgdac;² edIm,IRTbnÞúkemKuNcMp©it P = 1765kN . u
edayeRbI f ' = 30MPa / f = 400MPa / TTwgssr b = 30cm nigPaKryEdk ρ = 2% .
c y g
dMeNaHRsay³
bnÞúkemKuNEdlssrGacssrGacRT)an
Pu = φkAg [0.85 f 'c + ρ g ( f y − 0.85 f 'c )]
sMrab;ssrEdlmanEdkkgdac;² φ = 0.65 nig k = 0.8
⇒ Pu = 0.65 × 0.85 × Ag [0.85 f 'c + ρ g ( f y − 0.85 f 'c )]
kMNt;muxkat;ssr
Pu
Ag =
0.65 × 0.8 × [0.85 f 'c + ρ g ( f y − 0.85 f 'c )]
edaybnÞúkRtUvkarRTnUvbnÞúkcMp©it P = 1765kN nigssrRtUvmanPaKryEdk ρ
u g = 2%
1765 × 103
⇒ Ag = = 102887 mm 2
0.65 × 0.8 × [0.85 × 30 + 0.02(400 − 0.85 × 30)]
eday b = 30cm
102887
⇒a= = 343mm
300
yk a = 350mm = 35cm ⇒ A = 105000mm g
2
muxkat;Edk A = 0.02 × 102887 = 2057mm
s
2
ykEdk DB22 cMnYn 6 edIm ⇒ A = 2280mm s
2
Axial Loaded Column 194

7. T.Chhay NPIC
RtYtBinitübnÞúkKNnaEdlssrGacRT)an
Pu = 0.65 × 0.8[0.85 f 'c ( Ag − Ast ) + Ast f y ]
⇒ Pu = 0.65 × 0.8[0.85 × 30 × (105000 − 2280) + 2280 × 400] × 10−3 = 1836kN > 1765kN OK !
ykEdkkgmanGgát;p©it 10mm
KMlatEdkkg
⎧48φ ⎧48 × 10 ⎧480
⎪ ⎪ ⎪
min ⎨16d = min ⎨16 × 22 = min ⎨352 = 300
⎪ b ⎪ 300 ⎪300
⎩ ⎩ ⎩
dUcenHeRbIEdkkg DB10 @ 300 .
ssrrgkMlaMgcMG½kS 195