X axial loaded column
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1. The document discusses the design of reinforced concrete columns under axial load. 2. It provides guidelines on column dimension, reinforcement ratio, and confining reinforcement according to ACI code. 3. Formulas for calculating the nominal axial load capacity of a column based on its cross-sectional area and steel reinforcement are presented.
![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](https://image.slidesharecdn.com/xaxialloadedcolumn-100715083225-phpapp01/85/X-axial-loaded-column-5-320.jpg)
![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](https://image.slidesharecdn.com/xaxialloadedcolumn-100715083225-phpapp01/85/X-axial-loaded-column-6-320.jpg)
![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](https://image.slidesharecdn.com/xaxialloadedcolumn-100715083225-phpapp01/85/X-axial-loaded-column-7-320.jpg)
X axial loaded column
- 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