• Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Be the first to comment
No Downloads

Views

Total Views
520
On Slideshare
0
From Embeds
0
Number of Embeds
1

Actions

Shares
Downloads
0
Comments
0
Likes
2

Embeds 0

No embeds

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
    No notes for slide

Transcript

  • 1. T.Chhay NPIC XII. ssrEvg 1> esckþIepþIm sMrab;karKNnassrxøIEdl)anBnül;enAkñúgBIremeronxagedIm )ansnμt;fa karPøat; buckling karrYjxøI eGLasÞic elastic shortening nigm:Um:g;TIBIr secondary moment EdlbNþalmkBIPaBdabtamTTwg lateral deflection manT§iBlCaGb,brmaeTAelIersIusþg;cugeRkay ultimate strength rbs;ssr dUcenHktþaTaMgenH minRtUv)anrab;bBa©ÚleTAkñúgdMeNIrkarénkarKNnaeT. b:uEnþ enAeBlEdlssrEvg ktþaTaMgGs;enHRtUvEtyk mkBicarNa. RbEvgbEnßmnwgbNþaleGaymankarkat;bnßyersIusþg;rbs;ssr edayERbRbYlCamYynwgkMBs; RbsiT§PaB nigTTwgrbs;muxkat; pleFobrlas; slenderness ratio niglkçxNÐcugssr. ssrEdlman slenderness ratio FMnwgkat;bnßylT§PaBRTRTg;rbs;ssry:agxøaMg Et slenderness ratio tUcmann½yfassrxøI ehIykarkat;bnßyersIusþg;GacnwgminKYreGaycab;GarmμN_. pleFobrlas; slenderness ratio KWCapleFobrvagkMBs;ssr l CamYynwgkaMniclPaB radius of gyration r Edl r = I / A kñúgenaH I Cam:Um:g;niclPaBénmuxkat; moment of inertia of the section nig A CaRkLa 2 épÞmuxkat;. sMrab;muxkat;ctuekaNEdlmanTTwg b nigkMBs; h ¬rUbTI 1¦ I = bh / 12 nig A = bh dUcenH x 3 r = 0.288h ¬b¤ edaytMélRbEhl r = 0.3h ¦. dUcKña I = b h / 12 nig r = 0.288b ¬b¤ r = 0.3b ¦. x x y 3 y y sMrab;ssrmUlCamYynwgGgát;p©it D enaH I = I = πD / 64 nig A = πD / 4 dUcenH r = r = 0.25D . x y 4 2 x y CaTUeTA ssrGacRtUv)anBicarNa dUcteTA³ 1> EvgCamYynwg slenderness ratio FM RtUvkarCnÞl; b¤ shear wall. 2> EvgCamYynwg slenderness ratio lμmEdlbgáeGaymankarkat;bnßyersIusþg;ssr enaHCnÞl;Gac nwgminRtUvkar Etkarkat;bnßyersIusþg;RtUvEtBicarNa. 3> xøIEdl slenderness ratio tUcEdlbNþaleGaymankarkat;bnßyersuIsþg;sþÜcesþIg. karkat;Gac RtUv)anecal dUcerobrab;BIemeronmun. 2> RbEvgssrRbsiT§PaB Effective Column Length ( Klu ) pleFobrlas; slenderness ratio l / r GacRtUv)anKNnay:agsuRkitenAeBlEdlRbEvgRbsiT§PaB rbs;ssr ¬ Kl ¦ RtUv)aneRbI. RbEvgRbsiT§PaBenHGnuKmn_eTAnwgBIrktþaFM²³ u 1> RbEvgKμanTMr unsupported length l sMEdgnUvkMBs;minKitTMrrbs;ssrrvagBIrkMralxNÐ.va u RtUv)anvas;Ca clear distance rvagkMralxNÐ Fñwm b¤GgÁeRKOgbgÁúMEdlpþl;nUvTMrxagdl;ssr. ssrEvg 255
  • 2. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa enAkñúgRbBnæ½kMralxNÐ flat slab CamYynwg column capital kMBs; unsupported height rbs; ssrRtUv)anvas;BIépÞxagelIrbs;kMralxNÐxageRkameTA)atrbs; column capital. RbsinebI ssrRtUv)anRTCamYyFñwmEdlmankMBs;x<s;tamTismYyCagtamTismYyeTot enaH l KYrEt u KNnatamTisTaMgBIr ¬tamTis x nig y ¦énmuxkat;ssr. RtUvEdlFMCagRtUv)anBicarNakñúg karKNna. 2> emKuNRbEvgRbsiT§PaB K bgðajnUvpleFobéncMgayrvagcMnucénm:Um:g;sUnüenAkñúgssr nigkM Bs;KñanTMrrbs;ssrkñúgTisedAmYy. ]TahrN_ RbsinebIRbEvgKμanTMr unsupported height rbs; ssrTMrsnøak; hinged enAcugsgçag ¬Edlkareyalxag sidesway RtUv)anTb;¦ KW l nigcMnucm:U u m:g;sUnüenAcug nigKl;ssr EdlenAcugTMrRtIekaN hing enaHemKuN K = l / l KWesμInwg 1. Rb u u sinebIssr manTMrbgáb; fixed enAcugsgçag ehIykareyalxag sidesway RtUv)anTb; cMnucrbt; ¬cMnucm:Um:g;sUnü¦ sßitenA l / 4 BIcugTMr. dUcenH K = 0.5l / l = 0.5 ¬rUbTI2¦ edIm,IKNna u u u tMéld¾RtwmRtUvrbs; K krNI cMbgBIrRtUv)anBicarNa. - enAeBleRKagbgÁúMEdlpÁúMeLIgeday Fñwm nigssrRtUv)anBRgwgedayCBa¢aMg shear wall CnÞl;rwg rigid bracing b¤TMrxagEdl)anmkBIeRKagbgÁúMenACab;nwgva. cugrbs;ssrnwg sßitenATItaMgdEdl EdlkarrMkilxagrbs;tMNRtUv)ankarBar. CaTUeTAsMrab;eRKagBRgwg tMélrbs; K KWtUcCagb¤esμInwg 1. ACI code, section 10.12 esñIeGayeRbI K = 1 . - enAeBleRKagbgÁúMminRtUv)anBRgwg vanwgGaRs½yeTAnwgPaBrwgRkaj stiffness rbs;Fñwm nigssr edIm,ITb;nwgPaBdabxag. edaysarkarrMkilrbs;tMNrminRtUv)ankarBar eRKag egakeTAtamTisrbs;bnÞúkxag. tMélrbs; K sMrab;ssr nigeRKagRtUv)aneGayenAkñúg rUbTI2 edayBicarNakrNITaMgBIr KWenAeBlkareyalxag sidesway RtUv)ankarBar nig minRtUv)ankarBar. Slender Column 256
  • 3. T.Chhay NPIC 3> emKuNRbEvgRbsiT§PaB Effective Length Factor ( K ) RbEvgRbsiT§PaBrbs;ssrGacRtUv)anKNnaedayeRbIdüaRkam alignment chart kñúgrUbTI3. edIm,Irk emKuNRbEvgRbsiT§PaB K dMbUgeKcaM)ac;RtUvKNnarkemKuNTb; restraint factor ψ nig ψ enAxagcugnig A B Kl;ssrerogKña Edl EI / l rbs;ssr ψ =∑ c (-1) ∑ EI / l rbs;Fwm Edl l = RbEvgKitBIGkS½eTAGkS½éntMNrrbs;eRKag c l = RbEvgElVgKitBIGkS½eTAGkS½éntMNrrbs;eRKag ¬TaMgBIrsßitenAkñúgbøg;Bt;¦. emKuN ψ enAxagcugKYrEtrYmbBa©ÚlTaMgssr nigFñwmEdlCYbKñaenARtg; tMNr. sMrab;TMrsnøak; hinged end ψ KWGnnþ nigGacsnμt;esμI 10 . sMrab;TMrbgáb; fixed end ψ KWsUnü nig Gacsnμt;esμI 1. tMélsnμt;TaMgenHGaceRbI)anedaysarEtenAkñúgeRKagbgÁúMebtugGaem:Kμansnøak;Kaμ nkkit l¥tex©aH b¤TMrbgát;l¥tex©aHenaHEdr. dMeNIrkarrk K KWKNna ψ sMrab;cugssr nigψ sMrab;Kl;ssr. dak; ψ nig ψ eTAkñúgdüa A B A B Rkam alignment chart énrUbTI3 rYcP¢ab;cMnucTaMgBIredaykat;ExSkNþal EdlbgðajBItMél K . düaRkam BIrEdlmanlkçN³RsedogKñaRtUv)anbgðaj mYysMrab;eRKagBRgwg Edlkareyalxag sidesway RtUv)an karBar nigmYyeTotsMrab;eRKagFmμta Edlkareyalxag sidesway minRtUv)ankarBar. karbegáItdüaRkam enHKWQrelIkarsnμt;fa³ - eRKagbgÁúMpÁúMeLIgedayeRKagctuekaNsIuemRTI - m:Um:g;Bt;Fñwm)anEckmkssredayTak;TgnwgPaBrwgRkajrbs;va - ssrTaMgGs;TTYlnUvbnÞúkFMenAeBlCamYyKña edIm,ICMnYsnUvkareRbIdüaRkam alignment chart EdlbgðajkñúgrUbTI3 ACI Code Commentary )an esñInUvsmIkarsMrYldUcxageRkamsMrab;KNnaemKuNRbEvgRbsiT§PaB K . 1> sMrab;GgÁrgkarsgát;EdlmankarBRgwg tMélrbs; K GacRtUv)anyktMéltUcCageKkñúgcMeNam smIkarTaMgBIrxageRkam K = 0.7 + 0.05(ψ A + ψ B ) (-2) K = 0.85 + 0.05ψ min (-3) Edl ψ nig ψ CatMélrbs; ψ enAcugsgçagrbs;ssr nig ψ CatMéltUcbMputéntMélTaMgBIr. A B min 2> sMrab;GgÁrgkarsgát;EdlKμankarBRgwgEtRtUv)anTb;enAcugsgçag tMélrbs; K Gacsnμt;dUc xageRkam ssrEvg 257
  • 4. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa sMrab; ψ < 2 / K = 2020ψ 1 +ψ m − m m (-4) sMrab; ψ ≥ 2 / K = 0.9 1 +ψ m m (-5) Edl ψ CatMélmFümrbs; ψ enAcugsgçagGgÁrgkarsgát;. m 3> sMrab;GgÁrgkarsgát;KμankarBRgwgmanTMrsnøak; hinged enAcugmçag enaH K GacRtUv)ansnμt;dUc xageRkam K = 2 + 0.3ψ (-6) Edl ψ CatMélenAcugEdlmankarTb;. Slender Column 258
  • 5. T.Chhay NPIC ]TahrN_ 1³ edayeRbInUvsmIkarxagedIm cUrkMNt;emKuNRbEvgRbsiT§PaB K sMrab;Ggát;rgkarsgát;enAkñúg eRKagCamYynwglkçxNÐxageRkam³ 1> eRKagRtUv)anBRgwgedIm,ITb;nwgkareyalxag sidesway ehIy ψ A = 2 .0 nig ψ B = 3 .0 enAcug xagelI nigxageRkamrbs;Ggát;. ssrEvg 259
  • 6. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 2> eRKagminRtUv)anBRgwgedIm,ITb;nwgkareyalxag sidesway eT ehIy ψ A = 2 .0 nig ψ B = 3 .0 . ¬Ggát;RtUv)anbgáb;enAcugsgçag¦. 3> eRKagminRtUv)anBRgwgedIm,ITb;nwgkareyalxag sidesway eT ehIy ψ A = 0 .0 ¬TMrsnøak;¦ nig ψ = 3 .0 . B dMeNaHRsay³ 1> BIsmIkar (-2) nig (-3) K1 = 0.7 + 0.05(2 + 3) = 0.95 < 1.0 K 2 = 0.85 + 0.05(2) = 0.95 < 1.0 eRCIserIsyknUvtMéltUcCageKkñúgcMeNam K nig K . kñúgkrNIenH K = 0.95 . 1 2 2> tMélmFümrbs; ψ = (2 + 3) / 2 = 2.5 . eday ψ > 2 eRbIsmIkar (-5) m m K = 0.9 1 + 2.5 = 1.684 3> BIsmIkar (-6) K = 2 + 0.3(3) = 2.9 4> PaBrwgRkajrbs;Ggát; Member Stiffness ( EI ) PaBrwgRkajrbs;Ggát;eRKagesμInwgplKuNrvagm:UDuleGLasÞic E CamYynwgm:Um:g;niclPaBénmuxkat; I . tMélén E nig I sMrab;ebtugGaem:GacRtUv)anKNnadUcxageRkam³ 1> m:UDuleGLasÞicrbs;ebtugRtUv)anBnül;kñúgemeronTI2. bTdæan ACI Code eGaysmIkarxag eRkam E = 0.043w c 1.5 f' c b¤ E = 4780 f ' c c sMrab;ebtugTMgn;Fmμta. cMENkÉm:UDuleGLasÞicrbs;EdkKW E = 2.1⋅10 MPa . s 5 2> sMrab;Ggát;ebtugGaem: m:Um:g;niclPaB I ERbRbYltambeNþayrbs;Ggát; GaRs½yeTAnwgkMriteRbH nigPaBryEdkEdl)aneRbIR)as;. edIm,IkMNt;nUvemKuN ψ EI RtUvEt)ankMNt;sMrab;Fñwm nigssr. dUcenH EI GacRtUv)ankM Nt;dUcxageRkam ¬ACI Code, section 10.11.1¦³ sMrab;Fñwm I = 0.35 I g sMrab;ssr I = 0.70 I g sMrab;CBa¢aMg¬KμaneRbH¦ I = 0.70I g sMrab;CBa¢aMg¬maneRbH¦ I = 0.35I g Slender Column 260
  • 7. T.Chhay NPIC sMrab;kMralxNн (flat plate nig flat slab) I = 0.25 I g Edl I Cam:Um:g;niclPaBsMrab;muxkat;ebtugeBjeFobGkS½kat;tamTIRbCMuTMgn; edayecal g Edk. 3> RkLaépÞmuxkat; A = A ¬RkLaépÞmuxkat;eBj gross-sectional area¦ g 4> m:Um:g;niclPaBKYrEtRtUv)anEckeday (1 + β ) enAeBlEdlbnÞúkxagefr sustained lateral load d manGMeBIelIeRKagbgÁúM b¤sMrab;epÞógpÞat;esßrPaB stability check Edl maximum factored sustained axial load βd = total factored axial load 5> EdnkMNt;sMrab;pleFobrlas; Limitation of The Slenderness Ratio ( Klu / r ) 5>1> eRKagGt;eyal Nonsway Frames bTdæan ACI Code, section 10.12 ENnaMnUvEdnkMNt;xagRkamrvagssrxøI nigssrEvgenAkñúgeRKag BRgwg ¬Gt;eyaK nonsway¦³ 1> T§iBlrbs;PaBrlas; slenderness GacRtUv)anecal ehIyssrGacRtUv)anKNnaedayKitCassrxøI enAeBlEdl³ Klu 12 M 1 ≤ 34 − (-7) r M2 Edl M nig M Cam:Um:g;emKuNenAcugssr ehIy M 1 2 2 > M1 . ssrEvg 261
  • 8. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 2> pleFob M RtUvcat;Tukfa viC¢manRbsinebIGgát;RtUv)anenAkñúgkMeNageTal single curvature M 1 2 nigGviC¢mansMrab;kMeNagDub double curvature dUcbgðajkñúgrUbTI4. 3> GgÁ (34 − 12M / M ) KYrminRtUvFMCag 40. 1 2 4> RbsinebIm:Um:g;ssremKuN factored column moment esμIsUnü b¤ e = M / P < e tMélrbs; M u u min 2 KYrEtRtUv)anKNnaedayeRbIcMNakp©itGb,brma³ emin = (15.24 + 0.03h) (-8) M 2 = Pu (15.24 + 0.03h) (-9) Edl M Cam:Um:g;Gb,brma. m:Um:g; M KYrEtRtUv)anBicarNaedayeFobnwgGkS½nImYy²rbs;ssrdac; 2 2 edayELkBIKña. tMél K GacRtUv)ansnμt;esμInwg 1.0 sMrab;eRKagBRgwg braced frame elIkElgEt vaRtUv)anKNnaedayQrelIkarviPaK EI . 5>2> eRKageyal Sway Frames enAkñúgGgát;rgkarsgát;minBRgwgTb;nwgkareyalxag sidesway T§iBlrbs;pleFobrlas; slenderness ratio GacecalenABlEdl Klu < 22 (ACI Code, section 10.13) (-10) r 5>3> pleFobrlas;FM High slenderness ratio enAeBlEdlGgát;rgkarmYydac;edayELkenAkñúgeRKagmanpleFobrlas; slenderness ratio Kl / r > 100 viFIm:Um:g; magnifier (moment magnifier method) rbs; ACI Code minGacRtUv)aneRbI u ehIykarviPaK rigorous dWeRkTIBIr rigorous second-order RtUv)aneRbICMnYsvij. Et muxkat;GacRtUv)an tMeLIgedIm,Ikat;bnßypleFob Kl / r . tMé;l 100 bgðajBIkarBiesaFn_Cak;EsþgcMNat;fñak;x<s; (ACI u Code, section 10.10.5) . 6> viFIKNnabEnßmm:Umg; Moment-Magnifier Design Method 6>1> esckþIepþIm Introduction CMhandMbUgkñúgkarKNnam:Um:g;enAkñúgssrEvgKWkMNt;faetIeRKagEdlKNna CaeRKakBRgwg b¤min BRgwgTb;nwg sidesway . RbsinebImanGgÁBRgwgxag dUcCa shear walls nig shear trusses b¤ssrmanPaBrwg RkajTTwg lateral stiffness efr enaHPaBdabTTwg lateral deflection mantMéltUc ehIyT§iBlrbs;vaeTAelI ersIusþg;ssrk¾tUcEdr. eKGacsnμt;faeRKagbgÁúMenAkñúgmYyCan;²RtUv)anBRgwgRbsinebI Q = ∑ u o ≤ 0.05 PΔ (-11) Vus lc Slender Column 262
  • 9. T.Chhay NPIC Edl ∑ Pu nig V CabnÞúkbBaÄrsrub nigkMlaMgkat; erogKña ehIy Δ PaBdabeFobdWeRkTImYy first- us o order relative deflection rvagkMBUl nig)atrbs;Can;EdlbNþalmkBI V . RbEvg l CaRbEvgrbs;Ggát;rg us c karsgát;enAkñúgeRKagbgÁúM edayvas;BIGkS½eTAGkS½rbs;tMNrenAkñúgeRKag. CaTUeTA Ggát;rgkarsgát;GacrgnUgPaBdabTTwg lateral deflection EdlbNþalmkBIm:Um:g;TIBIr secondary moment. RbsinebIm:Um:g;TIBIr M ' RtUv)anbEnßmeTAelIm:Um:g;EdlGnuvtþelIssr M enaHm:Um:g;cug a eRkayKW M = M + M ' . viFIRbEhl approximate method sMrab;kMNt;m:Um:g;cugeRkay M KWCakarKuNm:U a m:g; M edayemKuNEdleKehAfa emKuNbEnßmm:Um:g; (magnifying moment factor) ehIyemKuNenHRtUvEt a FMCagb¤esμInwg 1.0 . b¤ M = δM nig δ ≥ 1.0 . m:Um:g; M RtUv)anTTYlBIkarviPaKeRKageGLasÞiceday max a a eRbIbnÞúkemKuN ehIyvaCam:Um:g;GtibrmaEdlmanGMeBIenAcugssr b¤enAkñúgssr RbsinebIbnÞúkxagmanvtþman. RbsinebIT§iBl P − Δ RtUv)anykmkBicarNa vanwgcaM)ac;RtUvEteRbIkarviPaKdWeRkTIBIr edIm,IKitBI TMnak;TMng nonlinear relationship rvagbnÞúk PaBdabTTwg nigm:Um:g;. eKGaceRbIkmμviFIkMuBüÚTr½edIm,IedaHRsay va. bTdæan ACI Code GnuBaØatieGayeRbIkarviPaKssrdWeRkTImYy b¤dWeRkTIBIr. karviPaKssrdWeRkTIBIr RtUv)antMrUveGayeRbIenAeBlEdl Klu / r > 100 . viFIKNnam:Um:g;bEnßmrbs; ACI Code CaviFIsMrYlsMrab; KNnaemKuNbnÞúkbEnßmTaMgeRKagBRgwg nigeRKagminBRgwg. 6>2> m:Um:g;bEnßmenAkñúgeRKagGt;eyal Magnified Moments in Nonsway Frames T§iBlrbs;pleFobrlas; slenderness ratio Klu / r enAkñúgGgát;rgkarsgát;éneRKagBRgwgGac RtUv)anecalRbsinebI Klu / r ≤ 34 − 12M1 / M 2 dUcbgðajenAkñúgEpñk 5>1 . RbsinebI Klu / r > 34 − 12 M1 / M 2 enaHT§iBlPaBrlas;RtUv)anBicarNa. dMeNIrkarkMNt;emKuNbEnßm δ ns enAkñúg eRKagmineyalGacRtUv)ansegçbdUcxageRkam (ACI Code, section 10.12)³ 1> kNt;faeRKagCaeRKagBRgwgTb;nwg sidesway b¤Gt; rYckMNt;RbEvgKμanTMr lu nigemKuNRbEvg RbsiT§PaB K ¬ K RtUv)ansnμt;eGayesμI 1.0 ¦ 2> KNnaPaBrwgRkajrbs;Ggát; EI edayeRbIsmIkar 0.2 Ec I g + Es I se EI = (-12) 1 + βd b¤smIkarEdlsMrYlCag 0.4 Ec I g EI = (-13) 1 + βd EI = 0.25Ec I g ¬sMrab; β d = 0.6 ¦ (-14) Edl Ec = 4780 f 'c Es = 2.1 ⋅105 MPa ssrEvg 263
  • 10. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa Ig = m:Um:g;niclPaBénmuxkat;ebtugtamGkS½NamYyEdleyIgBicarNaedayecal As I se = m:Um:g;nicalPaBénmuxkat;EdkeFobGkS½TIRbCMuTMgn;rbs;muxkat;ebtug maximum factored axial sustained load 1.2 D (sustained) βd = = maximum factored axial load 1.2 D + 1.6 L cMNaMfa³ β d xagelICapleFobEdlFøab;KNnam:Um:gbEnßmenAkñúgssrEdlbNþalmkBIbnÞúk ; sustained . smIkar (-13) nig (-14) manlkçN³suRkitticCagsmIkar (-12) . elIsBIenH smIkar (-14) TTYl)anedaysnμt; β d = 0.6 CMnYskñúgsmIkar (-13) . 3> kMNt;bnÞúk Euler buckling/ Pc ³ π 2 EI Pc = (-15) (Klu )2 eRbItMélrbs; EI / K nig lu dUcKNnaBICMhan 1> nigCMhan 2>. 4> KNnatMélénemKuN Cm edIm,IeRbIenAkñúgsmIkarénemKuNm:Um:g;bEnßm moment-magnifier factor. sMrab;Ggát;BRgwgedayKμanbnÞúkxag transverse load 0.4M1 Cm = 0.6 + ≥ 0.4 (-16) M2 Edl M1 / M 2 viC¢manRbsinebIssrRtUv)anBt;kñúgkMeNageTal. sMrab;Ggát;CamYybnÞúkxagenA cenøaHTMr Cm KYrRtUv)anykesμInwg 1.0 . 5> KNnaemKuNm:Um:g;bEnßm δ ns Cm δ ns = ≥ 1.0 (-17) 1 − ( Pu / 0.75Pc ) Edl Pu CabnÞúkemKuN nig Pc nig Cm RtUv)anKNnaBIxagelI. 6> KNnaGgát;rgkarsgát;edayeRbIbnÞúkemKuNtamGkS½ Pu BIkarviPaKeRKagd¾RtwmRtUv nigm:Um:g; bEnßm magnified moment M c EdlKNnadYcxageRkam³ M c = δ ns M 2 (-18) Edl M 2 Cam:Um:g;emKuNEdlFMCagEdlekItBIbnÞúk EdllT§plmineyal. sMrab;eRKagBRgwg Tb;nwg sidesway emKuNeyalKW δ s = 0 . enAkñúgeRKagGt;eyal nonsway frame PaBdab TTwgRtUv)anrMBwgeGaytUcCagb¤esμInwg H /1500 Edl H CakMBs;srubrbs;eRKag. 6>3> m:Um:g;bEnßmenAkñúgeRKageyal Magnified Moments in sway Frames Slender Column 264
  • 11. T.Chhay NPIC T§iBlrbs;PaBrlas;GacRtUv)anecalenAkúñgeRKageyal sway frame ¬KμanBRgwg unbraced¦ enAeBlEdl Klu / r < 22 . karKNnaemKuNbEnßm magnification factored δ s sMrab;eRKageyal ¬Kμan BRgwg¦ RtUv)ansegçbdUcxageRkam (ACI Code, Section 10.13)³ 1> kMNt;faeRKagCaeRKagKμanBRgwgTb;nwg sidesway b¤Gt; rYckMNt;RbEvgKμanTMr lu nigemKuN RbEvgRbsiT§PaB K EdlGacTTYlBIsmIkar (-4) (-5) nig (-6) b¤düaRkamrUbTI3. 2-4> KNna EI / Pc nig Cm dUceGaykñúgsmIkar (-12) dl; (-16). cMNaMfa βd ¬edIm,IKNna EI ¦KW CapleFobrvagkMlaMgkat;TTwgefremKuNGtibrma maximum factored sustained shear tamCan; nigkMlaMgkat;TTwgemKuNsrubenAkñúgCan;enaH. 5> KNnaemKuNm:Um:g;bEnßm moment-magnifier factor/ δ s ³ 1 δs = ≥ 1.0 (-19) 1 − (∑ Pu / 0.75∑ Pc ) Edl δ s ≤ 2.5 nig ∑ Pu CaplbUkbnÞúkbBaÄrTaMgGs;enAkñúgmYyCan; nig ∑ Pc CaplbUk bnÞúksMrab;ssrEdlTb;nwgkareyal sway enAkñúgmYyCan;. dUcKña³ M 2s δsM s = ≥ Ms (-20) 1 − (∑ Pu / 0.75∑ Pc ) Edl M s Cam:Um:g;emKuNxagcugbNþalmkBIbnÞúkEdlbegáItkareyalEdlTTYlyk)an. 6> KNnam:Um:g;cugbEnßm M1 nig M 2 enAxagcugGgát;rgkarsgát;EtÉg dUcxageRkam³ M1 = M1ns + δ s M1s (-21) M 2 = M 2ns + δ s M 2 s (-22) Edl M1ns nig M 2ns Cam:Um:g;EdlTTYlBIlkçxNÐGt;eyal b:uEnþ M1s nig M 2s Cam:Um:g;Edl TTYl)anBIlkçxNÐeyal. RbsinebI M 2 > M1 BIkarviPaKeRKag enaHkarKNnam:Um:g;bEnßmKW³ M c = M 2ns + δ s M 2 s (-23) m:Um:g;cug M1 nig M 2 enAkñúgsmIkar (-21) (-22) nig (-23) manm:Um:g;Gt;eyal bUknigm:Um:g; eyalbEnßm CamYynwglkçxNÐEdl lu 35 < (-24) r Pu / f 'c Ag enAkñúgkrNIenH Ggát;rgkarsgát;KYrEtRtUv)anKNnasMrab;bnÞúkemKuNtamGkS½ Pu nig M c . b:uEnþkñúgkrNIEdl lu 35 > (-25) r Pu / f 'c Ag Ggát;rgkarsgát;KYrEtRtUv)anKNnasMrab; Pu nigm:Um:g;Gt;eyalbEnßm δ ns M 2 bUkCamYy nwgm:Um:g;eyalbEnßm δ s M 2 CamYynwgm:Um:g;KNna M c = δ ns M 2ns + δ s M 2s . krNIenHGac ssrEvg 265
  • 12. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa ekItmansMrab;ssrEvg slender column CamYynwgbnÞúktamGkS½FM enAeBlEdlm:Um:g;Gtibrma ekItmanenAcenøaHcugssr nigminenAxagcug. bTdæan ACI Code, section 10.13.4 GnuBaØatinUvviFIepSgeTotsMrab;karKNna δ s M s én smIkar (-20) edayeRbIsnÞsSn_esßrPaB stability index Q EdleGaykñúgsmIkar (-11) Edl δ s ≤ 1.5 ³ Ms δsM s = ≥ Ms (-26) 1− Q ]TahrN_ 2³ muxkat;ssrdUcbgðajkñúgrUbTI5 RTbnÞúktamGkS½ P D nigm:Um:g; M D = 157kN .m = 605kN EdlbNþalmkBIbnÞúkefr nigbnÞúktamGk½S PL = 490kN nigm:Um:g; M L = 126kN .m EdlbNþalmkBIbnÞúk cl½t. ssrCaEpñkrbs;eRKagBRgwg nigmankMeNageTaltamGkS½em. RbEvgKμanTMrrbs;ssrKW lc = 5.8m ehIym:Um:g;enAcugTaMgsgçagrbs;ssrmantMélwsμIKña. epÞógpÞat;muxkat;ssredayeRbI f 'c = 28MPa nig f y = 400MPa . dMeNaHRsay³ 1> KNnabnÞúkcugeRkay ultimate load³ Pu = 1.2 PD + 1.6 PL = 1.2 × 605 + 1.6 × 490 = 1510kN M u = 1.2M D + 1.6M L = 1.2 × 157 + 1.6 × 126 = 390kN .m M 390 e= u = = 258.3mm Pu 1510 2> RtYtBinitüemIlfaetIssrEvgb¤xøI. edaysareRKagRtUv)anBRgwg snμt; K = 1.0 r = 0.3h = 0.3 × 550 = 165mm nig lu = 5.8m Klu 5800 = = 35.15 r 165 sMrab;ssrBRgwg RbsinebI Klu / r ≤ 34 − 12M1 / M 2 T§iBlénPaBrlas;GacRtUv)anecal. eday sarssrekagedaykMeNageTal enaH M1 / M 2 viC¢man. dUcenH Slender Column 266
  • 13. T.Chhay NPIC M1 34 − 12 = 34 − 12 = 22 M2 edaysar Klu / r = 35.15 > 22 enaHT§iBlénPaBrlas;RtUv)anBicarNa. 3> KNna EI BIsmIkar (-12)³ A. KNna E c Ec = 4780 f 'c = 4780 28 = 25293.4MPa Es = 2.1 ⋅105 MPa B. m:Um:g;niclPaBKW 350(550) 4π 282 3 Ig = = 4852.6 ⋅ 106 mm 4 As = A's = = 2463mm 2 12 4 ⎛ 550 − 120 ⎞ 2 I se = 2 × 2463⎜ ⎟ = 227.7 ⋅10 mm 6 4 ⎝ 2 ⎠ pleFobm:Um:g;GefrKW 1.2 × 605 βd = = 0.48 1510 C. PaBrwgRkajKW 0.2 Ec I g + Es I se EI = 1 + βd 0.2 × 25293.4 × 4852.6 ⋅106 + 2.1 ⋅105 × 227.7 ⋅106 = = 48.9 ⋅1012 N .mm 2 1 + 0.48 4> KNna P c π EI 2 π 2 48.9 ⋅1012 Pc = = = 14346.72kN (Klu )2 (5800) 2 5> KNna C BIsmIkar (-16)³ m M1 Cm = 0.6 + 0.4 ≥ 0.4 M2 = 0.6 + 0.4(1) = 1.0 6> KNnaemKuNm:Um:g;bEnßmBIsmIkar (-17)³ Cm 1 δ ns = = = 1.16 1 − ( Pu / 0.75Pc ) 1 − [1510 /(0.75 × 14346.72] 7> KNnam:Um:g;KNna design moment nigbnÞúkKNna design load edaysnμt; φ = 0.65 1510 Pn = = 2323kN 0.65 390 Mn = = 600kN .m 0.65 KNna M c = 1.16 × 600 = 696kN .m ssrEvg 267
  • 14. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa KNnacMNakp©it e= 696 2323 = 300mm 8> kMNt;ersIusþg; nominal load strength énmuxkat;edayeRbI e = 300mm edayeRbIsmIkar (-4) emeron eRKOgbgÁúMrgkarsgát; nigkarBt;³ Pn = 8.33a + 926.58 − 2.46 f s (I) h 550 e' = e + d − = 300 + 490 − = 515mm 2 2 1 ⎡ ⎛ a⎞ ⎤ Pn = ⎢8.33a⎜ 490 − 2 ⎟ + 926.58(490 − 60 )⎥ 515 ⎣ ⎝ ⎠ ⎦ −3 2 = 7.93a − 8.1 ⋅ 10 a + 773.65 (II) BIsmIkar (I) nig (II) eyIgTTYl)an a = 267mm / f = 338MPa nig P = 2319.2kN . s n edaysarEtersIusþg;bnÞúk load strength P = 2319.2kN nigbnÞúktMrUvkar required load n P = 2323kN mantMélRbhak;RbEhlKña enaHmuxkat;RtUv)ancat;TukfaRKb;RKan;. RbsinebI n muxkat;minRKb;RKan; RtUvtMeLIgmuxkat;Edk. 9> epÞógpÞat;tMélsnμt; φ a = 267 mm c = 314.12mm d t = 490mm ⎛ dt − c ⎞ εt = ⎜ ⎟0.003 = 0.00168 < 0.002 ⎝ c ⎠ dUcenH φ = 0.65 ]TahrN_ 3³ epÞógpÞat;PaBRKb;RKan;rbs;ssrkñúg]TahrN_TI2 RbsinebIRbEvgKμanTMr unsupported length l = 3m . kMNt;bnÞúk nominal load GtibrmaenAelIssr. u dMeNaHRsay³ 1> bnÞúkEdlGnuvtþKW P = 2323kN nig M = 600kN .m n n 2> epÞógpÞat;PaBEvgxøIrbs;ssr³ l = 3m / r = 0.3 × 550 = 165mm nig K = 1.0 ¬eRKagRtUv)anBRgwg u Tb;nwgkareyalxag sidesway ¦. Klu 3000 = = 18.2 r 165 epÞógpÞat; Kl u / r = 34 − 12M 1b / M 2b 34 − 12(1) = 22 eday Klu r = 18.2 < 22 enaH T§iBlénPaBrlas;Gacecal)an. Slender Column 268
  • 15. T.Chhay NPIC 3> kMnt;lT§PaBRTbnÞúk nominal load ebs;ssrxøI dUcBnül;enAkñúg]TahrN_TI4 én emeroneRKOgbgÁúM rgkarsgát; nigkarBt;;. eyIgTTYl)an Pn = 2574.9kN ¬sMrab; e = 258.3mm ¦ EdlFMCagbnÞúkcaM)ac; Pn = 2323kN . ]TahrN_ 4³ epÞógpÞat;PaBRKb;RKan;rbs;ssrkñúg]TahrN_TI2 RbsinebIeRKagminRtUv)anBRgwgTb;nwgeyal xag sidesway emKuNbgáb;cug end-restraint factor KW ψ A = 0.8 nig ψ B = 2 ehIyRbEvgKμanTMr unsupported length KW lu = 4850mm . dMeNaHRsay³ 1> kMNt;tMél K BIdüaRkam alignment chart rUbTI3 sMrab;eRKagminBRgwg. P¢ab;tMél ψ A = 0.8 nig ψ B = 2 kat;ExS K Rtg; K = 1.4 . Klu 1.4 × 4850 = = 41.15 r 165 2> sMrab;eRKagKμanBRgwg RbsinebI Klu / r ≤ 22 ssrGacRtUv)anKNnadUcssrxøI. edaysarEttM él Klu / r = 41.15 > 22 eKRtUvEtKitBIT§iBlénPaBrlas;. 3> KNnaemKuNm:Um:g;bEnßm δ ns eKeGay Cm = 1 / K = 1.4 / EI = 48.9 ⋅1012 N .m2 ¬BI]TahrN_TI2¦ nig π 2 EI π 2 × 48.9 ⋅ 1012 Pc = = = 10468.1kN (Klu )2 (1.4 × 4850)2 Cm 1 δ ns = = = 1.24 ⎛ Pu ⎞ ⎛ 1510 ⎞ 1− ⎜ 1− ⎜ ⎜ 0.75 × P ⎟ ⎟ ⎟ ⎝ 0.75 × 10468.1 ⎠ ⎝ c⎠ 4> BI]TahrN_TI2 Pu = 1510kN nig M u = 390kN .m b¤ Pn = 2323kN nig M n = 600kN .m m:Um:g;KNna M c = 1.24 × 600 = 744kN.m dUcenH δ ns M n 744 e= = = 320.3mm Pn 2323 5> epÞógpÞat;PaBRKb;RKan;rbs;ssrxøIsMrab; Pn = 2323kN / M c = 744kN .m nig e = 320.3mm . viFIsaRsþkñúgkaredaHRsayRtUv)anBnül;kñúg]TahrN_TI4 én emeroneRKOgbgÁúMrgkarsgát; nigkar Bt;. 6> BI]TahrN_TI4 én emeroneRKOgbgÁúMrgkarsgát; nigkarBt; eyIg)an Pn = 8.33a + 926.58 − 2.46 f s h 550 e' = e + d − = 320.3 + 490 − = 535.3mm 2 2 1 ⎡ ⎛ a⎞ ⎤ Pn = ⎢8.33a⎜ 490 − 2 ⎟ + 926.58(490 − 60)⎥ 535.3 ⎣ ⎝ ⎠ ⎦ ssrEvg 269
  • 16. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa = 7.625a − 0.00778a 2 + 744.31 eyIgTTYl)an a = 259.86mm dUcenH c = 305.7mm nig Pn = 2200kN . lT§PaBRTbnÞúkrbs;ssr Pn = 2200kN tUc CagbnÞúkEdlRtUvRT Pn = 2323kN . dUcenHmuxkat;minRKb;RKan;. 7> begáInmuxkat;EdkBI 4DB28 eTA 4DB30 ehIyeFVIkarKNnaepÞógpÞat;eLIgvij enaHeyIg TTYl)an Pn = 2335kN / ε t < 0.002 nig φ = 0.65 . ]TahrN_ 5³ KNnassrkaer:xagkñúgsMrab;Can;TImYyénGKarkariyal½y8Can;. kMBs; clear height énCan; TImYyKW 4.9m nigkMBs;sMrab;Can;d¾éTeTotKW 3.4m . GKarenHman 24RbGb; ¬rUbTI6¦ ehIyssrminRtUv)an BRgwgTb;nwgkareyalxag sidesway. bnÞúkEdlGnuvtþmkelIssrxagkñúgCan;TImYy bNþalmkBITMnajEpndI nigxül;dUcxageRkam³ bnÞúkefrtamGkS½ = 1690kN bnÞúkGefertamGkS½ = 623kN bnÞúkxül;tamGkS½ = 0kN m:Um:g;bnÞúkefr = 43.4kN.m ¬xagelI¦ 73.2kN.m ¬xageRkam¦ m:Um:g;bnÞúkGefr = 27.1kN.m ¬xagelI¦ 48.8kN.m ¬xageRkam¦ m:Um:g;bnÞúkxül; = 67.8kN.m ¬xagelI¦ 67.8kN.m ¬xageRkam¦ EI / l sMrab;Fñwm = 40 ⋅ 106 kN.mm eRbI f 'c = 35MPa / f y = 400MPa nigtMrUvkarrbs;bTdæan ACI Code. snμt;fa bnÞúkEdlmanGMeBI elIssrxageRkAesμI 2 / 3 énssrxagkñúg ehIybnÞúkEdlmanGMeBIelIssrRtg;RCugesμI 1 / 3 énssrxagkñúg ehIy β d = 0.55 . dMeNaHRsay³ 1> KNnabnÞúkemKuNedayeRbIkarpSMbnÞúk. sMrab;bnÞúkTMnajEpndI³ Slender Column 270
  • 17. T.Chhay NPIC Pu = 1.2 D + 1.6 L = 1.2 × 1690 + 1.6 × 623 = 3024.8kN M u = M 2ns = 1.2M D + 1.6M L = 1.2 × 73.2 + 1.6 × 48.8 = 165.92kN .m sMrab;bnÞúkTMnajEpndI nigbnÞúkxül; Pu = (1.2 D + 0.5L + 1.6W ) = 1.2 × 1690 + 0.5 × 623 + 0 = 2339.5kN M uns = M 2 ns = 1.2M D + 1.6M L = 1.2 × 73.2 + 1.6 × 48.8 = 165.92kN .m M us = M 2 s = 1.6M w = 1.6 × 67.8 = 108.48kN .m bnSMbnÞúkepSgeTotEdlminsMxan; Pu = 0.9 D + 1.6W = 0.9 × 1690 + 1.6 × 0 = 1521kN M 2 = 0.9 M D = 1.2 × 73.2 = 87.84kN .m M 2 s = 1.6M w = 1.6 × 67.8 = 108.48kN .m M M 165.92 e = u = 2ns = = 54.85mm Pu Pu 3024.8 emin = (15.24 + 0.03h) = 15.24 + 0.03 × 460 = 29.04mm < 54.85mm 2> eRCIserIsmuxkat;dMbUgrbs;ssredayEp¥kelIbnSMbnÞúkTMnajEpndIedayeRbItaragb¤düaRkam. eRCIserIsmuxkat;ssr 460 × 460 CamYynwgEdk DB32 cMnYn4edIm ¬rUbTI7¦. 3> epÞógpÞat; Klu / r 460 4 Ig = = 37.3 ⋅ 108 mm 4 Ec = 28278.9MPa 12 sMrab;ssr I = 0.7 I g sMrab;ssrEdlmankMBs; 4.9m EI 0.7 × 37.3 ⋅ 108 × 28278.9 = = 15.1 ⋅ 109 N .mm lc 4900 sMrab;ssrEdlmankMBs; 3.4m EI 0.7 × 37.3 ⋅ 108 × 28278.9 = = 21.7 ⋅ 109 N .mm lc 3400 ssrEvg 271
  • 18. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa sMrab;Fñwm EI g / lb = 40 ⋅109 N .mm / I = 0.35I g nig EI / lb = 0.35 × 40 ⋅ 109 = 14 ⋅ 109 N .mm ψ (top ) = ψ (bottom) = ∑ (EI / lc ) = (15.1 + 21.7) ⋅ 109 = 1.3 ∑ (EI / lb ) 2 × 14 ⋅ 109 BItarag alignment chart K = 1.4 sMrab;eRKagKμanBRgwg nig K = 0.8 sMrab;eRKag BRgwg. Klu 1.4 × 4900 = = 49.7 r 0.3 × 460 EdlFMCag 22 nigtUcCag 100 . dUcenH eKRtUvBicarNaBI slenderness ratio. 4> epÞógpÞat; lu / r = 4900 /(0.3 × 460) = 35.5 35 35 = = 54.8 (-24) Pu / f 'c Ag 3024800 /(35 × 460 × 460) edaysarEt lu / r < 54.8 m:Um:g; nonsway moment mincaM)ac;bEnßm. 5> KNna Pc Ec = 28278.9MPa Es = 2.1 ⋅ 105 MPa 2 460 4 4π 32 2 ⎛ 340 ⎞ Ig = = 37.3 ⋅ 108 mm 4 I se = ⎜ ⎟ = 93 ⋅ 10 mm 6 4 12 4 ⎝ 2 ⎠ β d = 0.55 0.2 Ec I g + Es I se EI = 1 + βd 0.2 × 28278.9 × 37.3 ⋅ 108 + 2.1 ⋅ 105 × 93 ⋅ 106 EI = = 26.2 ⋅ 1012 N .mm 2 1 + 0.55 edIm,IKNna δ s / β d = 0 enaH EI = 1.55 × 26.2 ⋅1012 = 40.63N .mm2 π 2 EI π 2 × 26.2 ⋅ 1012 Pc = ( Kl ) 2 = (0.8 × 4900) 2 = 16827.86kN ¬BRgwg¦ u π EI 2 π 2 × 40.63 ⋅ 1012 Pc = ( Klu ) 2 = (1.4 × 4900) 2 = 8521.15kN ¬KμanBRgwg¦ sMrab;mYyCan;enAkñúgGKar eKmanssrxagkñúg 14 ssrxageRkA 18 nigssrkac;RCug 4 . 2 1 ∑ Pu = 14(2339.5) + 18( × 2339.5) + 4( × 2339.5) = 63946.3kN 3 3 2 ∑ Pc = 14(8521.15) + 22( × 8521.15) = 244273kN 3 1 δs = = 1.54 63946.3 1− ( ) 0.75 × 244273 EdlFMCag 1 nigtUcCag 2.5 smIkar (-19) M c = M 2ns + δ s M 2 s = 165.92 + 1.54 × 108.48 = 333kN .m Slender Column 272
  • 19. T.Chhay NPIC 6> bnÞúkKNnaKW Pu = 2339.5kN nig M c = 333kN .m 333 e= = 142.34mm 2339.5 emin = (15.24 + 0.03h) = 15.24 + 0.03 × 460 = 29.04mm < e tamkarviPaK sMrab; e = 142.34mm nig A = 1608.5mm2 ¬ φ = 0.65 ¦ lT§PaBRTbnÞúkrbs; ssrmuxkat; 460 × 460 KW φPn = 2348.1kN nig φM n = 334.2kN .m dUcenHmuxkat;KWRKb; RKan;. ¬dMeNaHRsaymanlkçN³RsedogKñaeTAnwg]TahrN_TI4 kñúg emeroneRKOgbgÁúMrgkar sgát; nigkarBt;. tMél a = 242.86mm / c = 303.57mm / f s = 190.6MPa / f 's = 400MPa / φPb = 1676.8kN nig eb = 218mm ¦. 400 − 303.57 ε t = 0.003 = 0.00095 < 0.002 / φ = 0.65 303.57 ssrEvg 273