បេតុងពង្រឹងដោយដែក 16 xvi-continuous-beams-and-frames

T.Chhay NPIC

FñwmCab; nigeRKag 378

XVI. FñwmCab; nigeRKag Continuous Beams and Frames

1> esckþIepþIm Introduction

GKarebtugBRgwgedayEdkpÁúMeLIgedayGgát;eRKOgbgÁúMCaeRcInRbePTdUcCa kMralxNÐ½ (slab) Fñwm (beam) ssr (column) nigeCIgtag (footing) . Ggát;eRKOgbgÁúMTaMgenHGacRtUv)ancak;dac;eday ELkBIKña dUcCakMralebtugcak;eRsc (precast concrete slab) Fñwmcak;eRsc nigssrcak;eRsc eday manbnSl;TuksrésEdkedIm,IP¢ab;KñaBIGgát;eRKOgbgÁúMmYyeTAGgát;eRKOgbgÁúMmYyeTot edim,IeFVIeGayva køayCarcnasm<n§½EtmYy (monolithic structure). Ggát;Edlcak;eRscRtUv)anKNnadUcGgát;eRKOgbgÁúM enAelITMrsamBaØ eTaHbICaRbePTénPaBCab;xøHRtUv)anpþl;eGayenAEpñkcugrbs;va. sMrab;Ggát;Edlman lkçN³EtmYy (monolithic member) PaBCab;énGgát;nImYy²RtUv)anpþl;eGay EdleFVIeGayGgát; eRKOgbgÁúMRtUv)anviPaKdUcrcnasm<n§½sþaTicminkMNt; (statically indeterminate structure) .

karviPaK nigkarKNnakMralxNÐ½mYyTisCab;RtUv)anbgðajenAkñúgemeronTI 9 ehIyemKuNKNna (design coefficient) nigsrésEdklMGitRtUv)anbgðajenAkñúgrUbTI 9>8 nig 9>9. enAkñúgRbBn§½kMral xNÐ½mYyTis bnÞúkkMralxNÐ½RtUv)anbBa¢ÚnmkFñwmTMr dUcbgðajenAkñúgrUb 16>1 a . RbsinebIbnÞúkemKuN enAelIkMralxNÐ½KW uw enaHbnÞúkBRgayes μ IenAelIFñwm AB nig BC kñúgmYyÉktþaRbEvgKW swu bUknwg TMgn;pÞal;rbs;Fñwm. bnÞúkBRgayesμ IenAelIFñwm DE nig EF KW 2/swu bUknwgTMgn;pÞal;rbs;Fñwm. bnÞúkenAelIssr B esμ Inwg Lswu b:uEnþbnÞúkenAelIssr E / A nig D KW 2/Lsws / 2/Lsws nig

4/Lsws erogKña. enAkñúgkMralxNÐ½BIrTisEdlRTedayFñwmenARCugTaMgbYn bnÞúkkMralxNÐ½RtUv)anbBa¢ÚneTAFñwmBIRkLa

épÞcMNuHEdlBT§½edaybnÞat; o45 dUcbgðajenAkñúgrUbTI 16>1 b. EpñkxøHénbnÞúkkMralxNÐ½RtUv)anbBa¢Ún eTAFñwmEvg AB / BC / DE nig EF BIRkLaépÞctuekaNBñay b:uEnþbnÞúkkMralxNÐ½EdlenAsl;RtUv)an bBa¢ÚneTAFñwmxøI AD / BE nig CF BIRkLaépÞRtIekaN. sMrab;kMralxNÐ½kaer bnÞúkRtUv)anbBa¢ÚneTAFñwm EdlBT§½CMuvijBIRkLaépÞRtIekaN. FñwmenAxagkñúgTTYlbnÞúkBIRCugTaMgBIr b:uEnþFñwmxagrgbnÞúkEtmYyxag b:ueNÑaH. edaysarFñwmTaMgBIrTisRtUv)ancak;ebtugkñúgeBlCamYyKñanwgkMralxNÐ½ enaHvaRtUv)anviPaKCa FñwmCab;sþaTicminkMNt; (statically indeterminate continuous beam). FñwmbBa¢ÚnbnÞúkbnþeTAssr. bnÞúkenAelIssr B esμ Inwg Lswu enAeBlEdl bnÞúkenAelIssr E / A nig D KW 2/Lsws /

T.Chhay NPIC


2/Lsws nig 4/Lsws erogKña. RkLaépÞcMNuHsMrab;ssrnImYy²RtUv)anKitBIGkS½rbs;ElVgEdlenA Ek,rRKb;Tis.

2> m:Um:g;GtibrmaenAkñúgFñwmCab; Maximum Moment in Continuous Beams

2> 1> eKalkarN_viPaK Basic Analysis CaTUeTA karKNnam:Um:g;Bt; nigkMlaMgkat;TTwgenAkñúgFñwmCab;ebtugGarem:KWQrelIRTwsþIeGLasÞic

(elastic theory). enAeBlmuxkat;ebtugGarem:RtUv)anKNnaedayeRbIviFIKNnaersIusþg; (strength

design method) lT§plEdlTTYl)annwgmineqøIytbCamYynwgkarviPaKeGLasÞic (elastic analysis)

eT. b:uEnþ ACI Code min)anbBa¢ÚllkçxNÐsMrab;karKNna)øasÞic (provision for a plastic design) b¤ karKNnasßanPaBkMNt; (limit state design) éneRKOgbgÁúMCab;ebtugGarem: RKan;EtGnuBaØatkarEbg Eckm:Um:g;eLIgvij (moment redistribution) dUcEdlnwgBnül;enAkñúgemeronenH.

2> 2> karGnuvtþn_kardak;bnÞúk Loading Application m:Um:g;Bt;enARtg;cMnucNamYyenAkñúgFñwmCab; vaminGaRs½yEtnwgbnÞúkEdlmanTItaMgenAelIFñwmdUcKña

enaHeT b:uEnþvak¾GaRs½ynwgbnÞúkEdlsßitenAelIFñwmd¾éTeTotEdr. kñúgkrNIbnÞúkefr RKb;FñwmTaMgGs;RtUv Etdak;bnÞúkkñúgeBldMNalKña edaysarEtbnÞúkefrmanTItaMgnigtMélkMNt;. kñúgkrNIbnÞúkgl½t b¤ bnÞúkGefrEdlekIteLIgmþgmáal EbbbTénkardak;bnÞúkRtUv)anBicarNay:gNaedIm,IkMNt;m:Um:g;Gti -

T.Chhay NPIC


brmaenATItaMgeRKaHfñak;. ExS\T§iBlGacRtUv)aneRbIedIm,IkMNt;TItaMgrbs;bnÞúkGefredIm,IKNnam:Um:g; Gtibrma nigm:Um:g;Gb,brma. b:uEnþenAkñúgemeronenH k,Ünd¾samBaØEdlQrelIExSekagbnÞúk-PaBdab (load-deflection curve) RtUv)aneRbIedIm,IkMNt;EbbbTénkardak;bnÞúkEdlbegáItm:Um:g;Gtibrma.

2> 3> m:Um:g;viC¢manGtibrma nigGb,brmaenAkñúgElVg Maximum and Minimum Positive Moments within a Span

m:Um:g;Bt;viC¢manGtibrmaenAkñúgFñwmTMrsamBaØEdlrgbnÞúkBRgayesμ I w KWsßitenAkNþalElVg CamYy

nwg 8

2wlM = . RbsinebIcugrbs;vamYy b¤TaMgBIrRtUv)anbnþ karTb;enAcugEdlCab;nwgbegáItm:Um:g;GviC¢ manenAelITMr ehIyTItaMgénbnÞúkviC¢manGtibrmaGacpøas;bþÚrbnþicBIkNþalElVg. ragdabénFñwmCab;sM rab;kardak;bnÞúkEtelIElVgEtmYy RtUv)anbgðajenAkñúgrUbTI 16>2 a . PaBdabcuHeRkambgðajfam:Um:g;

T.Chhay NPIC


viC¢man ehIyPaBdabeLIgelIbgðajm:Um:g;GviC¢man. RbsinebIRKb;ElVgEdldabcuHeRkamRtUv)andak; bnÞúk enaHbnÞúknImYy²nwgbegáInm:Um:g;viC¢manenAkñúgElVg AB ¬rUbTI 16>2 d ¦. dUcenHedIm,IKNnam:U m:g;viC¢manGtibrmaenAkñúgElVgNamYy bnÞúkGefrRtUv)andak;enAelIElVgenaH nigenAelIElVgqøas;TaMg sgçag. m:Um:g;bnÞúkGefremKuNEdlKNnadUcBnül;BImunRtUv)anbEnßmBIelIm:Um:g;bnÞúkGefremKuNenA elImuxkat;dUcKñaedIm,ITTYl)anm:Um:g;viC¢manGtibrma.

düaRkamm:Um:g;Bt;Edl)anBIbnÞúkBRgayes μ IenAelIElVg AB RtUv)anbgðajenAkñúgrUbTI 16>2 b. PaBdab nigm:Um:g;Bt;fycuHy:agelOnCamYynwgcMgayBIElVg AB EdlrgbnÞúk. dUcenH edIm,IsMrYlkar viPaKFñwmCab; m:Um:g;enAkñúgElVgNamYyGacRtUv)anKNnaedayBicarNaEtFñwmEdlrgbnÞúk AB nigFñwm BIreTotEdlenAsgçagva nigsn μt;TMrbgáb;enAcugEdlq¶ayTaMgsgçag ¬rUbTI 16>2 c ¦.

RbsinebIElVgEdlCab;nwgElVg AB RtUv)andak;bnÞúk ExSekagdabRtUv)anbgðajenAkñúgrUb 16>2 e . PabdabenAkñúgElVg AB nwgeLIgelI ehIym:Um:g;GviC¢mannwgRtUv)anbegáItenAkñúgFñwm AB . m:Um:g;GviC¢ -manenHnwgRtUv)anbEnßmeTAelIm:Um:g;viC¢manEdl)anBIbnÞúkefredIm,ITTYl)anm:Um:g;Bt;cugeRkay. dUcenH edIm,IKNnam:Um:g;viC¢manGb,brma ¬b¤m:Um:g;GviC¢manGtibrma¦ enAkñúgElVg AB bnÞúkGefrRtUv)andak; enAElVgEk,rnwgElVg AB nigRKb;ElVgqøas;nwgElVgEdlrgbnÞúk ¬rUbTI 16>2 e ¦.

2> 4> m:Um:g;GviC¢manGtibrmaenAelITMr Maximum Negative Moments at Supports kñúgkrNIenH eKcaM)ac;kMNt;m:Um:g;GviC¢manGtibrmaenAelITMrNamYy dUcCaTMr A ¬rUbTI 16>3¦.

enAeBlEdlElVg AB RtUv)andak;bnÞúk m:Um:g;GviC¢manRtUv)anbegáItenAelITMr A . dUcKña bnÞúkénElVg AF k¾nwgbegáItm:Um:g;GviC¢manenAelI A Edr. dUcenH edIm,IKNnam:Um:g;GviC¢manGtibrmaenAelITMrNa mYy bnÞúkGefrRtUv)andak;enAelIElVgEk,rTaMgBIr nigenAelIRKb;ElVgqøas;TaMgsgçag ¬rUbTI 16>3¦.

enAkñúgkarviPaKeRKOgbgÁúM (structural analysis) énFñwmCab; RbEvgElVgRtUv)anKitBIGkS½eTAGkS½TMr EdlRTedayTMrcugkaMbiT (knife-edge support). enAkñúgkarGnuvtþn_ TMrRtUv)aneFVIeLIgedaymanTMhM RKb;RKan;edIm,ITTYlbnÞúkEdlbBa¢ÚnedayFñwm CaTUeTAm:Um:g;eFVIGMeBIenAnwgépÞénTMr. edIm,IKNnam:Um:g;enA nwgépÞénTMr eKGacdkedaym:Um:g;EdlesI μnwg 3/cVu BIm:Um:g;emKuNenAGkS½rbs;TMr Edl uV KWCakMlaMg kat;TTwgemKuN nig c CaTTwgssr.

T.Chhay NPIC


2> 5> m:Um:g;enAkñúgFñwmCab; Moments in Continuous Beams FñwmCab; nigeRKagCab;GacRtUv)anviPaKedayeRbIviFIRbhak;RbEhl (approximate method) b¤kmμ -

viFIkMuBüÚT½r. viFIepSgeTotdUcCa viFIbnÞúk nigbMlas;TI (displacement and force method) énkarviPaK EdlQrelIkarKNnaénm:aRTIsénPaBrwgRkaj nigPaBrlas; (stiffness and flexibility matrices) GacRtUvykmkeRbI. viFI slope deflection nigviFI moment-distibution k¾GacRtUv)aneRbI. viFITaMgenH manBnül;enAkñúgesovePAEdlniyayBIkarviPaKeRKOgbgÁúM (structural analysis) énFñwm nigeRKag. ACI Code, Section 8.3 pþl;nUvemKuNRbhak;RbEhlsMrab;KNnam:Um:g;Bt; nigkMlaMgkat;TTwgenAkñúg Fñwm nigkMralxNÐ½Cab;. emKuNTaMgenHRtUv)aneGayenAkñúgemeronTI 9. m:Um:g;EdlTTYl)anBIemKuN ACI nwgmantMélFMCagm:Um:g;EdlTTYl)anBIkarKNnaviPaKbnþic. eKRtUveKarBtamkarkMNt;Edlman EcgenAkñúgkareRbIR)as;emKuNTaMgenaH. ]TahrN_TI 16>1³ RbBn§½kMralxNÐ½-Fñwm Edl)anbgðajenAkñúgrUbTI 16>4 RTnUvbnÞúkGefrBRgayesμ I 2/2.6 mkN nigbnÞúkefrEdlrYmmanbnÞúkpÞal;rbs;kMralxNÐ½bUknwg 2/8.3 mkN . edayeRbIemKuNm:Um:g; ACI

KNnaFñwmCab;enAxagkñúg nigKUrnUvmuxkat;lMGit. eKeGay MPaf c 28' = / MPaf y 400= / TTWgFñwm mmb 300= / muxkat;ssr mm300300× nigkMras;kMralxNÐ½ mm125 .

T.Chhay NPIC


dMeNaHRsay³ 1> KNnakMralxNÐ½³ kMralxNÐ½mannaTICakMralxNÐ½mYyTis edaysarpleFobRCugEvgelIRCugxøI

FMCag 2 . karKNnaénRbePTkMralxNÐ½Cab;RtUv)anBnül;enAkñúg]TahrN_TI 9>4. 2> bnÞúkenAelIkMralxNÐ½³ bnÞúkefr 2/925.68.325125.0load Dead mkN=+×= bnÞúkGefr 2/2.6load Live mkN= bnÞúkemKuN 2/23.182.66.1925.62.1)( load Ultimate mkNwu =×+×=

bnÞúúúkenAelIFñwm³ Fñwmxagkñúg ABC RTbnÞúkkMralxNÐ½TaMgsgçag CamYynwgTTwgkMralxNÐ½srub m6.3

bnÞúkemKuNenAelIFñwm ( ) webbeam ofweight -self2.123.186.3beamon load Factored +×=

kMBs;rbs;FñwmGacRtUv)ankMNt;edayeRbIemKuNénkMras;FñwmGb,brmadUcEdl)anbgðajenAkñúgtarag]bsm<n§½ B.6. sMrab; MPaf y 420= kMBs;FñwmGb,brmarbs;FñwmTI1 AB KW 5.18/L

m389.018/2.7 == . sn μt;kMBs;Fñwmsrub mm550 kMBs;RTnugFñwmKW mm425125550 =− . dUcenHbnÞúkemKuNenAelIFñwm ABCD KW

( ) mkNwu /45.69253.0425.02.123.186.3 =××+×= yk mkNwu /5.69= 3> m:Um:g;enAkñúgFñwm ABC ³ emKuNm:Um:g;RtUv)anbgðajenAkñúgrUbTI 9>8. FñwmCab;Kñaman 5 ElVg

ehIysIuemRTIKñaeFobGkS½kNþalRtg;cMnuc D . dUcenH eKcaM)ac;KNnaEtFñwmBak;kNþal ABCD BIeRBaHFñwmBak;kNþaleTotnwgmanTMhMehIynwgbrimaNEdkdUcKña. edaysarElVg AB nig BC mines μIKñaEtmanpleFob 2.7/9.7 mantMéltUcCag 2.1 enaHemKuNm:Um:g; ACI

GacGnuvtþ)ansMrab;FñwmenH. elIsBIenHRbEvg clear span mFümEdlenAEk,rRtUv)aneRbIedIm,I KNnam:Um:g;GviC¢manenAelITMr.

m:Um:g;enAmuxkat;eRKaHfñak;RtUv)anKNnadUcxageRkam ¬rUbTI 16>4¦ 2tcoefficien nuu lwM ×=

T.Chhay NPIC


TItaMg ! @ # $ % ^ emKuNm:Um:g; 16

1−

141

+ 101

− 161

+ 111

− 161

+

uM ¬ mkN. ¦ 8.206− 35.236 3.365− 9.250 9.364− 9.250 4> kMNt;TMhMFñwm nigsrésEdk a. m:Um:g;GviC¢GtibrmaKW mkN.3.365− . edayeRbI 016.0max =ρ enaH MPaRu 5= / 9.0=φ

mmbR

Md

u

u 5.4933005

103.365 6=

×⋅

==

sMrab;EdkmYyRsTab; kMBs;FñwmsrubKW mm5.553605.493 =+ yk mm600 d EdleRbIR)as;BitR)akdKW mm54060600 =− 22592540300016.0 mmAs =××= eRbI 304DB ¬mYyRsTab;¦

cMNaMfa³ kMBs;FñwmEdleRbIenATIenHKW mm600 EdlFMCagkMBs;Fwñmsnμt;Edlesμ Inwg mm550 edIm,IkMNt;TMgn;rbs;Fñwm. edaysarbnÞúkbEnßmmantMéltUcGacecal)an eKmincaM)ac;eFVIkar KNnaeLIgvijeT.

b. muxkat;enATMreFVIGMeBICamuxkat;ctuekaNEkgCamYyEdkTajenAkñúgsøab. EdkcaM)ac;enAkñúgTMr mandUcxageRkam³ TItaMg ! # %

).( mkNMu 8.206− 3.365− 9.364− )(MPaRu 36.2 17.4 17.4

(%)ρ 74.0 39.1 39.1 )( 2mmAs 1199 2252 2252

cMnYnEdk 30DB 2 4 4 c. sMrab;muxkat;GkSr T enAkNþalElVg mkNMu .9.250= . sMrab; mma 25= nigTTwgsøab mb f 8.1= ( )

26

2.13215.125404009.0

109.250

2

mmadf

MAy

us =

−×⋅

=⎟⎠⎞

⎜⎝⎛ −

=φ

T.Chhay NPIC


RtYtBinitü a ³ mmbf

fAa

c

ys 34.1218002885.04002.1321

'85.0=

×××

==

CamYy mma 34.12= eKTTYl)an 25.1305 mmAs = . dUcenHeRbIEdk 253DB ¬ 26.1472 mmAs = ¦ sMrab;RKb;muxkat;kNþalElVgTaMgGs;. bøg;EdklMGitRtUv)anbgðajenA kñúgrUbTI 16>5.

5> KNnaFñwmsMrab;kMlaMgkat;TTwg dUcEdl)anBnül;enAkñúgemeronTI 8. 6> RtYtBinitüPaBdab nigsñameRbH dUcEdl)anBnül;enAkñúgemeronTI 9.

3> eRKagsMNg;GKar Building Frames

eRKagGKarKWCaRbBn§½eRKOgbgÁúMbITMhM ¬kñúglMh¦ (three-dimensional structural system) EdlpÁúM eLIgeday Ggát;Rtg;²Edlsagsg;CamYyKña (built monolithically) nigmantMNrwg. eRKagGacman mYyElVg nigmankMBs;mYyCan; dUcCa portal frame nig gable frame dUcbgðajenAkñúgrUbTI 16>6 a b¤ GacpSM eLIgedayeRcInElVg nigeRcInCan; dUcbgðajenAkñúgrUbTI 16>6 b. RKb;Ggát;rbs;eRKagRtUv)an cat;Tuk faCab;sMrab;TisTaMgbI ehIyssrcUlrYmCamYynwgFñwmedIm,ITb;bnÞúkxageRkA. eRkABIkarkat; bnßym:Um:g; edaysarPaBCab; eRKagGKarcg;)ankarBRgaybnÞúkkan;Etes μ Ikan;Etl¥. \T§iBlénbnÞúk xag dUcCabnÞúkxül; nigbnÞúkrBa¢ÜydI RtUv)anBRgayenAelIeRKagTaMgmUl edIm,IbegáInsuvtßiPaBrbs;va.

T.Chhay NPIC


sMrab;karKNna viFIRbhak;RbEhl (approximate method) GacRtUv)aneRbIedaysnμt;RbBn§½eRKag BIrTMhM ¬kñúgbøg;¦.

eRKagEdlrgnUvRbBn§½bnÞúkGacRtUv)anviPaKedayviFIeRKagsmmUl (equivalent frame method). enAkñúgviFIenH karviPaKtamCan;KWRtUveFVIeLIgedaysn μt;facugssrEdlenAq¶ayBIelI nigBIeRkamnIv:UkM-ralxNÐ½RtUv)anbgáb; ¬rUbTI 16>7¦. CaTUeTA karviPaKRtUv)aneFVIeLIgedayeRbIviFIEbgEckm:Um:g; (moment-distribution method).

enAkñúgkar TMhMkMral (panel) cMgaycenøaHssr/ cMnYnCan; nigkMBs;énCan;nImYy²RtUv)ansÁal;BI eRBaHBYkvaRtUv)anpþl;eGayedaykarKNnasßabtükm μ ehIyRbBn§½brikçaRtUv)anKitrYcCaeRsc. TMhM ssr nigTMhMFñwmRtUv)aneFVIkar)a:n;sμanCamun ehIypleFobPaBrwgRkajrbs;vaEdlQrelImuxkat;eb tugRtUv)aneRbI. enAeBlm:Um:g;RtUv)ankMNt; eKRtUvRtYtBinitümuxkat;Edl)ansnμt;BImun nigeFVIkaeEktMrUv RbsinebIcaM)ac;. karviPaKEdlmanlkçN³suRkitCagGaceFVIeLIgedayeRbIkmμviFIkMuBüÚTr½ EdlRtUv)an

T.Chhay NPIC


ENnaMsMrab;karviPaK eRKOgsþaTicminkMNt;EdlmanGBaØtieRcIn. viFIénkarviPaKRtUv)anBN’naenAkñúg esovePACaeRcInEdlniyayBIkarviPaKeRKOgbgÁúM.

4> Portal Frames

Portal frames pSMeLIgedayFñwmebtugGarem:EdlrwgRtUv)ancak;CamYynigTMrssrrbs;va. tMN rvagFñwm nigssrRtUv)anBicarNabgáb;rwgCamYynwgplbUkm:Um:g;enARtg;tMNesμ IsUnü. Portal frames RtUv)aneRbIenAkñúgsMNg;salEdlmanElVgFM (large-span halls)/erag (sheds)/ s<an nigs<ankat;RC lgPñM (viaducts). Ggát;EpñkxagelIrbs;eRKagGacedk (portal frames) b¤eRTt (gable frames) ¬rUb TI 16>8¦. eCIgeRkamrbs;eRKagGacCaTMrbgáb; b¤TMrsnøak;. Portal frames sþaTicminkMNt;GacRtUv)anviPaKedayviFIEbgEckm:Um:g; b¤viFIdéTeTotEdleRbI edIm,IviPaKeRKagsþaTicminkMNt;. Ggát;rbs;eRKagRtUv)anKNnasMrab;m:Um:g; kMlaMgkat;TTwg nigkMlaMg Ekg b:uEnþeCIgtagRtUv)anKNnaedIm,IRTkMlaMgEdlmanGMeBIenA)atssr. Fñwm nigssrrbs;eRKagGacmanTMhMesμI b¤ERbRbYl dUcbgðajenAkñúgrUbTI 16>8. kMlaMgenAkñúg portal frames EdlmanmYyElVgehIymanmuxkat;esμ IGacRtUv)anKNnadUcxageRkam³ 4> 1> cugsnøak;BIr Two Hinged Ends kMlaMgenAkñúgGgát;rbs; portal frames Edlmancugsnøak;BIrGacRtUv)anKNnaedayeRbIsmIkar xageRkam ¬rUbTI 16>9¦³ sMrab;krNIbnÞúkBRgayes μ IenAelIGgát; BC / yk ⎟⎟

⎠

⎞⎜⎜⎝

⎛×+=

Lh

IIK

1

223

Edl 1I nig =2I m:Um:g;niclPaBrbs;ssr nigFñwm h nig =L kMBs; nigRbEvgElVgrbs;eRKag m:Um:g;Bt;enAtMN B nig C KW

KwLMM CB 4

2−==

m:Um:g;viC¢manGtibrmaenAkNþalElVg BMwLBC +=8

2

kMlaMgRbtikm μtamTisedkenARtg;cMnuc A KW DBA HhMH == / kMlaMgRbtikm μtamTisQrenARtg;cMnuc A KW DA VwLV == 2/

T.Chhay NPIC


sMrab;bnÞúkBRgayes μ IenAelIEtBak;kNþalFñwm BC ¬rUbTI 16>9 b¦

KwLMM CB 8

2−==

h

MHH BDA ==

8/3wLVA = nig 8/wLVD =

4> 2> cugbgáb;BIr Two Fixed Ends kMlaMgenAkñúgGgát;rbs; portal frames Edlmancugbgáb;BIrGacRtUv)anKNnaedayeRbIsmIkar xageRkam ¬rUbTI 16>10¦³ sMrab;krNIbnÞúkBRgayes μ IenAelIGgát; BC / yk ⎟⎟

⎠

⎞⎜⎜⎝

⎛×+=

Lh

IIK

1

21 2

K

wLMM CB 4

2−==

T.Chhay NPIC


2

BDA

MMM ==

BMwLM +=8

)midspan(2

2

3 ADA

MHH == nig 2

wLVV DA == sMrab;bnÞúkBRgayes μ IenAelIEtBak;kNþalFñwm BC ⎟⎟

⎠

⎞⎜⎜⎝

⎛×+=

Lh

IIK

1

22 61

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

21

2

81

31

8 KKwLM A ⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

21

2

81

32

8 KKwLM B

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

21

2

81

32

8 KKwLMC ⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

21

2

81

31

8 KKwLM D

hK

wLHH DA1

2 18

×==

DA VwLV −=2

nig ⎟⎟⎠

⎞⎜⎜⎝

⎛−=

2411

8 KwLVD

T.Chhay NPIC


5> eRKagTUeTA General Frames

T.Chhay NPIC


rUbragcMbgrbs;eRKagKWtMNrwg EdlP¢ab;FñwmdMbUledk b¤eRTteTAnwgGgát;eRKOgbgÁúMEdlRTva. PaBCab;rvagGgát;nwgEbgEckm:Um:g;Bt;EdlmanCab;CamYynwgRbBn§½bnÞúkeTAGGát;eRKOgbgÁúMepSgeTot eTAtampleFobénPaBrwgRkajrbs;va. eRKagGacRtUv)ancat;cMNat;fñak;dUcxageRkam³

- eRKagsþaTickMNt; (statically determinate frame) ¬rUbTI 16>11 a¦ - eRKagsþaTicminkMNt; (statically indeterminate frame) ¬rUbTI 16>12¦ - eRKagsþaTicminkMNt; CamYynwgcMNg (statically indeterminate frame with tie) ¬rUbTI

16>13¦

T.Chhay NPIC


T.Chhay NPIC


6> karKNnasnøak;rbs;eRKag Design of Frame Hinges

RbePTd¾sMxan;énsnøak;EdleRbIenAkñúgeRKagebtugKW Mesnager hinges, Considère hinges

nig lead hinges. 6> 1> Mesnager hinges

CaTUeTA kMlaMgEdlmanGMeBIenAelIsnøak;KWkMlaMgedk H nigkMlaMgbBaÄr P . kMlaMgpÁÜbén kMlaMgTaMgBIr R RtUv)anbBa¢ÚneTAeCIgtagtamry³EdkExVg A nig B dUcEdl)anbgðajenAkñúgrUbTI 16>14. PaBeRTtrbs;r)ar A nig B eTAnwgGkS½edkERbRbYlBI o30 eTA o60 CamYynwgcMgay Gb,brma a ¬Edlvas;BIEpñkeRkameKrbs;eRKagssr¦ es μ Inwg D8 Edl D CaGgát;p©itrbs;EdkeRTt. cenøaH y rvageRKagssr nigEpñkxagelIrbs;eCIgtagERbRbYlcenøaHBI mm25 eTA '3.1 h Edl 'h Ca TTwgrbs;muxkat;ebtugenAnIv:Usnøak;. kMBs;cenøaHsMrab;karGnuvtþn_ERbRbYlBI mm50 eTA mm100 . karvilrbs;cugeRKagRtUv)aneFVIeLIgedaysnøak; ehIyCaTUeTAcenøaHRtUv)anbMeBjeday bituminous

cork nigsMPar³EdlmanlkçN³bt;EbnRsedogKña. Bitumen karBar corkkMueGayxUcedaysarkarb:H CamYydI. EdkExVg A nig B rgnUvkugRtaMgsgát;EdlminRtUvFMCag 3/1 énersIusþg;yal (yield

strength) rbs;Edk yf eRkambnÞúkeFVIkar (service load) b¤ yf55.0 eRkambnÞúkemKuN (factored

load). kugRtaMgtUcRtUv)ansnμt;edaysarkarvilenAsnøak;cg;Bt;Edk nigegáItkugRtaMgBt;TIBIr

T.Chhay NPIC


(secondary flexural stresses). CaTUeTA eKcaM)ac;RtUvrkSakugRtaMgsgát;eGaytUcl μmRbesIrCagKNna kugRtaMgTIBIr. RkLaépÞEdk A nig B RtUv)anKNnadUcxageRkam³

RkLaépÞmuxkat;Edk A ³ y

s fRA55.0

11 = ¬!^>!¦

RkLaépÞmuxkat;Edk B ³ y

s fRA55.0

22 = ¬!^>@¦

Edl 1R nig 2R CabgÁúMénkMlaMgpÁÜb R enAkñúgTisedAénEdkeRTt A nig B edayeRbIbnÞúkem KuN. CaTUeTA bgÁúMkMlaMg 1R nig 2R RtUv)anTTYledaysmIkarsþaTicxageRkam³

θθ sinsin 12 RRH =+ nig θsin12

HRR −= ¬!^># a¦ dUcKña ( ) uPRR =+ θcos21 dUcenH ⎥⎦

⎤⎢⎣⎡ −−=−=

θθθ sincoscos 121HRPRPR uu

⎥⎦⎤

⎢⎣⎡ +=

θθ sincos21

1HPR u ¬!^># b¦

Edksnøak;eRTtbBa¢ÚnkMlaMgrbs;vatamry³cMNgenAtamRbEvgEdkbgáb;eTAkñúgssreRKag nig eCIgtag. dUcenH EdkeRTtbeBa©jkMlaMgFak;ecjeRkA EdlRtUvTb;edayEdkcMNg. EdkcMNgRtUv)an dak;elIcMgay Da 8= ¬Ggát;p©itEdkEdlFMCageKkñúgcMeNam A nig B ¦ TaMgenAkñúgssr nigeCIgtag. kMlaMgFak;ecj (bursting force) GacRtUv)ankMNt;dUcxageRkam³

dHaPF u85.0

tan2

+= θ ¬!^>$¦ RbsinebIkarcUlrYmrbs;ebtugRtUv)anecal enaHRkLaépÞmuxkat;rbs;EdkcMNg stA EdlcaM)ac; Tb;kMlaMg F KW³

yyst f

FfFA

85.0==

φ ¬!^>%¦

kugRtaMgenAkñúgEdkcMNgk¾GacRtUv)ankMNt;dUcxageRkam³

yst

u

s fAab

dHaP

f 85.0)tie(005.0

85.0tan

2)tie( ≤+

+=

θ ¬!^>^¦

Edl =stA RkLépÞmuxkat;EdkkgkñúgcMgay Da 8= =d kMBs;RbsiT§PaBrbs;muxkat;ssr =b TTwgrbs;muxkat;ssr

T.Chhay NPIC


snøak;RbePTenHRtUv)aneRbIsMrab;kMlaMgl μm nigRtUv)ankMNt;edaycMnYnEdkeRTtGtibrmaEdl GacRtUv)andak;enAkñúgTTwgssr.

6> 2> Considère hinges PaBxusKñarvag Considère hinges nig Mesnager hinges KWfakMlaMgEkg uP RtUv)ansnμt;fa vaRtUv)anbBa¢ÚneTAeCIgtagedaykUnssrEdkkgvNÐ½ (spirally reinforced short columns) mYyb¤eRcIn Edldak;bBa©ÚleTAkñúgeCIgtag b:uEnþkMlaMgedk H RtUv)ansn μt;Tb;edayEdkeRTt A nig B ¬rUbTI !^>%¦. lT§PaBRTbnÞúkrbs;kUnssrEdkkgvNÐ½GacRtUv)ankMNt;edayeRbIsmIkar !^>& edayecalemKuN 85.0 sMrab;cMNakp©itGb,brma. ( )[ ]yststgcnu fAAAfPP +−== '85.070.0φ ¬!^>&¦

T.Chhay NPIC


Edl gA CaRkLaépÞmuxkat;rbs;muxkat;snøak;ebtug b¤ 'bh / nig stA CaRkLaépÞmuxkat;Edk beNþayenAkñúgEdkkgvNÐ½. EdkcMNgRtUv)andak;enAkñúgssrrhUtdl;cMgayEdles μ InwgRCugEvgrbs; muxkat;ssr h .

6> 3> Lead hinges

eBlxøH Lead hinges RtUv)aneRbIenAkñúgeRKagssrebtugGarem:. enAkñúgsnøak;RbePTenH CaTU eTA lead plate EdlmankMras;BI mm20 eTA mm25 RtUv)anebIedIm,IbBa¢ÚnkMlaMgtamGkS½ uP eTAeCIg tag. kMlaMgedk H RtUv)anTb;edayEdkbBaÄrEdldak;enARtg;GkS½rbs;ssr nigRtUv)andak;bBa©Úl

T.Chhay NPIC


eTAkñúgssr ¬rUbTI 16>16¦. enARtg;)atrbs;ssr kMlaMgEkg uP minRtUvFMCagersIusþg;Tb; ( )1'85.0 Af cφ ¬EdlkMNt;eday ACI Code, Section 10.15¦ Edl 65.0=φ nig '1 bhA = . RkLa

épÞmuxkat;EdkbBaÄrKW ys fHA 6.0/= Edl =H kMlaMgedkemKuN. ]TahrN_16>2 salmYymanTMhM m122.25 × RtUv)anRKbedaykMralebtugGarem:EdlRTeday portal frame Edlman snøak;enATMr. Portal frame manKMlatBIGkS½eTAGkS½ m6.3 ¬rUbTI 16>17¦. kMBs;eRKagKW m5.4 ehIyK μanssrenAkñúgsaleT. bnÞúkefrenAelIkMralxNÐ½KW)anBIbnÞúkpÞal;bUknwg 2/6.3 mkN Edl)an mkBIkargarbegðIyrbs;dMbUl. bnÞúk efrenAelIkMralxNÐ½KW 2/4 mkN . KNnaeRKagenAxagkñúgeday eRbI MPaf c 28' = nig MPaf y 400= sMrab;eRKag ehIymuxkat;ssrmanTTwg mmb 400= .

dMeNaHRsay³ karKNnaeRKageménGKarrYmmandUcxageRkam³

- KNnakMralxNÐ½mYyTis - viPaK Portal frame - KNnaFñwmeRKagEdlbNþalmkBIm:Um:g;

T.Chhay NPIC


- KNnaFñwmeRKagEdlbNþalmkBIkMlaMgkat; - KNnassr - KNnasnøak; - KNnaeCIgtag 1> kMralxNÐ½mYyTis³ kMras;Gb,brmarbs;kMralxNÐ½TI1KW 30/L edaysarcugmçagCab;

nigcugmçageTotminCab; ¬tarag B.6 enAkñúg]bsm<n§½ B¦. kMBs;Gb,brma mm120

303600

== karKNnakMralxNÐ½GnuvtþtamCMhanEdlmanenAkñúg]TahrN_9>5.

2> viPaK Portal frame enAxagkñúg³ a. bnÞúkenAelIkMralxNÐ½KW

bnÞúkefrenAelIkMralxNÐ½ 2/6.62512.06.3 mkN=×+= bnÞúkemKuNenAelIkMralxNÐ½ 2/32.140.46.16.62.1 mkN=×+×=

b. kMNt;bnÞúkenAelIeRKag³ eRKagxagkñúgRTbnÞúkBIkMralxNÐ½ m6.3 bEnßmBIelIbnÞúkpÞal;rbs; FñwmeRKag. sn μt;kMBs;rbs;FñwmKW mmL 50024/1200024/ == . edayeRbIkMBs;BIeRkam kMralxNÐ½ mm400 enaHkMBs;srubrbs;FñwmKW mm520 . bnÞúkefrBIbnÞúkpÞal;rbs;Fñwm mkN /4254.0 2 =×= bnÞúkemKuNsrubenAelIeRKag mkN /352.5642.16.332.14 =×+×= dUcenH mkNwu /5.56=

c. kMNt;m:Um:g;niclPaBénmuxkat;Fñwm nigmuxkat;ssr. FñwmeFVIkarCalkçN³muxkat;GkSr T . TTwgRbsiT§PaBrbs;kMralxNÐ½EdleFVIskmμPaBCamYynwgFñwmKWCatMéltUcCageKén 4/1 én RbEvgElVg m34/12 == / mbh ws 32.24.012.01616 =+×=+ nig m6.3 . yk

mb 32.2= . TIRbCMuTMgn;énmuxkat;BIsrésxagelIeKKW mmy 89.154

4004001202320320400400601202320

=×+×

××+××=

⎟⎟⎠

⎞⎜⎜⎝

⎛×++⎟

⎠⎞

⎜⎝⎛ ××+×= 22

423 11.165400

1240089.941202320120

122320)(beamIb

46109336 mm⋅=

T.Chhay NPIC


vaCakarGnuvtþn_TUeTAedayKitm:Um:g;niclPaBRbhak;RbEhlrbs;FñwmGkSr T esμ Inwg 2 dg énm:Um:g;niclPaBrbs;muxkat;ctuekaNEkgEdlmankMBs;srubCaplbUkrvagkMBs;RTnugFñwm nigkMras;kMralxNÐ½³

463

10937412

5204002)beam( mmIb ⋅=×

×= sMrab;Fñwmxag m:Um:g;niclPaBRbhak;RbEhlKW 12/5.1 3bhI ×= . sn μt;muxkat;ssres μ I mm500400× ¬EdlmanTTwgdUcTTwgFñwm¦

463

10416712

500400)column( mmIc ⋅=×

= d. KNnaemKuN K

68.4104167

450012000

1093742323 6

6=⎟

⎟⎠

⎞⎜⎜⎝

⎛

⋅+

⋅+=⎟⎟

⎠

⎞⎜⎜⎝

⎛×+=

c

bIh

LIK

tamrUbTI 16>17 nigsMrab;bnÞúkBRgayesμ I mkNwu /5.56= enAelIGgát; BC mkN

KLwMM u

CB .6.43468.44125.56

4

22−=

××

−=−== m:Um:g;viC¢manGtibrmaenAkNþalElVg BC esμ Inwg

mkNMLw Bu /4.5826.4348

125.568

22=−

×=+

kMlaMgRbtikm μedkenARtg;cMnuc A KW³ kN

hMHH B

DA 6.965.46.434====

kMlaMgRbtikm μbBaÄrenARtg; A KW³ column ofweight

2+==

LwVV uDA

kNVA 5.361255.45.04.02

125.56=×××+

×=

düaRkamm:Um:g;Bt;RtUv)anbgðajenAkñúgrUbTI 16>17. e. edIm,IBicarNa\T§iBl sideway enAelIeRKag bnÞúkGefrRtUv)andak;enAelIEtBak;kNþalFñwm

BC ehIym:Um:g;RtUv)anKNnaenARtg;muxkat;eRKaHfñak;. krNIenHmineRKaHfñak;enAkñúg]Ta- hrN_enHeT.

T.Chhay NPIC


f. kMlaMgkat;TTWgGtibrmaenAcugTaMgBIrrbs;Fñwm BC ekItmanenAeBlFñwmRtUv)andak;bnÞúkCa mYynwgbnÞúkemKuN uw b:uEnþkMlaMgkat;TTwgGtibrmaekItmanenAeBlEdlFñwmRtUv)andak; bnÞúkCamYynwgEtBak;kNþalbnÞúkGefr nigbnÞúkefreBj³

kNVu 3392

125.56)supportat ( =×

= kNLWVu 72.36

8126.347.1

8)midspanat ( 1 =×××==

g. kMlaMgtamGkS½enAkñúgssrnImYy²KW kNVV DA 5.361== h. ykcMnucm:Um:g;sUnüenAkñúgFñwm BC sßitenAcMgay x BI B / enaH

22

2xwxLwM uuB −=

2

5.562

125.566.4342xx

−×= b¤ 0384.15122 =+− xx mx 46.1= BITMr B

3> KNnaFñwm BC a. KNnamuxkat;eRKaHfñak;enAkNþalElVg. mkNMu .4.582= / TTwgRTnugKW mmbw 400=

TTwgsøabKW mmb 2320= nig mmd 43090520 =−= ¬snμt;eRbIEdkBIrRsTab;¦. RtYtBinitüfaetImuxkat;eFVIkarCaragmuxkat;ctuekaNCamYynwgTTwgRbsiT§PaB

mmb 2320= b¤Gt;? sn μt; mma 25= enaH 2

69.3874

2254304009.0

104.582

)2

(mmadf

MAy

us =

⎟⎠⎞

⎜⎝⎛ −×

⋅=

−=φ

mmmmbf

fAa

c

ys 1202823202885.04009.3874

'85.0<=

×××

==

a sn μt;mantMélRbhak;RbEhl a KNna. muxkat;eFVIkarCamuxkat;ragctuekaN dUcenH eRbIEdk 286DB . RtYtBinitü minb ¬edIm,Idak;EdkmYyCYr¦

mmmmb 400408801022811min >=+×+×= dak;EdkBIrCYr/ bgðajenAkñúgrUbTI 16>18.

b. KNnamuxkat;eRKaHfñak;enARtg; B ³ mkNMu .6.434= / mmb 400= nig 60520 −=d mm460= ¬sMrab;EdkmYyRsTab;¦. kMralxNÐ½rgkarTaj dUcenHEdkRtUv)andak;enAkñúgmux

kat;EpñkxagelI.

T.Chhay NPIC


MPabdMR u

u 135.5460400106.434

2

6

2 =×

⋅==

018.00166.0 max =<= ρρ 24.30544604000166.0 mmAs =××=

eRbI 285DB kñúgmYyCYr. 4> KNnaFñwm BC edaysarkMlaMgkat;TTwg

a. muxkat;eRKaHfñak;enAcMgay d BIépÞssrCamYycMgayBIGkS½ssr mm710460250 =+ dUcenH

298.9kN.71056.5-339d) distanceat ( =×=uV b. ersIusþg;kMlaMgkat;Edlpþl;edayebtug

kNdbfV wcc 7.1211046040028675.0'

63 =⋅××== −φφ

kMlaMgkat;Edlpþl;edayEdkRTnug (web reinforcement) KW kNVVV cus 2.1777.1219.298 =−=−= φφ

kNVs 3.23675.0

2.177==

c. eRCIserIsEdkkg 12DB nig 22 2264

122 mmAv =×=π

dUcenH mmV

dfAs

s

yv 176103.236

4604002263 =

⋅

××== yk mm175

d. KMlatGtibrmaénEdkkg 12DB KW mmds 230

2max == yk mm225

b¤ mmbfA

sw

yv 64640035.0400226

35.0max =××

==

RtYtBinitüsMrab;KMlatGtibrmaén 2d ³ dbfV wcs '

31

≤ b¤

kNVs 5.32410460400328 3 =⋅×≤ −

tMél kNVs 5.3243.236 <= . dUcenHeRbI mms 225max = . kN

sdfA

mmsV yvs 8.18410

225460400226)220for (' 3

max =××

=== − kNV s 6.1388.18475.0' =×=φ

cMgayBIépÞssreTATItaMgEdl mms 225max = RtUv)aneRbIesμ Inwg m56.1

T.Chhay NPIC


e. karBRgayEdkkg EdkkgTImYymanKMlat mms 752/ = 7 EdkkgmanKMlat mmmm 1225175 = 19 EdkkgmanKMlat mmmm 4275225 = ¬srub mm5575 ¦ cMgayBIépÞssreTAGkS½rbs;Fñwmes μ Inwg mmmmmm 57502506000 =− . BRgayEdkkg dUcKñasMrab;Bak;kNþalFñwmEdlenAsl; nigdak;EdkkgmYyeTotenAkNþalElVg. cMnYnEdk kgsrubKW 55 kg.

5> KNnamuxkat;ssrenAcMnuc B ³ mkNMu .6.434= / kNPu 339= / mmb 400= nig mmh 500=

a. sn μt;eRkamGMeBIbnÞúkEdleGayeRKagnwgminrgnUv sideway enaH\T§iBlrbs;PaBrlas; (slenderness ration) GacRtUv)anecal nigssrGacRtUv)anKNnaCassrxøIenAeBl

2

112344 M

MKLu −< ¬emIlEpñk 12>5¦

01 =M nig mkNM .6.4342 = yk 8.0=K ¬rUbTI 12>2¦ mLu 24.4

252.05.4 =−= nig mmr 1505003.0 =×= enaH

346.2215.024.48.0 <==

rKLu RbsinebI K RtUv)ansnμt;esμInwg 0.1 enaH

343.28 <=r

KLu dUcenH/ karKNnaGgát;CassrxøI.

b. dMeNIrkarKNnaRsedogKñanwg]TahrN_TI 11>16 nig 11>3. cMNakp©it ( ) m

PMe

u

u 282.1339

6.434===

vaCacMNakp©itFM nigvaRtUv)ansnμt;Camuxkat;enAkñúgtMbn; transition region/ 9.0<φ mmd 44060500 =−=

c. edaysar me 282.1= KWFMCag d q¶ayNas;/ kMNt;tMélRbhak;RbEhl sA nig sA' EtBI uM nigbnÞab;mkRtYtBinitümuxkat;cugeRkayedaysþaTic Edl)anBnül;enAkñúg]TahrN_

T.Chhay NPIC


11>3. sMrab; mkNMu .6.434= / mmb 400= / mmh 500= nig mmd 440= / ( ) MPabdMR uu 61.5440400/106.434/ 262 =⋅==

0183.0=ρ nig 28.3220 mmbdAs == ρ eRCIserIs 283DB nig 322DB ¬ 23456mmAs = ¦. eRCIserIs 210743/8.32203/' mmAA ss === nig 223DB ¬ 21140' mmA s = ¦ ¬rUbTI 16>18¦. enAeBlcMNakp©it e mantMélFM/ vaCakarGnuvtþn_Fm μta 3/' ss AA = b¤ 2/sA CMnYseGay ss AA '= .

d. RtYtBinitülT§PaBénmuxkat;cugeRkayedayeRbI 23456mmAs = nig 21140' mmA s = Rsedognwg]TahrN_ 11>3 GaRs½yeTAtamCMhanxageRkam³ i. TCCP scn −+=

aaabfC cc 95204002885.0'85.0 =××== ( ) ( ) kNffAC csss 4288682885.04001140'85.0'' =×−=−=

kNfAT ys 13824004003456 =×== 953532952013824004288689520 −=−+= aaPn (I)

ii. Kitm:Um:g;eFobRtg; sA ³ ( )⎥

⎦

⎤⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ −= '

2'1 ddCadCe

P scn

"' dee += Edl "d sßitenAcMgay sA eTATIRbCMuTMgn;énmuxkat;. TIRbCMuTMgn;ekItman enAcMgay mm68.276 BIsréssgát;xageRkAbMput nig mmxdd 32.163" =−=

mme 32.144532.1631282' =+= ( )⎥

⎦

⎤⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ −= 60440428868

24409520

32.14451 aaPn

1127572.28983.3 2 ++−= aa (II) iii. KNnasmIkar I nig II eKTTYl)an mma 150= nig kNPn 5.474= .

epÞógpÞat; ( ) ys fcdcf ≤−= /'600' / mmac 47.17685.0/ == / enaHeyIgTTYl)an ( ) MPaf s 39647.176/6047.176600' =−= EdlmantMélEk,r MPa400 dUc

Edl)ansn μt;kñúgkarKNna. eRCIserIsEdkkg 10DB EdlmanKMlat mm400 . iv. epÞótpÞat; φ ³ mmdt 440=

T.Chhay NPIC


0045.0003.047.176

47.176440003.0 =⎟⎠⎞

⎜⎝⎛ −

=⎟⎠⎞

⎜⎝⎛ −

=c

cdttε

( ) 858.03

250002.065.0 =⎟⎠⎞

⎜⎝⎛−+= tεφ

kNkNPn 3394075.474858.0 >=×=φ muxkat;RKb;RKan;.

T.Chhay NPIC


6> epÞógpÞat;muxkat;ssrenAkMBs; m25.2 ¬Bak;kNþal¦BI A . mkNMu .3.2172/6.434 == kNPu 25.35025.11339 =+=

eRbIEdk 283DBAs = nig 223' DBA s = . tamviFIedaHRsayRsedogKñakñúgCMhan 5> kNkNPn 25.3508.632 >=φ ¬Edk 32DB Gacpþac;)an EtRtUvBnøÚtRbEvgbgáb;BIeRkam

Bak;kNþalkMBs;ssr¦. 7> KNnasnøak;enARtg;cMnuc A ³ 0=uM / kNH 6.96= / kNPu 5.361=

a. eRCIserIssnøak; Mesnager hinge . edayeRbIsmIkar 16.3 a nig 16.3b/ kNR 3.3051 = nig kNR 1.1122 = ¬eyagtamrUbTI 16>19 CamYynwg o30=θ ¦

211 7.1387

40055.0305300

55.0mm

fRA

ys =

×==

eRCIserIs 253DB ¬ 26.1472 mmAs = ¦ 22

2 5.50940055.0

11210055.0

mmf

RAy

s =×

==

eRCIserIs 222DB ¬ 2760mmAs = ¦. tMerobEdkExVgedaydak; 25DB nigbnÞab;mkdak; 22DB dUcEdlbgðajenAkñúgrUbTI 16>19 ¬b¤eRbI 255DB ¦

b. EdkcMNgTTwgKYrdak;tambeNþaycMgay mmDa 2002588 =×== enAkñúgssr nigeCIgtag. kMlaMgFak;KW

dHaPF u85.0

tan2

+= θ o30=θ / mmd 440= nig mma 200=

kNF o 15644085.02006.9630tan

25.361

=××

+= RkLaépÞmuxkat;EdkcMNg 28.458

40085.0156000 mm=

×=

RbsinebIEdkcMNgbiTCit 10DB ¬eCIgBIr¦ RtUv)anerIs enaHRkLaépÞmuxkat;KW 2157mm . cMnYnEdkcMNgKW 9.2

1578.458= . eRbIEdkcMNg 3kgEdlmanKMlat mm1002/200 =

dUcbgðajenAkñúgrUbTI 16>19. 8> KNnaeCIgtag³ RbsinebIkMBs;eCIgtagRtUv)ansn μt;esμ I 'h enaHkMlaMgEdlmanGMeBIelIeCIgtag

CakMlaMgEkg P nigm:Um:g; '/ hHM = . sMBaFdIRtUv)anKNnaBIsmIkar !#>!$ BIemeronTI 13³ pressure soil allowable≤±+=

IMc

APq

T.Chhay NPIC


viFIsaRsþKNnaeCIgtagmanlkçN³RsedogKñaeTAnwg]TahrN_TI 13>7.

7> esckþIepþImBIkarKNnasßanPaBkMNt; Introduction to Limit Design

7>1> lkμN³TUeTA General karKNnasßanPaBkMNt;éneRKOgbgÁúMmanbICMhandUcxageRkam³

- karkMNt;bnÞúkKNnaemKuN EdlTTYledayKuNbnÞúkefr nigbnÞúkGefrCamYynwgemKuNbnÞúk. ACI Code TTYlnUvemKuNdUcEdleGayenAkñúgemeronTI3.

- viPaKeKOgbgÁúMeRkamGMeBIbnÞúkemKuN (ultimate or factor load) edIm,IkMNt;m:Um:g;emKuN nigkM laMgemKuNenAeBlEdleKOgbgÁúMdYl b¤)ak;. viFIénkarviPaKenHRtUv)aneRbIsMrab;karKNnaeRKOg bgÁúMEdk EtsMrab;eRKOgbgÁúMebtugGarem: ACI Code min)anTTYlykviFIenHTaMgGs;eT edaysar karxVHPaBsVit (ductility) rbs;Ggát;ebtugGarem:. ACI Code GnuBaØatEtEpñkénkarEbgEck eLIgvijnUvm:Um:g;edayEpñk (partial redistribution of moment) enAkñúgrcnasm<n§½edayQrelI PaKryEdl)anmkBIkarBiesaFn_ EdlnwgBnül;kñúgemeronenH.

T.Chhay NPIC


- KNnaGgát;nImYy²éneRKOgbgÁúMedaysnμt;fava)ak;edaym:Um:g;emKuN nigkMlaMgemKuNEdl)an mkBIkarviPaKeRKOgbgÁúM. viFIenHRtUv)aneRbIR)as;CaTUeTAsMrab;karKNnaebtugGarem: ehIy ACI

Code GnuBaØatnUvkareRbIR)as;viFIKNnalT§PaBRTRTg; (strength design method) dUcEdl)an Bnül;kñúgemeronknøgmk.

7> 2> KMniténkarKNnasßanPaBkMNt; Limit Design Concept karKNnasßanPaBkMNt;enAknúgebtugGarem:sMedAelIkarEbgEckm:Um:g;eLIgvijEdlekItman enAelIeRKOgbgÁúMTaMgmUl dUcEdlEdkBRgwgenAmuxkat;eRKaHfñak;eFVIkardl;ersIusþg;yal (yield

strength) rbs;va. ersIusþg;cugeRkay (ultimate strength) rbs;eRKOgbgÁúMekIneLIgenAeBlmuxkat;rbs; vaekIneLIg. eTaHbICakaryal (yielding) rbs;EdkeFVIeGaymanPaBdabFM EdlKYrEteCosvageRkam bnÞúkeFVIkar (service load) eRKOgbgÁúMsþaTicminkMNt;mindYlb¤)ak;enAeBlEdlEdkBRgwgénmuxkat;TI mYyyal. elIsBIenH ersIusþg;EdlbMrugTuky:ageRcInsßitenAcenøaHkaryaldMbUg nigkar)ak;rbs;eRKOg bgÁúM. kñúgkarKNnaeRKOgbgÁúMEdk BakükarKNna)øasÞic (plastic design) RtUv)aneRbIedIm,Ibgðajkar pøas;bþÚrkñúgkarEbgEckm:Um:g;enAkñúgeRKOgbgÁúMdUcCa steel fiber ¬enARtg;muxkat;eRKaHfñak;¦ rgkugRtaMg rhUtdl;ersIsþg;yal. karekIneLIgnUvkugRtaMgtamkMBs;rbs;muxkat;EdkeRkamkarekIneLIgrbs;bnÞúk RtUv)anbgðajenAkñúgrUbTI 16>20. Portal frame RtUv)anBiesaFn_edIm,IGegátlT§PaBRTRTg;karvil rbs;snøak;)øasÞicrbs;ebtugGarem:. b:uEnþ ACI Code tMrUveGaymankarsikSaRsavRCavCaeRcIneTotmun nwgTTYlykkarKNnasßanPaBkMNt;.

7> 3> eKalkarN_énsnøak;)aøsÞic Plastic Hinge Concept

ExSkMeNag φ rbs;Ggát;ekIneLIgCamYynwgm:Um:g;Bt; M . sMrab;FñwmebtugEdlmanbrmaNEdk tic düaRkamm:Um:g;-ExSkMeNag nigExSekagbnÞúk-PaBdab RtUv)anbgðajenAkñúgrUbTI 16>21. FñwmEdl

T.Chhay NPIC


manbrimaNEdk balanced nigbrimaNEdkeRcInminRtUv)anGnuBaØateGayeRbIeday ACI Code eT edaysarva)ak;edaykarpÞúHEbkebtug nigbgðajnUvRbeLaHExSkMeNagtUcenAeBlm:Um:g;emKuN ¬rUbTI 16>22¦.

T.Chhay NPIC


EpñksMxan;rbs;düaRkamExSrkMeNag-m:Um:g;enAkñúgrUbTI 16>21 KWsßitenAcenøaHcMnuc B nig C Edlm:Um:g; uM rkSatMélefrsMrab;RbeLaHéntMél φ d¾FM. kñúgkarviPaKsßanPaBkMNt; ExSekagExSkM eNag-m:Um:g;GacRtUv)ansn μt;manTMrg; idealized form dUcbgðajenAkñúgrUbTI 16>23 EdlExSkMeNag φ enAcenøaH B nig C RtUv)ansn μt;faefr edIm,IbegáItrUbragsnøak;)aøsÞic. edaysarebtugCasMPar³ RsYy CaTUeTAeK)anKitnUvEdnkMNt;edaleGayGgát;)ak;enARtg;ExSkMeNagGtibrmaRtg; C . elak Cranston )anbgðajfaeRKagebtugGarem:EdlKNnaCaTUeTA GacmanlT§PaBTb;nwgkar vil)anFM ehIyExSkMeNagGtibrmaenARtg;cMnuc C nwgminGaceTAdl; Tal;EteRKag)ak;sin. dUcenH enAeBlGgát;RTm:Um:g;es μ Inwgm:Um:g;emKuN uM rbs;va ExSkMeNagbnþekIneLIgcenøaHcMnuc B nig C edayK μankarERbRbYlm:Um:g; edIm,IbegáItsnøak;)aøsÞic. karekIneLIgénExSkMeNagGnuBaØateGayEpñkd¾éT eToténeRKOgbgÁúMsþaTicminkMNt;edIm,ITTYlbnÞúkbEnßm.

8> emkanicénkar)ak; The Collapse Mechanism

kñúgkarKNnasßanPaBkMNt; Ggát;ebtugGarem:GaceTAdl;ersIusþg;cugeRkay (ultimate

strength) enAeBlvaCitnwgrlM b¤)ak;. Ggát;dYlrlMenAeBlEdlcMnYnsnøak;)aøsÞicRKb;RKan;bMElgva eGaycUleTACaFñwmemkanicénkar)ak;. cMnYn caM)ac;énsnøak;)aøsÞic n GaRs½yeTAnwgdWeRk redundancy r rbs;eRKOgbgÁúM. TMnak;TMngrvag n nig r edIm,IbegáItFñwmemkanicénkar)ak;KW rn +=1 ]TahrN_ enAkñúgFñwmTMrsamBaØK μanGBaØtielIseT Edl 0=r . dUcenH FñwmkøayeTACaK μanesßrPaB ehIy)ak;enAeBlEdlsnøak;)aøsÞicmYyekItmanenARtg;muxkat;énm:Um:g;Gtibrma dUcbgðajenAkñúgrUbTI 16>24 a. karGnuvtþn_eTAelIFñwm nigeRKagk¾RtUv)anbgðajenAkñúgrUbTI 16>24.

9> eKalkarN_énkarKNnasßanPaBkMNt; Principles of Limit Design

eRkambnÞúkeFVIkar (working load) karEbgEckm:Um:g;enAkñúgeRKagsþaTicminkMNt;KWWWQrelIRTwsþI eGLasÞic ehIyeRKOgbgÁúMTaMgmUlenAEtrkSaenAkñúgEdneGLasÞic. enAkñúgkarKNnasßanPaBkMNt; enA eBlEdlvaeTAdl;emkanicénkarrlM karEbgEckm:Um:g;enAeBl)ak;edaybnÞúkemKuN xusKñaBIkarEbg EckedayQrelIRTwsþIeGLasÞic. karxusKñaenHbgðajeGayeXIjnUvkarEbgEckm:Um:g;eLIgvij (moment redistribution).

T.Chhay NPIC


sMrab;karKNnasßanPaBkMNt;mann½y lkçxNÐ 4 RtUvEteKarBdac;xat

- lkçxNÐemkanicénkar)ak; (Mechanism condition)³ snøak;)aøsÞicRKb;RKan;RtUv)anbegáIteLIg edIm,IbMElgeRKOg bgÁúMTaMgmUl b¤EpñkxøHrbs;eRKOgbgÁúMeTACaGgát;emkanicénkar)ak;.

- lkçxNÐlMnwg (Equilibrium condition)³ karEbgEckm:Um:g;RtUvEtmanlMnwgCamYynwgbnÞúkEdl Gnuvtþ.

T.Chhay NPIC


- lkçxNÐyal (Yield condition)³ m:Um:g;emKuNminRtUvelIsersIusþg;m:Um:g;enARKb;TItaMgrbs; eRKOgbgÁúM.

- lkçxNÐrgVil (Rotation condition)³ snøak;)aøsÞicRtUvEtmanlT§PaBTb;rgVil (rotation

capacity)RKb;RKan; edIm,IGnuBaØatkarekItmanFñwmemkanicénkar)ak;. manEtlkçxNÐbIdMbUgeTEdlGnuvtþkñúgkarKNna)aøsÞic edaysarlT§PaBTb;rgVilmanenAkñúg

sMPar³sVitdUcCaEdkrYceTAehIy. lkçxNÐTIbYnbegáInEdnkMNt;bEnßmeTAelIkarKNnakMNt;énGgát;eb tugGarem:edayeRbobeFobCamYykarKNna)aøsÞic (plastic design).

10> Ednx<s; nigEdnTabénemKuNbnÞúk Upper and Lower Bounds of Load Factors

eRKOgbgÁúMEdlCitdYlrlMRtUvEtmancMnYnsnøak;)aøsÞicRKb;RKan;edIm,IbMElgvaeTACaGgát;emkanic énkar)ak;. sMrab;TItaMgNamYyénsnøak;)aøsÞicenAelIeRKOgbgÁúM bnÞúkEdleFVIeGayrlMGacRtUv)anKNna EdlGacFMCag b¤esμ IbnÞúkBit. edaysarbnÞúkKNnaminGacFMCagbnÞúkEdleFVIeGayrlMBitsMrab;eRKOg bgÁúM enaHviFIsaRsþKNnabgðajnUvEdnsIueNm:aTic b¤Edkx<s; (upper or kinematic bound) rbs;bnÞúk EdleFVIeGayrlMBit. dUcenHRKb;Ggát;emkanicénkarrlMEdlGacekItmanRtUv)aneFVIkarGegát uM EdltUcCageK nwgekIteLIgedaybnÞúkBit. elak Horne )anBnül;Ednx<s;edaysnμt;eRKOgbgÁúMCa Ggát;emkanicénkar)ak; nigbnÞab;mkKNnakmμnþxageRkA eW EdleFVIedaybnÞúkxageRkA nigkmμnþkñúg

iW EdleFVIenAsnøak;)aøsÞic. RbsinebI ie WW = enaHbnÞúkEdlGnuvtþFMCag b¤esμIbnÞúkEdleFVIeGay)ak;. RbsinebIdüaRkamm:Um:g;enARtg;cMnucNamYyRtUv)anbegáItedIm,IbRgÁb;lMnwgsþaTiceRkamGMeBIbnÞúkGnuvtþenAeBl)ak; enaHbnÞúkEdlGnuvtþtUcCag b¤es μ IbnÞúkEdleFVIeGay)ak;Bit. sMrab;düaRkamm:Um:g; epSgeTot eKGacTTYlbnÞúkemKuNepSgeTot. tMélEdlFMCagénEdntUc b¤EdnsþaTic (lower or static

bound) RtUv)anTTYlenAeBlm:Um:g;enAmuxkat;CaeRcInsMrab;düaRkamm:Um:g;Edlsn μt;xiteTACitm:Um:g;Edl eFVIeGayrlM. elak Horne)anBnül;EdnTabedaysn μt;karEbgEckm:Um:g;xusKñaedIm,ITTYlnUveRKOgbgÁúM EdlsßitenAkñúgsßanPaBlMnwgCamYybnÞúkxageRkA nigeKarBlkçxNÐyalenAelIeRKOgbgÁúMTaMgmUl. kñúg krNIenH bnÞúkxageRkAtUcCag b¤esμIbnÞúkEdleFVIeGayrlM.

T.Chhay NPIC


11> karviPaKsßanPaBkMNt; Limit Analysis

sMrab;karviPaKedaydMeNIrkarKNnasßanPaBkMNt; viFIBIrGacRtUv)aneRbI viFIkm μnþCak;Esþg (virtual work method) nigviFIlMnwg (equilibrium method). sMrab;viFI virtual work kmμnþRtUv)aneFVI edaybnÞúkemKuN uP ¬b¤ uw ¦ edIm,IbegáItPaBdab virtual deflection EdleGay Δ RtUv)andak; eGayes μ Ikm μnþEdlRsUbykenAsnøak;)aøsÞic. km μnþxageRkAEdleFVIedaybnÞúkKW ( )∑ Δ= ue wW b¤

( )∑ ΔuP . kmμnþEdlRsUbykedaysnøak;)aøsÞicKWkmμnþ ( )∑== θui MW . ]TahrN_16>3 FñwmEdlbgðajenAkñúgrUbTI 16>25 RTnUvbnÞúkcMcMnucenAkNþalElVg. KNnam:Um:g;EdleFVIeGay)ak;enA muxkat;eRKaHfñak;.

T.Chhay NPIC


dMeNaHRsay 1> FñwmCaGgát;sþaTicminkMNt; 1 dWeRk

ehIycMnYnsnøak;EdlRtUvkaredIm,IbMElgFñwmeTACaFñwmemkanicénkar)ak;KW 211 =+=n snøak;)aøsÞic enARtg;cMnuc A nig C . snøak;)aøsÞicTImYyekItmanenARtg;cMnuc A ehIyFñwmeFVIkarCaFñwmTMrsamBaØrhUtdl;vaxiteTArkemkanicénkar)ak;.

2> RbsinebImMurgVil θ ekItmanenAsnøak;)aøsÞicenAcugbgáb; A enaHmMurgVilenARtg;cMnuc θ2=C . PaBdabenARtg;cMnuc C eRkambnÞúkKW ( )θ2/L ¬rUbTI 16>25¦.

∑ ⎟⎠⎞

⎜⎝⎛=Δ==

2 workexternal θLPPW uue

( ) ( )θθθ 2 workinternal 21 uuui MMMW +=== ∑ RbsinebImuxkat;BIrenARtg; A nig C manTMhM nigbrimaNEdkdUcKña enaH

uuu MMM == 21 nig θui MW 3= . edayeGay ie WW = uuuu MLPMM 3

22 21 ==+ nig

6LP

M uu =

]TahrN_16>4 KNnam:Um:g;EdleFVIeGay)ak;enAmuxkat;eRKaHfñak;sMrab;FñwmEdlbgðajenAkñúgrUbTI 16>26 EdlbNþal edaybnÞúkBRgayes μ I uw . dMeNaHRsay

1> cMnYcsnøak;)aøsÞicKW 2 . 2> sMrab;PaBdabenARtg; 0.1=C mMurgVilenARtg;cMnuc A aA /1=θ nig bB /1=θ ehIy

abL

abba

BAc =+

=+= θθθ

3> km μnþxageRkAKW ∑ =⎟⎠⎞

⎜⎝⎛ ×

=Δ=22

1 LwLwwW uuue

km μnþxagkñúgKW ∑ +== CuAuui MMMW θθθ 21 ⎟

⎠⎞

⎜⎝⎛ ++=

baM

aM uu

11121

dak;eGay eW nig iW ⎟⎠

⎞⎜⎝

⎛−

++=aL

Ma

Ma

ML

w uuuu

2212 ¬!^>(¦

RbsinebIm:Um:g;TaMgsgçagesμ IKña enaH

T.Chhay NPIC


( ) ( )⎥⎦⎤

⎢⎣

⎡−−

=⎥⎦

⎤⎢⎣

⎡−

+=aLaaL

LM

aLaLM

w uuu

22122 ¬!^>!0¦

T.Chhay NPIC


4> edIm,IKNnaTItaMgsnøak;)aøsÞicenARtg; C EdlbegáIttMélGb,brmaénbnÞúkEdleFIVeGay)ak; uw eFVIedrIevsmIkarTI !^>( eFobnwg a nigdak;eGayvaes μ IsUnü³

0=a

wuδδ

( )02

22

22

1 =⎟⎟⎠

⎞⎜⎜⎝

⎛

−−+−

aLM

aM

aM uuu

RbsinebI uuu MMM == 21 enaH ( )22

12aLa −

=

b¤ ( ) LLa 586.022 =−= BIsmIkar !^>!0 bnÞúkEdleFVIeGay)ak;KW ( )2/66.11 LMw uu = nigm:Um:g;EdleFVIeGay)ak; KW 20858.0 LwM uu = . Rbtikm μenAcMnuc A KW Lwu586.0 nig RbtikmμenARtg;cMnuc B KW Lwu414.0 . enAkñúgviFIlMnwg lMnwgrbs;Fñwm b¤rbs;Ggát;dac;edayELkrbs;FñwmRtUv)ansikSaeRkambnÞúk EdlbgðajenAeBl)ak;. edIm,IbgðajkarviPaKedayviFIenH ]TahrN_BIxagmuxTaMgBIr RtUv)aneFVIeLIgvijenATIenH.

]TahrN_16>5 sMrab;FñwmEdlbgðajenAkñúgrUbTI 16>25 kMNt;m:Um:g;EdleFVIeGay)ak;edayeRbIviFIlMnwg. dMeNaHRsay snøak;)aøsÞicBIrRtUv)anbegáItenAcMnuc A nigC . edayeyagtamrUbTI 16>25 e kMlaMgRbtikm μenAcMnuc A KW ( ) ( )LMP uu /2/ 1+ nig RbtikmμenAcMnuc B KW ( ) ( )LMP uu /2/ 1− KitlMnwgénFñwm BC nigKitm:Um:g;eFobcMnuc C /

21

22 uuu ML

LMP

=⎟⎠⎞

⎜⎝⎛⎟⎠

⎞⎜⎝

⎛ −

22 21

LPMM uuu =+ EdlRsedogKñanwgsmIkar !^>#. enAeBl uuu MMM == 21 / enaH

23 LPM uu = b¤

2LPM uu =

]TahrN_16>6

T.Chhay NPIC


KNnam:Um:g;EdleFVIeGay)ak; (collapse moment) sMrab;FñwmEdlbgðajenAkñúgrUbTI 16>26 edayviFI lMnwg. dMeNaHRsay

1> snøak;)aøsÞicBIrRtUv)anbegáItenARtg;cMnuc A nig C . eyagtamrUbTI 16>26 d / kMlaMgRbtikm μenA Rtg; ( ) ( )LMLwA uu /2/ 1+= nigkMlaMgRbtikmμenARtg;

( ) ( )LMLwB uu /2/ 1−= . bnÞúkenAelI BC KW bwu EdlmanGMeBIenA 2/b BI B Edl aLb −= . edayKitlMnwgénkMNat; BC nigKitm:Um:g; eFobcMnuc C /

( ) 21

22 uuu

u MbbwbL

MLw =−⎟⎠

⎞⎜⎝

⎛ −

RbsinebI uuu MMM == 21 enaH ( ) ( )aL

LM

LbMbLbw u

uu −=+=− 2)1(2

( )( )aLa

aLLM

w uu −

−×=

22

EdlRsedogKñanwgsmIkar !^>$ ( )( )aL

aLaLwM u

u −−

×=22

2> TItaMg a GacRtUv)ankMNt;dUcBImun Edl La 586.0= / 20858.0 LwM uu = nig ( )2/66.11 LMw uu = .

12> mMurgVilrbs;snøak;)aøsÞic Rotation of Plastic Hinges

12>1> RbEvg snøak;)aøsÞic Plastic Hinge Length karsnμt;rbs;RTwsþIeBlfamMurgVilminEmneGLasÞic (inelastic rotation) énebtugekItmanenA

cMnucm:Um:g;GtibrmaenAeBlEdlEpñkd¾éTeTotrbs;Ggát;eFVIkarCalkçN³eGLasÞic. tamBit mMu rgVil)aøsÞic (plastic rotation) ekItmanenATaMgsgçagénmuxkat;m:Um:g;GtibrmaelIRbEvgkMNt;mYy. RbEvgenHRtUv)aneKeGayeQ μaHfa RbEvgsnøak;)aøsÞic pl . RbEvgsnøak;)aøsÞic pl CaGnuKmn_eTAnwg kMBs;RbsiT§PaB d nigcMgayBImuxkat;énm:Um:g;x<s;bMput eTAcMnucm:Um:g;sUnü (contra-flexure) .

eyagtamrUbTI 16>27 a RbEvg 2/pl tageGayRbEvgsnøak;)aøsÞicenAelIEpñkmçagénGkS½ rbs;TMr. uM nig uφ Cam:Um:g;emKuN nigkMeNagemKuNenARtg;muxkat;eRKaHfñak; Edl yM nig yφ Ca

T.Chhay NPIC


m:Um:g; nigkMeNagenARtg;cMnucyaldMbUg (first yield). kMeNag)aøsÞicenARtg;muxkat;eRKaHfñak; pφ esμ I ( )yu φφ − ehIylT§PaBTb;rgViles μ Inwg ( )pplφ .

RbEvgsn μt;rbs;snøak;)aøsÞicRtUv)ansn μt;famanRbEvgRbEhlkMBs;RbsiT§PaB. Corley )anesñInUvsmIkarxageRkamsMrab;RbEvgsmmUlénsnøak;)aøsÞic ⎟

⎠⎞

⎜⎝⎛+=

dzddl p 2.05.0 ¬!^>!!¦

Edl =z cMgayénmuxkat;eRKaHfñak;eTAcMnucm:Um:g;sUnü nig =d kMBs;RbsiT§PaBrbs;muxkat;. Mattock )anesñInUvTMrg;d¾smBaØ zdl p 05.05.0 += ¬!^>!@¦ karBiesaFn_CaeRcInenAelIebtugGarem:Cab;bgðajfa pl GacRtUv)ansnμt;es μ Inwg d06.1 . va k¾)anbgðajEdrfaRbEvgénsnøak;)aøsÞicenAkñúgFñwmebtugGarem:Cab;EdlmanTMBk;enAxagcugekIneLIgCamYynwgnwgkarekIneLIgénbrimaNEdk fibers nigEdkemGaRs½ynwgsmIkarxageRkam³ ( )dl sp ρρ13.006.1 += ¬!^>!#¦

T.Chhay NPIC


Edl =ρ PaKryEdkemenAkñúgmuxkat; nig =sρ PaKryén fibers EdkedaymaD/ 2.10 ≤≤ sρ . ]TahrN_ RbsinebI %1=ρ nig %8.0=sρ enaH dl p 164.1= .

12>2> emKuNEbgEckkMeNag Curvature Distribution Factor

emKuNsMxan;mYyeTotEdlTak;TgkñúgkarKNnamMurgVil)aøsÞicKWemKuNEbgEckkMeNag β . kM

eNagtambeNþaysnøak;)aøsÞicERbRbYly:agFM ehIyenAkñúgkarKNnamMurgVilemKuNenHminRtUv)anKit EdleFVIeGaykarKNnasnøak;)aøsÞicmantMélFM. eyagtamrUbTI 16>27 RkLaépÞqUt ABC tag eGaymMurgVilminEmneGLasÞicEdlGacekItmanenAsnøak;)aøsÞic b:uEnþRkLaépÞGt;qUt EBF tageGay karcUlrYménlkçN³eGLasÞicrbs;mMurgVilelIRbEvgrbs;Ggát;. RkLaépÞqUt ABC GacRtUv)ansn μt;

T.Chhay NPIC


esμ InwgplKuNrvag β nigRkLaépÞsrub ABCD enAkñúgRbEvgsnøak;)aøsÞic 2/pl EdlenAelIRCugmçag rbs;muxkat;eRKaHfñak;. emKuNEbgEckkMeNag β CapleFobénmMurgVil)aøsÞicBit pcθ elI plφ Edl φ CakMeNag nig pl CaRbEvgénsnøak;)aøsÞic. tMél β sßitenAcenøaH 5.0 nig 6.0 . karBiesaFn_)an bgðajfa β GacRtUv)ansnμt;esμ Inwg 56.0 . enAeBlEdlEdk fibers EdlmanTMBk;cugRtUv)aneRbIenA kñúgFñwmebtug tMél β fycuHGaRs½yeTAnwgsmIkarxageRkam³

sρβ 16.056.0 −= ¬!^>!$¦ Edl sρ CaPaKry fibers Edk/ %2.10 ≤≤ sρ . karfycuHénemKuNEbgEckkMeNagénebtugEdl eRbIEdk fibers min)anbgðajfalT§PaBTb;rgVilfycuHeT. kMeNag)aøsÞicrbs;ebtugEdleRbIEdk fibers EtgEtFMCagkMeNag)aøsÞicrbs;ebtugEdlmineRbIEdk fibers. rUbTI 16>28 bgðajBIkarEbgEckkM eNagtambeNþayRbEvgsnøak;)aøsÞic. RkLaépÞ 1ABC tageGaymMurgVil)aøsÞicsMrab;ebtugEdlmin manEdk fibers/ 56.0=β b:uEnþRkLaépÞ 2ABC nig 3ABC tageGaymMurgVil)aøsÞicsMrab;ebtugEdl manEdk fibers %8.0 nig %2.1 erogKña.

12>3> snÞsSn_énPaBsVit Ductilty Index pleFobénkMeNagemKuNnigkMeNagyaldMbUgRtUv)aneKeGayeQ μaHfasnÞsSn_énPaBsVit/

yu φφμ /= . snÞsSn_énPaBsVitrbs;ebtugGarem:ERbRbYlcenøaH 4 nig 6 . RbsinebIEdk fibers RtUv)aneRbIenAkñúgFñwmebtugGarem: enaHsnÞsSn_énPaBsVitekIneLIgtamsmIkarxageRkam³ ( )μρμ s8.30.1' += ¬!^>!%¦ Edl =μ pleFobkMeNagemKuNelIkMeNagyaldMbUg ='μ snÞsSn_énPaBsViténebtugEdlmanEdk fibers =sρ PaKryénEdk fibers edaymaD/ %2.10 ≤≤ sρ

12>4> mMurgVilEdlRtUvkar Required Rotation eKRtUvkarmMurgVilénsnøak;)aøsÞicenAeRKOgbgÁúMminkMNt;ebtugGarem:edIm,IGnuBaØateGaysnøak; )aøsÞicekItman ehIyeRKOgbgÁúMEdlxiteTArkemkanicénkar)ak;GacRtUv)ankMNt;eday slope

deflection BIsmIkarxageRkam. sMrab;kMNat; AB cenøaHsnøak;)aøsÞicNIr mMurgVilenARtg; A KW ( ) ( )[ ]FBBFAA

cA MMMM

IEL

−+−= 26

θ ¬!^>!^¦

Edl AM nig =BM m:Um:g;emKuNenARtg;cMnuc A nig B erogKña FAM nig =FBM m:Um:g;bgáb;cugeGLasÞicenARtg;cMnuc A nig B

T.Chhay NPIC


=CE m:UDuleGLasÞicrbs;ebtug cf '4730= =I m:Um:g;niclPaBénmuxkat;eRbH ¬emeronTI 5¦

12>5> lT§PaBTb;mMurgVil Rotation Capacity Provided snøak;)aøsÞicrgkarTajKMrUenARtg;muxkat;TMr nigmuxkat;kNþalElVgéneRKagRtUv)anbgðajenA kñúgrUbTI 16>29.lT§PaBTb;mMurgVilGaRsy½CacMbgeTAnwg³

- Ultimate strain capacity rbs;ebtug c'ε EdlGacRtUv)ansn μt;esμ I 003.0 b¤ 0035.0 . - RbEvg pl EdlenAelIRbEvgenHsnøak;)aøsÞiceFVIkardl;yal.

RbEvgenHRtUv)ansnμt;mantMélRbEhlkMBs;RbsiT§PaBénmuxkat;Edlsnøak;)aøsÞicekItman ¬ dl p = ¦

- kMBs;rbs;bøúksgát; c enAkñúgebtugenAeBl)ak;enARtg;muxkat;énsnøak;)aøsÞic. mMurgVil θ énsnøak;)aøsÞicRtUv)anKNnatamsmIkarxageRkam³

cI ppεθ = ¬!^>!&¦

T.Chhay NPIC


Edl pε KWCakMeNInén strain enAkñúgebtugEdlvas;BI initial yielding rbs;EdkenAkñúgmux kat; ¬rUbTI 16>29 c ¦³ 11 0035.0' cccp εεεε −=−= RbsinebI dl p = ehIypleFob dc / esμ Inwg 5.0≤λ /

( )λ

ελ

εθ 11 0035.00035.0 cc

dd −=

−=

BIRtIekaNbMErbMrYlrageFob (strain triangle) rUbTI 16>29/ ⎟⎠⎞

⎜⎝⎛−

=⎟⎠⎞

⎜⎝⎛

−=⎟

⎠⎞

⎜⎝⎛

−=

λλ

λλεε

11s

y

s

yyc E

fdd

dEf

cdc

Edl =yf ersIusþg;yalrbs;Edk nig =sE m:UduleGLasÞicrbs;Edk MPa5102 ⋅= . dUcenH

( )λλλε

λθ

−−=−=

10035.00035.0 1

s

ycE

f ¬!^>!*¦

sMrab;Edk MPaf y 280= nigedayeRbItMélGtibrmaén 50.0=λ enaH rad3

5min 102.4)5.01(102

2805.0

0035.0 −⋅=−×⋅

−=θ

sMrab;Edk MPaf y 400= nig 44.0max =λ enaH rad3

5min 1038.4)44.01(102

28044.0

0035.0 −⋅=−×⋅

−=θ

minθ Edl)anKNnaenATIenH)anBIEtmçag ehIymMurgVilGnuBaØatsrubenARtg;snøk;)aøsÞices μ Inwg min2θ b¤ θ2 . λ BitGacRtUv)anKNnadUcxageRkam

eKman ca 1β= nig 85.01 =β sMrab; MPaf c 28' ≤

( ) bf

fAacc

ys

'85.0 21==

β

5.0'72.0'72.0≤===

c

y

c

ys

ff

bdffA

dc ρ

λ ¬!^>!(¦

Edl bdAs /=ρ . eKnwgTTYl)an maxλ enAeBlEdleRbI maxρ . RbsinebIlT§PaBTb;rgVilminRKb;RKan; eKGacbegáInmuxkat; b¤kat;bnßyPaKryEdkedIm,I TTYl)an c tUc/ λ tUc nig θ FM. RbsinebIeKeRbIEdkkgvNÐ½ bMErbMrYlrageFobemKuNEdleFVIeGay EbkebtugnwgekIneLIgx<s;dl; 012.0 . sMrab;snøak;)aøsÞicsgát; ¬dUcenAkñúgssr¦

T.Chhay NPIC


hl ppεθ = ¬!^>@0¦

Edl =h kMBs;srubrbs;muxkat; nig =pl RbEvgEdl yielding ekItman. enAkñúgsnøak;sgát; pl ErbRbYlcenøaH h5.0 nig h . enAeBlebtugrgkugRtaMgemKuNdl; cf ' / 002.0=cε dUcenH 002.0' −= cp εε

0015.0002.00035.0 =−= CamMurgVilGb,brmaenARCugmçag. dUcenH rad

hh 00075.05.00015.0

min =×

=θ CamYynwgEdkkgvNÐ½/ θ GacnwgekIneLIgdl;

( ) radh

h 005.05.0002.0012.0max =×−=θ tMél 012.0' =cε CatMélEdlFMNas; dUcenHtMéltUcCagenHGacRtUv)aneRbICamYyEdkkg

vNÐ½. RbsinebImindUcenHeT eKGaceRbImuxkat;epSgeTot. enAkñúgFñwmCab;ebtugGarem:EdlmanEdk fibers mMurgVil)aøsÞicGacRtUv)anKNnadUcxageRkam³

( )⎟⎟⎠

⎞⎜⎜⎝

⎛−

−=λλ

λβθ1

0035.0

s

yp E

f ¬!^>@!¦

Edl ( )sys f ρρρλ 17.400625.024.23.4 +−+= ¬!^>@@¦ sρβ 16.056.0 −= ¬!^>!$¦ =yf ersIusþg;yalrbs;Edk =sE m:UduleGLasÞicrbs;Edkem

=ρ PaKryEdkem =sρ PaKryEdk fibers KitmaD

smIkar !^>@! Bgðajy:agc,as;famMurgVil)aøsÞicénebtugGarem:EdleRbIEdk fibers KWGaRs½yeTA nwg PaKryEdkem/ PaKryEdk fibers nigersIusþg;yalrbs;va. karbegáInersIusþg;yalkat;bnßymMu rgVil)aøsÞic. smIkar !^>@! k¾rab;bBa©ÚlnUv\T§iBlénRbEvgsnøak;)aøsÞicenAelImMurgVilEdr.

xageRkamCaTMrg;EdlRtUv)amsMrYledIm,IKNnamMurgVil)aøsÞic³ ⎟⎠⎞

⎜⎝⎛=

λλβθ 003.0

p ¬!^>@#¦

T.Chhay NPIC


]TahrN_ RbsinebI 0=sρ nig MPaf y 400= enaH λθ /00289.01 =p nigRbsinebI %1=sρ / %5.1=ρ nig MPaf y 400= enaH λθ /01235.02 =p . enHmann½yfa lT§PaBTb;mMurgVilrbs;

FñwmebtugGarem:nwgekIneLIgRbEhlbYndgRbsinebIeKeRbIEdk fibers %1 .

13> segçbviFIsaRsþkñúgkarKNnasßanPaBkMNt; Summary of Limit Design Procedure

- KNnabnÞúkemKuNedayeRbIemKuNbnÞúkEdleGayenAkñúgemeronTI 3³ LDwu 6.12.1 += - kMNt;Ggát;emkanicénkar)ak;/ snøak;)aøsÞic/ nigm:Um:g;emKuN uM - KNnamuxkat;eRKaHfñak;edayeRbIviFIKNnaersIusþg; (strength design method) - kMNt;mMurgVilcaM)ac;énsnøak;)aøsÞic - KNnalT§PaBTb;mMurgVilenARtg;muxkat;énsnøak;)aøsÞic. lT§PaBTb;mMurgVilRtUvEtFMCagmMurgVil

caM)ac;. - RtYtBinitüemKuNRbqaMg yielding rbs;Edk nigsñameRbHFM² ¬EdlCapleFobrvag

load serviceat moment elastic/uMφ - epÞógpÞat;PaBdab nigsñameRbHeRkamGMeBIbnÞúkeFVIkar - RtYtBinitüemIlfaEdkkMlaMgkat;TTwgRKb;RKan;RtUv)andak;enARKb;muxkat;

]TahrN_16>7 FñwmdUcEdlbgðajenAkñúgrUbTI 16>30 RtUv)anbgáb;enAcugTaMgsgçag nigRTbnÞúkBRgayes μ IemKuN

mkN /80 nigbnÞúkcMcMnucemKuN kN5.213 . KNnaFñwmedayeRbIdMeNIrkarKNnasßanPaBkMNt;. eKeGay mmb 350= / MPaf c 21' = nig MPaf y 280= . dMeNaHRsay

1> bnÞúkBRgayes μ IemKuN mkNwu /80= . bnÞúkcMcMnucemKuN mkNPu /5.213= . 2> snøak;)aøsÞicekItmanenARtg;cMnuc A / B nig C EdlbNþaleGaymanemkanicénkar)ak;dUc

bgðajenAkñúgrUbTI 16>30. edayeRbIviFIkmμnþCak;Esþg (virtual work method) nigsnμt;PaB dabÉktþaenARtg;cMnuc C enaHkmμnþxageRkAesμ Inwg

mkNWe .5.5097.38015.213 =×+×= km μnþxagkñúgEdlRsUbedaysnøak;)aøsÞicKW

)Cat (2)Bat ()Aat ( θθθ uuui MMMW ++=

T.Chhay NPIC


7.34

4 uu

MM == θ

edayeGay ie WW = enaH mkNM u .3.471= . tamkarviPaKTUeTAeGay mkNLP

LwM u

uu .3.471

84.75.213

164.780

816

22=+=+=

3> KNnamuxkat;eRKaHfñak;enARtg;cMnuc A / B nig C sMrab; mkNM u .3.471= . BItaragenA kñúg]bsm<n§½ B nigsMrab; MPaf c 21' = / MPaf y 280= CamYynwgPaKryEdk 013.0=ρ eK)an MPaRu 95.2= ¬ %04.2max =ρ ¦

2bdRM uu = mmd 676

35095.2103.471 6

=×⋅

= kMBs;srubrbs;FñwmKW mmh 73660676 =+= yk mm740

28.3075676350013.0 mmbdAs =××== ρ eRbIEdk 285DB mYyRsTab; ¬ 23079mmAs = ¦/

mmmmb 35034270102289min <=+×+×= mm

bffA

ac

ys 1383502185.0

2803079'85.0

=××

×==

mmac 35.16285.0

== 24.0676

35.162===

dcλ

4> mMurgVilcaM)ac;rbs;snøak;)aøsÞicKW a. ( ) ( )[ ]FBBFAA

cA MMMM

IEL

−+−= 26

θ

MPafE cc 21676214730'4730 === MPaEs 200000= b. kMNt;m:Um:g;cugbgáb;enARtg; A nig B edayeRbIbnÞúkemKuN³ mkNLP

LwMM u

uFBFA .55.562

84.75.213

124.780

812

22=+=+==

m:Um:g;)aøsÞic mkNMM BA .3.471== c. m:Um:g;niclPaBénmuxkat;eRbHGacRtUv)anKNnadUcxageRkam

( )23

3xdnAxbI scr −+=

T.Chhay NPIC


Edl x CacMgayBIsrésrgkarsgát;eTAGkS½NWt ( )kd . edIm,IkMNt; x ¬emIlemeronTI 6¦/ mmx 4.257= nig 481044.68 mmIcr ⋅=

d. mMurgVilcaM)ac;Gb,brma³ edaycat;Tukm:Um:g;TaMgGs;enARtg; A nig B GviC¢man/ enaH ( ) ( )[ ] 6

8 1055.5623.47155.5623.47121044.68216766

7400⋅+−++−

⋅××=Aθ

rad00227.0=

5> lT§PaBTb;mMurgVilKW³ ( ) ( )24.01200000

28024.0

0035.01

0035.0−

−=−

−=λλ

θs

yA E

f

radrad 00227.00127.0 >= lT§PaBTb;mMurgVilesμ IRbEhl 5.5 dgénmMurgVilcaM)ac; enHbgðajfamuxkat;RKb;RKan;. 6> RtYtBinitüpleFobrvagm:Um:g;emKuNelIm:Um:g;eGLasÞiceRkambnÞúkeFVIkar

mkNLPwLMM BA .6.3518

4.74.13312

4.750812

22=

×+

×=+==

mkNadfAM ysn .471102

13867628030799.02

6 =⋅⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−××=⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−= φφ

pleFobKW 34.16.351

471= EdltMNageGayemKuNsuvtßiPaBRbqaMgnwg yielding rbs;Edk

enARtg;TMr. 7> RtYtBinitüPaBdabGtibrmaEdlbNþalmkBIbnÞúkeFVIkar ¬enAkNþalElVg¦³ ykbnÞúkeFVIkar

BRgayes μ I mkNw /50= nig kNP 4.133= enaH

EIwL

384

4

1 =Δ sMrab;bnÞúkcMcMnucenAkNþalElVg

EIPL

192

3

2 =Δ PaBdabsrubKW mm53.4

1044.68216761927400133400

1044.6821676384740050

8

3

8

4=

⋅××

×+

⋅××

×=Δ

1633

17400

53.4==

ΔL

EdlCapleFobtUcEmnETn 8> brimaNEdkkMlaMgkat;TTwgRKb;RKan;RtUv)andak;edIm,IeCosvagkar)ak;edaykMlaMgkat;TTwg

EdlGacekItman.

T.Chhay NPIC


14> karEbgEckm:Um:g;eLIgvijénm:Um:g;GviC¢manenAkñúgFñwmCab; Moment Distribution of Negative Moments in Continuous Beams

karEbgEckm:Um:g;GviC¢maneLIgvijenAkñúgGgát;rgkarBt;Cab;KWQrelIsac;lUteFobsuT§ (net

tensile strain NTS) tε sMrab;TaMgebtugGarem: nigebtugeRbkugRtaMg. rUbTI 16>31 bgðajlImIt GnuBaØatkñúgkarEbgEckm:Um:g;eLIgvij. vabgðajfaPaKrym:Um:g;GviC¢manekIneLIg b¤fycuHenAelITMr rbs;FñwmCab; 'q EdlKNnaedayRTwsþIeGLasÞicminRtUvFMCag %1000 tε CamYytMélGtibrma %20 . karEbgEckm:Um:g;eLIgvijRtUv)anGnuBaØatEtenAeBlEdl 0075.0≥tε EdlbgðajfavamanPaBsVit

T.Chhay NPIC


RKb;RKan;enARtg;muxkat;Edlm:Um:g;RtUv)ankat;bnßy. enAeBl 0075.0<tε karEbgEckm:Um:g;eLIgvij minRtUv)anGnuBaØateLIy. m:Um:g;GviC¢manEdl)anEktMrYvRtUv)aneRbIsMrab;KNnam:Um:g;viC¢manEdl)anEk tMrUv (ACI Code, Section 8.4) . karEbgEckm:Um:g;eLIgvijminRtUv)anGnuvtþcMeBaHGgát;EdlKNna edayviFIKNnaedaypÞal;sMrab;RbBn§½kMralxNÐ½eT ¬eyagtamemeronTI 17¦.

Casegçb PaBryekIneLIg nigPaKryfycuHénm:Um:g;GviC¢manmandUcxageRkam³

- enAeBlEdl 0075.0<tε karEbgEckm:Um:g;eLIgvijminRtUv)anGnuBaØat ¬ 476.0/ >bρρ ¦. - enAeBlEdl 0075.0=tε PaKryénkarEbgEckm:Um:g;eLIgvijKW %5.7 ¬ 476.0/ =bρρ ¦. - enAeBlEdl 020.0>tε PaKryénkarEbgEckm:Um:g;eLIgvijKW %20 ¬ 217.0/ =bρρ ¦. - enAeBlEdl 020.00075.0 << tε PaKryEbgEckm:Um:g;eLIgvijKW

tq ε1000'= ¬!^>@$¦ ]TahrN_ RbsinebI 010.0=tε enaHPaKryEbgEckm:Um:g;eLIgvijKW %10 . TMnak;TMngrvag

PaKryEdk ρ enAkñúgmuxkat; nigsac;lUteFobsuT§ tε KWmandUcxageRkam ¬eyagtamEpñk 3>9¦³

T.Chhay NPIC


003.0003.0

−

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=

b

s

y

tEf

ρρ

ε ¬#>@$¦

sMrab;Edk MPaf y 400= nig MPaEs 200000= . edaysn μt; 002.0/ =sy Ef enaH

003.0005.0−

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛=

b

t

ρρ

ε ¬#>@%¦

sMrab; 0075.0=tε / lImIténPaBsVitKW 75.3002.0/0075.0/ ==yt εε . PaKryEbgEckm:Um:g;eLIg vijERbRbYlGaRs½yeTAnwgkarkMNt;TaMgenH nigsMrab; MPaf y 400= RtUv)aneGayenAkñúgtaragTI 16>1 nig 16>2. RKb;PaKryEbgEckm:Um:g;eLIgvijEdlRtUv)aneRbI vacaM)ac;RtUvFanafamuxkat;minrgnUvkarxUc xat b¤mansñameRbHFMedaysarbnÞúkeFVIkar ehIyvaRtUvrkSalT§PaBTb;rgVilenARKb;muxkat;eRKaHfñak;enA kñúgeRKOgbgÁúM. karEbgEckm:Um:g;eLIgvijenAkñúgeRKOgbgÁúMsþaTicminkMNt;eFVIeGaym:Um:g;GviC¢manenAelI TMr nigm:Um:g;viC¢manenAkNþalElVgfycuH. karfycuHenHmin)aneFVIeGaysuvtßiPaBrbs;eRKOgbgÁúMfycuH b¤eFVIeGaymaneRKaHfñak;enaHeT ebIeRbobeFobCamYyeRKOgbgÁúMsþaTickMNt;. CakarBit PaBCab;enAkñúg rcnasm<n§½pþl;nUversIusþg;/ esßrPaB nigesdækic©bEnßmeTotkñúgkarKNna. emKuNEbgEckm:Um:g;eLIgvij q EdlQrelI (ACI Code 318-99) RtUv)anKNnadUcxageRkam

( )⎥⎦

⎤⎢⎣

⎡ −−=

bq

ρρρ '120 ¬!^>@%¦

enAkñúgsmIkarTI !^>@% PaKryEdk ρ b¤ )'( ρρ − enARtg;muxkat;Edlm:Um:g;RtUv)ankMNt; RtwmPaKryGtibrma bρ5.0 . PaKryEdkGb,brmaenAkñúgmuxkat;rgkarBt;RtUv)ankMNt;Rtwm

yyc fff /4.1)4/(' ≥ . edayeRbIkarkMNt;dac;xatTaMgenHPaKryEbgEckm:Um:g;eLIgvijGtibrma nigGb,brmaRtUv)anbgðajenAkñúgtarag 16>3. taragTI 16>1 karpøas;bþÚrPaKryEbgEckm:Um:g;eLIgvij )'(q MPaf y 400=

tε 0075.0 010.0 0125.0 0150.0 0175.0 020.0 0225.0 bρρ / 476.0 385.0 323.0 278.0 244.0 217.0 196.0

(%)'q 5.7 10 5.12 15 5.17 20 20

T.Chhay NPIC


taragTI 16>2 karpøas;bþÚrPaKryEbgEckm:Um:g;eLIgvij )'(q sMrab;kareGayPaKry bρρ / bρρ / 48.0 45.0 40.0 35.0 30.0 25.0 20.0

tε 0074.0 0081.0 0095.0 0113.0 0137.0 017.0 022.0 (%)'q 0.0 1.8 5.9 3.11 7.13 0.17 0.20

taragTI 16>3 karEbgEckm:Um:g;eLIgvijGtibrma nigGb,brma q ¬smIkar !^>@%¦

)(' MPaf c )(MPaf y bρ minρ )minρfor %(maxq )5.0%(for min bq ρ

21 400 0215.0 0033.0 9.16 10 28 400 0285.0 0033.0 7.17 10 35 400 0339.0 003.0 9.17 10 ]TahrN_16>8 kMNt;m:Um:g;eGLasÞicGtibrmaenARtg;TMr nigenAkNþalElVgénFñwmCab;EdlmanbYnElVgdUcbgðajenA kñúgrUbTI 16>32 a. Fñwmmanmuxkat;es μI nigRTnUvbnÞúkefrBRgayesμ I mkN /117 nigbnÞúkGefr

kN5.87 . sn μt;PaKryEbEckm:Um:g;eLIgvijGtibrma %10 nigBicarNanUvkrNIBIrxageRkam³ - enAeBlEdlbnÞúkGefrRtUv)andak;enAelIElVgqøas;Kña KNnam:Um:g;viC¢manGtibrmaenAkñúgElVg - enAeBlEdlbnÞúkGefrRtUv)andak;enAelIElVgCab;Kña KNnam:Um:g;GviC¢manGtibrmaenAelITMr

dMeNaHRsay 1> Fñwmmanm:Um:g;niclPaB I esμ IKña nigman E dUcKña. dUcenH EI efr. smIkarbIm:Um:g;

sMrab;viPaKFñwmnigsMrab; EI efrKW³ ( )

442

322

311

2211LwLw

LMLLMLM CbA −−=+++ edaysarElVgesμ IKña

( )21

2

44 wwLMMM CBA +−=++ ¬!^>@^¦

enAkñúg]TahrN_enH 0== EA MM . krNIénkardak;bnÞúk6EbbepSgKñaRtUv)an BicarNadUcbgðajenAkñúgrUbTI 16>32³

T.Chhay NPIC


krNITI1> bnÞúkefrRtUv)andak;enAelIFñwm ABCDE TaMgmUl ¬rUbTI 16>32 b¦. krNITI2> bnÞúkGefrRtUv)andak;enAelIElVg AB nig CD sMrab;m:Um:g;GtibrmaenAkñúg

ElVg AB nig CD ¬rUbTI 16>32 c¦. krNITI3> dUckrNITI 2 sMrab;ElVg BC nig DE ¬rUbTI 16>32 d¦. krNITI4> bnÞúkGefrRtUv)andak;enAelIElVg AB / BC nig DE sMrab;m:Um:g;GviC¢manenA

Rtg; B ¬rUbTI 16>32 e¦. krNITI5> bnÞúkGefrRtUv)andak;enAelIElVg CD nig DE ¬rUbTI 16>32 f¦. krNITI6> bnÞúkGefrRtUv)andak;enAelI BC nig CD sMrab;m:Um:g;GviC¢manGtibrmaenARtg;

C ¬rUbTI 16>32 g¦. 2> krNITI1> GnuvtþsmIkar !^>@^ eTAelIFñwmkMNat; ABC / BCD nig CDE erogKña

mkNMM CB .2106)117117(4

642

−=+−=+ mkNMMM DCB .21064 −=++

mkNMM DC .21064 −=+ KNnasmIkarTaMgeyIgTTYl)an

mkNMM DB .28.451−== nig mkNM C .9.300−= sMrab;karkat;bnßym:Um:g; %10

( ) mkNMM DB .2.40628.4519.0'' −=−×== ( ) mkNM C .81.2709.3009.0' −=−×=

m:Um:g;kNþalElVgEdlRtUvKñanwgm:Um:g;Edl)ankat;bnßyehIyKW ElVg mkNM

LwDEAB B

D .4.3232.40621

86117'

21

8

22=−

×=+==

ElVg ( ) mkNCDBC .18881.2702.40621

86117 2

=+−×

== 3> krNITI2> GnuvtþsmIkar !^>@@ eTAelIkMNat;Fñwm ABC / BCD nig CDE erogKña³

mkNMM CB .5.787)5.87(4

642

−=−=+ mkNMMM DCB .5.7874 −=++

mkNMM DC .5.7874 −=+

T.Chhay NPIC


KNnasmIkarTaMgeyIgTTYl)an mkNMM DB .75.168−==

nig mkNM C .5.112−= m:Um:g;eGLasÞickNþalElVgEdlRtUvKñanwgm:Um:g;xagelIKW Fñwm mkNMLwAB B

L .4.30975.16821

865.87

21

8

22=−

×=+=

mkNBC .6.140)5.11275.168(210 =+−=

mkNLwCD L .1.253625.1408

65.87)5.11275.168(21

8

22=−

×=+−=

mkNDE .4.8475.168210 =−=

edIm,Ikat;bnßym:Um:g;viC¢mankñúgElVg eKRtUvbegáInm:Um:g;Rtg;TMreday %10 nigKNnam:Um:g; kñúgElVgEdlRtUvKña. m:Um:g;viC¢manEdlTTYl)anRtUvEtes μ Iy:agtic %90 énm:Um:g;Edl KNnadMbUg.

( ) mkNMM DB .6.18575.1681.1'' −=−== mkNM C .75.123)5.112(1.1' −=−=

m:Um:g;eGLasÞickNþalElVgEdlRtUvKñanwgm:Um:g;xagelIKW Fñwm mkNM

LwAB B

L .95.3006.18521

865.87'

21

8

22=−

×=+=

mkNBC .7.154)75.1236.185(210 =+−=

mkNLw

CD L .05.2397.1548

65.87)6.18575.123(21

8

22=−

×=+−=

mkNDE .8.926.185210 =−=

4> krNITI3> RsedogKñanwgkrNITI2> ehIym:Um:g;RtUv)anbgðajenAkñúgrUbTI 16>32 d. 5> krNITI4> BicarNaElVg AB / BC nig DE EdlRTbnÞúkGefredIm,IKNnam:Um:g;GviC¢man

GtibrmaenARtg;TM B ³ mkNMM CB .1575)5.87(

264

2−=−=+

mkNMMM DCB .5.7874 −=++ mkNMM DC .5.7874 −=+

T.Chhay NPIC


KNnasmIkarTaMgeyIgTTYl)an mkNM B .7.379−= / mkNM C .3.56−=

nig mkNM D .8.182−= sMrab;karkat;bnßym:Um:g; %10 Rtg; B

( ) mkNM B .7.3417.3799.0' −=−= m:Um:g;kNþalElVgEdlRtUvKñaKW Fñwm mkNMLwAB B

L .9.2227.34121

865.87

21

8

22=−

×=+=

mkNLw

BC L .75.1941998

65.87)3.567.341(21

8

22=−

×=+−=

mkNCD .55.119)8.1823.56(210 −=+−=

mkNLw

DE L .35.3024.918

65.878.18221

8

22=−

×=−=

6> krNITI5> RsedogKñanwgkrNITI4> elIkElgEtElVgxagcugminRtUv)andak;bnÞúkedIm,I TTYl)anm:Um:g;viC¢manGtibrmarnARtg;TMr B ¬b¤TMr D sMrab;kardak;bnÞúkRsedogKña¦. düaRkamm:Um:g;Bt;RtUv)anbgðajenAkñúgrUbTI 16>32 f.

7> krNITI6> BicarNaElVg BC nig CD EdlRTbnÞúkGefredIm,IKNnam:Um:g;GviC¢man GtibrmaenARtg;TM B ³

mkNMM CB .5.787)5.87(4

642

−=−=+

mkNLwMMM LDCB .1575

24

2−=−=++

mkNLw

MM LDC .5.787

44

2−=−=+

KNnasmIkarTaMgeyIgTTYl)an mkNMM DB .5.112−==

nig mkNM C .5.337−= sMrab;karkat;bnßym:Um:g; %10 Rtg; C

( ) mkNM C .75.3035.3379.0' −=−= ( ) mkNMM DB .25.1015.1129.0'' −=−==

T.Chhay NPIC


m:Um:g;kNþalElVgEdlRtUvKñaKW Fñwm mkNDEAB .6.502.101

21

−=−==

mkNLwCDBC L .15.1916.2028

65.87)95.3032.101(21

8

22=−

×=+−==

8> m:Um:g;Gtibrma nigGb,brmaeRkaykarEbgEckm:Um:g;eLIgvijRtUv)anbgðajenAkñúgtarag 16>4. Moment envelop RtUv)anbgðajenAkñúgrUbTI 16>32 h.

9> enAkñúg]TahrN_renH muxkat;kNþalElVgRtUv)aneRbIsMrab;PaBgayRsYl. m:Um:g;kNþal ElVgmincaM)ac;Cam:Um:g;viC¢manGtibrmaeT. kñúgkrNIElVgcug AB nig DE m:Um:g;Gtibrma eRkayeBlBIkarEbgEckbnÞúkeLIgvij %10 KWwes μ Inwg 2.12/2LwD nigekItmanenAcMgay

L4.0 BI BC nig D . taragTI 16>4 m:Um:g;cugeRkayén]TahrN_TI 16>8 eRkayBIkarEbgEckm:Um:g;eLIgvij

krNI 1 2 3 4 ¬1 + 2¦ 5 ¬1 + 3¦ TItaMg

muxkat; m:Um:;g DL

m:Um:;gGviC¢man Gtibrma LL

m:Um:;gviC¢man Gtibrma LL

m:Um:;gGviC¢man Gtibrma LLDL +

m:Um:;gviC¢man Gtibrma LLDL +

TMr A 0 0 0 0 0 B 2.406− 7.341− 1.28+ *9.747− 1.378− C 9.300− 75.303− - *65.604− 9.300− D 2.406− 7.341− 1.28+ *9.747− 1.378− E 0 0 0 0 0

kNþalElVg

AB 4.323+ 8.92− 95.300+ 6.230+ *35.624+ BC 188+ 7.154− 05.239+ 3.33+ *05.427+ CD 188+ 7.154− 05.239+ 3.33+ *05.427+ DE 4.323+ 8.92− 95.300+ 6.230+ *35.624+

( * ) m:Um:g;KNnaGtibrma nigGb,brmacugeRkay.

T.Chhay NPIC


T.Chhay NPIC


T.Chhay NPIC


]TahrN_16>9 kMNt;karEbgEckm:Um:g;GviC¢maneLIgvijGnuBaØatenAelITMr B / C / D nig E énFñwmCab; ABCDE EdlbgðajenAkñúgrUbTI 1633. FñwmEdlmanmuxkat;ctuekaNEkg mmb 300= / mmh 550= nig

mmd 490= nigvaRtUv)anBRgwgdUcbgðajenAkñúgtarag ¬ MPaf c 28' = nig MPaf y 420= ¦ - edayeRbI]bsm<n§½ B . - edayeRbIkarkMNt; ACI Code.

dMeNaHRsay

1> sMrab; MPaf c 28' = nig MPaf y 420= / 0285.0=bρ . emKuNEbgEckm:Um:g;eLIgvij RtUv)aneGaydUcxageRkam³

⎥⎦

⎤⎢⎣

⎡ −−=

bq

ρρρ '120 ¬!^>@%¦

2> emKuNEbgEckm:Um:g;eLIgvijrbs; ACI Code CaGnuKmn_énsac;lUtEdksuT§ tε nigERbRbYlcenøaHBI %5.7 nig %20 dUcbgðajenAkñúgrUbTI 16>31

tq ε1000'= ¬!^>@$¦

003.0003.0

−+

=

b

s

y

tEf

ρρ

ε

T.Chhay NPIC


nig 003.0005.0−=

s

t

ρρ

ε sMrab; MPaf y 420=

taragxageRkambgðajBItMél q nig 'q EdlminRtUvKña.

TMr EdkTaj

sA ρ

Edksgát; sA'

'ρ bρρρ '−

%q tε '%q

B 283DB 0126.0 0 0 44.0 2.11 008.0 8 C 323DB 0164.0 0 0 58.0 4.8 0056.0 0 D 203DB 0064.0 0 0 225.0 5.15 0192.0 2.19 E 254DB 0134.0 203DB 0064.0 246.0 1.15 0173.0 3.17

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បេតុងពង្រឹងដោយដែក 16 xvi-continuous-beams-and-frames