vi deflection and control of cracking

Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa

Deflection and Control of Cracking 90

VI. PaBdab nigsñameRbH

1> sñameRbHenAkñúgeRKOgbgÁúMebtug Deflection of Structural Concrete Members Ggát;ebtugrgkarBt;RtUv)anKNnasMrab;suvtßiPaB nigkareRbIR)as; serviceability . Ggát;Edl)an

KNnaedayeKarBtamsmIkar nigkarkMNt;EdlEcgedaybTdæan ACI Code nwgmansuvtßPaB. dUcenH dUc karBnül;kñúgemeronmun TMhMGgát;nImYy²Edl)ankMNt; d¾dUcbrimaNEdkcaM)ac;edIm,IrkSanUvlT§PaBm:Um:g;kñúg esμ Ib¤FMCagm:Um:g;xageRkA. enAeBlEdl TMhMmuxkat;cugeRkayRtUv)anKNna FñwmRtUv)anepÞógpÞat;sMrab;lkç xNÐbMerIbMras; serviceability dUcCa sñameRbH nigPaBdab. edIm,IkarBarnUvsñameRbH nigPaBdabelIslb; eK caM)ac;manPaBrwgRkajrbs;Ggát;RKb;RKan;.

kareRbIR)as; ACI Code provision Edl)anBicarNanUvTMnak;TMng nonlinear relationship rvag stress nig strain enAkñúgebtug )anpþl;CalT§plnUvmuxkat;tUcCagmuxkat;EdlKNnadayRTwsþIeGLasÞic. bT dæan ACI Code ,Section 9.4 TTYlsÁal;nUvkareRbIR)as;EdkEdlman yield strength rhUtdl; MPa560 nig kareRbIR)as;nUvebtugersIusþg;x<s;. kareRbInUvebtug nigEdkersIusþg;x<s;pþl;CalT§plnUvmuxkat;tUcCag ehIy karbnßynUvPaBrwgRkajTb;nwgkarBt;rbs;Ggát; )aneGayPaBdabekInFMCag.

PaBdabEdlGacGnuBaØatiRtUv)ankMNt;edayktþaepSg²dUcCa RbePTGKar rUbragrbs;GKar vtþman rbs;Bidan nigCBa¢aMg karxUcxatrMBwgTukEdlbNþalBIPaBdabelIslb; nigRbePT nigTMhMrbs;bnÞúkcl½t.

bTdæan ACI Code , Section 9.5 kMNt;bBa¢ak;kMras;Gb,brmasMrab;Ggát;rgkarBt;mYyTis one-way

flexural members nigkMralxNÐmYyTis dUcbgðajkñúgtaragTI 1. tMélTaMgGs;kñúgtaragKwsMrab;Ggát;Edl minRT b¤EdlminP¢ab;eTAnwgCBa¢aMgxNÐ b¤sMng;epSgeTotEdlTMngeFVIeGayxUcxatedayPaBdabFM.

taragTI1³ kMras;Gb,brmarbs;Fñwm nigkMralxNÐmYyTis ¬ L RbEvgElVg¦

Ggát; Yield

Strength

)(MPaf y TMrsamBaØ cugmçagCab; cugsgçagCab; Cantilever

275 25/L 30/L 35/L 5.12/L 350 22/L 27/L 31/L 11/L

kMralxNÐtan;mYyTis

400 20/L 24/L 28/L 10/L 275 20/L 23/L 26/L 10/L 350 18/L 5.20/L 5.23/L 9/L

Fñwm b¤kMralxNÐ ribbed mYyTis

400 16/L 5.18/L 21/L 8/L

T.Chhay NPIC

PaBdab nigsñameRbH 91

kMras;Gb,brmaEdlbgðajenAkñúgtaragTI1 RtUv)aneRbIsMrab;Ggát;EdlplitBIebtugTMgn;Fm μta normal-weight concrete, 3/2320 mkgW = nigsMrab;EdkEdlman yield strength dUcbgðajkñúgtarag. tMélRtUv)anEktMrUvsMrab;krNIebtugTMgn;Rsal b¤ yield strength rbs;EdkxusBI MPa400 dUcxageRkam³

- sMrab;rbtugTMgn;RsalEdlmanTMgn;maDsßitkñúgcenøaH 33 /1900/1400 mkgmkg − tMélenAkñúgtarag sMrab; MPaf y 400= RtUvKuNnwg )0003125.065.1( cW− b:uEnþminRtUvtUcCag 09.1 . Edl cW Ca m:as;maDebtug.

- sMrab; yield strength rbs;EdkxusBI MPa400 tMélenAkñúgtarag sMrab; MPaf y 400= RtUvKuNnwg )5.689/4.0( yf+ .

2> PaBdabxN³ Instantaneous Deflection PaBdabrbs;Ggát;ekIteLIgCacMbgedaysarbnÞúkefrbUknwgbnÞúkGefrmYyEpñk b¤TaMgGs;. PaBdab

EdlekIteLIgPøam²bnÞab;BIGnuvtþbnÞúkeKeGayeQ μaHfa PaBdabPøam² immediate deflection b¤PaBdabxN³ instantaneous deflection . eRkambnÞúkEdlGnuvtþsßitesßr PaBdabnwgekIneLIgKYreGaykt;sMKal;CamYynwg eBl. eKmanviFIepSg²sMrab;KNnaPaBdabenAkñúgeRKOgbgÁúMsþaTickMNt; nigsþaTicminkMNt;. karKNnaPaB dab instantaneous deflection KWQrelI elastic behavior énGgát;rgkarBt;. PaBdabeGLasÞic ΔCaGnu-Kmn_eTAnwg bnÞúk W ElVg L m:Um:g;niclPaB I nigm:UDuleGLasÞicrbs;sMPar³ E ³

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟

⎟⎠

⎞⎜⎜⎝

⎛=⎟

⎠⎞

⎜⎝⎛=Δ

EIMLK

EIWL

EIWLf

23α (6-1)

Edl =W bnÞúksrubenAelIElVg ehIy α nig K CaemKuNEdlGaRs½yeTAnwgdWeRkénPaBbgáb;rbs;TMr bMErbMrYlm:Um:g;niclPaBtambeNþayElVg nigkarBRgaybnÞúk. ]TahrN_ PaBdabGtibrmaénbnÞúkBRgayesμ I enAelIFñwmTMrsamBaØKW³

EIwL

EIWL

3845

3845 43

==Δ (6-2)

Edl =W bnÞúksrubenAelIElVg wL= ¬bnÞúkBRgayesμ IelImYyxñatRbEvg × ElVg¦. PaBdabrbs;Fñwm CamYynwglkçxNÐbnÞúk niglkçxNÐTMrepSg² edayCab;GnuKmn_eTAnwgbnÞúk ElVg nig EI RtUv)aneGayenA kñúg ]bsm<n§½ C nigenAkñúgesovePAviPaKeRKOgbgÁúM.

edaysareKsÁal; W nig L enaHeKRKan;EtKNnam:UDuleGLasÞic E nigm:Um:g;niclPaB I énGgát;eb tug b¤PaBrwgRkajTb;karBt;rbs;Ggát; EI .

2>1> m:UDuleGLasÞic Modulus of Elasticity

bTdæan ACI Code , Section 8.5 kMNt;bBa¢ak;fa eKGacykm:UDuleGLasÞicrbs;ebtug cE



ccc fWE '043.0 5.1= sMrab;tMél cW enAcenøaH 3/1400 mkg eTA 3/2500 mkg (6-3) cc fE '4780= sMrab;ebtugTMgn;Fmμta normal-weight concrete 3/2320 mkgWc =

CaTUeTAm:UDuleGLasÞicRtUv)ankMNt;edayebtugsMNakKMrYsIuLaMgrgbnÞúkkñúgry³eBlxøI short-term

loading of concrete cylinder. enAkñúgGgát;BitR)akd creep EdlbNþalmkBIbnÞúkEdlGnuvtþmkelICab; lab; ¬y:agehacNas;k¾manbnÞúkefr¦ man\T§iBleTAelIm:UDulenAEpñkrgkarsgát;énGgát;. sMrab;Epñkrgkar Taj m:UDulenAkñúgEpñkTajRtUv)ansn μt;dUcKñanwgm:UDulenAkñúgEpñksgát; enAeBlEdltMél stress mantMéltUc. enAeBl stress FM m:UDuleGLasÞicfycuHCaxøaMg. elIsBIenH m:UDuleGLasÞicERbRbYltambeNþayElVgEdl bNþalmkBIbMErbMrYlénm:Um:g;nigkMlaMgkat;TTwg.

2>2> pleFobm:UDuleGLasÞic Modular Ratio

pleFobm:UDuleGLasÞic cs EEn /= EdlRtUv)aneRbIenAkñúgkarbMElgRkLaépÞ dUcEdl)anBnül;enA kñúgemeronTI2 EpñkTI10. vaRtUv)anKitCacMnYnKt; EtminGactUcCag 6 . ]TahrN_ enAeBlEdl

MPaf c 5.17' = enaH 10=n MPaf c 20' = enaH 9=n MPaf c 30' = enaH 8=n MPaf c 35' = enaH 7=n

sMrab;ebtugTMgn;Fmμta normal-weight concrete n Gacykesμ I cf '/42 . 2>3> m:Um:g;eRbH Cracking moment

dMeNIrkarénkar)ak;rbs;FñwmTMrsamBaØrgbnÞúkRtUv)anBnül;enAkñúgemeronTI3 EpñkTI3. enAeBlbnÞúk GnuvtþtUc ¬ekItmanm:Um:g;tUc¦ nig stress enAsésrrgkarTajeRkAbMputnwgmantMéltUcCagm:UDuldac; modulus of rupture rbs;ebtug cr ff '623.0= . RbsinebIeKbegáInbnÞúkrhUtdl;kugRtaMgTaj tensile

stress xiteTA CitkugRtaMgdac;mFüm rf enaHsñameRbHnwgcab;epþImekIteLIg. RbsinebIkugRtaMgTajFMCag rf muxkat;nwg eRbH ehIykrNImuxkat;eRbHnwgcab;epþImekIteLIg. enHmann½yfaeKmanbIkrNIRtUvBicarNa³

- enAeBlEdlkugRtaMgTaj tf tUcCag rf muxkat;Gt;eRbHTaMgmUlRtUv)anBicarNaedIm,IKNnalkçN³ rbs;muxkat;. enAkñgkrNIenH m:Um:g;niclPaB gI RtUv)aneRbI³ 12/3bhI g = Edl =bh muxkat;ebtugTaMg mUl.

- enAeBlEdlkugRtaMgTaj tf esμ Inwg cr ff '623.0= sñameRbHnwgcab;epþImekItman ehIym:Um:g;Edl begáItnUvkugRtaMgenHRtUv)aneKeGayeQ μaHfa m:Um:g;eRbH cracking moment . edayeRbIrUbmnþkugRtaMgBt;

gcrr I

cMf = b¤ cI

fM grcr = (6-4)

T.Chhay NPIC


Edl cr ff '623.0= / =gI m:Um:g;niclPaBmuxkat;l¥eBj nig =c cMgayBIGkS½NWteTAsésrrgkar TajEpñkxageRkAbMput. ]TahrN_ sMrab;muxkat;ctuekaNEkg 12/3bhI g = nig 2/hc =

- enAeBlEdlm:Um:g;xageRkAFMCagm:Um:g;eRbH cracking moment crM enaHkrNImuxkat;eRbHnwgcab; epþImekIteLIg ehIyebtugenAkñúgtMbn;rgkarTajRtUv)anecal. muxkat;eRbHbMElg transformed cracked

section RtUv)aneRbIedIm,IKNnam:Um:g;niclPaBeRbH cracking moment of inertia crI edayeRbIRkLaépÞ ebtugenAkñgtMbn;sgát; nigRkLaépÞEdkbMElg transformed steel area snA . ]TahrN_6>1³ muxkat;ebtugctuekaNEkgRtUv)anBRgwgedayEdk 283DB enAkñúgmYyCYr ehIymanTTwg

mm300 nigkMBs;srub mm650 cMENk mmd 585= ¬rUb 6>1¦. cUrKNnam:UDuldac; modulus of rupture

rf / m:Um:g;niclPaBmuxkat;l¥eBj gI nigm:Um:g;eRbH crM edayeRbI MPaf c 28' = nig MPaf y 400= . dMeNaHRsay³

1> m:UDuldac; modulus of rupture MPaff cr 28.3'623.0 == 2> m:Um:g;niclPaBénmuxkat;l¥eBj ( ) 4933 1087.612/65030012/ mmbhI g ⋅=== 3> m:Um:g;eRbH mkNcIfM grcr .3.69325/1087.628.3/ 9 =⋅×==

2>4> m:Um:g;niclPaB Moment of inertia

edayKuNm:Umg;niclPaBeTAnwg m:UDuleGLasÞiceyIgTTYl)anPaBrwgRkajTb;nwgkarBt;rbs;Ggát;. eRkambnÞúktUc m:Um:g;GtibrmaEdlekItmannwgmantMéltUc ehIy tensile stress enAsésrrgkarTajxageRkA bMputnwgmantMéltUcCagm:UDuldac;rbs;ebtug. enAkñúgkrNIenH muxkat;eRbHbMElgeBj gross transformed

cracked section nwgmanRbsiT§PaBkñúgkarpþl;nUvPaBrwgmaM. enAxN³bnÞúkkargar b¤bnÞúkFM sñameRbHenAtMbn; TajEdl)anmkBIkarBt;nwgekIteLIg. enARtg;muxkat;eRbH TItaMgGkS½NWtsßitenAx<s; b:uEnþenARtg;muxkat; kNþalcenøaHsñameRbHenAelIbeNþayFñwm TItaMgGkS½NWtsßitenATab ¬Ek,rEdkrgkarTaj¦. manEtTItaMgTaMg BIrenHeT Edlmuxkat;eRbHbMElgmanRbsiT§PaBkñúgkarkMNt;PaBrwbRkajrbs;Ggát;. dUcenH m:Um:g;niclPaB



RbsiT§PaBERbRbYly:agxøaMgtambeNþayElVg. enATItaMgm:Um:g;Bt;Gtibrma ebtugeRbH enaHEpñk enAtMbn;rgkar TajminRtUv)anKitkñúgkarKNnam:Um:g;niclPaB. enARtg;cMnucrbt; kugRtaMgtUc ehIymuxkat;TaMgmUlGacnwg mineRbH. sMrab;sßanPaBenH nigenAkñúgkrNIsMrab;FñwmEdlmanFñwmERbRbYl dMeNaHRsayd¾RtwmRtUvman lkçN³sμ úKsμaj.

rUb 6>2 a bgðajBIExSekagbnÞúk-PaBdabrbs;FñwmebtugEdlRtUv)aneFVIBiesaFn_rhUtdl;)ak;. Fñwm RtUv)anRTedayTMrsamBaØ manRbEvg ft17 nigrgnUvbnÞúkcMcMnucBIrEdlmancMgayBIKña ft5 edaysIuemRTInwgGkS½. FñwmRtUv)anrgnUvkardak;bnÞúkBIrCMu³ TImYy ¬ExSekag 1cy ¦ ExSekagbnÞúk-PaBdab CabnÞat;Rtg;eLIgelIdl; bnÞúk KP 7.1= enAeBlEdlFñwmcab;epþImekItmanenAkñúgFñwm. bnÞat; a bgðajnUvTMnak;TMngbnÞúk-PaBdab edayeRbIm:Um:g;niclPaBsMrab;muxkat;bMElgGt;eRbH. eKGacemIleXIjfaPaBdabBitR)akdrbs;FñwmeRkam bnÞúkEdltUcCagtUcCagbnÞúkeRbH ¬edayQrelImuxkat;Gt;eRbHsac;mYy homogeneous cracked section¦ mantMélEk,reTAnwgPaBdabEdl)anmkBIkarKNna ¬bnÞat; a ¦. ExSekag 1cy bgðajnUvExSekagPaBdabBit R)akd enAeBlEdlbnÞúkekIneLIgrhUtdl;Bak;kNþalbnÞúkcugeRkay ultimate load. CMral slop rbs;ExS ekag enARKb;nIv:UbnÞúkTaMgGs; mantMéltUcCagCMralrbs;bnÞat; a edaysarEtsñameRbHekItman ehIyEpñk EdleRbHénmuxkat;ebtug)ankat;bnßynUvPaBrwgRkajrbs;Fñwm. bnÞab;mkbnÞúkRtUv)andkecj PaBdabEdl enAesssl; residual deflection RtUv)anGegáteXIjmanenAkNþalElVgFñwm. enAeBlmansñameRbH karsnμt;BIkarRbRBwtþeTArbs;muxkat;Gt;eRbHeRkambnÞúktUcminRtUv)anykmkGnuvtþ.

sMrab;karGnuvtþn_bnÞúkCMuTIBIr PaBdab ¬ExSekag c ¦ )anekIneLIgkñúgkMritFMCagbnÞat; a edaysarEt ersIusþg;rbs;sésrebtugTajRtUv)an)at;bg;. enAeBlbnÞúkekIneLIg TMnak;TMngbnÞúk-PaBdabRtUv)anbgðaj edayExSekag 2cy . RbsinebIbnÞúkenACMuTImYyekIneLIgdl;bnÞúkcugeRkay enaHExSekag 1cy nwgcab;ykKnøg ExSekag 2cy enARtg;bnÞúkRbEhl uP6.0 . ExSekag c bgðajBIdMeNIrkarBitR)akdrbs;FñwmsMrab;karbEnßm bnÞúk b¤kardkbnÞúk.

bnÞat; b bgðajBITMnak;TMngbnÞúk-PaBdabedayQrelImuxkat;bMElgeRbH. eKeXIjfa PaBdabEdl KNnaedayQrelIeKalkarN_hñwg xusKñaBIPaBdabBitR)akd. rUb 6>2 b bgðajBIbMErbMrYlPaBrwgRkaj EI rbs;FñwmCamYynwgkarekIneLIgénm:Um:g;. bTdæan ACI Code, section 9.5 ENnaMnUvsmIkaredIm,IkMNt; m:Um:g;niclPaBRbsiT§PaBEdleRbIenAkñúgkarKNnaPaBdabenAkñúgm:Um:g;rgkarBt;. m:Um:g;niclPaBRbsiT§PaB EdleGayeday ACI Code (Eq. 9.8) edayQrelIsmIkarEdlesñIredayelak Branson nwgRtUv)anKNna dUcxageRkam³

gcra

crg

a

cre II

MMI

MMI ≤

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛=

33

1 (6-5)

T.Chhay NPIC


Edl =eI m:Um:g;niclPaBRbsiT§PaB =crM m:Um:g;eRbH/ ⎟⎟

⎠

⎞⎜⎜⎝

⎛

t

gr

YIf (6-6)

=rf m:UDuldac;rbs;ebtug cr ff '623.0= (6-7)

=aM m:Um:g;K μanemKuNGtibrmarbs;Ggát;enAxN³EdlPaBdabkMBugRtUv)anKNna =gI m:Um:g;niclPaBrbs;muxkat;ebtugl¥eBjeFobGkS½TIRbCMuTMgn; edayecalEdl =crI m:Um:g;niclPaBénmuxkat;bMElgeRbH =tY cMgayBIGkS½TIRbCMuTMgn;edayecalEdkeTAépÞrgkarTaj.



karkMNt;xageRkamRtUv)ankMNt;edaybTdæan³ 1> sMrab;FñwmCab; m:Um:g;niclPaBRbsiT§PaBGacRtUv)anyktMélmFüménm:Um:g;niclPaBénmuxkat;

Edlmanm:Um:g;viC¢man nigGviC¢manFMCageK. 2> sMrab;ebtugTMgn;Rsal m:UDuldac; rf edIm,IeRbIenAkñúgsmIkar (6-6) esμ Inwg

⎟⎠⎞

⎜⎝⎛=

556.0623.0 ct

rff Edl c

ct ff '556.0

≤ (6-8a)

Edl ctf CaersIusþg;TajedaykarbMEbk splitting tensile strength. enAeBlEdleKGt;sÁal; ctf enaH rf GacRtUv)anKitdUcxageRkam³

cr ff '465.0= (6-8b) sMrab;ebtugxSac;TMgn;Rsal sand-lightweight concrete

cr ff '532.0= (6-8c) 3> sMrab;Ggát;RBIs eI GacyktMélEdlTTYl)anBIsmIkar (6-5) enAkNþalElVgsMrab;FñwmTMrsamBaØ

nigFñwmCab; nigenATMrsMrab;Fñwm cantilever (ACI Code, section 9.5.2) . cMNaMfa eI Edl)anmkBIkarKNnatamsmIkar (6-5) pþl;nUvtMélEdlsßitenAcenøaHm:Um:g;nicl PaBl¥eBj gross moment of inertia gI nig m:Um:g;niclPaBeRbH cracked moment of inertia

crI edayGnuKmn_eTAnwgkMritéplpleFob a

crMM . Ggát;ebtugEdlmanbrimaNEdkeRcIn Gacnwg

man eI xiteTACit crI b:uEnþsMrab;Ggát;EdlmanRTnug flanged member Gacnwgman eI xiteTA Cit gI .

4> sMrab;FñwmCab; tMélRbEhléntMélmFümén eI sMrab;Ggát;RBIs b¤minRBIs edIm,IeFVIeGaylT§pl kan;EtRbesIreLIgmandUcxageRkam³ - sMrab;FñwmEdlmancugsgçagCab; )(15.07.0 Average 21 eeme IIII ++= (6-9) - sMrab;FñwmEdlmancugmçagCab; )(15.085.0 Average conme III += (6-10)

Edl em II = enAkNþalElVg É eee III =21, enAcugFñwmsgçag nig econ II = enARtg;cug Cab;. eI GacyktMélmFümén eI enARtg;muxkat;Edlmanm:Um:g;viC¢man nigGviC¢manFM. eKKYr eRbI moment envelope kñúgkarKNnatMélviC¢man nigGviC¢manén eI . enAkñúgkrNIEdlFñwmrg bnÞúkcMp©itFM manEt eI kNþalElVgKYrRtUv)aneRbI.

2>5> lkçN³rbs;muxkat; Properties of sections

edIm,IKNnam:Um:g;niclPaBmuxkat;eBj gross section nigmuxkat;eRbH cracked section eKcaM)ac;RtUv KNnacMgayBIsésrrgkarsgát; compression fiber eTAGkS½NWt neutral axis ¬ x b¤ kd ¦.

T.Chhay NPIC


1> m:Um:g;niclPaBeBj gI ¬ecalmuxkat;EdkTaMgGs;enAkñúgebtug¦ a. sMrab;muxkat;ctuekaNEkgEdlmanTTwg b nigkMBs;srub h enaH 12/3bhIg = . b. sMrab;muxkat; T-section EdlmanTTwgsøab b TTwgRTnug wb nigkMras;RTnug t KNna y

cMgayBIGkS½TIRbCMuTMgn;eTAcMnucx<s;bMputrbs;søab³ ( )

)(2

)(2

2

thbbttththbbt

yw

w

−+

⎥⎦⎤

⎢⎣⎡

+−

−+⎟⎟⎠

⎞⎜⎜⎝

⎛

= (6-11)

bnÞab;mkeTotKNna ( ) ( )

⎥⎦⎤

⎢⎣⎡ −

+⎥⎥⎦

⎤

⎢⎢⎣

⎡ −+

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −+=

33212

323 yhbtybtybtbtI wwg (6-11a)

2> m:Um:g;niclPaBeRbH crI ³ yk =x cMgayBIGkS½NWtmksésrrgkarsgát;eRkAbMput ¬ kdx = ¦ a. muxkat;ctuekaNEkgCamYyEtnwgEdkrgkarTaj sA

i. KNna x BIsmIkarxageRkam 0)(

2

2=−− xdnAbx

s (6-12) ii. KNna 23 )(3/ xdnAbxI scr −+= (6-12a)

b. muxkat;ctuekaNEkgCamYyEdkrgkarTaj sA nigEdkrgkarsgát; sA' i. KNna x ³ 0)()'(')1(

2

2=−−−−+ xdnAdxAnbx

ss (6-13) ii. KNna 223 )()'(')1()3/( xdnAdxAnbxI sscr −+−−+= (6-13a)

c. T-section CamYyEdkrgkarTaj sA i. KNna x ³ ( ) 0)(

2)

2(

2=−−

−+− xdnAtxbtxbt sw (6-14)

ii. KNna ( ) 2323

)(3212

xdnAtxbtxbtbtI swcr −+⎥⎥⎦

⎤

⎢⎢⎣

⎡ −+

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −+= (6-14a)

3> PaBdabry³eBlyUr Long-term Deflection PaBdabrbs;Ggát;ebtugEdkBRgwgbnþekIneLIgeRkambnÞúkEdlGnuvtþsßitesßr ebIeTaHbICavayWtebI

eRbobeFobCamYyeBlk¾eday. karrYmmaD nig creep CamUlehtueFVIeGayekItmanPaBdabbEnßmEdleKeGay eQ μaHfa PaBdabry³eBlyUr long-term deflection. varg\T§iBlCacMbgBI sItuNðPaB sMeNIm Gayurbs;eb tugenAxN³énkardak;bnÞúk karEfTaMebtug brimaNEdkrgkarsgát; nigdg;sIuetbnÞúkefr. bTdæan ACI Code,



Section 9.5 esñIfa y:agehacNas;tMélEdlTTYledaykarviPaKd¾RtwmRtUvmYy KWPaBdabry³eBlyUrbEnßm sMrab;Ggát;rgkarBt;ebtugFmμta nigebtugTMgn;RsalKYr)an TTYlBIkarKuNPaBdabPøam²CamYyemKuN

'501 ρζλ

+=Δ (6-15)

Edl =Δλ emKuNsMrab;PaBdabbEnßmEdlbNþalmkBI\T§iBlry³eBlyUr bdA s /''=ρ sMrab;muxkat;enAkNþalElVgrbs;FñwmTMrsamBaØ b¤FñwmCab; b¤sMrab;muxkat;enATMr

rbs;Fñwm cantilever . =ζ emKuNGaRs½yeBl time-dependent factor sMrab;bnÞúkefrEdlGacnwgykdUcbgðajkñúg

taragTI 6>2. emKuN Δλ RtUv)aneRbIedIm,IKNnaPaBdabEdlbNþalmkBIbnÞúkefr nigEpñkxøHénbnÞúkGefrEdlnwg

sßitenAzitezrsMrab;ry³eBlmYyRKb;RKan;edIm,IbegáItnUvPaBdabGaRs½ynwgeBlmYyKYreGaykt;sMKal;. em KuN Δλ CaGnuKmn_eTAnwglkçN³sMPar³ EdlsMEdgeday ζ niglkçN³muxkat; sMEdgeday )'501( ρ+ . enAkñúgsmIkar (6-15) \T§Blrbs;Edkrgkarsgát;KWTak;TgeTAnwgRkLaépÞebtugCagTak;TgeTAnwgpleFob rvagEdksgát;elIEdkTaj.

ACI Code Commentary, section 9.5 bgðajnUvExSekagedIm,IKNna ζ sMrab;ry³eBlticCag 60 Ex. tMélTaMgenHRtUv)anKNnadUcbgðajkñúgtaragTI 6>2.

PaBdabsrubes μ InwgplbUkPaBdabPøam² nigPaBdabbEnßmry³eBlyUr. ]TahrN_ PaBdabbEnßm ry³eBlyUrsrubrbs;FñwmrgkarBt;CamYy 01.0'=ρ enAry³eBl 5 qñaMesμ InwgplKuN Δλ CamYynwgPaBdab Pøam² Edl 33.1)01.0501/(2 =×+=Δλ .

tarag 6>2 emKuNGaRs½yeBlsMrab;PaBdabry³eBlyUr ry³eBl ¬Ex¦ 1 3 6 12 24 36 48 60 ζ 5.0 0.1 2.1 4.1 7.1 8.1 9.1 0.2

4> PaBdabGnuBaØati Allowable Deflection PaBdabKYrminRtUvelIstMéldUcxageRkamGaRs½yeTAtambTdæan ACI Code, Section 9.5 ³

- 180/L sMrab;PaBdabPøam²EdlbNþalmkBIbnÞúkGefrsMrab;dMbUlerobesμ IEdlminRTGgát;ÁEdlTMng eFVIxUcxat.

- 360/L sMrab;PaBdabPøam²EdlbNþalmkBIbnÞúkGefrsMrab;kMralxNÐEdlminRTGgát;EdlTMngeFVI xUcxat.

T.Chhay NPIC


- 480/L sMrab;EpñkénPaBdabsrubEdlekIteLIgeRkayBIkarP¢ab;GgÁ dUcCa plbUkPaBdabry³eBl yUrEdlbNþalmkBIbnÞúkefrTaMgGs; nigPaBdabPøam²EdlbNþalmkBIbnÞúkGefrbEnßm sMrab;kMral xNÐ b¤dMbUlEdlRTGgát;EdlTMngnwgeFVIeGayxUcxat.

- 240/L sMrab;EpñkénPaBdabsrubEdlekIteLIgeRkayBIGgát;RtUv)anP¢ab; sMrab;kMralxNÐ b¤dMbUl EdlminRTGgát;EdlTMngnwgeFVIeGayxUcxat.

5> PaBdabEdlbNþalmkBIbnSMbnÞúk Deflection Due to Combinations of Load RbsinebIFñwmrgnUvbnÞúkeRcInRbePT ¬BRgayes μ I BRgayminesμ I b¤bnÞúkcMcMnuc¦ b¤rgnUvm:Um:g;cug enaH

PaBdabGacRtUv)anKNnasMrab;bnÞúk b¤kMlaMgtamRbePTmYy²EdlGnuvtþmkelIFñwmdac;edayELkBIKña ehIy PaBdabsrubRtUvKNnaedayviFItMrYtpl superposition. enHmann½yfaPaBdabmYy²RtUveFVIplbUknBVnþCa mYyKñaedIm,ITTYl)anPaBdabsrub. PaBdabrbs;bnÞúkeRkambnÞúkmYy²RtUv)anbgðajenAkñúgtarag 6>3. ]TahrN_6>2³ KNnaPaBdabxN³kNþalElVgsMrab;FñwmTMrsamBaØdUcbgðajkñúgrUb 6>3 EdlRTnUvbnÞúkefr BRgayes μ I mkN /85.5 nigbnÞúkGefr mkN /75.8 rYmnwgbnÞúkefrcMcMnuc kN25.22 enARtg;kNþalElVg. eKeGay MPaf c 28' = / MPaf y 400= / mmb 330= nig mmd 530= nigkMBs;srub mm630 ¬ 8=n ¦.

dMeNaHRsay³

1> epÞógpÞat;kMBs;Gb,brmaGaRsy½eTAtambTdæan ACI Code tarag 6>1 kMBs;srubGb,brma mmL 5.762

1612200

16===

edaysarkMBs;srubEdleRbIR)as; mmmm 5.762630 < dUcenH eKRtUvkarepÞógpÞat;PaBdab. 2> PaBdabenAkNþalElVgEdlbNþalmkBIbnÞúkBRgayKW

ecIEwL

3845 4

1 =Δ

PaBdabenAkNþalElVgEdlbNþalmkBIbnÞúkcMcMnucKW



ecIEPL

48

3

2 =Δ

edaysarEteKsÁal; w / P nig L dUcenHeKRtUvKNnam:UDuleGLasÞic cE nigm:Um:g;niclPaBRbsiT§PaB eI .

3> m:UDuleGLasÞicrbs;ebtugKW MPaEc 4.25293284780 ==

4> m:Um:g;niclPaBRbsiT§PaB

gcra

crg

a

cre II

MMI

MMI ≤

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛=

33

1

kMNt;tMélTaMgGs;enAGgÁxagsþaM mkNPLwLMa .5.339

42.1225.22

82.12)85.575.8(

48

22=

×+

+=+=

4933

1088.612

)630(33012

mmbhIg ⋅===

t

grcr Y

IfM = eday MPaff cr 3.328623.0'623.0 === mmhYt 315

2==

mkNMcr .1.72315

1088.63.3 9=

⋅×=

m:Um:g;niclPaBénmuxkat;bMElgeRbH crI RtUv)anKNnadUcxageRkam³ kMNt;TItaMgGkS½TIRbCMuTMgn;sMrab;muxkat;eRbHedaysmIkarm:Um:g;énmuxkat;bMElgeFobGkS½TIRbCMuTMgn; eTA 0 yk == kdx cMgayBIGkS½TIRbCMuTMgn;

0)(2

2=−− xdnAbx

s 8==c

sEEn 23041mmAs =

01289384024328165 2 =−+ xx mmx 38.215= ( ) 492

32

3105.3)38.215530(30418

338.215330)(

3mmxdnAbxI scr ⋅=−×+=−+=

CamYynwgGgÁTaMgGs;Edl)anKNna eyIgTTYl)an 499

39

31053.3105.3

5.3391.7211088.6

5.3391.72 mmIe ⋅=⋅

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−+⋅⎟

⎠⎞

⎜⎝⎛=

5> KNnaPaBdabBIbnÞúkepSg²

1Δ ¬bNþalmkBIbnÞúkrayes μ I¦ecIE

wL384

5 4=

( ) mm2.471053.34.25293384

1220085.575.859

4

1 =⋅××

×+=Δ

T.Chhay NPIC


2Δ ¬bNþalmkBIbnÞúkcMcMnuc¦ecIE

PL48

3=

mm43.91053.34.2529348

12200222509

3

2 =⋅××

×=Δ

PaBdabPøam²srub mm63.5643.92.4721 =+=Δ+Δ= 6> eRbobeFobtMélEdl)anmkBIkarKNnaCamYyPaBdabGnuBaØati³

PaBdabPøam²Edl)anmkBIbnÞúkGefrBRgayesμ I mkN.75.8 esμ Inwg =+× )85.575.8/(2.4775.8 mm29.28 . RbsinebIGgát;CaEpñkmYyrbs;kMralxNÐEdlminRT b¤P¢ab;eTAnwgCBa¢aMgxNÐ½ b¤Ggát;epSg²eTot

EdlGacTMngeFVIeGayxUcxatedaysarPaBdabFM enaHPaBdabPøam²GnuBaØatiEdlbNþalmkBIbnÞúkGefres μ Inwg mmmmL 29.289.33

36012200

360>==

EtRbsinebIGgát;CaEpñkénkMralxNÐdMbUl nigRsedogKñaeTAGVIEdl)anerobrab;xagelI enaHPaBdab Pøam²GnuBaØatiEdlbNþalmkBIbnÞúkGefrKW mmmmL 29.288.67

18012200

180>== . tMélGnuBaØatiTaMgBIrFM

CagPaBdabBitR)akd mm29.28 EdlbNþalmkBIbnÞúkGefrBRgayesμ I. ]TahrN_6>3³ kMNt;PaBdabry³eBlyUr long-term deflection rbs;FñwmenAkñúg]TahrN_6>2 RbsinebIem KuNGaRs½yeBl time-dependent factor esμ Inwg 0.2 . dMeNaHRsay³

1> bnÞúkEdlGnuvtþn_zitezrbNþaleGaymanPaBdabry³eBlyUrKWekItmkBIbnÞúkGefr EdlrYmmanbnÞúk efrBRgayesμ I mkN /85.5 nigbnÞúkefrcMcMnuc kN25.22 EdlGnuvtþn;enAkNþalElVg. PaBdabbNþalmkBIbnÞúkBRgayes μ I mm9.18)85.575.8/(2.4785.5 =+×= PaBdabCaGnuKmn_bnÞat;eTAnwgbnÞúk w ehIytMélepSgeTot ¬ L / cE / eI ¦dUcKña PaBdabbNþalmkBIbnÞúkcMcMnuc mm43.9= PaBdabsrubEdlbNþalmkBIbnÞúkzitezr sustained load mm33.2843.99.18 =+=

2> sMrab;PaBdabry³yUrbEnßm PaBdabPøam²RtUv)anKuNnwgemKuN Δλ

012

'501 +=

+=Δ ρ

ζλ

kñúgkrNIenH 0' =sA dUcenH 0.2=Δλ PaBdabry³eBlyUrbEnßm mm66.5633.282 =×=

3> PaBdabry³eBlyUrsrubCaplbUkrvagPaBdabPøam²CamYynwgPaBdabry³eBlyUrbEnßm mm29.11366.5663.56 =+



4> PaBdabbNþalmkBIbnÞúkefrCamYynwgPaBdabry³eBlyUrbEnßmEdlbNþalmkBIkarrYmmaDnig creep KW mm8566.5633.28 =+

]TahrN_6>4³ KNnaPaBdabxN³ nigPaBdabenAry³eBl 1qñaM enAcugTMenrrbs;Fñwm cantilever dUcbgðaj kñúgrUbTI 6>4. FñwmmanRbEvg m1.6 nigRTbnÞúkefrBRgayesμ I mkN /85.5 bnÞúkGefrBRgayesμ I mkN /85.5 bnÞúkefrcMcMnuc kNPD 35.13= enAcugTMenr nigbnÞúkGefrcMcMnuc kNPL 8.17= EdlGnuvtþn_enAcMgay m05.3

T.Chhay NPIC


BITMrbgáb;. eKeGay MPaf c 28' = / MPaf y 400= / mmb 300= / mmd 550= / nigkMBs;muxkat;srub mm635 ¬sésrEdkrgkarTajKW 256DB nigEdkrgkarsgát; 252DB ¦.

dMeNaHRsay³

1> kMBs;Gb,brma mmmmL 6355.7628

61008

>== dUcenHeKRtUvepÞógpÞat;PaBdab. PaBdabGtibrmarbs;Fñwm cantilever KWsßitenAcugTMenr. PaBdabenAcugTMenrKWdUcxageRkam³ PaBdabEdlbNþalmkBIbnÞúkBRgay

EIwL8

4

1 =Δ PaBdabEdlbNþalmkBIbnÞúkefrcMcMnucenAcugTMenr

EILPD

3

3

2 =Δ PaBdabGtibrmaenAcugTMenrEdlbNþalmkBIbnÞúkGefrcMcMnucenA ma 05.3= BIcugbgáb;

)3(6

2

3 aLEIaPL −=Δ b¤ )

231(

3

3

ab

EIaPL +

2> m:UDuleGLasÞicrbs;ebtugTMgn;RsalKW MPaEc 4.25293284780 ==

3> m:Um:g;GtibrmaenAcugbgáb; mkNPPwLM LDa .5.2458.1705.35.131.6

21.685.505.31.6

2

22=×+×+

×=++=

4> m:Um:g;niclPaBeBj ¬Etebtug¦ 49

33104.6

12635300

12mmbhIg ⋅=

×==

5> mkNYIf

Mt

grcr .5.66

2635

104.628623.0 9=

⋅×==



6> kMNt;TItaMgGkS½NWt bnÞab;mkkMNt;m:Um:g;niclPaBénmuxkat;bMElgeRbH. Kitm:Um:g;énmuxkat; eFob GkS½TIRbCMuTMgn;nigdak;eGayvaesμ IsUnü. eRbI 8=n edIm,IKNnamuxkat;bMElgrbs; sA nig eRbI 7)1( =−n sMrab;KNnamuxkat;bMElgrbs; sA' . yk xkd = ( ) 0)()'(')1(

2

2=−−−−+ xdnAdxAnxb ss

01337044030434150 2 =−+ xx sMrab;muxkat;enH mmx 875.213=

49223 108.3)()'(')1(3

mmxdnAdxAnxbI sscr ⋅=−+−−+= 7> m:Um:g;niclPaBRbsiT§PaBKW

gcra

crg

a

cre II

MMI

MMI ≤

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛=

33

1

993

93

1085.3108.35.245

5.661104.65.245

5.66⋅=⋅

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−+⋅⎟

⎠⎞

⎜⎝⎛=eI

8> KNnaPaBdabeRkambnÞúkepSg²EdlmanGMeBIelIFñwm

1Δ ¬bNþalBIbnÞúkBRgayes μ I mkN /7.11 ¦ mm8.201085.34.252938

61007.119

4=

⋅×××

=

1Δ ¬bNþalBIbnÞúkefr¦ mm4.10=

2Δ ¬bNþalBIbnÞúkefrcMcMnuc¦enAcugTMenr mm5.101085.34.252933

6100135009

3=

⋅×××

=

3Δ ¬bNþalBIbnÞúkGefrcMcMnuc¦enA m05.3 BIcugbgáb;

3Δ mm3.41085.34.252936

)305061003(3050178009

2=

⋅××−×××

= PaBdabPøam²srub mm6.353.45.108.20321 =++=Δ+Δ+Δ=Δ

9> PaBdabbEnßmry³eBlyUr esμ InwgplKuNrvagPaBdabPøam²CamYynwgemKuN Δλ sMrab;ry³eBl 1qñaM 4.1=ζ

006.0550300

982'' =×

==bdA sρ

077.1006.0501

4.1=

×+=Δλ

PaBdabPøam²srub sΔ EdlbNþalmkBIbnÞúkzitezr sustained load ¬enATIenHmanEtbnÞúkefr mkN /85.5 nig kNPD 35.13= enAcugTMenr¦

mms 9.205.104.10 =+=Δ PaBdabry³eBlyUrbEnßm mm5.229.20077.1 =×=

T.Chhay NPIC


10> PaBdabry³eBlyUrsrubCaplbUkrvagPaBdabPøam²CamYynwgPaBdabry³eBlyUrbEnßm EdlekItBIkarrYmmaD nig creep .

mm1.585.226.35 Total =+=Δ ]TahrN_6>5³ KNnaPaBdabxN³enAkNþalElVgrbs;FñwmenAkñúgrUb 6>5 EdlFñwmenHmanRbEvg m8.9 . FñwmenHRtUv)anbnþedayTMrCaeRcInEdlmanRbEvgElVgepSg²Kña. düaRkamm:Um:g;Bt;nigmuxkat;rbs;FñwmenA kNþalElVg nigTMrk¾RtUv)anbgðaj. FñwmenHRTbnÞúkefrBRgayes μ I mkN /3.61 nigbnÞúkGefr mkN /5.52 . eKeGay MPaf c 20' = / MPaf y 400= nig 2.9=n .

m:Um:g;enAkNþalElVg mkNM D .260= mkNM LD .650)( =+ m:Um:g;enATMrxageqVg A mkNM D .75.242= mkNM LD .5.569)( =+ m:Um:g;enATMrxagsþaM B mkNM D .293= mkNM LD .735)( =+

dMeNaHRsay³ 1> Fñwm AB rgnUvm:Um:g;viC¢manEdleFVIeGaydabcuHeRkamenAkNþalElVg nigm:Um:g;GviC¢manenAcugTaMgBIr

EdleFVIeGaydabeLIgelIenAkNþalElVg. dUcEdl)anBnül;BIxagedIm PaBdabCaGnuKmn_eTAnwg m:Um:g;niclPaBRbsiT§ eI . enAkñúgFñwmCab; tMélrbs; eI EdlRtUv)aneRbICatMélmFümsMrab;tMbn;m:U m:g;viC¢man nigm:Um:g;GviC¢man. dUcenHmuxkat;bInwgRtUv)anBicarNa muxkat;enAkNþalElVg nigmuxkat; enATMrTaMgBIr.

2> KNna eI ³ sMrab;RkLaépÞeBjénmuxkat;TaMgGs; mmkd 356= nig 410102.5 mmIg ⋅= dUcKña MPaff cr 8.2'623.0 == nig MPafE cc 8.21376'4780 == sMrab;RKb;muxkat;. tMélrbs;

kd / crI nig crM sMrab;muxkat;eRbH/ eI sMrab;EtbnÞúkefr ¬edayeRbI aM sMrab;bnÞúkefr¦ nig eI sMrab;bnÞúkefr nigbnÞúkGefr ¬edayeRbI aM sMrab;bnÞúkefr nigbnÞúkGefr¦RtUv)anKNna nigbegáItCa taragdUcxageRkam³

muxkat; kd ¬ mm ¦ crI ¬ 4mm ¦ crM ¬ mkN. ¦ eI ¬ 4mm ¦ ¬bnÞúkGefr¦

eI ¬ 4mm ¦ ¬ LLDL + ¦

kNþalElVg 8.169 101012.2 ⋅ 226 101014.4 ⋅ 101025.2 ⋅ TMr A 281 101052.1 ⋅ 409 10102.5 ⋅ 101088.2 ⋅ TMr B 320 101084.1 ⋅ 409 10102.5 ⋅ 101042.2 ⋅ cMNaMfa enAeBlEdlFñwmrgEtbnÞúkefr ehIypleFob acr MM / FMCag 0.1 enaH eI esμ Inwg gI .

3> kMNt;tMélmFümrbs; eI BIsmIkar (6.9) ( ) ( ) 4101010

1 1037.21042.288.215.01025.27.0)average( mmIe ⋅=++⋅=



sMrab;bnÞúkefr nigbnÞúkGefr ( ) 41010 1065.21042.288.25.0)sections endfor average( mmIe ⋅=+=

( ) 41010102 1045.21065.21025.25.0)average( mmIe ⋅=⋅+⋅=

sMrab;EtbnÞúkefr 410102.5)sections endfor average( mmIe ⋅=

( ) 41010103 1067.4102.51014.45.0)average( mmIe ⋅=⋅+⋅=

T.Chhay NPIC


4> KNnaPaBdabPøam²enAkNþalElVg

1Δ ¬bNþalmkBIbnÞúkBRgay¦eEI

wL3845 4

= ¬cuHeRkam¦

2Δ ¬bNþalmkBIm:Um:g;enAcMnuc A / AM ¦e

AEI

LM16

2−= ¬eLIgelI¦

3Δ ¬bNþalmkBIm:Um:g;enAcMnuc B / BM ¦e

BEI

LM16

2−= ¬eLIgelI¦

PaBdabsrub 321 Δ−Δ−Δ=Δ PaBdabsMrab;bnÞúkefrBRgayesμ I mkN /3.61 edayyk mkNDLM A .75.242)( = /

mkNDLM B .293)( = nig 4103 1067.4 mmIe ⋅= CMnYseTAkñúgsmIkarxagelI eyIgTTYl)an³

mm1.48.15.14.7 =−−=Δ ¬cuHeRkam¦ PaBdabEdlbNþalBIbnSMbnÞúkefr nigbnÞúkGefrRtUv)anKNnaedayykbnÞúkefrbUknwgbnÞúkGefr

mkN /8.113= / mkNLLDLM A .5.569)( =+ / mkNLLDLM B .735)( =+ nig 410

2 1045.2 mmIe ⋅= mm2.114.85.61.26 =−−=Δ ¬cuHeRkam¦

PaBdabPøam²EdlbNþalBIEtbnÞúkGefrKW mm1.71.42.11 =− ¬cuHeRkam¦. RbsinebIkarkMNt;PaBGnuBaØatiKW mmL 4.20480/9800480/ == enaHmuxkat;KWRKb;RKan;. cMnucmYycMnYnEdlTak;TgnwglT§pl³ 1> RbsinebIeKeRbIEt eI énmuxkat;kNþalElVg 4101025.2 mmIe ⋅= enaHPaBdabEdlbNþalmkBI

bnÞúkefr nigbnÞúkGefrRtUv)anKNnaeday KuNtMélEdlTTYl)ankñúgCMhanTI4 CamYynwgpl eFobéntMél eI TaMgBIr³ Δ ¬bnÞúkefr + bnÞúkGefr¦ mm2.12

1025.21045.22.11 10

10=

⋅⋅

×= PaBxusKñamantMéltUc RbEhl %8 .

2> RbsinebI 1eI mFüm RtUv)aneRbI 4101 1037.2 mmIe ⋅= enaH

Δ ¬bnÞúkefr + bnÞúkGefr¦ mm8.111025.21037.22.11 10

10=

⋅⋅

×= . PaBxusKñamantMéltUc RbEhl %5 .

3> edIm,IPaBgayRsYleKGacRbI eI énmuxkat;kNþalElVg elIkElgEteKRtUvkartMélCak;lak;.



6> PaBdabenAkñúgGgát;rgkarBt; Cracks in Flexural Members

karsikSaBIkarkekItsñameRbH kareFVIkarrbs;sñameRbHenAeBlbnÞúkekIneLIg nigkarRtYtBinitüsñameRbH mansar³sMxan;Nas;sMrab;karKNnaeRKOgbgÁúMebtugEdkBRgwgd¾Cak;lak;mYy. enAkñúgGgát;rgkarBt; sñam eRbH ekIteLIgeRkambnÞúkeFVIkar working load nigedaysarebtugexSayTb;nwgkarTaj enaHEdkRtUv)andak; enAtMbn;TajEdleRbH edIm,ITb;nwgkarTajEdlbgáeLIgedaykMlaMgxageRkA.

sñameRbHedaykarBt;ekIteLIgenAeBlEdlkugRtaMgenAsésrrgkarTajxageRkAeKbMputmantMélelIsBI m:UDuldac;rbs;ebtug modulus of rupture of concrete . CamYynwgkareRbIR)as;EdkBRgwgEdlmanersIusþg; x<s; high-strength reinforcing bars sñameRbHGacnwgekItmaneRcInenAelIGgát;ebtugGarem:. CamYynwgkar eRbIR)as;EdkrgkarTajx<s; high-tensile steel manRbeyaCn_CaeRcIn b:uEnþeKminGacecosputBIsñameRbHEdl eKmincg;)anenaHeT. sñameRbHEdlmanTMhMFM² )anGnuBaØatieGaymanERcHsIuEdk b¤eFVIeGaymankarRCabTwk EdleFVIeGay)at;bg;esaPNÐPaBrbs;eRKOgbgÁúM.

sñameRbHekItmanenAelIebtug enAeBlEdlrn§tUc²EdlminGackMNt;)anekItmanenAkñúgFñwmebtugEdlCa lT§plénkugRtaMgTajxagkñúg. kugRtaMgkñúgTaMgenHGacnwgbNþalmkBIkrNImYy b¤eRcInCagmYyénkrNIxag eRkam³

- kMlaMgxageRkA dUcCa kMlaMgTajtamGkS½edaypÞal; kMlaMgkat;TTwg m:Um:g;Bt; b¤m:Um:g;rmYl - karrYmmaD - creep - karrIkmaDxagkñúgEdlCalT§plBIkarpøas;bþÚrlkçN³rbs;smasFatupSMebtug

CaTUeTA sñameRbHRtUv)anEbgEckCaBIrRbePTFM²KW³ sñameRbHbnÞab;bnSM secondary cracks nigsñam eRbHcMbg main cracks. 6>1> sñameRbHbnÞab;bnSM Secondary Cracks

sñameRbHbnÞab;bnSM CasñameRbHd¾tUc²ekItmanenAdMNak;kaldMbUgénkareRbH EdlekIteLIgedaykar rIkmaDxagkñúg nigkarRbTajKñaénsmasFatuebtug nigedaykugRtaMgEdl)anBIkarBt;tUcbNþalmkBITMgn; pÞal;rbs;Ggát; nigbnÞúkefrd¾éTeTot. sñameRbHmanbIRbePTKW³

- sñameRbHedaykarrYmmaD shrinkage cracks CasñameRbHsMxan; BIeRBaHvaCH\T§iBlelITMrg;ragrbs;kar eRbHEdlekIteLIgedaybnÞúkenAkñúgGgát;rgkarBt;. enAeBlEdlBYkvaekIteLIg BYkvabegáItnUvKnøgd¾ exSayenAkñúgebtug. enAeBlEdlbnÞúkRtUv)anGnuvtþn_ sñameRbHcab;epþImelcecjrUbragenAelImux kat;EdlexSayCageK dUcCatambeNþayEdkBRgwg. cMnYn sñameRbHEdlekIteLIgRtUv)ankMNt;eday

T.Chhay NPIC


brimaNénkarrYmmaDrbs;ebtug nigvtþmanénkarbgáb;TMr. eKBi)akkñúgkarRKb;RKgsñameRbHedaykar rYmmaDenHNas;.

- sñameRbHbnÞab;bnSMedaykarBt; secondary flexural cracks CaTUeTAvamanKMlatFM² ehIysñameRbH mYy²minman\T§BlkñúgkarbegáItsñameRbHd¾éTeToteT. vaRtUv)anrMBwgnwgekItmaneRkambnÞúktUc dUc CabnÞúkefr. enAeBlbnÞúkRtUv)anGnuvtþn_CabnþbnÞab;eTA elIFñwmsamBaØ kugRtaMgTajekItmanenA sésrxageRkam ehIyenAeBlEdlvaFMCagkugRtaMgTajEdl ekItBIkarBt;rbs;ebtug sñameRbHcab; epþImekIteLIg. vacab;epþImrIkFMCabnþbnÞab; niglatsn§wgeTAkan;GkS½NWt. vaCakarBi)ankñúgkarTsSn_ TaynUvmuxkat;EdlsñameRbHbnÞab;bnSMcab;epþImekItman BIeRBaH ebtugminEmnCasMPar³ homogeneous material nig isotropic material. elak Salinger nigelak Billing)an):an;RbmaNkugRtaMgEdkmunkareRbHRtwmEtBIRbEhl MPa42 eTA MPa49 . TMhMeRbHdMbUgRtUv)anrMBwgRbEhl mm025.0 enAsésrTajxageRkAbMputrbs;ebtug. enAeBlsñameRbHRtUv)anbegáIt kugRtaMgTajrbs;ebtugenAmuxkat;eRbHfycuHdl; 0 ehIysésrEdk TTYlnUvkMlaMgTajTaMgGs;. enAkñúgxN³enH vaekItmankarsNþkrvagsésrEdk nigebtugedaysar Etebtug nigEdkmansac;lUtxusKña niglatsn§wgeTAdl;muxkat;Edlebtug nigEdkman strain esμ IKña. rUbTI6>6 bgðajBIKMrUénkarEbgEckkugRtaMgrvagsñameRbHenAkñúgGgát;eRkamkMlaMgTajtamGkS½.

- sñameRbHbnÞab;bnSMERcH corrosion secondary cracks ekIteLIgenAeBlsMeNImmansarFatuKImIdUcCa

sUdüÚmkørY sodium chloride Nacl kabUnDIG‘uksIut carbon dioxide 2CO nig]sμn½G‘uksIuEsnRCabcUl



eTAkñúgépÞebtug ehIybegáItCaERcHsIuEdk. bnSMG‘uksIutEdlbegáItedaykarxUcxatrbs;EdkRKbdNþb; nUvbrimaNeRcInCagEdk nigCMrujsMBaFemkanicEdlbnþlatsn§wgsñameRbHkan;EtFM. sñameRbHRbePT enHmaneRKaHfñak;EdlGaceFVIeGayeRKOgbgÁúM)ak;. kar)ak;dMbUlenA Muskegan enArdæ Michigan kñúg qñaM 1955 bNþalmkBIERcHsIuEdk RtUv)anraykarN_eday Shermer. karrIkraldalnUvsñameRbH nig karpÞúHebtug spalling of concrete enAelIs<an San Mateo-Hayward kñúgGMLúgeBl 7qñaM enArdæ California RtUv)anraykarN_eday Stratfull. sñameRbHedayERcHGacRtUv)anbBaÄb;edayeRbInUv viFIsaRsþsagsg;RtwmRtUv nigebtugEdlmanKuNPaBx<s;. 6>2> sñameRbHcMbg Main Cracks

sñameRbHcMbg main cracks ekIteLIgnUvdMNak;kalbnÞab;BIsñameRbHbnÞab;bnSM secondary cracks. vaRtUv)anbegáIteLIgedayPaBxusKñaén strain enAkñúgEdk nigebtug enAmuxkat;eRbH. karRbRBwtþeTArbs;sñam eRbHcMbgpøas;bþÚrenABIrdMNak;kalepSgKña. enAeBlEdkrgkugRtaMgTajtUc cMnYnsñameRbHekIneLIg b:uEnþTMhM sñamenAmanTMhMtUc EtenAeBlEdlkugRtaMgTajekIneLIg va)aneTAdl;dMNak;kallMnwg. enAeBlEdlkug RtaMgekIneLIgkan;Etx<s; dMNak;kalTIBIrénkareRbHekIteLIg ehIyTMhMeRbHrIkFM b:uEnþBuMmankarekIneLIgcMnYn sñameRbHKYreGaykt;sMKal;eT. CaTUeTAsñameRbHmYy b¤BIrcab;epþImBRgIkTMhMFMCagsñameRbHdéT EdlbegáIt CasñameRbHeRKaHfñak; ¬rUbTI 6>7¦.

T.Chhay NPIC


sñameRbHenAkñúgFñwm nigeRKOgbgÁúMrgkarTaj Edl)ansikSaedayGñkGegát karTsSn_TayBITMhMsñam eRbH nigkarRKb;RKgsñameRbHCacMENkénbBaðaEdlRtUvsikSa.

TaMgenHRtUv)anBiPakSaenATIenH CamYynigtMrUvkarrbs;bTdæan ACI Code. - ebIeyagtamRTwsþIsñameRbHEdlmaneRsc TMhMsñameRbH crack width nigKMlatsñameRbH crack

spacing GaRs½yeRcInktþa EdlrYmmanPaKryEdk karBRgayEdkenAkñúgmuxkat;ebtug kugRtaMgBt; rbs;Edk enAbnÞúkeFVIkar service load kMras;ebtugkarBarEdk niglkçN³rbs;sarFatupSMebtug. smIkarepSg²sMrab;TsSn_TayTMhM nigKMlatsñameRbHenAkñúgGgát;ebtugGarem:RtUv)anbgðajenAkñúg snñisiT§sþIGMBIkarkekItkaretags¥it nigkarkekItsñameRbHenAkñúgebtugBRgWgedayEdk Symposium

on Bond and Crack Formation in Reinforced Concrete enA Stockholm RbeTs Sweden kñúgqñaM 1957. elak Chi nigelak Kirstein )anbgðajsmIkarsMrab;TMhMeRbH nigKMlatsñameRbHCaGnu-Kmn_eTAnwgRkLaépÞRbsiT§PaBrbs;ebtugEdlenACMuvijEdk³ RkLaépÞebtug mUlEdlmanGgát;p©ites μ I Ggát;EdkbYndgRtUv)aneRbIedIm,IKNnaTMhMeRbH. smIkardéTeTotRtUv)anbgðajenATsvtSr_eRkay ²eTot.

elak Gergely nigelak Lutz bgðajnUvrUbmnþxageRkamsMrab;kMNt;TMhMeRbH³ 63 1011 −×= cs AdfW β (6-16)

Edl β / A nig sf RtUv)ankMNt;BIxagedIm nig =cd kMras;karBarebtugEdlRtUv)anvas;BIsésrTaj EpñkxageRkAbMputeTAGkS½EdkCitCageK. tMél β GacRtUv)anykRbEhl 2.1 sMrab;Fñwm nig 35.1 sMrab;kM ralxNÐ. cMNaMfa sf KitCa MPa nig W KitCa mm .

pleFobrvagTMhMsñameRbHGtibrmaelITMhMsñameRbHmFümRtUv)anrkeXIjsßitenAcenøaH 5.1 nig 0.2 Edl)anraykarN_edayGñkGegátCaeRcIn. tMélmFümeKGaceRbI 75.1 .

- TMhMeRbHEdlGacGnueRKaH tolerable crack width ³ eKminGaceCosputBIkarkekItsñameRbHenAelI Ggát;ebtugGarem:)aneT. eTaHbICamankarsikSa nigkarsagsg;y:agykcitþTukdak;y:agNak¾eday k¾vaenAEtkekItnUvsñameRbHb:unsésrsk;Edr. CaTUeTAsñameRbHRtUv)anvas;enAelIépÞrbs;ebtug b:uEnþ Cak;EsþgsñameRbHmantaMgBInIv:UEdkemø:H EdlCakEnøgekItmanERcHsIuEdk. TMhMsñameRbHGnuBaØati RtUv)anCH\T§iBledaytMrUvkaresaPNÐPaB. sñameRbHEdlGacemIleXIjedayEPñkTeTrmanTMhMRb Ehl mm15.0 vaGaRs½yeTAnwg texture rbs;épÞebtug. tMélepSg²sMrab;sñameRbHGnuBaØatienAnIv:U EdkRtUv)anesñIeLIgedayGñkGegátCaeRcIn EdlvasßitenAcenøaH 25.0 nig mm40.0 sMrab;Ggát;xagkñúg nigsßitenAcenøaH 15.0 nig mm25.0 sMrab;Ggát;xageRkA. TMhMsñameRbH mm40.0 sMrab;Ggát;xagkñúg nig mm32.0 sMrab;Ggát;xageRkA eRkamlkçxNÐs¶Üt GacRtUv)anGnueRKaH.



- sñameRbH crack control eRcInekItmanenAelIGgát;ebtugGarem:EdleRbIEdkersIusþg;x<s; high-strength

steel . sñameRbHkan;EtFMekItmaneRkambnÞúkeFVIkar edaysarEtkugRtaMgGnuBaØatix<s;. karRKb;RKg sñameRbHGaRs½yeTAnwgTMhMsñameRbHGnuBaØati . vaCakarRbesIrEdlmansñameRbHtUc²EteRcIn Ca CagmansñameRbHFM²Ettic. sñameRbHbnÞab;bnSM secondary crack RtUv)ankat;bnßyedaykarRKb; RKgnUvbrimaNkMe)areRbgTaMgGs; pleFobTWk-sIum:g;t¾ PaBRCabTWkrbs;fμbMEbk nigebtug kMritén karEfTaMebtug niglkçxNÐbgák;cug end-restraint condition.

ktþaEdlTak;TgnwgkarRKb;RKgsñameRbHcMbg KWkugRtaMgEdk PaBetags¥itrbs;ebtug kar BRgayEdk Ggát;p©itEdk PaKryEdk kMras;karBarebtug niglkçN³rbs;sarFatupSMebtug. edIm,ICYy kat;bnßyTMhMsñameRbH eKRtUveFVIeGayktþaEdl)anerobrab;xagelIy:agehacmYymanlkçN³kan;Etl¥.

7> tMrUvkarrbs;bTdæan ACI Code ACI Code Requirement

edIm,IRKb;RKgsñameRbHenAkñúgGgát;ebtugGarem: bTdæan ACI Code, chapter 10 kMNt;nUvtMrUvkarxag eRkam³

1> manEtEdk deformed bar RtUv)anGnuBaØatieGayeRbICaEdkem main reinforcement 2> EdkrgkarTajKYrEtRtUv)anBRgayenAtMbn;TajGtibrma (ACI Code, section 10.6.3) 3> enAeBlEdlsøabrbs;muxkat;sßiteRkamkarTaj EpñkénEdkemKYrRtUv)anBRgayenAkñúgcMeNamtMél

EdltUcCageKkñúgcMeNamTTwgsøabRbsiT§PaB effective flange width nigmYyPaKdb;énElVg one-

tenth of the span (ACI Code, section 10.6.6). 4> ersIusþg;KNna design yield strength rbs;EdkminKYreGayelIsBI MPa560 (ACI Code, section

9.4). 5> KMlatGtibrma s BIEdkEdlmancMgayeTAépÞebtugrgkarTajCitCageK sMrab;FñwmebtugGarem: nigkM

ralxNÐmYyTisRtUv)ankMNt; cs Cfs 5.2/105000 −= (6-17)

b:uEnþminRtUvFMCag )/280(300 sf Edl =sf kugRtaMgKNnaenAkñúgEdkenAbnÞúkeFVIkarRtUv)ankMNt;edaypleFobrvagm:Um:g;K μanem

KuNnigplKuNrvagRkLaépÞEdknigRbEvgédXñas;kñúg )/( jdAMf ss = . ¬mü:agvijeTot eKGaceRbI 3/2 ys ff = edaysarEtkareRbItMélRbEhlrbs; djd 87.0= ¦.

=cC kMras;ebtugkarBarEdk clear cover BIépÞrgkarTajCitbMputeTAépÞEdkrgkarTaj. =s KMlatKitBIGkS½énEdkrgkarTajEdlCitCageKeTAépÞebtugrgkarTaj.

T.Chhay NPIC


karkMNt;enHRtUv)aneRbIsMrab;EtFñwmebtugGarem: nigkMralxNÐmYyTisEdlsßitenAkñúglkçxNÐ brisßanFm μta. karkMNt;KMlatminTak;TgnwgTMhMEdkeT EdlvanaMeGaymankareRbIR)as;TMhMEdktUc CagedIm,IbMeBjlkçxNÐKMlat. sMrab;krNIFñwmebtugGarem:EdleRbIEdk MPaf y 420= nig

mmCc 50= . enaHKMlatGtibrma s RtUv)anKNnadUcxageRkam³ sn μt; MPafs 28042066.0 =×=

( ) mms 250505.2280/105000 =×−= EdldUcKñaeTAnwg mm300)280/280(300 =

6> enAkñúgbTdæanBImun karRKb;RKgsñameRbHRtUv)anQrelIemKuN Z EdlkMNt;dUcxageRkam³ mmkNAdfZ cs /313 ≤= sMrab;Ggát;enAxagkñúg (6-18)

mmkNZ /26≤ sMrab;Ggát;enAxageRkA (6-19)

Edl =sf kugRtaMgBt;enAbnÞúkeFVIkar nigGacykes μ I 3/2 yf / A nig cd CatMbn;TajRbsiT§PaB rbs;ebtug nigkMras;ebtugkarBarEdk erogKña. smIkarenHQrelIsmIkar (6-16) edaysn μt;TMhMsñameRbH RtUv)ankMNt;Rtwm mm40.0 sMrab;Ggát;enAxagkñúg nig mm32.0 sMrab;Ggát;enAxageRkA. edIm,ITTYl)an Z tUc eKRtUvbnßykMras;karBarebtug. kMras;ebtugminRtUvelIsBI mm50 .

7> Edkxag skin reinforcement skA sMrab;FñwmkMBs;eRCA EdlmankMBs;RbsiT§PaB mmd 900≥ sésr EdkesþIgKYrRtUb\v)anbEnßmenAEk,répÞbBaÄrkñúgtMbn;TajedIm,IRKb;RKgsñameRbHenAelIRTnugBIelI Edkem. bTdæan ACI Code, section 10.6.7 )anbriyayBIEdkbEnßmEdlCaEdkxag skin

reinforcement skA . EdkxagKYrRtUv)anBRgayes μ IelIépÞTaMgsgçagsMrab;cMgay 2/d Ek,rEdkrgkar TajbMput. KMlat skS rvagEdkbeNþayénEdkxagminKYrFMCagtMélEdltUcCageKkñúgcMeNamtMél 6/d /

mm300 nig )750/(1000 −dAb Edl bA CaRkLaépÞénmuxkat;EdkmYy² KitCa 2mm ¬rUbTI6>8¦.

⎪⎩

⎪⎨

⎧

−=

)750/(1000300

6/min

dA

dS

b

sk

Edkxag k¾GacRtUv)anKitbBa©ÚlkñúgkarKNnaersIusþg; (strength) edayQrelIkarKNnakugRtaMg stress nigbMErbMrYlrageFob (strain). elIsBIenH EdkxagsrubenAépÞTaMgsgçagénGgát; minKYrelIsBIBak; kNþalmuxkat;EdkrgkarTajsrub sA eT.

eyagtamrUbTI 6>8 RbsinebI mmb 400= / mmd 950= nigeRCIserIsEdk 10DB ¬ =bA 278mm ¦CaEdkxag enaHKMlatrbs;Edk 10DB EdlCaEdkbeNþayKYryktMéltUcCageKkñúgcMeNam



mm300 / mm1586/950 = nig mm390)750950/()781000( =−× . dUcenH eyIgeRCIserIsykKMlat mm150 . EdkxagKYrRtUv)anBRgayedayEdk 10DB kñúgKMlat mm150 elIkMBs; 2/d sMrab;xagmYy² ¬rUb

TI 6>8¦. RkLaépÞsrubEdkxagsMrab;épÞTaMgBIr 2468786 mm=×= EdltUcCag 40215.05.0 ×=sA 25.2010 mm= .

taragxageRkampþl;nUvKMlatGtibrmaenAelIépÞmYy² skS RkLaépÞEdkxagGb,brmamYy² bA .

kMBs;Fñwm d / mm 800 900 1000 1100 1200 1300 1400 1500 KMlatGtibrma skS / mm 150 150 150 175 200 200 225 250

bA ¬Gb,brma¦/ 2mm 5.7 5.22 5.37 25.61 90 110 25.146 5.187

]TahrN_6>6³ muxkat;FñwmTMrsamBaØRtUv)anbgðajenAkñúgrUb 6>9 a. epÞógpÞat;muxkat;EdktamtMrUvkarrbs; ACI Code b. kMNt;TMhMeRbHEdlnwgGacekItman c. epÞógpÞat;emKuN Z tamsmIkar (6-18)

eKeGay MPaf c 28' = / MPaf y 400= nigEdkkg 10DB . dMeNaHRsay³

1> rUb 6>9 muxkat; a ³ a. sMrab; 283DB / 21847mmAs = / kMras;ebtugkarBarEdk mmCc 462/2860 =−= / sn μt;

MPaff ys 26440066.066.0 =×== / KMlatGtibrma mms 7.282465.2264/105000 =×−= EdltUcCag mm2.318)264/280(300 = .

T.Chhay NPIC


KMlatEdlpþl;eGay mm90)6060300(5.0 =−−= edayKitBIGkS½EdkeTAGkS½Edk EdltUcCag mm7.282 .

b. sMrab;muxkat;enH mmdc 60= . RkLaépÞebtugrgkarTajRbsiT§PaBsMrab;EdkmYyKW ( ) 2120003/602300 mmA =×=

KNnaTMhMsñameRbHtamsmIkar (6-16) 63 1011 −×= cs AdfW β

edayGgát;enHCaFñwmenaH 2.1=β nig MPafs 240= mmW 28.01060120002402.111 63 =⋅×××= −

EdltUcCag mm40.0 nig mm32.0 sMrab;Ggát;xagkñúg nigsMrab;Ggát;xageRkA. c. tamsmIkar (6-18)

mmkNAdfZ cs /5.21106012000240 333 =⋅×== − EdltUcCag mmkN /31 nig mmkN /26 sMrab;Ggát;xagkñúg nigsMrab;Ggát;xageRkA.

2> rUb 6>9 muxkat; b ³ a. karKNnaKMlatEdkmanlkçN³RsedogKñacMnuc a xagelI. b. sMrab;muxkat;enH mmdc 60= ehIyEdkRtUv)andak;CaBIrRsTab;. TIRbCMuTMgn;rbs;EdkKW mm90

BIsésrxageRkam. RkLaépÞebtugrgkarTajRbsiT§PaBsMrab;EdkmYyKW ( ) 290006/902300 mmA =×=

mmW 26.0106090002402.111 63 =⋅×××= − RKb;RKan; c. tamsmIkar (6-18)

mmkNAdfZ cs /5.1910609000240 333 =⋅×== − RKb;RKan;



karBiPakSa eyIgGaceXIjfaKMlat s enAkñúgsmIkar (6-17) CaGnuKmn_énkugRtaMgkñúgEdkTaj b¤CaGnuKmn_eday minpÞal;énbMErbMrYlrageFobenAkñúgEdkTaj sss Ef ε×= ehIy sE sMrab;EdkesμI MPa5101.2 ⋅ . dUcKñaKM latk¾GaRs½ynwgkMras;ebtugkarBarEdk cC . karekIneLIgnUvkMras;ebtugkarBar vanwgkat;bnßyKMlat Edlva minTak;TgeTAnwgTMhMEdkEdleRbIenAkñúgmuxkat;eT. enAkñúg]TahrN_enH TMhMsñameRbHEdlrMBwgTukRtUv)anKNnaedaysmIkar (6-16) edIm,Ipþl;eGay nisiSt nigvisVkrnUvtMrUvkarRKb;RKgsñameRbH nigTMhMsñameRbH. CaTUeTATMhMsñameRbHRtUv)anvas;enAelIFñwm EdleFVIkarBiesaFn_enAkñúgmnÞIrBiesaFn_ b¤k¾enAkñúgeRKOgbgÁúMCak;EsþgEdlsßiteRkambnÞúk EdleFVIeGayman sñameRbHeRKaHfñak;ekIteLIgenAkñúgFñwm nigkñúgkMralxNÐ ehIyEdlRtUvkarkarBiesaFn_. RbsinebITMhMsñam eRbHEdl)anvas;mun nigeRkaykardak;bnÞúkFMCag yield strain rbs;Edk enaHEdkemnwgmanlkçN³)øasic nig K μanRbsiT§PaB. eKGacvas;TMhMeRbHCak;Esþg)anedaybnÞat;sMrab;vas;sñameRbHEdleKGacrkTij)an. eRkABI kugRtaMgEdk nigkMras;ebtugkarBarEdk W enAGaRs½ynwgktþaTIbIKW A EdlCaRkLaépÞebtugrgkarTajBT§½CMu vijEdkrgkarTajmYy. ]TahrN_6>7³ KNnaFñwmTMrsamBaØEdlmanRbEvg m3.7 RTnUvbnÞúkefrBRgayes μ I mkN /9.21 nigbnÞúk GefrBRgayesμ I mkN /2.17 . eRCIserIsmuxkat;EdkRKb;RKan; nigepÞógpÞat;KMlatEdkedIm,IbMeBjlkçxNÐ ACI Code. eKeGay mmb 400= / MPaf c 28' = / MPaf y 400= PaKryEdk %8.0 nigkMras;ebtugkar BarEdk mmCc 50= .

dMeNaHRsay³

1> sMrab;PaKryEdk %8.0=ρ / MPaRu 7.2= ¬ 9.0=φ ¦. m:Um:g;emKuNxageRkAKW 8/2wLMu = nig mkNw /8.532.176.19.212.1 =×+×=

T.Chhay NPIC


mkNMu .624.3488/3.78.53 2 =×= 2bdRM uu = mmd 568= 26.1817568400008.0 mmAs =××=

eRbI 283DB ¬ 23.1847 mmAs = ¦mYyCYr. kMBs;srubrbs;muxkat;Fñwm mmh 650= . CaTUeTA

mmd 5862/2850650 =−−= ¬rUbTI6>10¦ 2> KNnabnÞúkeFVIkar service load nigm:Um:g;eFVIkar service moment

mkNw /1.392.179.21 =+= mkNMu .5.2608/3.71.39 2 =×=

3> KNnakMBs;GkS½NWt kd nigRbEvgédXñas; jd tamsmIkar (6-12) 0)(2/)( 2 =−− kddnAkdb s 8=n 23.1847 mmAs = mmd 586=

mmkd 4.174= mmkddjd 9.5273/ =−= 9.0586/9.527 ==j cMNaMfa eKGacyktMélRbEhlrbs; 87.0=j kñúgkrNIEdl kd minRtUv)anKNna.

4> KNnakugRtaMg sf jdfAM ss ⋅⋅=

MPafs 267)9.5273.1847/(105.260 6 =×⋅= 5> KNnaKMlat s tamrUbmnþ (6-17)

mms 3.268505.2267/105000 =×−= EdltUcCag mm6.314)267/280(300 = KMlatEdleGay ( ) mmmm 8.23013664644005.0 <=−−=

vi deflection and control of cracking

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