បេតុងពង្រឹងដោយដែក 19 xix-introduction-to-prestressed-concrete

8/11/2019 19 xix-introduction-to-prestressed-concrete

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T.Chhay NPIC

esckþ IENnaMBIebtugeRbkugRtaMg 560

XVIII. esckþIENnaMBIebtugkugRtaMgIntroduction to Prestressed Concrete

1> ebtugeRbkugRtaMgPrestressed Concrete

k> eKalkarN_énkareFVeRbkugRtaMg Principles of Prestressing karGnuvtþeRbkugRtaMgeTAelIGgát;eRKOgbgá úMKWCakarbegá ItkugRtaMgGciéRnþy_xagkñ úgEdlmanGMeBI

RbqaMgnwgkugRtaMgTajenAkñ úgebtugEdl)anbnÞ úkxageRkA. karGnuvtþeRbkugRtaMgenHbegáItCaEdnkugRtaMgEdlGgát;GacTb;Tl;)any:agmansuvtß iPaB. eKGacGnuvtþkMlaMgeRbkugRtaMgmun b¤kñ úgeBldMNalKñaénkarGnuvtþbnÞ úkxageRkA. kugRtaMgenAkñúgGgát;eRKOgbgÁ ú MRtUvEtenAsl; ¬RKb;TIkEnøg nigsMrab;RKb sßanPaBénkardak;bnÞúk¦ enAkñ úgEdnkMNt;rbs;kugRtaMgEdlsMPar³ GacRTRTg;)anK μanTIkMNt;. CaTUeTA karGnuvtþkugRtaMg ¬PaKeRcInCakugRtaMgsgát;¦ RtUv)anbegáIteLIgeday high-strength steel

tendon EdlrgkarTaj nig anchor eTAnwgGgát;ebtug. kugRtaMgRtUv)anepÞreTAebtugeday bond tamépÞrbs; tendon b¤eday anchorage enAxagcugrbs; tendon.

edIm,IgayRsYlkñ úgkarBnül; cUrBicarNaFñ wmmYyEdleFVIBIebtugsuT§ ehIyFñwmenaHRtUvRTnUvbnÞ úkTMnajxageRkA (external gravity load) dUcbgðajkñ úgrUbTI 19>1 a. muxkat;Fñ wmRtUv)aneRCIserIsCamYynwg tensile flexural stress EdlCalkçxNÐeRKaHfñak;sMrab;karKNna dUcenHeKTmuxkat;EdlminmanlkçN³esdækic©. mUlehtuKWedaysarebtugxøaMgkñ úgkarsgát;CagkarTaj. flexural

tensile strength b¤m: UDuldac ; (module of rupture) rbs;ebtug r f es μ Inwg c f '62.0 ¬rUbTI 19>1a¦. kñ úgkarKNnaebtugGarem:Fm μta eKminKit tensile strength rbs;ebtugeT ehIyEdksrés

RtUv)andak;enAkñúgtMbn;Tajrbs;ebtugedIm,ITb;Tl;nwgkugRtaMgTaj b: uEnþebtugTb;Tl;nwgkugRtaMgsgát; ¬rUbTI 19>1 b¦. kñ úgkarKNnaebtugeRbkugRtaMg kugRtaMgsgát;dMbUgRtUv)anGnuvtþeTAkñ úgFñ wmedIm,IeGaymanGMe

Tb;nwgkugRtaMgTajEdlekIteLIgedaysarbnÞúkxageRkA ¬rUbTI 19>1c¦. RbsinebIkugRtaMgEdldak; dMbUgenHes μ InwgkugRtaMgTajenAsréseRkambMput enaHkugRtaMgTaMgBIrRtUv)anlubecal b: uEnþkugRtaMgsgát;enAsrésEpñkxagelIbMputnwgmantMélDub. kñúgkrNIenH muxkat;Ggát;TaMgmUlrgkarsgát;. Rb



T.Chhay NPIC


sinebIkugRtaMgsgát;EdlGnuvtþdMbUgtUcCagkugRtaMgTajenAsrésEpñkxageRkambMput enaHsrésenAEpñkxageRkamenHrgkarTaj ÉsrésEpñkxagelIbMputrgkarsgát;.



T.Chhay NPIC


kñ úgkarGnuvtþ Ggát;ebtugGacrgeRbkugRtaMgtamviFImYykñ úgcMeNamviFIxageRkam³!> karTajeRkay (Posttensioning): kñ úgkareF V I posttensioning, eKTaj steel tendon

eRkayeBlebtugRtUv)ancak; nigkkrwg. kareFVI posttensioning RtUv)aneFV IeLIgtamviFI saRsþdUcteTA³ dMbUgeKeRbI hydraulic jack Taj steel wire b ¤strand eGaylUt bnÞab;mkCMnYs jack eday anchorage EdlGacrkSaeGay steel strand enAEtrgkarTaj. CaTU eTA tendon RtUv)aneFV IeLIgBI wire, strand b¤ bar . eKGacTaj wire nig strand CaRkum)anEteKTaj bar mþg)anEtmYy. kñ úgdMeNIrkareFVI posttensioning, eKdak ; steel tendon eTAkñ úgBum<muneBlcak;ebtug ehIy tendon RtUv)ankarBarkars¥ itCab;eTAnwgebtugeday

waterproof paper wrapping b¤ metal duct (sheath). tendon Edls¥ itCab;eTAnwgebutgRtUv)aneKehAfa boded tendon. Unbonded tendon/ RtUv)andak;edayK μan grout b¤RtUv)anlabeRbg.

@> karTajmun (pretensioning) : kñ úgkareF VI prettensioning eKTaj steel tendon muneBlcak; ebtug. eKTb; tendon CabeNþaHGasnñeday abutment ehIyeKkat;va bnÞab;ebtugRtUv)an

cak; nigkkrwg. kMlaMg prestessing

RtUv)anepÞreTAebtugeday PaBs¥ itenAtamRbEvgrbs ; tendon. CaTUeTA eKeRcIneFV I prettensioning enAkñ úgkardæan b¤eragcRkpliteRKOgbgÁ úMebtugeRbkugRtaMgcak;eRsc EdlmankMralrwgmaMCaGciéRnþy_.

#> kareFV IeRbkugRtaMgxageRkA (external prestressing): kñúgkareFVI external pretessing, eKGnuvtþkMlaMgeRbkugRtaMgeday flat jack EdlRtUv)andak;enAcenøaHcugGgát;ebtug nig

permanent rigid abutments. Ggát;minman prestressing tendon dUcviFITaMgBIrxagelI

EdleKGacehAfakareFV IeRbkugRtaMgxagkñ úgeT. External prestressing

mingayRsYlkñ úgkarGnuvtþeT edaysar shrinkage nig creep enAkñúgebtugEdlnaMeGaymankarkbnßykugRtaMgsgát;EdlGnuvtþdMbUg.

Profile rbs ; tenden GacRtg; ekag b¤ragrgVg;GaRs½yeTAelIkarKNnaGgát;eRKOgbgÁ ú M.CaTUeTAeKeRbI straight tendon enAkñ úg solid slab nig hollow-cored slab b: uEnþeKeRb I bent tendon enAkñ úgFñ wm nigGgát;eRKOgbgÁ úMPaKeRcIn. eKeRbI circular tendon enAkñúgeRKOgbgÁ úMEdlmanTMrg;mUldUc



T.Chhay NPIC


Catank, silo nig pipe. eKGacGnuvtþkMlaMgeRbkugRtaMgEtkñ úgmYydMNakkal b¤eRcIndMNakm,I karBarebtugkMurGayrgkugRtaMgelIs.

eK)anbegáItnUvRbB½n§eRbkugRtaMgCaeRcIn EdlkñúgcMeNamenaHman Freyssinet, Magnel Blaton,

B.B.R.V., Dywidag, CCL, Morandi, VSL, Western Concrete, Prescon, nig INRYCO. eBlxøHeKCYbnUvbBaðakñ úgkareRCIserIsRbB½n§eRbkugRtaMgsMrab;kargarBiess.

visVkrKYrBicarNanUvktþacMbgbIEdlnaMdl;kareRCIserIsRbB½n§enH³!> GaMgtg;sIueténkMlaMgeRbkugRtaMgEdlRtUvkar@> ragFrNImaRtrbs;muxkat; nigKMlatEdlGacmansMrab ; tendon #> tMélénRbB½n§eRbkugRtaMg ¬sMPar³ nigkMlaMgBlkm μ¦]TahrN_xageRkambgðajBIlkçN³Biessrbs;ebtugeRbkugRtaMg.

]TahrN_ 9> ³ sMrab;Fñ wmTMrsamBaØEdlbgðajenAkñúgrUbTI 19>2 cUrkMNt;kugRtaMgRtg;muxkat; kNþalElVgEdlbNþalmkBITMgn;pÞal;xø Ünva nigkrNIénkardak;bnÞ úk nigeRbkugRtaMg³

!> bnÞ úkGefrBRgayes μ I

mkN /15.13

@> bnÞ úkGefrBRgayes μ I mkN /15.13 nigkMlaMgsgát;tambeNþaycMp© it kN P 1132= #> bnÞ úkGefrBRgayes μ I mkN /61.30 nigkMlaMgsgát;tambeNþaycakp©it kN P 1132= Edl

manGMeBIRtg;cMNakp©it cme 10= $> bnÞ úkGefrBRgayes μ I mkN /28.39 nigkMlaMgsgát;tambeNþaycakp© it kN P 1132= Edl

manGMeBIRtg;cMNakp©itGtibrmasMrab;muxkat ; cme 15=

%> bnÞ úkGefrGtibrmaenAeBl kN P 1132=

EdlmanGMeBIRtg; cme 15=

eRbI cmb 30= / cmh 60= / MPa f c 31' = nigkugRtaMgGnuBaØat MPa f c 14.14' = dMeNaHRsay³

!> kugRtaMgEdlbNþalmkEtBIbnÞúkefr nigbnÞúkGefr bnÞúkpÞal;rbs;Fñ wm ( ) mkN /32.4246.03.0 =×= m: Um:g;bnÞúkefr ( )

mkN wL

M L D .288

2.732.48

22

.. === kugRtaMgenARtg;srésEpñkxageRkAbMputEdlbNþalBIbnÞ úkefrKW



T.Chhay NPIC


( )23

612/2/

bh

M

bh

h M I

Mc ===σ MPa D 56.110

6.03.0

286 32

±=

×

×= −σ m: Um:g;EdlbNþþalBIbnÞúkGefr mkN L /15.131 = KW

mkN M L L .2.858

2.715.13 2

.. =×= kugRtaMgEdlbNþalBIbnÞ úkGefrKW

MPabh

M L 73.410

6.03.02.8566 3

221 ±=×

×== −σ edayeFV IkarbUkbBa©ÚkkugRtaMgEdl)anBIbnÞ úkefr nigbnÞúkGefr ¬rUbTI 19>2 a¦ eyIg)an

kugRtaMgxagelI MPa29.673.456.1 −=−−= ¬rgkarsgát;¦kugRtaMgxageRkam MPa29.673.456.1 =++= ¬rgkarTaj¦

edaysarkugRtaMgTajFMCagm: UDuldac;rbs;ebtug MPa f r 45.33162.0 == dUcenHFñwmnwg)ak;. @> kñ úgkrNIEdlkugRtaMgbNþalBIeRbkugRtaMges μ I RbsinebIeKGnuvtþkMlaMgsgát; KN P 1132=

Rtg;TIRbCM uTMgn;rbs;muxkat; enaHmuxkat;tambeNþyFñ wmnwgrgkugRtaMges μ I MPa

area

P p

29.6106.03.0

1132 3 ±=×

== −σ

kugRtaMgcugeRkayEdlbNþalBIbnÞ úkGefr nigbnÞ úkefrbUknwgbnÞ úkeRbkugRtaMgenARtg;srésxagelI nigxageRkambMputKW MPa58.12 nig 0 erogKña ¬rUbTI 19>2 b¦. kñ úgkrNIenH kMlaMgeRbkugRtaMg)anebgáInkugRtaMgsgát;enARtg;srésEpñkxagelIbMputeGaymantMélBIrdg nig)ankat;bnßykugRtaMgTajenARtg;srésEpñkxageRkameGay es μ Inwg 0 . kugRtaMgsgát;Gtibrma

MPa58.12 mantMéltUcCagkugRtaMgGnuBaØat MPa f c 14.14' = .

#> sMrab;kugRtaMgEdlbNþalBIeRbkugRtaMgcMNakp©it ¬ mme 100= ¦RbsinebIeKGnuvtþkMlaMgeRbkugRtaMg KN P 1132= enARtg;cMNakp©it mme 100= BI eRkamTI RbCM uTMgn;rbs;muxkat; kugRtaMgenARtg;srésEpñkxagelI nigEpñkxageRkambMputRtUv)ankMNt; dUcxageRkam. m:Um:g;EdlbNþalBIeRbkugRtaMgcMNakp©itKW Pe

( ) ( )2

6bh

Pe A P

I c Pe

A P

p ±−=±−=σ ( ) 3

23 10

6.03.0

1.011326106.03.0

1132 −−

×

×±

×

−=



T.Chhay NPIC


29.629.6 ±−= enAsrésEpñkxageRkam MPa p 58.12−=σ nig 0= pσ enAsrésEpñkxageRkambMBicarNaGMBIkardak;bnÞ úkGefr mkN L /61.302 =

mkN M L L .36.1988

2.761.30 2

.. =×= ( )

MPa L 02.11106.03.0

36.1986 322

±=×

= −σ kugRtaMgcugeRkayEdlbNþalBIbnÞúkefr/ bnÞ úkGefr nigkMlaMgeRbkugRtaMgenAsrésEpñkxagelI nigEpñkxageRkambMputK W MPa58.12 nig 0 erogKña ¬rUbTI 19>2c¦. cMNaMfa kugRtaMgcug

eRkaydUcKñanwgkrNIelIkmunenAeBlEdlbnÞ úkGefres μ Inwg mkN /15.13 . edayGnuvtþkMlaMgeRbkugRtaMgenARtg;cMNalp©it cm10 Fñ wmenHGacRTbnÞ úkGefrEfm eTot ¬ mkN /46.17 ¦.



T.Chhay NPIC


$>sMrab;kugRtaMgEdlbNþalBIeRbkugRtaMgcakp© itRtg;cMNakp© itGtibrmasn μt;facMNakp©itGtibrmasMrab;muxkat;enHKW cme 15= .m:Um:g;Bt;EdlekItedaysarkMlaMgeRbkugRtaMgcakp©itK W mkN Pe .8.16915.01132 =×=



T.Chhay NPIC


kugRtaMgEdlbNþalBIkMlaMgeRbkugRtaMgKW ( ) 3

23 10

6.03.08.169610

6.03.01132 −−

×±

×−= pσ

41.929.6 ±−= MPa7.15−= nig 12.3+

begá InbnÞ úkGefrdl ; mkN L /28.393 = . m:Um:g;Edl)anBIbnÞ úkenHKWmkN M L L .5.254

82.728.39 2

.. =×= kugRtaMgEdlbNþalmkBIbnÞúkGefrKW

( ) MPa L 14.14106.03.05.2546

323 ±=×= −

σ kugRtaMgcugeRkayenAsrésEpñkxagelI nigEpñkxageRkambMputEdlbNþalBIbnÞ úkefr nigbnÞ úkGefrK W MPa58.12 nig 0 erogKña ¬rUbTI 19>2 d ¦. cMNaMfa kugRtaMgcugeRkaydUcKñanwgkrNI mun²Edr b: uEnþbnÞ úkGefr)anekIneLIgdl ; mkN /28.39 . kugRtaMgTaj MPa56.1 RtUv)anbegáIteLIgenAsrésEpñkxagelIbMput enAeBlEdleKGnuvtþkMlaMgeRbkugRtaMg. kugRtaMgenHmantMéltUcCagm: UDuldac;rbs;ebtug MPa f r 45.3= dUcenHvaminekItmansñameRbHenAelIFñ wmeT.

%>eKkMNt;bnÞ úkGefrGtibrmaenAeBlkMlaMgeRbkugRtaMgcakp©iteFV IGMeBIenARtg; cme 15= dUcteTA. kñ úgkrNImun² kugRtaMgsgát;cugeRkayes μ Inwg MPa58.12 EdltUcCagkugRtaMg GnuBaØat

MPa f c 14.14' = . dUcenH bnÞúkGefrGacekIneLIgdl ; mkN L /6.434 = .mkN M L L .5.282

82.76.43 2

.. =×= MPa L 7.1510

6.03.05.2826 324 =××= −σ

kugRtaMgcugeRkayEdlbNþalBIbnÞ úkefr nigbnÞ úkGefr4 L ehIynigkMlaMgeRbkugRtaMg KW MPa14.14− nig MPa56.1+ ¬rUbTI 19>2 e¦. kugRtaMgsgát;KWes μ InwgkugRtaMgGnuBaØat

MPa14.14 ehIykugRtaMgTajKWtUcCag modulus of rupture rbs;ebtug MPa45.3 . kñ úgkrNIenH eKGacKNnabnÞ úkGefrBRgayEdles μμ Inwg mkN /6.43 dUcteTA³ bUkkugRtaMgsgát; GnuBaØatGtibrma MPa14.14 CamYynwgkugRtaMgTajdMbUgenARtg ;srésEpñkxagelIbMput



T.Chhay NPIC


MPa56.1 edIm,ITTYl)an MPa7.15 . m:Um:g;Edlnwgbegá ItkugRtaMgenAsrésEpñkxagelIbMput MPa7.15 es μ Inwg

=

62bh M σ ( )( ) mkN .6.282106.03.0

67.15 32 ==

8

2 LW M L= eyIgTTYl)an

mkN W L /6.432.7

6.28282

=×=

cMNaMfa³!> muxkat;ebtugTaMgmUlKWskm μkñ úgkarTb;Tl;CamYykMlaMgxageRkA@> kugRtaMgTajcugRkayenAkñ úgmuxkat;tUcCagmodulus of rupture rbs;ebtug Edlbgðaj

famuxkat;ebtugminmansñameRbHeRkamGMeBIrbs;bnÞúkGtibrma#> bnÞ úkGnuBaØatenAelIFñwmekIneLIgeRcInKYrsmedaysarkarGnuvtþrbs;kMlaMgeRbkugRtaMg$> karekIneLIgnUvcMNakp©itrbs;kMlaMgeRbkugRtaMgk¾begá InkMlaMgGnuvtþn_GnuBaØat EdleFVIeGay

kugRtaMgenAelImuxkat;minFMCagkugRtaMgGnuBaØat.

x> karGnuvtþeRbkugRtaMgedayEpñkPartial Prestressing eKkMNt;Ggát;ebtugeRbkugRtaMgedayEpñk (partially prestressed concrete member) CaGgát;

Edl³- kugRtaMgxagkñ úgEdlmanGMeBITb;EpñkénkugRtaMgEdlekItBIbnÞ úkxageRkA

- kugRtaMgTajekItmanenAkñ úgebtugeRkamGMeBIbnÞúkeFVIkar (service load) - EdkBRgwgminEmnCaEdkeRbkugRtaMgRtUv)andak;bEnßmedIm,Ibegá InlT§PaBrbs;Ggát; edIm,ITb; nwgm: Um:g;

eKGacBicarNa partially prestressed concrete tamBIrkrNI³!> eKeRbIEdkeRbkugRtaMg nigEdkminEmneRbkugRtaMgenAkñ úgmuxkat;EtmYy. ExSkabeRbkugRtaMg

begá ItkugRtaMgxagkñúgRtUv)anKNnaedIm,ITTYl)an ultimate capacity rbs;muxkat;ebtugEt

mYyEpñkb: ueNÑaH. cMENkÉcapacity EdlenAsl;RtUv)anTTYlBIEdkminEmneRbkugRtaMg



T.Chhay NPIC


Edldak;tamTisdUcKñanwgkabeRbkugRtaMg. EdkEdleRbICaEdkminEmneRbkugRtaMgGacCaRbePTEdkFm μta dUcCaEdkcarbon steel b¤CaEdkhigh-tensile-strength. kabeRbkugRtaMgk¾ CaRbePTEdkFm μtadUcEdkminEmneRbkugRtaMgEdr Etvaman ultimate strength es μ Inwg

MPa1725 ¬ ksi250 ¦. kareRCIserIsGaRs½ynwgktþacMbgBIrKW³ PaBdabGnBaØat nigTMhM sñameRbHGnuBaØat. dUcKñaACI Code kMNt;nUvpleFobGtibrmaénRbEvgElVgelIkkBs;énGgát;ebtugGarem: sMrab;PaBdab. eKminGnuBaØateGaymanPaBdabFMelIslubCamYynwgkMBs;rbs;muxkat;ebtugeRbkugRtaMgtUc nigedaysarkareRbIPaKryEdktic. sñameRbHekItmanenAtMbn;rgkarTajrbs;muxkat;ebtug b¤enARtg;nIv: UEdkedaysareKGnuBaØateRtaMgTajekItmaneRkamGMeBI working load . eKGnuBaØatsñameRbHGtibrmaRtwm .016.0 in

)41.0( mm sMrab;Ggát;xagkñ úg nig .013.0 in )33.0( mm sMrab;Ggát;xagkñ úg.@> kugRtaMgxagkñ úgEdleFV IGMeBIelIGgát;)anEtBI prestrssed steel b: ueNÑaH b: uEnþvaRtUv)anTajCa

mYynwgEdnkMNt;TabCag. kñ úgkrNIenHsñameRbHekItmanelOnCagGgát;rgeRbkugRtaMgeBjeljeRkambnÞ úkdUcCaKña.

eKGacBicarNa partially prestresssed concrete kñúgTMrg;kNþalrvagebtugGarem: nigebtugeRbkugRtaMgeBj(fully prestressed concrete). enAkñúgGgát;ebtugGarem: sñameRbHekItmaneRkamGMeBI bnÞ úkeFV Ikar dUcenHeKdak;EdkBRgwgenAkñ úgtMbn;Taj. CaTUeTAenAkñ úgGgát;ebtugeRbkugRtaMg sñameRbHminekItmaneRkamGMeBIbnÞúkeFV IkareT. kugRtaMgsgát;EdlbNþalBIkMlaMgeRbkugRtaMgGaces μ I b¤elIsBI kugRtaMgTajEdlbNþalBIbnÞ úkxageRkA. dUcenHeKGacBicarNaGgát; partially prestressed concrete CaGgát;ebtugGarem:EdlkugRtaMgxagkñ úgrbs;vamanGMeBITb;nwgEpñkxøH rbs;kugRtaMgEdl)anBIbnÞ úkxageRkA dUcenHkugRtaMgTajenAkñúgebtugminRtUvFMCagtMélkMNt;eRkambnÞ úkeFV IkareT. eKKitvaCaebtugGarem:enAeBlNaEdlminmankugRtaMgxagkñúgeFV IGMeBIelIGgát;. ebtugeRbkugRtaMgeBjCakMritx<s;bMputrbs;ebtugeRbkugRtaMgedayEpñk EdlenAkñ úgenaHEdkminEmneRbkugRtaMgRtUv)ankat;bnßydl;sUnü.

enAcenøaHGgát;ebtugGarem:EdlmaneRbH nigGgát;ebtugeRbkugRtaMgeBjEdlminmaneRbH eKmanEdnd¾FMsMrab;KNnaebtugeRbkugRtaMgedayEpñk ¬rUbTI 19>3¦. kareRCIserIskMriténkareFV IeRbkugRtaMgd¾l¥ nwgbegá ItnUveRKOgbgÁú MEdlmansuvtß iPaB nigmanlkçN³esdækic©.



T.Chhay NPIC


rUbTI 19>3 bgðajBIExSekagPaBdab-bnÞ úkrbs;Fñ wmebtugGarem:EdlmanbrimaNEdk nigRbePTEdkxusKña. ExSekaga bgðajBIFñ wmebtugGarem: EdlmansñameRbHFm μtaeRkambnÞ úktUccr W . eKGackMNt;m: Um:g;EdleFVIeGayeRbH (cracking moment) dUcxageRkam³

c I f M r

cr = Edl =r f m: UDuldac;rbs;ebtug c f '62.0=

= I m: Um:g;niclPaBén gross concrete section =c cMgayBIG½kSNWteTAsrésrgkarTajxageRkAbMput

eKGackMNt;ebtugEdleFV IeGayeRbH(cracking load) BI cracking moment enAeBlRbEvgElVg nigRbePTénkardak;bnÞúkRtUv)ankMNt;. sMrab;Fñ wmTMrsamBaØEdlrgbnÞ úkcMcMnugenAkNþalElVg

( ) L M W cr cr /4= .



T.Chhay NPIC


ExSekage nig f bgðajBIFñ wmebtugeRbkugRtaMgeBjEdlmanEdktic nigEdkeRcIn erogKña. FñwmebtugGarem:EdlmanbrimaNEdkeRcIn)ak;edaysarkarEbkebtugmunnwgEdkeTAdl;yield strength b¤ proof stress rbs;va. Fñ wmmanPaBdabtUc nwgrgkar)ak;edayPaBRsYy(brittle failure). FñwmEdlmanbrimaNEdktic)ak;edaysarEdkeFV Ikardl;yield nig ultimate strength rbs;va. vabgðajnUv)abdnigsñameRbHEdlbNþalBIkarlUtsac;rbs;EdkmuneBlebtugEbkCabnþbnÞab; ehIyFñ wm)ak;rlM.

enAcenøaHExSekaga nig e CaEdnd¾FMrbs;Fñ wmebtugCamYynwgbrimaNERbRbYlrbs;Edk nigrgnUvbrimaNERbRbYlrbs;kMlaMgeRbkugRtaMg. Fñ wmEdlrgkMlaMgeRbkugRtaMgtUcenAEk,rExSekaga ehIyFñwmEdlmaneRbkugRtaMgFMenAEk,rExSekage . eKeRCIserIsbnSMEdkeRbkugRtaMg nigEdkminEmneRbkgRtaMgsMrab;karKNnaKWGaRs½yelIkugRtaMgebtugGnuBaØat PaBdab nigTMhMsñameRbHGtibrma.

ExSekagb tMNageGayFñwmEdlnwgeRbHeRkamGMeBIénbnÞ úkeFV IkareBjelj. RbsinebIEtEpñkxøHrbs;bnÞ úkGefrekItmanenAelIeRKOgbgÁ úMCaerOy² enaH1W tMNageGaybnÞ úkefrsrub nigEpñkxøHrbs;bnÞ úkGefr1 L .

ExSekagc tMNageGayFñ wmcab;epþ ImeRbHeRkamGMeBIworking load . kugRtaMgTajGtibrmaenAkñ úgebtug cr f f '62.0== .

ExSekagd tMNageGayFñ wmEdlmankMlaMgeRbkugRtaMgkMNt;. muxkat;eRKaHfñak;rbs;FñwmnwgmineRbHeRkambnÞ úkeFV IkareBjeljeT b: uEnþvanwgmankugRtaMgTajGtibrma cr f f '62.00 << . ACI

Code GnuBaØatkugRtaMgTajGtibrmaenAkúñgebtugRtwmc f '5.0 .ExSekage nig'e tMNageGayFw ñmebtugeRbkugRtaMgeBjeljEdlminmankugRtaMgTajeRkam

bnÞ úkeFVIkar ¬emIlrUbTI 19>4¦.sar³RbeyaCn_d¾sMxan;bMputrbs;kMlaMgeRbkugRtaMgedayEpñkKWlT§PaBkúñgkarRKb;RKgkMeN

(camber). edaykat;bnßykMlaMgeRbkugRtaMg camber nwgRtUv)ankat;bnßy ehIysnSMnUvbrimaNEdkeRbkugRtaMg brimaNkargarkú ñgkarTaj nigcMnYnend anchorage.

GaRs½ynwgGaMgtg;sI ueténkMlaMgeRbkugRtaMg sñameRbHenAkñ úg partially prestressed member

ekIteLIgelOnCagenAkñúg fully prestressed concrete member eRkamGMeBIrbs; service load . enAeBlEdlsñameRbHekItman m:Um:g;niclPaBRbsiT§PaBrbs;muxkat;eRKaHfñak;RtUv)ankat;bnßy ehIyeKnwgTTYl)anPaBdabFMCagmun. b: uEnþ kareRbIkMlaMgeRbkugRtaMgedayEpñkKWeKTTYl)anlT§plKYrCaTUeBjcitþ ehIyvaTTYl)ankareBjniym.



T.Chhay NPIC


K> karcatcMNatfñak Ggát rgkarBtebtugeRbkugRtaMgClassification of Prestressed Concrete Flexural Members ACI Code, Section 18.3 )anEckGgát;ebtugeRbkugRtaMgCabIfñak;edayQrelIkugRtaMgTajenAelIsrésxageRkAbMputt f enAkñúgtMbn;TajeRkamGMeBIbnÞúkeFVIkardUcxageRkam³

!> fñak; U (uncracked section) Edlman ct f f '62.0≤ . enAkñúgmuxkat;ebtugEdlK μansñameRbHenH eKeRbIlkçN³éngross section edIm,IRtYtBinitüPaBdabeRkamGMeBIbnÞ úkeFVIkar.K μansñameRbHekItmanenAkñúgmuxkat; nigeKminRtUvkarskin reinforcement eT.

@> fñak;T

(

muxkat;enAkñúg transition zone)

Edlmanct c f f f ''62.0 ≤<

. muxkat;RbePTenHmankugRtaMgTajenAkñ úgebtugFMCagm: UDuldac; (modulus of rupture) rbs;ebtugcr f f '62.0= EdlbegáItnUvkrNIcenøaHmuxkat;eRbH nigmuxkat;Gt;eRbH. enAkñ úgkrNIenH

eKeRbIlkçN³én gross section edIm,IRtYtBinitükugRtaMg ehIyeKeRbI bilinear section rbs;muxkat;eRbHedIm,IKNnaPaBdab. eKmincaM)ac;eRbI skin reinforcement enAkñúgtMbn;TajeT.

#> fñak; C (cracked section) Edlman ct f f '> . kugRtaMgTajenAkú ñgmuxkat;FMCagmodulus of rupture

rbs;ebtug6.1

dg. dUcenH sñameRbHnwgekItmandUckñ úgkrNIGgát;ebtugeRbkugRtaMgedayEpñk. enAkñ úgkrNIenH eKeRbIlkçN³énmuxkat;eRbHedIm,IRtYtBinitükug



T.Chhay NPIC


RtaMg sñameRbH nigPaBdab. eKKYreRbIkarpþl;eGayedIm,IRKb;RKgsñameRbH nigeRbIskin

reinforcement dUckarBnül;enAkñ úgEpñk 6>7 sMrab;Ggát;ebtugGarem:EdlmankMBs;RbsiT§-PaB mmd 915> .

2> sMPar³ nigtMrUvkarsMrab;bMerIbMras; Material and Serviceability Requirement

k> ebtug Concrete lkçN³rbs;ebtugRtUv)anbgðajenAkñ úgCMBUk 2. eTaHbICaerOy² Ggát;ebtugGarem:RtUv)anpl

BIebtugEdlmanersI usþg;sgát; MPa21 eTA MPa35 k¾eday k¾Ggát;ebtugeRbkugRtaMgRtUv)anplitBIsMPar³EdlmanersIusþg;x<s;Cag CaTUeTAsß itenAcenøaH MPa28 eTA MPa56 . eKeRbIebtugersI usþg;x<s;sMrab;Ggát;ebtugcak;eRsc nigGgát;ebtugeRbHkugRtaMg Edlkarlay karcak; karbgðab; nigkarEfTaMebtugsß iteRkamkarRtYtBinitüy:agm:t;ct;.

kugRtaMgGnuBaØatenAkñúgebtugEdleyagtamACI Code, Section 18.4 mandUcxageRkam³!> kugRtaMgeRkayeBlepÞreRbkugRtaMg (prestress transfer) nigmuneBl)at;bg;eRbkugRtaMg

(prestress losses):

a. kugRtaMgsgát;Gtibrmaes μ Inwg ci f 6.0 b. kugRtaMgTajGtibrma ¬elIkElgGVIEdl)anGnuBaØatdUcxageRkam¦ es μ Inwg ci f 25.0 c. kugRtaMgTajGtibrmaenARtg;cugénGgát;TMrsamBaØes μ Inwg ci f 5.0 Edl ci f CaersI usþg;rbs;ebtugenAeBlepÞrRbsinebIkugRtaMgTajmantMélFMCagenH eKRtUvdak;EdkenAtMbn;sgát;edIm,ITb;Tl;kMlaMgTajsrubenAkñ úgebtug ¬edayQrelI uncracked gross section¦.

@> kugRtaMgeRkamGMeBIbnÞ úkeFVIkareRkayeBlkMhatbg;(loss) TaMgGs; ¬sMrab;fñak; U nigfñak; T ¦mandUcteTA³ kugRtaMgsgát;Gtibrma c f '45.0 EdlbNþalBIkMlaMgeRbkugRtaMgbUknwgbnÞ úkefrnigkugRtaMg c f '05.0 EdlbNþalBIkMlaMgeRbkugRtaMgbUknwgbnÞ úksrub.

#> kugRtaMgTaMgenHGacmantMélFMCagenH RbsinebIkarBiesaF nigkarviPaKbgðajfakaRbRBwtþeTArbs;vaRKb;RKan;.



T.Chhay NPIC


x> EdkeRbkugRtaMgPrestressing Steel Edktendon EdleKniymeRbICageKenAkñ úgebtugeRbkugRtaMgCastrands ¬b¤kab¦ Edlplit

eLIgCamYynwglYssrésr(wire) CaeRcIn CaTUeTAmancMnYn7 b¤19 . Wire nig bar k¾RtUv)aneKeRbI R)as;pgEdr. Stand nig wire RtUv)anpliteLIgedayeKarBtamASTM Standard 421 A sMrab;uncoated stress-relieved wire nig 416 A sMrab; uncoated seven-wire stress-relieved strand .lkçN³rbs;EdkeRbkugRtaMgRtUv)aneGayenAkñ úgtarag 19>1.

EdkeRbkugRtaMgEdleRbIenAkñúgebtugeRbkugRtaMgRtUvEtmanersI usþg;x<s; CaTUeTAman

ultimate strength pu f enAcenøaH MPa1730 eTA MPa1860 . eKcaM)ac;GnuBaØateGayEdkersI usþg; x<s;mansac;lUtFM nigrkSakugRtaMgenAkñ úgebtugeGayRKb;RKan; nigGciéRnþy_bnÞab;BI inelastic

shortening rbs;ebtug.

tarag 19>1Type Diameter

(mm)Area

(mm2)Mass

(kg/m)Seven-wire strand (grade 250) 6.350 23.2 0.179

7.950 37.4 0.2989.525 51.6 0.402

11.125 69.7 0.55112.700 92.9 0.72915.240 139.4 1.101

Seven-wire strand (grade 270) 9.525 54.8 0.43211.125 74.2 0.59512.700 98.7 0.78915.250 138.7 1.101

Prestressing wire grades (250) 4.877 18.7 0.146(250) 4.978 19.4 0.149(240) 6.350 31.6 0.253(235) 7.010 38.7 0.298

Prestressing bars (smooth) 19.050 283.9 2.232(grade 145 or 160) 22.225 387.1 3.036

25.400 503.2 3.97328.575 638.7 5.03031.750 793.5 6.20634.925 954.8 7.515

Prestressing bars (deformed) 15.875 180.6 1.458(grade 150-160) 19.050 271.0 2.21825.400 548.4 4.48031.750 806.5 6.53534.925 1006 8.274



T.Chhay NPIC


kugRtaMgGnuBaØatenAkñ úgEdkeRbkugRtaMgeyagtam ACI Code, Section 18.5 mandUcxageRkam!> kugRtaMgGtibrmaEdlbNþalBI tendon jacking force minRtUvFMCagtMélEdltUcCageKkñ

gcMeNam pu f 8.0 nig py f 94.0 . tMélEdltUcCagminRtUvFMCagkugRtaMgEdlENnaMeda plit tendon b¤ anchorage eT.

@> kugRtaMgGtibrmaenAkñ úg pretensioned tendon Pøam²eRkayeBlepÞrminRtUvFMCagtMéltUcCageKkñ úgcMeNam pu f 74.0 nig py f 82.0 .

#> kugRtaMgGtibrmaenAkñúg postensioned tendon eRkayeBltendon RtUv)ananchor KW pu f 70.0 .

K> EdkBRgwg Reinforcing Steel

CaTUeTA eKeRbIEdkBRgwgminEmneRbkugRtaMgenAkú ñgGgát;eRKOgbgÁú MebtugeRbkugRtaMgCaBiessenAkñ úgsMNg;ebtugeRbkugRtaMgcak;eRsc. eKeRbIEdkBRgwgCaEdkkMlaMgkat;TTwg CaEdkbEnßmsMrab;kardwkCBa¢Ún nigkarelIkdak;Ggát;cak;eRsc ehIynigeRbIenAkñ úgGgát;ebtugeRb

kugRtaMgedayEpñkEdlcUlrYmCamYynwgEdkeRbkugRtaMg. RbePT nigkugRtaMgGnuBaØatrbs;EdkRtUvENnaMenAkñúgCMBUk 2 nigCMBUk 5 rYcehIy.

3> kMhatbg;eRbkugRtaMgLoss of Prestress

k>Lump-sum losses

kMhatbg;énkMlaMgeRbkugRtaMgCabnþbnÞab;ekItmaneRkayeBlkMlaMgeRbkugRtaMgRtUv)anepÞrBI jack eTaGgát;ebtug. kMhatbg;eRbkugRtaMgCakarkat;bnßykMlaMgeRbkugRtaMgkñ úgmYyCIviténeRKOgbgÁ úM. brimaNkMhatbg;enAkñ μ úgtendon ERbRbYlcenøaHBI%15 eTA%30 énkugRtaMgedIm edayGaRs½ynwgktþaCaeRcIn. sMrab;eRKOgbgÁ ú MebtugGarem:TMgn;Fm μtaPaKeRcInEdlsagsg;edstandard method, tendon stress loss bNþalmkBI elastic shortening, shrinkage, creep nigrelaxation rbs;EdkKWmantMélRbEhlnwg ( ) MPaksi 24135 sMrab; pretensioned member nigsMrab;



T.Chhay NPIC


posttensioned member KWRbEhlbwg( ) MPaksi 17225 . kMlaMgkkit niganchorage slip minRtUv)anrab;bBa©ÚleT.

karENnaMBIrsMrab;kar)a:n;s μankMhatbg;srubenAkñ úgGgát;ebtugeRbkugRtaMgRtUv)anbgðajedayAASTHO nig Posttensioning Institute (PTI). AASTHO ENnaMeGayykkMhatbg;srub(edayminKitkMlaMgkkit ) ( ) MPaksi 31045 sMrab; pretensioned strand nig ( ) MPaksi 22833 sMrab; postentioned strand nig wire enAeBlEdleKeRbIersIusþg;sgát;ebtug MPa f c 35' = . PTI ENnaM lump-sum prestress loss sMrab; posttensioned member ( ) MPaksi 24135 sMrab;Fñ wm nig

( ) MPaksi 20730 sMrab;kMralxNÐ ¬edayminKitkMlaMgkkit¦. eKGaceRbItMélTaMgGs;enH)anluHRtaEteK)aneFVIkar)a:n;RbmaNkMhatbg;eRbkugRtaMgedayRbPBénkMhatbg;nImYy²dac;edayELkBIKña)anl¥ dUcEdl)anENnaMy:agsegçb.

CaTUeTA RbPBénkMhatbg;eRbkugRtaMgKW- Elastic shortening rbs;ebtug- Shrinkage rbs;ebtug - Creep rbs;ebtug - Relaxation rbs;Edktendon - kMlaMgkkit - Anchorage set

x> kMhatbg edaysarElastic Shortening of Concrete

kar)a:n;RbmaNkMhatbg ;

elastic shortening

rbs;ebtugenAkñ úg

pretensioned member

RtUv)aneFV IeLIgdUcteTA. BicarNa pretensioned concrete member énmuxkat;efr nigkugRtaMgBRgayes μ ItambeNþayG½kSTIRbCM uTMgn;rbs;vaedaysarkMlaMg o F . eRkayBIkarepÞrkMlaMgeRbkugRtaMgFñ wmebtugnig prestressing tendon rYjxø IedaybrimaNes μ IKña edaysarPaBs¥ itrvagsMPar³TaMgBIr. dUcenH kMlaMgeRbkugRtaMgEdlcab;epþ Imo F Føak;mkRtwm i F ehIykMhatbg;kMlaMgeRbkugRtaMgKWio F F − . dUcKñastrain enAkñ úgebtug cε RtUvEtes μ InwgbMErbMrYlstrain rbs; tendon sε Δ . dUcenH sc ε ε Δ= b¤( ) ( ) s scc E f E f // Δ=

ehIykMhatbg;kugRtaMgEdlbNþalBI elastic shortening

KW



T.Chhay NPIC


c

o

c

icc

c

s s A

nF AnF

nf f E E

f ≈==×=Δ (19.1) Edl =c A RkLaépÞrbs;muxkat;ebtug

== c s E E n / pleFobm: UDul (modular ratio) =c f kugRtaMgrbs;ebtugenARtg;TIRbCMuTMgn;rbs;EdkeRbkugRtaMg

KuNkugRtaMgnwgRkLaépÞrbs;EdkeRbkugRtaMg sp A edIm,ITTYl)ankMlaMgsrub .Elastic loss KW ( ) sp

c

o spc sp sio A

AnF

Anf A f F F ES

≈=Δ=−= (19.2)

( ) spcoi Anf F F −= (19.3)

sMrab;karKNnaGnuvtþn_ kMhatbg;kugRtaMgénkMlaMgeRbkugRtaMg ¬ s f Δ

kñúgmYyktþaépÞ sp A ¦ mantMélRbhak;RbEhlnwg co AnF / . RbsinebI kMlaMg o F manGMeBIRtg;cMNakp© ite enaH elastic loss EdlbNþalBIvtþmanéno F nigbnÞúkefrGnuvtþn_enAeBlepÞrKW

( ) spc Anf ES −= ¬EdlbNþalBIeRbkugRtaMg¦ ( ) spc Anf + ¬bnÞ úkefr¦ sp

D sp

iiio nA

I e M

nA I e F

A F

F F ES

+

+−=−=

2

(19.4)

eKGaceRbItMélRbhak;RbEhlén sp pui A f F 63.0= enAkñúgsmIkarxagelI.( )

++=+

I e

AnA F nA f F spi spco

211D.L. (19.5) ( )

( )

++

+=

I e

AnA

f nA F F

sp

c spoi 211

D.L.

sMrab; posttensioned member Edltendon nig individual strand minrgkugRtaMgdMNalKña enaHeK

GackMhatbg;eRbkugRtaMges μ InwgBak;kNþaléntMél

ES

sMrab; prestensioned member

.dUcKña eKGacykelastic shortening loss enAkñ úgkMralxNÐes μ InwgmYyPaKbYnéntMél ES sMrab; prestensioned member edaysarkarlUtrbs; tendon mYyman\T§ iBltictYceTAelIkugRtaMgéntendon d¾éTeTot.

K> kMhatbgedaysarkarrYmmaDLoss Due to Shrinkage

kMhatbg;eRbkugRtaMgEdlbNþalBIkarrYmmaDKWGaRs½ynwgeBl. eKGac)a:n;RbmaNvadUcxageRkam³



T.Chhay NPIC


s f SH Δ= (shrinkage) s sh E ε = (19.6) Edl MPa E s

5102= nig = shε shrinkage strain enAkñúgebtug

eKGacsn μt; Strain mFümEdlbNþalBIkarrYmmaDmantMéldUcxageRkam³- 0003.01 = shε sMrab; pretensioned member

- 0002.02 = shε sMrab; posttentioned member

RbsinebIeKGnuvtþ posttensioning kñúgcenøaH5eTA7 éf¶eRkayBIcak;ebtug/ eKGacykshrin-

kage strain es μ Inwg 18.0 shε . RbsinebIeKGnuvtþ posttensioning kñ úgcenøaH1 s)aþh_eTA2 s)aþh_ eKGaceRbI 17.0 sh sh ε ε = nigRbsinebIeKGnuvtþ posttensioning eRkayeBlcak;ebtugeRcInCag2 s)aþh_

enaHeKGacyk2 sh sh ε ε = . eKk¾Gac)a:n;RbmaNkMhatbg;edaykarrYmmaDSH dUcxageRkam³( ) RH

S V

E K SH s sh −

−×= − 10006.01102.8 6

Edl =S V / pleFobmaDelIépÞ nig = RH average relative humidity. 0.1= sh K sMrab; pretensioned

member niges μ Inwg8.0 / 73.0 / 64.0 nig 58.0 sMrab; posttensioned member RbsinebIeKGnuvtþ posttensioning eRkayeBlcak;ebtug5/10/ 20 nig30éf¶ erogKña.

X> kMhatbgedaysar creep rbsebtug Creep CakMhUcRTg;RTayGaRs½ynwgeBlEdlekIteLIgenAkñ úgebtugeRkamGMeBIbnÞ úkefr. kMhUc

RTg;RTayEdlekIteLIgedaysarcreep eFV IeGay)at;bg;kMlaMgeRbkugRtaMgBI %5 eTA%7 .Creep strain ERbRbYlCamYynwgGaMgtg;sI ueténkugRtaMgedImenAkñúgebtugrelative humidity

nigeBl. eKGackMNt;kMhatbg;kugRtaMgEdlbNþalBI creep dUcxageRkam³ s f CR Δ= (creep) ( ) ( ) scr ccc E C nf C ε == (19>7)

Edl =cC emKuNcreep icp

ε

ε

strain,elasticinitial n,creepstrai

= eKGacyktMélcC dUcxageRkam³

ersI usþg;ebtug MPa f c 28' ≤ MPa f c 28' > Relative humidity %100 %50 %100 %50

cC 21−

42 −

5.17.0 −

35.1 −



T.Chhay NPIC


eKGaceFV I interpolation sMrab;tMélEdlenAcenøaHtMélEdlenAkñ úgtaragxagenH. edayKitcreep EtBak;kNþalekIteLIgkñ úgGMLúg134ExdMbUgén6 ExdMbUgbnÞab;BIkarepÞreRbkugRtaMgeTAebtugnigeRkamlkçxNÐsMeNImFm μta enaHeKGacsn μt; creep strain sMrab;karKNnaGnuvtþn_dUcxageRkam³

!> sMrab; pretensioned members, ×= −5107cr ε kugRtaMgenAkñ úgebtug@> sMrab; postensioned members, ×= −5102.5cr ε kugRtaMgenAkñ úgebtug. eKeRbItMélenH

enAeBlEdleKGnuvtþ posttensionning kñ úgGMLúg2 eTA3s)aþh_. sMrab;karGnuvtþ posten-

sioning elOnCagenH eKGaceRbItMélkNþal.eKeRbItMélTaMgenH enAeBlEdlersI usþg;rbs;ebtugenAeBlepÞrKW MPa f c 28' ≥ . enAeBlEdl MPa f c 28' < creep strain KYrekIneLIgkñúgGRta/4 ersI usþg;Cak;Esþg.kMhatbg;eRbkugRtaMgsrubEdlbNþalBI creep scr E ε = (19.8)

g> kMhatbgedaysar Relaxation rbsEdk Relaxation rbs;EdkbNþaleGaymankMhatbg;enAkñ úgEdkeRbkugRtaMgGaRs½ynwgeBl Edl

RsedogKñanwgcreep enAkñ úgebtugEdr. kMhatbg;edaysarrelaxation ERbRbYleTAtamRbePTEdk.

CaTUeTA tMélrbs;vaRtUv)anpþl;eGayedayGñkplitEdk. CaFm μta eKsn μt;kMbaatbg;enHes μ Inwg%3 énkugRtaMgedImrbs;EdksMrab; posttensioned member nig %2 eTA%3 sMrab; pretensioned

members. RbsinebIeKminmanB½t’manBIkarBiesaFeT eKGacPaKrykMhatbg;sMrab; relaxation enAh1000 dUcxageRkam³

!> enAkñúglow-relaxation strands, enAeBlEdleRbkugRtaMgedImes μ Inwg pu f 7.0 nig pu f 8.0 /relaxation (RE) KW%5.2 nig %5.3 erogKña.

@> enAkñúgstress-relieved strand b¤ wire, enAeBlEdleRbkugRtaMgedImes μ Inwg pu f 7.0 nig pu f 8.0 /relaxation (RE) KW %8 nig%12 erogKña.

c> kMhatbg edaysarkMlaMgkkit Loss Due to Friction

CamYynwgEdkrg pretensioning kMhatbg;edaysarkMlaMgkkitekItmanenAeBlEdl wires b¤strand dabtam diaphragm. CaFm μtakMhatbg;enHmantMéltUc ehIyeKGacecalva)an.



T.Chhay NPIC


enAeBlEdlstrand dabtamconcordant profile enaHkMhatbg;edaysarkMlaMgkkitGacmantMélFM.enAkrNIEbbenH CaFm μtaeKeRbI]brkrN_Edlvas;bnÞúkCak;EsþgedIm,IkMNt;kMlaMgenAkñ úgtendon.

CamYynwgEdkrg posttensioning, \T§iBlénkMlaMgkkitmantMélFMedaysarktþacMbgBIrKW kMeNagrbs; tendon nigkar)at;bg;PaBRtg;rbs;bMBg; (wobble). RbsinebIeKTb;cugbgáb;mçagrbs; tendon edaykMlaMg 2 P nigeKTajcugTMenrmçageTotrbs; tendon edaykMlaMg1 P edIm,IeGaytendon enaHrGiltamTisrbs;kMlaMg1 P )anluHRtaEt

pxe P P μα

21 = (19.9) Edl =emKuNmMukkitsþaTic nig = pxα mM urvag1 P nig 2 P . CaTUeTAeKKit wobble effect tamviFI

RsedogKña( ) x Kl

s x e P P +−= μα

px p px Kl px pj e P P

α μ ++= px p px Kl

pj px e P P α μ +−= (19.10)

Edl = pj P kMlaMgeRbkugRtaMgenARtg;cMnuc= px P kMlaMgeRbkugRtaMgenARtg; jacking end = p emKuNkMlaMgkkitedaysarkMeNag= pxα bMErbMrYlmMusrubénragtambeNþayrbs;EdkeRbkugRtaMgBI jacking end eTAdl;cMnuc x

KitCara:düg;

kaMkMeNaggRbEvgkMeNa=

= K emKuNkMlaMgkkit wobble kñ úgmYyÉktþaRbEvgrbs; tendon CakarsMrYl ACI Code eGaynUvsmIkarxageRkamsMrab;krNI 30.0≤+ x px p Kl α . lT§plEdlTTYl)anBIsmIkarCatMélRbEhl

( )11 −++= px p px pj px Kl P P α μ (AIC Code, eq. 18.2) (19.11) emKuNkMlaMgkkit nig K GaRs½ynwgRbePTénstrand b¤ wire, RbePTbMBg; niglkçxNÐépÞ

b:H.ACI Commentaru, Sectin 18.6 nigenAkñ úgtarag19.2 eGaynUvtMélRbhak;RbEhlrbs; nig K .

kMhatbg;edaysarkMlaMgkkitenAkñ úg jack ERbRbYl nigGaRs½ynwgktþaCaeRcIn edayrab;bBa© ÚlTaMgRbEvgrbs; tendon. eKENnaMeGayeRbI accurate load ceel edIm,Ivas;kMlaMgedaypÞal;.



T.Chhay NPIC


kareRbI pressure gauge pþl;nUvlT§plminsuRkit luHRtaEteKeFV IkarEktMrUveTAtamkMlaMgEdleKsÁal; enAkúñ úgtendon.

kMhatbg;edaysarkMlaMgkkitenAkñ úgcnchorage KWGaRs½ynwgRbePTanchorage nigbrimaNéndeviation rbs; tendon Edlqøgkat; anchorage. CaFm μtakMhatbg;enHmantMéltUcEdlGacecal)an. karENnaMkñ úgkrNIBiessKYrTTYl)anBIplitkr.

tarag 19>2 emKuNkMlaMgkkitsMrab; posttensioned tendon

RbePTtendon

emKuNkMlaMgkkit wobble K kñ úgmYyÉktþaRbEvg( )310−

emKuNkMlaMgkMlaMgkkit edaysarkMeNag

Tendon in flexible metal sheathing(grouted)

Wire tendon0.533.3 − 25.015.0 −

Seven-wire strand67.667.1 − 25.015.0 −

High-strength bars233.0 − 30.008.0 −

Pregreased unbonded tendon

Wire tendon and seven-wire strand 67.61− 15.005.0 −

Mastic-coated unbonded tendon

Wire tendon and seven-wire strand 67.033.0 − 15.005.0 −

q> kMhatbg edaysarAnchor set

enAeBlkMlaMgenAkñ úg tendon RtUv)anepÞrBI jack eTAanchorage unit, clnart;cUlkñ úgbnþ icrbs;tendon ekIteLIgedaysarkardak;gripping device b¤ wedge. karrGilenHbNþaleGaymantendon rYjxø I EdleFV IeGay)at;bg;kMlaMgeRbkugRtaMg. RbEvgrGilERbRbYlBImm5.2 eTAmm6 ehIyCaTUeTARtUv)ankMNt;edayplitkr. eKGacKNnakMhtbg; anchor set edayrUbmnþxageRkam³

s s s E L L

E f ×Δ=Δ=Δ ε (19.12)

Edl=Δε

GaMgtg;sI ueténkarrGil anchor

MPa E s5102=



T.Chhay NPIC


= L RbEvgrbs; tendon edaysarkMhatbg;eRbkugRtaMgCacMras;smamaRteTAnwgRbEvgrbs; tendon ¬b¤RbEhlCaBak;kNþalénRbEvgrbs;tendon RbsinebIvargkugRtaMgBIcugsgxagkñúgeBlEtmYy¦PaKrykMhatbg;enAkñ úgkugRtaMgEdknwgRtUv)ankat;bnßyenAeBlEdlRbEvgrbs;tendon ekIneLIg. RbsinebI tendon lUteday

ε Δ enAeBlepÞr enaHeKecalkMhatbg;eRbkugRtaMgedaysarkarrGil.

]TahrN_ 9>2³Fñ wmTMrsamBaØrg pretensionning RbEvgm11 manmuxkat;ctuekaNEkgCamYynwgcmb 45= nig cmh 80= . KNnakMhatbg;eGLasÞ ic nigkMhatbg;EdlGaRs½ynwgeBlTaMgGs;. eK

eGay³ kMlaMgeRbkugRtaMgenAeBlepÞrKW kN F i 1935= / RkLaépÞrbs;EdkeRbkugRtaMgKW= ps A 21935mm / MPa f c 35' = / MPa E c 34500= / MPa E s

5102= / profile rbs; tendon manragCa)a:ra:bUl/ cMNakp© itenAkNþalElVg cm15= nigcMNakp©itenAcug0= .dMeNaHRsay³

!> kMhatbg;edaysarelastic shortening: kugRtaMgEdl)anBIkMlaMgeRbkugRtaMgenAeBlepÞrKW MPa

A F

ps

i 10001019351935 3 ==

strain rbs;EdkeRbkugRtaMg 35 105

1021000 −===

s

s

E f

edayeRbIsmIkar 19>18.5

34500102 5

===c

s

E E

n yk6 MPa

AnF

f c

i s 25.3210

80045019356 3 =×

×==Δ

edayKitbMErbMrYlcMNakp©ittambeNþayFñ wmstrain enAmuxkat;xagcug 43 1056.110

345008004501935 −=

××==

cc

i

E A F

strain enAkNþalElVgc

i

cc

i

IE e F

E A F 2

+= ( ) 410

331092.1

12800450

12mm

bh I ===

strain 4310

24 1022.210

345001092.1

15019351056.1 −− =

×

×+=



T.Chhay NPIC


strain mFüm( ) 44 1089.11022.256.121 −− =+=

kMhatbg;eRbkugRtaMg=strain MPa E s 8.371021089.1 54 =×=× − PaKrykMhatbg; %78.3

10008.37 ==

@> kMhatbg;edaysarshrinkage: shrinkage strain 0003.0=

MPa E f s sh s 602000000003.0 =×==Δ ε PaKrykMhatbg; %6

100060 ==

#> kMhatbg;edaysar creep rbs;ebtug³ edaysn μt; 0.2=cC enaH ( ) scr c s E C f ε =Δ Elastic strain 41056.1 −==

cc

i

E A F ( ) MPa f s 4.622000001056.12 4 =×=Δ −

PaKrykMhatbg; %24.61000

4.62 == b¤edaytMélRbhak;RbEhl eyIgyk ×= −5107cr ε kugRtaMgenAkñ úgebtug

435 1076.310800450

1935107 −− =

×=cr ε

MPa E f scr s 2.752000001076.3 4 =×==Δ −ε PaKrykMhatbg; %52.7

10002.75 ==

vaCatMélEdlmansuvtßiPaB ehIyeKnwgTTYl)anGRtadUcKñasMrab;karKNnaxagelIRbsinebIeKyk41.2=cC .

$> kMhatbg;edaysarrelaxation rbs;Edk³ sMrab; low-relaxation strand eKsn μt;ykkMhatbg;

es μ Inwg%5.2

MPa f s 25%5.21000 =×=Δ %> sn μt;kMhatbg;edaysarkarBt; kMlaMgkkitrbs; cable spacer nigbøúkxagcugrbs;RbB½n§

pretensioning KW%2 . MPa f s 20100002.0 =×=Δ

^> kMhatbg;edaysarkMlaMgkkitenAkñ úg tendon KWsUnü.

&> kMhatbg;srubmandUcxageRkam



T.Chhay NPIC


Elastic Shortening 37.8MPa 3.78%Shrinkage loss 60.0MPa 6.00%Creep of concrete loss 62.4MPa 6.24%Relaxation of steel loss 25.0MPa 2.50%Other loss 20.0MPa 2.00%Total loss 205.2MPa 20.52%

eRbkugRtaMgRbsiT§PaB MPa6.8324.1671000 =−= kMlaMgeRbkugRtaMgRbsiT§PaB kN F 16111019356.832 3 =×= −

( ) ii F F F 833.0167.01 =−= sMrab; i F F η =

dUcenH833.0=η

]TahrN_ 9>3³KNnakMhatbg;TaMgGs;én posttensioned beam EdlmanRbEvgm36 . RkLaépÞ rbs;muxkat;ebtug ( ) 241049 mm Ac = / m: Um:g;niclPaB( ) 4101083.6 mm I g = / kMlaMgeRbkugRtenAeBlepÞr ( ) kN F i 4950= / RkLaépÞEdkeRbkugRtaMg( ) 24840mm A ps = / MPa f c 35' = /

MPa E c 34500= / nig MPa E s5102= . Profile rbs; tendon manragCa)a:ra:bUl/ cMNakp©itenA

kNþalElVgcm50=

nigcMNakp© itenAxagcug0=

.dMeNaHRsay³ !> kMhatbg;edayelastic shortening:

kugRtaMgEdkenAeBlepÞr MPa A F

ps

i 7.10221048404950 3 ===

kugRtaMgenAkú ñgebtugRtg;muxkat;xagcug MPa1.10101049

4950 34

==

kugRtaMgenAkú ñgebtugRtg;muxkat;kNþalElVg I

e M

I

e F

A

F Di

c

i −+=2

TMgn;rbs;Fñwm mkN /25.12251049 2 =×= −

mkN M D .5.19848

3625.122

==

kugRtaMgenAkNþalElVg 610

310

23

4 101083.6

5005.1982101083.6500495010

10494950 ×−×+=

MPa72.135.1412.181.10 =−+=

kugRtaMgmFüm MPa9.11272.131.10

=+

=



T.Chhay NPIC


strain mFüm 41045.334500

9.119.11 −===c E

kMhatbg;eGLasÞ icKW MPa E f sc s 691021045.3 54 =×==Δ −ε edaysn μt;faeKTajtendon mþgBIrkñ úgeBlEtmYy. KUrTImYynwgmankMhatbg;FMCageK b: uEnþKUrcugeRkaynwgmankMhatbg;es μ IsUnü.dUcenH kMhatbg;eGLasÞ icmFüm MPa f s 5.342/69 ==Δ .

PaKrykMhatbg; %37.37.1022

5.34 == @> kMhatbg;edaysarkarrYmmaDrbs;ebtug

s f Δ (shrinkage) MPa E s 402000000002.00002.0 =×== PaKrykMhatbg; %91.3

7.1022

40 == #> kMhatbg; ;edaysarcreep rbs;ebtug³ sn μt; 5.1=cC

elastic strain 434 1093.210

3450010494950 −=

×==

cc

i

E A F

s f Δ (creep) ( ) ( ) MPa E C scr c 9.872000001093.25.1 4 =×== −ε PaKrykMhatbg; %59.8

7.10229.87 ==

$> kMhatbg;edaysarrelaxation rbs;Edk³ sMrab; low-relaxation strand, kMhatbg;KW%5.2 MPa f s 6.257.1022025.0 =×=Δ

%> karrGilrbs; anchorage: sMrab;karTajEtBIcugmçag sn μt;RbEvgrGil mm8.3 MPa E

L L

f s s 1.2120000036000

8.3 ==Δ=Δ edIm,IGnuBaØateGaymankarrGilrbs; anchorage eKRtUvkMNt;kugRtaMgkñ úgkarTaj 1.217.1022 +

MPa8.1043= enAelI pressure gauge edIm,ITTYlnet stress MPa7.1022 enAkñúg tendon.^> kMhatbg;EdlbNþalBIkMlaMgkit³ smIkar parabolic profile KW

( )22

4 x Lx

L

ee x −=

Edl = xe cMNakp©itenARtg;cMgay Edlvas;BITMr nig =e cMNakp©itenAkNþalElVg( ) ( ) x L

L

edxed x 24

2 −=

CaCMerl(slope) rbs; tendon enARKb;cMnucTaMgGs;. enARtg;TMr0=e eyIgTTYl)anslop ( )

056.036000

50044 =×== L

edxed x



T.Chhay NPIC


slope enAkNþalElVges μ IsUnü. dUcenH 056.0= pxα . edayeRbIflexible metallic sheath, 5.0= p nig 00333.0= K . enAkNþalElVg m x 18= . RtYtBinitüfaetI 30.0≤+ x px p Kl α

3.0088.01800333.0056.05.0 <=×+×=+ x px p Kl α px p px pj px Kl P P α ++= 1

( ) x x P P 088.1088.01 =+= MPa7.11127.1022088.1 =×= ¬kMlaMgenAcug jacking¦

MPa f s 907.10227.1112 =−=Δ PaKrykMhatbg; %8.8

7.102290 ==

&> kMhatbg;srubElastic Shortening 34.5MPa 3.37%Shrinkage loss 40.0MPa 3.91%Creep of concrete loss 87.9MPa 8.59%Relaxation of steel loss 25.6MPa 2.50%Friction loss 90.0MPa 8.80%Total loss 278.0MPa 27.17%

eRbkugRtaMgRbsiT§PaB MPa2.7795.2439.1022 =−=

kMlaMgeRbkugRtaMgRbsiT§PaB( ) ( ) ii F F F 762.0238.01 =−= kN F 37724950762.0 =×=

sMrab; i F F η = dUcenH762.0=η

4> viPaKGgát;rgkarBt;begáag Analysis of Flexural Members

k> kugRtaMgEdlbNþalBIlkçxNÐmanbnÞk niglkçxNÐK anbnÞkStresses Due to Loaded and Unloaded condition enAkñ úgkarviPaKFñ wmebtugeRbkugRtaMg CaTUeTAkardak;bnÞ úkBIrmaneRKaHfñak;CageK. TImYyKWekIt

manenAeBlepÞr KWenAeBlFñwmrgkMlaMgeRbkugRtaMgi F ehIyTMgn;rbs;Fñ wm b¤bnÞ úkefrGnuvtþn_enAxN³énkarepÞrkMlaMgkugRtaMg. eKminKitlkçxNÐbnÞ úkefrbEnßm b¤bnÞ úkGefreT. kñ úglkçxNÐK μanbnÞ úkenH kugRtaMgenAsrésEpñkxagelIbMput nigEpñkxageRkambMputénmuxkat;eRKaHfñak;minRtUvFMCagkugRtaMgenAeBlepÞr ci f nigti f sMrab;kugRtaMgrgkarsgát; nigkugRtaMgrgkarTajrbs;ebtugerogKña.



T.Chhay NPIC


krNITIBIrénkardak;bnÞ úkekIteLIgenAeBlEdlFñwmrgkMlaMgeRbkugRtaMgeRkayBIekItmankMhatbg;TaMgGs; nigrgnUvbnÞ úkefr nigGefr. enAkñ úglkçxNÐmanbnÞ úkenH kugRtaMgenAsrésEpñkxagelIbM put nigEpñkxageRkambMputénmuxkat;eRKaHfñak;dac;xatminRtUvFMCagkugRtaMgGnuBaØat c f nigt f sMrab; kugRtaMgrgkarsgát; nigkugRtaMgrgkarTajrbs;ebtugerogKña.

lkçxNÐTaMgenHGacsresrCaTMrg;KNitviTüadUcxageRkam³!> sMrab;lkçxNÐK μanbnÞ úk ¬enAeBlepÞr¦

- enAsrésEpñkxagelIbMput( )

tit Dt ii

ti f I

y M I

ye F A F ≤−+−=α (19.14)

- enAsrésEpñkxageRkambMput( )

cib Dbii

bi f I

y M I

ye F A F −≥−−−=α (19.15)

@> sMrab;lkçxNÐmanbnÞ úk ¬bnÞ úkTaMgGs;RtUv)andak;eRkayBIkMhatbg;eRbkugRtaMg¦- enAsrésEpñkxagelIbMput- ( )

ct Lt Dt

t f I

y M I

y M I

y Fe A F −≥−−+−=σ (19.16)

- enasrésEpñkxageRkambMput- ( )

t b Lb Db

b f I

y M I

y M I

y Fe A F ≤−−−−=σ (19.17)

Edl i F nig= F kMlaMgeRbkugRtaMgenAeBlepÞr nigeRkayBIkMhatbg;ti f nig =t f kugRtaMgrgkarTajenAkñúgebtugenAeBlepÞr nigeRkayBIkMhatbg; ci f nig =c f kugRtaMgrgkarsgát;enAkú ñgebtugenAeBlepÞr nigeRkayBIkMhatbg; D M nig = L M m: Um:g;EdlbNþalBIbnÞúkefr nigbnÞ úkGefr

t y nig =b y cMgayBIG½kSNWteTAsrésEpñkxagelIbMput nigEpñkxageRkambMputenAkú ñgkarviPaK eKsn μt;fasMPar³manlkçN³eGLasÞ icenAkúñgEdneFV IkarénkugRtaMgEdlGnuvtþ.

x> EdnkMNtsñl Kern Limits RbsinebIeKGnuvtþkMlaMgeRbkugRtaMgenARtg;TIRbCM uTMgn;rbs;muxkat; vanwgekItmankugRtaMg

BRgayes μ I. RbsinebIGnuvtþkMlaMgeRbkugRtaMgenARtg;cMNakp© ite BIeRkamTIRbCMuTMgn; EdleFV Iy:agNaeGaykugRtaMgenAsrésEpñkxagelIbMputes μ IsUnü enaHeKcat;TukkMlaMgeRbkugRtaMgenHmanGMeBIRtg;cMnug



T.Chhay NPIC


lower kern ¬rUbTI 19>5¦. enAkñ úgkrNIenHe RtUv)ansMKal;edayb K ehI IykarBRgaykugRtaMgmanragRtIekaN EdlmankugRtaMgsgát;GtibrmaenasréseRkameKbMput. kugRtaMgenAsrésxagelIbMputKW

( ) 0=+−= I

ye F A F t iit σ == b K e lower kern

t Ay I = (19.17)

dUcKña RbsinebIeKGnuvtþkMlaMgeRbkugRtaMgenARtg;cMNap©it 'e BIelITIRbCM uTMng; EdleFVIy:agNaeGaykugRtaMgenAsrésEpñkxageRkambMputes μ IsUnü enaHkMlaMgeRbkugRtaMgRtUv)aneKcat;TukfamanGMeBIRtg;cMnucupper lower ¬rUbTI 19>5¦. enAkñ úgkrNIenHcMNap©it 'e RtUv)ansMKal;edayt K ehIykarBRgaykug

RtaMgmanragRtIekaN EdlmankugRtaMgsgát;GtibrimaenAsrésEpñkxagelIbMput. kugRtaMgenAsrésEpñkxageRkambMputKW ( )

0=+−= I

ye F A F bii

bσ == t K e' upper kern

b Ay I = (19.18)

Kern limits énmuxkat;RtIekaNRtUv)anbgðajenArUbTI 19>5.



T.Chhay NPIC


K> karkMNttMéléncMNakp©tLimiting Values of Eccentricity eKGacsresrsmIkarkugRtaMgTaMgbYn ¬BIsmIkar19.13 dl;19.16¦CaGnuKmn_éncMNakp©it e

sMrab;lkçxNÐénkardak;bnÞ úkepSg². Ca]TahrN_ eKGacsresrsmIkar19.13 dUcxageRkam( )

tit Dt ii

ti f I

y M I

ye F A F ≤−+−=σ

( ) I

y M A F

f I

ye F t Diti

t i ++≤

++≤ ti

t Di

t i f

I y M

A F

y F I

e (19.19) RbsinebIeKeRbI lower kern limit t b Ay I K /= / enaH

i

bti

i

Db F

AK f F

M K e ++≤ (19.20) tMéle CacMNakp©itGtibrmaEdlQrelIsrésEpñkxagelIbMputsMrab;lkçxNÐK μanbnÞúk.

dUcKña BIsmIkar19.14

++−≤ ci

b Di

bi f

I y M

A F

y F I

e (19.21)

i

t ci

i

Dt F

AK f F

M K e ++−≤ (19.22)

tMéle CacMNakp©itGtibrmaEdlQrelIsrésEpñkxageRkambMputsMrab;lkçxNÐK μanbnÞ úk. eKKNnatMélGtibrmae BIsmIkarelITaMgBIredayyktMélEdltUcCagmkeRbI.

BIsmIkar19.15

−+≥ c

t T

t f

I y M

A F

Fy I

e (19.23)

F AK f

F M

K e bcT b −+≥ (19.24)

Edl =T M m:Um:g;EdlbNþalBIbnÞ úkefr nigbnÞ úkGefr( ) L D M M += . tMélenHCacMNakp©itGb,-brma EdlQrelIsrésEpñkxagelIbMputsMrab;lkçxNÐRTbnÞ úk. BIsmIkar19.16

−+−≥ t

bT

b f

I y M

A F

Fy I

e (19.25)

F AK f

F M

K e t t T t −+≥ (19.26)



T.Chhay NPIC


tMélenHCacMNakp©itGb,brmaEdlQrelIsrésEpñkxageRkambMput sMrab;lkçxNÐmanbnÞ úk. eKKYrKNnatMélGb,brmae TaMgBIrenHBIsmIkarTaMgBIrxagelI ehIyeKykcMNakp© itGb,brmaNaEdlmantMélFMCageKmkeRbI.

X> tMélkMNtémkMlaMgeRbkugRtaMgenAeBlepÞrLimiting Values of the Prestessing Force at Transfer

edayKitfa i F F η = Edlη CapleFobénnet prestressing force eRkayBIkMhatbg; nigsMrab;krNIepSg²énkardak;bnÞ úk eKGacsresrsmIkar19.20, 19.22, 19.24 nig19.26 eLIgvijdUc

xageRkam³( ) bti Dib AK f M F K e +≤− (19.27) ( ) t ci Dit AK f M F K e +≤+ (19.28) ( ) ( )bc

L Dib AK f

M M F K e

η η η 1−+≥− (19.29)

( ) ( )t t L D

it AK f M M

F K eη η η 1−+≥+ (19.30)

CMnYsmIkar19.27 eTAkñ úgsmIkar19.30 eKTTYl)an( ) t tit t L Dt bi AK f AK f M M K K F −−+

−≥+ η η η 11

b¤ ( ) ( )−

−+

−+

≥ btit t L

Dt b

i AK f AK f M

M K K

F η η η

111 (19.31) tMéli F CatMélGb,brmaénkMlaMgeRbkugRtaMgenAeBlepÞredaymineGayFMCagkugRtaMgGnuBaØateRkamlkçxNÐmanbnÞ úk nigK μanbnÞ úk. CMnYssmIkar19.29 eTAkñ úgsmIkar19.28 edIm,ITTYl)an

( ) ( )+

+−

−+

≤ t cibc L

Dt b

i AK f AK f M

M K K

F η η η

111 (19.32) tMéli F CatMélGtibrmaénkMlaMgeRbkugRtaMgenAeBlepÞredaymineGayelIskugRtaMgGnuBaØateRkamlkçxNÐmanbnÞ úk nigK μanbnÞ úk. edayCMnYssmIkar19.31 eTAkñúgsmIkar19.32

02211 ≥

++

++−

− t

t cib

cti

L D AK

f f AK

f f

M M

η η η η (19.33) smIkarenHbgðajfa 0minmax ≥− ii F F . eKeRbIsmIkarenHsMrab;bgðajfamuxkat;NamYymanlkçN³RKb;RKan;.



T.Chhay NPIC


]TahrN_ 9>4³FñwmTMrsamBaØEdlrgeRbkugRtaMgmunEdlmanRbEvgm4.14 manmuxkat;dUcbgðajenAkñ úgrUbTI 19>6a. Fñ wmenHRTnUvbnÞ úkefr mkN /15.13 ¬edayminrYmbBa©ÚlTMgn;pÞal;¦ nigrgnUvbnÞ úkGefr mkN /16 . edaysn μt;faEdkeRbkugRtaMgpSMeLIgedaytendon 20 Edltendon mYymanGgát; p© it mm125.11 CamYynwg MPa E s

5102= / MPa F o 1200= nig ultimate strength

MPa f pu 1725= .

!> kMNt;TItaMgEdnkMNt;xagelI nigEdnkMNt;xageRkamrbs;tendon profile ¬TIRbCM uTMgn;rbs; EdkeRbkugRtaMg¦ sMrab;muxkat;enAkNþalElVg nigsMrab;muxkat;bIepSgeTotenAcenøaHmuxkat;kNþalElVg nigcugFñ wm.



T.Chhay NPIC


@> dak; tendon cMTItaMgedIm,IbMeBjEdnkMNt;TaMgenH edayeGay tendon xøHegIbeLIgcab;BI cMnucmYyPaKbIénRbEvgElVg. RtYtBinitütMélkMNt;énkMlaMgeRbkugRtaMgenAeBlepÞr.

#> RtYtBinitüeLIgvijnUvkMhatbg; edayKit tendon profile Edl)aneRCIserIs nigbMErbMrYlcMNakp©it e .

eRbI ci f ¬enAeBlepÞr¦ MPa28= / MPa f c 35' = / MPa E c 27600= nig MPa E ci 24800= .

dMeNaHRsay³

!> kMNt;lkçN³rbs;muxkat;

RkLaépÞ24

1025.23250300150450150600 mm=×+×+×=



T.Chhay NPIC


kMNt;TIRbCM uTMgn;rbs;muxkat;edayKitm: Um:g;eFob)atrbs;muxkat; ( ) mm yb 522925105.6755010901251075

1025.231 333

4 =×+×+×=

mm yt 4785221000 =−= KNna gross moment of inertia g I

( ) ( )( )( ) ( ) ( )( )( )+++= 23

23

2860015012600150403150450

12150450

g I

( ) ( )( )( )++ 23

39725030012250300

41010607.2 mm=

mm Ay

I K

t b 6.235

4781025.2310607.24

10=

×==

mm Ay

I K

bt 8.214

5221025.2310607.24

10=

×==

@> )a:n;RbmaNkMhatbg;eRbkugRtaMg eday MPa F o 1200= a. sn μt;elastic loss es μ I %4 b¤ MPa48120004.0 =×

b. kMhatbg;edaysarkarrYmmaDKW MPa E s 601020003.00003.0 5 =×= c. kMhat;bg;edaysarcreep rbs;ebtug ³ kar)a:n;RbmaNdMbUgd¾l¥bMputénkMhatbg;eday

sarcreep KW 67.1 dgénelastic loss MPa804867.1 ≈×

d. kMhatbg;edaysarrelaxation énEdkKW%4 ³ MPa48120004.0 =× kMhatbg;GaRs½ynwgeBlKW MPa188488060 =++

PaKrykMhatbg; %7.15

1200

188 ==

e. kMhatbg;srubKW MPa23648188 =+ PaKryénkMhatbg;srubKW

%7.191200236 =

f. kugRtaMgkMlaMgeRbkugRtaMg MPa F i 1152481200 =−= ¬enAeBlepÞr¦ MPa F 9642361200 =−=



T.Chhay NPIC


i F F η = −=1η pleFobkMhatbg;GaRs½ynwgeBl

837.01152964 == #> EdnkMNt;éncMNakp©it e Rtg;kNþalElVg³ kMNt;kugRtaMgGnuBaØat nigm:Um:g;. enAeBlepÞr

MPa f ci 28' = / MPa f ci 8.16286.0 =×= nig MPa f f citi 32.1'25.0 == . enAeBlrgbnÞúkeFV Ikar MPa f c 35' = / MPa f f cc 75.15'45.0 == nig MPa f f ct 96.2'5.0 == .

bnÞ úkpÞal;rbs;Fñ wm mkN /81.5251025.23 2 =×= − D M

¬bnÞ úkpÞal;¦( )

mkN .6.1508

4.1481.5 2==

a M ¬bnÞ úkbEnßm nigbnÞ úkGefr¦ 8

2 Lwa= ( )

mkN .6.7558

4.141615.13 2=+=

m:Um:g;srub( ) mkN M M M L DT .2.906=+= =i F kugRtaMgenAeBlepÞr ×RkLaépÞEdkeRbkugRtaMg

RkLaépÞrbs; tendon 20 Edltendon nImYy²manGgát;p© it mm125.11 KW 213947.6920 mm=×

kN F i 16061011521394 3 =×= − kN F 1344109641394 3 =×= −

a. BicarNamuxkat;enAkNþalElVgsrésxagelIbMput kñ úglkçxNÐminrgbnÞ úk

i

bti

i

Db

F

AK f

F

M K e ++≤

)( )mm4.37410

16066.2351025.2332.110

16066.1506.235 3

43 ≤++≤ −

srésxageRkambMput kñ úglkçxNÐK μanbnÞ úk

i

t ci

i

Dt F

AK f F

M K e ++−≤

mm4.401101606

8.2141025.238.16101606

6.1508.214 34

3 ≤++−≤ −

yktMél e EdltUcCageKkñ úgcMeNamlT§plTaMgBIrxagelICatMélGtibrma.



T.Chhay NPIC


dUcenH tMélGtibrmarbs; mme 374= srésxagelIbMput kñ úglkçxNÐrgbnÞúk

F AK f

F M K e bcT b −+≥

mm268101344

6.2351025.2375.15101344

2.9066.235 34

3 ≥−+≥ − srésxageRkambMput kñ úglkçxNÐmanbnÞ úk

F AK f

F M

K e t t T t −+−≥

) mm5.349101344

8.2141025.2396.2101344

2.9068.214 34

3 ≥−+−≥ − tMélGb,brmarbs;e CatMéltUcCageKkñ úgcMeNamlT§plTaMgBIrxagelI.

dUcenH tMélGb,brmarbs; mme 350= b. BicarNamuxkat;EdlenAcMgaym4.2 BIkNþalElVg ¬muxkat;elx @ kñúgrUbTI 19>6a¦³

D M ¬bnÞ úkpÞal;¦ ( ) ( )28.42

8.4 D A

w R −= ( )( )( ) ( ) mkN .9.1338.4

281.58.42.781.5 2 =−=

( )( )( ) ( ) mkN M a .6.6718.4215.29

8.42.715.292

=−= mkN M T .5.8056.6719.133 =+=

srésxagelIbMput sMrab;lkçxNÐminrgbnÞúk³)( )

mme 364101606

6.2351025.2332.1101606

9.1336.235 34

3 ≤++≤ − srésxageRkambMput sMrab;lkçxNÐminrgbnÞ úk

) mme 391101606

8.2141025.238.16101606

9.1338.214 34

3 ≤++−≤ −

tMélGtibrmarbs; mme 364=

srésxagelIbMput sMrab;lkçxNÐRTbnÞ úk) mme 19310

13446.2351025.2375.1510

13445.8056.235 3

43 ≥−+≥ −

sésrxageRkambMput sMrab;lkçxNÐRTbnÞúk)

mme 5.2741013448.2141025.2396.2

1013445.805

8.2143

43

≥−+−≥ −



T.Chhay NPIC


tMélGb,brmarbs; mme 5.274= c. BicarNamuxkat;Rtg;cMgay m8.4 BIkNþalElVg ¬muxkat;elx # kñ úgrUbTI 19>6a¦³

D M ¬bnÞ úkpÞal;¦ mkN .7.83= mkN M a .8.419= mkN M T .5.503=

- srésxagelIbMput sMrab;lkçxNÐK μanbnÞúk mme 333≤ ¬Gtibrma¦- srésxageRkambMput sMrab;lkçxNÐK μanbnÞ úk mme 360≤ - srésxagelIbMput sMrab;lkçxNÐrgbnÞ úk mme 32−≥ - srésxageRkambMput sMrab;lkçxNÐrgbnÞ úk mme 50≥ ¬Gb,brma¦

d. BicarNamuxkat;Rtg;cMgay m9.0 BIcugFñ wm ¬RbEvganchorage¦³ D M ¬bnÞ úkpÞal;¦ mkN .3.35= / mkN M a .1.177= nig mkN M T .4.212=

- srésxagelIbMput sMrab;lkçxNÐK μanbnÞúk mme 303≤ ¬Gtibrma¦- srésxageRkambMput sMrab;lkçxNÐK μanbnÞ úk mme 330≤ - srésxagelIbMput sMrab;lkçxNÐrgbnÞ úk mme 248−≥ - srésxageRkambMput sMrab;lkçxNÐrgbnÞ úk mme 167−≥ ¬Gb,brma¦

$>Tendon profile RtUv)anbgðajenAkñ úgrUbTI 19>6 b. cMNakp©itEdl)aneRCIserIsenAkNþalElVgKWmme 364= EdlvaRKb;RKan;sMrab;muxkat; BenAcMgay m4.2 BIkNþalElVg. TIRbCM uTMgn;énEdk

eRbkugRtaMgmanlkçN³edkcenøaH A nig BnigbnÞb;mkeTreLIgEdlmanlkçN³CabnÞat;cenøaHBI B eTA E . cMNakp©itenARtg;muxkat; C nig D RtUv)anKNnaedayeRbIbnÞat;eRTt BE EdlmanCMerl

mmm /83.758.4/364 = . cMNakp©itRtg; C KW mm182 nigRtg; D KWmm68 . Tendon profile

Edl)aneRCIserIsbMeBjlkçxNÐEdnkMNt;xagelI nigEdnkMNt;xageRkamrbs;cMNakp© itenARKb;muxkat;TaMgGs;.

karelIktendon eLIgRtUv)aneFV IdUcxageRkam³a. dak;tendon TaMg20 ¬Ggát;p©it mm125.11 ¦

enAmYyPaKbIénkNþalElVgrbs;Fñ wmedaymanKMlat mm50 BIKñadUcbgðajenAkñúgrUbTI 19>6a.edIm,IKNnacMNakp©itCak;EsþgenARtg;muxkat;kNþalElVg Kitm: Um:g;sMrab;tendon eFobnwg)atrbs;muxkat;³



T.Chhay NPIC


cMgayBI)at ( ) mm155275412516201 =×+×=

e ¬kNþalElVg¦ mm yb 367155522155 =−=−= EdlvaEk,rnwgmm364 Edl)ansn μt;. RbsinebIebIeKdak; tendon BIrenAcMgay mm75 BI tendon EdlenAxageRkam enaHcMgayBI)atkøayeTACa

( ) mm1583252250212516201 =×+×+×

enaHcMNakp©itnwgkøayeTACa mm364158522 =− Edles μ I weTAnwgcMNakp©itEdl)ansn μt;. CakarGnuvtþ eKdak;tendon TaMgGs;edaymanKMlatBIKñamm50 .

b.

elIkEttendon

EdlenAkNþalcMnYn12

eGayegIbeLIg. karBRgay tendon

enAmuxkat;xagcugRtUv)anbgðajenAkñúgrUbTI 19>6 a. RtYtBinitücMNakp© itrbs; tendon edayKitm:Um:g;eFobTI RbCM uTMgn;rbs;muxkat;ebtugsMrab; tendon 12 enAxagelI nigtendon 8eTotEdlRtUv)andak; enAxageRkam³

( ) mme 10226123648201 =×−×=

tMéle enHtUc nigRKb;RKan;. cMNakp©itCak;EsþgenAcMgay m9.0 BImuxkat;xagcug( ) mme 7610103648.4

9.0=+−=

cMNakp©itCak;EsþgenAcMgay m4.2 BImuxkat;xagcugKW( ) mme 1871010364

21 =+−=

%> tMélkMNt;rbs; i F ³ tMélrbs; i F EdleRbIsMrab;karKNnaBIxagelIKW kN F i 1606= .RtYtBinitü i F Gb,brmaedayeRbIsmIkar19.31:

( )

( ) ( )−−+

−+

= btit t L

Dt b

i AK f AK f M

M K K

F η η η

111min

( )

( )

( ) ××−

×−+

−

+=

−

6.2351025.2332.1

837.08.2141025.2396.2

837.0106.755106.1501

837.01

8.2146.23510

4

4663

kN 8.1516=

vamantMéltUcCagi F EdleRbI. RtYtBinitü i F GtibrmaedayeRbIsmIkar19.32:

( ) ++−

−+= t cibc L Dt b

i AK f AK f M M K K

F η η η 111max



T.Chhay NPIC


( )

( )

( ) +

+−

−

+=

−

8.2141025.238.16

837.06.2351025.2375.15

837.0106.755106.150

837.011

8.2146.23510

4

4663

kN 9.2081= vamantMélFMCagi F EdleRbI. dUcenHmuxkat;eRKaHfñak;enAkNþalElVgKWRKb;RKan;.

^> RtYtBinitükMhatbg;eRbkugRtaMg edayeyIgman MPa F o 1200= nig 21394mm A ps = kMlaMg o F srub kN 8.16721013941200 3 =××= −

MPa E c 27600= 25.7

27600

200000 ===c

s

E

E n

yk7=n

D M enAkNþalElVg mkN .6.150=

( )

( )

++

×+=

I e

AnA

L D f nA F F

ps

c pso

i 211

32..

tMélrbs;c f Edl)anBIkarBRgaybnÞ úkefrRtUvKuNnwg3/2 edIm,IbgðajBIbMErbMrYlrag)a:ra:bUl

rbs;kugRtaMgbnÞ úkefrtambeNþayFñ wm Edlpþl;eGaynUvtMélRbhak;RbEhlrbs;i F

)anRbesIrCag.a. kMNt;tMélmFümrbs; 2e EdlTTYlenAkñ úgFñwm. ExSekagtMNageGay2e RtUv)anbgðajenA

kñ úgrUbTI 19>6c³2e ¬mFüm¦ ( ) ( ) ( )

( )

×+

×+×+×=

1324964.2

9.3126720319.357769.05776

31

2.71

27.70414 mm=

mme 265= RkLaépÞrbs;)a:ra:bUles μ InwgRkLaépÞrbs;ctuekaNEkg.

b. kugRtaMgEdlbNþalBIbnÞ úkefrenARtg;nIv: Urbs; tendon KW( ) MPa L D f c 53.110

10607.22656.150.. 6

10 =×=



T.Chhay NPIC


dUcenH( )

( )kN F i 1.157510

10607.2

7.70414

1025.23

1139471

3253.113947108.1672

3

104

3

=

++

××+= −

elastic loss KW %8.57.971.15758.1672 ==− kN . tMélenHKWFMCagelastic loss Edl)ansn μt; %4 .

elastic loss kñ úgmYyÉktþaRkLaépÞEdk MPa70101394

7.97 3 == i F kñ úgmYyÉktþaRkLaépÞ MPa113010

13941.1575 3 ==

c. kMhatbg;GaRs½ynwgeBlkMhat;bg;edaysarkarrYmmaDebtug MPa60= ¬dUcelIkmun¦

kMhatbg;edaysarcreep elastic strain ( )

434 1045.210

276001025.231.1575 −===

cc

i

E A F ( ) scr c s E C f ε =Δ

yk 5.1=cC enaH MPa f s 5.732000001045.25.1 4 ==Δ −

PaKrykMhatbg; %5.61130

5.73 == kMhatbg;edaysarrelaxation rbs;EdkKW MPa48 ¬dUcelIkmun¦. kMhatbg;GaRs½ynwgeBles μ Inwg MPa5.181485.7360 =++ ehIyPaKrykMhatbg;KW %161130/5.181 = EdlmantMélEk,rnwgtMélEdl)ansn μt; %7.15 .

( ) iii F F F F 84.016.01 =−==η 84.0=η

5> KNnaGgát;rgkarBt;begáagDesign of Flexural Members

k> sBaØaNTUeTAGeneral EpñkBIedIm)anbBa¢ak;fakugRtaMgenAsrésxagelIbMput nigsrésxageRkambMputénmuxkat;eRKaH

fñak;rbs;Ggát;ebtugeRbkugRtaMgminRtUvFMCagkugRtaMgGnuBaØatsMrab;RKb;krNITaMgGs; b¤dMNak;kalén



T.Chhay NPIC


kardak;bnÞ úk. bEnßmBIelIlkçxNÐTaMgenH eKRtUvKNnaGgát;ebtugeRbkugRtaMgCamYynwgemKuNsuvtßi-PaBRKb;RKan;edIm,IRbqaMgnwgkar)ak;. ACI Code tMrUveGaym:Um:g;Edl)anBIbnÞúkemKuN u M minRtUvFM CagersIusþg;rgkarBt;n M φ énmuxkat;Edl)anKNna.

sMrab;krNI tension-controlled section, FñwmebtugeRbkugRtaMgcab;epþIm)ak;enAeBlEdlkugRtaMgEdkFMCagyield strength rbs;EdkEdleRbIenAkñ úgmuxkat;ebtug. EdkeRbkugRtaMgersIusþg;nwgminbgðajcMnucyield c,as;las;dUcEdkFm μtaEdleRbIenAkñ úgebtugGarem:eT. b: uEnþeRkamkarbEnßmbnÞúkstrain enAkñ úgEdkekIneLIgedayGRtay:agelOn ehIykar)ak;ekIteLIgenAeBlcompressice strain Gtibrmarbs;ebtugmantMéles μ Inwg003.0 ¬rUbTI 19>7¦.

EdnkMNt;sMrab;EdkBRgwgrbs;Ggát;rgkarBt;ebtugeRbkugRtaMgEdlGaRs½yeTAtamACI Code,

Section 18.8 KWQrelI net tensile strain sMrab;tension-controlled, transition b¤ compression-



T.Chhay NPIC


controlled section edayeKarBtamACI Code, Section 10.3 dUcEdl)anBnül;enAkñ úgCMBUk 3. emKuNkat;bnßyersI usþg; φ RtUv)aneGayenAkñ úgCMBUkTI 3 edayQrelI ACI Code, Section 9.3.

x> muxkat ctuekaNRectangular Sections eKGackMNt; Nominal moment capacity rbs;muxkat;ctuekaNdUcxageRkam ¬eyagtamrUb

TI 19>7¦³

−=

−=

22a

d T a

d C M n (19.34) Edl s ps f AT = nig ab f C c'85.0= . sMrab; T C =

d f

f

b f

f Aa

c

ps p

c

ps ps

'85.0'85.0 ρ == (19.35|

EdlpleFobEdkeRbkugRtaMgKW bd A ps p /= ρ ehIy ps A nig ps f CaRkLaépÞ nigkugRtaMgTajrbs;EdkeRbkugRtaMg. yk

132.0'

β ρ ω ≤

=

c

ps p p f

f

bnÞab;mkd a p

85.0

ω =

(19.36)

tMél p CakMlaMgenAkñ úgtendon EdlRtUv)anvas;edaypÞal;. edIm,IFananUvtesion-controlled

behavior, ACI Code, Section 18.8.1 kMNt;fa p minRtUvFMCag 132.0 β EdkRtUvKñanwgnet tensile

strain 005.0=t ε . cMNaMfa 85.01 = β sMrab; MPa f c 28' ≤ nwgkat;bnßyeday05.0 sMrab;ral; MPa7 sMrab; MPa f MPa c 56'28 << ehIyes μ Inwg65.0 sMrab; MPa f c 56' > . eKk¾Gacsresr

−=

2a

d f A M ps psn

−=

c

ps p ps psn f

f d f A M '7.1

1 ρ (19.37)

−=

7.11 p

ps psn d f A M ω (19.38)

nig nu M M φ = enAkú ñgsmIkarBImun ps f CakugRtaMgenAkñ úgEdkeRbkugRtaMgenAeBl)ak;. eKminGackMNt;tMél

Cak;Esþgrbs; ps f edaygayRsYleT. dUcenHACI Code, Section 18.7.2 GnuBaØateGay)a:n;RbmaNtMél ps f dUcxageRkam.



T.Chhay NPIC


sMrab; bonded tendons

×−=

c

pu p

p pu ps f

f f f

'1

1

ρ β

γ (19.39)

sMrab; unbonded tendon enAkñ úgGgát;EdlmanpleFobElVgelIkMBs;tUcCag b¤es μ I35 py

p

c se ps f

f f f ≤

++=

ρ 100'69 (19.40)

RbsinebI pu se f f 5.0≥ nigRbsinebI ps f sMrab; unbonded tendon minFMCag py f b¤ MPa f se 415+ .sMrab; unbonded tendon enAkñ úgGgát;EdlmanpleFobElVgelIkMBs;FMCag35

++=

p

c se ps

f f f

ρ 300

'69

(19.41)

b: uEnþminRtUvFMCag py f b¤ MPa f se 207+ Edl

= pγ emKuNsMrab;RbePTrbs; tendon eRbkugRtaMg55.0= sMrab; pu py f f / EdlmintUcCag8.0 4.0= sMrab; pu py f f / EdlmintUcCag85.0 28.0= sMrab; pu py f f / EdlmintUcCag9.0

= pu f ersI usþg;TajEdlkMNt;rbs;EdkeRbkugRtaMg= se f kugRtaMgRbsiT§PaBenAkñ úgEdkeRbkugRtaMgeRkayeBlkMhatbg;TaMgGs;= py f specified yield strength rbs;EdkeRbkugRtaMg

enAkñ úgkrNIEdl 132.0 β ω > p Fñ wmebtugeRbkugRtaMgCacompression-controlled section.edIm,IFananUv ductile failure eKkMNt; p RtwmtMélGtibrma 132.0 β . sMrab; 132.0 β = nig

d a 1377.0 β = eyIgTTYl)an

−=

7.132.01 1 β d f A M ps psn

( )1188.01 β ρ −= d f bd ps p ( ) 2

1188.01' bd f c p β ω −= ( ) 22

11 '06.032.0 bd f c β β −= (19.42) sMrab; MPa f c 35' = / 8.01 = β . enaH

22 09.1'22.0 bd bd f M cn == dUcKña/ sMrab; MPa f c 28' = / 2915.0 bd M n = nigsMrab; MPa f c 42' = / 2238.1 bd M n =



T.Chhay NPIC


K> muxkatEdlmansøab Flanged Sections sMrab;muxkat;mansøab(T- or I-section) RbsinebIkMBs;bø úk a sßitenAkñúgsøab eKnwgKitvaCa

muxkat;ctuekaNEkg. RbsinebI a sß itenAkñ úgRTnug enaHeKKitRTnugCamuxkat;ctuekaNEkgedayeRbI TTwgRTnug nigTTwgsøabEdlelIs ( )wbb − RtUv)anKitdUcKñanwgebtugGarem: T-section Edl)anBnül; enAkñ úgCMBUk 3 nig4. eKGacKNnadesign moment strength rbs; flanged section dUcxageRkam¬emIlrUbTI 19>7¦.

1nn M M = ¬ersI usþg;m: Um:g;rbs;RTnug¦2n M + ¬ersI usþg;m: Um:g;rbs;søabEdlelIs¦

−+

−=

22

f p ps pf p ps pwn

hd f A

ad f A M (19.43)

nu M M φ = nigwc

ps pw

b f

f Aa

'85.0=

Edl pf ps pw A A A −= ( ) ps f wc pf f hbb f A /'85.0 −=

= f h kMras;rbs;søabcMNaMfaRkLaépÞEdkeRbkugRtaMgsrub ps A EckecjCaBIrEpñk pw A nig pf A Edlbegá It web

moment capacity nigflange moment capacity. sMrab;muxkat;Edlmansøab snÞsSn_EdkBRgwg(reinforcement index) pwω minRtUvFMCag 132.0 β sMrab; tension-controlled section Edl

=

=

c

ps

w

pw pw f

f

d b

A

'ω GRtaEdkRTnugeRbkugRtaMg

×

c

ps

f

f

'

X> EdkBRgwgrgeRbkugRtaMg Nonprestressed Reinforcement

kñ úgkrNIxøH eKdak;EdkminrgeRbkugRtaMg s A enAkñ úgtMbn;Tajrbs;Ggát;rgkarBt;ebtugeRbkugRtaMgCamYynwgEdkeRbkugRtaMg ps A edIm,Ibegá InersI usþg;m: Um:g;(moment strength) rbs;Fñ wm. enAkñúgkrNIenH Edksrub ¬ ps A nig s A ¦ RtUv)anBicarNaenAkñ úgkarviPaKm:Um:g;. sMrab;muxkat;ctuekaNEdlmanEdkrgeRbkugRtaMg nigEdkminrgeRbkugRtaMg eKKNnadesign moment strength n M φ dUcxageRkam³

−+

−=

22a

d f Aa

d f A M y s p ps psn (19.44)



T.Chhay NPIC


Edl b f

f A f Aa

c

y s ps ps

'85.0

+= / ehIy pd nigd CacMgayBIsrésrgkarsgát;xageRkAbMputeTATIRbCM uTMgn;

rbs;EdkrgeRbkugRtaMg nigEdkminrgeRbkugRtaMg erogKña. sMrab;muxkat;Edlmansøab

−+

−+

−=

222 f

p ps pf s s p ps pwnh

d f Aa

d f Aa

d f A M (19.45) Edl pf ps pw A A A −=

wc

y s ps ps

b f

f A f Aa

'85.0

+=

sMrab;muxkat;ctuekaNEkgEdlmanEdkrgkarsgát; ehIym:Um:g;RtUv)anKiteFobnwgkMlaMgC

−+

−+

−= '2

'22

d a

f Aa

d f Aa

d f A M y s y s p ps psn

(19.46)

Edl b f

f A f A f Aa

c

y s y s ps ps

'85.0'−+

= smIkarenHmann½yEtenAeBlEdlEdkrgkarsgát; yield . lkçxNÐsMrab;Edkrgkarsgát; yield KW

−≥

−+

y

c y s y s ps ps

f d d f

bd

f A f A f A

600600''85.0

'1 β

RbsinebIeKminCYblkçxNÐenHeT enaHEdkrgkarsgát;min yield eT. enAkñúgkrNIenH eKGacecal s A'

¬yk 0' = s A ¦ b¤mü:ageTot eKGackMNt;kugRtaMgenAkñ úg s A' edaykarviPaKTUeTA dUcEdlBnül;enAkñ úgCMBUk 3.

enAeBleKeRbIEdkrgeRbkugRtaMg nigEdkminrgeRbkugRtaMgenAkñúgmuxkat;dUcKña eKKYrG19.39 dUcxageRkam³

( )

−+−= '

'1

1ω ω ρ

β

γ

pc

pu p

p pu ps d

d f

f f f (ACI Code, Eq. 18.3) (19.47)

RbsinebIeKKitEdkrgkarsgát;TaMgGs; enAeBlKNna ps f enaHtY ( ) 17.0'

'≥−+ ω ω ρ

pc

pu p d

d f

f

nig pd d 15.0'≤ Edld / 'd nig pd CacMgayBIsrésrgkarsgát;xageRkAbMputeTATIRbCMuTMgn;rbs;EdkTajEdlminrgeRbkugRtaMg Edkrgkarsgát; nigEdkrgeRbkugRtaMg erogKña.

= pγ emKuNsMrab;RbePTrbs; tendon eRbkugRtaMg55.0= sMrab; pu py f f / EdlmintUcCag80.0



T.Chhay NPIC


4.0= sMrab; pu py f f / EdlmintUcCag85.0 28.0= sMrab; pu py f f / EdlmintUcCag9.0

85.01 = β sMrab; MPa f c 28' ≤ nwgkat;bnßyeday05.0 sMrab;ekIneLIg MPa7 rbs; c f ' Et65.01 ≥ β .!> sMrab;muxkat;ctuekaNEkgACI Cose,Section 18.8 kMNt;pleFobEdkdUcxageRkam

¬ 005.0≥t ε sMrab;tension –controlled section¦³132.0 β ω ≤+

p p d

d w

Edl

=

c

ps

p p f

f

' ρ ω

nig bd

A ps

p = ρ

¬EdkrgeRbkugRtaMg¦

=

c

y

f

f

' ρ ω nig bd

A s= ρ ¬EdkminrgeRbkugRtaMg¦@> RbsinebIeKeRbIEdkFm μta s A' enAkñ úgtMbn;sgát; enaHlkçxNÐkøayeTACa

( ) 132.0' β ω ω ω ≤−+ p

p d d

Edl c y f f '/'' ρ = nig bd A s /''= ρ . EdnkMNt;Edk (reinforcement limitation) mansar³sMxan;edIm,I Fana plastic failure rbs;Fñ wmebtugGarem:EdkmanEdktic.

#> sMrab;muxkat;mansøab RkLaépÞEdlcaM)ac;edIm,Ibegá ItersIusþg;rbs;RTnug pw A RtUv)aneRbI edIm,IRtYtBinitüreinforcement index.

pw ¬RTnug¦ 132.0'

β ρ ≤

=

c

ps pw f

f

Edld w

pw pw d b

A= ρ

RbsinebIeKeRbIEdkminrgeRbkugRtaMg enaHreinforcement limitation KW ( ) 132.0' β ω ω ω ≤−+ ww

pw pw d

d

Edl

=

c

y

w

sw f

f

d b A

'ω nig

=

c

y

w

sw f

f

d b A

'''ω

enAeBleKmineRbIEdkrgkarsgát; s A' enaH 0' =wω . kñ úgkarKNna nigkarviPaKGgát; ebtugeRbkugRtaMgedayEpñk(partially prestressed concrete member) eKRtUvEtCYblkçxNÐEdkxagelI.



T.Chhay NPIC


sMrab;fñak;C énGgát;ebtugeRbkugRtaMgrgkarBt; Edl ct f f '> ¬muxkat;EdleRbH¦eKKYreRbIcrack control provision EdlBnül;enAkñ úgEpñk 6>7 . enAeBleRbIsmIkar6.18

sMrab;KMlatGtibrma s /ACI Code, Section 18.4 kMNt;dUcxageRkam³a. sMrab; tendon eRbIKMlat mm s 17= .

b. sMrab;bnSMénEdkminrgeRbkugRtaMg nigtonden eRbIKMlat mm s 20= .c. sMrab; tendon eRbI ps f Δ CMnYseGay s f Edl ps f Δ CaPaBxusKñarvagkugRtaMgEdl

KNnaenAkñúgtendon eRbkugRtaMgeRkambnÞúkeFV IkaredayQrelImuxkat;eRbH nigdecompression stress dc f enAkñúgtendon eRbkugRtaMg EdlRtUv)anKiteGayes μ InwgeRbkugRtaMgRbsiT§PaB(effective prestress) se f . cMNaMfa ps f Δ minKYrelIsBI MPa250 .RbsinebIvaticCag b¤es μ Inwg MPa140 eKminGacGnuvtþKMlatEdlTamTareT.

eKGacsresrsmIkar8.18 dUcxageRkam³−

Δ

= c

psC

f s 5.23700

32

6> m:Um:g;eRbH Cracking Moment

sñameRbHekItmanenAkñúgFñ wmebtugeRbkugRtaMgenAeBlEdlkugRtaMgTajenAsrésEpñkxageRkAbMputrbs;muxkat;eRKaHfñak;es μ I b¤elIsmodulus of rupture rbs;ebtug r f . eKGacsn μt;tMélrbs;

r f sMrab;ebtugTMgn;Fm μtaeGayes μ Inwg c f '62.0 . kugRtaMgenAsrésxageRkambMputrbs;Fñ wmTMrsamBaØEdlbegáItedaykMlaMgeRbkugRtaMg nigcracking moment KW

( ) I

y M

I

y Fe

A

F bcr bb +−−=σ

enAeBlEdl cr b f f '62.0==σ enaHcracking moment KW( )

++=

I y Fe

A F

f y I

M bc

bcr '62.0 (19.48)

kugRtaMgTajGtibrmaeRkayBIkMhatbg;KW c f '62.0 EdltMNageGayr f . enAkñ úgkrNIenH Fñ wmebtugeRbkugRtaMgenArkSamuxkat;minmansñameRbHeRkamGMeBIbnÞúkefr. edIm,IFanaPaBRKb;RKan;ersI usþg;RbqaMgnwgsñameRbHACI Code, Section 18.8.3 TamTarfa ultimate moment strength rbs;Ggát; n M φ y:agticRtUves μ Inwgmoment cracking 1.2 dg.



T.Chhay NPIC


]TahrN_ 9>5³sMrab;Fñ wmén]TahrN_ 19>4 cUrRtYtBinitüdesign strength nigtMrUvkarrbs; ACI

Code EdlRbqaMgnwgcracking moment.dMeNaHRsay³!> RtYtBinitüemIlfakMBs;bøúkkugRtaMga sß itenAkñ úgsøabb¤Gt;.

b f

f Aa

c

ps ps

'85.0= (19.35)

ps A ¬én20 tendon Edltendon mYy²manGgát;p© it mm125.11 ¦= 21394mm yk 85.0/ =u py f f / 4.0= p ρ nig 5.08.0/4.0/ 1 == β γ p . sMrab; bonded tension

×−=

c

pd

p

p

pu ps f

f f f

'1

1 ρ

β

γ

(19.39)

mmd 8421581000 =−=

31068.3842450

1394 −=×

==bd

A ps p ρ

edayeKeGay MPa f pu 1725= ( ) MPa f ps 6.1568

3517251068.35.011725 3 =−= −

( )( ) mma 3.1634503585.0

6.15681394==

edayvamantMélFMCakMras;søab mm150 . dUcenH muxkat;enHeFV IkarCamuxkat;mansøab.@> sMrab;muxkat;mansøab

−+

−=

22 f

ps pf ps pwnh

d f Aa

d f A M Edl pf ps pw A A A −=

( )[ ] f wc ps pf hbb f

f A −=

'85.0

1

( )( )[ ] 25.8531501504503585.0

6.15681

mm=−= 25.5405.8531394 mm A pw =−=

( )( )

mmb f

f Aa

wc

ps pw 1901503585.0

6.15685.540'85.0

=== ( ) ( ) mkN M n .2.166010

2150

8426.15685.853102

1908426.15685.540 66 =

−+

−= −−



T.Chhay NPIC


( ) mkN M n .2.14942.16609.0 ==φ RtYtBinitü reinforcement index sMrab;muxkat;mansøab

31028.48421505.540 −=×==

d b A

w

pw pw ρ

256.08.032.032.0' 1 =×=≤= β ρ ω c

ps pw pw f

f ¬ 9.0=φ ¦#> KNnam:Um:g;emKuNxageRkAEdl)anBIbnÞ úkefr nigGefr

bnÞúkefr = TMgn;pÞal; + bnÞ úkefrbEnßmmkN .96.1815.1381.5 =+=

bnÞúkGefr mkN /16= L DU 6.12.1 +=

[ ] mkN M u .3.1253166.196.182.184.14 2

=×+×= m: Um:g;emKuNxageRkAenHmantMéltUcCag ultimate moment capacity rbs;muxkat; mkN .2.1494 dUcenHmuxkat;enHRKb;RKan;.

$>cracking moment ¬smIkar !(>$*¦ KW ( )

++=

I y

Fe A F

f y I

M bc

bcr '62.0

BI]TahrN_ 19>4 kN F 1344= / 241025.23 mm A = / mme 364= / mm yb 522= /41010607.2 mm I = / MPa f c 35' = nig MPa f c 67.3'62.0 =

( ) 610

34

31010

10607.2522364101344

1025.2310134467.3

52210607.2 −

×++=cr M

mkN .2.961=

RtYtBinitüemIlfa ncr M M φ ≤2.1 ( ) mkN M cr .4.11532.9612.12.1 ==

tMélenHKWtUcCag mkN M n .2.1494=φ . dUcenH Fñ wmenHRKb;RKan;kñ úgkarTb;nwgkareRbH.



T.Chhay NPIC


7> PaBdab Deflection

PaBdabrbs;cMnucmYyenAelIFñ wmCabMlas;TIsrubrbs;cMnucenaH eTaHCaeLIgelI b¤cuHeRkamEdlbNþalBIkarGnuvtþrbs;bnÞ úkenAelIFñ wmenaH. enAkñ úgFñ wmebtugeRbkugRtaMgEdlRTedayTMrsamBaØ CaTUeTAkMlaMgeRbkugRtaMgRtUv)aneKGnuvtþenABIeRkamTIRbCM uTMgn;rbs;muxkat; Edlbegá ItCaPaBdabeLIgelI EdleKeGayeQ μaHfacamber . TMgn;pÞal;rbs;Fñwm nigbnÞúkTMnajxageRkAEdlmanGMeBIenAelIFñ wmnwgeFVI eGaymanPaBdabcuHeRkam. Net deflection CaplbUkBiCKNiténPaBdabTaMgBIr.

enAkñ úgkarKNnaPaBdab eKcaM)ac;RtUvBicarNaTaMgPaBdabry³eBlxø I (short-term deflection) b¤PaBdabPøam²(immediate deflection) nigPaBdabry³eBlyUr(long-term deflection). edIm,IFanaeGayeRKOgbgÁ úMGaceFV IkareTA)an PaBdabry³eBlxø IGtibrma nigPaBdabry³eBlEvgGtibrmaeRKb;dMNak;kalénkardak;bnÞ úkEdlmanlkçN³eRKaHfñak;TaMgGs;minRtUvFMCagtMénkMNt;Edl)ankMNt;edayACI Code ¬emIlEpñk 6>3¦.

eKGacKNnaPaBdabrbs;Ggát;ebtugeRbkugRtaMgedaysmIkarPabdabsþg;dar b¤edayconven

tional method EdlmanenAkñ úgesovePAviPaKeRKOgbgÁ úM. ]TahrN_ PaBdabenAkNþalElVgrbs;Fñ wmTMrsamBaØEdlrgbnÞ úkTMnajBRgayes μ Iw es μ Inwg EI wL 384/5 4 . m: UDuleGLasÞ icrbs;ebtugKW

ccc f f w E '4780'043.0 5.1 == sMrab;ebtugTMgn;Fm μta.eKKNnam:Um:g;niclPaBrbs;muxkat;ebtug I edayQrelIlkçN³rbs;gross section sMrab;

FñwmEdlK μansñameRbH. eKGaceRbIkrNIenH)anenAeBlEdlkugRtaMgTajGtibrmaenAelIsrésxageRkAbMputrbs;ebtugminelIs modulus of rupture rbs;ebtug cr f f '62.0= ¬Fñ wmfñak; U ¦. enAeBlEdlkugRtaMgTajGtibrmaEdlWrelIlkçN³rbs; gross section FMCag c f '62.0 eKRtUveRbIm: Um:g;niclPaBRbsiT§PaB(effective moment of inertia) e I EdlQrelImuxkat;EdlmansñameRbH b¤Gt;mansñameRbH dUcEdl)anBnül;enAkñ úgCMBUk 6 ¬Fñwmfñak; T nigC ¦. PaBdabkNþalE;lVgsMrab;Fñ wmTMrsamBaØEdlbNþalBIbnÞ úkTMnaj nigkMlaMgeRbkugRtaMgRtUv)anbgðajenAkñúgtarag 19>3.

]TahrN_ 9>6³sMrab;FñwmenAkñ úg]TahrN_ 19>4 cUrKNnacamber enAeBlepÞr nigbnÞab;mkKNnaPaBdabPøam²EdlrMBwgTukcugeRkayEdlrgbnÞ úkeFV Ikar.dMeNaHRsay³

!> PaBdabenAeBlepÞr



T.Chhay NPIC


a. KNnaPaBdabcuHeRkamEdlbNþalBIbnÞ úkefrenAeBlepÞr ¬kñ úgkrNIenHbnÞúkefrCabnÞ úkpÞal;¦sMrab;Fñ wmTMrsamBaØEdlrgbnÞ úkBRgayes μ I

DΔ ¬bnÞúkefr¦ EI wL

3845

4=

BI]TahrN_ 19>4/ mkN w D /81.5= / m L 4.14= / MPa E ci 24800= nig41010607.2 mm I =



T.Chhay NPIC


( )( )

mm D 510607.224800384

1440081.5510

4==Δ ¬cuHeRkam¦

b.

KNnacamber

EdlbNþalBIkMlaMgeRbkugRtaMgsMrab;FñwmTMrsamBaØEdleKelIktendon xøHenAcMnucmYyPaKbI CamYynwgcMNakp© itenAcMENkmYyPaKbIkNþalFñ wm mme 3641 = nigenAcugFñ wm02 =e .

( ) I E Le F

ci

i p 216

23 21=Δ

)( )

mm2010607.224800216

144003641016062310

23−=×= ¬eLIgelI¦

Camber

cugeRkayenAeBlepÞrKW mm15520 −=+−

¬eLIgelI¦c. PaBdabeRkambnÞúkeFV IkarbnÞúkeFV IkarBRgayes μ IsrubKW mkN W T /351615.1381.5 =++= nig MPa E c 27600= . PaBdabcuHeRkamEdlbNþalBIT W KW

( )( )

mm I E

LW

c

T w 27

10607.22760038414400355

3845

10

44===Δ ¬cuHeRkam¦

Camber EdlekItBIkMlaMgeRbkugRtaMg kN F 1344= nig MPa E c 27600= KW

( ) mm p 15

10607.2276002161440036410134423

1023 −=×=Δ ¬eLIgelI¦

PaBdabPøam²cugeRkayeRkambnÞ úkeFVIkarKWmm pw 121527 =−=Δ−Δ=Δ ¬cuHeRkam¦

8> KNnasMrab;kMlaMgkat;TTwgDesign for Shear

viFIKNnaedIm,IkMNt;EdkkMlaMgTTwg(shear reinforcement) enAkñ úgFñwmebtugeRbkugRtaMgesÞ IrEtdUcKñanwgviFIKNnasMrab;Fñ wmebtugGarem:. eKsn μt;sñameRbHedaysarkMlaMgkat;TTwg(shear crack) ekIteLIgtammM u o45 edayvas;BIG½kSrbs;Fñwm. CaTUeTA TMrg;énsñameRbHEdlTak;TgnwgkMlaMgkat;TTwgcMnYnBIrRbePT. mYyRbePTKWbNþalBI\T§ iBlEdlrYmpSMénkarBt; nigkMlaMgkat;TTwg³ sñameRbHcab;epþ ImeLIgedaysñameRbHedaykarBt; ehIybnÞab;mksñameRbHenHcab;epþ Imgak ehIyraltamTiseRTtEdlbNþalBI\T§iBlénkMlaMgTajGgát;RTUg. RbePTTIBIrCa web-shear cracking ekItmanenAkñ úgFñ wmEdlkugRtaMgTajem b¤kugRtaMgTajGgát;RTUg(principal tensile stress) enAkñ úgRTnugd¾tUcrbs;vaman



T.Chhay NPIC


tMélFMebIeRbobeFobnwgkugRtaMgBt;. eKRtUveRbIEdkkgedIm,IFana principal tensile stress enAkñ úgkrNITaMgBIr. eyIgnwgeRbIlkçNvinicä½ykñ úgkarKNnarbs; ACI sMrab;kMlaMgkat;TTwg.

k> viFIcMbg Basic Approach ACI design approach QrelItMrUvkarersIusþg;cugeRkay(ultimate strength requirement)

edayeRbIemKuNbnÞ úkEdl)anbgðajenAkñúgCMBUk 3. enAeBlEdlkMlaMgkat;TTwgemKuN uV FMCagBak; kNþalénnominal shear strength ( 2/cV φ ) eKmindak;EdkkgeT. . kMlaMgkat;TTwgKNnaEdlRtUvkaruV enARtg;muxkat;nImYy²minRtUvFMCagnominal design strength nV φ rbs;muxkat;EdlQrelI nominal shear capacity Edl)anBIkarbUkpSMénebtug nigEdkRTnug.

( ) scnu V V V V +≤≤ φ φ (19.49) Edl =cV nominal shear strength rbs;ebtug

= sV nominal shear capacity rbs;Edk=φ emKuNkat;bnßyersI usþg; 75.0=

enAeBlEdlkMlaMgkat;emKuNuV tUcCag2/uV φ eKRtUvkardak;EdkkMlaMgkat;Gb,brma.

x> ersIsþgkMlaMgkatEdlpþl edayebtugShear Strength Provided by Concrete ACI Code, Section 11.4 bgðajsmIkary:agsamBaØEdl)anBIkarBiesaFedIm,I)a:n;RbmaN

nominal shear capacity rbs;Ggát;ebtugeRbkugRtaMg EdlenAkñ úgGgát;enaHtendon mankMlaMgeRbkugRtaMg se f y:agtic%40 ersI usþg;Taj pu f ³

d b M d V

f V wu

ucc

+= 8.4'05.0 (ACI Code, Eq. 11.9) (19.50)

Edl uV nig =u M kMlaMgkat;emKuN nigm: Um:g;emKuNenARtg;muxkat;EdlBicarNa=wb TTwgrbs;RTnug

d ¬kñúgtYu

u

M d V ¦ =cMgayBIsrésrgkarsgát;eTATIRbCMuTMgn;rbs;EdkeRbkugRtaMg

d ¬enAkñ úgsmIkarciV b¤ cwV ¦ =tMélEdlFMCageKkñ úgcMeNamd xagelI nigh8.0 (ACI Code,Section 11.4.2)

kareRbIsmIkar19.50 RtUv)ankMNt;tamlkçxNÐxageRkam³



T.Chhay NPIC


!> 0.1/ ≤uu M d V ¬edIm,IKittMéltUcénuV nig u M ¦@> ) d b f V wcc '17.0≥ ¬ cV Gb,brma¦#> ) d b f V wcc '42.0≤ ¬ cV Gtibrma¦

karERbRbYlénshear capacity rbs;ebtugsMrab;Fñ wmebtugeRbkugRtaMgEdlRTedayTMrsamBaØrgnUvbnÞ úkBRgayes μ IRtUv)anbgðajenAkú ñgrUbTI 19>8. cMNaMfa eKcaM)ac;dak;EdkkMlaMgkat;GtibrmaEk,rTMr nigEk,rcMnucmYyPaKbYnénElVgEdl sV φ manxiteTArktMélGtibrma. pÞ úymkvij Fñ wmebtugGarem:RtUvkarEdkkMlaMgkat;TTwg ¬b¤KMlatGb,brma¦ EtEk,rTMrEdl sV φ mantMélGtibrma.

eBlxøH tMél cV EdlKNnaedaysmIkar19.50 GacmantMéltUc dUcenH ACI Code, Section

11.4.2

eGaynUvviFImü:ageTotsMrab;KNnacV

EdlKitBicarNaersI usþg;bEnßmrbs;ebtugenAkñ úgmuxkat;.



T.Chhay NPIC


enAkñ úgviFIenHcV CatMélEdltUcCageKkñúgcMeNamersI usþg;kMlaMgkat;rbs;ebtug ciV nig cwV ¬rUbTI 19>8¦.

ersI usþg;kMlaMgkat; ciV RtUv)anQrelIkarsn μt;faflexural-shear cracking ekIteLIgEk,rEpñkq¶aybMputrbs; flexural cracking EdlenAcMgayRbEhl2/d BIcMnucrgbnÞ úkénkarfycuHm: Um:g;.ACI

Code kMNt;fa ciV RtUv)anKNnadUcxageRkam³( )

++=

max'05.0

M M V

V d b f V cr id wcci (19.51)

b:uEnþvaminRtUvtUcCag ) d b f wc'14.0 Edl=d V

kMlaMgkat;TTwgEdlbNþalBIbnÞ úkefrK μanemKuN=iV kMlaMgkat;TTwgemKuNEdlbNþalBIbnÞ úkEdlGnuvtþBIxageRkA EdlekItmandMNalKña

CamYynwg max M =max M m:Um:g;emKuNGtibrmabNþalBIbnÞúkEdlGnuvtþxageRkA

=cr M m: Um:g;eRbH(cracking moment) eKGackMNt;cracking moment BIsmIkarxageRkam³

( )d pect cr f f f

y

I M −+= '5.0

(ACI Code, Eq. 11.11)

(19.52)

Edl = I m: Um:g;niclPaBEdlTb;Tl;nwgbnÞúkemKuNxageRkA

=t y cMgayBIG½kSTIRbCMuTMgn;én gross section EdlminKitsrésEdkeTAsrésrgkarTajeRbMput

= pe f ersI usþg;rgkarsgát;enAsrésxageRkAbMputrbs;muxkat;ebtugedaysarkMlaMgeRbkugRtaMgeRkaykMhatbg;

=d f kugRtaMgEdlbNþalBIbnÞúkefrK μanemKuNenAsrésxageRkAbMput EdlkugRtaMgTajbNþalBIbnÞúkxageRkA

Web-shear strength cwV KWQrelIsñameRbHedaykMlaMgkat;TTwgenAkñúgFñ wmEdlminEmneRbedaysarkarBt;eT. sñameRbHEbbenHekItmanenAEk,rTMrEdlmanRTnugtUc. ACI Code, Section

11.4.2 bBa¢ak;fa cwV RtUv)anKNnatamsmIkarxageRkam³) pw pcccw V d b f f V ++= 3.0'29.0 (19.53)

Edl = pV bgÁM úkM;laMgeRbkugRtaMgbBaÄrenARtg;muxkat;EdlBicarNa



T.Chhay NPIC


= pc f kugRtaMgsgát;enAkñúgebtug ¬eRkaykarGnuBaØatsMrab;kMhatbg;eRbkugRtaMg¦ enARtg;TIRbCM uTMgn;rbs;muxkat;EdlTb;Tl;nwgbnÞ úkEdlGnuvtþ b¤enARtg;TIRbsBVrvagRTnug nigsøabenAeBlEdlTIRbCMuTMgn;sß itenAkñ úgsøab

müa:gvijeTot eKGackMNt; cwV CakMlaMgkat;Edlbegá ItkugRtaMgTajem(principle tensile

stress) c f '33.0 enARtg;G½kSTIRbCM uTMgn;rbs;Ggát; b¤Rtg;RbsBVénsøab nigRTnugenAeBlEdlTIRbCM uTM-gn;sß itenAkñ úgsøab. eKGacsresrsmIkarG½kSdUcxageRkam³

22'33.0

22 pc pccwct

f f v f f −

+==

b¤ d b f

f f V wt

pct cw

+= 1 (19.54)

Edl ct f f '33.0= . enAeBlGnuvtþsmIkar19.51 nig19.53 b¤19.54 tMélrbs; d RtUv)anKitCacM-gaycenøaHsrésrgkarsgát; nigTIRbCMuTMgn;rbs; tendon eRbkugRtaMg b: uEnþvaminRtUvtUcCagh8.0 .

muxkat;eRKaHfñak;sMrab;kMlaMgkat;GtibrmaRtUv)anykRtg; 2/h BIépÞrbs;TMr. eKRtUveRbIEdkkMlaMgkat;dUcKñaRtg;muxkat;cenøaHTMr nigmuxkat;Rtg; 2/h .

K> EdkkMlaMgkat Shear Reinforcement eKRtUvKNnatMél sV edIm,IkMNt;RkLaépÞcaM)ac;rbs;EdkkMlaMgkat;

( ) scu V V V += φ (19.49) ( )cu s V V V φ

φ −= 1 (19.55)

sMrab;EdkkgbBaÄr

s

d f AV

yv s = (19.56)

nig d f sV

A y

sv = b¤

s

yv

V

d f A s = (19.57)

Edl =v A RkLaépÞrbs;EdkkgbBaÄr nig= s KMlatrbs;Edkkg. smIkarsMrab;EdkkgeRTtdUcKñanwgsmIkarEdl)anbgðajenAkñúgCMBUk 8.



T.Chhay NPIC


X> EdnkMNt Limitation

!> KMlatGtibrmamax s rbs;EdkkgminRtUvFMCag 4/3h b¤ cm60 . RbsinebI sV FMCag( ) d b f wc'4 enaHKMlatGtibrmaxagelIRtUv)ankat;bnßymkRtwmBak;kNþal (ACI Code, Section 11.5.4).

@> kMlaMgkat;Gtibrma sV minRtUvFMCag( ) d b f wc'8 . RbsinebImindUcenaHeT eKRtUvbegá InTMhMrbs;muxkat; (ACI Code, Section 11.5.6).

#> EdkkMlaMgkat;Gb,brmav A EdlTamTaredayACI Code KW

≤=

y

wc

y

wv

f

sb f

f

sb A '062.035.0

min (19.58)

enAeBlEdlkMlaMgeRbkugRtaMgRbsiT§PaB pu pe f f 4.0≥ EdkkMlaMgkat;Gb,brmav A Kw

w y

pu psv b

d d f

s f A A

80= (19.59)

eKmincaM)ac;ykkMBs;RbsiT§PaB hd 8.0< eT. CaTUeTA smIkar19.59 pþl;eGaynUvEdkkMlaMgkat;Gb,brmaFMCagkarpþl;eGayedaysmIkar19.58.

]TahrN_ 9>7³

sMrab;Fñ wmenAkñ úg]TahrN_ 19>4 cUrkMNt; nominal shear strength

nigEdkkMlaMgkat;caM)ac;. RtYtBinitümuxkat;Rtg; 2/h nig m3 BIcugrbs;Fñ wm. eRbI MPa f y 400= sMrab;EdkkMlaMgkat; nigbnÞ úkGefr mkN /4.19= .dMeNaHRsay³ !> sMrab;muxkat;enARtg;2/h

mmh

5002

10002

== BIxagcug

@> bnÞ úkBRgayes μ IemKuNenAelIFñ wm( ) mkN W u /8.534.196.115.1381.52.1 =×++=

uV enAcMgay ( ) kN h

5.3605.02.78.532

=−= kMNt; u M enARtg;muxkat; 2/h

( ) mkN M u .18725.08.535.02.78.53

2=−=

tMélrbs; d Rtg;muxkat; 2/h BIxagcug ¬rUbTI 19>6 b¦ KW



T.Chhay NPIC


( ) ( )mmd 516364

8.45.08.41581000 =−−−=

0.1995.0

187

516.05.360 ≤=×=

u

u

M d V

dUckarTamTarrbs; ACI Code

d b M

d V f V w

u

ucc

+= 8.4'05.0

( ) kN 6.39210516150995.08.43505.0 3 =×××+= − tMélGb,brmarbs; ( ) kN d b f V wcc 8.77105161503517.0'17.0 3 === − tMélGtibrmarbs; ( ) kN d b f V wcc 3.192105161503542.0'42.0 3 === − tMélGtibrmarbs; kN V c 3.192= manlkçN³lub.

#> viFIepSgeTotEdlbgðajedayACI Code KWfaeKGacyktMélcV CatMéltUcCageKkñ úgcMeNamciV nigcwV a. edayQrelI flexural-shear cracking strength

( )

++=

max'05.0

M M V

V d b f V cr id wcci

KNnatYnImYy²dac;edayELkBIKña( ) ( ) kN d b f wc 9.22105161503505.0'05.0 3 == − =d V kMlaMgkat;efrK μanemKuN ( )( ) kN 4.1295.02.715.1381.5 =−+=

=max M m: Um:g;emKuNGtibrma ¬elIkElgTMgn;rbs;Fñwm¦bnÞúkemKuN mkN /8.464.196.115.132.1 =×+×=

mkN M .6.16225.05.02.78.46

2

max =−×= ( ) kN V i 6.3135.02.78.46 =−= ( )d pec

t cr f f f

y I

M ++= '5.0 41010607.2 mm I = / mm yb 522=

= pe f kugRtaMgrgkarsgát;EdlbNþalBIkMlaMgeRbkugRtaMg I

Fey A F b+=

MPa8.610607.2

522381013441025.23101344

10

3

4

3=××+=



T.Chhay NPIC


=d f kugRtaMgbnÞúkefr I y M b D=

mkN M D .9.652

5.05.02.796.182

=−×= ( )

MPa f d 32.110607.2

105229.6510

6==

( ) mkN M cr .4.4121032.18.6355.0522

10607.2 610

=−+= − dUcenH kN V ci 7.947

6.1624.4126.3134.1299.22 =++=

ciV minRtUvtUcCag( ) ( ) kN d b f wc 1.64105161503514.0'14.0 3 == − b. ersI usþg;kMlaMgkat;EdlQrelI web-shear cracking KW ) pw pcccw V d b f f V ++= 3.0'29.0

MPa f pc 78.51025.23101344

4

3==

mmd 516= b¤ mmh 8008.0 = yk mmd 800=

kN V p 8.1012.13

11344 =×= Edl =2.13/1 slop rbs; tendon profile 4800/364=

MPa72.13529.0 = dUcenH( ) kN V cw 3.5168.1011080015078.53.072.1 3 =+×××+= −

c. edaysar cicw V V < dUcenH kN V cw 3.516= Canominal shear strength enARtg;muxkat; 2/h BIcugrbs;Fñ wm. kñúgkrNICaeRcIn cwV lubRtg; 2/h BITMr.

$> EdkRTnug (web reinforcement)

kN V u 5.360= kN V cw 2.3873.51675.0 =×=φ edaysar cwu V V φ < / 0= sV dUcenHeRbIEdkkgGb,brma. eRbIEdkkg10 DB .

22 1574/102 mm Av =×= π KMlatGtibrmaCatMélEdltUcCageKkñúgcMeNam

mmh s 75043

1 == mm s 6002 =

KNna3 s BIsmIkarEdkRTnugGb,brma



T.Chhay NPIC


w y

pu psv b

d d s

f

f A A ×××=

80min

150516

5164001725

801394

1573 s××=

mm s 5813 = yk mm s 5003 =

müa:gvijeTot

≤=

y

wc

y

wv f

sb f

f sb

A '062.035.0min 367.0'062.0 =c f

mmb

f A s

w

yv 1140150367.0

400157367.04 =

××==

dUcenHeyIgeRbI 500@10 DB .%> sMrab;muxkat;enAcMgaym3 BIxagcug viFIsaRsþkñ úgkarKNnaKWRsedogKñasMrab;muxkat;enARtg;2/h .

edayeRbIviFIEdlsMrYlrbs; ACI ( ) kN V u 22632.78.53 =−=

mkN M u .9202

332.78.532

=−×= ( ) ( )

mmd 7053648.4

38.41581000 =−−−= 0.1173.0920705.0226 <=×=

uu

M d V

( ) kN d b M

d V f V w

u

ucc 1.11910705150173.08.43505.08.4'05.0 3 =×××+=

+= −

kN V c 8.77min = nig kN V c 3.192max = dUcenH kN V c 1.119= ¬lub¦

^> eRbIsmIkar ACI Code edIm,IKNnaciV nigcwV . dMbUgKNnaciV ¬EdllubsMrab;muxkat;enH¦( ) ( ) kN d b f wc 3.31107051503505.0'05.0 3 ==

−

=d V ( )( ) kN 6.7932.715.1381.5 =−+

mkN M .3.8002

332.78.462

max =−×= ( ) kN V i 6.19632.78.46 =−=

MPa f pe 9.1110607.2

5225.2271013441025.23101344

10

3

4

3=××+=



T.Chhay NPIC


mkN M D .2.3242

332.796.182

=−×= ( )

MPa f d 5.610607.2105222.324

10

6

== ( ) mkN M cr .4.417105.69.11355.0

52210607.2 6

10=−+= −

dUcenH kN V ci 4.2133.8004.4176.1966.793.31 =++=

=minciV ( ) ( ) kN d b f wc 6.87107051503514.0'14.0 3 == − dUcnH kN V ci 4.213=

bnÞab;mkKNnacwV

MPa f pc 78.5= kN V p 8.101= ¬dUcelIkmun¦mmd 705= b¤ mmh 8008.0 =

yk mmd 800= dUcenH ( ) kN V cw 3.5168.1011080015078.53.072.1 3 =+×××+= − tMélrbs; cwV minmaneRKaHfñak;eT. enARtg;mYyPaKbYnénRbEvgElVg tMélkMlaMgkat;eRKaHfñak;K

ciV ¬rUbTI 19>8¦.&> KNnaEdkRTnugkN V u 226= kN V ci 1604.21375.0 =×=φ

( ) scu V V V += φ ( ) kN V s 88160226

75.01 =−=

Edkkg10 DB / 2157mm Av = . RtYtBinitüKMlatGtibrma mm s 500max = ¬dUcelIkmun¦

muxkat;EdlEdlRtUvkar 156705400

50010883

=××==d f sV A

y

sv

v A EdleRbIKW 22 156157 mmmm > . dUcenH yk 400@10 DB .



T.Chhay NPIC


9> KNnaCMhandMbUgénGgát;ebtugeRbmugRtaMgrgkarBt; Preliminary Design of Prestressed Concrete Flexural Members

k> rUbrag nigTMhM Shapes and Dimensions

kar)a:n;s μanTMhMrbs;muxkat;d¾RtwmRtUveFV IeGaykarKNnacMNayeBltic nigmins μ úKs μaj. dUcenH karKNnaCMhandMbUgmansar³sMxan;Nas; edIm,IFanafaTMhMmuxkat;manlkçN³smrmümunnwgcab epþ ImKNnalMGit.

enAkñ úgdMNak;kalKNnaCMhandMbUg CaFm μtaeKmanTinñn½yxøHEdlGacCYykñúgkareRCIserIsTMhM

d¾smRsb. ]TahrN_ m: Um:g;Bt;Edl)anBIbnÞ úkGnuvtþn_xageRkA kugRtaMgGnuBaØat nigTinñn½ysMrab;kMNt;kMhatbg;RtUv)andwg b¤RtUv)ankMNt;.rUbragrbs;muxkat;Ggát;ebtugeRbkugRtaMgGacCactuekaNEkg GkSrT GkSr I b¤RbGb;. kMBs;

srubrbs;muxkat; h RtUv)ankMNt;edaykarBicarNakMBs;rbs;lMh b¤k¾minRtUv)ankMNt;. kareRCIserIsTMhMrbs;muxkat;sMrab;karKNnaCMhandMbUgmandUcxageRkam ¬rUbTI 19>9¦³

!> kMBs;srubénmuxkat;KW 20/1=h eTA30/1 énRbEvgElVg. sMrab;karrgbnÞ úkF¶n; 20/ Lh = nigsMrab;karrgbnÞ úkRsal 30/ Lh = b¤ L D M M h += 6.43 Edlh KitCamm nig

KitCa mkN . .@> kMras;rbs;søabxagelIKW 8/hh f = eTA6/h .#> TTwgrbs;søabxagelIKW 5/2hb ≥ .$> kMras;rbs;RTnugKW mmbw 100≥ . CaTUeTA eKyk 10030/ += hbw .



T.Chhay NPIC


%> kareRCIserIs wb nig t KWERbRbYleTAtamkarBRgaytendon eRbkugRtaMg edayeFV Iy:agNarkSakMras;ebtugkarBarEdk.

^> RkLaépÞEdlsmrmürbs;muxkat;ebtugEdlRtUvkarKW h

M M m A L D

c 1450)( 2 += ¬Edl L D M M + KitCamkN . nig h KitCam ¦

sMrab;karKNnakñ úgkarGnuvtþ nigkarKNnaEdlmanlkçN³esdækic© ]sSahkm μpliteRKOgsMNg;BIebtug)anbegá ItnUvrUbrag nigTMhMbTdæanCaeRcIn EdlGñkKNnaGaceRCIserIsnUvGgát;NaEdlRtUvkar. taragénmuxkat;sþg;darmanenAkñ úgPCI Design Handbook . AASTHO k¾)anENnaMnUvgirder sþg;daredIm,IeRbIR)as;enAkñ úgsMNg;s<an ¬tarag 19>4¦.tarag 19>4 AASTHO Girders, ebtugTMgn;Fm μta

RbePT A ( )2.in

I ( )4.in

b y ( ).in

b Z ( )3.in

t Z ( )3.in

TMgn; ( ) ft lb /

Type II 369 50979 15.83 3220 2527 384

Type III 560 125390 20.27 6186 5070 593

Type IV 789 260741 24.73 10544 8908 822

x> kMlaMgeRbkugRtaMg nigRkLaépÞEdk Shapes and Dimensions

enAeBlEdleKeRCIserIsrUbrag kMBs; nigTMhMepSgeTotrbs;muxkat;rYcehIy eKGac)a:n;s μantM-élRbhak;RbEhlrbs;kMlaMgeRbkugRtaMg nigRkLaépÞrbs;EdkeRbkugRtaMg ps A . BIm: Um:g; couple xagkñúg m:Um:g;srubT M EdlekItBIbnÞúkefr nigbnÞ úkGefreFV Ikares μ InwgkMlaMgTajT KuNnwgédXñas; jd .



T.Chhay NPIC


( ) ( ) jd C jd T M T == ( ) jd f A M se psT = ( ) jd f

M A

se

T ps =

Edl ps A CaRkLaépÞEdkeRbkugRtaMg nig se f CakugRtaMgeRbkugRtaMgRbsiT§PaBeRkaykMhatbg;. tM-élrbs;édXñas; jd ERbRbYlBI h4.0 eTA h8.0 Edlkñ úgkarGnuvtþeKykvaenAkñúgcenøaHh6.0 eTA h7.0 .eKGaceRbItMélmFüm65.0 )an. dUcenH

( ) se

T ps f h

M A

65.0= (19.60)

ehIykMlaMgeRbkugRtaMgKW h

M f AT F

T se ps 65.0=== (19.61)

kMlaMgeRbkugRtaMgenAeBlepÞrKW η / F F i = Edlη CaemKuNénkMhatbg;GaRs½ynwgeBl.kMlaMgsgát; C enAelImuxkat;es μ InwgkMlaMgTajT ³

se ps f AT C == KitCakugRtaMg 1c

c

se ps

c f

A

f A

AC ==

Edl 1c f CakugRtaMgBRgayes μ IEdlsn μt;enAelImuxkat; sMrab;karKNnaCMhandMbUg eKsn μt;srésxageRkArbs;karEbgEckkugRtaMgragRtIekaNes μ Inwg

kugRtaMgsgát;GnuBaØatGtibrmaca f . dUcenHkugRtaMgmFümKW15.0 cca f f = . kugRtaMgsgát;GnuBaØatenAkñ úgebtugKW cca f f '45.0= . dUcenH eKGacsn μt;RkLaépÞebtugEdlRtUvkarc A BIkMlaMgTajT dUcxageRkam³

c

se ps

ca

se ps

c

se ps

cc f

f A

f

f A

f

f A

f T

A'225.05.011

==== (19.62)

( )( ) cT

caT

caT

cac f M f M f h M f T A '15.033.05.065.05.0 ==== (19.63)

karviPaKenHKWQrelIkarKNnasMrab;bnÞúkeFV Ikar minEmnsMrab;bnÞ úkemKuNeT. cMNakp© ite RtUv)anvas;BITIRbCM uTMgn;rbs;muxkat;eTATIRbCM uTMgn;rbs;EdkeRbkugRtaMg ehIyeKGacKNnaCatMélRbhak;RdUcxageRkam³

i

Db F

M K e += (19.64)

Edl b K Calower kern limit ehIy D M Cam:Um:g;Edl)anBIbnÞ úkefrK μanemKuN.



T.Chhay NPIC


10> kugRtaMgbø úkxagcugEnd-Block Stresses

k> Ggát rgkugRtaMgTajmun Pretensioned Members

dUcKñanwgEdkenAkñ úgGgát;ebtugGarem:EdlRtUvkarRbEvgbgáb;Cak;lak; enaHkMlaMgeRbkugRtaMgenAkñ úgGgát;ebtugrgkugRtaMgmunRtUv)anepÞreTAebtugedaykarbgáb; b¤edaykarf<k;cug b¤edaybnSMTaMgBIr.enAkñ úgGgát;rgkugRtaMgmun eKehARbEvgrbs;EdkeRbkugRtaMgEdlkMlaMgeRbkugRtaMgRtUv)anepÞreTAeb-tugfa RbEvgepÞr(transfer length) t l . eRkayeBlepÞr kugRtaMgenAkñ úgtendon Rtg;cugbMputrbs;Ggát; es μ InwgsUnü b:uEnþkugRtaMgenARtg;cMgayt l BIcugGgát;es μ InwgkMlaMgeRbkugRtaMgRbsiT§PaB pe f . transfer

length t l GaRs½ynwgTMhM nigRbePTrbs; tendon, lkçxNÐépÞb:H ersI usþg;ebtugc f ' kugRtaMg nigviFIénkarepÞrkMlaMg. kar)a:n;RbmaNt l EdlGacTTYlyk)anKWes μ Inwg50dgénGgát;p©itrbs;tendon b: uEnþ sMrab;single wires eKykt l es μ Inwg100dgénGgát;p©itrbs;wire.

edIm,IeGaykMlaMgTajenAkñ úgEdkeRbkugRtaMgbegáIt ultimate flexural strength eBjelj vaRtUvkarnUvRbEvgcMNg(bond length). eKalbMNgKWedIm,IkarBarkarrGilTUeTAmunnwgkar)ak;rbs;FñwmeRkamdesign strength eBjelj. RbEvgbgáb; d l (development length) es μ InwgplbUkrvag bond

length nigtransfer length. edayEp¥kelIkarBiesaFACI Code, Section 12.9.1 eGaynUvsmIkarxageRkamsMrab;KNnaRbEvgbgáb;énthree- or seven-wire pretensioning strand:

e se psd d f f l

−=

32 (19.65)

Edl = ps f kugRtaMgenAkñ úgEdkeRbkugRtaMgeRkamnominal strength = se f kugRtaMgRbsiT§PaBenAkñúgEdkeRbkugRtaMgeRkaykMhatbg; =bd nominal diameter rbs;wire b¤strand

enAkñúg pretensioned member kugRtaMgTajx<s;manenAtMbn;xagcug EdleKRtUvkardak;EdkBiess.EdkenHmanTMrg;CaEdkkgbBaÄrehIyRtUv)anBRgayes μ IkñúgKMlat 5/h Edlvas;BIxagcugrbs;Fñwm. CaTUeTA eKdak;EdkkgTImYyenAcMgaymm25 eTAmm75 BIxagcugFñ wm. vaCaKarGnuvtþFm μtakñ úgkarbEnßmnominal reinforcement sMrab;cMgayd Edlvas;BIcugrbs;Fñ wm. RkLaépÞrbs;EdkbBaÄrv A EdlRtUv)aneRbIenAtMbn;xagcugGacRtUv)anKNnaedaytMélRbhak;RbEhlBIsmIkarxageRkam³

t sa

iv l f

h F A 021.0= (19.66)

Edl = sa f kugRtaMgGnuBaØatenAkñ úgEdkkg ¬CaTUeTA MPa140 ¦ nig 50=d l dgénGgát;tendon



T.Chhay NPIC


]TarhN_ 9>8³kMNt;EdkkgcaM)ac;EdlRtUvkarenAtMbn;xagcugrbs;Fñ wmEdleGayenAkñ úg]TahrN_ 19>4.dMeNaHRsay³

kN F i 1606= / mmh 1000= / MPa f sa 140= / mml t 556125.1150 =×= dUcenH 2

3433

5561401000101606021.0 mm Av =

××=

mmh 200

51000

5==

eRbIEdkkgbiTCit 10 DB cMnYnbYnkg EdlEdkkgTImYysßitenAcMgaymm200 BITMrv

A

¬Edldak;¦26284157 mm=×=

x> GgátrgkugRtaMgTajeRkay Posttensioned Members

enAkñúg posttensioned concrete member kMlaMgeRbkugRtaMgRtUv)anepÞrBItendon ¬sMrab; bonded nig unbonded tendon¦ eTAebtugRtg;cugrbs;Ggát;edayspecial anchorage device. enAkñ úganchorage zone Rtg;cugrbs;Ggát; kugRtaMgsgát;mantMélx<s;Nas; ehIytransverse tensile stress



T.Chhay NPIC

ekItman dUcbgðajenAkñ úgrUbTI 19>10. enAkñ úgkarGnuvtþ eKeXIjfaRbEvgénanchorage zone minFM CagkMBs;rbs;cugGgát;eT RbsinebImindUcenaHeT sßanPaBénkugRtaMgenAkñúgtMbn;enaHnwgmanlkçN³s μ úKs μaj.

karBRgaykugRtaMgEdl)anBI tendon mYyenAkñ úganchorage zone RtUv)anbgðajenAkñúgrUbTI 19>11. enARtg;cMgayh BImuxkat;xagcug eKsn μt;kugRtaMgBRgayes μ IelImuxkat;TaMgmUl. edayKitExSkMlaMg(trajectories) CaFatumYy²EdlmanGMeBICacurved strut enaHExSkMlaMgmanGMeBItamTisedkeTArkExSG½kSrbs;Fñ wmenAkñ úgtMbn; edaybegá ItCakugRtaMgsgát;. enAkñ úgtMbn; B ExSkMlaMg)anbEgVrTis ehIy strut manGMeBIecjeRkAEdlbegá ItCakugRtaMgTaj. enAkñ úgtMbn;C strut esÞ IrEtRtg;edaybegáItkarBRgaykugRtaMges μ I.

EdkBRgwgEdlRtUvkarsMrab; anchorage zone xagcugrbs; posttentioned member CaTUeTApSMeLIgedayRkLaénEdkbBaÄr nigEdkedkEdlmanKMlatCit²KñaeBjRbEvgénbø úkxagcugedIm,ITb;Tl;nwgkugRtaMgpÞ úH(bursting stress) nigkugRtaMgTaj. CakarGnuvtþTUeTAeKmineGayKMlatEdkFMCagmm75

enAkñ úgTisnImYy²eT ehIyminRtUvdak;EdkenAcMgayFMCagmm50 BIépÞxagkñúgrbs; bearing plate eT.

បេតុងពង្រឹងដោយដែក 19 xix-introduction-to-prestressed-concrete

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