Post on 03-Jun-2018
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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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 561
sinebIkugRtaMgsgát;EdlGnuvtþdMbUgtUcCagkugRtaMgTajenAsrésEpñkxageRkambMput enaHsrésenAEpñkxageRkamenHrgkarTaj ÉsrésEpñkxagelIbMputrgkarsgát;.
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 562
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 563
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 564
( )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 −−
×
×±
×
−=
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 565
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 ¦.
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 566
$>sMrab;kugRtaMgEdlbNþalBIeRbkugRtaMgcakp© itRtg;cMNakp© itGtibrmasn μt;facMNakp©itGtibrmasMrab;muxkat;enHKW cme 15= .m:Um:g;Bt;EdlekItedaysarkMlaMgeRbkugRtaMgcakp©itK W mkN Pe .8.16915.01132 =×=
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 567
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 568
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 569
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©.
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 570
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= .
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 571
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.
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 572
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 573
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;.
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 574
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 575
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;
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 576
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 577
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 578
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 −
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 579
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.
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 580
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;.
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 581
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=
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 582
= 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 −− =
×
×+=
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 583
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 584
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
=+
=
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 585
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 586
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.
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 587
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 588
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.
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 589
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)
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 590
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;.
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 591
]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.
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 592
@> 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=×+×+×=
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 593
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 =−=
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 594
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.
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 595
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
≥−+−≥ −
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 596
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 597
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 598
( )
( )
( ) +
+−
−
+=
−
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 =×=
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 599
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 600
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-
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 601
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.
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 602
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 =
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 603
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)
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 604
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 605
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.
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 606
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.
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 607
]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 =
−+
−= −−
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 608
( ) 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.
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 609
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 610
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 =
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 611
( )( )
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 612
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 613
!> 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;.
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 614
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 615
= 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.
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 616
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 617
( ) ( )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=××+=
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 618
=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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 619
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=××+=
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 620
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 .
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 621
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 .
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 622
%> 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 .
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 623
( ) ( ) 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.
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 624
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
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T.Chhay NPIC
esckþ IENnaMBIebtugeRbkugRtaMg 625
]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
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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.