Khmer Prestressed Concrete - Unknown

NPIC

eKal KMnit 1

I. KMniteKal Basic Concepts

1> esckIepIm Introduction ebtugmanersIusg;xaMgkgkarsgt; b:uEnmanersIusg;exSaykgkarTaj EdlenAcenaHBI %8 eTA

%12 nersIusg;sgt;. edaysarersIusg;rgkarTajtUcEbbenH sameRbHEdlekItBIkarBt;nwgekIt manenAdMNak;kaldMbUgnkardak;bnk. edIm,Ikat;bny bkarBarmineGaymansameRbHenH eKRtUv GnuvtkMlaMgcMpit bcakpittamTisbeNayrbs;Ggt;eRKOgbgM. dUcenHkMlaMgenH)anbegInersIusg; kgkarBt; ersIusg;kgkarkat; nigersIusg;kgkarrmYlrbs;muxkat;. bnab;mkmuxkat;GaceFVIkarCa lkNeGLasic ehIymuxkat;manersIusg;rgkarsgt;esIrEteBjenAeBlEdlbnkTaMgGs;manGMeBI mkelIeRKOgbgM.

T.Chhay

Basic Concept 2

kMlaMgEdleKGnuvttamTisbeNayenHRtUv)aneKeGayeQ aHfa kMlaMgeRbkugRtaMg (prestres-sing force). kMlaMgeRbkugRtaMgCakMlaMgsgt;tamTisbeNayrbs;Ggt;EdleFVIeGaymuxkat;rg kugRtaMgmunnwgGgt;rgbnkefr nigbnkGefr. eKkMNt;RbePTkMlaMgeRbkugRtaMg nigGaMgtg;sIuetrbs; vaedayQrelIRbePTnsMNg; RbEvgElVg nigPaBrlas; (slenderness). rUbTI 1>1 bgajBITMrg;rbs; kMlaMgeRbkugRtaMgBIrRbePT.

k> eRbobeFobCamYynwgebtugGarem: Comparison with Reinforced Concrete EdkenAkgebtugGarem:min)anGnuvtkMlaMgrbs;vaeTAelIGgt;eT EdlpyBIGMeBIrbs;EdkeRbkug RtaMg. enAeBlEdlkugRtaMgTajedaykarBt;FMCagersIusg;Tajrbs;ebtug ebtugeRbkugRtaMgcab;epIm eFVIkarCaebtugGarem:.

edayRKb;RKgbrimaNrbs;kMlaMgeRbkugRtaMg eKGaceFVIrcnasm

NPIC

eKal KMnit 3

long-term shrinkage nig creep. sMrab;s Rbvtirbs;ebtugeRbkugRtaMg Historical Development of Prestressing ebtugeRbkugRtaMgminEmnCabeckeTsf IeT enAqaM 1872 visVkr P. H. Jackson EdlmkBI California TTYl)annUvnIybRttkkmsMrab;karrkeXIjRbBneRbkugRtaMgedayeRbI tie rod edIm,I begItFwm bFBIdMubkdac;BIKa emIlrUbTI 1>1 a. enAqaM 1888 visVkrsBaatiGaLWm:g; C. W. Doehring TTYl)annIybRttkkmsMrab;kareRbIRbBneRbkugRtaMgenAkgkMraledayeRbI metal wire. b:uEnsMrab;kareRbIR)as;elIkdMbUgenHminsUvTTYl)aneCaKCyeT edaysarkMhatbg;eRbkugRtaMgGaRsy nwgeBl. eRkaymkenAedImstvtSTI20 J. Lund mkBI Norway nig G.R. Steiner mkBIshrd)an BayamedIm,IedaHRsaybBaaenH EtminTTYl)anlTpleT. kgGMLgeBldyUrCamYynwgkarvivDdtictYcedaysarminTan;rkeXIjnUvEdlersIusg;x esckIepIm Introduction kMlaMgeRbkugRtaMg P EdlbMeBjlkxNragFrNImaRt niglkxNdak;bnkrbs;Ggt;RtUv)an kMNt;edayeRbIeKalkarN_emkanik nigTMnak;TMngkugRtaMg-sac;lUteFob rUbTI 1>2. eBlxHeKRtUv karsnt;eGayFwmebtugeRbkugRtaMgCa homogeneous nigeGLasic.

T.Chhay

Basic Concept 4

enAkgrUbTI 1>2 (a) bgajBIFwmctuekaNTMrsamBargnUvkMlaMgeRbkugRtaMgcMpit P . muxkat; FwmrgnUvkugRtaMgsgt;es IKW

cAPf = (1.1)

Edl bdAc = CaRkLaprbs;muxkat;FwmEdlmanTTwg b nigkMBs;srub d . sBaadkRtUv)aneRbI sMrab;kugRtaMg bkMlaMgsgt; nigsBaabUksMrab;kugRtaMg bkMlaMgTaj. RbsinebImankMlaMgTTwgGkS (transverse load) GnuvteTAelIFwm enaHkugRtaMgEdl)anm:Um:g; Gtibrma M EdlekItmanenAkNalElVgKW

gc

tIMc

APf = (1.2a)

NPIC

eKal KMnit 5

nig gc

b IMc

APf += (1.2b)

Edl =tf kugRtaMgenAsrsxagelIbMput =bf kugRtaMgenAsrsxageRkambMput hc

21= sMrab;muxkat;ctuekaN

=gI m:Um:g;niclPaBrbs;muxkat;TaMgmUl sMrab;muxkat;ctuekaN 123bh=

BIrUbTI 1>2 (b) eyIgeXIjfaersIusg;rgkarsgt;rbs;FwmedIm,ITb;nwgkMlaMgxageRkARtUv)ankat; bnyedaykMlaMgeRbkugRtaMgcMpit. edIm,Ikat;bnykugRtaMgTajenAsrsxagelIbMput eKRtUvdak; prestressing tendon BIeRkamGkSNWtsMrab;muxkat;kNalElVg rUbTI 1>2 (c) nig (d) . RbsinebIeK dak; tendon enAcMNakpit eBITIRbCMuTMgn;rbs;muxkat; eKTTYl)anm:Um:g; Pe eFobnwgGkS cgc ehIy kugRtaMgenAkNalElVgkayCa

ggc

tIMc

IPec

APf += (1.3a)

nig ggc

b IMc

IPec

APf += (1.3b)

edaysarmuxkat;enARtg;TMrsamBaminrgm:Um:g;Edl)anBIbnkTTwgGkSxageRkA enaHsrsxag elIbMputrbs;muxkat;GacrgkugRtaMgTajFMedaysarkMlaMgeRbkugRtaMgcakpit. edIm,IkMritkugRtaMgenH eKRtUvdak; prestressing tendon CamYynwgcMNakpittUcCagcMNakpitenAkNalElVg bGacsitenAelI GkS cgc.

x> Basic Concept Method enAkg basic concept method eKkMNt;kugRtaMgnsrsxageRkAbMputrbs;muxkat;ebtug eRbkugRtaMgedaypal;BIkMlaMgeRbkugRtaMgEdlGnuvttambeNayGkS nigbnkTTwgGkS. RbsinebI iP CakMlaMgeRbkugRtaMgedImmunkMhatbg; nig eP CakMlaMg eRbkugRtaMgRbsiTPaBeRkaykMhatbg; enaH

i

ePP=

Edl = emKuNeRbkugRtaMgenAsl; (residual prestress factor). edayCMnYs cg AIr /2 = Edl r CakaMniclPaBnmuxkat;TaMgmUl enaHeyIg)ansmIkardUcxageRkam

a. manEtkMlaMgeRbkugRtaMg

T.Chhay

Basic Concept 6

= 21 rec

APf tc

it (1.4a)

+= 21 rec

APf bc

ib (1.4b)

Edl tc nig bc CacMgayBITIRbCMuTMgn;rbs;muxkat; (GkS cgc ) eTAsrsxagelIbMput nig xageRkambMput erogKa.

b. kMlaMgeRbkugRtaMgrYmnwgTMgn;pal; RbsinebITMgn;pal;rbs;FwmbegItm:Um:g; DM enARtg;muxkat;EdlBicarNa smIkar 1.4a nig 1.4b kayCa tDt

c

it

SM

rec

APf

= 21 (1.5a)

b

Db

c

ib S

Mrec

APf +

+= 21 (1.5b)

Edl tS nig bS Cam:UDulnmuxkat;sMrab;srsxagelIbMput nigxageRkambMput erogKa.

rUbTI 1>3 bgajBIKngrbs;EdkeRbkugRtaMg. rUbTI 1>3 (a) bgajBIKngrbs;EdkeRbkugRtaMg kgTMrg; harped EdlRtUv)aneKeRbIenAkg pretensioned beam nigsMrab;bnkTTwkGkSmanGMeBIcMcMnuc. rUbTI 1>3 (b) bgajBIKngrbs;EdkeRbkugRtaMgkgTMrg; draped EdlRtUv)aneKeRbIenAkg post-tensioning beam.

NPIC

eKal KMnit 7

bnab;BIkarsagsg; nigkartMeLIgkMralehIy eRKOgbgMrgbnkGefrEdlbegIt)anCam:Um:g; sM . CaTUeTA GaMgtg;sIueteBjeljrbs;bnkenHekItmanbnab;BIsMNg;RtUv)ansagsg;rYcral; ehIykMhat

T.Chhay

Basic Concept 8

bg;GaRsynwgeBlkgebtugeRbkugRtaMgekIteLIgrYcehIy. dUcenH kMlaMgeRbkugRtaMgCakMlaMgeRbkug RtaMgRbsiTPaB eP . RbsinebIm:Um:g;srubEdlbNalBIbnkTMnajCa TM enaH LSDDT MMMM ++= (1.6) Edl =DM m:Um:g;EdlbNalBITMgn;pal; =SDM m:Um:g;EdlbNalBIbnkefr =LM m:Um:g;EdlbNalBIbnlGefr ehIysmIkar 1.5 nwgkayCa tTt

c

et

SM

rec

APf

= 21 (1.7a)

b

Tb

c

eb S

Mrec

APf +

+= 21 (1.7b)

rUbTI 1.4 bgajBIKMrUnkarBRgaykugRtaMgenAelImuxkat;mansabeRKaHfak;rbs;Ggt;eRbkug RtaMg. eKminGnuBaateGaykugRtaMgTajenAkgebtugenAelIsrsxageRkAbMputrbs;muxkat;FMCagkug RtaMgGnuBaatGtibrmaEdleGayedaybTdaneT dUcCa ct ff '5.0= enAkg ACI Code. Rb sinebIvaFMCagtMlGnuBaat eKRtUvdak;EdkBRgwgminEmneRbkugRtaMgeTAtamsmamaRtedIm,ITb;Tl;nwg kMlaMgTajsrubEdlmankgeKalbMNgRKb;RKgsameRbHenAdMNak;kalrgbnkeFIVkar.

K> C-Line Method sMrab; C-Line method b line-of-pressure concept b thrust concept FwmebtugeRbkugRtaMg RtUv)aneKsn t;CaFwmebtugsuTeGLasic ehIyeKviPaKvaedayeRbIeKalkarN_eKalrbs;saTic. eKcat; TukkMlaMgeRbkugRtaMgCakMlaMgsgt;xageRkA CamYynwgkMlaMgTajefr T enAkg tendon. eKeRbIsmI-karlMnwg 0=H nig 0=M edIm,IrkSalMnwgrbs;muxkat;. rUbTI 1>5 bgajBIkareRbobeFobExSskmnkMlaMgsgt; C nigkMlaMgTaj T enAkgebtug Garem: nigebtugeRbkugRtaMg. dXas; a sMrab;ebtugeRbkugRtaMgmantMlefr EtvaERbRbYlBIsUnenA eBlrgeRbkugRtaMgeTAtMlGtibrmaenAeBlEdlvarg bnkxageRkAeBjeljsMrab;ebtugeRbkugRtaMg. BIdaRkamGgesrIrbs;kMNt;FwmEdlbgajenAkgrUbTI 1>6 eyIg)an TaCaM == (1.8) eae =' (1.9a) edaysar TC = / TMa /= eK)an

NPIC

eKal KMnit 9

e

TMe =' (1.9b)

BIrUbeyIg)an

g

t

c

tIcCe

ACf '= (1.10a)

g

b

cb I

cCeACf '+= (1.10b)

b:uEnenAkg tendon kMlaMg T es InwgkMlaMgeRbkugRtaMg eP dUcenH

g

te

c

etIceP

APf '= (1.11a)

g

be

c

eb I

cePAPf '+= (1.11b)

T.Chhay

Basic Concept 10

edaysar 2rAI cc = enaHeyIgGacsresrsmIkar 1.11a nig b dUcxageRkam

+= 2

'1rce

APf tc

et (1.12a)

= 2'1rce

APf bc

eb (1.12b)

smIkar 1.12 a nig b nigsmIkar 1.7 a nig b RtUveGaytMlkugRtaMgenAsrsxageRkAdUcKa.

X> Load-Balancing Method eKGacKNna nigviPaKFwmebtugeRbkugRtaMgedayeRbI load-balancing method EdlbegIt eday Lin. viFIenHEpkelIkareRbIR)as;kMlaMgtamTisQrrbs;EdkeRbkugRtaMgEdlmanTMrg; draped b harped edIm,ITb;Tl;nwgbnkTMnajEdlmanGMeBIelIGgt;. rUbTI 1>7 bgajBIkMlaMglMnwg (balancing forces) sMrab;FwmebtugebkugRtaMgEdlmanEdkeRbkugRtaMgTMrg; draped nig harped. kMlaMglMnwg Rbtikm R es InwgbgMkMlaMgbBarrbs;kMlaMgeRbkugRtaMg P . bgMkMlaMgedkrbs;kMlaMgeRbkugRtaMg P mantMles InwgkMlaMg P eBjEtmgsMrab;karKNnakugRtaMgsrsxageRkArbs;ebtugEdlenAkNal ElVgsMrab;FwmTMrsamBaEdlmanRbEvgEvg. sMrab;muxkat;dTeTot eKeRbIbgMkMlaMgedkrbs;kMlaMg P Cak;Esg.

NPIC

eKal KMnit 11

A. Loading-Balancing Distributed Loads and Parabolic Tendon Profile BIrUbTI 1>8 eyIgGacsresrGnuKmn_)a:ra:bUldUcxageRkamsMrab;tMNageGayTMrg;rbs;

tendon

yCBxAx =++2 (1.13)

sMrab; 0=x eyIgman 0=y dUcenH 0=C ehIy 0=

dxdy dUcenH 0=B

sMrab; 2/lx = eyIg)an ay = dUcenH 24laA =

eyIgman 22

xyTq

= (1.14) eFVIDIepr:g;EslBIrdgeTAelIsmIkar 1.13 ehIyCMnYs 22 / xy eTAkgsmIkar 1.14 eyIg)an

22824lTa

laTq == (1.15a)

b a

qlT8

2= (1.15b)

8

2qlTa = (1.15c) dUcenH RbsibebI tendon manTMrg;)a:ra:bUlehIykMlaMgeRbkugRtaMgRtUv)ansMKal;eday P enaH balanced-load Edl)anBIsmIkar 1.15a kayCa

28lPawb = (1.16)

BIrUbTI 1>9 bnkTTwgGkS bw BIrEdlmantMles IKa TisedApyKa)anTUTat;KaGs; dUcenHmin mankugRtaMgBt;ekIteLIgeT. edaysar CT = dUcenHeyIgGacCMnYs C eTAkg T )an. eday sarK anm:Um:g;Bt; FwmenArkSaPaBRtg; edayminmanragekag bptenApxagelIbMput. kugRtaMgsrsxageRkAbMputrbs;ebtugeBjkMBs;rbs;muxkat;EdlenAkNalElVgKW

T.Chhay

Basic Concept 12

cc

tb A

CAPf == ' (1.17)

kugRtaMgenHmantMlefr ehIykMlaMg cos' PP = . rUbTI 1>10 bgajBIplbUkkugRtaMgedIm,I TTYl)an net stress. cMNaMfakMlaMgeRbkugRtaMgenAkg load-balancing method RtUvmanGMeBIenARtg; TIRbCMuTMgn; (cgc) rbs;muxkat;Rtg;TMrsMrab;FwmTMrsamBa nigenARtg; cgc rbs;muxkat;cugTMenrrbs;Fwm cantilever. eKRtUvdak;lkxNEbbenHedIm,IkarBarm:Um:g;EdlKanlMnwgcakpit (eccentric unbalanced moment).

enAeBlEdlbnkTTwgGkSFMCag balancing load bw dUcenHbnkKanlMnwgbEnm (additional unbalanced load) ubw begIt)anm:Um:g; 8/2lwM ubub = enAkNalElVg. kugRtaMgsrsxageRkA EdlRtUvKanwgkrNIenHRtg;kNalElVgkayCa

NPIC

eKal KMnit 13

g

ub

c

tb I

cMAPf m'= (1.18)

eKGacsresrsmIkar 1.18 CaBIrsmIkardUcxageRkam tub

c

t

SM

APf = ' (1.19a)

nig b

ub

cb S

MAPf += ' (1.19b)

smIkar 1.19 nwgeGaytMlkugRtaMgsrsdUcKanwgsmIkar 1.12 nigsmIkar 1.7 Edr. cMNaMfa eKyk PP =' enARtg;muxkat;kNalElVgeRBaHkMlaMgeRbkugRtaMgmanTisedkenARtg;muxkat; enaH Edl 0= . 4> Computation of Fiber Stresses in a Prestressed Beam by the Basic Method ]TaheN_ 1>1 rUbTI 1>11 bgajBIragFrNImaRtrbs;Fwm pretensioned dpble T 10LDT24 EdlRT edayTMrsamBamanRbEvg ( )mft 51.1964 . vargnUvbnkTMnajefr SDW nigbnkGefr LW Edlmanpl bnksrub ( )mkNplf /13.6420 . kMlaMgeRbkugRtaMgedImmunkMhatbg;KW ksiff pupi 18970.0 = ( )MPa1300 . ehIykMlaMgeRbkugRtaMgeRkaykMhatbg;KW ( )MPaksif pe 1034150= . KNnakugRtaMg srsxageRkAbMputenAkNalElVgEdlbNalmkBI

a. kMlaMgeRbkugRtaMgedImTaMgmUl nigKanbnkTMnajxageRkA b. lkxNbnkeFVIkarcugeRkayenAeBlEdlkMhatbg;eRbkugRtaMgekItmanehIy. kugRtaMgGnuBaatmandUcxageRkam

ksif c 6' = TMgn;Rsal ( )MPa4.41 ksif pu 270= stress relieved ( ) =MPa1860 specified tensile strength rbs; tendon

( ) == MPaksif py 1520220 specified yield strength rbs; tendons ( ) === MPapsiff ct 4.6930'12 kugRtaMgTajGnuBaatGtibrmaenAkgebtug

( ) == MPaksif ci 1.338.4' kugRtaMgsgt;rbs;ebtugenAeBlrgeRbkugRtaMgedIm ( ) === MPaksiff cici 9.1988.2'6.0 kugRtaMgGnuBaatGtibrmaenAeBlrgeRbkugRtaMgedIm

== cc ff '45.0 kugRtaMgGnuBaatGtibrmaenAkgebtugenAeBleFVIkar sn t;eRbI seven-wire-strand Ggt;pit ( )mmin 7.12.5.0 cMnYndb;. ( )22 2897.449 cminAc =

T.Chhay

Basic Concept 14

( )44 935346.22469 cminI g = ( )222 323.04.50/ cminAIr cg == ( )mmincb 451.77.17=

( )mminct 158.23.6= ( )mminec 375.77.14=

( )mminee 4.197.77.7= ( )33 20713.1264 cminSb = ( )33 59108.3607 cminS t =

( )mkNplfWD /24.5359=

dMeNaHRsay

a. lkxNdMbUgenAeBlrgeRbkugRtaMgedIm ( )22 990.53.1153.010 mminAps ==

( )kNlbfAP pipsi 128728917018900053.1 === ( )kNlbPe 102022950015000053.1 ==

NPIC

eKal KMnit 15

m:Um:g;Edl)anBIbnkpal;enAkNalElVg ( ) ( )mkNlbinlWM DD .249.2205696128

643598

22===

BIsmIkar 1.5 nig 1.7 eyIg)an tDt

c

it

SM

rec

APf

= 21

36072205696

04.5023.677.141

449289170

=

( )( )MPaCpsi 5.0705.6113.540 +=

b

Db

c

ib S

Mrec

APf +

+= 21

12642205696

04.5077.1777.141

440289170 +

+=

( )( )MPaCpsi 8.15227717451.4022 += psifci 2880= O.K.

b. lkxNcugeRkayenAeBlrgbnkeFVIkar m:Um:g;kNalElVgbNalmkBIbnkbEnmefr nigGefrKW ( ) lbinMM LSD ==+ .2580480128

64420 2 m:Um:g;srub ( )mkNlbinMT .541.478617625804802205696 =+= kugRtaMgenAsrsxagelIbMput tTt

c

et

SM

rec

APf

= 21

36074786176

04.5023.677.141

449229500

=

( )( )MPaCpsi 3.68981327429 =+= psifc 2700600045.0 ==< O.K.

kugRtaMgenAsrsxagelIbMput

b

Tb

c

eb S

Mrec

APf +

+= 21

12644786176

04.5077.1777.141

449229500 +

+=

( )( )MPaTpsi 1.459437863192 +=+= psiff ct 930'12 ==< O.K.

T.Chhay

Basic Concept 16

5> C-Line Computation of Fiber Stresses ]TahrN_ 1>2 edaHRsay]TahrN_ 1>1 sMrab;lkxNcugeRkayeBlbnkeFVIkar edayeRbI C-line method. dMeNaHRsay lbPe 229500= lbinMT = .4786176 .85.20

2295004786176 in

PMae

T ===

.08.677.1485.20' ineae === BIsmIkar 1.12

+= 2

'1rce

APf tc

et

( )Cpsi89804.50

23.608.61449

229500 =

+=

= 2'1rce

APf bc

eb

( )Tpsi59404.50

77.1708.61449

229500 +=

=

6> Load-Balancing Computation of Fiber Stresses ]TahrN_ 1>3 edaHRsay]TahrN_ 1>1 sMrab;lkxNcugeRkayeBlbnkeFVIkareRkayeBlkMhat bg; edayeRbI load-balancing method. dMeNaHRsay lbPP e 229500' == enAkNalElVg enAkNalElVg ftinea c 231.1.77.14 === eyIgman balancing load ( )mkNplf

lPaWb /1.855264

231.122950088 22 ===

dUcenHRbsinebIbnkTMnajsrubmanRtwmEt plf552 FwmnwgrgkugRtaMg cAP /' RbsinebIFwm man tendon TMrg;)a:ra:bUledayminmancMNakpitenAelITMr. enHedaysarEtbnkTMnajRtUv)an rkSalMnwgeday tendon enAkNalElVg. dUcenH bnkTMnajsrubEdlFwmRtUvTTYl LSDD WWW ++=

plf779420359 =+=

NPIC

eKal KMnit 17

plfWub 227552779 == ( ) ( ) lbinlWM ubub === .1394688128

642278

22

BIsmIkar 1.19 eyIg)an

36071394688

449229500' == tub

c

t

SM

APf

( )Cpsi898387511 ==

12641394688

449229500' +=+=

b

ub

cb S

MAPf

( )Tpsi5941104511 += psift 930= O.K.

T.Chhay

Materials and Systems for Prestressing 18

II. sMPar nigRbBnkMlaMgeRbkugRtaMg

Materials and Systems for Prestressing

1> ebtug Concrete k> esckIepIm Introduction sMrab;Ggt;ebtugeRbkugRtaMg ebtugersIusg;x )a:ra:Em:RtEdlCH\TiBldl;KuNPaBrbs;ebtug Parameters Affecting the Quality Concrete ersIusg; nigPaBFn;CaKuNPaBcMbgBIrEdlmansarsMxan;enAkgeRKOgbgMebtugeRbkugRtaMg.

\TiBlnkarxUcKuNPaBebtugryeBlEvgGackat;bnykMlaMgeRbkugRtaMgy:agelOn nignaMeGay eRKOgbgM)ak;edaymin)anrMBwgTuk. dUcenH eKRtUvmanviFankarht;ct;CaeRcInedIm,IRKb;RKg nigFanaKuN PaBrbs;ebtugenAkgdMNak;kalnkarplit dMNak;kalnkarsagsg; kdUcCadMNak;kaltMEhTaM. rUbTI 2>1 bgajBIktaCaeRcInEdlGaceGayeyIgTTYl)anebtugEdlmanKuNPaBl.

K> lkNnebtugEdlkkrwg Properties of Hardened Concrete eKEcklkNemkanicrbs;ebtugEdlkkrwgCaBIrRbePTKW lkNxN blkNryeBlxI

(short-term or instantaneous properties) niglkNryeBlEvg (long-term properties). lkN ryeBlxIrYmmanersIusg;sgt; ersIusg;Taj ersIusg;kat; nigPaBrwgRkaj (stiffness) Edlvas;eday m:UDuleGLasic. lkNryeBlEvgman creep nigkarrYjmaD (shrinkage).

!> ersIusg;sgt; Compressive Strength

GaRsynwgRbePTrbs;TWkfaMKImI lkNrbs;fbMEbk ryeBlnkarEcTaMebtug nigKuNPaBn karEfTaMebtug eKGacTTYl)anersIusg;sgt;rbs;ebtugrhUtdl; ( )MPaksi 13820 bFMCagenH. CaTU

NPIC

sMPar nigRbBnkMlaMgeRbkugRtaMg 19

eTAersIusg;sgt;rbs;ebtugEdlplitedaylkNesdkicCamYynwgfbMEbkFm tasitenAcenaH ( )MPaksi 284 eTA ( )MPaksi 8312 . ebtugEdleKeRbIPaKeRcInmanersIusg;sgt; ( )MPaksi 426 .

ersIusg;sgt; cf ' )anmkBIsMNakKMrUsIuLaMgsg;darTMhM cmcm 3015 EdlEfTaMeRkamlkxN BiesaFn_sg;dar nigRtUv)aneFVIBiesaFn_edayrgkMlaMgsgt;enAGayu 28 f. sg;darEdleKeRbIsMrab;Bi-esaFn_ersIusg;sgt;KW ASTM C-39. ersIusg;rbs;ebtugenAkgeRKOgbgMCak;EsgmindUcKanwgersIusg; rbs;sMNakKMrUsIuLaMgedaysarlkxNnkarbgab; niglkxNnkarEfTaMxusKa.

T.Chhay


sMrab;karBiesaFersIusg; ACI Code kMNt;eRbInUvmFmPaKrbs;sMNakKMrUsIuLaMgBIrnsMPar dUcKa ehIyRtUv)aneFVIkarBiesaFenAGayudUcKaEdlCaTUeTAenAGayu 28 f. sMrab;karBiesaFEdlman lkNjwkjab; kUdkMNt;faersIusg;rbs;cMNat;fak;ebtugnImYybMeBjlkxN)ankgkrNI (1) mFmPaKnsMnMusMNakKMrUTaMgGs;nkarBiesaFbIdgCab;RtUvFMCag bes Inwg cf ' EdlRtUvkar nig (2) K ankarBiesaFsMNakKMrUmgNa mFmPaKnsIuLaMgBIr tUcCag cf ' EdlRtUvkar MPa5.3 eT.

@> ersIusg;Taj Tensile Strength ersIusg;Taj ctf rbs;ebtugmantMltUc EdltMlRbhak;RbEhlrbs;vasitenAcenaH cf '10.0 nig ctf20.0 . eKBi)aknwgvas;ersIusg;TajCagersIusg;sgt;edaysarEtkarKabsMNakKMrUeTAnwgm:asIun BiesaFn_. eKmanviFICaeRcInkgkarBiesaFersIusg;Tajrbs;ebtug EtviFIEdleKniymeRbICageKKWkar BiesaFsgt;bMEbksIuLaMg (cylinder splitting or Brazilian test). enAkgkarKNna eKcUlciteRbItMlrbs;m:UDuldac; rf (modulus of rupture) CagkareRbI ersIusg;Tajedaykarsgt;bMEbk ctf (tensile splitting test) sMrab;Ggt;rgkarBt;. m:UDuldac;RtUv)an vas;edaykarBiesaFkac;bM)ak;;sMNakKMrURBIsebtugsuTedayrgbnkcMnucTIbI (third point) (ASTM C-78) . sMNakKMrUenHmanmuxkat;ragkaer: EdlRCugrbs;vamanTMhM cm15 nigmanRbEvg cm45 . m:UDul dac;rbs;ebtugmantMlFMCagersIusg;Tajedaykarsgt;bMEbk. ACI kMNt;ykm:UDuldac;es Inwg

( )MPafpsif cc '623.0'5.7 sMrab;ebtugTMgn;Fmta. CaTUeTA ebtugTMgn;RsalmanersIusg;TajtUcCagebtugTMgn;Fm ta. xageRkamenHCakarkMNt; m:UDuldac;rbs;ebtugTMgn;Rsal

a. RbsinebIersIusg;Tajedaykarsgt;bMEbk ctf RtUv)ankMNt; cctr fff '623.009.1 = (2.1)

b. RbsinebI ctf minRtUv)ankMNt; eRbIemKuN 75.0 sMrab;RKb;ebtugTMgn;Rsal nig 85.0 sMrab;ebtugTMgn;RsalEdlplitBIxSac;. eKGaceRbI linear interpolation

sMrab;karlayedayeRbIl,ayxSac; nigfbMEbklitTMgn;Rsal.

#> ersIusg;kat; Shear Strength ersIusg;kat;BitCamankarBi)akkgkarkMNt;edaykarBiesaFCageK edaysarPaBBi)akkgkar dak;eGaykugRtaMgkat;enAdac;edayELkBIkugRtaMgdT. vaCamUlehtuEdleFVIeGaymanbMErbMrYly:agFM

NPIC


ntMlrbs;ersIusg;kat; EdlERbRbYlBI %20 nersIusg;sgt;sMrab;kardak;bnkFmta eTAdl; %85 nersIusg;sgt;sMrab;krNImanbnSMkMlaMgsgt; nigkMlaMgkat;edaypal;. karRtYtBinitkarKNna eRKOgbgMedayersIusg;kat;CakrNIkMrbMput edaysarersIusg;kat;RtUv)ankMNt;edaytMltUcedIm,Ikar BarebtugBIkar)ak;edaykMlaMgTajGgt;RTUg. 2> ExSekagkugRtaMg-bMErbMrYlrageFobrbs;ebtug

Stress-Strain Curve of Concrete

cMeNHdwgBITMnak;Tng stress-train rbs;ebtugmansarsMxan;Nas;sMrab;dMeNIrkarviPaK nig KNnaeRKOgbgMEdleFVIBIebtug. rUbTI 2>2 bgajBIExSekag stress-strain KMrUEdlTTYl)anBIkar BiesaFedayeRbIsMNakKMrUebtugsIuLaMgEdlrgbnksgt;tamGkSeTalryeBlCaeRcInnaTI. eKGac cat;TukEpkTImYyrbs;ExSekagRbEhl %40 nersIusg;x3 bgajBIExSekag stress-strain rbs;ebtugEdlmanersIusg;eRcInRbePTEdleFVIeLIgeday Portland Cement Association.

T.Chhay


eyIgeXIjfa (1) ebtugEdlmanersIusg;kan;EttUc manbMErbMrYlrageFobkan;EtFM (2) RbEvgncMENk smamaRtdMbUgekIneLIgCamYynwgkarkarekIneLIgnersIusg;sgt;rbs;ebtug (3) PaBsVit (ductility) RtUv)ankat;bnyCamYynwgkarekIneLIgnersIusg;.

NPIC


3> m:UDuleGLasic nigkarERbRbYlersIusg;sgt;CamYynwgeBl Modulus of Elasticity and Change in Compressive Strength with Time

edaysarExSekag stress-strain EdlbgajenAkgrUbTI 2>4 manlkNekag (curvilinear) taMg BIdMNak;kaldMbUgnRbvtinkardak;bnkrbs;va. eKGacTTYl)anm:UDuleGLasicEtBIbnat;b:HeTA nwgExSekagRtg;cMnuceKal. CMraldMbUg (initial slope) rbs;bnat;b:HeTAnwgExSekagRtUv)ankMNt;Ca m:UDulb:HedIm (initial tangent modulus) ehIyeKGacsg;bnat;b:HRKb;cMnucTaMgGs;enAelIExSekag. bnat;eRTtRtg;EdlPab;BIcMnuceKaleTAkugRtaMgEdleGay RbEhl cf '4.0 kMNt;nUv secant modulus of elasticity rbs;ebtug. tMlenHbMeBjlkxNsn t;fasMParmanlkxNeGLasic edaybMErbMrYlerogeFobEdlekItmankgGMLgnkardak;bnkrt;eTArkTItaMgedImEdlminTan;rgbnkvij ehIybMErbMrYlerogeFobbnbnab;eTotedaykardak;bnkbEnmRtUv)ancat;TukCa creep. ACI Code eGaysmIkarxageRkamsMrab;KNna secant modulus of elasticity rbs;ebtug/

cE PsifwE ccc '33 5.1= sMrab; 3/15590 ftlbwc

T.Chhay


k> ebtugersIusg;x5 bgajBIdaRkamersIusg;sgt;-GayuedayeRbIBum< cmcm 2010 sMrab;l,ay ebtugEdl)anlaydUcbgajkgtarag 2>1. tarag 2>2 bgajBIl,ayebtugEdl)an design sMrab;ersIusg; MPa84 enAGayu 7 f. pleFob sIum:g;t / fbM-Ebklit / fbMEbkFM KW 06.2:22.1:1 ehIyPaBravERbRbYlcenaH mm150100 . rUbTI 2>6 bgajBI muxkat;FwmsmasEdleRbIRBIsebtugeRbkugRtaMgenAelIsabRtg;TMr. tarag 2>1 l,aypSMsMrab; ( )MPapsif c 12418000' >

Superplasticizer W. R. Grace

Dartard 40

Mighty 150

fbMEbbFM ( )mmin 5.9.83 ( )kg

fbMEbklit xSac; ( )kg

sIum:g;t ( )kg

Twk ( )kg

Silica fume ( )l kgg 100/ sIum:g;t

1104 687 565 128 64.5 116 540 1117 687 564 128 64.5 116 904

(1065) (649) (561) (w/c=0.22) (41kg)a (330) (up to 1323) a EtTMrgn;rbs; silica fume dMu. TwkEdlCaEpknl,ayTwkRtUv)andkecjBITwkEdlGnuBaatsrub.

NPIC


tarag 2>2 l,aypSMsMrab; ( )MPapsif c 12418000' > fbMEbbFM ( )mmin 5.9.83 ( )kg

fbMEbklit xSac; ( )kg

sIum:g;tBrELn RbePT III

( )kg Twk ( )kg

Powder Silica fume force 10000 ( )l

Liquid Superplasticizer

(Grace) (1) (2) (3) (4) (5) (6)

1092 649 425 170 106 32

x> ersIusg;sgt;edIm nigm:UDuleGLasic Initial Compressive Strength and Modulus edaysareKGnuvtkMlaMgeRbkugRtaMgmuneBlebtugTTYl)anersIusg;enAGayu 28 f eKcaM)ac;

kMNt;ersIusg;sgt;rbs;ebtug cif ' enAfGnuvtkMlaMgeRbkugRtaMg kdUcCam:UDuleGLasic cE rbs;va enAdMNak;kalepSgnRbvtinkardak;bnkeTAelIGgt;. smIkarTUeTAnersIusg;sgt;EdlCaGnuKmn_ GaRsynwgeBlKW

T.Chhay


cci ft

tf '' += (2.4a) Edl =cf ' ersIusg;sgt;enAGayu 28 f =t ryeBlKitCaf = emKuNGaRsynwgRbePTrbs;sIum:g;t niglkxNnkarEfTaMebtug

NPIC


0.4= sMrab;sIum:g;tRbePT I CamYynwgkarEfTaMedaysMeNIm (moist-cured type I cement) 3.2= sMrab;sIum:g;tRbePT III CamYynwgkarEfTaMedaysMeNIm (moist-cured type I

cement)

0.1= sMrab;sIum:g;tRbePT I CamYynwgkarEfTaMedaycMhayTwk (steam-cured type I cement)

7.0= sMrab;sIum:g;tRbePT III CamYynwgkarEfTaMedaycMhayTwk (steam-cured type I cement)

= emKuNGaRsynwg)a:ra:Em:RtEdlRtUvKanwgemKuN . vaes Inwg 85.0 / 92.0 / 95.0 nig 98.0 erogKa.

dUcenHsMrab;ebtugEdlplitBIsIum:g;t_RbePT I CamYynwgkarEfTaMedaysMeNIm cci ft

tf '85.00.4

' += (2.4b) m:UDuleGLasicRbsiTPaB (effective modulus) rbs;ebtugKW

strain creepstrain elastic

stress' +=cE (2.5)

ehIym:UDuleGLasicRbsiTPaBx

T.Chhay


4> Creep Creep b lateral material flow CakarekIneLIgnbMErbMrYlrageFob (strain) CamYynwgeBl evlaEdlbNalmkBIbnkGciny_. kMhUcRTg;RTayedIm (initial deformation) EdlbNalmkBI bnk KWbMErbMrYlrageFobeGLasic (elastic strain) cMENkbMErbMrYlrageFobbEnmEdlbNalmkBI bnkdEdlKWCa creep strain. rUbTI 2>7 bgajBIkarekIneLIgrbs; creep strain CamYynwgeBl. enAkgkrNI shrinkage eyIgeXIjfa creep stain fycuHeTAtameBl. eKminGacemIleXIj creep edaypal; EteKGackMNt; vaedaykardk elastic strain nig shrinkage strain BI total strain )an. eTaHbICa shrinkage nig creep minEmnCa)atuPUtEdlkraCBIKakeday eKsn t;faeKGaceRbIviFItMrYtpl (superposition) sMrab; strain )an. dUcenH ( ) ( ) ( ) ( )shcet shrinkagecreepstrain elasticstrain Total ++=

rUbTI 2>8 bgajKMrUkglMhrn strain bIRbePTEdlbNalBIbnksgt;Gciny_ nig shrinkage. edaysar creep GaRsynwgeBl dUcenHGkSEkgrbs;vaKW kMhUcRTg;RTay kugRtaMg nig eBl. karBiesaFCaeRcIn)anbgajeGayeXIjfa creep deformation smamaRteTAnwgbnkGnuvtn_ b:uEnPaBsmamaRtenHmantMlsMrab;EtkMritkugRtaMgtUc. eKminGackMNt;EdnkMNt;x

NPIC


rUbTI 2>9a bgajBImuxkat;rbs;KMrUkglMhrenAkgrUbTI 2>8 EdlRsbeTAnwgbg;EdlmanGkSkMhUcRTg; RTay nigGkSkugRtaMgenARtg;eBl 1t . vabgajfa TaMg elastic strain nig creep strain smamaRteTA nwgkugRtaMgEdlGnuvt. dUcKarUbTI 2>9 b bgajmuxkat;RsbeTAnwgbg;EdlmanGkSeBl nigGkSkMhUc RTg;RTay enARtg;kugRtaMg 1f . dUcenH vabgajnUvPaBdUcKarvagTMnak;TMngn creep nigeBl nigTMnak; TMngn shrinkage nigeBl.

T.Chhay


enAkgkrNI shrinkage, kMhUcRTg;RTayedaysar creep eRkamGMeBInbnkGciny_minRtLb; eTArkPaBedImTaMgRsugrbs;vavijeT. RbsinebIeKdkbnkBIsMNakKMrUbnab;BIryeBlrgbnkdyUr eK TTYl)ankarRtLb;eTArkPaBedImeGLasicPamEttUcCagbMErbMrYlrageFobeRkamGMeBIrbs;bnk. kar RtLb;eTArkPaBedImxNbnedaykarkat;bnybMErbMrYleFoby:agsnSwm EdleKeGayeQ aHfa creep recovery. karRtLb;eTArkPaBedImvijGaRsyeTAnwgGayurbs;ebtugenAeBlrgbnk ebtugkat; EtmanGayueRcIn creep recovery kan;EtFM rUbTI 2>10.

Creep manTMnak;TMngy:agCitsitCamYynwg shrinkage ehIytamc,ab;TUeTA ebtugEdlTb;Tl; nwg shrinkage )an kman creep tUcEdr Edl)atuPUtTaMgBIrenHmanTMnak;TMngeTAnwg hydrated cement paste. dUcenH creep TTYl\TiBlBIFatupSMrbs;ebtug lkxNbridan nigTMhMrbs;sMNakKMrU. b:uEnCa eKalkarN_ creep GaRsynwgkardak;bnkEdlCaGnuKmn_nwgeBl. eKkMNt;FatupSMrbs;sMNakKMrUebtugedaypleFobTwkelIsIum:g;t_ nigpleFobTwkelIsarFatu m:t;pg;enAeBleKeRbITw kfaMKImI/ edayfbMEbk nigRbePTsIum:gt_/ nigedayf bMEbk nigbrimaNsIum:g;t_. dUcenH kalNapleFobTwkelIsIum:g;t_ nigbrimaNsIum:g;t_kan;EteLIgx

NPIC


k> Effects of Creep dUcKanwg shrinkage Edr creep begInPaBdabrbs;Fwm nigkMralxN ehIyeFVIeGay)at;bg;kM-

laMgeRbkugRtaMg. elIsBIenH cMNakpitedImrbs;ssrebtugGarem:ekIneLIgeTAtameBledaysar creep EdleFVIeGaymankareprkMlaMgsgt;BIebtugeTAEdk.

enAeBlEdlEdk yield, ebtugnwgrgbnkbEnm. dUcenH ersIusg;rbs;ssrbnycuH ehIykM-eNagrbs;ssrekIneLIg EdleFVIeGayebtugrgkugRtaMgelIs nignaMdl;kar)ak;.

x> Rheological Models Rheological model Ca]bkrN_emkanicEdlBNnaBIkMhUcRTg;RTayTUeTArbs;sMPareRkam

GMeBIrbs;kugRtaMg. Model enHpSMeLIgedayrWusreGLasic (elastic spring) nig dashpot EdlkMNt; CakugRtaMg/ elastic strain, delayed elastic strain, irrecoverable strain nigeBl. rWusrtMNageGay PaBsmamaRtrvagkugRtaMg nigbMErbMrYlrageFob ehIy dashpot tMNageGayPaBsmamaRtrvagkug RtaMg nigGRtanbMErbMrYlerogeFob. rWusr nig dashpot EdltMerobCaExgbegIt)anCa Kelvin unit kartMerobCaesrIbegIt)anCa Maxwell unit. rUbTI 2>11 bgajBI Burgers model EdleKGacBiesaFBIkareFVIkarCaTMnak;TMngrvag kugRtaMg -strain-eBl rbs;ebtugenARtg;EdnsmamRtCamYynwgkarkMNt;xH. Model enHBiesaFrkbMErbMrYlrag eFobEdlGacRtLb;eTArkPaBedImxN (instantaneous recoverable strain) a / delayed recover-able elastic strain enAkgrWusr b nig irrecoverable time-dependent strain enAkg dashpot c nig d . PaBTn;exSayrbs; model enHKWfavabnxUcRTg;RTayeRkamGRtaefrenAeBlEdlbnkRtUv)anTb; Tl;eday Maxwell dashpot EdlkareFVIkarEbbenHminRsedogKanwgebtugeT Edl creep eTAdl;tMl kMNt;CamYynwgeBl dUcbgajenAkgrUbTI 2>7.

T.Chhay


Ross rheological model EdlbgajenAkgrUbTI 2>12 Ca model Edl)anEkERbedIm,Ilub bM)at;PaBxVHxatrbs; Burger model. A enAkg model enHtMNageGayPaBsmamaRtn stress-strain rbs;sMPartamc,ab;hUk/ D Ca dashpot ehIyB nigC CarWusreGLasicEdlGacbBankMlaMg Gnuvtn_ ( )tP prbs;sIuLaMgbiTCitedaykMlaMgkkit.

smIkarKNitviTamYytamry Ross model sMrab;kMNt; creep eRkamGMeBIrbs;bnkkgcenaH ryeBl t KW

btatC += (2.7)

Edl a nig b CatMlefrEdlGackMNt;)anBIBiesaFn_. Brason )ansMrYlkarvaytMlrbs; creep. eKGackMNt;bMErbMrYlrageFobbEnm cu Edl bNalBI creep KW ciucu f = (2.8) Edl =u emKuN creep kta EdlCaTUeTAeKehAvafa specific creep

=cif GaMgtg;sIuetkugRtaMgenAkgGgt;eRKOgbgMEdlRtUvKanwgbMErbMrYlrageFobkta cu Ultimate creep coefficient uC manrag cuu EC = (2.9) btMlmFmrbs;vaKW 35.2uC .

emKuN creep enARKb;xN sMrab;lkxNsg;dar manrag ut Ct

tC 6.06.0

10 += (2.10)

bma:geTot 6.06.0

10 tt

t += (2.11)

NPIC


Edl t CaeBlKitCaf nig t CaemKuNeBl. lkxNsg;darEdlkMNt;eday Brason KWebtugRtUvman PaBragticCag bes I cm10 nigmansMeNImbriyakas (relative humidity) %40 . RbsinebIlkxN minsg;dar eKRtUvGnuvtemKuNEksMrYl creep eTAelIsmIkar 2.10 nig 2.11 dUcxageRkam

(a) sMrab; moist-cured concrete EdlrgbnkenAGayu 7 f beRcInCagenH 118.025.1 = tka (2.12)

(b) sMrab; steam-cured concrete EdlrgbnkenAGayu 1feTA 3 f beRcInCagenH 095.013.1 = tka (2.13)

sMrab; relative humidity FMCag %40 eKRtUvKuNemKuNEksMrYlxageRkameTAelIsmIkar 2.12 nig 2.13 Hkc 0067.027.11 = (2.14) Edl =H relative humidity KitCa % . 5> karrYmmaD Shrinkage CaTUeTA shrinkage manBIrRbePTKW plastic shrinkage nig drying shrinkage. Plastic shrin-kage ekItmankgGMLgeBlb:unanem:ageRkayeBlcak;ebtugRss;cUlkgBum

T.Chhay


dUcenHvargnUv shrinkage tictYcedaybMErbMrYlrageFobedaysar shrinkage esIrb:Hnwgbnat;GasIumtUt EdlRsbnwgbnat;eBl.

ktaCaeRcInCH\TiBldl;TMhMrbs; drying shrinkage KW

a. fbMEbk (aggregate) fbMEbkeFVIskmPaBTb;karrYmmaDrbs;TwksIum:g;t_ dUcenHebtugEdl manbrimaNfbMEbkeRcInRbQmnwgkarrYmmaDtictYc. elIsBIenH lkNrbs;f bMEbkCa GkkMNt;kMritTb;Tl;karrYmmaD. fbMEbkEdlmanm:UDuleGLasickan;FM bmanpeRKImkan; FM kan;EtmansmtPaBkgkarTb;Tl;karrYmmaDrbs;ebtug.

b. pleFobTwkelIsIum:g;t_ (water/cement ratio) pleFobTwkelIsIum:g;t_kan;EtFM kan;Etman shrinkage FM. rUbTI 2>14 CadaRkamnTMnak;TMngrvagbrimaNfbMEbk nigpleFobTwk elIsIum:g;t_.

NPIC


c. TMhMrbs;ebtug (size of the concrete element) TaMgGRta nigTMhMsrubrbs;karrYmmaD fycuHCamYynwgkarekIneLIgnmaDrbs;ebtug. b:uEn eRKOgbgMEdlmanTMhMFMRtUvkarry eBlnkarrYmmaDyUrCag edaysarvaRtUvkareBlevlasMrab; drying shrinkage eTAdl; tMbn;xagkg. vaGacRtUvkarryeBl 1qaMsMrab;dMeNIrkar drying shrinkage cab;epImenA CMerA cm25 BIprgsMBaF ehIyvaRtUvkarryeBl10qaMedIm,Icab;epImenACMerA cm60 BI eRkampxageRkA.

d. lkxNbriyakasmFm (medium ambient condition) Relative humidity mFmCH \TiBly:agxaMgdl;karrYmmaD. GRtankarrYmmaDnwgtUc enAeBl relative humidity x

T.Chhay


Edl mmmmuSH /10800 6, = RbsinebIeKKanTinnykgtMbn;eTenaH z sMrab; steam-cured concrete bnab;BIGayu 1feTA 3 f

( )uSHtSH tt ,, 55 += (2.16)

sMrab;lkxNeRkABIlkxNsg;dar eKRtUvGnuvtemKuNEttMrUveTAelIsmIkar 2.15 nig 2.16 dUc xageRkam

z sMrab; %80%40 < H HkSH 010.040.1 = (2.17a)

z sMrab; %100%80 < H HkSH 30.000.3 = (2.17b)

6> EdkminEmneRbkugRtaMg Nonprestressing Reinforcement EdkBRgwgFmtasMrab;ebtugrYmman bar, wire nig welded wire fabric EdlvaRtUv)anplit edayeKarBtam ASTM standard. lkNsMxan;rbs;EdkBRgwgrYmman

a. m:UDuleGLasic bm:UDulyuaMg (Youngs modulus) sE b. ersIusg;yal (yield strength) yf c. ersIusg;x15. ExSvNEdleljecj enHRtUvbMeBjlkxN ASTM Specification A616-76 edIm,ITTYlsal;Ca deformed bar.

NPIC


rUbTI 2>16 bgajBIExSekag stress-strain sMrab;Edk garde 40 / 60 nig 70 Edlman yield strength MPa276 / MPa345 nig MPa517 erogKa nigCaTUeTAmancMnuc yield c,as;las;. sMrab; EdkEdlminmancMnuc yield c,as;las; eKkMNt;yktMlrbs; yield strength CaersIusg;EdlRtUvKanwg bMErbMrYlrageFob 005.0 sMrab;Edk grade 40 / 60 ehIy 0035.0 sMrab; grade 80 . ersIusg;Tajcug eRkay (ultimate tensile strength) EdlRtUvKanwgEdk grade 40 / 60 nig80 KW MPa483 / MPa621 nig MPa690 erogKa. RbePTEdkxHeTotmanenAkgtarag 2>3. PaKrysac;lUtenAeBldac;Edl ERbRbYleTAtam grade rbs;Edk/ Ggt;pitEdk/ sarFatuedIm sitenAcenaH %5.4 eTA %12 elIRbEvg Rkit cm20 .

kareRbIR)as; welded wire fabric )anekIneLIgy:agxaMgsMrab;kMralxN edaysarPaBgay

RsYlkgkartMeLIg karRKb;RKgKMlatEdk nigPaBetagebtug)anl. Fabric reinforcement RtUv)an plitBIEdkrelag b deformed wire Edlrt;kgTisEkgKa ehIyRtUv)anpSarPab;KaRtg;kEngEdlkat; Ka. tarag 2>5 bgajBIlkNFrNImaRtsMrab; standard wire reinforcement xH.

sMrab; mild steel PaKeRcIn kareFVIkarrbs;vaRtUv)ansn t;Ca eGLas)asic nigmanm:UDuleGLa- sices Inwg MPa310200 . tarag 2>3 bgajBI reinforcement grade nig strength nigtarag 2>4 bgajBIlkNFrNImaRtnTMhMepSgrbs;Edk.

T.Chhay


tarag 2>3 reinforcement grade and strength cMnucyalGb,brma bersIusg;yal yf ersIusg;x4 TMgn; RkLap nigbrimaRtrbs; bar

Standard nominal dimensions Bar designation

number TMgn;kgmYyktaRbEvg

( )[ ]mkgplf / Ggt;pit bd

( )[ ]mmin. RkLapmuxkat; bA ( )[ ]22. mmin

brimaRt ( )[ ]mmin.

3 0.376 (0.56) 0.375 (9) 0.11 (71) 1.178 (30) 4 0.668 (0.99) 0.500 (13) 0.20 (129) 1.571 (40) 5 1.043 (1.55) 0.625 (16) 0.31 (200) 1.963 (50) 6 1.502 (2.23) 0.750 (19) 0.44 (284) 2.356 (60) 7 2.044 (3.04) 0.875 (22) 0.60 (387) 2.749 (70) 8 2.670 (3.97) 1.000 (25) 0.79 (510) 3.142 (80) 9 3.400 (5.06) 1.128 (28) 1.00 (645) 3.544 (90) 10 4.303 (6.40) 1.270 (31) 1.27 (819) 3.990 (101) 11 5.313 (7.91) 1.410 (33) 1.56 (1006) 4.430 (113) 14 7.65 (11.38) 1.693 (43) 2.25 (1452) 5.32 (135) 18 13.60 (20.24) 2.257 (56) 4.00 (2581) 7.09 (180)

NPIC


7> EdkeRbkugRtaMg Prestressing Reinforcement k> RbePTEdkeRbkugRtaMg Type of Reinforcement

edaysarkar)at;bg;edaysar shrinkage nig creep x

T.Chhay


sIusg;FMEbbenHGacTb;Tl;nwgkar)at;bg;enACMuvijebtug nigmankugRtaMgsl;RKb;RKan;edIm,IFananUvkMlaMg eRbkugRtaMgEdlRtUvkar. TMhMnkMhatbg;kugRtaMgFm tasitenAcenaH ( )MPaksi 24135 eTA ksi60 ( )MPa414 . dUcenHkMlaMgeRbkugRtaMgdMbUgKYrmanTMhMFM EdlsitenAcenaH ( )MPaksi 1241180 eTA

( )MPaksi 1517220 . EdkeRbkugRtaMgGacmanTMrg;Ca single wire, strand EdlpSMeLIgeday wire CaeRcInrmYlcUlKa

begIt)anCa single element nig high-strength bar. EdkeRbkugRtaMgEdleKniymeRbIKW a. Uncoated stress-relieved or low-relaxation wire. b. Uncoated stress-relieved strand and low-relaxation strand. c. Uncoated high-strength steel bar.

Straightened wire b tempered wire bgajnUv relaxation loss x Stress-Relieved and Low-Relaxation Wires and Strand Stress-relieved wire KWCakarhUt single wire RtCak;edayeKarBtam ASTM standard A421

stress-relieved strand eKarBtam ASTM standard A416. Strand RtUv)anplitecjBI wire 7 Edl wire 6 rMurmYlCMuvij wire Rtg; 1 EdlmanTMhMFMCagbnic. eKeFVI stress-relieve eRkayeBlEdl eKrMu wire rYc. lkNFrNImaRtrbs; wire nig strand EdlTamTareday ASTM RtUv)aneGayenAkg tarag 2>6 nig tarag 2>7 erogKa. edIm,IbegInRkLapEdkrbs; 7 wire-strand sMrab; nominal diameter , eKGachUt standard wire edIm,IbegItCa compacted strand dUcbgajenAkgrUbTI 2>17 (b). rUbTI 2>17 (a) bgajBI standard 7 wire strand. ASTM standard A779 RtUvkarersIusg; niglkNGb,brmadUcbgajenA kgtarag 2>8.

NPIC


rUbTI 2>18 (a) bgajBIdaRkam stress-strain sMrab;EdkeRbkugRtaMg wire nig strand. rUb

TI 2>18 (b) bgajBItMleRbobeFobrvagEdkeRbkugRtaMg nigEdkFm ta.

T.Chhay


NPIC


K> High-Tensile Strength Prestressing Bars High-tensile-strength alloy steel bar sMrab;eFVIeRbkugRtaMgGacrelag b deformed ehIyGac

man nominal diameter BI ( )mmin 19.43 eTA ( )mmin 35.1 83 . vaRtUveKarBtam ASTM standard A722. karhUtRtCak;KWedIm,IbegIn yield strength nig ductility rbs;va. eKTTYl)an stress relieve edaykardutkMedA bar b strand eRkamsItuNPaBsmRsb EdlCaTUeTAeRkam Co500 . EdkeRbkug RtaMgRtUvmanersIusg;Tajy:agtic ( )MPaksi 1034150 CamYynwg yield strength Gb,brmaesI %80 n ultimate strength sMrab; smooth bar nig %80 sMrab; deformed bar.

tarag 2>9 bgajBIlkNFrNImaRtrbs; prestressing bar EdlTamTareday ASTM standard A722 nigrUbTI 2>18 bgajBIdaRkamkugRtaMg-bMErbMrYlrageFobKMrUsMrab; bar enH.

X> Steel Relaxation

Steel relaxation enAkgEdkeRbkugRtaMgCakMhatbg;eRbkugRtaMgenAeBlEdl wire b strand RbQmnwgbMErbMrYlrageFobefr. vadUcKanwg creep enAkgebtug EtvaxusKaRtg; creep CabMErbMrYln strain steel relaxation CakMhatbg;kugRtaMgrbs;Edk. eKGackMNt;kMhatbg;edaysar relaxation enAkg stress-relieved sires nig strand eRkayeBlrgeRbkugRtaMgedaysmIkarxageRkam

= 55.0

10log

py

pipiR f

ftff (2.18)

T.Chhay


kgkrNIEdl 55.0/ pypi ff nig pupy ff 85.0 sMrab; stress-relieved strands nig pyf puf90.0 sMrab; low-relaxation strand. ehIy pypi ff 82.0= PameRkayeBlepr b:uEn pif puf74.0 sMrab; pre-tensioned concrete nig pupi ff 70.0= sMrab; post-tensioned concrete. Ca

TUeTA pupi ff 70.0 . eKGackat;bnykMhatbg;edaysar stress relaxation edayeGay strand rgnUvkugRtaMgdMbUg rbs;vaes Inwg %70 n ultimate strength rbs;vaenAsItuNPaB Co20 eTA Co100 sMrab;ryeBlEdl yUrCagkgeKalbMNgbegItsac;lUtGciny_ EdldMeNIrkarenHRtUv)aneKeGayeQ aHfa stabilization. kMhatbg;eRbkugRtaMgedaysar stress relaxation rbs; low-relaxation steel es Inwg %25 nkMhat bg;eRbkugRtaMgedaysar stress relaxation rbs; stress-relieves steel. smIkarsMrab;kMhatbg;edaysar relaxation enAkg low-relaxation prestressing steel KW

= 55.0

45log

py

pipiR f

ftff (2.19)

rUbTI 2>19 bgajBI relaxation loss sMrab; stress-relieved steel nig low-relaxation steel sMrab; 7-wire strands EdlekItmanelIRbEvgefrenAsItuNPaB Co5.29 .

NPIC


g> ERcH nigkarxUcxatrbs;EdkeRbkugRtaMg Corrosion and Deterioration of Strands

karkarBarRbqaMgnwgERcHsIuEdkeRbkugRtaMgmansarsMxan;CagsMrab;krNIEdkFmta edaysar EtersIusg;rbs;Ggt;ebtugeRbkugRtaMgCaGnuKmn_nwgkMlaMgeRbkugRtaMg bkRkLaprbs; prestressing tendon. karkat;bnyRkLapEdkeRbkugRtaMgEdlbNalmkBIERcHnwgkat;bny nominal moment strength rbs;muxkat;eRbkugRtaMgy:agxaMg EdlGacnaMdl;kar)ak;rbs;RbBneRKOgbgMmunGayu. sMrab; pre-tensioned member karkarBarERcHKWpl;edayebtugEdlBTCMuvij tendon. sMrab; post-tensioned member eKGacTTYl)ankarkarBarERcHedaykarbMeBj grout eTAkgbMBg; (duct) eRkayeBleFVIeRb kugRtaMgehIy bedaykarlabeRbg (greasing). TMrg;nkarxUcxatma:geTotrbs; wire b strand KW stress corrosion EdlRtUv)ankMNt;lkN edaykarbegIteLIgn microscopic crack enAkgEdk EdlnaMeGayEdkmanPaBRsYy nigRsYldac;. karkat;bnyersIusg;RbePTenHGacekItmanEteRkamkugRtaMgx kugRtaMgGnuBaatGtibrmarbs; ACI enAkgebtug nigEdk

ACI Maximum Permissible Stresses in Concrete and Reinforcement xageRkamenHCanimitsMxan;EdleyIgnwgeRbIjwkjab; =pyf yield strength rbs; tendon eRbkugRtaMg =yf yield strength rbs;EdkFmta =puf ersIusg;Taj (tensile strength) rbs; tendon eRbkugRtaMg =cf ' ersIusg;sgt;rbs;ebtug =cif ' ersIusg;sgt;rbs;ebtugenAxNrgeRbkugRtaMgdMbUg

k> kugRtaMgebtugEdlrgkarBt; Concrete Stresses in Flexure kugRtaMgEdlekItmanPamenAkgebtugeRkayeBlepreRbkugRtaMg munkMhatbg;eRbkugRtaMg GaRsynwgeBl minKYrFMCagtMlxageRkam !> kugRtaMgsrsxageRkAbMputrgkarsgt; >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cif '60.0 @> kugRtaMgsrsxageRkAbMputrgkarTaj elIkElgcMnuc #> >>>>>>> ( )MPafpsif cc '25.0'3 #> kugRtaMgsrsxageRkAbMputrgkarTajRtg;cugrbs;Ggt;TMrsamBa >>>>>> psif c'6

T.Chhay


RbsinebIkugRtaMgTajEdlKNnamantMlFMCagtMlxagelI eKRtUvdak; bonded auxiliary reinforce-ment (nonprestressed b prestressed) enAkgtMbn;TajedIm,IkarBarkMlaMgTajsrubenAkgebtugEdl RtUv)anKNnaedayeRbImuxkat;Gt;eRbHsnt;. kugRtaMgenAkgebtugeRkamGMeBInbnkeFVIkar bnab;BIkMhatbg;eRbkugRtaMgTaMgGs; minKYrFM CagtMlxageRkam !> kugRtaMgsrsxageRkAbMputrgkarsgt;edaysarkMlaMgeRbkugRtaMg nigbnkefr >>>> cf '45.0 @> kugRtaMgsrsxageRkAbMputrgkarsgt;edaysarkMlaMgeRbkugRtaMg nigbnksrub>>> cf '60.0 #> kugRtaMgsrsxageRkAbMputrgkarTajenAkgtMbn;rgkarTajEdlrgkarsgt;

dMbUg >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ( )MPafpsif cc '5.0'6 $> kugRtaMgsrsxageRkAbMputrgkarTajenAkgtMbn;rgkarTajEdlrgkarsgt;

dMbUgrbs;Ggt; elIkElgRbBnkMralxNBIrTis EdlkarviPaKQrelImux kat;eRbHedaykarbMElg (transformed cracked section) nigenAelITMnak; TMngPaBdab nigm:Um:g;BIrTisbgajfaPaBdabPam nigPaBdabryeBlEvg eKrBtamtMrUvkarrbs; ACI nigtMrUvkarkMras;ebtugkarBarGb,brma >>>>> psif c'12

x> kugRtaMgEdkeRbkugRtaMg Prestressing Steel Stresses kugRtaMgTajenAkg tendon eRbkugRtaMgminRtUvFMCagkugRtaMg !> EdlbNalmkBI tendon jacking force pyf94.0

b:uEnminRtUvFMCagtMlEdltUcCageKkgcMeNam puf80.0 nigtMlGtibrmaEdl ENnaMedayGkplit tendon eRbkugRtaMg nig anchorage eT.

@> PameRkayeBlkMlaMgeRbkugRtaMgRtUv)anepr>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> pyf82.0 b:uEnminRtUvFMCag puf74.0

#> Post-tensioning tendons, enARtg; anchorage nig coupler, eRkayBI tendon anchorage Pam>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> puf70.0

9> kugRtaMgGnuBaatGtibrmarbs; AASHTO enAkgebtug nigEdk

AASHTO Maximum Permissible Stresses in Concrete and Reinforcement

k> kugRtaMgebtugmunkMhatbg;edaysar creep nig shrinkage Concrete Stresses before Creep and Shrinkage Losses

NPIC


kugRtaMgsgt; Pre-tensioned members . cif '60.0 Post-tensioned members. cif '55.0 kugRtaMgTaj tMbn;TajEdlrgkugRtaMgsgt;dMbUg >>>>>>>>>>>>>>>>>>>>>>>>>>>>> minmankugRtaMgGnuBaatbeNaHGasn

NamYyRtUv)ankMNt; EpkepSgeTot enAkgtMbn;TajEdlminmaneRbIEdkFmta>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> psi200 b psif ci'3 enAeBlEdlkugRtaMgTajEdl)anBIkarKNnaFMCagtMlenH eKRtUvdak; bonded reinforce-ment edIm,IkarBarkMlaMgTajsrubenAkgebtugEdlKNnaedayeRbImuxkat;Gt;eRbHsnt;. kugRtaMgTaj GtibrmaminRtUvFMCag >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ( )MPafpsif cci '623.0'5.7

x> kugRtaMgebtugeRkamGMeBIbnkeFVIkareRkaykMhatbg; Concrete Stresses at Service Load after Losses

kugRtaMgsgt; >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cf '40.0 kugRtaMgTajenAkgtMbn;TajEdlrgkugRtaMgsgt;dMbUg

!> sMrab;Ggt;EdleRbI bonded reinforcement >>>>>>>>>>>>>>>>>>>>>>>> ( )MPafpsif cc '5.0'6 sMrab;lkxNEdlGaceFVIeGaymanERcHsIuEdkFn;F dUcCaenAtMbn;eqrsmuRT psif c'3 @> sMrab;Ggt;Edlminman bonded reinforcement>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>0

kugRtaMgTajenAkgkEngepSgeTotRtUv)ankMNt;edaykugRtaMgGnuBaatEdlkMNt;enAkgEpk 8>k. !> kugRtaMgeRbH Cracking Stresses sMrab;ebtugTMgn;Fmta>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ( )MPafpsif cc '623.0'5.7 sMrab;ebtugTMgn;RsalEdlplitBIxSac;>>>>>>>>>>>>>>>>>>>>>> ( )MPafpsif cc '523.0'3.6 sMrab;ebtugTMgn;RsaldTeTot>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ( )MPafpsif cc '457.0'5.5

@> Anchorage-Bearing Stresses Post-tensioned anchorage eRkamGMeBIbnkeFVIkar >>>>>>>>>>>>>>>>>>>>> ( )MPapsi 213000 b:uEnminRtUvFMCag cif '90.0

T.Chhay


K> kugRtaMgEdkeRbkugRtaMg Prestressing Steel Stresses !> EdlbNalBI tendon jacking force >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> pupy ff 80.094.0 @> eRkayeBlkMlaMgeRbkugRtaMgRtUv)aneprPam >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> pupy ff 74.082.0 #> Post-tensioning tendons enARtg; anchorage/ eRkayeBl anchor tendon Pam puf7.0

pupy ff 85.0 sMrab; low-relaxation pupy ff 90.0= dUcenHsMrab; tendon EdlmanersIusg;Taj ksi270 man pif enAeBlepr 27070.0 = ( )MPaksi 1300189= .

X> Relative Humidity Values rUbTI 2>20 bgajnUvtMl relative humidity mFmRbcaMqaMsMrab;tMbn;TaMgGs;enAshrdeday

KitCaPaKry edIm,IeRbIsMrab;KNnakMhatbg;edaysarkarrYmmaDrbs;ebtug.

NPIC


10> RbBnkMlaMgeRbkugRtaMg nig Anchorages Prestressing Systems and Anchorages

k> karGnuvtkugRtaMgTajCamun Pretensioning sMrab; pretensioned beam EdkeRbkugRtaMgrgkugRtaMgTajCamunEdlTb;eday anchorage

munnwgebtugRtUv)ancak;. Anchorage RtUv)anRTeday bulkhead y:agFM nigmanesrPaBedIm,ITb;Tl; nwgkMlaMgy:agFMEdlGnuvteTAelI tendon nImYy. eKEtgEtGnuvtkugRtaMgTajCamunenAeragcRkplit eRKOgbgMdMeLIg edaysarvaRtUvkarkMralebtugGarem:drwgmuaM CamYynwg anchor bulkhead bCBaaMgenA cugsgxag. eKGacGnuvteRbkugRtaMgeTAelI strand mgmYy bmgTaMgGs;kgeBlEtmYyBI jacking operation.

T.Chhay


sMrab; harped tendon profiles eKeRbI]bkrN_ hold-down dUcbgajkgrUbTI 2>21. eday sarkMralmanRbEvgEvgeKGacplit prestressed element )aneRcInkgeBlEtmYy ehIyEdkeRbkug RtaMgEdlenAcenaHGgt;TaMgenaHGacRtUv)ankat;enAeBlebtugmanersIusg;RKb;RKan;. rUbTI 2>22 bgajBI schema kgkarplit prestressed element eRcInelIkMralEtmYy. ehIyrUbTI 2>23 bgajBI tendon Edl harp enAkgRbBnkMralsMrab;plit prestressed element.

NPIC


enAkgkarGnuvtkugRtaMgCamun strand nig single wire RtUv)an anchor edayRbBnCaeRcIndUc bgajenAkgrUbTI 2>24. rUbTI 2>25 nig 2>26 bgajBIRbBnkMralsMrab;plit prestressed element ehIyeKkeRbIvasMrab;karGnuvteRbkugRtaMgCaeRkay. ehIyrUbTI 2>27 TMhMlMGitsMrab;RbBnenH.

T.Chhay


NPIC


T.Chhay


NPIC


x> karGnuvtkugRtaMgTajCaeRkay Post-Tensioning enAkgRbBn post-tensioning eKGnuvtkugRtaMgTajeTAelI strand, wire b bar eRkayeBl

ebtugkkrwg nigmanersIusg;RKb;RKan;. eKdak; strand enAkgbMBg; (duct) EdlRtUv)antMerobenAkg Ggt;ebtug. kMlaMgeRbkugRtaMgRtUv)aneprtamry end anchorage dUcCa Supreme Product chuck EdlRtUv)anbgajenAkgrUbTI 2>24. EdkeRbkugRtaMgminRtUv)an bonded b grouted munnwgGnuvt kMlaMgeRbkugRtaMgeT.

K> Jacking System Jacking system CasmasFatumYydcaM)ac;mYyn prestressing operation edayGnuvtkMlaMg

eRbkugRtaMgEdlRtUvepreTAEdkeRbkugRtaMg. kMlaMgeRbkugRtaMgRtUv)anGnuvttamry hydraulic jack EdlmankMlaMg t10 eTA t20 nig stroke BI ( )cmin 15.6 eTA ( )cmin 120.48 GaRsynwgkarGnuvt post-tensioning b pretensioning nigGaRsynwgkarGnuvtkMlaMgeRbkugRtaMgeTAelIEdkeRbkugRtaMgmgmYy bmgTaMgGs;. eKRtUvkar large-capacity jack Edlman stroke y:agtic ( )mmin 762.30 sMrab;kar GnuvtkMlaMgeRbkugRtaMgeTAelIEdkeRbkugRtaMgmgTaMgGs;. tMlsMrab;kargarEbbenHBitCafCagkar GnuvtkMlaMgeRbkugRtaMgeTAelI tendon mgmYy. rUbTI 2>28 bgajBI double acting hydraulic jack sMrab;Taj (jack) EdkeRbkugRtaMgmgTaMgGs;kgeBlCamYyKa.

T.Chhay


X> Grouting of Post-Tensioned Tendons edIm,Ipl;CaGciny_nUvkarkarBar post-tensioned steel nigedIm,IbegItPaBsitrvagEdkeRbkug

RtaMg nigebtugEdlBTCMuvij duct eKRtUvbMeBj prestressing duct eday)aj;bBal cement grout. 1. Grouting material

A. Portland Cement suIm:g;t_BrELnRtUvEteKarBtam specification ASTM C150 Type I, II nig III. sIum:g;t_EdleRbIsMrab; grouting RtUvmanKuNPaBl minrgGIuRdakm.

B. Twk TwkEdleRbIsMrab; grout RtUvEtCaTwkEdlGacpwk)an sat nigminmansarFatuEdl GacCH\TiBlminldl;sIum:g;t_BrELn nigEdkeRbkugRtaMg.

C. TwkfaMKImI RbsinebIeKeRbITwkfaMKImI vaRtUvpl;nUvlkNbrimaNTwkTab/ good flow, minimum bleed nig expansion. vaminmansarFatuKImIEdlCH\TiBlminldl;Edk eRbkugRtaMg bsIum:g;t_. TwkfaMKImIEdlmansUlusgkr EdlsarFatukFMCag %5.0 nTMgn;rbs;TwkfaMKImI edaysnt;TwkfaMKImI ( )kglb 45.01 kgsIum:g;t_mYy)av eKminRtUv eRbIsUluysgPyGr sUluysgsulpat bsUluysgGasUt. eKGaceRbIemS:A GaluymIjmkgbrimaNsmrmNamYy bsarFatuKImIdTeTotEdlekItBI]s n edIm,ITTYl)an karrIkmaDrbs; grout RbEhlBI %5 eTA %10 .

2. Ducts A. Forming

z Formed Ducts: bMBg;RtUv)anbegIteLIgedaysMbkEdlminGnuBaateGayTwk sIum:g;t_cUl)an. vaRtUveprkugRtaMgsitdUcEdlRtUvkar nigrkSaragrbs;vaeRkamTMgn; rbs;ebtug. Metallic sheath KYrCa ferrous metal EtvakGacCaRbePT galvanized pgEdr.

z Cored Ducts: bMBg;enHRtUv)anpliteLIgedaymanPaBTUlayEdlminpl;]b- sKdl;lMhUrrbs; grout.

B. Grout Opening or Vents: bMBg;TaMgGs;RtUvEtman grout opening enAcugsg xag. sMrab; draped cable cMnucx

NPIC


C. TMhMbMBg; RbsinebIeKeRbI tendon EdlpSMeLIgeday wire, bar b strand eRcIn RkLa prbs;bMBg;RtUvEtmanTMhMy:agtices Inwg neat area rbs;EdkeRbkugRtaMgBIrdg. sMrab;bMBg;EdleRbICamYynwg wire, bar b strand eTal Ggt;pitrbs;bMBg;RtUvFMCag normal diameter rbs; wire, bar b strand ( )mmin 6.4/1 .

D. Placement of Ducts: eRkayeBlbMBg; Edk nig forming RtUv)andak;cb;sBVRKb; eKRtUvRtYtBinitnUvTItaMgrbs;bMBg;EdlGacxusqg. eKRtUvPab;bMBg;edayKMlatCit l medIm,IeCosvagkarpas;TIrbs;bMBg;enAeBlcak;ebtug. eKRtUvCYsCulrn bRbehag TaMgGs;EdlmanenAelIbMBg;munnwgcak;ebtug. eKRtUvPab; Grout opening nig vent edaysuvtiPaBeTAnwgbMBg; nigeTABum< beTAEdkFmta edIm,IkarBarkarpas;TIkgGMLg eBlcak;ebtug.

T.Chhay

Partial Loss of Prestress 58

III. kMhatbg;eRbkugRtaMg Partial Loss of Prestress

1> esckIepIm Introduction vaCakarBitEdlkMlaMgeRbkugRtaMgedImEdlGnuvtmkelIGgt;ebtugGarem:rgnUvkarkat;bnyCa

bnbnab;kgGMLgeBlRbEhlCaR)aMqaM. dUcenH eKcaM)ac;RtUvkMNt;kMlaMgeRbkugRtaMgenARKb;dMNak; kalnkardak;bnknImYy taMgBIdMNak;kaleprkMlaMgeRbkugRtaMgeTAebtug eTAdMNak;kaleRbkugRtaMg CaeRcIneTot dUcCaeRkamlkxNbnkeFVIkarrhUtdl;lkxN ultimate load. eKGacEbgEckkarkat; bnykMlaMgeRbkugRtaMgCaBIrRkumKW

z kMhatbg;eGLasicPam (immediate elastic loss) kgdMNak;kalplit EdlrYmman elastic shortening rbs;ebtug anchorage loss nigkMhatbg;edaysarkMlaMgkkit (frictional loss).

z kMhatbg;GaRsynwgeBl (time-dependent loss) EdlmandUcCa creep, shrinkage kMhatbg;edaysar\TiBlrbs;sItuNPaB nig steel relaxation. eKGackMNt;kMhatbg; TaMgenHBIkugRtaMgenAkgGgt;ebtugeRbkugRtaMgenAsanPaBkMNt;bnkeFVIkar.

vaminEmnCakargayRsYlkgkarkMNt;TMhMrbs;kMhatbg;TaMgenH)anCak;lak;eT CaBiess sMrab;kMhatbg;GaRsynwgeBl edaysarvaGaRsynwgmKuNEdlCab;Bak;BnKay:ags Ksaj. viFIkM Nt;kMhatbg;eRbkugRtaMgedaykarBiesaFmanlkNxusKaeTAtam code nigeTAtamkarENnaM dUcCa tamviFIrbs;viTasanebtugeRbkugRtaMg (Prestressed Concrete Institute), ACI-ASCE joit committee approach, AASHTO lump-sum approach, Comite Eurointernational du beton

(CEB), nig FIP (Federation International de la Precontrainte). kMritlM)aknviFITaMgenHGaRsy nwgviFIEdleRCIserIs nigeTAelIyl;RBmTTYlnkarGnuvt.

eKminRtUvkarkarkMNt;kMhatbg;eRbkugRtaMgEdlmankMritRbesIrx1 bgajBItaragsegbnkMhatbg;eRbkugRtaMgEdlKNnatam AASTHO lump-sum loss nig tarag 3>2 sMrab;karKNnatam PTI (Post-Tensioning Institute). varYmbBalman elastic

NPIC

kMhatbg;eRbkugRtaMg 59

shortening, relaxation enAkgEdkeRbkugRtaMg/ creep nig shrinkage ehIyvaGacGnuvt)ansMrab;Et lkxNbnksg;darEdleFVIsarcuHsareLIg/ lkxNebtugFm taEdlmankarRtYtBinitKuNPaB. Rb sinebIvamineKarBnUvlkxNTaMgenHeT eKRtUvKNnaedaykarviPaKEdlmanlkNlMGit.

karsegbBIRbPBnkMhatbg;eRbkugRtaMgdac;edayELkBIKa nigdMNak;kalnkarekIteLIg rbs;RtUv)aneGayenAkgtarag 3>3 EdlGkSr I mannyfadMbUg (initial) nigGkSr j manyfadMNak; kalnkardak;bnkeRkay jacking. BItaragenHkMhatbg;eRbkugRtaMgsrubRtUv)anKNnasMrab;Ggt; GnuvteRbkugRtaMgCamun (pretensioned member) nig Ggt;GnuvteRbkugRtaMgCaeRkay (post-tensioned member) dUcxageRkam

T.Chhay


a. Pretensioned member

pSHpCRpRpESpT fffff +++= (3.1a) Edl ( ) ( )strpRtropRpR ttfttff ++= , =ot GayuenAeBl jacking =trt GayuenAeBlepr =st GayuenAeBlkMhatbg;manlMnwg dUcenH eKRtUvGnuvtkarKNnasMrab; steel relaxation sMrab;ryeBlcenaH 1t dl; 2t n dMNak;kalnkardak;bnkEdlRtUvKa. ]TahrN_ dMNak;kaleprKWenAGayu h18 dUcenHeyIg)an =trt

ht 182 = nig 01 == tto . RbsindMNak;kalnkardak;bnkbnab;sitenAcenaHeBlepr nigGayu 5 qaM ( )h17520 CaGayuEdleKKitfakMhatbg;manlMnwg enaH htt s 175202 == nig ht 181 = . bnab;mk RbsinebI pif kMlaMgeRbkugRtaMgedImEdlGgt;ebtugRtUvrg nig pJf Ca jacking stress enAkg tendon enaH ( ) pEStropRpJpi fttfff = , (3.1b)

b. Post-tensioned member

pSHpCRpRpESpFpApT fffffff +++++= (3.1c) Edl pESf GacGnuvt)anEtenAeBleK jack tendon mgmYy minEmnmgTaMgGs;eT. sMrab;krNI post-tensioned member karKNna relaxation loss cab;epImcenaHeBlepr =1t trt nigcugbBab;ncenaHeBl 2t EdleKBicarNa. dUcenH

pFpApJpi ffff = (3.1d)

NPIC


2> Elastic Shortening of Concrete (ES) ebtugrYjxIenAeBleKGnuvtkM;laMgeRbkugRtaMg. edaysar tendon EdlsitCab;CamYynwgebtug rYjdMNalKa dUcenHvaxatbg;nUvkMlaMgeRbkugRtaMgEdlvaman.

k> Pretensioned Element

sMrab; pretensioned element cak;eRsc (precast) kMlaMgsgt;EdlGnuvteTAelIFwmeday

tendon TTYl)anBIkarrYjtambeNayrbs;Fwm dUcbgajenAkgrUbTI 3>1. karrYjxIktaenAkgebtug KW LESES /= dUcenH

cc

i

c

cES EA

PEf == (3.2a)

edaysar tendon eRbkugRtaMgrgnUvTMhMnkarrYjxIdUcKa enaH cs

c

i

cc

isESspES nfA

nPEAPEEf ==== (3.2b)

kugRtaMgenAkgebtugenARtg;TIRbCMuTMgn;rbs;EdkEdlbNalBIeRbkugRtaMgedImKW

c

ics A

Pf = (3.3)

RbsinebI tendon enAkgrUbTI 3>1 mancMNakpit ekNalElVgrbs;Fwm nigeKKitm:Um:g; Edl)anBITMgn;pal;rbs;va DM enaHkugRtaMgebtugenARtg;muxkat;kNalElVgenARtg;nIv:Urbs;EdkeRb kugRtaMgkayeTACa

c

D

c

ics I

eMre

APf +

+= 2

21 (3.4)

T.Chhay


Edl iP mantMltUcCagbnab;BIkMlaMgeRbkugRtaMgRtUv)anepr. karkat;bnytMlrbs; JP eTA iP tic tYcekIteLIgedaysarkMlaMgenAkgEdkeRbkugRtaMgbnab;BIkareprPamtUcCag kMlaMgeRbkugRtaMg jacking edIm JP . b:uEn edaysareKBi)akkgkarkMNt;tMlrbs; iP EdlRtUv)ankat;bnyy:agsuRkit nigedaysarkarGegtbgajfa karkat;bnyenHmanPaKrytictYc dUcenHeKGaceRbItMl iP edImmun eBlepreTAkgsmIkar 3.2 rhUtdl; 3.4 bkat;bnyva %10 RbsinebIeKcg;)ankarKNnaEdlRbesIr Cag. !> kMhatbg;edaysar Elastic shortening enAkgFwm pretensioned ]TahrN_ 3>1 FwmebtugeRbkugRtaMg pretensioned mYymanElVgRbEvg ( )mft 2.1550 dUcbgajenA kgrUbTI 3>2. sMrab;FwmenH ( )MPapsif c 4.41600' = ( )MPapsif pu 1862270000= ( )MPapsif ci 314500' = =psA seven-wire-strand tendon Ggt;pit .2

1 in cMnYn10 2.53.1153.010 in==

( )MPapsiEps 1862001027 6= KNnakugRtaMgsrsebtugenARtg;TIRbCMuTMgn;rbs; tendon sMrab;muxkat;kNalElVgrbs;Fwm nigKNnaTMhMnkMhatbg;eRbkugRtaMgedaysar\TiBl elastic shortening rbs;ebtug. sn t;famun nwgepreRbkugRtaMg jacking force enAelI tendon mantMles Inwg puf%75 .

dMeNaHRsay 2.4503015 inAc == ( ) 33 .33750

123015 inIc ==

NPIC


22 .75inAIrc

c ==

2.53.1153.010 inAps == .114

230 inec ==

lbAfP psui 30982553.127000075.075.0 === ( ) lbinwlMD === .1757813128

50150144

30158

22

BIsmIkar 3.4 kugRtaMgsrsebtugenARtg;TIRbCMuTMgn;rbs;EdknFwmenAeBlepr edaysn t;fa Ji PP KW

c

D

c

ics I

eMre

APf +

+= 2

21

33750111757813

75111

450309825 2 +

+=

( )MPapsi 5.84.12269.5723.1799 =+= ehIyeyIgkman ciE edIm psif ci 610824.3450057000'57000 === pleFobm:UDuledIm 06.7

10824.31027

6

6=

==ci

sEEn

cE ersIusg;Gayu 28 f psi610415.4600057000 == pleFobm:UDulenAGayu 28 f 12.6

10415.41027

6

6=

=n BIsmIkar 3.2b kMhatbg;eRbkugRtaMgedaysar elastic shortening KW ( )MPapsinff cspES 7.592.86594.122606.7 === RbsinebIeKeRbI iP Edlkat;bnyedaysn t;kat;bny %10 ( )MPapsif pES 7.533.77932.865990.0 == PaBxusKankugRtaMgEdkRtwm psi9.865 minFMeT RbsinebIeKeRbobeFobnwgkMhatbg;eRbkug RtaMgsrubEdlbNalBIktaTaMgGs;EdlmantMlRbEhlBI psi45000 eTA Psi55000 .

x> Post-Tensioned Element enAkgFwm post-tensioned kMhatbg;edaysar elastic shortening ERbRbYlBIsUn RbsinebI tendon TaMgGs;RtUv)an jack kgeBldMNalKa eTABak;kNalntMlEdlKNnaenAkg krNI

T.Chhay


pretensioned RbsinebIeKeRbICMhann jacking CaeRcIndMNak;kal dUcCa jacking tendon mgBIrkg eBlEtmYy. RbsinebI n CacMnYnrbs; tendon ehIyeKTaj tendon mgBIr enaH ( )

==

n

jjpESpES

fn

f1

1

Edl j CacMnYnnkarGnuvt jacking. cMNaMfa tendon EdlrgnUvkarTajcugeRkayeKminrgnUvkMhat bg;edaysar elastic shortening eT enAeBlEdl tendon EdlrgkarTajdMbUgeKrgnUvbrimaNkMhat bg;Gtibrma.

!> kMhatbg;edaysar Elastic shortening enAkgFwm post-tensioned ]TahrN_ 3>2 edaHRsay]TahrN_ 3>1 RbsinebIFwmCa post-tensioned ehIykarGnuvteRbkug RtaMgdUcxageRkam

a. eKTaj tendon mgBIrkgeBlEtmYy b. eKTaj tendon mgmYy c. eKTaj tendon mgTaMgGs;

dMeNaHRsay a. BI]TahrN_ 3>1 eyIgman psif pE 2.8659= . eyIgdwgehIyfa tendon cugeRkayminrg

kMhatbg;kugRtaMgedaysar elastic shortening eT. dUcenH manEt tendon $KUreT Edlrg karxatbg;eRbkugRtaMg EdlKUrTImYyrgkMhatbg;GtibrmaesInwg psi2.8659 . BIsmIkar 3.5 kMhatbg;edaysar elastic shortening enAkgFwm post-tensioned KW

( )2.86595

4/14/24/34/4 +++= pESf ( ) ( )MPapsi 9.2943302.8659

2010 ==

b. ( )2.865910

9/19/89/9 +++= LpESf ( ) ( )MPapsi 9.2943302.8659

9045 ==

enAkgkrNITaMgBIr kMhatbg;eRbkugRtaMgenAkgFwm post-tensioned es InwgBak;kNalkMhat bg;eRbkugRtaMgenAkgFwm pretensioned.

c. 0= pESf

NPIC


3> Steel Stress Relaxation (R) Steel-relieved tendon rgkMhatbg;kMlaMgeRbkugRtaMgedaysarsac;lUtefreTAtameBl dUc)anerobrab;enAkgCMBUk2. TMhMnkarkat;bnyeRbkugRtaMgminEmnGaRsyEtelIryeBlrkSakMlaMg eRbkugRtaMgb:ueNaHeT EtvaenAGaRsynwgpleFobeRbkugRtaMgedImelI yield strength rbs;Edk

pypi ff / . kMhatbg;kugRtaMgEbbenHRtUv)aneKeGayeQ aHfa stress relaxation. ACI 318-99 Code kMNt;kugRtaMgTajenAkg tendon eRbkugRtaMgdUcxageRkam

a. sMrab;kugRtaMgEdlbNalBIkMlaMgTaj tendon (jacking force) pypJ ff 94.0= b:uEnmin RtUvFMCagtMltUcCageKkgcMeNam puf80.0 nigtMlGtibrmaEdlENnaMedayGkplit tendon nig anchorage.

b. eRbkugRtaMgEdleRkayBIeprPam pypi ff 82.0= b:uEnminRtUvFMCag puf74.0 . c. enAkg post-tensioned tendon kugRtaMgeRkayBIeprPamenARtg; anchorage nig coupler

puf70.0= . tMl pyf GaRsynwgRbePTEdkeRbkugRtaMgRtUv)aneGaydUcxageRkam - Prestressing bar pupy ff 80.0= - Stress-relieved tendon pupy ff 85.0= - Low-relaxation tendon pupy ff 90.0= RbsinebI pRf CakugRtaMgeRbkugRtaMgEdlenAsl;enAkgEdkeRkayBI relaxation smIkarxag

eRkamkMNt; pRf sMrab; stress-relieved steel:

= 55.010

loglog1 12py

pi

pi

pR

fftt

ff (3.6)

enAkgsmIkarenH tlog RtUvKitCaem:agedaymaneKal 10 / pypi ff / RtUvFMCag 55.0 nig 12 ttt = . sMrab; low-relaxation steel tYEckntY log RtUvEcknwg 45 CMnYseGay 10 vij. rUbTI 3>3 bgajBI daRkamnsmIkar 3.3. eKGaceGaytMlRbhak;RbEhlrbs;tY ( )12 loglog tt es Inwg ( )12loglog ttt = edaymin mankMhatbg;FMEdlb:HBal;dl;PaBsuRkiteT. enAkgkrNIenH kMhatbg;edaysar stress-relaxation kayCa

= 55.0'

10log'

py

pipipR f

ftff (3.7)

T.Chhay


Edl pif ' CakugRtaMgedImenAkgEdkEdlGgt;ebtugRtUvrg.

RbsinebIeKcaM)ac;viPaKkMhatbg;CaCMhan eKGackMNt;kMeNInkMhatbg;enARKb;dMNak;kalCa lkNBiesseday

= 55.0'10

loglog' 12py

pipipR f

fttff (3.8)

Edl 1t CaeBlcab;epImTaj nig 2t CaeBlEdleKBicarNaelIkMhatbg;.

k> Relaxation Loss Computation ]TahrN_ 3>3 kMNt;kMhatbg;enAkg]TahrN_ 3>1 edaysar relaxation enAGayu 5 qaM eday sn t; relaxation loss cab;BIeBl jacking dl;karepr/ kMhatbg;edaysar elastic shortening nigkMhatbg;ryeBlEvg EdlbNalmkBI creep nig shrinkage k gGMLgeBlenaHKWes Inwg %20 n eRbkugRtaMgedIm. snt;fa ( )MPapsif py 1571230000= . dMeNaHRsay BIsmIkar 3.1b sMrab;dMNak;kalenH ( )tropRpJpi ttfff ,=

( )MPapsi 139620250027000075.0 == kugRtaMgEdlkat;bnysMrab;karKNnakMhatbg; relaxation KW

( ) ( )MPapsif pi 117016200020250020.01' == ryeBlndMeNIrkar stress relaxation KW

NPIC


44000243655 em:ag BIsmIkar 3.7

= 55.0'

10log'

py

pipipR f

ftff

= 55.0230000162000

1044000log162000

( )MPapsi 80116061543.04643.0162000 ==

x> ACI-ASCE Method of Accounting for Relaxation Loss viFI ACI-ASCE eRbIkarcUlrYmn elastic shortening, creep nig shrinkage dac;edayELkBIKa sMrab;karKNna steel stress-relaxation loss edayeRbIsmIkarxageRkam ( )[ ] CfffJKf pSHpCRpESrepR ++= tMlrbs; reK / J nig C RtUv)aneGayenAkgtarag 3>4 nigtarag 3>5.

T.Chhay


4> Creep Loss (CR) kargarBiesaFn_CagknHstvtSbgajeGayeXIjfakMhUcRTg;RTayrbs;sMParekItmanGa- RsyeTAtameBlenAeBlEdlvargbnkefr bkugRtaMgefr. kMhUcRTg;RTay bkarrIkxagEdlbNal mkBIkugRtaMgGciny_tambeNayenHRtUv)aneKeGayeQ aHfa creep. kMhUcRTg;RTay bbMErbMrYlrag eFobEdlekItBIkareFVIkarGaRsynwgeBlenHCaGnuKmn_nTMhMrbs;bnkGnuvtn_/ ryeBlrgbnk/ lkNrbs;ebtugrYmmansmamaRtrYmpSMrbs;va/ lkxNtMEhTaM/ Gayurbs;Ggt;enAeBlrgbnkdMbUg niglkxNbrisan. edaysarTMnak;TMng stress-strain EdlbNalBI creep manlkNCabnat; dUc enHeKmanPaBgayRsYlkgkarPab; creep strain CR eTAnwg elastic strain EL edIm,IkMNt;emKuN creep uC

EL

CRuC

= (3.9a)

bnab;mkeKGackMNt;emKuN creep RKb;ryeBl t EdlKitCafdUcxageRkam ut Ct

tC 60.060.0

10 += (3.9b) dUcerobrab;enAkgCMBUkTI 2 tMlrbs; uC sitenAcenaH 2 nig 4 CamYynwgtMlmFm 35.2 sMrab; ultimate creep. eKGackMNt;kMhatbg;enAkgGgt;eRbkugRtaMgEdlbNalBI creep sMrab; bonded member tamrUbmnxageRkam cs

c

pstpCR fEE

Cf = (3.10)

Edl csf CakugRtaMgenAkgebtugenARtg;nIv:UnTIRbCMuTMgn;rbs;EdkeRbkugRtaMg. CaTUeTA kMhatbg;enH CaGnuKmn_eTAnwgkugRtaMgenAkgebtugRtg;muxkat;EdlkMBugviPaK. enAkg post-tensioned nonbonded

NPIC


member eKGacBicarNakMhatbg;manlkNesIeBlbeNayrbs;ElVg. dUcenH tMlmFmrbs;kug RtaMgebtug csf cenaH anchorage point EdleKGaceRbIvasMrab;KNna creep enAkg post-tensioned members. smIkarrbs; ACI-ASCE Committee sMrab;kMNt;kMhatbg;eday creep manTMrg;dUc KanwgsmIkar 3.10 ( )csdcs

c

psCRpCR ffE

EKf = (3.11a)

b ( )csdcsCRpCR ffnKf = (3.11b) Edl 0.2=CRK sMrab; pretensioned member

60.1= sMrab; post-tensioned member =csf kugRtaMgenAkgebtugenARtg;nIv:Urbs;Edl cgs eRkaykareprPam

=csdf kugRtaMgenAkgebtugenARtg;nIv:Urbs;Edk cgs EdlbNalmkBIbnkefrEdlGnuvt bEnmeRkayeBleKGnuvteRbkugRtaMgrYcral;ehIy

=n pleFobm:UDul cMNaMfa eKkat;bny crK %20 sMrab;ebtugTMgn;Rsal.

k> KNnakMhatbg;edaysar creep ]TahrN_ 3>4 kMNt;kMhatbg;eRbkugRtaMgedaysar creep sMrab;Ggt;enAkg]TahrN_ 3>1 Edl bnkGnuvtbEnm elIkElgTMgn;pal;rbs;Fwm eRkayeBleprKW ( )mkNplf /5.5375 . dMeNaHRsay enAeBlersIusg;ebtugeBlelj ( )MPapsiEc 36 104.3010415.4600057000 == 12.6

10415.41027

6

6=

==c

sEEn

( ) ( )mkNlbinMSD .9.158.140625012850375 2 ==

( )MPapsiI

eMfc

SDcsd 2.33.45833750

111406250 ===

BIsmIkar 3.1 ( )MPapsif cs 5.84.1226= sMrab;ebtugFm taeRbI 0.2=CRK (pretensioned beam) dUcenHBIsmIkar 3.11a ( )csdcsCrpCR ffnKf =

T.Chhay


( )3.4584.12260.212.6 = ( )MPapsi 8.645.9401=

5> kMhatbg;edaysarkarrYmmaD Shrinkage Loss (SH) dUcKanwg creep rbs;ebtug TMhMn shrinkage rbs;ebtugrgnUv\TiBlCaeRcInkta EdlrYmman smamaRtnkarrYmpSMrbs;ebtug/ RbePTfbMEbk/ RbePTsIum:g;t_/ ryeBltMEhTaM/ ryeBlcenaHeBl tMEhTaMcb;sBVRKb; nigkarGnuvteRbkugRtaMg/ TMhMrbs;Ggt;eRKOgbgM/ niglkxNbrisan. TMhM nigrUb ragrbs;Ggt;kCH\TiBldl;karrYmmaDEdr. RbEhl %80 n shrinkage ekItmanenAqaMTImYynGayu rbs;eRKOgbgM. enAkg ACI 209 R-92 Report eKykTMhMmFmrbs; ultimate shrinkage strain enA kg moist-cured concrete nig steam-cured concrete es Inwg mmmm /10780 6 . tMlmFmenHrg \TiBledayryeBlntMEhTaMgdMbUg/ sMeNImbriyakas/ pleFobmaDelIp/ sItuNPaB nigsma-masFaturYmpSMrbs;ebtug. edIm,Iyk\TiBlTaMgenHmkKitbBalkgtMlmFmnbMErbMrYlrageFob edaysarkarrYmmaD (shrinkage strain) eKRtUvKuNvanwgemKuNEktMrUv SH dUcxageRkam SHSH 610780 = (3.12) SH CaemKuNsMrab;lkxNbrisanEdlmanenAkg ACI Committee 435 Sec.2.

sMrab;lkxNsg;dar Prestressed Concrete Institute yktMlmFmsMrab; nominal ulti-mate shrinkage strain ( ) mmmmuSH /10820 6= . RbsinebI SH Ca shrinkage strain eRkayBI EktMrUvsMrab; relative humidity eTAtampleFobmaDelIp SV / kMhatbg;eRbkugRtaMgenAkg preten-sioned member KW psSHpSH Ef = (3.13) sMrab; post-tensioned member kMhatbg;eRbkugRtaMgedaysarkarrYmmaDKWtUcCagsMrab; pretension-ed member edaysarGgt;)anrYmmaDxHehIymuneBlrg post-tensioning. RbsinebIeKKit relative humidity CaPaKry nigeKBicarNaBI\TiBlnpleFob SV / enaHkMhatbg;eRbkugRtaMgEdlbNal BIkarrYmmaDkayeTACa ( )RH

SVEKf psSHpSH

= 10006.01102.8 6 (3.14)

Edl 0.1=SHK sMrab; pretensioned member. tarag 3>6 eGaynUvtMl SHK sMrab; post-tensioned member.

NPIC


eKGacTTYlkarEktMrUv shrinkage loss sMrab;lkxNsg;darCaGnuKmn_eTAnwgeBl t KitCa f tamsmIkarxageRkam

a. Moist curing, eRkay 7f ( ) ( )uSHtSH t

t += 35 (3.15a) Edl ( )uSH Ca ultimate shrinkage strain/ =t eBlEdlKitCaf

b. Steam curing, eRkayBI 1eTA 3f ( ) ( )uSHtSH t

t += 55 (3.15b) eyIgKYrkt;sMKal;fakarKNna creep nig shrinkage dac;edayELkBIKaenAkgCMBUkenHRtUv)an TTYlyksMrab;karGnuvt. ehIybMErbMrYldFMEdlekIteLIgenAkgtMl creep nig shrinkage KWbNal mkBIbMErbMrYlnsmamaRtsarFatupSMrbs;sMPar ebIeTaHbICaplitplenaHRtUv)anplitecjBIeragcRk (pretensioned beam) keday. dUcenHeKRtUvTTYlykBtmanBIlTplBiesaFn_Cak;EsgsMrab;plit-plEdlplitecjBIeragcRk/ sMrab;krNIpleFobElVgelIkMBs;mantMlFM nigsMrab;kardak;bnkFn; minFmta.

k> KNnakMhatbg;edaysar Shrinkage ]TahrN_ 3>5 KNnakMhatbg;eRbkugRtaMgEdlbNalmkBI shrinkage enAkg]TahrN_ 3>1 nig 3>2 enAGayu 7feRkay moist curing edayeRbITaMg ultimate SHK method EdleRbIsmIkr 3.14 nigviFIGaRsynwgeBl (time-dependent method) EdleRbIsmIkar 3.15. sn t;fa relative humidity

%70=RH nigpleFobmaDelIpes Inwg 0.2 . dMeNaHRsay

A. viFI SHK (a) pretensioned beam 0.1=SHK

T.Chhay


BIsmIkar 3.14 ( )( )701000.206.0110270.1102.8 66 = pSHf

( )MPapsi 3.405845= (b) Post-tensioned member BItarag 3>6 eyIg)an 77.0=SHK

( )MPapsif pSH 0.317.4500584577.0 == B. viFIGaRsynwgeBl

BIsmIkar 3.15a mmmm

tt

tt

SHtSH /1013010780353566

, =+=+=

( )MPapsiEf stSHpSH 0.243510102710130 66, ===

6> kMhatbg;edaysarkarkkit Losses Due to Friction (F) kMhatbg;eRbkugRtaMgekItmanenAkg post-tensioning member KWbNalmkBIkMlaMgkkitrvag

tendon nigbMBg;EdlBTCMuvijva. TMhMnkMhatbg;enHCaGnuKmn_nTMrg;rbs;EdkeRbkugRtaMg (tendon form or alignment) EdleKeGayeQaHfa\TiBlkMeNag (curvature effect) niglMgakecjBIKng rbs;EdkeRbkugRtaMg EdleKehAfa\TiBlgakcuHeLIg (wobble effect). CaerOy eKGaceFVIeGay tMlemKuNkMhatbg;manlkNRbesIrenAeBlkMBugerobcM shop drawing edayeFVIkarERbRbYlRbePT tendon nigkartMrg;bMBg; (duct alignment). eKGackMNt; curvature effect Camun)an Et wobble effect CalTplEdl)anBIPaBminRtg;rbs;bMBg;edaycdn bminGaceCosvag)an EdlekIteLIg edaysarEt karerobcMdak;bMBg;min)anl.

eyIgKYrcMNaMfakMhatbg;kugRtaMgkkitGtibrmanwgekItmanenAcugmageTotrbs;Fwm RbsinebIeK TajEdkeRbkugRtaMgenAcugmageTot. dUcenH kMhatbg;edaysarkMlaMgkkitERbRbYlCalkNsma-maRttambeNayElVgFwm ehIyeKGaceFVI interpolation sMrab;TItaMgBiessNamYy RbsinebIeKcg;Fa nanUvkarKNnamYyEdlmanlkNkan;EtRbesIr.

k> \TiBlkMeNag Curvature Effect edaysareKTaj tendon CamYynwgkMlaMg 1F enAcugmag dUcenH tendon RtUvrgnUvkMlaMgkkit CamYynwgbMBg; EdleFVIeGaykugRtaMgenAkg tendon ERbRbYlBITItaMgEdlTajeTAcMgay L tam beNayElVg dUcbgajkgrUbTI 3>4. RbsinebIeKykRbEvgGnntUcrbs; tendon minKitCadaRkam

NPIC


GgesrIdUcbgajenAkgrUbTI 3>5 ehIyedaysnt; CaemKuNkMlaMgkkitrvag tendon nigbMBg;Edl bNalmkBI\TiBlkMeNag enaHeyIg)an

dFdF 11 = b d

FdF =

1

1 (3.16a)

T.Chhay


edayeFVIGaMgetRkaleTAelIsmIkarxagelIeyIgTTYl)an =1log Fe (3.16b) RsbinebI RL /= enaH ( )RLeFeFF /112 == (3.17)

x> \TiBlgaker Wobble Effect ]bmafa K CaemKuNkMlaMgkkitrvag tendon nigbMBg;EdlbNalmkBI wobble effect b \TiBlRbEvg (length effect). kMhatbg;edaysarkugRtaMgkkitKWekIteLIgedaysarPaBminRtg; lrbs; tendon tamRbEvgrbs;va edayminKitfavaRtUv)aneKtMerobRtg; b draped alignment eT. bnab;mktameKalkarN_dUcKaEdl)anerobrab;kgkarbegItsmIkar 3.16 eyIg)an KLFe =1log (3.18) b KLeFF = 12 (3.19) edaybUk\TiBlTaMgBIrbBalKaeyIgTTYl)an KLeFF = 12 b edayKitCakugRtaMg KLeff = 12 (3.20) bnab;mkeyIgTTYl)ankMhatbg;kugRtaMgedaysarkMlaMgkkit pFf dUcxageRkam ( )KLpF effff == 1121 (3.21) edaysn t;fakMlaMgeRbkugRtaMgcenaHcMnucab;epImkMeNag nigcMnuccugbBab;kMeNagmantMltUc Rb Ehl %15 dUcenHvamanlkNsuRkitRKb;RKan;kgkareRbIkMlaMgeRbkugRtaMgedImsMrab;kMeNagTaMg mUlenAkgsmIkar 3.21. eKGacsresrsmIkar 3.21 EdlsMrYlrYcdUcxageRkam ( )KLff pF += 1 (xat US) (3.22) ( )KLff pF 28.31 += (xat SI) Edl L KitCa ft b m . edaysarpleFobkMBs;rbs;FwmelIRbEvgElVgrbs;vatUc eKGaceRbIRbEvgcMeNalrbs; tendon )ansMrab;KNna )anedayenAEtmanlkNsuRkitRKb;RKan;dEdl. edaysn t;kMeNagrbs; tendon manragCaFrgVg; mMupit tambeNaykMNat;kMeNagenAkgrUbTI 3>6 es InwgmMuCMralenAxagcug rbs;kMNat;kMeNag 2dg. dUcenH

xm

xm 2

2/2tan ==

NPIC


RbsinebI my21 nig xy /42/ =

enaH xy /8= ra:dg; tarag 3>7 eGaynUv design value rbs;emKuNkkitedaysarkMeNag nigemKuNkkitedaysarkargak er bedaysarRbEvg K EdlTTYl)anBI ACI 318 Commentary.

K> karKNnakMhatbg;edaysarkarkkit Computation of Friction Loss

]TahrN_ 3>6 sn t; alignment characteristic rbs; tendon enAkg post-tensioned beam n]TahrN_ 3>2 dUcbgajenAkgrUbTI 3>7. RbsinebI tendon EdleRbIenAkgFwmenHCa 7-wire uncoated strand EdleRsabeday flexible metal sheathing KNnakMhatbg;kugRtaMgedaysar kMlaMgkkitenAkgEdkeRbkugRtaMgEdlbNalmkBI curvature effect nig wobble effect.

T.Chhay


dMeNaHRsay lbPi 825,309= psif 500,202

53.1825,309

1 == BIsmIkar 3.23

1467.050

"12/1188 ===xy ra:dg;

BItarag 3>7 yk 0020.0=K nig 20.0= . BIsmIkar 3.22 kMhatbg;eRbkugRtaMgEdl bNalmkBIkMlaMgkkitKW ( )KLff pipF +=

( )50002.01467.020.0500,202 += ( )MPapsi 6.180191,261293.0500,202 ==

kMhatbg;edaysarkarkkitenHes Inwg %93.12 neRbkugRtaMgedIm. 7> Anchorage-Seating Losses (A) Anchorage-seating losses ekIteLIgenAkg post-tensioned members bNalmkBIkardak; estenAkg anchor enAeBlkMlaMg jacking RtUv)anepreTA anchorage. vakGacekItmanenAkgkMral Bum

NPIC


bNalmkBIkarEktMrUv anchorage enaH. RbsinebI A CaTMhMnkarrGil/ LCaRbEvgrbs; tendon nig psE Cam:UDulnEdkeRbkugRtaMg enaHkMhatbg;eRbkugRtaMgedaysarkarrGil anchorage KW

psApA ELf= (3.24)

k> Computation of Anchorage-seating Loss ]TahrN_ 3>7 KNna anchorage-seating loss enAkg post-tensioned beam n]TahrN_ 3>2 RbsinebIkarrGil)a:n;sanKW ( )mmin 35.6.4/1 . dMeNaHRsay psiEps 61027= .25.0 inA = ( )MPapsiE

Lf psApA 6.77250,1110271250

25.0 6 ===

cMNaMfaPaKrykMhatbg;edaysarkarrGil anchorage mantMlFMsMrab;FwmxI dUcenHeKBi)ak nwgeFVI post-tension elIFwmxICamYynwgPaBsuRkitx kMhatbg;eRbkugRtaMgbNalBIkarekagrbs;Ggt; Change of Prestress Due to Bending of Members ( pBf )

FwmekagedaysarrgeRbkugRtaMg bbnkxageRkA. vaekag bptGaRsynwgRbePTbnk dUc bgajenAkgrUbTI 3>8. RbsinebIbMErbMrYlrageFobsgt;ktaenAkgebtugtambeNaynIv:Urbs; tendon KW c enaHkMhatbg;eRbkugRtaMgenAkgEdkEdlRtUvnwgbMErbMrYlrageFobenHKW pscpB Ef = Edl sE Cam:UDulrbs;Edk. cMNaMfa sMrab;krNITUeTA eKmincaM)ac;KitBicarNaBIkMhatbg;eday sarkarekagNamYyeT RbsinebIeKvas;kMriteRbkugRtaMgeRkayFwmekagrYcehIy. rUbTI 3>9 bgajBI flowchart sMrab;karkMNt;kMhatbg;eRbkugRtaMgGaRsynwgeBlCaCMhan edayminmanPaBdab.

T.Chhay


NPIC


T.Chhay


9> karKNnakMhatbg;kugRtaMgenAkgFwmrgeRbkugRtaMgCamun Step-by-Step Computation of All Time-Dependent Losses in a Prestensioned Member

]TahrN_ 3>8 FwmeRbkugRtaMg pretensioned EdleFVIBIebtugTMgn;Rsal nigTTYl steam-cured man muxkat; T Dub RTedayTMrsamBamanRbEvg ( )mft 3.2170 dUcbgajenAkgrUbTI 3>10. FwmenHrgeRb kugRtaMgeday 270-K grade stress-relieved strand EdlmanGgt;pit ( )mmin 71221 ./ cMnYndb;BIr. Tendon RtUv)an harped nigmancMNakpitenAkNalElVg ( )mmin 4767318 .. nigenAxagcug .98.12 in ( )mm330 . KNnakMhatbg;eRbkugRtaMgenARtg;muxkat;eRKaHfak;Rtg; 400. nElVgEdlbNalmkBI bnkefr nig bnkefrbEnmenAeBl

a. dMNak;kalTI 1 KWeBlepr b. dMNak;kalTI 2 KWeRkayBIeFVIkargarbegIy (topping) c. BIrqaMeRkayBIeFVIkargarbegIyehIy

NPIC


sn t;fakargarbegIyCaebtugTMgn;RsalEdlmankMras; ( )mmin 512 . RtUv)ancak;enAGayu 30 f. elIsBIenH eKsnt;fakarepreRbkugRtaMgekItmanenA 18 em:ageRkayBITaj strand. eKeGay

psif c 0005,' = TMgn;Rsal ( )MPa534. ( )MPapsif ci 1245003 .,' =

ehIyxageRkamCalkNmuxkat; noncomposite ( )22 9683615 cminAc ,.= ( )464 1049272059 cminIc = .., ( )cmincb 8559821 ...= ( )cminct 5250210 ...= ( )33 520447172 cminSb ,.,= ( )33 670979605 cminS t ,.,= DW minmankargarbegIy ( )mkNplf /.27491= SDW kargarbegIy .in2 ( )mkNplf /.653250= ( )PapsfWL 915140 ,= minzitezr ( )MPapsif pu 8621000270 ,,= ( )MPapsiff pupy 5891000230850 ,,. = ( )MPapsifffff pupupypupi 3031000189700850820820700 ,,..... ==== ( )MPapsiEps 36 1011931028 = . dMeNaHRsay psif ci 5003,' = ( ) psiEci 651 10412500333115 == .,. ( ) psiEc 651 10882000533115 == .,. dMNak;kalTI 1 eBleprkugRtaMg (a) Elastic shortening:

tamsmtikmmuxkat;eRKaHfak;sitenAcMgay ft2870400 == . e enARtg;muxkat;eRKaHfak; ( ) ...... in581798127318809812 =+= m:Um:g;EdlekItBIbnkefrenARtg; 400. nElVg

( ) ( )2870228491

2

== XLXWM DD

T.Chhay


( )mkNlbinlbft ..,,, 3914964643708288 == psiff pupi 000189000270700700 ,,.. ===

sn t;kMhatbg;edaysar elastic shortening nigkMhatbg;edaysar steel-relaxation psi00018, / enaH net-steel stress psif pi 00017100018000189 ,,, == nig

lbfAP pipsi 956313000171153012 ,,. === 22 1197

61572059 in

AIrc

c ., ===

c

D

c

ics I

eMre

APf +

+= 2

21

( )72059

581749646431197

58171615

956313 2

..,,

.., +

+=

( )MPapsi 77311519019121352 ..,.,., =+= 6211

104121028

6

6.

.=

==ci

ps

EE

n

( )MPapsifnf cspES 48595812311516211 .,.,. === RbsinebIeKeRbI psif pi 000189,= enaH net-steel stress

psif pi 04217695812000189 ,,, == nigeyIgman psif cs 3178190191000171

04217623152 .,.,,,., =+=

( )MPapsifnf cspES 9469013317816211 ,.,. === CamYynwg psi95812, eyIgeXIjfamanPaBxusKatictYcRbEhl %6 . dUcenHkar

sn t;kMhatbg; %10 taMgBIdMbUg eday)a:n;san Ji PP 900. GacRKb;RKan;. (b) Steel-Stress Relaxation:

psif py 000230,= psif pi 000189,= beKGaceRbI net psif pi 000171,=

18=t em:ag

= 55.010

loglog 12py

pipipR f

fttff

= 55.0000,230000,189

1018log000,189

psipsi 447,69.446,6 =

NPIC


psiff pRpES 000,18405,19447,6958,12 =+=+ karsnt; OK (c) Creep Loss: 0= pCRf (d) Shrinkage Loss: 0= pSHf kMhatbg;kugRtaMgenAkgEdksrubsMrab;dMNak;kalTI 1KW pSHpCRpRpESpT fffff +++=

( )MPapsi 134405,1900447,6958,12 =+++= kugRtaMgrbs; strand pif enAcugndMNak;kalTI 1 ( )MPapsi 169,1595,169405,19000,189 ==

EdleGay psiPi 376,311= .

dMNak;kalTI 2 eRkayBIeFVIkargarbegIyehIy KWenAeBlebtugmanGayu 30 f (a) Creep Loss: psiEc 61088.2 = psiEps 61028= 72.9

1088.21028

6

6=

==c

ps

EE

n

psif cs 3.115,1= m:Um:g;EdlekItBIkargarbegIy .2in ( ) ( ) ( )mkNlbinxLxWM SDSD .199000,764,11228702

282502

=

=

=

psiI

eMcsdfc

SD 3.519720,59

58.17000,764,1 ===

eTaHbICaryeBl 30 fCaryeBlxIsMrab;\TiBlryeBlEvgkeday keKGacEksMrYltMlRbhak; RbEhlRKb;RKan;enAkgdMNak;kalTI 2 edayeRbIemKuN CRK nsmIkar 3.11 edIm,IKitkgdMNak; kalTI 3 pgEdr emIldMNak;kalTI 3 karKNna creep . sMrab;ebtugTMgn;Rsal eRbI 6.1%800.2 ==CRK . bnab;mk BIsmIkar 3.10 kMhatbg; eRbkugRtaMgEdlbNalBI creep ryeBlyUrKW ( ) ( ) ( )MPapsiffnKf csdcsCRpCR 3.63269,93.5193.115,16.172.9 === (b) Shrinkage Loss:

T.Chhay


sn t;sMeNImbriyas (relative humidity) %70=RH . BIsmIkar 3.14 kMhatbg;eRbkug RtaMgEdlbNalmkBIkarrYmmaDryeBlyUrKW ( )RH

SVEKf psSHpSH

= 10006.01102.8 6

69.1364615 ==

SV

0.1=SHK sMrab; pretensioned member dUcenH ( )( )7010069.106.0110280.1102.8 66 = pSHf

( )MPapsi 7.42190,6=

(c) Steel Relaxation Loss enAGayu 30 f: 181 =t em:ag 302 =t f 7202430 == em:ag psif pe 595,169= )anBIdMNak;kalTI 1 ( )MPapsif pR 1.35091,555.0000,230

595,16910

18log720log595,169 =

=

kMhatbg;srubenAkgdMNak;kalTI 2 KW ( )MPapsiffff pRpSHpCRpT 142550,20091,5190,6269,9 =++=++= karekIneLIgkugRtaMgenAkg strand bNalmkBIkargarbegIyKW ( )MPapsifnf csdSD 8.34048,53.51972.9 === dUcenH kugRtaMgenAkg strand enAcugbBab;ndMNak;kalTI 2 KW ( )MPapsiffff SDpTpspe 062,1093,154048,5550,20595,169 =+=+=

dMNak;kalTI 3 eRkayGayu)anBIrqaM sn t;fatMlrbs; creep ryeBlyUr nig shrinkage ryeBlyUrEdl)ankMNt;enAkgdMNak; kalTI2 minekIneLIgeRcInKYreGaykt;sMKal;eT edaysarkareRbItMlryeBlyUrrbs; CRK nig

SHK . dUcenH ( )MPapsif pe 066,1093,154= 301 =t f 720= em:ag 22 =t qaM 520,17243652 == em:ag

NPIC


kMhatbg;kugRtaMgedaysar steel relaxation KW ( )MPapsif pR 7.17563,255.0000,230

093,15410

720log520,17log093,154 =

=

dUcenHkugRtaMgenAkug strand pef enAcugbBab;ndMNak;kalTI 3 KW ( )MPapsif pe 033,1530,151563,2093,154 =

PaKrynkMhatbg;srub %9.191.80100 == b %20 sMrab; pretensioned beam. 10> karKNnakMhatbg;kugRtaMgenAkgFwmrgeRbkugRtaMgCaeRkay

Step-by-Step Computation of All Time-Dependent Losses in a Post-Tensioned Member

]TahrN_ 3>9 edaHRsay]TahrN_ 3>8 edaysn t;faFwmrgnUveRbkugRtaMgCaeRkay. snt;fakM hatbg;edaysar anchorage seating KW .4/1 in ehIy strand TaMgGs;RtUv)anTajkgeBlCamYyKa enAkg flexible duct. elIsBIenHsn t;fakMlaMg jacking srubmuneBlekItmankMhatbg;edaysar kMlaMgkkit nig anchorage seating KW psif pi 000,189= pipJ ff = sMrab;smIkar 3.1d sMrab;krNI enH. dMeNaHRsay (a) Anchorage seating loss

"25.04"1 ==A ftL 70=

BIsmIkar 3.24 kMhatbg;edaysarkarrGil anchorage KW ( )MPapsiE

Lf psApA 2.40333,810281270

25.0 6 ==

(b) Elastic shortening

T.Chhay


edaysarEdkeRbkugRtaMgTaMgGs;RtUv)anTajkgeBlCamYyKa dUcenH elastic shortening minRtUv)anKitkgGMLgeBlTajeT. CalTplKakMhatbg;kugRtaMgedaysar elastic shortening enAkg tendon eT. dUcenH 0= pESf . (c) Friction loss

sn t;farag)a:ra:bUlrbs; tendon Rbhak;RbEhlnwgFrbs;rgVg;. BIsmIkar 3.23 ( ) 0548.0

127098.1273.1888 =

==xy ra:dg;

BItarag 3>7 yk 001.0=K nig 25.0= . bnab;mk BI]TahrN_ 3>8 ( )MPapsif pi 303,1000,189=

BIsmIkar 3.22 kMhatbg;kugRtaMgenAkgEdkeRbkugRtaMgedaysarkMlaMgkkitKW ( )KLff pipF +=

( )70001.00548.025.0000,189 += ( )MPapsi 109819,15=

kugRtaMgEdlenAsl;enAkgEdkeRbkugRtaMgeRkayBIkMhatbg;TaMgGs;KW ( )MPapsif pi 136,1848,164819,150333,8000,189 == dUcenH net prestressing force KW lbPi 762,296153.012848,164 == Edl lbPi 376,311= sMrab;krNI pretensioned enAkg]TahrN_ 3>8.

dMNak;kalTI 1 kugRtaMgenAeBlepr (a) Anchorage Seating Loss

kMhatbg; psi333,8= net stress psi848,164=

(b) Relaxation Loss

= 55.0000,230848,164

1018log848,164pRf

( )MPapsi 8.23450,3 (c) Creep Loss

0= pCRf (d) Shrinkage Loss

NPIC


0= pSHf dUcenHkugRtaMgenAkg tendon pif enAcugbBab;ndMNak;kalTI 1KW ( )MPapsif pi 113,1398,161450,3848,164 ==

dMNak;kalTI 2 eRkayBIeFVIkargarbegIyehIy KWenAeBlebtugmanGayu 30 f (a) Creep Loss

lbPi 327,296153.012398,161 ==

c

D

c

ics I

eMre

APf +

+= 2

21

720,5958.17496,464,3

11.9758.171

615327,296 2 +

+=

( )MPapsi 94.62.99600.020,120.016,2 =+= dUcenH creep loss KW ( )csdcsCRpCR ffnKf =

( ) ( )MPapsi 2.51417,73.5192.9966.172.9 = (b) Shrinkage Loss

BI]TahrN_ 3>8 nigBItarag 3>6 58.0=SHK enAGayu 30 f enaH ( )MPapsif pSH 8.24590,358.0190,6 ==

(c) Steel Relaxation Loss enAGayu 30 f psif pe 398,161=

Relaxation loss kayCa

= 55.0000,230398,161

1018log720log398,161pRf

( )MPapsi 0.27923,3 kMhatbg;kugRtaMgsrubenAkgdMNak;kalTI 2 KW

pRpSHpCRpT ffff ++= ( )MPapsi 0.103930,14923,3590,3417,7 =++=

BI]TahrN_ 3>8 karekIneLIgkugRtaMgenAkg strand EdlbNalBIbnkbEnmrbs;kargar begIyKW ( )MPapsifSD 8.34048,5= . dUcenH strand stress enAcugbBab;rbs;dMNak;kalTI 2 KW

T.Chhay


( )MPapsiffff SDpTpspe 045,1516,151048,5930,14398,161 =+=+=

dMNak;kalTI 3 eRkayGayu)anBIrqaM psif pe 516,151= 7201 =t em:ag 520,172 =t em:ag kMhatbg;kugRtaMgedaysar steel relaxation KW

= 55.0000,230516,151

10720log520,17log516,151pRf

( )MPapsi 8.15284,2 edayeRbIkarsn t;dUcKanwg]TahrN_ 3>8 sMrab; creep nig shrinkage, kugRtaMgenAkg tendon pef enAcugbBab;ndMNak;kalTI 3 mantMlRbhak;RbEhlnwg

( )MPapsif pe 029,1232,149284,2516,151 ==

11> karKNnakMhatbg;kugRtaMgtamviFIplbUksrub

Lump-Sum Computation of Time-Dependent Losses in Prestress ]TahrN_ 3>10 edaHRsay]TahrN_ 3>8 nig 3>9 eday approximate lump-sum method nigeRbobeFoblTplrbs;va.

NPIC


dMeNaHRsay BItarag 3>1 kMhatbg;srubsMrab;]TahrN_ 3>8 tam lump-sum method KW ( )MPapsif pT 310000,45= dUcenH net final strand stress KW ( )MPapsif pe 993000,144000,45000,189 ==

tMlrbs; pef EdlKNnaCaCMhan psi530,151= PaKryxusKa %9.3

000,189000,144530,151 ==

BItarag 3>2 kMhatbg;srubsMrab;]TahrN_ 3>9 tam lump-sum method KW ( )MPapsif pT 241000,35= dUcenH net final strand stress KW ( )MPapsif pe 062,1000,154000,35000,189 ==

tMlrbs; pef EdlKNnaCaCMhan psi232,149= PaKryxusKa %5.2

000,189232,149000,154 ==

eyIgeXIjfa PaBxusKarvagviFIEdlKNnaCak;Esg KNnaCaCMhan nig approximate lump-sum method mantMltUc EdlbBaak;fasMrab;krNIsg;dar nigFm taeKGaceRbIviFITaMgBIrenH CMnYsKa)an.

T.Chhay

Flexural Design of Prestressed Concrete Elements 90

IV. karKNnamuxkat;Ggt;ebtugeRbkugRtaMgrgkarBt;

Flexural Design of Prestressed Concrete Elements

1> esckIepIm Introduction kugRtaMgBt;CalTplnbnkxageRkA nigm:Um:g;Bt;. kgkrNICaeRcIn vaCaGkkMNt;kgkar eRCIserIsTMhMFrNImaRtrbs;ebtugeRbkugRtaMgedayminKitfavargkarTajCamun (pretensioned) brg karTajCaeRkay (post-tensioned) eT. dMeNIrkarKNnacab;epImCamYynwgkareRCIserIsmuxkat; bzm nigedaykarsakl,g nigkarEktMrUveKnwgTTYl)anmuxkat;cugeRkayCamYynwgTMhMlMGitrbs;muxkat; ehIynwgTMhM nigKngrbs;EdkeRbkugRtaMg. muxkat;RtUvbMeBjnUvkarkMNt;rbs;kugRtaMgBt;EdlRtUvkar rbs;ebtug nigEdk. bnab;BIenH vaRtUv)anviPaK nigbMeBjktamYycMnYneTotdUcCa lTPaBrgkarkat; lTPaBrgkarrmYl PaBdab nigsameRbH. edaysarTinnysMrab;karviPaKxusKaBITinnyEdlcaM)ac;sMrab;karKNna karKNnaTaMgGs;Ca karviPaK. dMbUgeKsn t;lkNmuxkat;FrNImaRtEdlRtUvrgeRbkugRtaMg nigbnab;mkeKcab;epmkMNt; faetImuxkat;GacrgkMlaMgeRbkugRtaMg nigkMlaMgGnuvtn_xageRkA)anedaysuvtiPaBbkGt;. dUcenHeyIg RtUvyl;BIeKalkarN_mUldannkarviPaK nigkarKNnamuxkat;EdlmanlkNsMrYly:agxaMgEdl)an ENnaMkgemeronenH. dUc)aneXIjBICMBUkTI1 lkNemkanicmUldanrbs;sMPar eKalkarN_lMnwgrbs; m:Um:g; couple xagkg nigeKalkarN_eGLasicntMrYtpl (superposition) RtUv)aneRbIenARKb;dMNak; kalnkardak;bnk. eKKNnamuxkat;ebtugGarem:rgkugRtaMgBt;EtkgsanPaBkMNt;nkugRtaMgenAeBl)ak;sMrab; muxkat;EdleRCIserIs RbsinebIvabMeBjnUvtMrUvkardTeTotdUcCa serviceability, lTPaBkgkarkat;/ nigPaBsitrvagebtug nigEdk. b:uEn kgkarKNnaGgt;ebtugeRbkugRtaMg eKcaM)ac;RtUveFVIkarRtYtBinit bEnmeTotenAeBleprkMlaMg nigsanPaBkMNt;enAeBlrgbnkeFVIkar kdUcCasanPaBkMNt;enA eBl)ak;. karRtYtBinitTaMgenHmansarsMxan;sMrab;Fanafa sameRbHedaysarbnkeFVIkarGac ecal)an ehIyeKGacRKb;RKg)annUv\TiBlryeBlyUrrbs;PaBdab nigPaBekag. eKeRbIsBaadked

Khmer Prestressed Concrete - Unknown

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