1. T.Chhay
II. sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg
Materials and Systems for Prestressing
1> ebtug Concrete
k> esckþIepþIm Introduction
sMrab;Ggát;ebtugeRbkugRtaMg ebtugersIusþg;x<s; (high-strength concrete) CaFaturYmpSMd¾sMxan;
mYy. dUcenH eKRtUvFananUvKuNPaB nigRKb;RKgKuNPaBrbs;vaedIm,ITTYl)anersIusþg; (strength)
nigPaBFn;ry³eBlEvg (long-term endurance) enAdMNak;kalénkarplitebtug.
x> )a:ra:Em:RtEdlCHT§iBldl;KuNPaBrbs;ebtug
Parameters Affecting the Quality Concrete
ersIusþg; nigPaBFn;CaKuNPaBcMbgBIrEdlmansar³sMxan;enAkñúgeRKOgbgÁúMebtugeRbkugRtaMg.
T§iBlénkarxUcKuNPaBebtugry³eBlEvgGackat;bnßykMlaMgeRbkugRtaMgy:agelOn nignaMeGay
eRKOgbgÁúM)ak;edaymin)anrMBwgTuk. dUcenH eKRtUvmanviFankarhμt;ct;CaeRcInedIm,IRKb;RKg nigFanaKuN
PaBrbs;ebtugenAkñúgdMNak;kalénkarplit dMNak;kalénkarsagsg; k¾dUcCadMNak;kaltMEhTaM.
rUbTI 2>1 bgðajBIktþaCaeRcInEdlGaceGayeyIgTTYl)anebtugEdlmanKuNPaBl¥.
K> lkçN³énebtugEdlkkrwg Properties of Hardened Concrete
eKEcklkçN³emkanicrbs;ebtugEdlkkrwgCaBIrRbePTKW³ lkçN³xN³ b¤lkçN³ry³eBlxøI
(short-term or instantaneous properties) niglkçN³ry³eBlEvg (long-term properties). lkçN³
ry³eBlxøIrYmmanersIusþg;sgát; ersIusþg;Taj ersIusþg;kat; nigPaBrwgRkaj (stiffness) Edlvas;eday
m:UDuleGLasÞic. lkçN³ry³eBlEvgman creep nigkarrYjmaD (shrinkage).
!> ersIusþg;sgát; Compressive Strength
GaRs½ynwgRbePTrbs;TWkfñaMKImI lkçN³rbs;fμbMEbk ry³eBlénkarEcTaMebtug nigKuNPaBén
karEfTaMebtug eKGacTTYl)anersIusþg;sgát;rbs;ebtugrhUtdl; 20ksi(138MPa ) b¤FMCagenH. CaTU
Materials and Systems for Prestressing 18

2. NPIC
eTAersIusþg;sgát;rbs;ebtugEdlplitedaylkçN³esdækic©CamYynwgfμbMEbkFmμtasßitenAcenøaH
4ksi (28MPa ) eTA 12ksi(83MPa ) . ebtugEdleKeRbIPaKeRcInmanersIusþg;sgát; 6ksi(42 MPa ) .
ersIusþg;sgát; f 'c )anmkBIsMNakKMrUsIuLaMgsþg;darTMhM 15cm × 30cm EdlEfTaMeRkamlkçxNÐ
BiesaFn_sþg;dar nigRtUv)aneFVIBiesaFn_edayrgkMlaMgsgát;enAGayu 28 éf¶. sþg;darEdleKeRbIsMrab;Bi-
esaFn_ersIusþg;sgát;KW ASTM C-39. ersIusþg;rbs;ebtugenAkñúgeRKOgbgÁúMCak;EsþgmindUcKñanwgersIusþg;
rbs;sMNakKMrUsIuLaMgedaysarlkçxNÐénkarbgðab; niglkçxNÐénkarEfTaMxusKña.
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 19

3. T.Chhay
sMrab;karBiesaFersIusþg; ACI Code kMNt;eRbInUvmFümPaKrbs;sMNakKMrUsIuLaMgBIrénsMPar³
dUcKña ehIyRtUv)aneFVIkarBiesaFenAGayudUcKñaEdlCaTUeTAenAGayu 28 éf¶. sMrab;karBiesaFEdlman
lkçN³jwkjab; kUdkMNt;faersIusþg;rbs;cMNat;fñak;ebtugnImYy²bMeBjlkçxNÐ)ankñúgkrNI (1)
mFümPaKénsMnMusMNakKMrUTaMgGs;énkarBiesaFbIdgCab;²RtUvFMCag b¤esμInwg f 'c EdlRtUvkar nig (2)
KμankarBiesaFsMNakKMrUmþgNa ¬mFümPaKénsIuLaMgBIr¦ tUcCag f 'c EdlRtUvkar 3.5MPa eT.
@> ersIusþg;Taj Tensile Strength
ersIusþg;Taj fct rbs;ebtugmantMéltUc EdltMélRbhak;RbEhlrbs;vasßitenAcenøaH 0.10 f 'c
nig 0.20 fct . eKBi)aknwgvas;ersIusþg;TajCagersIusþg;sgát;edaysarEtkarKabsMNakKMrUeTAnwgm:asIun
BiesaFn_. eKmanviFICaeRcInkñúgkarBiesaFersIusþg;Tajrbs;ebtug EtviFIEdleKniymeRbICageKKWkar
BiesaFsgát;bMEbksIuLaMg (cylinder splitting or Brazilian test).
enAkñúgkarKNna eKcUlcitþeRbItMélrbs;m:UDuldac; f r (modulus of rupture) CagkareRbI
ersIusþg;Tajedaykarsgát;bMEbk fct (tensile splitting test) sMrab;Ggát;rgkarBt;. m:UDuldac;RtUv)an
vas;edaykarBiesaFkac;bM)ak;;sMNakKMrURBIsebtugsuT§edayrgbnÞúkcMnucTIbI (third point) (ASTM C-
78) . sMNakKMrUenHmanmuxkat;ragkaer: EdlRCugrbs;vamanTMhM 15cm nigmanRbEvg 45cm . m:UDul
dac;rbs;ebtugmantMélFMCagersIusþg;Tajedaykarsgát;bMEbk. ACI kMNt;ykm:UDuldac;esμInwg
7.5 f 'c psi (0.623 f 'c MPa ) sMrab;ebtugTMgn;Fmμta.
CaTUeTA ebtugTMgn;RsalmanersIusþg;TajtUcCagebtugTMgn;Fmμta. xageRkamenHCakarkMNt;
m:UDuldac;rbs;ebtugTMgn;Rsal³
a. RbsinebIersIusþg;Tajedaykarsgát;bMEbk f ct RtUv)ankMNt;
f r = 1.09 f ct ≤ 0.623 f 'c (2.1)
b. RbsinebI fct minRtUv)ankMNt; eRbIemKuN 0.75 sMrab;RKb;ebtugTMgn;Rsal nig
0.85 sMrab;ebtugTMgn;RsalEdlplitBIxSac;. eKGaceRbI linear interpolation
sMrab;karlayedayeRbIl,ayxSac; nigfμbMEbkl¥itTMgn;Rsal.
#> ersIusþg;kat; Shear Strength
ersIusþg;kat;BitCamankarBi)akkñúgkarkMNt;edaykarBiesaFCageK edaysarPaBBi)akkñúgkar
dak;eGaykugRtaMgkat;enAdac;edayELkBIkugRtaMgd¾éT. vaCamUlehtuEdleFVIeGaymanbMErbMrYly:agFM
Materials and Systems for Prestressing 20

4. NPIC
éntMélrbs;ersIusþg;kat; EdlERbRbYlBI 20% énersIusþg;sgát;sMrab;kardak;bnÞúkFmμta eTAdl; 85%
énersIusþg;sgát;sMrab;krNImanbnSMkMlaMgsgát; nigkMlaMgkat;edaypÞal;. karRtYtBinitükarKNna
eRKOgbgÁúMedayersIusþg;kat;CakrNIkMrbMput edaysarersIusþg;kat;RtUv)ankMNt;edaytMéltUcedIm,Ikar
BarebtugBIkar)ak;edaykMlaMgTajGgát;RTUg.
2> ExSekagkugRtaMg-bMErbMrYlrageFobrbs;ebtug
Stress-Strain Curve of Concrete
cMeNHdwgBITMnak;Tng stress-train rbs;ebtugmansar³sMxan;Nas;sMrab;dMeNIrkarviPaK nig
KNnaeRKOgbgÁúMEdleFVIBIebtug. rUbTI 2>2 bgðajBIExSekag stress-strain KMrUEdlTTYl)anBIkar
BiesaFedayeRbIsMNakKMrUebtugsIuLaMgEdlrgbnÞúksgát;tamG½kSeTalry³eBlCaeRcInnaTI. eKGac
cat;TukEpñkTImYyrbs;ExSekagRbEhl 40% énersIusþg;x<s;bMput (ultimate strength) manlkçN³
smamaRt (linear) sMrab;RKb;karBiesaFTaMgGs;. bnÞab;mkRbEhl 70% énkugRtaMg)ak; (failure
stress) )at;bg;PaBrwgrbs;vay:ageRcIn edaybegáInkMeNag. enARtg; ultimate load sñameRbHtam
beNþayTisénkardak;bnÞúkcab;epþImelcecjy:agc,as; ehIysMNakKMrUsIuLaMgPaKeRcIn ¬elIkElg
sMNakKMrUEdlmanersIusþg;tUcNas;¦ EbkPøam²kñúgry³eBld¾xøI. rUbTI 2>3 bgðajBIExSekag stress-
strain rbs;ebtugEdlmanersIusþg;eRcInRbePTEdleFVIeLIgeday Portland Cement Association.
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 21

5. T.Chhay
eyIgeXIjfa (1) ebtugEdlmanersIusþg;kan;EttUc manbMErbMrYlrageFobkan;EtFM (2) RbEvgéncMENk
smamaRtdMbUgekIneLIgCamYynwgkarkarekIneLIgénersIusþg;sgát;rbs;ebtug (3) PaBsVit (ductility)
RtUv)ankat;bnßyCamYynwgkarekIneLIgénersIusþg;.
Materials and Systems for Prestressing 22

6. NPIC
3> m:UDuleGLasÞic nigkarERbRbYlersIusþg;sgát;CamYynwgeBl
Modulus of Elasticity and Change in Compressive Strength with Time
edaysarExSekag stress-strain EdlbgðajenAkñúgrUbTI 2>4 manlkçN³ekag (curvilinear)
taMg BIdMNak;kaldMbUgénRbvtþiénkardak;bnÞúkrbs;va. eKGacTTYl)anm:UDuleGLasÞicEtBIbnÞat;b:HeTA
nwgExSekagRtg;cMnuceKal. CMraldMbUg (initial slope) rbs;bnÞat;b:HeTAnwgExSekagRtUv)ankMNt;Ca
m:UDulb:HedIm (initial tangent modulus) ehIyeKGacsg;bnÞat;b:HRKb;cMnucTaMgGs;enAelIExSekag.
bnÞat;eRTtRtg;EdlP¢ab;BIcMnuceKaleTAkugRtaMgEdleGay ¬RbEhl 0.4 f 'c ¦ kMNt;nUv secant
modulus of elasticity rbs;ebtug. tMélenHbMeBjlkçxNÐsnμt;fasMPar³manlkçxN³eGLasÞic
edaybMErbMrYlerogeFobEdlekItmankñúgGMLúgénkardak;bnÞúkrt;eTArkTItaMgedImEdlminTan;rgbnÞúkvij
ehIybMErbMrYlerogeFobbnþbnÞab;eTotedaykardak;bnÞúkbEnßmRtUv)ancat;TukCa creep.
ACI Code eGaysmIkarxageRkamsMrab;KNna secant modulus of elasticity rbs;ebtug/
Ec
sMrab; 90 < wc < 155lb / ft 3
Ec = 33w1.5 f 'c Psi
c
Edl wc Cadg;sIuetrbs;ebtug nig f 'c CaersIusþg;sgát;. sMrab;ebtugTMrg;Fmμta
Ec = 57000 f 'c psi (4700 f 'c MPa )
b¤ Ec = 0.043w1.5 f 'c MPa
c
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 23

7. T.Chhay
k> ebtugersIusþg;x<s; High-Strength Concrete
ebtugersIusþg;x<s;CaebtugEdlmanersIusþg;sgát;edayeRbIsMNakKMrUsIuLaMgFMCag 6ksi
(41.4MPa ) . sMrab;ebtugEdlmanersIusþg;enAcenøaH 42MPa − 84MPa smIkarsMrab;m:UDuleGLasÞic
rbs;ebtugKW
[ ]
1.5
⎛w ⎞
Ec ( psi ) = 40000 f 'c + 10 6 ⎜ c ⎟ (2.3a)
⎝ 145 ⎠
[ ]
1.5
⎛ w ⎞
b¤ Ec (MPa ) = 3.32 f 'c + 6895 ⎜ c ⎟
⎝ 2320 ⎠
(2.3b)
sBVéf¶enH eKGacTTYl)anersIusþg;rbs;ebtugrhUtdl; 138MPa edayeRbIfμbMEbkTMhM
3
8
in.(9.5mm ) nig pozzolamic cementitious CMnYseGaysIum:g;t¾dUcCa silica fume. eKGacTTYl)an
ersIusþg;EbbenHenAkardæaneRkamlkçxNÐkarFanaKuNPaB nigkarRKb;RKgKuNPaBy:agditdl;. sMrab;
ersIusþg;EdlenAcenøaH 138MPa − 206MPa eKRtUvbEnßmsarFaturYmpSMd¾éTeTotdUcCaEdk b¤ carbon
fiber. sMrab;RKb;krNITaMgGs;enH eKRtUveFVIkarsakl,glayl,ayebtugCaeRcInKMrU ¬y:agtic 5 ¦
enAkardæan edayEkERbsarFatupSMedIm,ITTYl)anPaBgayRsYleFVIkar (workability) EdlRtUvkarkñúgkar
cak;ebtug. eKeRbIBum<sIuLaMgEdkEdlmanGgát;p©it 10cm nigmankMBs; 20cm edayGnuvtþkarEkERb
TMhM. tarag 2>1 raynUvsarFatupSMedIm,ITTYl)anersIusþg;sgát;FMCag 18000 psi(124MPa) enAGayu
56 éf¶ EdlelxenAkñúgvg;RkckCatMél design mixture. rUbTI 2>5 bgðajBIdüaRkamersIusþg;sgát;-
GayuedayeRbIBum< 10cm × 20cm sMrab;l,ay ebtugEdl)anlaydUcbgðajkñúgtarag 2>1. tarag 2>2
bgðajBIl,ayebtugEdl)an design sMrab;ersIusþg; 84MPa enAGayu 7 éf¶. pleFob sIum:g;t¾ / fμbM-
Ebkl¥it / fμbMEbkFM KW 1 : 1.22 : 2.06 ehIyPaBravERbRbYlcenøaH 100 − 150mm . rUbTI 2>6 bgðajBI
muxkat;FñwmsmasEdleRbIRBIsebtugeRbkugRtaMgenAelIsøabRtg;TMr.
tarag 2>1 l,aypSMsMrab; f 'c > 18000 psi(124MPa)
Superplasticizer
W. R. Grace
fμbMEbbFM fμbMEbkl¥it Dartard
40
Mighty
150
3
in. (9.5mm) ¬xSac;¦ sIum:g;t¾ Twk Silica
8
fume g / 100kg sIum:g;t¾
(kg ) (kg ) (kg ) (kg ) (l )
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. TwkEdlCaEpñkénl,ayTwkRtUv)andkecjBITwkEdlGnuBaØatsrub.
Materials and Systems for Prestressing 24

8. NPIC
tarag 2>2 l,aypSMsMrab; f 'c > 18000 psi(124MPa )
fμbMEbbFM fμbMEbkl¥it sIum:g;t¾Br½ELn Powder
3
8
in.(9.5mm) ¬xSac;¦ RbePT III Twk Silica fume
force 10000
Liquid
Superplasticizer
(kg ) (kg ) (kg ) (kg ) (l ) (Grace)
(1) (2) (3) (4) (5) (6)
1092 649 425 170 106 32
x> ersIusþg;sgát;edIm nigm:UDuleGLasÞic
Initial Compressive Strength and Modulus
edaysareKGnuvtþkMlaMgeRbkugRtaMgmuneBlebtugTTYl)anersIusþg;enAGayu 28 éf¶ eKcaM)ac;
kMNt;ersIusþg;sgát;rbs;ebtug f 'ci enAéf¶GnuvtþkMlaMgeRbkugRtaMg k¾dUcCam:UDuleGLasÞic Ec rbs;va
enAdMNak;kalepSg²énRbvtþiénkardak;bnÞúkeTAelIGgát;. smIkarTUeTAénersIusþg;sgát;EdlCaGnuKmn_
GaRs½ynwgeBlKW
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 25

9. T.Chhay
t
f 'ci = f' (2.4a)
α + βt c
Edl ersIusþg;sgát;enAGayu 28 éf¶
f 'c =
t = ry³eBlKitCaéf¶
α = emKuNGaRs½ynwgRbePTrbs;sIum:g;t¾ niglkçxNÐénkarEfTaMebtug
Materials and Systems for Prestressing 26

10. NPIC
sMrab;sIum:g;t¾RbePT I CamYynwgkarEfTaMedaysMeNIm (moist-cured type –I cement)
= 4 .0
= 2.3 sMrab;sIum:g;t¾RbePT III CamYynwgkarEfTaMedaysMeNIm (moist-cured type –I
cement)
= 1 .0 sMrab;sIum:g;t¾RbePT I CamYynwgkarEfTaMedaycMhayTwk (steam-cured type –I
cement)
= 0 .7 sMrab;sIum:g;t¾RbePT III CamYynwgkarEfTaMedaycMhayTwk (steam-cured type –I
cement)
β= emKuNGaRs½ynwg)a:ra:Em:RtEdlRtUvKñanwgemKuN α . vaesμInwg 0.85 / 0.92 / 0.95 nig
0.98 erogKña.
dUcenHsMrab;ebtugEdlplitBIsIum:g;t_RbePT I CamYynwgkarEfTaMedaysMeNIm
t
f 'ci = f 'c (2.4b)
4.0 + 0.85t
m:UDuleGLasÞicRbsiT§PaB (effective modulus) rbs;ebtugKW
stress
E 'c = (2.5)
elastic strain + creep strain
ehIym:UDuleGLasÞicRbsiT§PaBx<s;bMput (ultimate effective modulus) KW
Ec
Ecn = (2.6a)
1+ γt
Edl γ t Ca creep ratio Edl
ultimate creep strain
γt =
elasticstrain
Creep ratio γ t manEdnkMNt;x<s;bMput nigTabbMputsMrab;ebtugeRbkugRtaMgEdlmanKuNPaB
x<s;.
⎛ 100 − H ⎞
EdnkMNt;x<s;bMput³ γ t = 1.75 + 2.25⎜
⎝ 65 ⎠
⎟ (2.6b)
⎛ 100 − H ⎞
EdnkMNt;TabbMput³ γ t = 0.75 + 0.75⎜
⎝ 50 ⎠
⎟ (2.6c)
Edl H CasMeNImmFüm (mean humidity) KitCa % .
BIsmIkarxagelI eyIgeXIjfaktþaEdlCHT§iBlelItMélrbs;m:UDuleGLasÞicEdleRkAebIbnÞúk
enAmansMeNImenAkñúgebtug pleFobTwkelIsIum:g;t_ Gayurbs;ebtug nigsItuNðPaB. dUcenHsMrab;eRKOg
EdlmanlkçN³BiessdUcCa arches, tunnel nig Gag eKcaM)ac;kMNt;m:UDuleGLasÞicrbs;ebtugBI
lT§plénkarBiesaF. edaysarEtersIusþg;Tajrbs;ebtugmantMéltUcdUcenHeKmin)ankMNt;m:UDul
eGLasÞickñúgkarTajeT EteKsnμt;m:UDuleGLasÞickñúgkarTajesμInwgm:UDuleGLasÞickñúgkarsgát;.
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 27

11. T.Chhay
4> Creep
Creep b¤ lateral material flow CakarekIneLIgénbMErbMrYlrageFob (strain) CamYynwgeBl
evlaEdlbNþalmkBIbnÞúkGcié®nþy_. kMhUcRTg;RTayedIm (initial deformation) EdlbNþalmkBI
bnÞúk KWbMErbMrYlrageFobeGLasÞic (elastic strain) cMENkÉbMErbMrYlrageFobbEnßmEdlbNþalmkBI
bnÞúkdEdlKWCa creep strain.
rUbTI 2>7 bgðajBIkarekIneLIgrbs; creep strain CamYynwgeBl. enAkñúgkrNI shrinkage
eyIgeXIjfa creep stain fycuHeTAtameBl. eKminGacemIleXIj creep edaypÞal; EteKGackMNt;
vaedaykardk elastic strain nig shrinkage strain BI total strain )an. eTaHbICa shrinkage nig creep
minEmnCa)atuPUtEdlÉkraCüBIKñak¾eday eKsnμt;faeKGaceRbIviFItMrYtpl (superposition) sMrab;
strain )an. dUcenH
Total strain (ε t ) = elastic strain (ε e ) + creep(ε c ) + shrinkage(ε sh )
rUbTI 2>8 bgðajKMrUkñúglMhrén strain bIRbePTEdlbNþalBIbnÞúksgát;Gcié®nþy_ nig
shrinkage. edaysar creep GaRs½ynwgeBl dUcenHG½kSEkgrbs;vaKW kMhUcRTg;RTay kugRtaMg nig
eBl.
karBiesaFCaeRcIn)anbgðajeGayeXIjfa creep deformation smamaRteTAnwgbnÞúkGnuvtþn_
b:uEnþPaBsmamaRtenHmantMélsMrab;EtkMritkugRtaMgtUc. eKminGackMNt;EdnkMNt;x<s;bMput)any:ag
suRKiteT b:uEnþvaGacERbRbYlcenøaHBI 0.2 eTA 0.5 én f 'c . tMélénEdnkMNt;enHbNþalmkBIkarral
dalén microcrack enAeBlEdlvargbnÞúk)anRbEhl 40% ultimate load.
Materials and Systems for Prestressing 28

12. NPIC
rUbTI 2>9a bgðajBImuxkat;rbs;KMrUkñúglMhrenAkñúgrUbTI 2>8 EdlRsbeTAnwgbøg;EdlmanG½kSkMhUcRTg;
RTay nigG½kSkugRtaMgenARtg;eBl t1 . vabgðajfa TaMg elastic strain nig creep strain smamaRteTA
nwgkugRtaMgEdlGnuvtþ. dUcKñarUbTI 2>9 b bgðajmuxkat;RsbeTAnwgbøg;EdlmanG½kSeBl nigG½kSkMhUc
RTg;RTay enARtg;kugRtaMg f1 . dUcenH vabgðajnUvPaBdUcKñarvagTMnak;TMngén creep nigeBl nigTMnak;
TMngén shrinkage nigeBl.
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 29

13. T.Chhay
enAkñúgkrNI shrinkage, kMhUcRTg;RTayedaysar creep eRkamGMeBIénbnÞúkGcié®nþy_minRtLb;
eTArkPaBedImTaMgRsugrbs;vavijeT. RbsinebIeKdkbnÞúkBIsMNakKMrUbnÞab;BIry³eBlrgbnÞúkd¾yUr eK
TTYl)ankarRtLb;eTArkPaBedImeGLasÞicPøam²EttUcCagbMErbMrYlrageFobeRkamGMeBIrbs;bnÞúk. kar
RtLb;eTArkPaBedImxN³bnþedaykarkat;bnßybMErbMrYleFoby:agsnSwm² EdleKeGayeQμaHfa
creep recovery. karRtLb;eTArkPaBedImvijGaRs½yeTAnwgGayurbs;ebtugenAeBlrgbnÞúk ebtugkat;
EtmanGayueRcIn creep recovery kan;EtFM ¬rUbTI 2>10¦.
CreepmanTMnak;TMngy:agCitsñitCamYynwg shrinkage ehIytamc,ab;TUeTA ebtugEdlTb;Tl;
nwg shrinkage )an k¾man creep tUcEdr Edl)atuPUtTaMgBIrenHmanTMnak;TMngeTAnwg hydrated cement
paste. dUcenH creep TTYlT§iBlBIFatupSMrbs;ebtug lkçxNÐbridæan nigTMhMrbs;sMNakKMrU. b:uEnþCa
eKalkarN_ creep GaRs½ynwgkardak;bnÞúkEdlCaGnuKmn_nwgeBl.
eKkMNt;FatupSMrbs;sMNakKMrUebtugedaypleFobTwkelIsIum:g;t_ nigpleFobTwkelIsarFatu
m:t;pg;enAeBleKeRbITw kfñaMKImI/ edayfμbMEbk nigRbePTsIum:gt_/ nigedayfμ bMEbk nigbrimaNsIum:g;t_.
dUcenH kalNapleFobTwkelIsIum:g;t_ nigbrimaNsIum:g;t_kan;EteLIgx<s; creep nig shrinkage kan;Et
FM. kalNabrimaNfμbMEbkkan;eLIgeRcIn shrinkage nig creep kan;Etkan;bnßy.
Materials and Systems for Prestressing 30

14. NPIC
k> Effects of Creep
dUcKñanwg shrinkage Edr creep begáInPaBdabrbs;Fñwm nigkMralxNÐ ehIyeFVIeGay)at;bg;kM-
laMgeRbkugRtaMg. elIsBIenH cMNakp©itedImrbs;ssrebtugGarem:ekIneLIgeTAtameBledaysar
creep EdleFVIeGaymankarepÞrkMlaMgsgát;BIebtugeTAEdk.
enAeBlEdlEdk yield, ebtugnwgrgbnÞúkbEnßm. dUcenH ersIusþg;rbs;ssrbnßycuH ehIykM-
eNagrbs;ssrekIneLIg EdleFVIeGayebtugrgkugRtaMgelIs nignaMdl;kar)ak;.
x> Rheological Models
Rheological model Ca]bkrN_emkanicEdlBN’naBIkMhUcRTg;RTayTUeTArbs;sMPar³eRkam
GMeBIrbs;kugRtaMg. Model enHpSMeLIgedayrWus½reGLasÞic (elastic spring) nig dashpot EdlkMNt;
CakugRtaMg/ elastic strain, delayed elastic strain, irrecoverable strain nigeBl. rWus½rtMNageGay
PaBsmamaRtrvagkugRtaMg nigbMErbMrYlrageFob ehIy dashpot tMNageGayPaBsmamaRtrvagkug
RtaMg nigGRtaénbMErbMrYlerogeFob. rWus½r nig dashpot EdltMerobCaExñgbegáIt)anCa Kelvin unit É
kartMerobCaes‘rIbegáIt)anCa Maxwell unit.
rUbTI 2>11 bgðajBI Burgers model EdleKGacBiesaFBIkareFVIkarCaTMnak;TMngrvag kugRtaMg
-strain-eBl rbs;ebtugenARtg;EdnsmamRtCamYynwgkarkMNt;xøH. Model enHBiesaFrkbMErbMrYlrag
eFobEdlGacRtLb;eTArkPaBedImxN³ (instantaneous recoverable strain) a / delayed recover-
able elastic strain enAkñúgrWus½r b nig irrecoverable time-dependent strain enAkñúg dashpot c nig
d . PaBTn;exSayrbs; model enHKWfavabnþxUcRTg;RTayeRkamGRtaefrenAeBlEdlbnÞúkRtUv)anTb;
Tl;eday Maxwell dashpot EdlkareFVIkarEbbenHminRsedogKñanwgebtugeT Edl creep eTAdl;tMél
kMNt;CamYynwgeBl dUcbgðajenAkñúgrUbTI 2>7.
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 31

15. T.Chhay
Ross rheological model EdlbgðajenAkñúgrUbTI 2>12 Ca model Edl)anEkERbedIm,Ilub
bM)at;PaBxVHxatrbs; Burger model. A enAkñúg model enHtMNageGayPaBsmamaRtén stress-
strain rbs;sMPar³tamc,ab;h‘Uk/ D Ca dashpot ehIy B nig C CarWus½reGLasÞicEdlGacbBa¢ÚnkMlaMg
Gnuvtþn_ P(t ) épÞrbs;sIuLaMgbiTCitedaykMlaMgkkit.
smIkarKNitviTüamYytamry³ Ross model sMrab;kMNt; creep eRkamGMeBIrbs;bnÞúkkñúgcenøaH
ry³eBl t KW
t
C= (2.7)
a + bt
Edl a nig b CatMélefrEdlGackMNt;)anBIBiesaFn_.
Brason )ansMrYlkarvaytMélrbs; creep. eKGackMNt;bMErbMrYlrageFobbEnßm ε cu Edl
bNþalBI creep KW
ε cu = ρu f ci (2.8)
Edl ρu = emKuN creep Éktþa EdlCaTUeTAeKehAvafa specific creep
f ci = GaMgtg;sIuetkugRtaMgenAkñúgGgát;eRKOgbgÁúMEdlRtUvKñanwgbMErbMrYlrageFobÉktþa ε cu
Ultimate creep coefficient Cu manrag
Cu = ρ u Ec (2.9)
b¤tMélmFümrbs;vaKW Cu ≈ 2.35 .
emKuN creep enARKb;xN³ ¬sMrab;lkçxNÐsþg;dar¦ manrag
t 0.6
Ct = Cu (2.10)
10 + t 0.6
t 0. 6
b¤müa:geTot ρt =
10 + t 0.6
(2.11)
Materials and Systems for Prestressing 32

16. NPIC
Edl t CaeBlKitCaéf¶ nig ρt CaemKuNeBl. lkçxNÐsþg;darEdlkMNt;eday Brason KWebtugRtUvman
PaBragticCag b¤esμI 10cm nigmansMeNImbriyakas (relative humidity) 40% . RbsinebIlkçxNÐ
minsþg;dar eKRtUvGnuvtþemKuNEksMrYl creep eTAelIsmIkar 2.10 nig 2.11 dUcxageRkam³
(a) sMrab; moist-cured concrete EdlrgbnÞúkenAGayu 7 éf¶ b¤eRcInCagenH
k a = 1.25t −0.118 (2.12)
(b) sMrab; steam-cured concrete EdlrgbnÞúkenAGayu 1éf¶eTA 3 éf¶ b¤eRcInCagenH
k a = 1.13t −0.095 (2.13)
sMrab; relative humidity FMCag 40% eKRtUvKuNemKuNEksMrYlxageRkameTAelIsmIkar 2.12
nig 2.13
k c1 = 1.27 − 0.0067 H (2.14)
Edl H = relative humidity KitCa % .
5> karrYmmaD Shrinkage
CaTUeTA shrinkage manBIrRbePTKW plastic shrinkage nig drying shrinkage. Plastic shrin-
kage ekItmankñúgGMLúgeBlb:unμanem:ageRkayeBlcak;ebtugRss;cUlkñúgBum<. épÞkMralxNÐgayrg
xül;s¶ÜtedaysarépÞb:Hrbs;vaFM. kñúgkrNIEbbenH sMeNImrbs;vahYtBIépÞxagelIrbs;ebtugelOnCag
clnasm<aFTwkrt;eLIgelIBIRsTab;xageRkamrbs;ebtug. cMENkÉ Drying shrinkage ekItmaneRkay
eBlEdlebtugTTYl)an final set ehIydMeNIrkarGIuRdatkmμKImIrbs;TwksIum:g;t_RtUv)anbBa©b;.
Drying shrinkage Cakarkat;bnßymaDrbs;ebtugenAeBlEdlva)at;bg;sMeNImedaysarrMhYt.
)atuPUtEdlpÞúynwg shrinkage CakarekInmaDtamry³karbWtTwk EdleKeGayeQμaHfaehIm (swelling).
eKGacniyaymüa:geTotfa shrinkage nig swelling Caclnaecj cUlrbs;TwkenAkñúgrcnasm<½n§rbs;
TwksIum:g;t_énsMNakKMrUebtugEdlbNþalmkBIkMritsMeNIm nigkMritEq¥tTwkxusKñarvagsMNakKMrU nig
briyakasEdlenACMuvijvaedayminKitbnÞúkxageRkA.
Shrinkage minmandMeNIrRtLb;eTArkPaBedImeBjeljeT. eTaHbICaeKdak;dMuebtugEdlrYm
maDRKb;RKan;RtaMTwkeGayEq¥t k¾vaminGacrIkeTArkmaDedImrbs;vavij)aneT. rUbTI 2>13 bgðajBIkar
ekIneLIgbMErbMrYlrageFobedaysar shrinkage ε sh CamYynwgeBl. GRtaénkarekIneLIgenHfycuH
CamYynwgeBlsMrab;ebtugEdlmanGayueRcInEdlmanlT§PaBeRcInkñúgkarTb;Tl;CamYynwgkugRtaMg
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 33

17. T.Chhay
dUcenHvargnUv shrinkage tictYcedaybMErbMrYlrageFobedaysar shrinkage esÞIrb:HnwgbnÞat;GasIumtUt
EdlRsbnwgbnÞat;eBl.
ktþaCaeRcInCHT§iBldl;TMhMrbs; drying shrinkage KW³
a. fμbMEbk (aggregate) ³ fμbMEbkeFVIskmμPaBTb;karrYmmaDrbs;TwksIum:g;t_ dUcenHebtugEdl
manbrimaNfμbMEbkeRcInRbQmnwgkarrYmmaDtictYc. elIsBIenH lkçN³rbs;fμbMEbkCa
GñkkMNt;kMritTb;Tl;karrYmmaD. fμbMEbkEdlmanm:UDuleGLasÞickan;FM b¤manépÞeRKImkan;
FM kan;EtmansmtßPaBkñúgkarTb;Tl;karrYmmaDrbs;ebtug.
b. pleFobTwkelIsIum:g;t_ (water/cement ratio)³ pleFobTwkelIsIum:g;t_kan;EtFM kan;Etman
shrinkage FM. rUbTI 2>14 CadüaRkaménTMnak;TMngrvagbrimaNfμbMEbk nigpleFobTwk
elIsIum:g;t_.
Materials and Systems for Prestressing 34

18. NPIC
TMhMrbs;ebtug (size of the concrete element)³ TaMgGRta nigTMhMsrubrbs;karrYmmaD
c.
fycuHCamYynwgkarekIneLIgénmaDrbs;ebtug. b:uEnþ eRKOgbgÁúMEdlmanTMhMFMRtUvkarry³
eBlénkarrYmmaDyUrCag edaysarvaRtUvkareBlevlasMrab; drying shrinkage eTAdl;
tMbn;xagkñúg. vaGacRtUvkarry³eBl 1qñaMsMrab;dMeNIrkar drying shrinkage cab;epþImenA
CMerA 25cm BIépÞrgsMBaF ehIyvaRtUvkarry³eBl10qñaMedIm,Icab;epþImenACMerA 60cm BI
eRkamépÞxageRkA.
d. lkçxNÐbriyakasmFüm (medium ambient condition)³ Relative humidity mFümCH
T§iBly:agxøaMgdl;karrYmmaD. GRtaénkarrYmmaDnwgtUc enAeBl relative humidity x<s;.
sIutNðPaBCaktþamYyepSgeTot EdlkarrYmmaDnwgmanlMnwgenAeBlsItuNðPaBTab.
e. brimaNrbs;EdkBRgwg (amount of reinforcement)³ ebtugBRgwgedayEdkrYmmaDticCag
ebtugsuT§. PaBxusKñarbs;vaCaGuKmn_nwgPaKryEdk.
f. TwkfñaMKImI (admixture)³ T§iBlrbs;TwkfñaMKImIGaRs½ynwgRbePTrbs;va. TwkfñaMKImIBenøÓn
karkkrwg (accelerator) dUcCa calcium chloride eFVIeGaykarrYmmaDekIneLIg. Pozzolan
k¾begáIn drying shrinkage Edr Et air-entraining agent manT§iBltictYcb:ueNÑaH.
g. RbePTsIum:g;t_ (type of cement)³ sIum:g;t_EdlkkrwgelOnrYmmaDxøaMgCagRbePTsIum:g;t_
epSg²eTot. EtsIum:g;t_EdlTUTat;karrYmmaDkat;bnßy b¤lubbM)at;sñameRbHedaykar rYm
maD RbsinebIeKeRbIvaCamYyEdkBRgwg.
h. Rbtikmμ]sμ½nkabUnic (carbonation)³ karrYmmaDedaysarRbtikmμ]sμ½nkabUnicRtUv)anbegáIt
eLIgedaysarRbtikmμrvag]sμ½nkabUnicEdlmanenAkñúgbriyakasCamYynwg]sμ½nkabUnic
EdlmanenAkñúgTwksIum:g;t_. brimaNénkarrYmpSMénkarrYmmaDedaysar drying nigeday
sar carbonation ERbRbYlGaRs½ynwgPaBjwkjab;énkarRbRBwtþeTArbs;va. RbsinebI)atu-
PUtTaMgBIrenHekIteLIgkñúgeBldMNalKña karrYmmaDnwgmanTMhMtUcCag. EtdMeNIrkarénkar
rYmmaDeday carbonation RtUv)ankat;bnßyy:agxøaMgenA relative humidity eRkam 50% .
Brason ENnaMnUvTMnak;TMngxageRkamsMrab; shrinkage strain CaGnuKmn_nwgeBlsMrab;lkçxNÐ
sMeNImbriyakassþg;dar ¬ H ≅ 40% ¦³
sMrab; moist-cured concrete enAey³eBl t eRkay 7 éf¶
ε SH ,t =
t
(ε SH ,u ) (2.15)
35 + t
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 35

19. T.Chhay
Edl ε SH ,u = 800 ⋅10−6 mm / mm RbsinebIeKKμanTinñn½ykñúgtMbn;eTenaH
sMrab; steam-cured concrete bnÞab;BIGayu 1éf¶eTA 3 éf¶
ε SH ,t =
t
(ε SH ,u ) (2.16)
55 + t
sMrab;lkçxNÐeRkABIlkçxNÐsþg;dar eKRtUvGnuvtþemKuNEttMrUveTAelIsmIkar 2.15 nig 2.16 dUc
xageRkam³
sMrab; 40% < H ≤ 80% k SH = 1.40 − 0.010 H (2.17a)
sMrab; 80% < H ≤ 100% k SH = 3.00 − 0.30 H (2.17b)
6> EdkminEmneRbkugRtaMg Nonprestressing Reinforcement
EdkBRgwgFmμtasMrab;ebtugrYmman bar, wire nig welded wire fabric EdlvaRtUv)anplit
edayeKarBtam ASTM standard. lkçN³sMxan;²rbs;EdkBRgwgrYmman³
a. m:UDuleGLasÞic b¤m:UDulyuaMg (Young’s modulus) Es
b. ersIusþg;yal (yield strength) f y
c. ersIusþg;x<s;bMput (ultimate strength) f u
d. Steel grade designation
e.TMhM nigGgát;p©itrbs; bar b¤ wire
edIm,IbegáInPaBs¥itrvagEdk nigebtug eK)anplitEdkEdlelcecjnUvExSvN½ÐCuMviépÞrbs;Edk
ehIyEdkTaMgenaHRtUv)aneKehAfa deformed bar dUcbgðajenAkñúgrUbTI 2>15. ExSvNнEdleljecj
enHRtUvbMeBjlkçxNÐ ASTM Specification A616-76 edIm,ITTYlsÁal;Ca deformed bar.
Materials and Systems for Prestressing 36

20. NPIC
rUbTI 2>16 bgðajBIExSekag stress-strain sMrab;Edk garde 40 / 60 nig 70 Edlman yield
strength 276 MPa / 345MPa nig 517 MPa erogKña nigCaTUeTAmancMnuc yield c,as;las;. sMrab;
EdkEdlminmancMnuc yield c,as;las; eKkMNt;yktMélrbs; yield strength CaersIusþg;EdlRtUvKñanwg
bMErbMrYlrageFob 0.005 sMrab;Edk grade 40 / 60 ehIy 0.0035 sMrab; grade 80 . ersIusþg;Tajcug
eRkay (ultimate tensile strength) EdlRtUvKñanwgEdk grade 40 / 60 nig 80 KW 483MPa / 621MPa
nig 690MPa erogKña. RbePTEdkxøHeTotmanenAkñúgtarag 2>3. PaKrysac;lUtenAeBldac;Edl
ERbRbYleTAtam grade rbs;Edk/ Ggát;p©itEdk/ sarFatuedIm sßitenAcenøaH 4.5% eTA12% elIRbEvg
Rkit 20cm .
kareRbIR)as; welded wire fabric )anekIneLIgy:agxøaMgsMrab;kMralxNÐ edaysarPaBgay
RsYlkñúgkartMeLIg karRKb;RKgKMlatEdk nigPaBetagebtug)anl¥. Fabric reinforcement RtUv)an
plitBIEdkrelag b¤ deformed wire Edlrt;kñúgTisEkgKña ehIyRtUv)anpSarP¢ab;KñaRtg;kEnøgEdlkat;
Kña. tarag 2>5 bgðajBIlkçN³FrNImaRtsMrab; standard wire reinforcement xøH.
sMrab; mild steel PaKeRcIn kareFVIkarrbs;vaRtUv)ansnμt;Ca eGLasþÚ)aøsÞic nigmanm:UDuleGLa-
sÞicesμInwg 200 × 103 MPa . tarag 2>3 bgðajBI reinforcement grade nig strength nigtarag 2>4
bgðajBIlkçN³FrNImaRténTMhMepSg²rbs;Edk.
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 37

21. T.Chhay
tarag 2>3 reinforcement grade and strength
cMnucyalGb,brma b¤ersIusþg;yal fy ersIusþg;x<s;bMput fu
1982 standard type
( psi ) (MPa ) ( psi ) (MPa )
Billet steel ( A615)
Grade (40 ) 40000 276 70000 483
Grade (60 ) 60000 345 90000 621
Axle steel ( A617 )
Grade (40 ) 40000 276 70000 483
Grade (60 ) 60000 345 90000 621
Low-alloy steel ( A706 )
Grade (60 ) 60000 345 80000 551
Deformed wire
Reinforced 75000 517 85000 586
Fabric 70000 483 80000 551
Smooth wire
Reinforced 70000 483 80000 551
75000
Fabric 65000 b¤ 56000 448 b¤ 386 b¤70000 517 b¤ 483
tarag 2>4 TMgn; RkLaépÞ nigbrimaRtrbs; bar
Standard nominal dimensions
Bar designation TMgn;kñúgmYyÉktþaRbEvg Ggát;p©it db RkLaépÞmuxkat; brimaRt
Ab [in.2 (mm 2 )]
number
[ plf (kg / m)] [in.(mm)] [in.(mm)]
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)
Materials and Systems for Prestressing 38

22. NPIC
7> EdkeRbkugRtaMg Prestressing Reinforcement
k> RbePTEdkeRbkugRtaMg Type of Reinforcement
edaysarkar)at;bg;edaysar shrinkage nig creep x<s;enAkñúgebtug eKGacTTYlkMlaMgeRb-
kugRtaMgRbsiT§PaBedayeRbIEdkersIusþg;x<s;EdlmanersIusþg;FMCag b¤esμI 270ksi(1862MPa) . Edker-
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 39

23. T.Chhay
sIusþg;FMEbbenHGacTb;Tl;nwgkar)at;bg;enACMuvijebtug nigmankugRtaMgsl;RKb;RKan;edIm,IFananUvkMlaMg
eRbkugRtaMgEdlRtUvkar. TMhMénkMhatbg;kugRtaMgFmμtasßitenAcenøaH 35ksi(241MPa ) eTA 60ksi
(414MPa ) . dUcenHkMlaMgeRbkugRtaMgdMbUgKYrmanTMhMFM EdlsßitenAcenøaH 180ksi(1241MPa ) eTA
220ksi(1517 MPa ) .
EdkeRbkugRtaMgGacmanTMrg;Ca single wire, strand EdlpSMeLIgeday wire CaeRcInrmYlcUlKña
begáIt)anCa single element nig high-strength bar. EdkeRbkugRtaMgEdleKniymeRbIKW³
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 bgðajnUv relaxation loss x<s;Cag stress-relieved wire b¤
strand.
x> Stress-Relieved and Low-Relaxation Wires and Strand
Stress-relieved wireKWCakarhUt single wire RtCak;edayeKarBtam ASTM standard A421
É stress-relieved strand eKarBtam ASTM standard A416. Strand RtUv)anplitecjBI wire 7
Edl wire 6 rMurmYlCMuvij wire Rtg; 1 EdlmanTMhMFMCagbnþic. eKeFVI stress-relieve eRkayeBlEdl
eKrMu wire rYc. lkçN³FrNImaRtrbs; wire nig strand EdlTamTareday ASTM RtUv)aneGayenAkñúg
tarag 2>6 nig tarag 2>7 erogKña.
edIm,IbegáInRkLaépÞEdkrbs; 7 wire-strand sMrab; nominal diameter , eKGachUt standard
wire edIm,IbegáItCa compacted strand dUcbgðajenAkñúgrUbTI 2>17 (b). rUbTI 2>17 (a) bgðajBI
standard 7 wire strand. ASTM standard A779 RtUvkarersIusþg; niglkçN³Gb,brmadUcbgðajenA
kñúgtarag 2>8.
Materials and Systems for Prestressing 40

24. NPIC
rUbTI 2>18 (a) bgðajBIdüaRkam stress-strain sMrab;EdkeRbkugRtaMg wire nig strand. ÉrUb
TI 2>18 (b) bgðajBItMéleRbobeFobrvagEdkeRbkugRtaMg nigEdkFmμta.
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 41

25. T.Chhay
Materials and Systems for Prestressing 42

26. NPIC
K> High-Tensile Strength Prestressing Bars
sMrab;eFVIeRbkugRtaMgGacrelag b¤ deformed ehIyGac
High-tensile-strength alloy steel bar
man nominal diameter BI 3 in.(19mm) eTA 1 83 in.(35mm) . vaRtUveKarBtam ASTM standard
4
A722. karhUtRtCak;KWedIm,IbegáIn yield strength nig ductility rbs;va. eKTTYl)an stress relieve
edaykardutkMedA bar b¤ strand eRkamsItuNðPaBsmRsb EdlCaTUeTAeRkam 500o C . EdkeRbkug
RtaMgRtUvmanersIusþg;Tajy:agtic 150ksi(1034MPa ) CamYynwg yield strength Gb,brmaesμI 80%
én ultimate strength sMrab; smooth bar nig 80% sMrab; deformed bar.
tarag 2>9 bgðajBIlkçN³FrNImaRtrbs; prestressing bar EdlTamTareday ASTM
standard A722 nigrUbTI 2>18 bgðajBIdüaRkamkugRtaMg-bMErbMrYlrageFobKMrUsMrab; bar enH.
X> Steel Relaxation
Steel relaxationenAkñúgEdkeRbkugRtaMgCakMhatbg;eRbkugRtaMgenAeBlEdl wire b¤ strand
RbQmnwgbMErbMrYlrageFobefr. vadUcKñanwg creep enAkñúgebtug EtvaxusKñaRtg; creep CabMErbMrYlén
strain É steel relaxation CakMhatbg;kugRtaMgrbs;Edk. eKGackMNt;kMhatbg;edaysar relaxation
enAkñúg stress-relieved sires nig strand eRkayeBlrgeRbkugRtaMgedaysmIkarxageRkam³
log t ⎛ f pi
⎜
⎞
Δf R = f pi − 0.55 ⎟ (2.18)
10 ⎜ f py
⎝
⎟
⎠
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 43

27. T.Chhay
kñúgkrNIEdl f pi / f py ≥ 0.55 nig f py ≅ 0.85 f pu sMrab; stress-relieved strands nig f py ≅
0.90 f pu sMrab; low-relaxation strand. ehIy f pi = 0.82 f py Pøam²eRkayeBlepÞr b:uEnþ f pi ≤
0.74 f pu sMrab; pre-tensioned concrete nig f pi = 0.70 f pu sMrab; post-tensioned concrete. Ca
TUeTA f pi ≅ 0.70 f pu .
eKGackat;bnßykMhatbg;edaysar stress relaxation edayeGay strand rgnUvkugRtaMgdMbUg
rbs;vaesμInwg 70% én ultimate strength rbs;vaenAsItuNðPaB 20o C eTA 100o C sMrab;ry³eBlEdl
yUrCagkñúgeKalbMNgbegáItsac;lUtGcié®nþy_ EdldMeNIrkarenHRtUv)aneKeGayeQμaHfa stabilization.
kMhatbg;eRbkugRtaMgedaysar stress relaxation rbs; low-relaxation steel esμInwg 25% énkMhat
bg;eRbkugRtaMgedaysar stress relaxation rbs; stress-relieves steel.
smIkarsMrab;kMhatbg;edaysar relaxation enAkñúg low-relaxation prestressing steel KW
log t ⎛ f pi
⎜
⎞
Δf R = f pi − 0.55 ⎟ (2.19)
45 ⎜ f py
⎝
⎟
⎠
rUbTI 2>19 bgðajBI relaxation loss sMrab; stress-relieved steel nig low-relaxation steel sMrab; 7-
wire strands EdlekItmanelIRbEvgefrenAsItuNðPaB 29.5o C .
Materials and Systems for Prestressing 44

28. NPIC
g> ERcH nigkarxUcxatrbs;EdkeRbkugRtaMg
Corrosion and Deterioration of Strands
karkarBarRbqaMgnwgERcHsIuEdkeRbkugRtaMgmansar³sMxan;CagsMrab;krNIEdkFmμta edaysar
EtersIusþg;rbs;Ggát;ebtugeRbkugRtaMgCaGnuKmn_nwgkMlaMgeRbkugRtaMg b¤k¾RkLaépÞrbs; prestressing
tendon. karkat;bnßyRkLaépÞEdkeRbkugRtaMgEdlbNþalmkBIERcHnwgkat;bnßy nominal moment
strength rbs;muxkat;eRbkugRtaMgy:agxøaMg EdlGacnaMdl;kar)ak;rbs;RbB½n§eRKOgbgÁúMmunGayu. sMrab;
pre-tensioned member karkarBarERcHKWpþl;edayebtugEdlB½T§CMuvij tendon. sMrab; post-tensioned
member eKGacTTYl)ankarkarBarERcHedaykarbMeBj grout eTAkñúgbMBg; (duct) eRkayeBleFVIeRb
kugRtaMgehIy b¤edaykarlabeRbg (greasing).
TMrg;énkarxUcxatmüa:geTotrbs; wire b¤ strand KW stress corrosion EdlRtUv)ankMNt;lkçN³
edaykarbegáIteLIgén microscopic crack enAkñúgEdk EdlnaMeGayEdkmanPaBRsYy nigRsYldac;.
karkat;bnßyersIusþg;RbePTenHGacekItmanEteRkamkugRtaMgx<s;bMput EtvaminekIteLIgjwkjab;eT
ehIyeKk¾Bi)aknwgkarBarvaNas;Edr.
8> kugRtaMgGnuBaØatGtibrmarbs; ACI enAkñúgebtug nigEdk
ACI Maximum Permissible Stresses in Concrete and Reinforcement
xageRkamenHCanimitþsMxan;²EdleyIgnwgeRbIjwkjab;
f py = yield strength rbs; tendon eRbkugRtaMg
f y = yield strength rbs;EdkFmμta
f pu = ersIusþg;Taj (tensile strength) rbs; tendon eRbkugRtaMg
f 'c = ersIusþg;sgát;rbs;ebtug
f 'ci = ersIusþg;sgát;rbs;ebtugenAxN³rgeRbkugRtaMgdMbUg
k> kugRtaMgebtugEdlrgkarBt; Concrete Stresses in Flexure
kugRtaMgEdlekItmanPøam²enAkñúgebtugeRkayeBlepÞreRbkugRtaMg ¬munkMhatbg;eRbkugRtaMg
GaRs½ynwgeBl¦ minKYrFMCagtMélxageRkam³
!> kugRtaMgsrésxageRkAbMputrgkarsgát; >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 0.60 f 'ci
@> kugRtaMgsrésxageRkAbMputrgkarTaj elIkElgcMnuc #> >>>>>>> 3 f 'c psi(0.25 f 'c MPa)
#> kugRtaMgsrésxageRkAbMputrgkarTajRtg;cugrbs;Ggát;TMrsamBaØ >>>>>> 6 f 'c psi
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 45

29. T.Chhay
RbsinebIkugRtaMgTajEdlKNnamantMélFMCagtMélxagelI eKRtUvdak; bonded auxiliary reinforce-
ment (nonprestressed b¤ prestressed) enAkñúgtMbn;TajedIm,IkarBarkMlaMgTajsrubenAkñúgebtugEdl
RtUv)anKNnaedayeRbImuxkat;Gt;eRbHsnμt;.
kugRtaMgenAkñúgebtugeRkamGMeBIénbnÞúkeFVIkar ¬bnÞab;BIkMhatbg;eRbkugRtaMgTaMgGs;¦ minKYrFM
CagtMélxageRkam³
!> kugRtaMgsrésxageRkAbMputrgkarsgát;edaysarkMlaMgeRbkugRtaMg nigbnÞúkefr >>>> 0.45 f 'c
@> kugRtaMgsrésxageRkAbMputrgkarsgát;edaysarkMlaMgeRbkugRtaMg nigbnÞúksrub>>> 0.60 f 'c
#> kugRtaMgsrésxageRkAbMputrgkarTajenAkñúgtMbn;rgkarTajEdlrgkarsgát;
dMbUg >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 6 f 'c psi(0.5 f 'c MPa)
$> kugRtaMgsrésxageRkAbMputrgkarTajenAkñúgtMbn;rgkarTajEdlrgkarsgát;
dMbUgrbs;Ggát; ¬elIkElgRbB½n§kMralxNÐBIrTis¦ EdlkarviPaKQrelImux
kat;eRbHedaykarbMElg (transformed cracked section) nigenAelITMnak;
TMngPaBdab nigm:Um:g;BIrTisbgðajfaPaBdabPøam² nigPaBdabry³eBlEvg
eKrBtamtMrUvkarrbs; ACI nigtMrUvkarkMras;ebtugkarBarGb,brma >>>>> 12 f 'c psi
x> kugRtaMgEdkeRbkugRtaMg Prestressing Steel Stresses
kugRtaMgTajenAkñúg tendon eRbkugRtaMgminRtUvFMCagkugRtaMg³
!> EdlbNþalmkBI tendon jacking force…………………………… 0.94 f py
b:uEnþminRtUvFMCagtMélEdltUcCageKkñúgcMeNam 0.80 f pu nigtMélGtibrmaEdl
ENnaMedayGñkplit tendon eRbkugRtaMg nig anchorage eT.
@> Pøam²eRkayeBlkMlaMgeRbkugRtaMgRtUv)anepÞr>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 0.82 f py
b:uEnþminRtUvFMCag 0.74 f pu
#> Post-tensioning tendons, enARtg; anchorage nig coupler, eRkayBI tendon anchorage
Pøam²>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 0.70 f pu
9> kugRtaMgGnuBaØatGtibrmarbs; AASHTO enAkñúgebtug nigEdk
AASHTO Maximum Permissible Stresses in Concrete and Reinforcement
k> kugRtaMgebtugmunkMhatbg;edaysar creep nig shrinkage
Concrete Stresses before Creep and Shrinkage Losses
Materials and Systems for Prestressing 46

30. NPIC
kugRtaMgsgát;
Pre-tensioned members ……………………………………………. 0.60 f 'ci
Post-tensioned members……………………………………………. 0.55 f 'ci
kugRtaMgTaj
tMbn;TajEdlrgkugRtaMgsgát;dMbUg >>>>>>>>>>>>>>>>>>>>>>>>>>>>> minmankugRtaMgGnuBaØatbeNþaHGasnñ
NamYyRtUv)ankMNt;
EpñkepSgeTot
enAkñúgtMbn;TajEdlminmaneRbIEdkFmμta>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 200 psi b¤ 3 f 'ci psi
enAeBlEdlkugRtaMgTajEdl)anBIkarKNnaFMCagtMélenH eKRtUvdak; bonded reinforce-
ment edIm,IkarBarkMlaMgTajsrubenAkñúgebtugEdlKNnaedayeRbImuxkat;Gt;eRbHsnμt;. kugRtaMgTaj
GtibrmaminRtUvFMCag >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 7.5 f 'ci psi(0.623 f 'c MPa)
x> kugRtaMgebtugeRkamGMeBIbnÞúkeFVIkareRkaykMhatbg;
Concrete Stresses at Service Load after Losses
kugRtaMgsgát; >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 0.40 f 'c
kugRtaMgTajenAkñúgtMbn;TajEdlrgkugRtaMgsgát;dMbUg
!> sMrab;Ggát;EdleRbI bonded reinforcement >>>>>>>>>>>>>>>>>>>>>>>> 6 f 'c psi(0.5 f 'c MPa)
sMrab;lkçxNÐEdlGaceFVIeGaymanERcHsIuEdkF¶n;F¶ dUcCaenAtMbn;eqñrsmuRT 3 f 'c psi
@> sMrab;Ggát;Edlminman bonded reinforcement>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 0
kugRtaMgTajenAkñúgkEnøgepSgeTotRtUv)ankMNt;edaykugRtaMgGnuBaØatEdlkMNt;enAkñúgEpñk
8>k.
!> kugRtaMgeRbH Cracking Stresses
sMrab;ebtugTMgn;Fmμta>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 7.5 (
f 'c psi 0.623 f 'c MPa )
sMrab;ebtugTMgn;RsalEdlplitBIxSac;>>>>>>>>>>>>>>>>>>>>>> 6.3 f 'c psi (0.523 f 'c MPa )
sMrab;ebtugTMgn;RsaldéTeTot>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 5.5 f 'c psi (0.457 f 'c MPa )
@> Anchorage-Bearing Stresses
Post-tensioned anchorage eRkamGMeBIbnÞúkeFVIkar >>>>>>>>>>>>>>>>>>>>> 3000 psi(21MPa)
¬b:uEnþminRtUvFMCag 0.90 f 'ci ¦
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 47

31. T.Chhay
K> kugRtaMgEdkeRbkugRtaMg Prestressing Steel Stresses
!> EdlbNþalBI tendon jacking force >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 0.94 f py ≤ 0.80 f pu
@> eRkayeBlkMlaMgeRbkugRtaMgRtUv)anepÞrPøam² >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 0.82 f py ≤ 0.74 f pu
#> Post-tensioning tendons enARtg; anchorage/ eRkayeBl anchor tendon Pøam² 0.7 f pu
f py ≈ 0.85 f pu ¬sMrab; low-relaxation f py = 0.90 f pu ¦
dUcenHsMrab; tendon EdlmanersIusþg;Taj 270ksi man f pi enAeBlepÞr = 0.70 × 270
= 189ksi(1300 MPa ) .
X> Relative Humidity Values
rUbTI 2>20 bgðajnUvtMél relative humidity mFümRbcaMqñaMsMrab;tMbn;TaMgGs;enAshrdæeday
KitCaPaKry edIm,IeRbIsMrab;KNnakMhatbg;edaysarkarrYmmaDrbs;ebtug.
Materials and Systems for Prestressing 48

32. NPIC
10> RbB½n§kMlaMgeRbkugRtaMg nig Anchorages
Prestressing Systems and Anchorages
k> karGnuvtþkugRtaMgTajCamun Pretensioning
sMrab; pretensioned beam EdkeRbkugRtaMgrgkugRtaMgTajCamunEdlTb;eday anchorage
munnwgebtugRtUv)ancak;. Anchorage RtUv)anRTeday bulkhead y:agFM nigmanesßrPaBedIm,ITb;Tl;
nwgkMlaMgy:agFMEdlGnuvtþeTAelI tendon nImYy². eKEtgEtGnuvtþkugRtaMgTajCamunenAeragcRkplit
eRKOgbgÁúMdMeLIg edaysarvaRtUvkarkMralebtugGarem:d¾rwgmuaM CamYynwg anchor bulkhead b¤CBa¢aMgenA
cugsgxag. eKGacGnuvtþeRbkugRtaMgeTAelI strand mþgmYy² b¤mþgTaMgGs;kñúgeBlEtmYyBI jacking
operation.
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 49

33. T.Chhay
sMrab; harped tendon profiles eKeRbI]bkrN_ hold-down dUcbgðajkñúgrUbTI 2>21. eday
sarkMralmanRbEvgEvgeKGacplit prestressed element )aneRcInkñúgeBlEtmYy ehIyEdkeRbkug
RtaMgEdlenAcenøaHGgát;TaMgenaHGacRtUv)ankat;enAeBlebtugmanersIusþg;RKb;RKan;. rUbTI 2>22
bgðajBI schema kñúgkarplit prestressed element eRcInelIkMralEtmYy. ehIyrUbTI 2>23 bgðajBI
tendon Edl harp enAkñúgRbB½n§kMralsMrab;plit prestressed element.
Materials and Systems for Prestressing 50

34. NPIC
enAkñúgkarGnuvtþkugRtaMgCamun strand nig single wire RtUv)an anchor edayRbB½n§CaeRcIndUc
bgðajenAkñúgrUbTI 2>24. rUbTI 2>25 nig 2>26 bgðajBIRbB½n§kMralsMrab;plit prestressed element
ehIyeKk¾eRbIvasMrab;karGnuvtþeRbkugRtaMgCaeRkay. ehIyrUbTI 2>27 TMhMlMGitsMrab;RbB½n§enH.
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 51

35. T.Chhay
Materials and Systems for Prestressing 52

36. NPIC
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 53

37. T.Chhay
Materials and Systems for Prestressing 54

38. NPIC
x> karGnuvtþkugRtaMgTajCaeRkay Post-Tensioning
enAkñúgRbB½n§ post-tensioning eKGnuvtþkugRtaMgTajeTAelI strand, wire b¤ bar eRkayeBl
ebtugkkrwg nigmanersIusþg;RKb;RKan;. eKdak; strand enAkñúgbMBg; (duct) EdlRtUv)antMerobenAkñúg
Ggát;ebtug. kMlaMgeRbkugRtaMgRtUv)anepÞrtamry³ end anchorage dUcCa Supreme Product chuck
EdlRtUv)anbgðajenAkñúgrUbTI 2>24. EdkeRbkugRtaMgminRtUv)an bonded b¤ grouted munnwgGnuvtþ
kMlaMgeRbkugRtaMgeT.
K> Jacking System
Jacking systemCasmasFatumYyd¾caM)ac;mYyén prestressing operation edayGnuvtþkMlaMg
eRbkugRtaMgEdlRtUvepÞreTAEdkeRbkugRtaMg. kMlaMgeRbkugRtaMgRtUv)anGnuvtþtamry³ hydraulic jack
EdlmankMlaMg 10t eTA 20t nig stroke BI 6in.(15cm) eTA 48in.(120cm) GaRs½ynwgkarGnuvtþ post-
tensioning b¤ pretensioning nigGaRs½ynwgkarGnuvtþkMlaMgeRbkugRtaMgeTAelIEdkeRbkugRtaMgmþgmYy
b¤mþgTaMgGs;. eKRtUvkar large-capacity jack Edlman stroke y:agtic 30in.(762mm) sMrab;kar
GnuvtþkMlaMgeRbkugRtaMgeTAelIEdkeRbkugRtaMgmþgTaMgGs;. tMélsMrab;kargarEbbenHBitCaéføCagkar
GnuvtþkMlaMgeRbkugRtaMgeTAelI tendon mþgmYy. rUbTI 2>28 bgðajBI double acting hydraulic jack
sMrab;Taj (jack) EdkeRbkugRtaMgmþgTaMgGs;kñúgeBlCamYyKña.
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 55

39. T.Chhay
X> Grouting of Post-Tensioned Tendons
edIm,Ipþl;CaGcié®nþy_nUvkarkarBar post-tensioned steel nigedIm,IbegáItPaBs¥itrvagEdkeRbkug
RtaMg nigebtugEdlB½T§CMuvij duct eKRtUvbMeBj prestressing duct eday)aj;bBa©Úl cement grout.
1. Grouting material
A. Portland Cement suIm:g;t_B½rELnRtUvEteKarBtam specification ASTM C150
Type I, II nig III. sIum:g;t_EdleRbIsMrab; grouting RtUvmanKuNPaBl¥ minrgGIuRdakmμ.
B. Twk³ TwkEdleRbIsMrab; grout RtUvEtCaTwkEdlGacpwk)an s¥at nigminmansarFatuEdl
GacCHT§iBlminl¥dl;sIum:g;t_B½rELn nigEdkeRbkugRtaMg.
C. TwkfñaMKImI³ RbsinebIeKeRbITwkfñaMKImI vaRtUvpþl;nUvlkçN³brimaNTwkTab/ good flow,
minimum bleed nig expansion. vaminmansarFatuKImIEdlCHT§iBlminl¥dl;Edk
eRbkugRtaMg b¤sIum:g;t_. TwkfñaMKImIEdlmansUlusüúgkør ¬EdlsarFatukøFMCag 0.5%
énTMgn;rbs;TwkfñaMKImI edaysnμt;TwkfñaMKImI 1lb(0.45kg ) kñúgsIum:g;t_mYy)av¦ eKminRtUv
eRbIsUluysüúgPøúyGr sUluysüúgs‘ulpat b¤sUluysüúgGasUt. eKGaceRbIemS:A
GaluymIjÚmkñúgbrimaNsmrmüNamYy b¤sarFatuKImIdéTeTotEdlekItBI]sμ½n
edIm,ITTYl)an karrIkmaDrbs; grout RbEhlBI 5% eTA10% .
2. Ducts
A. Forming
Formed Ducts: bMBg;RtUv)anbegáIteLIgedaysMbkEdlminGnuBaØateGayTwk
sIum:g;t_cUl)an. vaRtUvepÞrkugRtaMgs¥itdUcEdlRtUvkar nigrkSaragrbs;vaeRkamTMgn;
rbs;ebtug. Metallic sheath KYrCa ferrous metal Etvak¾GacCaRbePT
galvanized pgEdr.
Cored Ducts: bMBg;enHRtUv)anpliteLIgedaymanPaBTUlayEdlminpþl;]b-
sKÁdl;lMhUrrbs; grout.
B. Grout Opening or Vents: bMBg;TaMgGs;RtUvEtman grout opening enAcugsg
xag. sMrab; draped cable cMnucx<s;TaMgGs;RtUvEtman grout vent elIkElgEtkEnøg
NaEdlmankMeNagtUc dUcCaenAkñúgkMralxNÐCab;. eKRtUvdak; grout vent b¤ drain
hole enAcMnucTabRbsinebI tendon RtUv)aneRbI/ dak;kugRtaMg nig)aj;bBa©Úl grout enA
kñúgsItuNðPaBRtCak;. Grout opening b¤ vent TaMgGs;RtUv)anpþl;nUvkarkarBarkar
ehorecj grout.
Materials and Systems for Prestressing 56

40. NPIC
C. TMhMbMBg;³ RbsinebIeKeRbI tendon EdlpSMeLIgeday wire, bar b¤ strand eRcIn RkLa
épÞrbs;bMBg;RtUvEtmanTMhMy:agticesμInwg neat area rbs;EdkeRbkugRtaMgBIrdg.
sMrab;bMBg;EdleRbICamYynwg wire, bar b¤ strand eTal Ggát;p©itrbs;bMBg;RtUvFMCag
normal diameter rbs; wire, bar b¤ strand 1 / 4in.(6mm ) .
D. Placement of Ducts: eRkayeBlbMBg; Edk nig forming RtUv)andak;cb;sBVRKb;
eKRtUvRtYtBinitünUvTItaMgrbs;bMBg;EdlGacxusqÁg. eKRtUvP¢ab;bMBg;edayKMlatCit
lμmedIm,IeCosvagkarpøas;TIrbs;bMBg;enAeBlcak;ebtug. eKRtUvCYsCulrn§ b¤Rbehag
TaMgGs;EdlmanenAelIbMBg;munnwgcak;ebtug. eKRtUvP¢ab; Grout opening nig vent
edaysuvtßiPaBeTAnwgbMBg; nigeTABum< b¤eTAEdkFmμta edIm,IkarBarkarpøas;TIkñúgGMLúg
eBlcak;ebtug.
sMPar³ nigRbB½n§kMlaMgeRbkugRtaMg 57