long-term behaviour of balanced cantilever bridges
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7/27/2019 Long-Term Behaviour of Balanced Cantilever Bridges
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LONGLONG--TERM BEHAVIOUR OFTERM BEHAVIOUR OFBALANCED CANTILEVER BRIDGESBALANCED CANTILEVER BRIDGES
MilanMilan KalnýKalný
Petr SoučekPetr SoučekVáclav KvasničkaVáclav Kvasnička
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LongLong--term behaviour of balanced cantilever bridgesterm behaviour of balanced cantilever bridges ACES Workshop, ACES Workshop,
Corfu, 2010Corfu, 2010
7/27/2019 Long-Term Behaviour of Balanced Cantilever Bridges
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LongLong--term behaviour of balanced cantilever bridgesterm behaviour of balanced cantilever bridges ACES Workshop, ACES Workshop,
Corfu, 2010Corfu, 2010
7/27/2019 Long-Term Behaviour of Balanced Cantilever Bridges
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LongLong--term behaviour of balanced cantilever bridgesterm behaviour of balanced cantilever bridges ACES Workshop, ACES Workshop,
Corfu, 2010Corfu, 2010
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Koror Koror --BabbelaobBabbelaob Bridge, Palau, MicronesiaBridge, Palau, Micronesia•• Construction:Construction: 19771977 – – span of 241m (WR)span of 241m (WR)
•• Depth above support 14.2 mDepth above support 14.2 m
•• Excessive deflectionExcessive deflection
•• Reconstruction: 1996Reconstruction: 1996 – – external tendonsexternal tendons
•• Collapse several months after the reconstructionCollapse several months after the reconstruction
LongLong--term behaviour of balanced cantilever bridgesterm behaviour of balanced cantilever bridges ACES Workshop, ACES Workshop,
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Supposed reasons for excessive deflectionSupposed reasons for excessive deflection
1.1. Actual Actual prestressingprestressing of theof the super super structure is lower than it was assumedstructure is lower than it was assumed
in the design due to the losses namely greater relaxation of in the design due to the losses namely greater relaxation of
prestressingprestressing steel.steel.
This effect might be increased by very high level of initialThis effect might be increased by very high level of initial prestressingprestressing,,
which was allowed by some previous national design codes.which was allowed by some previous national design codes.
In the Czech Republic the permissible limit of 0.935 fpIn the Czech Republic the permissible limit of 0.935 fp0.20.2 was allowedwas allowedand even its "improving" by 5and even its "improving" by 5% overstressing was possible.% overstressing was possible.
LongLong--term behaviour of balanced cantilever bridgesterm behaviour of balanced cantilever bridges ACES Workshop, ACES Workshop,
Corfu, 2010Corfu, 2010
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LongLong--term behaviour of balanced cantilever bridgesterm behaviour of balanced cantilever bridges ACES Workshop, ACES Workshop,
Corfu, 2010Corfu, 2010
Lana s normální relaxací (popouštěná)
Srovnání pr ůběhu relaxace v čase př i sigma/Rm = 0,8
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0 1 1 0
1 0 0
1 0 0 0
1 0 0 0 0
1 0 0 0 0 0
1 0 0 0 0 0 0
čas [hod]
z t r á
t a [ % ]
ČSN 736207
pr EN 1992-1-1:2003
AASHTO ASBI
ČSN P ENV 1992-1-1:1991
Norma:
Lana s normální relaxací (popouštěná)
Srovnání pr ůběhu relaxace v čase př i sigma/Rm = 0,7
0,00
0,05
0,10
0,15
0,20
0,25
0 1 1 0
1 0 0
1 0 0 0
1 0 0 0 0
1 0 0 0 0 0
1 0 0 0 0 0 0
čas [hod]
z t r á t a [ % ]
ČSN 736207
pr EN 1992-1-1:2003
AASHTO ASBI
Cerifikáty SRN
ČSN P ENV 1992-1-1:1991
Norma:
strands 1500/1770 MPa EN 10138strands 1500/1770 MPa EN 10138
σσ0,10,1 = f = f p0,1kp0,1k = 1500 MPa= 1500 MPa
σσ0,20,2 = 1570 MPa= 1570 MPa
RRmm = f = f pkpk = 1770 MPa= 1770 MPa
Permissible stress at jacking (ČSN):Permissible stress at jacking (ČSN):
93,5% of 93,5% of σσ0,20,2 or 80%or 80% f f pkpk
i.e. 1416i.e. 1416 MPaMPa for 1500/1770for 1500/1770 MPaMPa
i.e. 1546i.e. 1546 MPaMPa overstressoverstress
(87%(87% f f pkpk))
Permissible stress at jacking (EC):Permissible stress at jacking (EC):
90% f 90% f p0,1kp0,1k
i.e. 1368i.e. 1368 MPaMPa for 1500/1770 MPafor 1500/1770 MPa
((7777%% f f pkpk))
Effect of the steel relaxationEffect of the steel relaxation
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Supposed reasons for excessive deflectionSupposed reasons for excessive deflection
2.2. Actual friction of tendons was probably greater then calculated Actual friction of tendons was probably greater then calculated due todue to
sheath splicing at the contact joints, insufficient tightness of sheath splicing at the contact joints, insufficient tightness of sheaths,sheaths,
delayed grouting etc.delayed grouting etc.
3.3. Effective modulus of elasticity of concrete may be lower due toEffective modulus of elasticity of concrete may be lower due to thethe
loading of a very young concrete in context of the balanced cantloading of a very young concrete in context of the balanced cantilever ilever
method of construction.method of construction.
4.4. Deflection may be affected by the shear lag which formerly was nDeflection may be affected by the shear lag which formerly was notot
considered.considered.
LongLong--term behaviour of balanced cantilever bridgesterm behaviour of balanced cantilever bridges ACES Workshop, ACES Workshop,
Corfu, 2010Corfu, 2010
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Modulus of elasticity according to EN 1992Modulus of elasticity according to EN 1992--11--11
( )3.0
10/*22 cmcm f E =
zz secant modulussecant modulus EEcmcm is derived from the workingis derived from the working diaghramdiaghramat the stress level of 40%at the stress level of 40% f f cmcm
zz It depends also on concrete composition:It depends also on concrete composition: – – tables are for tables are for quar quar ttz aggregatez aggregate – – limestone aggregatelimestone aggregate --10%10% – – sandstone aggregatesandstone aggregate --30%30% – – basalt aggregatebasalt aggregate +20%+20%
zz Table values should be used when more precise values areTable values should be used when more precise values are
not available or no precise analysis is not required!not available or no precise analysis is not required!zz Testing of concrete properties is required for FCM!Testing of concrete properties is required for FCM!
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Moduly pružnosti podle ČSN, ČSN EN
15000
20000
25000
30000
35000
40000
45000
5 1 5
2 5
3 5
4 5
5 5
fck [MPa]
M o d u l y [ M P a ]
ČSN 73 2011
ČSN 73 6206
ČSN 73 6207
ČSN EN 1992-1-1
Modulus of elasticity according to EN 1992Modulus of elasticity according to EN 1992--11--11,, ČSNČSN, etc, etc..
Moduly pružnosti podle zahraničních př edpisů
15000
20000
25000
30000
35000
40000
45000
50000
5 1 5
2 5
3 5
4 5
5 5
6 5
7 5
8 5
fck [MPa]
M o d u l y [ M P a ]
DIN 1045-1 r.2003
EN 1992-1-1:2004
AASHTO r. 1996
FIP Recom. 1999
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Výsledky zkoušek modulů pružnosti
betonu C30/37 v čase 28dní
z betonárek Berger Beton a Holcim Pardubice
25000
30000
35000
40000
3 5
4 0
4 5
5 0
pevnost fck [MPa]
M o d u l p r u ž n o s t i [ M P a ]
Modulus of elasticity of C30/37 as tested according to ČSN ISO 6Modulus of elasticity of C30/37 as tested according to ČSN ISO 6784:1993, Z1:2003784:1993, Z1:2003betonu C30/37 v čase 28dní
z betonárek Berger Beton a Holcim Pardubice
25000.00
30000.00
35000.00
40000.00
3 5 4 0 4 5 5 0
M o d u l p r u ž n o s t i [ M P a ]
Berger
Holcim
Lineární (Holcim)
Lineární (Berger)
25000,00
30000,00
35000,00
40000,00
45000,00
50000,00
3 0
3 5
4 0
4 5
5 0
5 5
6 0
6 5
7 0
pevnost fck [MPa]
M o d u l p r u ž n o s t i [ M P a
zz Concrete C35/45, 28 days oldConcrete C35/45, 28 days oldzz Distribution up to 25% from averageDistribution up to 25% from average
zz Samples from TBGSamples from TBG ChomutovChomutov oothersthers
Výsledky zkoušek modulů pružnosti
betonu C35/45 v čase 28dní
25000,00
30000,00
35000,00
40000,00
45000,00
50000,00
3 0
3 5
4 0
4 5
5 0
5 5
6 0
6 5
7 0
pevnost fck [MPa]
M o d u
l p r u ž n o s t i [ M P a
TBG Chomutov TBG Chabař ovice
TBG Libouchec TBG Nakléř ov
TBG Trmice Lineární (TBG Chomutov)
Lineární (TBG Chabař ovice) Lineární (TBG Libouchec)
Lineární (TBG Nakléř ov) Lineární (TBG Trmice)
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Modulus of elasticity with respect to time courseModulus of elasticity with respect to time course
Časový pr ůběh modulu pružnosti
podle ČSN EN 1992-1-1:2006
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1 1 0
1 0 0
1 0 0 0
1 0 0 0 0
1 0 0 0 0 0
čas (dny)
p
o m ě r E c m ( t ) / E c m ( 2 8 )
CEM tř ídy R
CEM tř ídy N
CEM tř ídy S
( ) cmcmcmcm E f t f t E */)()(
3.0=
cmcccm f t t f *)()( β =
EN 1992EN 1992--11--11 FormulaFormula for for estimationestimation::
zz wherewhere::
]})/28(1[*exp{)( 2/1t st cc −= β
zz s = 0,2s = 0,2 -- 0,38 due to cement class0,38 due to cement class
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Corfu, 2010Corfu, 2010
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Modulus of elasticity with respect to time courseModulus of elasticity with respect to time course as testedas testedVýsledky zkoušek modulů pružnosti
betonu C35/45 v čase 3, 7 a 28dní
z betonárky TBG Chomutov
20000.00
25000.00
30000.00
35000.00
40000.00
1 5
2 0
2 5
3 0
3 5
4 0
4 5
5 0
5 5
6 0
pevnost fck [MPa]
M o d u l p r u ž n o s t i [ M P a ]
3 dni
7 dní
28 dní
Lineární (3 dni)
Lineární (7 dní)
Lineární (28 dní)
24000
2600028000
30000
32000
3400036000
1 1 0
1 0 0
čas (dny)
M o d
u l p r u ž n o s t i
[ M p a ]
prEN - CEM tř ídy R
prEN - CEM tř ídy N
prEN - CEM tř ídy SVzorek TBG Most
Pr ůměr vzorků TBG Chomutov
z Concrete C35/45, age of 3, 7 and 28 days,
z Composition with CEM 52,5N – class R
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Supposed reasons for excessive deflectionSupposed reasons for excessive deflection
5.5. Theoretic values of deflection are affected by the creep functioTheoretic values of deflection are affected by the creep function. In then. In the
analysis theanalysis the MoerschMoersch' function was often utilized. Application of ' function was often utilized. Application of
currently recommended function (EC2) may lead to increase of currently recommended function (EC2) may lead to increase of
calculated deflection by up to +100%.calculated deflection by up to +100%.
6.6. There may be influence of differential creep and shrinkage of coThere may be influence of differential creep and shrinkage of concretencrete
in box section (the bottom slab and the walls are at supports muin box section (the bottom slab and the walls are at supports muchch
thicker than the top slab). Delayed shrinkage should be taken althicker than the top slab). Delayed shrinkage should be taken also intoso intoaccount.account.
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Supposed reasons for excessive deflectionSupposed reasons for excessive deflection
7.7. There may be fatigue influence of repeated live load and thermalThere may be fatigue influence of repeated live load and thermal
effects.effects.
8.8. Load of the main span was greater due to increased thickness of Load of the main span was greater due to increased thickness of thethepavement layers (blinding concrete).pavement layers (blinding concrete).
9.9. Finally theFinally the prestressingprestressing tendon's area might be reduced or even lost bytendon's area might be reduced or even lost by
corrosion.corrosion.
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Basic dataBasic data of some bridgesof some bridges
erected by the free cantilever methoderected by the free cantilever method
BridgeBridge
River or River or
ValleyValley
CompletionCompletion
timetime
Main spanMain span
[m][m]
Depth atDepth at
supportsupport[m][m]
Depth atDepth at
midspanmidspan[m][m]
DeflectionDeflection
[cm][cm]
DDěčěčíínn LabeLabe 19901990 104104 5,85,8 3,03,0 ~ 20~ 20
MMěělnlnííkk LabeLabe 19931993 146146 9,09,0 2,652,65 1111
VepVepřřekek VltavaVltava 19961996 125125 6,96,9 2,52,5 n.a.n.a.
ÚÚhlavkahlavka valleyvalley 19971997 130130 7,57,5 2,82,8 44
DoksanyDoksany OhOhřřee 19981998 137137 7,07,0 3,03,0 11
HaHaččkaka valleyvalley 20072007 106106 6,256,25 2,652,65 --
LitomLitoměřěřiceice LabeLabe 20092009 151151 7,57,5 3,53,5 --
LahoviceLahovice
VltavaVltava
20102010
104104
5,25,2
2,62,6
--
LongLong--term behaviour of balanced cantilever bridgesterm behaviour of balanced cantilever bridges ACES Workshop, ACES Workshop,
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Monitoring of the main span deflections [cm] against time [years]
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Monitoring of the main span deflections [cm] against time [years]
LongLong--term behaviour of balanced cantilever bridgesterm behaviour of balanced cantilever bridges ACES Workshop, ACES Workshop,
Corfu, 2010Corfu, 2010
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ZvíkovZvíkov Bridge over the VltavaBridge over the Vltava
-- max. span of 84mmax. span of 84m
-- Completed in 1963Completed in 1963-- Rehabilitation in 1996Rehabilitation in 1996
-- MidspanMidspan hinges were fixedhinges were fixed
-- ExternalExternal prestressingprestressing
ZvíkovZvíkov Bridge rehabilitationBridge rehabilitation
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Corfu, 2010Corfu, 2010
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Bridges on I/13 road over the Labe River Bridges on I/13 road over the Labe River
-- Main span of 104mMain span of 104m
-- Completed in 1985Completed in 1985
-- Both bridges with excessive deflection of Both bridges with excessive deflection of
2020--25 cm with progressive increase of 25 cm with progressive increase of
1 cm/year without any stabilization1 cm/year without any stabilization
-- In 2004In 2004 -- 2005 rehabilitation and2005 rehabilitation and
strengthening by external tendonsstrengthening by external tendons
DěčínDěčín BridgeBridge
rehabilitationrehabilitation
LongLong--term behaviour of balanced cantilever bridgesterm behaviour of balanced cantilever bridges ACES Workshop, ACES Workshop,
Corfu, 2010Corfu, 2010
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Děč
ínDěč
ín BridgeBridge RehabilitationRehabilitation
LongLong--term behaviour of balanced cantilever bridgesterm behaviour of balanced cantilever bridges ACES Workshop, ACES Workshop,
Corfu, 2010Corfu, 2010
Monitoring of the main span deflections [cm] against time [years]
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Monitoring of the main span deflections [cm] against time [years]
LongLong--term behaviour of balanced cantilever bridgesterm behaviour of balanced cantilever bridges ACES Workshop, ACES Workshop,
Corfu, 2010Corfu, 2010
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Spans 43+64+72+90+151+102+60Spans 43+64+72+90+151+102+60
Spans 1Spans 1--3, 7 casted on fixed scaffolding3, 7 casted on fixed scaffolding
Spans 4, 5, 6 balanced cantileveringSpans 4, 5, 6 balanced cantilevering((DokaDoka formform--travellerstravellers))
Depth of superstructure 3.5 / 7.5 mDepth of superstructure 3.5 / 7.5 m
DSI bondedDSI bonded prestressingprestressing
Week construction cycleWeek construction cycle
LitomLitoměř ěř
ice Bridgeice Bridge
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Corfu, 2010Corfu, 2010
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LongLong--term behaviour of balanced cantilever bridgesterm behaviour of balanced cantilever bridges ACES Workshop, ACES Workshop,
Corfu, 2010Corfu, 2010
Spans 68+104+62.7Spans 68+104+62.7
D th 2 6 / 5 2D th 2 6 / 5 2
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Depth 2.6 m / 5.2 mDepth 2.6 m / 5.2 m
RampsRamps joined to the joined to the midspanmidspan
Construction cycle 9Construction cycle 9--13 days13 daysLLahoviceahovice BridgeBridge acrossacross the Vltavathe Vltava
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LLahoviceahovice BridgeBridge
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LLahoviceahovice BridgeBridgeacrossacross the Vltavathe Vltava
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9.06.9.06.
20092009
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OparnoOparno BridgeBridge processing of surveying measurementprocessing of surveying measurement
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OparnoOparno BridgeBridge – – processing of surveying measurementprocessing of surveying measurement
Výztuž a betonáž lamely
Měř ení B
Aktivace závěsů
Měř ení C
Vysunutí vozíku
Měř ení D
Měř ení A, nastavení vozíku
Designer
Projektan
t
Projektan
t
Measurment A, FT setting
Measurment B
Measurment C
Measurment D
Reinforcement,segment casting
Stressing of stays
Form-traveller move
Designer
Designer
Designer
Numbering of points for outline setting and surveying
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Deflections after castingDeflections after casting
of the 13L segmentof the 13L segment
DeflectionDeflection of of – – 4 cm4 cm
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Deflections after stressing of Deflections after stressing of stays of the 13L segmentstays of the 13L segment
DeflectionDeflection of of ++ 114 cm4 cm
InfluenceInfluence of of temperaturetemperature ±± 8 cm8 cm
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Conclusions from the testing of modulus of elasticityConclusions from the testing of modulus of elasticity
zz Values of modulus of elasticity of concrete received from compar Values of modulus of elasticity of concrete received from compar able samples areable samples arevery variable, influence of the real aggregate is a principle onvery variable, influence of the real aggregate is a principle one.e.
zz Statistic distribution of samples from one concrete plant is higStatistic distribution of samples from one concrete plant is high, however the basich, however the basictrend is clearly visible.trend is clearly visible.
zz Indicative values given in the EN 1992Indicative values given in the EN 1992--11--1 are basically correct and usable in1 are basically correct and usable instandard design practice with given limits.standard design practice with given limits.
zz In the previous Czech standards ČSN 73 6206 and ČSN 73 6207 moduIn the previous Czech standards ČSN 73 6206 and ČSN 73 6207 modulus of lus of elasticity was overestimated by up to 10% for reinforced structuelasticity was overestimated by up to 10% for reinforced structures (ČSN 73 6206)res (ČSN 73 6206)and by 5and by 5--15% for prestressed structures15% for prestressed structures (ČSN 73 6207), the difference is growing(ČSN 73 6207), the difference is growingwith the concrete class.with the concrete class.
zz In previous Czech standards no data were available on the time dIn previous Czech standards no data were available on the time development of Ec.evelopment of Ec.In the new ČSN EN 1992In the new ČSN EN 1992--11--1 the given formulas are reasonable and useful for 1 the given formulas are reasonable and useful for current analytical software.current analytical software.
zz For evaluation of the pumping effect we have not sufficient dataFor evaluation of the pumping effect we have not sufficient dataset. However theset. However thetendency to 5% reduction behind the pump is clear.tendency to 5% reduction behind the pump is clear.
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Conclusions for the balanced cantilever bridgesConclusions for the balanced cantilever bridges
z Reliable deflection control during construction as well as back analysis of executed structures isnot possible without actual testing of modulus of elasticity of the concrete supplied to the site.This complies with the recommendation in EN 1992-1-1.
z Wide range of distribution for the samples from one concrete plant brings doubts aboutpurposefulness of advance testing for the structural analysis. For slender structures with largespan strict supervision during production, transport and casting is vital for successfulapplications.
z For demanding structures with many phases of construction and loading of young concretecomputational method using time-dependent modulus should be used. Values received fromsamples are better however standardized procedures can be also implemented.
z Road vertical alignment should be designed as curved when possible.
z If any doubts are raised, the designer should propose a sufficient initial camber and providedetails for additional superstructure strengthening by external prestressing if necessary duringits lifetime.
LongLong--term behaviour of balanced cantilever bridgesterm behaviour of balanced cantilever bridges ACES Workshop, ACES Workshop,
Corfu, 2010Corfu, 2010
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ExampleExample 11:: HačkaHačka BridgeBridge – –
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partially prestressed deck slabpartially prestressed deck slab
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ExampleExample 11:: HačkaHa
čka BridgeBridge – – partially prestressed deck slabpartially prestressed deck slab
zz EC2 requirement: RC or fullEC2 requirement: RC or full prestressingprestressing
zz Design: Economic solution, wDesign: Economic solution, wdd
= 0.2 mm= 0.2 mm
⇒⇒ Transversal partialTransversal partial prestressingprestressing 44∅15,715,7 / / 5500 mm00 mm
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Discrepancy: different requirements for longitudinal and transvDiscrepancy: different requirements for longitudinal and transversal directionersal direction
inin spite of one exposure class and one protection level for spite of one exposure class and one protection level for prestressingprestressing
Design of partially/limited prestressed concrete structuresDesign of partially/limited prestressed concrete structures
Example 2: PartialExample 2: Partial prestressingprestressing
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Example 2: PartialExample 2: Partial prestressingprestressingfor continuity of precast girdersfor continuity of precast girders
Design of partially/limited prestressed concrete structuresDesign of partially/limited prestressed concrete structures
•• Even very low level of Even very low level of prestressingprestressingis helpful for serviceability behaviour is helpful for serviceability behaviour and robustnessand robustness
•• ProgressiveProgressive prestressingprestressing of of composite structure is possiblecomposite structure is possible
=> cost effectiveness=> cost effectiveness
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Example 3: Net arch with partially prestressedExample 3: Net arch with partially prestressed tietie
zz calculated crack width of wcalculated crack width of wdd = 0.2 mm does not represent any problem= 0.2 mm does not represent any problem
Design of partially/limited prestressed concrete structuresDesign of partially/limited prestressed concrete structures
Anchor head
Prestressing steel
Temporary protection cap
Sheet metal duct
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g
Anchorage
Cement grout
≥ 60mm
Sheet metal duct
Permanent protection cap
Anchor head
Prestressing steel Plastic duct
Cement grout
Anchorage ≥ 60mm
the resistance measurement
Isolating insert
AnchorageElectrical connection for
Prestressing steel
Isolating protection cap
Anchor head
Plastic duct
Cement grout
≥ 60mm
Protection levelProtection level
of of prestressingprestressing steelsteel
Design of partially/limited prestressed concrete structuresDesign of partially/limited prestressed concrete structures
fib Bulletin No. 33fib Bulletin No. 33
DurabilityDurability of postof post--tensioningtensioning tendonstendons
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SLS: Limit state of crackingSLS: Limit state of crackingDraft of Draft of thethe Model Code 2010Model Code 2010
Exposure ClassExposure ClassReinforcedReinforcedmembers andmembers andprestressedprestressed
members withmembers withunbonded tendonsunbonded tendons
PostPost--tensionedtensionedmembers withmembers withbonded groutedbonded grouted
reinforcement andreinforcement andplastic ductsplastic ducts
QuasiQuasi--permanentpermanentload combinationload combination Frequent loadFrequent loadcombinationcombination
0,0,22
XCXC 0,30,3 0,20,2 0,20,2 DDeeccompreompressssionion
0,0,22
0,30,3
0,30,3
PostPost--tensionedtensionedmembers withmembers withbonded groutedbonded grouted
reinforcement andreinforcement andsteel ductssteel ducts
PretensionedPretensionedmembers withmembers with
bondedbondedreinforcementreinforcement
Frequent loadFrequent loadcombinationcombination Frequent loadFrequent loadcombinationcombination
X0X0 0,20,2 0,20,2
XD, XS, XXD, XS, XFF DDeeccompreompressssionion DDeeccompreompressssionion
Remarks:Remarks: PrestressingPrestressing protection level should be more emphasized, one load combinatioprotection level should be more emphasized, one load combination only wouldn only wouldbe better for design process, partial and limitedbe better for design process, partial and limited prestressingprestressing should not beshould not be handicapedhandicaped
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SLS: Limit state of crackingSLS: Limit state of crackingPProposalroposal for ČSN EN 1992for ČSN EN 1992--2 NA2 NA
Exposure ClassExposure ClassReinforcedReinforcedmembers andmembers andprestressedprestressed
members withmembers withunbonded tendonsunbonded tendons
PostPost--tensionedtensionedmembers withmembers withbonded groutedbonded grouted
reinforcement andreinforcement andplastic ductsplastic ducts
Frequent loadFrequent loadcombinationcombination Frequent loadFrequent loadcombinationcombination
0,0,33
XCXC 0,0,44 0,0,33 0,20,2 0,0,11
0,0,22
0,40,4
0,0,44
PostPost--tensionedtensionedmembers withmembers withbonded groutedbonded grouted
reinforcement andreinforcement andsteel ductssteel ducts
PretensionedPretensionedmembers withmembers with
bondedbondedreinforcementreinforcement
Frequent loadFrequent loadcombinationcombination Frequent loadFrequent loadcombinationcombination
X0X0 0,20,2 0,20,2
XD, XS, XXD, XS, XFF 0,0,11 DDeeccompreompressssionion
Remark: DraftRemark: Draft,, not yet approved by the Czech Standards Committee for bridges.not yet approved by the Czech Standards Committee for bridges.
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OptimalOptimal
prestressingprestressing
Reinforced concreteReinforced concrete< Structural Concrete >< Structural Concrete >
Fully prestressedFully prestressedconcreteconcrete
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frequent combinationof loading
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SLSSLS
::
Limitation of concrete tensile stressesLimitation of concrete tensile stresses
No direct requirementsNo direct requirements in EN 1992in EN 1992--1 or MC20101 or MC2010 are available, however the design value of are available, however the design value of
the concrete tensile strength is given in the material chapter bthe concrete tensile strength is given in the material chapter by the formula:y the formula:f f ctdctd == ααctct f f ctk0,05ctk0,05 / / γcc , (i.e. for C30/37 ~ 2,0, (i.e. for C30/37 ~ 2,0 MPaMPa))
where the recommended values in SLS are:where the recommended values in SLS are:αα
ctct = 1,0= 1,0
coefficient taking account of longcoefficient taking account of long
--term effects on the tensile strengthterm effects on the tensile strength
coefficientcoefficient
and of and of unfavourableunfavourable effects, resulting from the way the load is applied,effects, resulting from the way the load is applied,γcc = 1,0 partial safety factor for concrete in SLS.= 1,0 partial safety factor for concrete in SLS.
For the combination of compression and bending this value can beFor the combination of compression and bending this value can be increased by up to ~1,6,increased by up to ~1,6,which depends on the depth, way of loading and sensitivity of thwhich depends on the depth, way of loading and sensitivity of the steel to corrosion.e steel to corrosion.
For theFor the prestressedprestressed structures we can assume that if the concrete tensile stress dostructures we can assume that if the concrete tensile stress does notes notexceed the value of exceed the value of f f ctdctd == f f ctctmm for frequent andfor frequent and / /or or f f ctdctd == f f ctk0,05ctk0,05 for for quasiquasi--permanentpermanent
combination of load, no cracking is developcombination of load, no cracking is developeded =>=> structurestructure comply with SLS conditions.comply with SLS conditions.
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Thanks for your kind attention.Thanks for your kind attention.
MilanMilan KalnýKalný
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