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



LongLong--term behaviour of balanced cantilever bridgesterm behaviour of balanced cantilever bridges ACES Workshop, ACES Workshop,

Corfu, 2010Corfu, 2010



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





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.







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




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.





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!





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





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


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)





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





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]


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






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.






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.





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

--



Monitoring of the main span deflections [cm] against time [years]



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





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





Děč

ínDěč

ín BridgeBridge RehabilitationRehabilitation






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







Spans 68+104+62.7Spans 68+104+62.7

D th 2 6 / 5 2D th 2 6 / 5 2



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



LLahoviceahovice BridgeBridge



LLahoviceahovice BridgeBridgeacrossacross the Vltavathe Vltava





9.06.9.06.

20092009



OparnoOparno BridgeBridge processing of surveying measurementprocessing of surveying measurement



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



Deflections after castingDeflections after casting

of the 13L segmentof the 13L segment

DeflectionDeflection of of – – 4 cm4 cm





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





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.





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.





ExampleExample 11:: HačkaHačka BridgeBridge – –



partially prestressed deck slabpartially prestressed deck slab

Design of partially/limited prestressed concrete structuresDesign of partially/limited prestressed concrete structures



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




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


Example 2: PartialExample 2: Partial prestressingprestressing



Example 2: PartialExample 2: Partial prestressingprestressingfor continuity of precast girdersfor continuity of precast girders


•• 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



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


Anchor head

Prestressing steel

Temporary protection cap

Sheet metal duct



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


fib Bulletin No. 33fib Bulletin No. 33

DurabilityDurability of postof post--tensioningtensioning tendonstendons



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


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




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


reinforcement andreinforcement andplastic ductsplastic ducts


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


reinforcement andreinforcement andsteel ductssteel ducts

PretensionedPretensionedmembers withmembers with

bondedbondedreinforcementreinforcement


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.




OptimalOptimal

prestressingprestressing

Reinforced concreteReinforced concrete< Structural Concrete >< Structural Concrete >

Fully prestressedFully prestressedconcreteconcrete


frequent combinationof loading



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.




Thanks for your kind attention.Thanks for your kind attention.

MilanMilan KalnýKalný

Long-Term Behaviour of Balanced Cantilever Bridges

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