long-term behaviour of balanced cantilever bridges … · koror-babbelaob bridge, palau, micronesia...

LONGLONG--TERM BEHAVIOUR OF TERM BEHAVIOUR OF BALANCED CANTILEVER BRIDGESBALANCED CANTILEVER BRIDGES

Milan Milan KalnýKalnýPetr SoučekPetr SoučekVáclav KvasničkaVáclav Kvasnička

LongLong--term behaviour of balanced cantilever bridgesterm behaviour of balanced cantilever bridges ACES Workshop, ACES Workshop, Corfu, 2010Corfu, 2010

KororKoror--BabbelaobBabbelaob Bridge, Palau, Micronesia Bridge, Palau, Micronesia •• Construction:Construction: 1977 1977 –– span of 241m (WR)span of 241m (WR)•• Depth above support 14.2 mDepth above support 14.2 m•• Excessive deflection Excessive deflection •• Reconstruction: 1996 Reconstruction: 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 the of the supersuperstructure is lower than it was assumed structure 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 initial This 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 allowed was allowed and even its "improving" by 5and even its "improving" by 5% overstressing was possible.% overstressing was possible.



Lana s normální relaxací (popouštěná)Srovnání průběhu relaxace v čase při sigma/Rm = 0,8

0,000,050,100,150,200,250,300,350,40

0 1 10 100

1 00

0

10 0

00

100

000

1 00

0 00

0

čas [hod]

ztrá

ta [%

]

ČSN 736207pr EN 1992-1-1:2003AASHTO ASBIČSN P ENV 1992-1-1:1991

Norma:

Lana s normální relaxací (popouštěná)Srovnání průběhu relaxace v čase při sigma/Rm = 0,7

0,00

0,05

0,10

0,15

0,20

0,25

0 1 10 100

1 00

0

10 0

00

100

000

1 00

0 00

0čas [hod]

ztrá

ta [%

]

ČSN 736207pr EN 1992-1-1:2003AASHTO ASBICerifikáty SRNČSN P ENV 1992-1-1:1991

Norma:strands 1500/1770 MPa EN 10138strands 1500/1770 MPa EN 10138

σσ0,10,1 = f= fp0,1kp0,1k = 1500 MPa = 1500 MPa σσ0,20,2 = 1570 MPa = 1570 MPa

RRmm = f= fpkpk = 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% ffpkpk

i.e. 1416 i.e. 1416 MPaMPa for 1500/1770 for 1500/1770 MPaMPa

i.e. 1546 i.e. 1546 MPaMPa overstress overstress (87% (87% ffpkpk))

Permissible stress at jacking (EC):Permissible stress at jacking (EC):

90% f90% fp0,1kp0,1k

i.e. 1368 i.e. 1368 MPaMPa for 1500/1770 MPa for 1500/1770 MPa ((7777%% ffpkpk))

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 to due to sheath splicing at the contact joints, insufficient tightness ofsheath 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 to Effective modulus of elasticity of concrete may be lower due to the the 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 not ot considered.considered.


Modulus of elasticity according to EN 1992Modulus of elasticity according to EN 1992--11--11

( ) 3.010/*22 cmcm fE =secant modulus secant modulus EEcmcm is derived from the working is derived from the working diaghramdiaghramat the stress level of 40% at the stress level of 40% ffcmcmIt depends also on concrete composition:It depends also on concrete composition:

–– tables are for tables are for quarquarttz aggregatez aggregate–– limestone aggregate limestone aggregate --10%10%–– sandstone aggregate sandstone aggregate --30%30%–– basalt aggregate basalt aggregate +20%+20%

Table values should be used when more precise values are Table 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!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 15 25 35 45 55

fck [MPa]

Mod

uly

[MP

a]

ČSN 73 2011ČSN 73 6206ČSN 73 6207ČSN 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 předpisů

15000

20000

25000

30000

35000

40000

45000

500005 15 25 35 45 55 65 75 85

fck [MPa]

Mod

uly

[MP

a]DIN 1045-1 r.2003EN 1992-1-1:2004AASHTO r. 1996FIP Recom. 1999


Výsledky zkoušek modulů pružnostibetonu C30/37 v čase 28dní

z betonárek Berger Beton a Holcim Pardubice

25000

30000

35000

40000

35 40 45 50

pevnost fck [MPa]

Mod

ul p

ružn

osti

[MP

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, Z1:2003 784:1993, Z1:2003

betonu C30/37 v čase 28dníz betonárek Berger Beton a Holcim Pardubice

25000.00

30000.00

35000.00

40000.00

35 40 45 50

Mod

ul p

ružn

osti

[MP

a]

Berger

Holcim

Lineární (Holcim)

Lineární (Berger)

25000,00

30000,00

35000,00

40000,00

45000,00

50000,00

30 35 40 45 50 55 60 65 70

pevnost fck [MPa]

Mod

ul p

ružn

osti

[MP

a]

Concrete C35/45, 28 days oldConcrete C35/45, 28 days oldDistribution up to 25% from averageDistribution up to 25% from averageSamples from TBG Samples from TBG ChomutovChomutov oothers thers

Výsledky zkoušek modulů pružnostibetonu C35/45 v čase 28dní

25000,00

30000,00

35000,00

40000,00

45000,00

50000,00

30 35 40 45 50 55 60 65 70

pevnost fck [MPa]

Mod

ul p

ružn

osti

[MP

a]

TBG Chomutov TBG ChabařoviceTBG Libouchec TBG NakléřovTBG Trmice Lineární (TBG Chomutov)Lineární (TBG Chabařovice) Lineární (TBG Libouchec)Lineární (TBG Nakléřov) Lineární (TBG Trmice)


Modulus of elasticity with respect to time courseModulus of elasticity with respect to time course

Časový průběh modulu pružnostipodle ČSN EN 1992-1-1:2006

0.60

0.700.80

0.90

1.001.10

1.20

1 10 100

1 00

0

10 0

00

100

000

čas (dny)

poměr

Ecm

(t)/E

cm(2

8)

CEM třídy RCEM třídy NCEM třídy S

( ) cmcmcmcm EftftE */)()( 3.0=

cmcccm fttf *)()( β=

EN 1992EN 1992--11--1 1 FormulaFormula forfor estimationestimation::

wherewhere::

]})/28(1[*exp{)( 2/1tstcc −=β

s = 0,2 s = 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 tested

Výsledky zkoušek modulů pružnostibetonu C35/45 v čase 3, 7 a 28dní

z betonárky TBG Chomutov

20000.00

25000.00

30000.00

35000.00

40000.00

15 20 25 30 35 40 45 50 55 60

pevnost fck [MPa]

Mod

ul p

ružn

osti

[MP

a]

3 dni7 dní28 dníLineární (3 dni)Lineární (7 dní)Lineární (28 dní)

24000

26000

2800030000

32000

34000

36000

1

10

10

0

čas (dny)

Mo

du

l p

ružn

osti

[Mp

a]

prEN - CEM třídy RprEN - CEM třídy NprEN - CEM třídy SVzorek TBG MostPrůměr vzorků TBG Chomutov

Concrete C35/45, age of 3, 7 and 28 days, 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 the n. In the analysis the analysis 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 concrete ncrete in box section (the bottom slab and the walls are at supports muin box section (the bottom slab and the walls are at supports much ch thicker than the top slab). Delayed shrinkage should be taken althicker than the top slab). Delayed shrinkage should be taken also into so into account.account.



7.7. There may be fatigue influence of repeated live load and thermalThere may be fatigue influence of repeated live load and thermaleffects.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 the the pavement layers (blinding concrete).pavement layers (blinding concrete).

9.9. Finally the Finally the prestressingprestressing tendon's area might be reduced or even lost by tendon's area might be reduced or even lost by corrosion.corrosion.


Basic dataBasic data of some bridges of some bridges erected by the free cantilever methoderected by the free cantilever method

BridgeBridge River or River or ValleyValley

CompletionCompletiontimetime

Main span Main span [m][m]

Depth at Depth at support support

[m][m]

Depth at Depth at midspanmidspan

[m][m]

Deflection Deflection [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-- External External prestressingprestressing

Zvíkov Zvíkov Bridge rehabilitationBridge rehabilitation


Bridges on I/13 road over the Labe RiverBridges 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 2004 In 2004 -- 2005 rehabilitation and2005 rehabilitation andstrengthening by external tendonsstrengthening by external tendons

DěčínDěčín Bridge Bridge rehabilitationrehabilitation


DěčínDěčín BridgeBridge RehabilitationRehabilitation


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


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 cantilevering Spans 4, 5, 6 balanced cantilevering ((DokaDoka formform--travellerstravellers))

Depth of superstructure 3.5 / 7.5 m Depth of superstructure 3.5 / 7.5 m

DSI bonded DSI bonded prestressing prestressing

Week construction cycleWeek construction cycle

LitomLitoměřěřice Bridge ice Bridge


Spans 68+104+62.7Spans 68+104+62.7Depth 2.6 m / 5.2 mDepth 2.6 m / 5.2 m

RampsRamps joined to thejoined to the midspanmidspanConstruction cycle 9Construction cycle 9--13 days13 days

LLahoviceahovice Bridge Bridge acrossacross the Vltava the Vltava


LLahoviceahovice Bridge Bridge acrossacross the Vltava the Vltava


9.06.9.06.20092009


OparnoOparno Bridge Bridge –– processing of surveying measurementprocessing of surveying measurement

Výztuž a betonáž lamely

Měření B

Aktivace závěsů

Měření C

Vysunutí vozíku

Měření D

Měření A, nastavení vozíku

Designer

Projektant

Projektant

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 casting Deflections 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 ofof ++ 114 cm4 cm

InfluenceInfluence ofoftemperaturetemperature ±± 8 cm8 cm


Conclusions from the testing of modulus of elasticityConclusions from the testing of modulus of elasticity

Values of modulus of elasticity of concrete received from comparValues of modulus of elasticity of concrete received from comparable samples are able samples are very variable, influence of the real aggregate is a principle onvery variable, influence of the real aggregate is a principle one. e.

Statistic distribution of samples from one concrete plant is higStatistic distribution of samples from one concrete plant is high, however the basic h, however the basic trend is clearly visible. trend is clearly visible.

Indicative values given in the EN 1992Indicative values given in the EN 1992--11--1 are basically correct and usable in 1 are basically correct and usable in standard design practice with given limits.standard design practice with given limits.

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 growing with the concrete class.with the concrete class.

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.

For evaluation of the pumping effect we have not sufficient dataFor evaluation of the pumping effect we have not sufficient dataset. However the set. However the tendency 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

Reliable deflection control during construction as well as back analysis of executed structures is not 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.

Wide range of distribution for the samples from one concrete plant brings doubts about purposefulness of advance testing for the structural analysis. For slender structures with large span strict supervision during production, transport and casting is vital for successful applications.

For demanding structures with many phases of construction and loading of young concrete computational method using time-dependent modulus should be used. Values received from samples are better however standardized procedures can be also implemented.

Road vertical alignment should be designed as curved when possible.

If any doubts are raised, the designer should propose a sufficient initial camber and provide details for additional superstructure strengthening by external prestressing if necessary during its lifetime.


SLS: Limit state of cracking SLS: Limit state of cracking

as introduced in EN 1992as introduced in EN 1992--2 2

Exposure ClassExposure ClassReinforced members and Reinforced members and

prestressed members with prestressed members with unbonded tendonsunbonded tendons

Prestressed members Prestressed members with bonded with bonded

reinforcementreinforcement

QuasiQuasi--permanent load permanent load combinationcombination

Frequent load Frequent load combinationcombination

X0, XC1X0, XC1 0,30,3a)a) 0,20,2

XC2, XC3, XC4XC2, XC3, XC4 0,20,2b)b)

XD1, XD2, XD3, XS1, XS2, XS3XD1, XD2, XD3, XS1, XS2, XS3 DecompressionDecompression !!

a)a) For X0, XC1 exposure classes, crack width has no influence on duFor X0, XC1 exposure classes, crack width has no influence on durability and this limit is set to guarantee rability and this limit is set to guarantee acceptable appearance. In the absence of appearance conditions tacceptable appearance. In the absence of appearance conditions this limit may be relaxed. his limit may be relaxed.

b) For these exposure classes, in addition, decompression shouldb) For these exposure classes, in addition, decompression should be checked under the quasibe checked under the quasi--permanent permanent combination of loads.combination of loads.

0,30,3

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

ExampleExample 11: : HačkaHačka Bridge Bridge ––partially prestressed deck slab partially prestressed deck slab


ExampleExample 11: : HačkaHačka Bridge Bridge –– partially prestressed deck slab partially prestressed deck slab

EC2 requirement: RC or full EC2 requirement: RC or full prestressingprestressingDesign: Economic solution, wDesign: Economic solution, wdd = 0.2 mm= 0.2 mm

⇒⇒ Transversal partial Transversal partial prestressingprestressing 44∅∅15,715,7 // 5500 mm00 mm


Discrepancy: different requirements for longitudinal and transvDiscrepancy: different requirements for longitudinal and transversal direction ersal 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: Partial Example 2: Partial prestressingprestressingfor continuity of precast girders for 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

•• Progressive Progressive prestressingprestressing of of composite structure is possible composite structure is possible

=> cost effectiveness=> cost effectiveness

Example 3: Net arch with partially prestressedExample 3: Net arch with partially prestressed tie tie 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

Anchorage

Cement grout

≥ 60mm

Temporary protection cap

Sheet metal duct

Permanent protection capAnchor head

Prestressing steel Plastic duct

Cement grout

Anchorage ≥ 60mm

the resistance measurement

Isolating insert

Anchorage Electrical connection for

Prestressing steel

Isolating protection cap Anchor head

Plastic duct

Cement grout

≥ 60mm

Protection level Protection level of of prestressingprestressing steelsteel


fib Bulletin No. 33fib Bulletin No. 33DurabilityDurability of postof post--tensioningtensioning tendonstendons

SLS: Limit state of crackingSLS: Limit state of cracking

Draft ofDraft of the the Model Code 2010Model Code 2010

Exposure ClassExposure Class

Reinforced Reinforced members and members and prestressed prestressed

members with members with unbonded tendonsunbonded tendons

PostPost--tensioned tensioned members with members with

bonded grouted bonded grouted reinforcement and reinforcement and

plastic ductsplastic ducts

QuasiQuasi--permanent permanent load combinationload combination


0,0,22

XCXC 0,30,3 0,20,2 0,20,2 DDeeccompreompressssionion

0,0,22

0,30,3

0,30,3



steel ductssteel ducts

PretensionedPretensionedmembers with members with

bonded bonded reinforcementreinforcement



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 would n only would be better for design process, partial and limited be better for design process, partial and limited prestressingprestressing should not be should not be handicapedhandicaped


SLS: Limit state of crackingSLS: Limit state of cracking

PProposalroposal for ČSN EN 1992for ČSN EN 1992--2 NA2 NA

Exposure ClassExposure Class

Reinforced Reinforced members and members and prestressed prestressed

members with members with unbonded tendonsunbonded tendons



plastic 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



steel ductssteel ducts

PretensionedPretensionedmembers with members with

bonded bonded reinforcementreinforcement



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.


Optimal Optimal prestressingprestressing

Reinforced concreteReinforced concrete< Structural Concrete > < Structural Concrete >

Fully prestressed Fully prestressed concreteconcrete


frequent combinationof loading

SLSSLS: : Limitation of concrete tensile stressesLimitation of concrete tensile stresses

No direct requirements No direct requirements in EN 1992in EN 1992--1 or MC2010 1 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:

ffctdctd = = ααctct ffctk0,05ctk0,05 / / γγcc , (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: ααctct = 1,0 = 1,0 coefficient taking account of longcoefficient taking account of long--term effects on the tensile strength term effects on the tensile strength coefficient coefficient

and of and of unfavourableunfavourable effects, resulting from the way the load is applied,effects, resulting from the way the load is applied,γγcc = 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 the For the prestressedprestressed structures we can assume that if the concrete tensile stress dostructures we can assume that if the concrete tensile stress does not es not exceed the value of exceed the value of ffctdctd = = ffctctmm for frequent andfor frequent and//oror ffctdctd == ffctk0,05ctk0,05 forfor quasiquasi--permanent permanent

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 … · koror-babbelaob bridge, palau, micronesia...

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