TheeffectoncrackingofhighcoversinRCbeamsFilipa Marques Guedes

Instituto Superior Técnico, University of Lisbon, Portugal

Abstract:Thisstudyfocusesontheeffectof largecoversinRCbeamsoncrackformation.The

motivation for thiswork came from the need to clarify the implications of using these high

covers.WiththehelpofRegulationssuchasREBAP,EC2-2010,NBR6118,ACI318-95,CEB-FIP

ModelCode1990and2010,andwiththeresultsoftestspreformedbyAlejandroCaldenteyit

waspossibletoconcludethatthesizeof crackwidth increaseswiththesizeofthecoverof

thereinforcement.

Key-Words:crack formation,RCbeams, cover,REBAP,EC2-2010,NBR6118,ACI318-95,CEB-FIP

MC90,Model2010andcrackwidht.

1 IntroductionThe main goal of this work is to study theeffect of cover on the cracking behavior ofreinforced concrete elements. Importanttheoretical aspects are discussed, includingwhere the crackwidth is estimatedby currentcodes formulations aswell as a detailed studyof each Code,mentioned above. And to finishthisstudy,acomparisonbetweenresultsgivenby current codes and experimental tests ismade, concluding that crack widths estimatedbymathematicalformulations,givenbyREBAP,EC2, NBR, ACI, CEB-FIP 90 and Model Code2010, are smaller that the ones estimated byexperimentaltests.

These experimental programme involving 12beamsspecimenswascarriedoutatStructuresLaboratory of the Civil Engineering School ofthePolytechnicUniversityofMadridfromMaytoOctober2009.

The specimens were coded XX-YY-ZZ, with XXreferring to bar diameter (12 or 25), YYreferringtocover(20or70cm)anZZreferringtostirrupspacing(00fornostirrup,10and30,for10cmand30cmspacing,respectively.

2 CrackwidthbyRegulations2.1 RebapREBAPrequiresthatcrackingshouldbelimited

to a level that does not impair the proper

functioning of the structure or cause its

appearance to be unacceptable. The code

stipulatesthatthedesignandmeancrackwidth

beevaluatedfromthefollowingexpression:

𝑤! =1,7.𝑤!(2.1)

𝑤!=𝑆!".𝜀!"(2.2)

with,

𝑆!":averagestabilizedcrackspacing;

𝜀!":averagereinforcementstrainwthin

segmentlenght𝑙!,!á!;

Average Stabilized crack spacing is expressed

as:

𝑆!"=2. 𝑐 +!!"

+ 𝜂!. 𝜂!.!!! (3)

with,

c:coverofreinforcement;

s:spacingofthereinforcement;

𝜂!=0,4fordeformedbars;

=0,8forplainbars;

𝜂!=0,25.!!!!!!!!

𝜙:bardiameter;

𝜌!:effectivereinforcementratio !!!!,!""

;

TheeffectiveconcreteareaiseshowninFigure

2-1.

The average reinforcement strain is obtained

fromthefollowingexpression:

𝜀!"=!!!!. ( 1 − 𝛽!.𝛽!. (

!!"!!)!)(4)

with,

𝜎!:reinforcementstressatthecrack;

𝐸!:Modulusofelastecityofthereinforement;

𝛽!:coefficientaccountingforbarbond

characteristics(=1,0fordeformnedbarsand

0,5forplainbars);

𝛽!:coefficientaccountingforloadduration

(=1,0forsingleshort-termloadingand0,5for

sustainedorcyclicloading);

𝜎!":stressinthetensionreinforcement

computedonthebasisofacracksectionunder

loadingconditionsthatcausethefirstcrack;

𝜀!"≥0,4.( 𝜎!/𝐸!). (5)

2.2 EC2

TheEurocodeEC2requiresthatcrackingshould

belimitedtoavalueofmaximumdesigncrack

of 0,3 mm, for sustained load under normal

environmental conditions. This ceiling is

expected to be satisfactory with respect to

appearance and durability. Strcker

requirements are stipulated for more severe

environmentalconditions.

Thecodestipulatesthatthedesigncrackwidth

beevaluatedfromthefollowingexpression:

𝑤!=𝑆!,!á!.( 𝜀!"-𝜀!")(2.2.1)

( 𝜀!"- 𝜀!") is obtained from the following

expression:

𝜀!"-𝜀!"=!!!!!.

!"#,!""!!,!""

.(!!!!.!!,!"")

!!≥ 0,6. !!

!!

(2.2.2)

with,

𝛼!=𝐸!/𝐸!";

ℎ!,!""=min(2,5.(h-d),(h-x)/3,h/2);

𝑘!:coefficientaccountingforloadduration

(=0,6forshort-termloadingand0,4for

sustainedorcyclicloading);

TheeffectiveconcreteareaiseshowninFigure

2-2

Figure1-1:EffectiveconcreteáreaforREBAP

The average Stabilized crack spacing is

expressedas:

𝑆!,!á!=𝑘!.c+𝑘!. 𝑘!. 𝑘!.Φ/𝜌!,!""(2.2.3)

𝑆!,!á!=1,3.(h-x) (2.2.4)

Expression (2.2.3) isusedwhens ≤5(c+Φ/2

and(2.2.4)whens>5(c+Φ/2.

with,

𝑘!=0,8fordeformnedbarsand01,6forplain

bars;

𝑘!=0,5forbendingand1,0forpuretension;

𝑘!=3,4(accordingtoA.N.);

𝑘!=0,425(accordingtoA.N.);

2.3 NBR6118

Thecodestipulatesthatthedesigncrackwidth

istheminimumfromthefollowingexpressions:

(2.3.1)

(2.3.2)

with,

𝜂!=2,25fordeformedbars;

TheeffectiveconcreteareaiseshowninFigure

2-3.

2.4 ACI318-95

Theequationsthstwereconsideredtobest

predicttheprobablemaximumbottomand

sidecrackwidthsareexpressedin(2.4.1)and

(2.4.2).

𝑤!=0,091. 𝑡! .𝐴! .𝛽. 𝑓! − 5 . 10!!(in)(2.4.1)

𝑤!=!,!"#. !!.!

!

!! !!!!. 𝑓! − 5 . 10!!(in)(2.4.2.)

𝑤!:mostprobablemaximumcrackwidthat

bottomofbeam,in;

𝑤!:mostprobablemaximumcrackwidthat

levelofreinforcement,in;

𝑓!:reinforcingsteelstress,ksi;

A:areaofconcretesymmetricwithreinforcing

steeldividedbynumberofbars,𝑖𝑛!;

𝑡!:bottomcovertocenterofbar,in;

𝑡!:sidecovertocenterofbar,in;

𝛽:1,2inbeams;

ℎ!:distancefromneutralaxistothereinforcing

steel,in;

ACICommittee318nowbelievesthatitcanbe

misleadingtopurporttoeffectivelycalculate

crackwidths,giventheonherentvariabilityin

Figure2-2:EffectiveconcreteareaforEC2.

Figure2-3:EffectiveconcreteareaforNBR.

cracking.Thethreeimportantparametersin

flexuralcrackingaresteelstress,cover,andbar

spacing.Althought,steelstressisthemost

importanteparameter.

Areevaluationofcrackingdata(Frosch1999)

showedthatpreviouscrackwidthequations

arevalidforarelativelynarrowrangeofcovers

(upto63mm).

2.5 CEB-FIPMC90

Forallstagesofcracking,thedesigncrack

widthmaybecalculatedaccordingto(2.5.1):

𝑤!=𝑙!,!á!.(𝜀!"- 𝜀!"- 𝜀!")≤𝑤!"#(2.5.1)

𝑙!,!á!:denotesthelenghtoverwhichslip

betweensteelandconcreteoccurs;steeland

concretestrains,whichoccurwithinthislength,

contributetothewidthofthecrack;

𝜀!":istheaveragesteelstrainwithin𝑙!,!á!;

𝜀!":istheaverageconcretestrain

within 𝑙!,!á!;

𝜀!":denotesthestrainofconcretedueto

shrinkage;ithastobeintroducedalgebraically;

𝑤!"#:shouldbeconsultedinTableofFigure2-4

If(2.5.2)happensitmaybeassumedthatthe

stabilizedcrackingconditionhasbeenreached,

otherwuisetheformationofsinglecracks

shouldbeconsidered.

𝜌!,!"" .𝜎!!>𝑓!"# .(1+𝛼! . 𝜌!,!"")(2.5.2)

where,

𝜌!,!"":istheeffectivereinforcementratio;

𝑓!"# :isthemeanvalueofthetensilestrenght

oftheconcrete;

𝜎!!:isthesteelstressatthecrack;

𝑙!,!á!isobtainedfromthefexpressions(2.5.2)

and(2.5.3).,forstabilizedcrackingandfor

singlecrackformation,respectively.

𝑙!,!á!=!!

!,!.!!,!""(2.5.2)

𝑙!,!á!=!!! !.!!"

.𝜙!.!

!!!!: .!!,!""(2.5.3)

where,

𝜏!":isthelowerfractilevalueoftheaverage

bondstress;itmaybetakenfromthetableof

Figure2-4.

For simplicity (1+𝛼!: . 𝜌!,!"") can be sete qual

to1.

(𝜀!"- 𝜀!")isestimatedaccordingto(2.5.4).

(𝜀!"-𝜀!").=𝜀!!-β.𝜀!"!(2.5.4)

whith,

𝜀!"!=𝑓𝑐𝑡𝑚 (𝑡)𝜌𝑠,𝑒𝑓𝑓.!"

. (1 + 𝛼𝑒.𝜌𝑠,𝑒𝑓𝑓)(2.5.5)

where,

𝜀!!:isthesteelstrainatthecrack;

Figure2-5:𝑤!"#forCEB-FIPMC90

Figure2-4:𝜏!"andβ.

𝜀!"!:isthesteelstrainatthecrack,under

forcescausing𝑓!"# within𝐴!,!"";

Forstabilizedcrackingtheaveragewidhtmay

beestimaedonthebasisofanaveragecrack

spacingof:

𝑆!"=!!. 𝑙!,!á! (2.5.6)

TheeffectiveconcreteareaiseshowninFigure

2-6.

2.6 ModelCode2010Itshouldbeensuredthatcrackswillnotimpair

the serviceability and durability of the

structure. cracks donot, per se, indicate a lack

of serviceability or durability, in reinforced

concretestructures

For all stages of cracking, the designg crack

width𝑤!maybecalculatedby(2.6.1):

𝑤!=2.𝑙!,!á!.(𝜀!"- 𝜀!"- 𝜀!")(2.6.1)

where,

𝑙!,!á!: denotes the length over which slip,

betweenconcreteandsteeloccurs.

𝜀!":istheaveragesteelstrainoverthelenght

𝑙!,!á!;

Thelength𝑙!,!á!,canbeexpressedby(2.6.2):

𝑙!,!á!=k.c+!!.!"#$!!"#

. !"!!,!""

(2.6.2)

k : is an empirical parameter to take the

influence of the concrete cover into

consideration.Asasimplificationk=1,0canbe

assumed;

c:istheconcretecover;

𝜏!"# : is mean bond strength between steel

andconcrete;

Therelativemeanstrainfollowsfrom:

𝜀!"- 𝜀!"- 𝜀!"=!!!!.!!"

!"+ 𝜂! . 𝜀!! (2.6.3)

where,

𝜎!:isthesteelstraininacrack;

𝜎!":isthemaximumsteelstressinacrack

formationstage,which,forpurtensionis:

𝜎!"=!"#$!!,!""

(1 + 𝛼! . 𝜌!,!"")(2.6.4)

𝛽:isanempiricalcoefficienttoassessthemean

strainover𝑙!,!á! ,dependingonthetypeof

loading;

𝜂!:isacoefficientforconsideringtheshrinkage

contribution;

𝜀!!:istheshrinkagestrain;

Thevaluefor𝜏!"#,𝛽and𝜂!canbetakenfrom

Figure2-7:

Figure2-6:effectiveconcreteareaforCEB-FIPMC90.

Figure2-7: 𝜏!"#,𝛽and𝜂! values.

Inordertoestimatethevalueofthecrack

widthattheextremetensilefibre,thecrack

widthmaybemultipliedwithafactor(h-x)/(d-

x).

Equation(2.6.2)Isvalidforstructureswhere

theconcretecoverisnotlargerthan75mm.

TheeffectiveconcreteareaiseshowninFigure

2-6,sameasCEB-FIPMC90.

3 ExampleofcrackwidhtcalculationaccordingtoRegulations

3.1 ExampleDefinition

FortheRCbeamshowedinFigure3-1,astudy

ofcrackwidthwasmade,forthis,itwasuseda

rangeofcovers,startingat3cm,followedby5,

7and10cm.

Thedataforthisexerciseisshowedbellow:

• M=1090kN.m;

• 𝐴!=24,544𝑐𝑚!;

• 𝐴500NRandC25/30;

• ℎ=2,0mandb=1,0m;

• Shorttermloading;

3.2 ComparisonofRegulationsResults

Thiscomparisonismadeforcracksat

reinforcementlevel,calculatedbyallsix

Regulationsmentionedabove.Table2-1and

Figure3-2showsthefinalresults.

To this end, and with the help of Regulations

such as REBAP, EC2-2010,NBR 6118, ACI 318-

95,CEB-FIPModelCode1990and2010,which

wereanalyzedindividuallyforthecalculationof

crackwidht,forthisrangeofvaluesforcovers,

thefirstimmediateconclusionwasthatthesize

of crack width increases with the size of the

coverofthereinforcement.

These results confirm that cover is an

important factor in the development of the

crackingpattern.

Figure3-1:RCbeamstudiedforcrackwidth.

Table2-1:Crackwidthsaccordingtoregulations

Figure3-2:crackwidthaccordingtoregulations.

4 Comparisonwithexperimentaltests4.1 Descriptionoftests

An experimental programme involving 12

beams specimens was carried out at the

Structures Laboratory of the Civil Engineering

SchoolofthePolytechnicUniversityofMadrid.

Allbeamshada rectangular cross-section0,35

mwide and 0,45m deep, all specimens were

concreted at the same time using the same

concreteofstrengthclassC25/33.

Theparametersstudiedwerecover(20and70

mm) and stirrup spacing 𝑠!. For this, three

configurations were considered, no stirrups,

and stirrups spaced at 10 and 30 cm. Stirrup

diameter was 12 mm, the specimens were

coded XX-YY-ZZ, with XX referring to bar

diameter(25mm),YYreferringtocover(20or

70mm)andZZ referring tostirrupspacing (00

fornostirrups,10for10cmspacingand30for

30 cm spacing). The cross-sections of the

specimensareshowninFigure4-1.

4.2 TestResults

Asummaryoftestresultsintermsofmean𝑠!,!

andmaximum 𝑠!,!"# crack spacing is given in

Table4-1.

Figure 4-2 shows very clearly how cover

increases crack width. This increase is clearly

related to an increase in crack spacing. These

resultsconfirmthatoverisanimportantfactor

inthedevelopmentofthecrackingpattern.

Assaidin 7 “Fromatheoreticalpointofview,

the effect of cover on crack spacing can be

understood by the need to transmit tension

stresses generated at the bar-concrete

Figure4-2:Cross-sectionofthespecimens.

Table4-1:testresultsintermsof𝑠!,!and𝑠!,!"#

Figure4-1:Sidemaximumcrackwidthvseffectofcover(ϕ=25mm)

interface to the effective concrete area

surroundingthebarinordertogenerateactual

cracking.

4.3 ExperimentaltestsvsRegulationresults

To make the comparison with test results, it

was taken from Figure 4-2 the values of crack

widthsfor𝜎!=350and415Mpa,thevaluesare

showedbellow.

ThefinalresultsareshowninTables4-4and4-

5aswellasinFigures4-3and4-4.

5 Conclusions

Thefirstconclusionisthatcoverincreasescrack

width.Itwasprovedbothwithregulationsand

withexperimentaltests.

It was also possible to conclude that a large

increase in the crack width happens as the

crack is measured further away from the bar,

theworkofHusain and Ferguson canbe cited

asexampleofsuchresults.

Table4-2:testresultsintermsofwkfor𝜎!=350Mpa

Table4-3::testresultsintermsofwkfor𝜎!=415Mpa

Table4-4:𝑤! forc=2cmandsteelstressof415Mpa

Table4-5::𝑤! forc=7cmandsteelstressof350Mpa

Figure4-3: 𝑤! forc=2cmandsteelstressof415Mpa

Figure4-4: 𝑤! forc=7cmandsteelstressof350Mpa

Figure5-1:TestsofHusainandFerguson.

The large difference between crack spacing at

thereinforcementsurfaceandcrackspacingat

the concrete surface observed in tests can be

attributed to internal cracking, At the bar

surface the differential strain between steel

and concrete is distributed among the passing

crackandtheinternalnon-passingcrack.

Other important fact verified was that crack

width calculations using current codes is

actualllysmallerthattheonesmeasuredinthe

experimentaltests.

Itcanbeseen,byFigure5-2,thatcrackstendto

developatthestirruppositions.

Tests have also confirmed that stirrup spacing

has an influence on crack spacing, but this

influence is mainly relevant for mean crack

spacing, we know that the variable important

for the verification of serviceability limit state

ofcracking ismaximumcrackspacing,andthis

itsinfluenceonmaximumcrackspacingismuch

smaller.

References

1 REBAP1SÉRIE–N.ª174–30/07/1983

2 NPEN1992-1-1Eurocódigo2-Projectode

estruturasdebetãoParte1-1:Regrasgeraise

Regrasparaedifícios

3 ABNTNBR6118_2003NORMABRASILEIRA,

PROJETODEESTRUTURASDECONCRETO-

PROCEDIMENTO

4 ACI224R–01CONTROLOFCRACKINGIN

CONCRETESTRUCTURES

5 CEB-FIPMODELCODE–1990COMITEEURO

–INTERNATIONALDUBETON

6 MODELCODE2010FINALDRAFTSPECIAL

ACTIVITYGROUP5

7 A.Caldentey,H.Peiretti,J.Iribarren,A.

Soto,“CrackingofRCmembersrevisited:

Influenceofcover,Φ/𝜌!,!",andstirrupspacing

–anexperimentalandtheoreticalstudy”

8 Appleton,J.2013:“Estruturasdebetão-

Volumes1e2”,EdiçõesOrion,Amadora

9 CritériosdeProjectocivildeusinas

hidrelétricas.Eletrobrás.CBDB.Outobro2003

Figure5-2:Crackpatterngovernedbystirrup

spacinginatestcarriedoutbyGómezNavarro.