Cracking and Deflections (1)

8/12/2019 Cracking and Deflections (1)

1/21

Prediction of Cracking and Deflections;International Code Provisions and Recent Research

Doug JenkinsInteractive Design Services Pty Ltd

Hornsby, S!, "ustralia

The most common requirements that need to be satisfied for Serviceability Limit State design arethe limitation of deflections and crack widths to the requirements of the applicable code.Moreover the stiffness of concrete members has a significant effect on load distribution throughthe structure, and can have a major influence on design loads in situations such as temporarypropping and design for soilstructure interaction. !owever the accurate prediction of crackingand deflections is very difficult, due to the inherently random nature of the cracking process, andthe lack of agreement on a standard procedure to approach the task.

"n this paper the provisions of the #ustralian and major international concrete design codes arecompared, and recent relevant research is summarised.

$ase studies are presented, comparing actual measured deflections with those predicted at the

time of design, and backcalculated estimates including all the significant influences on deflection.%ecommendations are given for procedures to estimate fle&ural crack widths and upperboundlimits to deflections.


2/21

#$ I%R&D'C%I&

The purpose of this paper is to summarise #ustralian and international concrete code provisionsand recent research on the prediction of fle&ural cracking and deflections, to compare theseprovisions with some measured deflections on recent projects, and to make recommendations fordesign for cracking and deflection in practice.

The following topics will be discussed'

(hy is the prediction of cracking and deflection important)

(hy is it difficult)

!ow do cracks develop and propagate, how does this affect deflections)

Time related effects

(hat do the codes say)

%ecent research on fle&ural cracking and deflections.

$ase studies

$onclusions

*or deflections, this paper will concentrate on lightly reinforced members, where the fle&ural

strength of the concrete and shrinkage effects dominate the behaviour. The effect of differentialshrinkage on prestressed members is also considered.

($ !H) IS %H* PR*DIC%I& &+ CR"CI- "D D*+L*C%I& I.P&R%"%/

Limits on cracking and deflection are the two most common requirements for Serviceability LimitState +SLS design. #s well as the specific code requirements, cracking has a direct influence onother SLS requirements, such as control of corrosion and spalling, and deflections have a largeinfluence on load distribution, both to other structural members and to nonstructural elements.

"n addition to specific code requirements, there are often additional contract specificationrequirements +particularly for crack widths, and for many structures clients will have ane&pectation that there is no visually obvious cracking, no sagging or other obvious e&cessive

deflections, and that the aesthetics of the finished structure are not affected by e&cessivedeflections or cracking. -&cessive deflections or cracking may also affect the functionality of thefinished structure, through reduced clearances, ponding of water, or leaking of water retainingstructures for instance.

0$ !H) IS I% DI++IC'L%/

esign codes recognise that the accurate prediction of the long term behaviour of reinforcedconcrete is not possible. *or instance #S /011 +2 states'

3Consideration shall be given to the fact that cs (the design shrinkage strain) has a range of

30%.

"n addition to the variability of shrinkage, variability in the following properties is also important'

The concrete tensile strength, and loss of tensile strength over time.

$oncrete short term stiffness in compression and tension.

Time related deformation +creep and shrinkage, and the effect of environmental

conditions on the rate of deformation.

$oncrete behaviour under unloading and reloading


3/21

The load at cracking, and location and spacing of cracks is also inherently unpredictable, and thishas a direct effect on the section stiffness and deflections.

4ariations in the manufacturing and5or construction process and programme, which cannot beknown at design time, also have a significant effect on the cracking and deflection of thestructure.

"n addition to the variable nature of cracking and time related deformations in concrete, codeprovisions have much less uniformity than is the case than for instance the provisions forcalculation of bending strength. ifferent codes have completely different approaches to dealingwith the calculation of cracking and section stiffness, and the resulting design values can vary by2116 or more. "n addition some significant effects are not covered by some codes, or areincluded in empirical coefficients, making comparison of the provisions of different codes difficult.

The inherent variability of concrete cracking and deflection in practice is illustrated by *igure 2,taken from the #$" recommendations for the prediction of deflection of concrete structures +7.8okinen and Scanlon measured the deflections of 91 nominally identical slab panels in a 7: storybuilding and found deflections varying in the range from about 2; to


4/21

=oth crack width and deflections are strongly affected by crack spacing, but location and spacingof cracks is controlled by random factors which cannot be predicted by any deterministic process.The crack formation process is illustrated in the following diagrams +*igures 79, taken from=eeby and Scott>s paper, %ef'+/.

+igure (3 Stress conditions in the region ofcracks during crack for4ation

+igure 0 5to673 +re8uency distribution ofcrack s6acing+igure 1 5botto473 2ariation in reinforce4entstrain in the region of a crack

"f an increasing tensile load is applied to a member the first crack will form anywhere along themember, depending on local imperfections or variations in concrete tensile strength. There willbe a transfer of stress from the reinforcement to the concrete over a length S1 either side of thecrack, depending on the concrete5reinforcement bond characteristics, the cracking stress, and thesi?e of the tension block. The concrete tension will be reduced over this region, so the secondcrack will form anywhere along the member greater than S 1 from the crack. Subsequent crackswill be subject to the same constraints, so it would be e&pected that cracks will appear at a

spacing in the range S1 to 7S1. (hen cracks are spaced closer than 7S1 there is insufficientlength for the stress transferred from the reinforcement to reach the concrete cracking stress.

"n practice it is found that the range of crack widths is much greater than would be e&pected fromthis analysis +*igure /. The greater variability in crack spacing can be accounted for byvariations in the concrete cracking strength along the member, such that new cracks may occurwithin the transfer ?one, or regions of length greater than 7S 1may remain uncracked. Statisticalanalysis of cracking with a varying cracking stress has achieved crack spacing distributionsreasonably close to the e&perimental pattern +/.


5/21


6/21

Aote' #S


7/21

+igure :3 Design crack idths to *urocode ( at 4a3 Design crack idths to *urocode ( at 4a


8/21


9/21

The basic formula for crack width' crack spacing & +mean steel strain C mean concrete strainmakes no allowance for variation in crack width between the level of the reinforcement and thesurface of the concrete, however the crack spacing is mainly related to the cover depth, and thecrack width is directly proportional to crack spacing, so the depth of cover has a significant effecton crack widths.

The e&pression for DsmC Dcmlimits the effect of tension stiffening to 916 of the steel strain. *orlong term effects the tension stiffening coefficient is reduced by 25/, from 1.0 to 1.9.

:$0$0 A@S 91== and @S ?##=

The =ritish concrete design codes specify a design crack width at the surface of the concrete asfollows'

The basic approach is similar to -urocode 7, e&cept that the crack width is projected from thereinforcement level to the concrete surface.

The main differences between =S


10/21

This is the only code of those studied that includes the effect of concrete shrinkage in the crackwidth calculation.

:$0$9 A "CI 0#? A ?B,BB -ergely A Lut e8uation

The #$" requirements are based on stress limits derived from the EergelyLut? equation'

The #$" /2: equation makes no allowance for tension stiffening, and predicts crack width at theupper bound of those studied in this paper. %esults are usually similar to those from the =S


11/21

#ll codes predicted increasing crack width with increasing bar spacing and constant

reinforcement area steel stress.


12/21

+igure B3 2arying tension reinforce4ent stress

+igure #=3 2arying cover


13/21

+igure ##3 2arying bar s6acing ith constant reinforce4ent area and stress

+igure #(3 2arying bar s6acing ith constant reinforce4ent area and 4a


14/21


15/21

(hen the steel stress was adjusted to the ma&imum allowable under #S /011 +i.e.

reduced for increasing bar spacing and increasing bar diameter the predicted crackwidths were reasonably uniform in the spacing range


16/21

:$1$( @S 91==, @S ?##=

eflections in =S


17/21

:$1$1 Su44ary

The main differences in approach to the calculation of deflections are summarised below'

#ustralian and #merican codes are based on the =ranson equation, using a uniform

average effective stiffness value.

#ustralian codes allow for loss of tension stiffening through a reduction of the cracking

moment related to the free concrete shrinkage.

#llowance for shrinkage curvature in the #ustralian codes is simplified and will

underestimate curvature in symmetrically reinforced sections.

=ritish codes allow only a low tension value for cracked sections, which is further

reduced for long term deflections

-uropean codes adopt an intermediate approach for cracked sections, with an

allowance for loss of tension stiffening.

=ritish and -uropean code provisions for shrinkage curvature are essentially the same

-ffective stiffness, calculated according to #S /011, -urocode 7, =S $ R*C*% R*S*"RCH

#ll of the codes studied, other than #$" /2:, include some allowance for loss of tension stiffeningover time, but they give no guidance on the rate of this mechanism, other than in #S /011 and #S


18/21

There is evidence that final tension stiffening may be largely independent of concrete strength +


19/21

$racking and deflections may be highly variable, even under nominally identical

conditions.

$odes do not make specific provisions for all the relevant factors affecting cracking and

deflection of concrete structures.

#S /011 and #S


20/21

*igure 2/' -ffective stiffnes vs =ending Moment with no shrinkage

*igure 29' -ffective stiffnes vs =ending Moment with /11 Microstrain shrinkage


21/21

*igure 2

Documents

Cracking and Deflections (1)