ACI 224R-90

Control of in Concrete

Reported by AC

The principal causes of cracking in concrete and recom-mended crack control procedures are presented. The cur-rent state of knowledge in microcracking and fracture me-chanics is discussed. The control of cracking due to dryingshrinkage and crack control for flexural members, layeredsystems and mass concrete are covered in detail. Long-term effects on cracking are considered, and crack controlprocedures used in construction are presented. Informa-tion is provided to assist the engineer and the constructorin developing practical and effective crack control pro-grams for concrete structures.

Keywords: adiabatic conditions; aggregates: air entrainmechorage (structural); beams (supports); bridge decks; cgregate reactions; cement content; cement types; comstrength: computers; c o n c r e t e c o n s t r u c t i o n ; concrete pavemenconcrete slabs; c o n c r e t e s ; conductivity: consolidation; coolicrack propagation; cracking ( f r a c t u r i n g ) ; crack width and spacicreep properties; diffusivity; drying shrinkage; end blockssive cement concretes; extensibility; failure; fibers; heat otion; insulation; joints (junctions); machine bases; mass microcracking; mix proportioning; modulus of elasticity; mcontent; Poisson ratio; polymer-portland cement concretpozzo-lans; prestressed concrete; reinforced concrete; reinforcinrestraints; shrinkage: specifications; specific heat; straistrains; stresses; structural design; temperature; temper(in concrete); tensile stress; tension; thermal expansionchange.

ACI Committee Reports, Guides, Standard Practices , and Com-mentaries are Intended for guidance in designing, planning,executing, or inspecting construction, and in preparing speci-fications Reference to these documents shall not be made inthe Project Documents. If items found in these documents aredesired to be part of the Project Documents, they should bephrased in mandatory language and incorporated into the Proj-ect Documents.

Copyright 0 1990, American Concrete Institute. All rights reserved incrights of reproduction and use in any form or by any means, including thcopies by any photo process, or by any electronic or mechanical device

224RCracking Structures

I Committee 224

nt; an-ement-ag-

pressivets;ng;

ContentsChapter 1 - Introduction, page 224R-2

Chapter 2 - Crack mechanisms in concrete,page 224R-22.1 - Introduction2.2 - Microcracking2.3 - Fracture

Chapter 3 - Control of cracking due to dryingshrinkage, page 224R-93.1 - Introduction3.2 - Crack formation3.3 - Drying shrinkageng:; expan-f hydra-

concrete;oisture

e; g steels;n gages;ature rise; volume

ludinge making of, printed or

3.4 - Factors influencing drying shrinkage3.5 - Control of shrinkage cracking3.6 - Shrinkage-compensating concretes

Chapter 4 - Control of cracking in flexuralmembers, page 224R-164.1 - Introduction4.2 - Crack control equations for reinforced concrete beams4.3 - Crack control in two-way slabs and plates4.4 - Tolerable crack widths versus exposure conditions in re-

inforced concrete4.5 - Flexural cracking in prestressed concrete4.6 - Anchorage zone cracking in prestressed concrete4.7 - Tension cracking

Cbapter 5 - Long-term effects on cracking,page 224R-215.1 -5.2 -5.3 -5.4 -5.5 -

IntroductionEffects of long-term loadingEnvironmental effectsAggregate and other effectsUse of polymers in improving cracking characteristics

written or oral, or recording for sound or visual reproduction or for use in any knowledge or retrieval system or device, unless permission in writing is obtainedfrom the copyright proprietors.

-1

ea

hspnes

o c frf k

s,ind

ara

leti

s have

pre-re useful

on the

oncrete,ve been the mosts. In ad-

devel-ications.servand as ack con-

construc-

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d Con-

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sity inrnedth at theecial in-tion that

e as wellormationess, mi-

through

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ation be-nges inm at the

form un-nt of the

hout the load

pressiveo propa-ontinuesltimately

rimentalgins atChapter 7 - Control of cracking in mass con-crete, page 224R-267.1 - Introduction7.2 - Crack resistance7.3 - Determination of temperatures and tensile strains7.4 - Control of cracking7.5 - Testing methods and typical data7.6 - Artificial cooling by embedded pipe systems7.7 - Summary - Basic considerations for construction co

and specifications

Chapter 8 - Control of cracking by correctconstruction practices, page 224R-368.1 - Introduction8.2 - Restraint8.3 - Shrinkage8.4 - Settlement8.5 - Construction8.6 - Specifications to minimize drying shrinkage8.7 - Conclusion

Chapter 9 - References, page 224R-429.1- Specified and/or recommended references9.2 - Cited references

Chapter 1 - IntroductionCracks in concrete structures can indicat

structural problems and can mar the appemonolithic construction. They can expose resteel to oxygen and moisture and make tmore susceptible to corrosion. While the causes of cracking are manifold, cracks are caused by stresses that develop in concretthe restraint of volumetric change or to loadare applied to the structure. Within each categories there are a number of factors atsuccessful crack control program must rethese factors and deal with each of them, in

This report presents the principal causes oing and a detailed discussion of crack contcedures. The body of the report consists ochapters designed to help the engineer andtractor in the development of effective cracmeasures.

This report is an update of a previous comreport, issued in 1972.1.1 The original report wasupplemented by an ACI Bibliography on cracking1.2

also issued by this committee. In the updatcess, many portions of the report have unsizeable revision, and the entire document hasubjected to a detailed editorial review. Chon crack mechanisms, has been completely to take into account the experimental and work that has been done since the completiofirst committee report. Chapter 6, on crack controin concrete layered systems, is new to thand deals with a form of concrete construc

was in its infancy at the time the first repdrafted. Individual chapters on crack contron re-inforcing2.1 - Introductionlayered systems, page 224R-236.1 - Introduction6.2 - Fiber reinforced concrete (FRC) overlays6.3 - Latex modified concrete (LMC) overlays6.4 - Polymer impregnated concrete (PIC) systemsACI COMMIT

Chapter 6 - Control of cracking in concreteol reporton that

at an accelerated rate until the material ufails. For concrete in uniaxial tension, expework indicates that major microcracking beewrittennalyticaln of the

reaches approximately 70 percent of the comstrength, at which time microcracks begin tgate through the mortar. Mortar cracking cs beenpter 2,value, additional bond cracks initiate througmatrix. Bond cracking increases until theergonecompressive strength of the concrete. Above thise steelecific

ormally due to whichf thesework. Aognizeturn. crack-ol pro- seventhe con- control

mittee

g pro-

Beginning with the work at Cornell Univerthe early 1960s,2.1 a great deal has been leaabout the crack mechanisms in concrete, bomicroscopic and the macroscopic level. Of spterest during the early work was the realizathe behavior of concrete, under compressivas tensile loads, was closely related to the fof cracks. Under increasing compressive strcroscopic cracks (or microcracks) form at the mortar-coarse aggregate boundary and propagatethe surrounding mortar, as shown in Fig. 2.1.

During the first decade of research, a picveloped that closely linked formation and ption of these microcracks to the load-deformhavior of concrete. Prior to load, volume chacement paste cause interfacial cracks to formortar-coarse aggregate boundary.2.2,2.3 Under short-term compressive load, no additional cracks til the load reaches approximately 30 perce

2.1 majorrance of

key tool in the development of practical cratrol procedures in both the design and the tion of concrete structures.

References1.1. ACI Committee 224, Control of Cracking in Con

crete Structures, ACI JOURNAL, Proceedings V. 69, NO.12, Dec. 1972, pp. 717-753.

1.2. ACI Committee 224, Causes, Mechanism, antrol of Cracking in Concrete, A C I B i b l i o g r a p h y No. 9,American Concrete Institute, Detroit, 1971, 92 pp

Chapter 2 - Crack mechanisms in concrete*TEE REPORT

ntrols

inforced and prestressed concrete memberbeen condensed into a single chapter, Chapter 4, oncrack control in flexural members. The resulting sentation is more concise and, hopefully, moto the structural designer. Chapter 5, on long-termeffects, details some interesting findings change of crack width with time. Chapters 3, 7, and8, which consider drying shrinkage, mass cand construction practices, respectively, haexpanded and updated to take into accountrecently developed procedures in these areadition, new sections have been added to Chapters 7and 8 which provide specific guidance for theopment of crack control programs and specif

The committee hopes that this report will e asa useful reference to the causes of cracking rt wasiabout 60 percent of the ultimate tensile strength.2.4

Principal author: David Darwin.

a

cc

esen

copt

etn

l

The earliest experimental work utilized tension and beam specimens of mortar con-

cking,f Con-re ofn,

d inhe onsettoter in-f paste, tough-

ortar in-but that

he frac-

asing aire effec-with in-hness ofaximum

or

f speci-, mortars a func- lead toure me-Becausere frac-ay only

fy all oftic frac-

of theconcreteiffithstudy of

uctures.sidered as is con-tool for

appliedhe-ion of apic, elas-stress in-geom-ass-in-in. f the ma-heo insureip of the(LEFM)

rialmetry (asstrength).

creased with decreasing water-cement ratio, the water-cement ratio had little effect on tture toughness of concrete. They found that KIc in-creased with age, and decreased with increcontent for paste, mortar, and concrete. Thtive fracture toughness of mortar increased creasing sand content, and the fracture tougconcrete increased with an increase in the msize of coarse aggregate.

Additional work by Naus,2.17 presented just prito the previous committee report,1.1 indicated thatfracture toughness was not independent omen geometry for tensile specimens of pasteand concrete and that fracture toughness wation of the crack length. These observationsthe possibly erroneous conclusion that fractchanics may not be applicable to concrete. certain size requirements must be met, befoture mechanics is applicable, these results mindicate that the test specimen did not satisthe minimum size requirements of linear elasture mechanics.

The balance of this chapter describes somemore recent studies of crack mechanisms in

and gives a somewhat different picture from thatCONTROL OF

Studies of the stress-strain behavior and change of concrete 2.5 indicate that the initiationmajor mortar cracking corresponds with an oincrease in the Poissons ratio of concrete. Tdiscontinuity stress is used for the stress this change in material behavior occurs.

In general, it has been agreed that the micro-cracking that occurs prior to loading has veeffect on the strength of concrete. Howeveby Brooks and Neville2.6 indicates that the effeearly volume change on microcracking of may result in a reduction of both tensile anpressive strength as concrete dries out. Thshows that upon drying, the strength of temens first increases and then decreases. Thlate that the initial increase is due to the istrength of the drier cement paste and thatmate decrease in strength is due to the formshrinkage induced microcracks.

Work by Meyers, Slate, and Winter2.7 and Shahand Chandra2.8 demonstrates that microcrackcrease under the effect of sustained and cying. Their work indicates that the total ammicrocracking is a function of the total comstrain in the concrete and is independenmethod in which the strain is applied. StShah, and Winter2.9 found that the total degremicrocracking is decreased and the total spacity in compression is increased when cosubjected to a strain gradient.

At about the same time that the microcstudies began, investigators began applyingmechanics to the studies of concrete under field of fracture mechanics, originated by Gr2.10

in 1920, serves as the primary tool for the brittle fracture and fatigue in metal strSince concrete has for many years been conbrittle material in tension, fracture mechanicsidered to be a potentially useful analysis concrete by many investigators. 2. .12

The field of fracture mechanics was first to concrete by Kaplan2.11 in 1961. The classical tory serves to predict, the rapid propagatmacrocrack through a homogeneous, isotrotic material. The theory makes use of the tensity factor, KI , which is a function of crack etry and stress. Failure occurs when KI reaches critical value, KIc , known as the critical stretensity factor under conditions of plane straKIc isthus a measure of the fracture toughness oterial. To properly measure KIc for a material, ttest specimen must be of sufficient size tmaximum constraint (plane strain) at the tcrack. For linear elastic fracture mechanics to be applicable, the value of KIc must be a mateconstant, independent of the specimen geoare other material constants such as yield naCRACKING 224R-3

volumeofbservedhe termt which

ry littler, workt ofoncreted com-ir studyt speci-y postu-creasedthe ulti-ation of

s in-lic load-unt ofressive

of theurman, ofrain ca-crete is

racking fractureoad. The

$EGlrgyjm 0.0012 m 0. CKI

STRAIN STRAIN

Fig. 2 . 1 - C r a c k i n g m a p s a n d s t r e s s - s t r a i n c u r v e sf o r c o n c r e t e l o a d e d i n u n i a x i a l compression. *

*From S. P. Shah, and F. O. Slate, Internal MicrocraMortar-Aggregate Bond and the Stress-Strain Curve ocrete, P r o c e e d i n g s , International Conference on the StructuConcrete (London, Sept. 1965), Cement and Concrete AssociatioLondon, 1968, pp. 82-92.

crete.2.11-2.14 The crack resistance was expresseterms of the strain energy release rate at tof rapid crack growth, G , which is directly related the fracture toughness of the material. Lavestigations evaluated the crack resistance omortar and concrete in terms of the fractureness, itself.2.15 Work by Naus and Lott2.16 indicatedthat the fracture toughness of paste and motchednd presented in the previous committee report.

S dtudies.ot in-ncrease

c ributed olymer

he im-

htnt

thin coating of polystyrene on natural coarse aggre-

ementior ofork of

hysicalmodel of concrete, Buyukozturk was able to simulate

l loading.

*lementr-gate. They found that a large reduction in interfacialbond strength causes no change in the initial stiff-ness of concrete under short-term compressive loadsand results in approximately a 10 percent reductionin the compressive strength as compared to similarconcrete made with aggregate with normal inter-facial strength (see Fig. 2.4). They also found thatthe lower interfacial strength had no appreciable ef-fect on the total amount of microcracking. However,in every case, the average amount of mortar crack-ing was slightly greater for the specimens madewith coated aggregate. This small yet consistent dif-ference may explain the differences in the stress-strain curves.

the overall crack patterns under uniaxia

Perry and Gillott 2.37used glass spheres with dif-ferent degrees of surface roughness as coarse aggre-gate. Their results indicate that reducing the inter-facial strength of the aggregate decreases theinitiation stress by about 20 percent, but has verylittle effect on the discontinuity stress. They also ob-served a 10 percent reduction in the compressivestrength for specimens with low mortar-aggregate

Mortar

Fig. 2.5 - S t r e s s - s t r a i n c u r v e s f o r c o n c r e t e m o d e l . *From A. Maher. and D. Darwin, Microscopic Finite E

Model of Concrete, presented at the First International Confeence on Mathematical Modeling (St. Louis. Aug.-Sept. 1977).1 6 0 0MICRO

F i g . 2 . 4 - S t r e s s - s t r a i n c u r v e s a s i n f l u e n c e d b y c o a t i n g a g g r e g a t e s (2.36 ).

seemed to indicate a very large effect, thus sizing the importance of interfacial strength behavior of concrete. These studies utilized tively thick, soft coatings on the coarse aggre reduce the bond strength. Since these soft isolated the aggregate from the surrounding the effect was more like inducing a large num voids in the concrete matrix.

Two other studies2.36,2.37 which did not isolate tcoarse aggregate from the mortar indicate interfacial strength plays only a minor role itrolling the stress-strain behavior and ulstrength of concrete. Darwin and Slate2.36 used abond strength.224R-5

l/30woz

z- 10

OUNCOATEDAGG.l COATED AGG.

2 0 0 0 2 4 0 0 2 8 0 0 3 2 0 0TRAIN

R e f e r e n c e

empha-Work by Carino,2.38 using polymer impregnateon theconcrete, seems to corroborate these two s rela-Carino found that polymer impregnation did ngate tocrease the interfacial bond strength, but did ioatingsthe compressive strength of concrete. He attmortar,the increase in strength to the effect of the pber ofon the strength of mortar, thus downgrading tportance of the interfacial bond.

ehat the con-imate

The importance of mortar, and ultimately cpaste, in controlling the stress-strain behavconcrete is illustrated by the finite element wBuyukozturk2.37 and Maher and Darwin.2.31,2.32 Usinga linear finite element representation of a p

Et

enbrr

ehavior

plified using

differsormal,

rimaryminantlateralis gov-urs atr alone.

oncretefunction

te theirscopic

tress at

bout 60ses in-mortarryhe

ems toimaryrt-termregate initial paste. of thelume

ant ef-el that

e ulti-

f con-age ofitional

ort, aal light con-

b-

mortar)224R-6 ACI COMMl=lT

w-

\. _

-- Normal fnterfaclal Str.- ._ I nfuxte I nterfaciaf Str

._ Zwo Tenstle and CoheweI nterfaclal Str.

- - - Z e r o InterfacIal Str.

S t r e s s . PSI4 lMPar

L_._ 1

*l. 0 *2. 0 0. 0 1.0Strdln. 0.001 In/in

,

A g g r e g a t eMortar

.?. 0

Fig. 2.6 - Stress-strain curve for finite elemmodel of concrete with varying values of morgregate bond strength (Reference 2.32).

However, his finite element model could nocate the nonlinear experimental behaviorphysical model using the formation of intbond cracks and mortar cracks as the only effect. Maher and Darwin 2 .31,2.32 have shown that using a nonlinear representation for the mostituent of the physical model, a very close tation of the actual behavior can be obtainresults for Buyukozturks model are shown Fig.25. .

The inability of linear elastic models2.25,2.26,2.39 toduplicate the nonlinear behavior of concretemicrocracking alone has been explained as bto the fact that concrete is really a statisticrial. When the proper statistical variationlected, the nonlinear behavior of concrete

v MORTAR@21 v0 CONCRETE 0

ti* OS I I I I I *

lJ4 l/2 314 1(6.4) (12.7)(19. 1)(2X 4)

NOTCH DEPTH, INCHES (mm)Fig. 2.7 - Effect of notch depth on flexure stre(Reference 2.42).E REPORT

enttar-ag-

dupli- of therfacialonlinearytar con-epresen-ed. Thein

utilizingeing dueal mate- is se-can be

duplicated2.25 While the statistical variations un-doubtedly play a part, the major nonlinear bcan also be matched by considering thenon-linearities of the mortar constituent.2.31,2.32 Fig. 2.6 il-lustrates the results obtained for a highly simmodel of concrete under uniaxial compressiona nonlinear representation for mortar. The stress-strain curve for the model without cracking very little from that of models that have a nor above normal, amount of microcracking. Micro-cracks have a relatively minor effect on the pstress-strain behavior of the models. The doeffect of microcracking is to increase the strain. In every case the failure of the model erned by crushing of the mortar which occan average strength below that of the morta

Newman2.5s and Tasuji, Slate, and Nilson2.40 lhaveobserved that the principal tensile strain in cat the discontinuity stress appears to be a of the mean normal stress, 0, = (0,+0,+0,)/3. Intheir study of the biaxial strength of concre, Ta-suji, et al., observe that the final failure ofspecimens consists of the formation of macrotensile cracks. They also observe that the sdiscontinuity occurs at approximately 75 percent ofthe ultimate strength in compression and at apercent of the ultimate strength for those cavolving tension, matching the levels at which cracking begins.2.3,2.4 l Their work seems to point vestrongly toward a limiting tensile strain as tgoverning factor in the strength of concrete.

Overall, the damage to cement paste seplay an important role in controlling the prstress-strain behavior of concrete under shoaxial load. In normal weight concrete, aggparticles act as stress-raisers, increasing thestiffness and decreasing the strength of theFor cyclic and sustained loading, a great dealbond cracking results from load induced vochanges within the paste, but has no significfect on strength. A number of investigators fethe onset of mortar cracking marks the trumate strength of concrete.2.6-2.8,2.33,2.34,2.41 l Whethermortar cracking itself controls the strength ocrete or whether it only signals intimate damthe cement paste remains to be seen. Addstudies in this area are clearly warranted.

2.3 - FractureSince the publication of the previous rep

number of investigations have shed additionon the applicability of fracture mechanics tocrete and its constituent materials.

Shah and McGarry utilized flexure specimens sujected to three-point loading.2.42 Their work indicatesthat while paste is notch sensitive, neither nor concrete are affected by a notch (Fig. 2.7. Shahngthand McGarry also ran a series of tests using notchedtensile specimens and determined that paste speci-

Fei

nanheefT

trst

lytyd

ff.

cwif

bwdnc

bii-olc

t tua

afn

pe

e

usingsed bye- notch. They

lier re-e load-acturenotch width on K I for both mortar and concrete2.20Utilizing notched beam specimens of constanand depth, with varying widths, they founwithin the range studied, there was no depof fracture toughness upon the length of craSince their work utilized small specimens depth of only about 50 mm (2 in.), there is some dication that rather than measuring the toughness of the material, they were simply measur-ing the modulus of rupture.

The applicability of these results, and muchother fracture mechanics work, has been into perspective based on the experimental Walsh. In separate investigations of notchespecimens2.21 and beams with right angle re-enotches2.22 Walsh has demonstrated that spesize has a marked influence on the applicalinear elastic fracture mechanics to the faplain concrete specimens. As illustrated in Ffor specimens of similar geometry but below a certain critical size, the specimen capacity is gby the modulus of rupture of concrete, cafrom the linear stress distribution. For speabove this size, the strength is governed by ture toughness, which he approximated as aof the square root of the compressive strengconcrete. Walsh concluded that, for valid totesting of concrete, the depth of notched bemust be at least 230 mm (9 in.). This type of behior is also observed in metals, i.e., for valid mechanics test results, the test specimemeet minimum size requirements (ASTM E 399).These size requirements are dependent usquare of the toughness levels being measura material whose toughness level is twice another material (all other properties beingmust have specimen dimensions four times that ofthe first material for the test results to be valid.Gjorv, Sorensen and, Arnesen2.23 investigated thn-racture

of theroughtork by

beamtrantimen

ility oflure ofg. 2.8,

vernedulated

cimenshe frac-functionh of theghnessms

v-ractures must

on thed. Thusthat ofequal),

qually

0.10 L I I1 4

a/a0 (log scale)

F i g . 2.8 - R e l a t i o n s h i p b e t ween t e s t r e s u l t s a n dt h e o r y f o r n o t c h e d c o n c r e t e b e a m s ( R e f e r e n c e 2 . 2 2 ) .

L-__ -- ~_. - -~ 1

Fig. 2. 9 - E f f e c t o f n o t c h d e p t h o n flexural s t r e n g t h(Reference 2.23).

notch sensitivity of paste, mortar and concretethree-point bend specimens similar to those uShah and McGarry2.42 As shown in Fig. 2.9, they dtermined that both mortar and concrete aresensitive, but less sensitive than cement pasteconclude that the disagreement with the earsults is due in part to their improvement in thing procedure. They feel that linear elastic frCONTROL O

mens, and mortar specimens made with fingate that passed the #30 sieve, are notch sensitbut that mortar specimens containing largeraggregate are not notch sensitive.

Brown utilized notched flexure specimedouble cantilever beam specimens of paste d mor-tar2.18 8 His tests show that the fracture toughcement paste is independent of crack lengttherefore a material constant. The fracturness of mortar, however, increases as thpropagates, indicating that the addition of gregate improves the toughness of paste. havior is similar to the behavior found in ssteels that exhibit a plane strain-plane stretion. Because the plane strain-plane stress occurs beyond the limits of LEFM, the anamore complex. To re-establish the applicabiliLEFM, larger test specimens must be usetougher materials such as mortar.

Mindess and Nadeau investigated the e CRACKING 224R-7

aggre-ve,sizes of

s andness of and is tough- crackine ag-his be-ucturals transi-ransitionsis is of with

ect of

t lengthd thatendencek front.ith ae mechanics is applicable to the small specimens of

ow

n

io

i

y

g

r

e

a

ofoncrete,pp.

and Con-

racking,

avior ofs, Pro-ture ofsso-

son ofsion and

Winter,Deforma-

Fractureoading,

Winter,ro-e,2. andn,

rac-

tures of

an, V. 2,

-

icro-ring,

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66, pp.

ture

c Frac-s,

nessACI COMMIT

paste, but not to the small size specimens of and concrete. Even the small specimens ofand concrete, however, have some degree sensitivity since the failure is not consistent modulus of rupture based on the net cross Citing Walshs earlier work,2.21 they agree thatLEFM is applicable to large concrete specimethat it is not applicable to small specimens.

Hillemeier and Hilsdorf2.43 utilized wedge loadecompact tension specimens to measure the toughness of paste, aggregate and the pasgate interface. They feel that, while the faconcrete in tension and compression is contrmany interacting cracks rather than by the tion of a single crack, fracture mechanics doan important tool for evaluating the constituterials of concrete. They found that paste is sensitive material and that the addition of eair or soft particles has only a small affect K I c .Their work indicates that the KIc values for inter-facial strength between paste and aggregateabout one-third of the KIc value for paste alone, athat the characteristic value of KIC for aggregate approximately ten times that of paste.

Swartz, Hu, and Jones2.24 used compliance mesurement to monitor crack growth in notchecrete beams subjected to sinusodial loadingconclude that this procedure is useful for mocrack growth in concrete due to fatigue. Bathe appearance of the fracture surface, whica combination of both aggregate fracture anfailure, they feel that fracture toughness ispertinent material property. However, thethat an effective fracture toughness might bsignificant material property if related to smaterial and specimen variables such as asize and gradation, and proportions of the mif the calculation considers the nonlinear matsponse of concrete.

A number of investigators do not feel thGriffith theory of linear fracture mechanics rectly applicable to all concrete2.23, 2.24* 2.42 (ASTM E399). Some like Swartz, et a1.2.24 feel that the theohas application when the limitations and snonhomogenous effects are taken into acClearly, specimen size requirements must bemore attention. Of key interest in future wothe observations by Walsh2.21 2.22 that show that the specimens are large enough, the effheterogeneity are greatly reduced and that may approximate a homogenous material tothe principles of fracture mechanics can be

References2.1. Hsu, Thomas T. C.; Slate, Floyd O.; Sturman, Ger

ald M.; and Winter, George, Microcracking of Plain Cocrete and the Shape of the Stress-Strain Curv ACI

J OURNAL Proceeding s V. 60, No. 2, Feb. 1963, pp. 209-22TEE REPORT

mortar mortarf notchith the

section.

s, but

d,fracturete-aggre-lure oflled by

propaga-es offerent ma-a notchntrainedon

is onlynds

a-d con-. Theynitoringsed onh showsd bond not a statee apecificgregateix, anderial re-

at theis di-

ypecificcount. givenrk are

ifcts of

concrete whichpplied.

-n-e,

2.2. Hsu, Thomas, T. C., Mathematical Analysis Shrinkage Stresses in a Model of Hardened CACI JOURNAL, Proceedings V. 60, No. 3, Mar. 1963, 371-390.

2.3. Slate, Floyd O., and Matheus, Ramon E., VolumeChanges on Setting and Curing of Cement Paste crete from Zero to Seven Days, ACI JO U R N AL, P r o -c e e d i n g s V. 64, No. 1, Jan. 1967, pp. 34-39.

2.4. Evans, R. H., and Marathe, M. S., Microcand Stress-Strain Curves for Concrete in TensionMate-r i a l s a n d S t r u c t u r e s , R e s e a r c h a n d T e s t i n g (Paris), V. 1,No. 1, Jan. 1968, pp. 61-64.

2.5. Newman, Kenneth, Criteria for the BehPlain Concrete Under Complex States of Stresc e e d i n g s , International Conference on the StrucConcrete (London, Sept. 1965), Cement and Concrete Aciation, London, 1968, pp. 255-274.

2.6. Brooks, J. J., and Neville, A. M., A CompariCreep, Elasticity and Strength of Concrete in Tenin Compression, Magazine of Concrete Researc h (London),V. 29, No. 100, Sept. 1977, pp. 131-141.

2.7. Meyers, Bernard L.; Slate, Floyd O.; and George, Relationship Between Time-Dependent tion and Microcracking of Plain Concrete, ACI JOURNAL ,P r o c e e d i n g s V. 66, No. 1, Jan. 1969, pp. 60-68.

2.8. Shah, Surendra P., and Chandra, Sushil, of Concrete Subjected to Cyclic and Sustained LACI JOURNAL, P r o c e e d i n g s V. 67, No. 10, Oct. 1970, pp.816-824.

2.9. Sturman, Gerald M.; Shah, Surendra P.; andGeorge, Effects of Flexural Strain Gradients on Miccracking and Stress-Strain Behavior of Concret ACIJOURNAL, P r o c e e d i n g s V. 62, No. 7, July 1965, pp. 805-82

2.10. Griffith, A. A., The Phenomena of RuptureFlow in Solids, T r a n s a c t i o n s , Royal Society of LondoNo. 221A, 1920, pp. 163-198.

2.11. Kaplan, M. F., Crack Propagation and the Fture of Concrete, ACI JOURNAL , P r o c e e d i n g s V. 58, No. 5,Nov. 1961, pp. 591-610.

2.12. Glucklich, Joseph, Static and Fatigue FracPortland Cement Mortars in Flexure, Proceedings, FirstInternational Conference on Fracture, Sendai, Jap1965, pp. 1343-1382.

2.13. Romualdi, James P., and Batson, Gordon B., Mechanics of Crack Arrest in Concrete, Proceedings, ASCE,V. 89, EM3, June 1963, pp. 147-168.

2.14. Huang, T. S., Crack Propagation Studies in Mconcrete, MSc Thesis, Department of Civil EngineeUniversity of Colorado, Boulder, 1966.

2.15. Lott, James L., and Kesler, Clyde E., Crack Propagation in Plain Concrete, Symposium on StructurePortland Cement Paste and Concrete, S p e c i a l R e p o r t No.90, Highway Research Board, Washington, D.C., 19204-218.

2.16. Naus, Dan J., and Lott, James L., FracToughness of Portland Cement Concretes, ACI JOURNAL,Proceedings V. 66, No. 6, June 1969, pp. 481-489.

2.17. Naus, Dan J., Applicability of Linear-Elastiture Mechanics to Portland Cement Concrete PhDThesis, University of Illinois, Urbana, Aug. 1971.

2.18. Brown, J. H., Measuring the Fracture Toughof Cement Paste and Mortar, M a g a z i n e o f C o n c r e t e R e -4. s e a r c h (London), V. 24, No. 81, Dec. 1972, pp.185-196.

pA

l

No. 1, Jan. 1969, pp. 69-72.

ncrete

-

d

Con-

riticalrete,p.

Me-fort

i

8

g7

y

v

e is a archi-herne of

oncreteracticeminateate re-

cipalemical

tensilee fre- con-ncrete

cernsncretehrink-ive ce-

cifica-d intweene

Chapter 8 (Sections 8.3 and 8.6) of this report.es inthe most serious problems encountered in cconstruction. Good design and construction pcan minimize the amount of cracking and eliCONTROL OF C

2.19. Evans, A. G.; Clifton, J. R.; and Anderson,The Fracture Mechanics of Mortars, C e m e n t a n d C o n -crete Research, V. 6, No. 4. July 1976, pp. 535-547.

2.20. Mindess, Sidney, and Nadeau, John S., EffeNotch Width of KIC for Mortar and Concrete, C e m e n tand Concrete Research, V. 6, No. 4, July 1976, pp. 529-534.

2.21. Walsh, P. F., Fracture of Plain Concrete, IndianConcrete Journal (Bombay), V. 46, No. 11, Nov. 1972, p469-470, 476.

2.22. Walsh, P. F., Crack Initiation in Plain ConcrMagazine of Concrete Research (London), V. 28, No. 94,Mar. 1976, pp. 37-41.

2.23. Gjorv, O. E.; Sorensen, S. I.; and Arnesen, Notch Sensitivity and Fracture Toughness of ConCement and Concrete Research, V. 7, No. 3, May 1977, pp.333-344.

2.24. Swartz, Stuart E.; Hu, Kuo-Kuang; and JoGary L., Compliance Monitoring of Crack Growth in crete, Proceedings, ASCE, V. 104, EM4, Aug. 1978, pp.789-800.

2.25. Shah, Surendra P., and Winter, George, InBehavior and Fracture of Concrete, ACI JOURNAL, P ro -ceedings V. 63, No. 9, Sept. 1966, pp. 925-930.

2.26. Testa, Rene B., and Stubbs, Norris, Bond Faiand Inelastic Response of Concrete, Proceedings, ASCE,V. 103, EM2, Apr. 1977, pp. 296-310.

2.27. Darwin, David, Discussion of Bond Failure anelastic Response of Concrete, by Rene B. Testa and Nor-ris Stubbs, Proceedings, ASCE, V. 104, EM2, Apr. 1978,pp. 507-509.

2.28. Spooner, D. C., The Stress-Strain Relationship Hardened Cement Pastes in Compression, M a g a z i n e o fConcrete Research (London), V. 24, No. 79, June 1972, pp85-92.

2.29. Spooner, D. C., and Dougill, J. W., A QuantitativeAssessment of Damage Sustained in Concrete DCompressive Loading, Magazine of Concrete Research(London), V. 27, No. 92, Sept. 1975, pp. 151-160.

2.30. Spooner, D. C.; Pomeroy, C. D.; and Dougill, J. W.,Damage and Energy Dissipation in Cement PasCompression, Magazine of Concrete Research (London),V. 28, No. 94, Mar. 1976, pp. 21-29.

2.31. Maher, Ataullah, and Darwin, David, A FinElement Model to Study the Microscopic Behavior ofConcrete, CRINC Report-SL-76-02, The University ofKansas Center for Research, Lawrence, Nov. 1976,

2.32. Maher, Ataullah, and Darwin, David, MicroscoFinite Element Model of Concrete, Proceedings, First In-ternational Conference on Mathematical ModelinLouis, Aug.-Sept. 1977), University of Missouri-Rolla, 197v. III, pp. 1705-1714.

2.33. Karsan, I. Demir, and Jirsa, James 0.. Behaviorof Concrete under Compressive Loadings, Proceedings,ASCE, V. 95, ST12, Dec. 1969, pp. 2543-2563.

2.34. Neville, A. M., and Hirst, G. A., MechanismCyclic Creep of Concrete, Douglas McHenry Symposiumon Concrete and Concrete Structures, SP-55, AmericanConcrete Institute, Detroit, 1978, pp. 83-101.

2.35. Nepper-Christensen, Palle, and Nielsen, TommP. H., Modal Determination of the Effect of Bond BeCoarse Aggregate and Mortar on the CompressiStrength of Concrete, ACI JO U R N A L, Proceedings V. 66,te Plain

3 pp.pic

(St.,

of

the visible large cracks by the use of adequinforcement and contraction joints.

Although drying shrinkage is one of the princauses of cracking, temperature stresses, chreactions, frost action, as well as excessive stresses due to loads on the structure, arquently responsible for cracking of hardenedcrete. Cracking may also develop in the coprior to hardening due to plastic shrinkage.

Information presented in this chapter cononly the subjects of cracking of hardened codue to drying shrinkage; factors influencing sage; control of cracking; and the use of expansments to minimize cracking.

The subject of construction practices and spetions to minimize drying shrinkage is covere.

uring

Chapter 3 - Control of cracking due to dryingshrinkage*3.1 - Introduction

Cracking of concrete due to drying shrinkagsubject which has received more attention bytects, engineers, and contractors than any otcharacteristic or property of concrete. It is oRACKING 224R-9

E.,

ct of

.

ete,

.,crete,

nes,Con-

elastic

ure

d In-

2.36. Darwin, David, and Slate, F. O., Effect of Paste-Aggregate Bond Strength on Behavior Concrete, Jour-nal of Materials, V. 5, No. 1, Mar. 1970, pp. 86-98.

2.37. Perry, C., and Gillott, J. E., The Influence of Mor-tar-Aggregate Bond Strength on the Behavior of Coin Uniaxial Compression, Cement and Concrete Research,V. 7, No. 5, Sept. 1977, pp. 553-564.

2.38. Carino, Nicholas J., Effects of Polymer Impregnation on Mortar-Aggregate Bond Strength, Cement andConcrete Research, V. 7, No. 4, July 1977, pp. 439-447.

2.39. Buyukozturk, Oral, Stress-Strain Response anFracture of a Model of Concrete in Biaxial Loading, PhDThesis, Cornell University, Ithaca, June 1970.

2.40. Tasuju, M. Ebrahim; Slate, Floyd 0.; and Nilson,Arthur H., Stress-Strain Response and Fracture of crete in Biaxial Loading, ACI JO U R N A L, Proceedings V .75, No. 7, July 1978, pp. 306-312.

2.41. Shah, Surendra P., and Chandra, Sushil, CStress, Volume Change, and Microcracking of ConcACI JO U R N A L, Proceedings V. 65, No. 9, Sept. 1968, p770-781.

2.42. Shah, Surendra P., and McGarry, Fred J., GriffithFracture Criterion and Concrete, Proceedings, ASCE, V.97, EM6, Dec. 1971, pp. 1663-1676.

2.43. Hillemeier, B., and Hilsdorf, H. K., Fracture chanics Studies of Concrete Compounds, Cement and Con-crete Research, V. 7, No. 5, Sept. 1977, pp. 523-535.*Principal author: Miloss Polivka.

hi

ht

m

nke

ge, (b)lasticity o

nlking isd highesirablestresses.ld haveigh de-eep) asrge ex-o bend-

s, andvolume are ant con- the ce-elling ofinternalgnitude

chem-mmonlyct con-s (prin-unt ofmoritearticlesa hard-he capil-nt is inloss of

irst wa-y large of wa-he lossthe hy-e paste.ditions,ass of evapo-causing

t paste actione onally cal- ofbyoes nothrinkagein theDEVELOPS TENSILE STRESS

IF TENSILE STRESS ISGREATER THAN TENSILESTRENGTH, CONCRETE CRACKS

Fig. 3.1 - Cracking of concrete due to drying224R-10 ACI COMMITT

3.2 - Crack formationWhy does concrete crack due to shrinkage?

shrinkage of concrete caused by drying couplace without any restraint, the concrete wocrack. However, in a structure the concreteways subject to some degree of restraint bythe foundation or another part of the structurthe reinforcing steel embedded in the concrecombination of shrinkage and restraint develosile stresses. When this tensile stress reactensile strength, the concrete will crack. This trated in Fig. 3.1.

Another type of restraint is developed by tference in shrinkage at the surface and in the inrior of a concrete member, especially at earlSince the drying shrinkage is always larger exposed surface, the interior portion of the restrains the shrinkage of the surface concredeveloping tensile stresses. This may cause cracking, which are cracks that do not pedeep into the concrete. These surface cracwith time penetrate deeper into the concretber as the interior portion of the concrete is to additional drying.

ORIGINAL LENGTHI I

UNRESTRAINEDSHRINKAGE t-

RESTRAINED SHRINKAGEshrinkage.EE REPORT

If theld takeuld not is al- eithere or byte. Thisps ten-es thes illus-

e dif-e-y ages.at the

emberte, thussurfaceetrates may mem-subject

The magnitude of tensile stress developed duringdrying of the concrete is influenced by a combinationof factors, such as (a) the amount of shrinkathe degree of restraint, (c) the modulus of eof the concrete, and (d) the creep or relaxationf theconcrete. Thus, the amount of shrinkage is oy onefactor governing the cracking. As far as cracconcerned, a low modulus of elasticity ancreep characteristics of the concrete are dsince they reduce the magnitude of tensile Thus, to minimize cracking, the concrete shoulow drying shrinkage characteristics and a hgree of extensibility (low modulus and high crwell as a high tensile strength. However, a latensibility of a concrete member subjected ting will cause larger deflections.

3 . 3 - Drying shrinkageWhen concrete dries, it contracts or shrink

when it is wetted again, it expands. These changes, with changes in moisture content,inherent characteristic of hydraulic cemencretes. It is the change in moisture content ofment paste that causes the shrinkage or swconcrete, while the aggregate provides an restraint which significantly reduces the maof these volume changes.

When cement is mixed with water, severalical reactions take place. These reactions, cocalled hydration, produce a hydration produsisting essentially of some crystalline materialcipally calcium hydroxide) and a large amohardened calcium silicate gel called tobergel. This rigid gel consists of colloidal size pand has an extremely high surface area. In ened cement paste, some of the water is in tlary pores of the paste, but a significant amouthe tobermorite gel. Shrinkage is due to the adsorbed water from the gel. On drying the fter lost is that which occupies the relativelsize capillaries in the cement paste. This losster causes very little, if any, shrinkage. It is tof the adsorbed and inter-layer water from drated gel that causes the shrinkage of thWhen a concrete is exposed to drying conmoisture slowly diffuses from the interior mthe concrete to the surface where it is lost byration. On wetting this process is reversed, an expansion of the concrete.

In addition to drying shrinkage, the cemenis also subject to carbonation shrinkage. Theof carbon dioxide, CO2, present in the atmospherthe hydration products of the cement, principcium hydroxide, Ca(OH)2, results in the formationcalcium carbonate, CaCO,, which is accompanied a decrease in volume. Since carbon dioxide dpenetrate deep into the mass of concrete, sdue to carbonation is of minor importance

overall shrinkage of a concrete structure. However,

d 75majorderedhosey the will

bilitye in-

he ex-dntar-com-

st in-e of

ty ofg theggre-s its

ually

rying

retest

, and

slate,he ri-lime- their will

por-ncreten ap-

sand-capac-

us of

gradeCONTROL OF

carbonation does play an important role shrinkage of small laboratory test specimensularly when subjected to long-term exposdrying. Thus, the amount of shrinkage observsmall laboratory specimen will be greater tshrinkage of the concrete in the structure. Tject of shrinkage due to carbonation is discudetail by Verbeck.3.1

3.4 - Factors influencing drying shrinkageThe major factors influencing shrinkage i

the composition of cement, type of aggregacontent, and mix proportions. The rate of mloss or the shrinkage of a given concrete isinfluenced by the size and shape of the cmember, the environment, and the time oexposure. These and other factors influencingtude and rate of shrinkage are herein discu

3 . 4 . 1 E f f e c t of cement - Results of an extensistudy made by Blaine, Arni, and Evans,3.2 of the Na-tional Bureau of Standards on a large numportland cements indicate that it is not posssay that a cement, because it conforms toquirements of one of the standard types of will have greater or less shrinkage than a cemenmeeting requirements for some other typement. Their results on neat cement pastes swide distribution of shrinkage values especithe Type I cements. The 6 month drying shstrain of the neat pastes ranged from abouto more than 0.0060 with an average for thements tested of about 0.0030. They found thshrinkage of pastes was associated with: 1C

3A/SO

3 ratios, 2. lower Na

2O and K

2O contents,

and 3. higher C4AF contents of the cement. Tes

Brunauer. Skalny, and Yudenfreund3.3 show that foshort curing periods Type II cement pastesited considerably less shrinkage than Type IHowever, the shrinkage of pastes cured for was about the same for the two types of ce

Tests made by the California Division of ways3.4 on mortar or paste as a measure of bin concrete indicate that Type II cements gproduce lower shrinkage than Type I cemenmuch lower than Type III cements. Tests by Lerch1.5show that the proportion of gypsum in the has a major effect on shrinkage. Cement pmoderate the differences in shrinkage due tocomposition by optimizing its gypsum conten

The fineness of a cement can have some ion drying shrinkage. Tests by Carlson3.6 showed thafiner cements generally result in greater shrinkage, but the increase in shrinkage wcreasing fineness is not large. His results shthe composition of the cement is a factor afor some cements an increase in fineness mlittle change and in some cases even a low

crete shrinkage. CRACKING 224R-11

in the, partic-ure toed on ahan thehe sub-ssed in

ncludete, water

oisture greatlyoncretef drying magni-

ssed.

ve

ber ofible to the re-cements,t of ce-howed aally forrinkaget 0.0015 182 ce-at lower. lower

ts byr exhib- pastes.28 daysments.

High-ehaviorenerallyts, and

cementroducers cementt.

nfluencetconcreteith in-ow thatnd thusay shower con-

TABLE 3.1 - Effect of type of aggregate onshrinkage of concrete3.6

Specif icl-year

Absorption, shrinkage,Aggregate gravity percent percenttSandstone 2.47 5.0 0.116Slate 2.75 1.3 0.068Granite 2.67 0.8 0.047Limestone 2.74 0.2 0.041Quartz 2.66 0.3 0.032

3 . 4 . 2 I n f l u e n c e o f t y p e o f a g g r e g a t e - Coarse andfine aggregates, which occupy between 65 anpercent of the total concrete volume, have a influence on shrinkage. Concrete may be consito consist of a framework of cement paste wlarge potential shrinkage is being restrained baggregate. The drying shrinkage of a concretebe only a fraction (about l/4 to l/6) of that of the ce-ment paste. The factors which influence the aof the aggregate particles to restrain shrinkagclude (a) the compressibility of aggregate and ttensibility of paste, (b) the bond between paste anaggregate, (c) the degree of cracking of cemepaste, and (d) the contraction of the aggregate pticles due to drying. Of these several factors, pressibility of the aggregate has the greatefluence on the magnitude of drying shrinkagconcrete.

The higher the stiffness or modulus of elastician aggregate, the more effective it is in reducinshrinkage of concrete. The absorption of an agate, which is a measure of porosity, influencemodulus or compressibility. A low modulus is usassociated with high absorption.

The large influence of type of aggregate on dshrinkage of concrete was shown by Carlson.3.6 As anexample some of his shrinkage data for concwith identical cements and identical water-cemenratios are given in Table 3.1.

Quartz, limestone, dolomite, granite, feldsparsome basalts can be generally classified as low-shrinkage producing types of aggregates. High-shrinkage concretes often contain sandstone, hornblende and some types of basalts. Since tgidity of certain aggregates, such as granite, stone or dolomite, can vary over a wide range,effectiveness in restraining drying shrinkagevary accordingly.

Although the compressibility is the most imtant single property of aggregate governing coshrinkage, the aggregate itself may contract apreciable amount upon drying. This is true for stone and other aggregates of high absorption ity. Thus, in general, aggregate of high modulelasticity and low absorption will produce a low-shrinkage concrete. However, some structural

lightweight aggregates, such as expanded shales,

n

t

h

n

soaf

con-otal ag-ossible. unit

ignifi-ropor- high

eater sand

hrinkageent fac-

nstant,ced.

oncretee max-f aggre-ste, de-he large has on in

gregate

aterkag

p onrequire--

ductiondrying

the wa- shrink-te. Thisas given

freshto 1tent bymecontentge.cluded

oncrete, a min-ter re-igh tem-f smallerse224R-12 ACI COMMIT

+ 119 142 166 1905 0.060u% 0.050

I

," 0.020zz 0.010is 200 240 280 320

WATER CONTENT OF CONCRETE

kg/m3

Ib/yd3

Fig. 3.2 - Typical effect of water content of con-crete on drying shrinkage (Reference 3.8).

clays, and slates which have high absorptioduced concretes exhibiting low shrinkage character-istics.3.7

Maximum size of aggregate has a significanon drying shrinkage. Not only does a largegate size permit a lower water content of tcrete, but it is more effective in resisting theage of the cement paste. Aggregate gradahas some effect on shrinkage. The use of agraded fine or coarse aggregate may resuoversanded mix, in order to obtain desiredability, and thus prevent the use of the mamount of coarse aggregate resulting in inshrinkage.3 . 4 . 3 E f f e c t o f w a t e r c o n t e n t a n d m i x p r o p o r t i o n s -The water content of a concrete mix is anotimportant factor influencing drying shrinkaglarge increase in shrinkage with increase icontent was demonstrated in tests made byBureau of Reclamation.3.8 A typical relationship btween water content anddrying shrinkage iin Fig. 3.2. An increase in water content alsduces the volume of restraining aggregate results in higher shrinkage. The shrinkage o

400(237)

350(208)

3 0 0(178)

2 5 0(148)

200

2.5 19.0 37.5 75 150 m m

(119) 3/8 3/4 1 1/2 3 6 in.

MAXIMUM SIZE OF AGGREGATE

Fig. 3.3 - Effect of aggregate size on water require-

ment of non-air-entrained concrete (ACI 211.1).s, pro-

t effectaggre-

he con- shrink-ion also poorlylt in an work-aximumcreased

er verye. The waterthe U.S.e- shown re-nd thus a con-

Tests reported by Tremper and Spellman showthat the cement factor has little effect on sof concrete. Their data show that as the cemtor was increased from 470 to 752 lb/yd3 (279 to 446kg/m3) the water content remained nearly cowhile percentage of fine aggregate was redu

The amount of mixing water required for cof a given slump is greatly dependent on thimum size of aggregate. The surface area ogate, which must be coated by cement pacreases with increase in size of aggregate. Teffect that the maximum size of aggregatethe water requirement of concrete is shownFig.3.3. The data plotted in this figure, taken from ACI211.1 shows, for example, that for a 3 to 4 in. (75 to100 mm) slump concrete, increasing the agsize from 3/4 in. (19 mm) to 11/2 in. (38 mm) decreasesthe water requirement from 340 to 300 lb/yd3 (202 to178 kg/m3). This 40 lb (24 kg) reduction in wcontent would reduce the 1 year drying shrine byabout 15 percent.

Also shown in Fig. 3.3 is the effect of slumwater requirement. For example, the water ment of a concrete made with 3/4 in. (19 mm) size aggregate is 340 lb/yd3 (202 kg/m3) for a 3 to 4 in.slump, but only 310 lb/yd3 (184 kg/m31 for a 1 to 2in. slump (25 to 50 mm). This substantial rein water content would result in a lower shrinkage.

Another important factor which influences ter requirement of a concrete, and thus itsage, is the temperature of the fresh concreeffect of temperature on water requirement by the U.S. Bureau of Reclamation3. is shown inFig. 3.4. For example, if the temperature ofconcrete were reduced from 100 to 50 F (38 0 C),it would permit a reduction of the water con33 Ib/yd3 (20 kg/m3) and still maintain the saslump. This substantial reduction in water would significantly reduce the drying shrinka

From the above discussion it must be conthat, to minimize the drying shrinkage of cthe water content of a mix should be kept toimum. Any practice that increases the waquirement, such as the use of high slumps, hperatures of the fresh concrete or the use osize coarse aggregate, will substantially increaTEE REPORT

crete can be minimized by keeping the watertent of the paste as low as possible and the tgregate content of the concrete as high as pThis will result in a lower water content pervolume of concrete and thus lower shrinkage.

The total volume of coarse aggregate is a scant factor in drying shrinkage. Concrete ptioned for pump placement with excessivelysand contents will exhibit significantly grshrinkage than will similar mixes with normalcontents.

3.4shrinkage and thus cracking of the concrete.

ea

nvw

ts

a

e

c

the con-f some of althought of the

on dryingshrinkagere basedze speci-

wer theifferenceith andhrinkagery tests

of con- shrink-ts of the

concreteretendencyst curinggh thef elastic-rcentage,e in theand.hich isst struc-e duce awill re-

t whichhus in-some of these admixtures may even increashrinkage at early ages of drying, although tage shrinkage of these concretes will be absame as that of corresponding mixes with notures.

The use of calcium chloride, a common accelwill result in a substantial increase in drying age, especially at the early ages of dryingmade by the California Department of Transporta-tion3.44showed that the 7 day shrinkage of a cocontaining 1.0 percent of calcium chloride wadouble that obtained for the control mix withmixture. However, after 28 days of dryingshrinkage of the concrete containing calcium was only about 40 percent greater than that ofcontrol mix.3 . 4 . 5 Effect of pozzolans - Fly ash and a number natural materials such as opaline cherts and shales,diatomaceous earth, tuffs and pumicites arepozzo-lans used in portland cement concrete. The useCONTROL OF

00

4. 4 10.0 15.6 21.1 26. 7 32.2 378 OC310084)

300(I 78)

290(I 72)

280(166)

270(160)

260(154140 50 60 70 80 90 100 OF

TEMPERATURE OF FRESH CONCRETE

Fig. 3 . 4 - Effect of temperature of fresh concreteon its water requirement (Reference 3.8).

3.4.4 Effect of chemical admixtures - Chemical ad-mixtures are used to impart certain desirableerties to the concrete. Those most commonlyinclude air-entraining admixtures, water-radmixtures, set-retarding admixtures, and tors.

It would be expected that when using antraining admixture, the increase in the amouvoids would increase drying shrinkage. Howecause entrainment of air permits a reduction in ter content with no reduction in slump, theage is not appreciably affected by air contenabout 5 percent.3.8 Some air-entraining agentsstrong retarders and contain accelerators whincrease drying shrinkage by 5 to 10 percen

Although the use of water-reducing and tarding admixtures will permit a reductionwater content of a concrete mix, it will usuresult in a decrease in drying shrinkage. Asome natural pozzolans can increase the wade-se thehe laterout the admix-

rator,shrink-. Tests

ncretes aboutout ad-, thehloride

the

of

of

show substantially the same shrinkage in that was moist cured for 7, 14, and 28 days befodrying was started. As far as the cracking of the concrete is concerned, prolonged moimay not necessarily be beneficial. Althoustrength increases with age, the modulus oity also increases by almost as large a peand the net result is only a slight increastensile strain which the concrete can withst

Steam curing at atmospheric pressure, wcommonly used in the manufacture of precatural elements, will reduce drying shrinkag(AC1517). Also, because stream curing will prohigh early-age strength of the concrete, it duce its tendency to crack, since the precast mem-bers are unrestrained.3 . 4 . 7 I n f l u e n c e o f s i z e o f m e m b e r - The size of aconcrete member will influence the rate amoisture moves from the concrete and ta-shrink-ts up toareich may.et-re-

in thelly notctually

3.6, the larger the concrete member, the loshrinkage. This may explain the negligible din shrinkage cracking of field structures, wwithout pozzolan, despite clearly greater sof the concretes with pozzolans in laboratoon small size specimens.3.4.6 Effect of duration of moist curing - Car1son3.6reported that the duration of moist curingcrete does not have much effect on dryingage. This is substantiated by the test resulCalifornia Department of Transportation3. whichCRACilNG 224R-13Fig. 3 . 5 - Rates of drying of concrete exposed to 50percent relative humidity (Reference 3.9).

prop- usedducingccelera-

air-en-t of airer, be-

mand as well as the drying shrinkage of crete. Also, it was observed that the use othese pozzolans increased drying shrinkagethey had little effect on the water contenconcrete. Some fly ashes have little effect shrinkage, while others may increase the of the concrete. All of these observations aon results of tests made on laboratory simens. However, as noted in Section 3.4.7 and Fig.

wiiiaa

-0 4 8 I2 16 20 24 28 in.w DEPTH BELOW CONCRETE SURFACEter fluence the rate of shrinkage. Carlson3* has shown

Eit

z

ee

ene ruoslr

oft rela-ncretee. Theackingp-ntrol

of ex-nsatingare dis-

ue not224R-14 ACI COMMITT

that for a concrete exposed to a relative hum50 percent, drying will penetrate only abou(75 mm) in 1 month and about 2 ft (0.6 m) in 10years. Fig. 3.5 shows his theoretical curves fordrying of slabs. Hansen and Mattock3.10 made anextensive investigation of the influence of sishape of member on the shrinkage and creep crete. They found that both the rate and thvalues of shrinkage and creep decrease as thber becomes larger.

This significant effect of size of member on shrinkage of concrete must be considered whuating the potential shrinkage of concrete itures based on the shrinkage of concrete spin the laboratory. The rate and magnitude ofage of a small laboratory specimen will begreater than that of the concrete in the stTest results of several studies carried out tpare the shrinkage of concrete in walls and the field with the shrinkage of small labo ce rs

riei

e h

the de-nd the

factorse de-e mod-lp toplaced,roduce

ce the crack-ed byregateby us-cy, ands dis-ofadmix-

y is toregate and atain a to re-

may re-racking

y is toch willn. Thisused tonsider-a

permitreaches

ere arew thespecimens have shown, as expected, that theage of the concrete in a field structure is onlytion of that obtained on the laboratory speEven in laboratory tests the size of the spused has a significant influence on shrinkage.example of the effect of specimen size on shis the data presented in Fig. 3.6, giving the resultof shrinkage tests obtained on four differenconcrete prisms. It will be noted that the shof the prisms having a cross section of 3 x 3 x 7.5 cm) was more than 50 percent greatthat of the concrete prism having a cross sectx 6 in. (12.5 x 15 cm).

3 . 5 - Control of shrinkage crackingConcrete tends to shrink due to drying wh

its surfaces are exposed to air of low relativeity. Since various kinds of restraint prevent te con-

7.5x7.5 10 x 10 10x12 5 12.5x 15 cm

I II I3x3 4 x 4 4x5 5x6 in

AVERAGE END AREA DIMENSION OF CONCRETE PRISM( LOG SCALE )

F i g . 3 . 6 - E f f e c t o f s p e c i m e n s i z e o n d r y i n g s h r i n k -

age of concrete (Principal authors data).Another way to reduce the cracking tendencuse a larger aggregate size. A larger aggsize allows an increase in aggregate volumereduction in the total water required to obgiven slump. The larger aggregate also tendsstrain the concrete more, and although this sult in internal microcracking, such internal cis not necessarily harmful.

A third way to reduce the cracking tendencapply a surface coating to the concrete, whiprevent the rapid loss of moisture from withimeans of controlling cracking has not been its full potential and should be given better coation. However, many surface coatings such s all-purpose paints are ineffective, because theythe moisture to escape almost as fast as it the surface. Chlorinated rubber and waxy or resin-ous materials are effective coatings, but thprobably many other materials which will sloE REPORT

dity of3 in.

the

e andof con- final mem-

dryingn eval- struc-cimensshrink-muchctures. com-abs inatory shrink-a frac-imens.cimenAs aninkage

t sizeinkagen. (7.5r thanon of 5

neverhumid-

crete from contracting freely, the possibilitycracking must be expected unless the ambientive humidity is kept at 100 percent or the cosurfaces are sealed to prevent loss of moisturcontrol of cracking consists of reducing the crtendency to a minimum, using adequate and proerly positioned reinforcement, and using cojoints. The CEB-FIP Code give quantitative recom-mendations on the control of cracking due to shrink-age, listing various coefficients to determine theshrinkage levels that can be expected. Control ofcracking by correct construction practices is coveredin Chapter 8 of this report, which includes specifica-tions to minimize drying shrinkage (Section 8.6).

Cracking can also be minimized by the use pansive cements to produce shrinkage-compeconcretes. Shrinkage-compensating concretes cussed in Section 3.6.3 . 5 . 1 R e d u c t i o n o f c r a c k i n g t e n d e n c y - As men-tioned previously, the cracking tendency is donly to the amount of shrinkage, but also to gree of restraint, the modulus of elasticity, acreep or relaxation of the concrete. Some which reduce the shrinkage at the same timcrease the creep or relaxation and increase thulus of elasticity, thus offering little or no hethe cracking tendency. Emphasis should be therefore, on modifying those factors which pa net reduction in the cracking tendency.

Any measure that can be taken to redushrinkage of the concrete will also reduce theing tendency. Drying shrinkage can be reducusing less water in the mix and larger aggsize. A lower water content can be achieved ing a well-graded aggregate, stiffer consistenlower initial temperature of the concrete. Acussed in Section 3.4.4, however, the reduction water content by the use of water-reducing tures will not usually reduce shrinkage.evaporation enough to be beneficial. Any slowing of

ta

n

rCONTROL OF

the rate of shrinkage will be beneficial, becaucrete has a remarkable quality of relaxing untained stress. Thus, concrete may be able stand two or three times as much slowly shrinkage as it can rapid shrinkage.3.5.2 R e i n f o r c e m e n t - Properly placed reinforcement, used in adequate amounts, will reduce the amount of cracking but prevent ucracking. By distributing the shrinkage strainthe reinforcement through bond stresses, thare distributed in such a way that a larger of very fine cracks will occur instead of a fewcracks. Although the use of such reinforcemcontrol cracking in a relatively thin concreteis practical, it is not needed in massive stsuch as dams due to the low drying shrinkthese mass concrete structures. The miamount and spacing of reinforcement to be c

te,

cg

e n

n

f

o

e

i

eec

g

tensilerinkage,o crack-ive ce-concrete

-oncrete

is avail-floors, roof slabs, and walls is given in AC1 318.

3.6.3 J o i n t s - The use of joints is the most effemethod of preventing formation of unsightlying. If a sizable length or expanse of concreas walls, slabs or pavements, is not providadequate joints to accommodate shrinkagemake its own joints by cracking.

Contraction joints in walls are made, for exby fastening to the forms wood or rubberwhich leave narrow vertical grooves in the on the inside and outside of the wall. Crackinwall due to shrinkage should occur at the grelieving the stress in the wall and thus prformation of unsightly cracks. These groovesbe sealed on the outside of the wall to prevetration of moisture. Sawed joints are commoin pavements, slabs and floors.

Joint location depends on the particulars oment. Each job must be studied individuallytermine where joints should be placed.*

3 . 6 - S h r i n k a g e - c o m p e n s a t i n g c o n c r e t e sShrinkage-compensating concretes made w

pansive cements can be used to minimize nate shrinkage cracking. The properties andexpansive cement concretes is published inous papers and reports.3-11* 3*12 Of the several typof expansive cements produced, the Tyshrinkage-compensating expansive cement commonly used in the United States.

In a reinforced concrete, the expansion ofment paste during the first few days of curdevelop a low level of prestress inducingpressive stresses in the concrete and tensilin the steel. The level of compressive stressoped in the shrinkage-compensating conranges from 25 to 100 psi (0.2 to 0.7 MPal. Whensubjected to drying shrinkage, the contractioconcrete will result in a reduction or elimina

its precompression. The initial precompressionCRACKING 224R-15

se con-der sus-o with-pplied

-ot onlynsightlys alonge cracksnumber wideent tosectionucturesage ofnimumused in

tive crack-e, suchd with it will

ample, stripsoncrete of therooves,ventingshouldt pene-

ly used

place-to de-

ith ex-r elimi- use ofnumer-spe Kis most

the ce-ng will com- stressess devel-retes

n of thetion of

STEEL\_B--- _----

ORIGINAL LENGTH

t

T A b T___++IC~*___

EXPANSION PUTS STEEL INTENSION AND CONCRETE INCOMPRESSION M

STRESS LOSS DUE TOSHRINKAGE AND CREEP

RESIDUAL EXPANSION OR, -+jSMALL CONTRACTION

.Qrl 3 7 -.concretes.

Basic concept of shrinkage-compensatin

CURINGr/ .p- DRYINGSHRINKAGE- COMPENSATINGCONCRETE, p = 0.16Ym

PORTLAND CEMENT

;CONCRETE

, I I I I0 50 100 150 2oc

AGE OF CONCRETE, DAYS

F i g . 3 . 8 - L e n g t h c h a n g e c h a r a c t e r i s t i c s o f s h r i n k -a g e - c o m p e n s a t i n g a n d p o r t l a n d c e m e n t c o n c r e t e s( R e l a t i v e h u m i d i t y = 5 0 p e r c e n t ) .

concrete minimizes the magnitude of any stress that may ultimately develop due to shand thus reduce or eliminate the tendency ting. This basic concept of the use of expansment to produce a shrinkage-compensating is illustrated in Fig. 3.7.

A typical length change history of a shrinkage-compensating concrete is compared to that ofa port-land cement concrete in Fig. 3.8. The amount of reinforcing steel normally used in reinforced c

*Guidance on joint sealants and control joint location in slabs

of theable in ACI 504 and in ACI 302, respectively.

Mn dl geinfad iml m

fulnsinn

or

5

In:e

,n-

Sie

tP

,

e

n

, a

e

9491 pp.

orcingor re-ses inrackingtion ine can

to pro-and for

portantpossi-

h, to-rrosion.racksper-lead to

ruc-ns and

ation

g be-he last

ncretek pre- com-eivesuation

as a

d witht. It isdocu-

usingto use.

for thettter- e max-abouter arech hasess of can73,lized. Inadequate curing of shrinkage-compeconcrete may result in an insufficient expanately after final finishing. For slabs on welrated subgrades, curing by sprayed-on meor moisture-proof covers have been successelongate the steel and thus subsequent cracking drying shrinkage. Specific recommendatioinformation on the use of shrinkage-compeconcrete are contained in ACI 223.

References3.1. Verbeck, George J., Carbonation of Hydrated P

land Cement, C e m e n t a n d C o n c r e t e , STP-205, AmericanSociety for Testing and Materials, Philadelphia, 1917-36.

3.2. Blaine, R. L.; Arni, H. T.; and Evans, D. N., relations Between Cement and Concrete Properties- Shrinkage of Hardened Portland Cement PastConcrete, B u i l d i n g Science Series No. 15, National Bu-reau of Standards, Washington, D.C., Mar. 1969, 77 pp.

3.3. Brunauer, S.; Skalny, J.: and YudenfreundHardened Cement Pastes of Low Porosity: DimeChanges, R e s e a r c h R e p o r t No. 69-8, Engineering Research and Development Bureau, New York Statement of Transportation, Albany, Nov. 1969, 12 pp.

3.4. Tremper, Bailey, and Spellman, Donald L., age of Concrete - Comparison of Laboratory and FPerformance, H i g h w a y R e s e a r c h R e c o r d . Highway Re-search Board, No. 3, 1963, pp. 30-61.

3.5. Lerch, William, The Influence of Gypsum on Hydration and Properties of Portland Cement Proceedings, ASTM, V. 46, 1946, pp. 1252-1297.

3.6. Carlson, Roy W., Drying Shrinkage of ConcreteAffected by Many Factors, P r o c e e d i n g s , ASTM, V. 38,Part II, 1938, pp. 419-437.

3.7. Reichard, T. W., Creep and Drying ShrinkageLightweight and Normal Weight Concrete, M o n o g r a p h74, National Bureau of Standards, Washington, D.C.30 pp.

3.8. C o n c r e t e M a n u a l , 8th Edition, U.S. Bureau of Rclamation, Denver, 1975, 627 pp.

3.9. Carlson, Roy W., Drying Shrinkage of Large Cocrete Members, ACI JOURNAL , P r o c e e d i n g s V. 33, No. 3,Jan.-Feb. 1937, pp. 327-336.

3.10. Hansen, Torben C., and Mattock, Alan H.fluence of Size and Shape of Member on the ShrinkCreep of Concrete, ACI JOURNAL, P r o c e e d i n g s V. 63, No.2, Feb. 1966, pp. 267-290.

3.11. ACI Commit tee 223, Expans ive CemConcretes-Present State of Knowledge, ACI J OURNAL,P r o c e e d i n g s V. 6 7 , N o . 8 , Aug. 1970, pp. 583-610.

3.12. K l e i n S y m p o s i u m o n E x p a n s i v e C e m e n t C o n c r e t e s ,SP-38, American Concrete Institute, Detroit, 1224R-16 ACI COM

made with portland cements is usually more thaequate to provide the elastic restraint neeshrinkage-compensating concrete. To take fultage of the expansive potential of shrinkapensating concrete in minimizing or preventshrinkage cracking of unformed concrete suris important that positive and uninterruptecuring (wet covering or ponding) be started ld

heastes,

as

of

1964,

-

-

In-ge and

nt

the European approach to crack width evaland permissible crack widths.

Recently, fiber glass rods have been usedreinforcing material.4.4To date, experience is lim-ited, and crack control in structures reinforcefiber glass rods is not addressed in this reporexpected, however, that future committee ments will address crack control in structuresthis and other new systems as they come in

4 . 2 - C r a c k c o n t r o l e q u a t i o n s f o r r e i n f o r c e d c o n -c r e t e b e a m s

A number of equations have been proposed prediction of crack widths in flexural members; mosof them are reviewed in the previous commie re-port1.1Pand in key publications listed in the refe ences. Most equations predict the probablimum crack width, which usually means that 90 percent of the crack widths in the membbelow the calculated value. However, researshown that isolated cracks in beams in exctwice the width of the computed maximumsional

Depart-

hrink-

extensive review of cracking in reinforced costructures. Several of the most important cracdiction equations are reviewed in the previousmittee report. 1.1Additional work presented in thCEB-FIP Model Code for Concrete Structure gITTEE REPORT

ad-ed foradvan--com-

gces, itwatermedi-

satu-branesly uti-satingion tong dur-s andsating

t-

8, pp.

ter- Part 4s and

H.,

Chapter 4 - Control of cracking in flexuralmembers*4 . 1 - I n t r o d u c t i o n

With the regular use of high strength reinfsteel and the strength design approach finforced concrete, and higher allowable stresprestressed concrete design, the control of cmay be as important as the control of deflecflexural members. Internal cracking in concretstart at stress levels as low as 3000 psi (20.7 MPa) inthe reinforcement. Crack control is important mote the aesthetic appearance of structures, many structures, crack control plays an imrole in the control of corrosion by limiting the bilities for entry of moisture and salts whicgether with oxygen, can set the stage for co

This chapter is concerned primarily with ccaused by flexural and tensile stresses, but temature, shrinkage, shear and torsion may also cracking.4.1 Cracking in certain specialized sttures, such as reinforced concrete tanks, bisilos, is not covered in this report. For informon cracking concrete in these structures, seeRefer-ence 4.2 and ACI 313.

Extensive research studies on the crackinhavior of beams have been conducted over t50 years. Most of them are reported in ACIBibliography No. 9 on crack control.4.3 Others arereferenced in this chapter. Reference 4.1 contains an*Principal authors: Edward G. Nawy and Peter Gergely.

it

y

a

c

u

ir

f

g

to

is

t.s isslabs

re6 in.

value based

ck withith

ever,limitlabs.

ca-

Codes welled as

l.

usingeteCONTROL OF

sometimes occur,*-4 though generally the coefficof variation of crack width is about 40 percent.4-1Evidence also exists indicating that this racrack width randomness may increase with tof the member? Besides limiting the compumaximum crack width to a given value, the dshould estimate the percentage of cracks abvalue which can be tolerated.

Crack control equations recommended bACICommittee 224 and the Comite Euro-Internationaldu Beton (CEB) are presented below.4.21 A C I C o m m i t t e e 2 2 4 r e c o m m e n d a t i o n s - Re-quirements for crack control in beams and thone-way slabs in the ACI Building Code (ACI 318) arebased on the statistical analysis4-6 of maximumcrack width data from a number of sources. Bthe analysis, the following general conclusionreached:

1. The steel stress is the most important va2. The thickness of the concrete cover is an

tant variable, but not the only geometric cotion.

3. The area of concrete surrounding eainforcing bar is also an important geometriable.

4. The bar diameter is not a major variable5. The size of the bottom crack width is infl

by the amount of strain gradient from the lthe steel to the tension face of the beam.

The equations that were considered to bet prediet the most probable maximum bottom ancrack widths are:

W* =

w, =

whereW* =

w, =

fJ =A =

tb =t, =P =

h 1 =

0.091 v-a p (f, - 5) x 10-3 (4.la)

0.091 rt,, Al

-1-G. t,l&.. (f, - 5) x 1 0- 3 (4.lb)

most probable maximum crack width attom of beam, in.most probable maximum crack width aof reinforcement, in.reinforcing steel stress, ksiarea of concrete symmetric with reinfsteel divided by number of bars, in.2bottom cover to center of bar, in.side cover to center of bar, in.ratio of distance between neutral axtension face to distance between neutand centroid of reinforcing steel = 1.20 inbeamsdistance from neutral axis to the reinsteel, in.

Simplification of Eq. (4.la) yielded the followinequationw = 0.076~fs ~AX D3 (4.2)sd side

bot-

t level

orcing

s andal axis

orcing

control values, its application to one-way slabsstandard 3/4 in. (19 mm) cover and reinforced wsteel of 60 ksi (414 MPa) or lower yield strengthresults in large reinforcement spacings. Howthe provisions of Code Section 7.6.5 indirectly the spacing of such reinforcement in one-way s

AC1 340.1R contains design aids for the applition of Eq. (4.2a).

4.2.2 CEB recommendations - Crack control recom-mendations proposed in the European Model for Concrete Structures apply to prestressed aas reinforced concrete and can be summarizfollows:

The mean crack width, wm in beams is expressedin terms of the mean crack spacing, s

rm such that

Kn = L&n

where

and represents the average strain in the stee

(4.4)

(4.5)

f s f II =

steel stress at the cracksteel stress at the crack due to forces cacracking at the tensile strength of concrCRACKING 224R-17

ent

nge inhe sizeedesignerove this

ick

sed ons were

riable. impor-nsidera-

h re-c vari-

.enced

evel of

whereW = most probable maximum crack width, in.dc = thickness of cover from tension fiber

center of bar closest thereto, in.

When the strain, Ed, in the steel reinforcement used instead of stress, f,, Eq. (4.2) becomes

w = 2.2 p L, V-JX (4.3)

E, = strain in the reinforcement

Eq. (4.3) is valid in any system of measuremenThe cracking behavior in thick one-way slab

similar to that in shallow beams. For one-way having a clear concrete cover in excess of 1 in. (25.4mm), Eq. (4.2) can be adequately applied if p = 1.25to 1.35 is used.

AC1 318 Section 10.6 uses Eq. (4.2) with p = 1.2 inthe following form

2 = f,cQi- (4.2a)

Using the specified cover in AC1 318, maximiumallowable z = 175 kips per in. for interior exposucorresponds to a limiting crack width of 0.01(0.41 mm).

The Code allows a value of z = 145 kips per in.for exterior exposure based on a crack width of 0.013 in., (0.33 mm), which may be excessiveon Table 4.1. While application of Eq.(10.4) of AC1 318-771 to beams gives adequate craK = bond coefficient, 1.0 for ribbed bars, reflectinginfluence of load repetitions and load duration

di

p

a

l

tio

een

el, orth

ection, in.n

per-

theon fore

ured near-

ection

aused

of re-

of flat

r

rackncretented asss. The224~018 ACI COMMIT

The mean crack spacing is

S rm (4.6)

where

c =S

x2 =

x3 =

QR =

At

=

clear concrete coverbar spacing, limited to 15d,0.4 for ribbed barsdepends on the shape of the stress 0.125 for bendingA, /A,effective area in tension, depending rangement of bars and type of exforces; it is limited by a line c + 7d, from thetension face for beams; in the case of not more than halfway to the neutral ax

A simplified formula canbe derived for the meancrack width in beams with ribbed bars,

fw, = 0 . 7 _-

d3c + 0.05 -!

E S QR( 4 . 7 )

A characteristic value of the crack wpresumably equivalent to the probable maxivalue, is given as 1.7~~.

4 . 3 - Crack control i n two-way slab s and p l a t e sCrack control equations for beams underethe crack widths developed in two-way slaplates4.7 and do not tell the designer how to sthe reinforcement. The cracking mechanism two-way slabs and plates is controlled primarilysteel stress level and the spacing of tinforcement in the two perpendicular directaddition, the clear concrete cover in two-wand plates is nearly constant [3/4 in. (19 mm) for intrior exposure], whereas it is a major variabcrack control equations for beams.

Analysis of data in the only major work oning in two-way slabs and plates4s7 has provided thfollowing equation for predicting the maxcrack width:

&,sI:w=ws ( 4 . 8 )n

where the radical rl = db,s21et, is termed the gridindex, and can be transformed into

]k = fracture coefficient, having a value k = 2.8 xlO-5 for uniformly loaded restrained two-waiagram,

on ar-ternal

slabs,s

idth,mum

stimatebs andacein by thehe re-ions. Iny slabs

e-e in the

crack-eimum

f =s

db1 =

s1 =

s2 =

46 "1 =

Q rl =

=

w =

actual average service load stress lev40 percent of the design yield strengfy,ksidiameter of the reinforcement in dir1 closest to the concrete outer fibersspacing of the reinforcement in directiol,in.spacing of the reinforcement in pendicular direction 2, in.direction of reinforcement closest toouter concrete fibers; this is the directiwhich crack control check is to be madactive steel ratioArea of steel A, per ft width_ - V - - P - - - -

12 (dbt + 2CJ

where Cl is clear concrete cover measfrom the tensile face of concrete to theest edge of the reinforcing bar in dirb& VW1crack width at face of concrete, in., cby flexural load

Subscripts 1 and 2 pertain to the directionsinforcement.

For simply supported slabs, the value of k shouldbe multiplied by 1.5. Interpolated k values apply forpartial restraint at the boundaries. For zonesplates where transverse steel is not used or when itsspacing s2 exceeds 12 in., use s2 = 12 in. in theequation.

If strain is used instead of stress, Eq. (4.8)becomes

(4.9)

where values of the kl = 29 x 100~ times the kvalues previously listed.

References 4.8 and 340.1R contain design aids fothe application of these recommendations.

4.4 - Tolerable crack widths versus exposure condi-tions in reinforced concrete

Table 4.1 is a general guide for tolerable cwidths at the tensile face of reinforced costructures for typical conditions and is presean aid to be used during the design procetable is based primarily on Reference 4.9. It is im-P =

action square slabs and plates. For concen-trated loads or reactions, or when the raof short to long span is less than 0.75 butlarger than 0.5, a value of k = 2.1 x 1O-5 isapplicable. For span aspect ratios 0.5, k =1.6 x 1O-s(as defined in Section 4.2.1) 1.25 (chosen tosimplify calculations though varies betw1.20 and 1.35)TEE REPORTy portant to note that these values of crack width are

Fia

e

bs

t

s

s

e

nces in

lexitympres-e steel meth-eth-These com-a, cov-ludes

n foressed

fromuations

bonded mem-used to levels.rs areioned

eressedrea of

etween

, andon the

ncho- due tooncen-inof the must

crackse) ande, andof the

takee anal-le-ns forever,

highern-members.

4 . 5 . 1 C r a c k p r e d i c t i o n e q u a t i o n s - One approach tcrack prediction, wh ich re la tes i t to the non-prestressed case, has two steps. First the decpression moment is calculated, at which the the tension face is zero. Then the member isas a reinforced concrete member and the incstress in the steel is calculated for the adloading. The expressions given for crack prin nonprestressed beams may be used to the cracks for the load increase above the pression moment. A multiplication factor of ab1.5 is needed when strands, rather than dCONTROL O

TABLE 4.1 - Tolerable crack widths,reinforced concrete

Exposure conditionTolerable

crack width, in. (mm)

Dry air or protective membraneHumidity, moist air, soilDeicing chemicalsSeawater and seawater spray:

wetting and dryingWater retaining structures*

0.016 (0.41)0.012 (0.30)0.007 (0.18)

0.006 (0.15)0.004 (0.10)

*Excluding nonpressure pipes

not always a reliable indication of the corrosdeterioration to be expected. In particular, cover, even if it leads to a larger surfacewidth, may sometimes b e preferable for corrosicontrol in certain environments. Thus, the dmust exercise engineering judgment on the crack control to be used. When used in conwith the recommendations presented in Sections4.2.1 and 4.2.3 to limit crack width, it should pected that a portion of the cracks in the will exceed these values by a significant amo

4 . 5 - Flexural cracking in prestressed concretePartially prestressed members, in which

may appear under working loads, are usedsively. Cracks form in these members when sile stress exceeds the modulus of ruptureconcrete (Sfl to 90 under short-term conditioThe control of these cracks is necessary maesthetic reasons. The residual crack width, amoval of the major portion of the live load, i[about 0.001 in. to 0.003 in. (0.03 to 0.08 mtherefore, crack control is usually not necethe live load is transitory.

The prediction of crack widths in prestressecrete members has received far less attentin reinforced concrete members. The availaperimental data are limited and, at the samthe number of variables is greater in prebars, are used nearest to the beam surfac CRACKING 224R-19

on and larger

crackonesignerxtent of

junction

e ex-tructureunt.

cracks exten-he ten- of thens).inly forfter re- small

m)] andssary if

d con-ion thanble ex-e time,tressed

o

om-stress at treatedrease inditionaldiction

estimatedecom-

outeformed

prestressed member to account for the differebond properties.

The difficulty with this approach is the compof calculations. The determination of the decosion moment and, especially, the stress in this complicated and unreliable unless elaborateods are used.4.10 For this reason, approximate mods for crack width prediction are attractive. are not much less accurate than the moreplicated methods, and the lack of sufficient datering large variations in the variables, precfurther refinements at this date.

The CEB Model Code has the same equatiothe prediction of the crack width in prestrmembers as in nonprestressed members (see Section4.2.2). The increase in steel strain is calculatedthe decompression stage. Several other eqhave been proposed.4.11-4.0

Limited evidence seems to indicate that unmembers develop larger cracks than bondedbers. Nonprestressed deformed bars may be reduce the width of the cracks to acceptableThe cracks in bonded post-tensioned membenot much different from cracks in pretensbeams.

4 . 5 . 2 A l l o w a b l e c r a c k w i d t h s - Some authors statthat corrosion is a greater problem in prestconcrete members because of the smaller asteel used. However, recent research results4. indi-cate that there is no general relationship bcracking and corrosion in most circumstances. Fur-

thermore cracks close upon removal of the loadthe use of crack width limits should depend fluctuation and magnitude of the live load.

4 . 6 - Anchorage zone cracking in prestressed con-crete

Longitudinal cracks frequently occur in the arage zones of prestressed concrete memberstransverse tensile stresses set up by the ctrated forces.4.22T 4.23 Such cracks may lead to (or certain cases are equivalent to) the failure member. Transverse reinforcement (stirrups)be designed to restrict these cracks.

Two types of cracks may develop: spalling which begin at the end face (loaded surfacpropagate parallel to the prestressing forcbursting cracks which develop along the line force or forces, but away from the end face.

For many years stirrups were designed tothe entire calculated tensile force based on thysis of the uncracked section. Classical and finite-ement analyses show similar stress distributiowhich the stirrups are to be provided. Howsince experimental evidence shows that stresses can result.4.23 than indicated by these ae in thealyses, and the consequences of under-reinforcement

ee

achpropagate parallel to the prestressing formay cause gradual failure, especially when tacts near and parallel to a free edge. Since i

dshow that the spalling stresses in an uncrackedmember are confined to near the end face, portant to place the first stirrup near the eface, and to distribute the stirrups over a

e

e

,

4.6. Gergely, Peter, and Lutz, Leroy A., MaximumCrack Width in Reinforced Concrete Flexural Members,1969, pp. 457-462.4.20. Nawy, E. G., and Huang, P. T., Crack and

Deflection Control of Pretensioned Prestressed Beams,Journal, Prestressed Concrete Institute, V. 22, No. 3, 1977,Concrete Beams with Limited Prestress, BuildingScience, V. 8, No. 2, June 1973, pp. 179-185.

4.19. Stevens, R. F., Tests on Prestressed ReinforcedConcrete Beams, Concrete (London), V. 3, No. 11, Nov.equal to at least the depth of the member tocount for both spalling and bursting stressecast blocks with helica