Special Report

Cracks and Crack Controlin Concrete Structures

Fritz LeonhardtProfessor EmeritusDr.-Ing. Dr.-Ing. h.c. mull.Consulting EngineerStuttgart, FRG

T he material presented in this paper isbased on more than 30 years of re-

search, observations and experienceconcerning causes, control, and conse-quences of cracking in concrete struc-tures. This extensive background washelpful in the preparation of this paperwhich deals with questions of concretecracking.

The presence of cracking does notnecessarily indicate deficiency instrength or serviceability of concretestructures. While currently available de-sign code provisions lead to reasonablecontrol of cracking, additional controlcan be achieved by understanding thebasic causes and mechanisms of crack-

Note: This paper is a revised and updated version ofan article originally published in the Proceedings ofthe International Association for Bridge and Struc-tural Engineering (1ABSE), Zurich, Switzerland,1987, p. 109.

ing in concrete structures. In this paper,causes of concrete cracking are dis-cussed, including tensile strength ofconcrete, temperature, shrinkage andcreep effects. Recommended crackwidths are presented along with designmethods for sizing reinforcement tocontrol crack widths.

CAUSES OF CRACKINGConcrete can crack due to a number of

causes. Some of the most significantcauses are discussed in detail.

Tensile Strength of ConcreteThe tensile strength of concrete is a

widely scattering quantity. Cracking oc-curs when tensile stresses exceed thetensile strength of concrete. Therefore,to control concrete cracking, the tensilestrength of concrete is of primary im-

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portance. Laboratory test data con-ducted by H. Busch were analyzedstatistically. As presented in Ref. 1, thisanalysis furnished the following re-lationships for the mean direct tensilestrength, f tm , related to the 28-daycompressive cylinder strength f,' of con-crete:

fcm = 2.1 (fc)z /3 (psi)

fi'm = 0.34 (ff)2"'(N/mm2)

The statistical analysis indicated thatthe coefficient in this equation can bemodified to 1.4 (0.22) and 2.7 (0.45) toobtain the 5 and the 95 percentiles, re-spectively, of the tensile strength, fI.The tensile strength of concrete isslightly higher in flexure. However, it isrecommended that values for direct ten-sion be used in practice. Concretecracks when the tensile strain, € °t , ex-ceeds 0.010 to 0.012 percent. Thislimiting tensile strain is essentially in-dependent of concrete strength.

The 5 percentile of the tensilestrength, f, should be used in design tolocate areas in the structure that arelikely to crack by comparing calculatedstresses with the expected concretestrength. The 95 percentile, f 5 , shouldbe used to obtain conservative values forrestraint forces that might occur beforethe concrete cracks. These restraintforces are used to calculate the amountof reinforcement needed for crack widthcontrol.

Causes of Cracking DuringConcrete Hardening

Concrete cracking can develop duringthe first days after placing and beforeany loads are applied to the structure.Stresses develop due to differentialtemperatures within the concrete.Cracking occurs when these stresses ex-ceed the developing tensile strength, f;,of the concrete as indicated in Figs. 1and 2. Differential temperatures aremainly due to the heat of hydration of

SynopsisSimple design rules are presented

to control cracking in concrete struc-tures. Causes of cracking and its ef-fect on serviceability and durability arediscussed. The paper is primarily ap-plicable to large structures such asbridges. However, general conceptspresented are applicable to any con-crete structure. Prestressing forcesare considered. A numerical exampleshowing application of the methodand use of simple design charts is in-cluded.

cement during concrete hardening. Thiseffect is usually neglected except inmassive structures as indicated in Ref. 2.However, depending on cement contentand type of cement, the temperaturewithin concrete members with dimen-sions of 12 to 36 in. (30 to 91 cm) canincrease approximately 36°F to 108°F(20°C to 60°C) during the first 2 daysafter casting.

If concrete members are allowed tocool quickly, tensile stresses may reachvalues higher than the developing ten-sile strength of the concrete. Even if thisprocess results only in microcracking,the effective tensile strength of thehardened concrete is reduced. How-ever, very often wide cracks appeareven when reinforcement is provided.In addition, the reinforcement may notbe fully effective since bond strength isalso developing and is yet too low. It isnecessary to minimize such early cracksby keeping temperature differentialswithin the concrete as low as possible.This can be done by one or more of thefollowing measures:

1. Choice of cement — A cement withlow initial heat of hydration should beselected. Table 1 shows that there is asignificant variation in heat develop-

PCI JOURNAUJuly-August 1988 125

b concrete

compression

GT+ +G = OT a T Ec

tension

Internal stressesin equilibrium

Fig. 1. Temperature distribution due to heat of hydration andinternal stresses caused by outside cooling in a free standingconcrete block.

ment among different types of cements.The cement content of concrete shouldbe kept as low as possible by goodgrading of the aggregates. Heat de-velopment can also be reduced by ad-ding fly ash or using slag furnace ce-ment.

2. Curing — Evaporation of watermust be prevented by using curingcompounds or by covering the concretewith a membrane. Rapid evaporationcan lead to plastic shrinkage cracking.

3. Curing by thermal insulation -Rapid cooling of the surface must beprevented. The degree of thermal insu-lation depends not only on the climate,but also on the thickness of the concretemember and on the type of cement used.Spraying cold water on warm young

concrete, as it was done years ago, is notrecommended.

4. Precooling — This is a necessity forlarge massive concrete structures suchas dams. For more usual structures, inwhich shortening after cooling can takeplace without creating significant re-straint forces, precooling is expensiveand unnecessary. In this case, thermalinsulation is preferable and it also hasthe benefit of accelerating concretestrength development. An exceptionmay be made in very hot climates sinceprecooling can keep concrete workablefor a longer period of time.

Often shrinkage is considered as acause of early cracking. However, this isnot true under normal climatic condi-tions. Shrinkage needs time to produce a

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Table 1: Heat of hydration of various types ofcements.*

Type ofcementt

Heat of hydration (Btu/1b)

1 day 3 days 7 days 28 days

I 92 144 157 167

II 76 115 135 148

III 139 184 194 205

IV 50 81 94 117

V 58 88 101 124

*Data obtained from Concrete Manual, U.S. Bureau ofReclamation, 1975, pp. 45-46.t Federal Specifications SS-C-192G, including InterimAmendment 2, classified the live types according to usage asfollows: Type I for use in general concrete construction whenTypes 11, 111, 1V, and V are not required; Type 11 for use inconstruction exposed to moderate sulfate attack; Type III for usewhen high early strength is required; Type IV for use when lowheat of hydration is required; and Type V for use when high sulfateresistance is required.Note: 1.0 Btu/Ib = 2.32 J/g.

shortening as high as the tensile rupturestrain. Only in very hot and dry airshrinkage can cause early cracks inyoung concrete, if measures againstevaporation are not applied.

Causes of Cracking AfterConcrete Hardening

Tensile stresses due to dead and liveloads cause cracking. Normal rein-

cracking due to restraint

tensile strength fit

Internal Stress

5 10 15 20 h

Concrete hardening time, hours

Fig. 2. Development of the tensile strength and stresses due to nonlineartemperature distribution within the concrete.

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Deformed Shape considering Upper Faceof Beam Warmer Than Bottom Face andassuming beam freed from interior Supports^

I I I

I MDTMoment Diagram

VAT

Shear Diagram

Fig. 3. Forces in a concrete beam due to a temperature rise OT atthe upper face of the beam and external restraint provided byinterior supports.

forcement or prestressing should be de-signed to provide required strength andkeep crack widths within permissiblelimits. Tensile stresses due to serviceloads can be controlled by prestressing.The degree of prestressing can be cho-sen based on structural or economicconsiderations. Normally, partial pre-stressing leads to better serviceabilitythan full prestressing.

Cracks can also be initiated by ten-sile stresses due to restrained defor-mations from temperature variations orfrom shrinkage and creep of concrete.Imposed deformations such as differ-ential settlement between foundationscan also cause cracks.

There are two types of restraint whichcause stress in concrete members,namely, internal restraint as shown inFig. 1, and external restraint in indeter-minate structures, as shown in Fig. 3.Restrained deformations caused crack-ing in concrete bridges and it wasprimarily due to temperature differ-ences produced by heating under thesun and cooling during the night. Ex-

treme temperatures that occur at 20 to50-year intervals must be considered. Asindicated in Refs. 3, 4, 5 and 6, temper-atures in bridge structures were mea-sured in several countries. Recently, theU.S. Transportation Research Boardpublished in Ref. 7 temperature data forbridge design.

Temperature differentials should beconsidered along with recommendedmean temperatures, Tm, used for cal-culating maximum and minimumchanges in the lengths of structuralmembers. In Central Europe values forT. are specified for concrete bridges asvarying from +68°F to –22° (+20°C to–30°C).

The temperature distribution over abeam cross section can be subdividedinto three parts as shown in Fig. 4. Theconstant part, 0 T,, causes axial forces ifoverall length changes are restrained.The linear part, AT,, causes restraintforces, M AT and V AT, in indeterminatestructures as shown in Fig. 3 for a threespan continuous beam. The nonlinearpart, AT3i causes stresses, which are in

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Table 2. Recommended cross section temperaturedifferentials for bridge design in Europe.

Box girder T-beamsType ofcross section Mari- Conti- Mari- Conti-and exposure time nental time nental

Top ofcross sectionwarmer thanbottom (°F) 18 27 14.4 21.6

Bottom ofcross sectionwarmer thantop(F) 9 14.4 7.2 10.8

Note: 1.0 A N' _ (9/5) A°C.

equilibrium over the cross section andproduce no action forces. Thesestresses, which also exist in staticallydeterminate structures, can be calcu-lated by imposing equilibrium condi-tions and considering that:

JcT = AT3aTEc

where a T is equal to 6 x 10 -6 /0 F(10-5/° C), the coefficient of thermal ex-

pansion for concrete. Cooling causestensile stresses in areas near extremitiesof the section.

For bridges in Europe, the AT valuesgiven in Table 2 are recommended. Inaddition to temperature, restrained con-crete creep and shrinkage can causestresses. Shrinkage often leads to cracksbetween connected members of signifi-cantly different sizes. Stress due to re-strained creep and shrinkage can be cal-

rig. 4. uivision of temperature aiagram into its constant, unear ana noniinear parts.

PCI JOURNAL/July-August 1988 129

plan A-A

i i h i i

H

G

compressive Gdue to DL+w LL+ P

'—_–'-- cracks due toAT, AS and ACr

Fig. 5. Transverse cracks in thin bottom slab of box girder due todifferential temperature, creep and shrinkage despite prestressing.

culated in the same way as stresses dueto temperature.

Transverse cracks due to temperature,creep and shrinkage effects are fre-quently found in the relatively thinbottom slabs of box girders despite thefact that calculations show considerablelongitudinal compressive stresses due toprestressing. Compressive stresses tendto shift towards the thick webs whichundergo less creep and shrinkage strainsas illustrated in Fig. 5.

Box sections are indeterminate struc-tures. Therefore, restraint moments aredeveloped when the section is heatedon one side by the sun. This leads tovertical cracking in bridge piers andtower shafts as shown in Fig. 6. Ref. 8shows examples of temperature cracksin prestressed concrete structures.

Determination of AreasLikely to Crack

Cracking occurs whenever the princi-pal stresses due to service loads or dueto restraint forces or due to a combina-tion of service loads and restraints ex-ceed the tensile strength of concrete.These stresses can be calculated using

the linear theory of elasticity, consider-ing the structure initially uncracked. Inthese calculations, f,s should be taken asthe tensile strength of the concrete. Inthe tension side of a beam, cracking willoccur in areas where bending momentsdue to service loads and restraint causestresses in the extreme tensile fiberabove f15 . As bending increases, thedepth of cracking can be calculated byconsidering a maximum concrete tensilestrain of 0.015 percent as shown in Fig.7.

Calculation of possible maximumbending moments due to restraintshould be based on f 5 . As shown in Fig.8, consideration of such moments in-creases the areas in which cracking maybe expected to occur.

Bending moments due to restraintdefine only the location and quantity ofreinforcement or prestressing necessaryto limit the crack width for serviceabilitypurposes. As proven long ago byPriestley, and illustrated in Fig. 9,these moments do not decrease the ul-timate strength of the structure becausethey are reduced and finally disappeardue to cracking and plastic deformationas service loads are increased until the

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deflection line

vertical cracks

-MAT

II

+ +MOT

+ MAT

Fig. 6. Bridge pier cross section and moments dueto temperature rise on one side of the pier.

-EGXII

-O,015°/.cracked

Zone of web

rLE 7,5db+ill

flange Zone S

Fig. 7. Cracked zones in webs of beams under combined moment dueto dead load, live load and restraint.

limit state is reached. However, thestructure must be checked for possiblebrittle failure of the compression zone ifa relatively high degree of prestressingis used, especially for continuous T-beains. Therefore, to satisfy strength re-quirements, bending moments due torestraint should not be added to mo-

ments due to service loads in sizing ofmain reinforcement. It must, however,be observed that restraint due to pre-stressing does not decrease on the wayup to limit state.

Restraint forces decrease beginningwith the first crack since the stiffness ofthe structure is progressively reduced

PCI JOURNAL/July-August 1988 131

Fig. 8. Increased cracked area due to restraint moment.

with each crack that occurs. Steelstresses due to restraint are highestwhen the first crack occurs and decreasewith each further crack. This tends to re-duce crack widths. Fig. 9 shows the effecton moment due to reduction of restraint.

Evaluation of CracksAs indicated in Fig. 10, crack widths

are greater at the surface and decreasetowards the reinforcement. Long yearsof research reported in Refs. 9 and 10,and experience indicate that crack

service loads ultimate lim. stateM due to load and

restraint forces brittle failureby too high prestress

1,75MDL+LL ductile failure

MAT 1,75 MDL

M DL+ LL effect of AT effect of 1,5T

MDL

0 Curvature 4 D CurvatureOT OT

Fig. 9. Illustration of reduction of restraint forces as the limit state is approached.

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Ag. 10. Crack width at the surface is used as a measure ofthe effect of cracking on concrete members.

Table 3. Allowable crack widths.

Ambientcondition of w90t Maximum w Crackexposuret (in.) permitted (in.) appearance

Mild 0.012 0.020 Easilyvisible

Moderate 0.008 0.016 Difficult to seewith the naked

Severe 0.004 0.0012 eye

* w90 denotes the 90 percentile of the crack width, w.t Defined as indicated in the CEB-FIP Model Code:Mild exposure— The interiors of buildings for normal habitation or offices.— Conditions where a high level of relative humidity is reached

for a short period only in any one year (for example 60 percentrelative humidity for less than 3 months per year).

Moderate exposure— The interior of buildings where the humidity is high and

where there is a risk for the temporary presence of corrosivevapors.

— Running water.— Inclement weather in rural or urban atmospheric conditions,

without heavy condensation of aggressive gases.— Ordinary soils.Severe exposure— Liquids containing slight amounts of acids, saline or strongly

oxygenated waters.— Corrosive gases or particularly corrosive soils.— Corrosive industrial or maritime atmospheric conditions.

Note: 1 in. = 2.54 cm.

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