ACI Structural Journal/September-October 2006 747

ACI Structural Journal, V. 103, No. 5, September-October 2006.MS No. 03-398 received March 26, 2006, and reviewed under Institute publication

policies. Copyright © 2006, American Concrete Institute. All rights reserved, includingthe making of copies unless permission is obtained from the copyright proprietors.Pertinent discussion including author’s closure, if any, will be published in the July-August 2007 ACI Structural Journal if the discussion is received by March 1, 2007.

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

Interfacial bond stress-slip between the concrete and longitudinalreinforcement always occurs in reinforced concrete (RC) members.For strength design purposes, the effect of interfacial bond stress-slip does not have a significant effect on the overall strength of theRC members with adequate reinforcement development length. Theresults in a companion paper, however, showed that the directapplication of the Modified Compression Field Theory (MCFT) ledto an overestimation of the post-cracking stiffness of the RC bentcap members. This may be attributed to the inadequate representationof bond-slip using tension-stiffening in MCFT. Constitutive modelsfor bond-slip between the concrete and reinforcement available inthe literature are normally applied to RC members where flexuraldeformations are dominant, but these may not be applicable toshear-dominated RC members. A parametric study on the effect ofinterfacial bond-slip modeling in shear-dominated RC members ispresented. Results from the analytical investigation are comparedwith experimental results on RC bent caps. Based on this parametricstudy, a new bond-slip model is proposed for RC members prone toshear deformations with lumped longitudinal reinforcement.

Keywords: concrete; longitudinal reinforcement; shear.

INTRODUCTIONThe behavior of shear-dominated reinforced concrete (RC)

members is different from the conventional RC memberswhere flexural deformations normally control the overallresponse. One of the differences between flexural and shear-dominated RC members is in distribution of the reinforcementstresses. In flexural members, the stress in reinforcementdepends directly upon the bending moment at that particularcross section and the assumption that plane sections remainplane. In shear-dominated RC members, however, the stressdistribution may be nonlinear. Ferguson (1964) performedan experimental program on RC cantilever bent caps withshort shear span-to-depth ratios similar to that shown in Fig. 1.Because of the experimental setup, at the point of loadapplication, the bending moment diagram varies linearlyfrom zero to the maximum value at the centerline of column.If the shear span-to-depth ratio is high, that is, if the memberdeformations are controlled by flexural action, the recordedstress or strain at the loading point should be negligible at allstages of loading. However, Ferguson (1964) indicated formembers with short shear span-to-depth ratios that a consid-erable amount of reinforcement strain at the loading pointdevelops at higher load levels. This high magnitude of stressat the point of zero bending moment was attributed to theeffect of interfacial bond stress-slip between the main flex-ural reinforcement and the surrounding concrete. Ferguson(1964) also performed an experimental investigation on theeffect of the embedment length of main longitudinal rein-forcement extending beyond the center of the applied loadlocation and concluded that an embedment length exceeding

381 mm could eliminate the concern for bond-slip failure atthe cantilevered end of the cap.

In a companion paper, Powanusorn and Bracci (2006)presented an analytical investigation on the effect ofconfinement due to transverse reinforcement on bothstrength and deformation of RC bent caps specimens byincorporating the effect of confinement into the ModifiedCompression Field Theory (MCFT) (Vecchio and Collins1986). Although excellent results were obtained forpredicting the strength, the proposed analytical model over-estimated the post-cracking stiffness of the bent cap specimens.Parametric studies showed that the overestimation was notcaused by changes in the constitutive relationship forconcrete that incorporated the effect of confinement. In fact,

Title no. 103-S77

Behavior of Reinforced Concrete Members Prone to Shear Deformations: Part II—Effect of Interfacial Bond Stress-Slipby Suraphong Powanusorn and Joseph M. Bracci

Fig. 1—Behavior of reinforced concrete bent caps withsmall shear span ratios.

ACI Structural Journal/September-October 2006748

the effect of confinement was only mobilized at higher levelsof load as the analytical predictions on the load-displacementdiagrams were virtually the same before the first reinforcementyielding for models with and without confinement. The effectof the base curves for the confined and unconfined concretestress-strain relationships in compression (Mander et al. 1988)model and Hognestad parabola (Vecchio and Collins 1982)respectively, on the predicted load-deformation was alsonegligible.

Despite the large number of parameters affecting theconstitutive model of RC elements, two likely sources ofdiscrepancies that led to an underestimation of the RC bentcap deformations were identified: (1) shrinkage of the concrete;and (2) interfacial bond slip between the concrete andreinforcing steel. Parametric studies (Powanusorn and Bracci2003), using the ACI 209-78 model (Bažant and Wittmann1982), on the effect of shrinkage showed that uniformmember shrinkage caused a reduction in the predictedcracking strength of the RC bent cap members and a slightshift to the right of the predicted the predicted load-deformationbehavior, which improved the correlation of the simulatedresponse to the experimental results as shown in Fig. 2. Theincorporation of concrete shrinkage, as expected, had negligibleinfluence on the ultimate strength, as predicted strengths ofa RC bent cap member with and without shrinkage were

virtually identical. Although the simulated response includinguniform shrinkage better correlated with the experimentalresults, the slope of the predicted post-cracking load-deformation curve remained unchanged, regardless of themagnitude of shrinkage strains used in the parametricstudies. Therefore, it was concluded that the effect ofshrinkage was not the real physical reason behind the too stiffpost-cracking response of the proposed constitutive relationship.

Under the context of the MCFT, the effect of crackingin RC members in the principal tensile direction ishandled by decreasing the tensile stress according to theconstitutive relationship of concrete in tension. It wasexperimentally determined, however, that the post-peaktensile stress-strain relationship of concrete in RC membersis generally much higher than that of unreinforced concrete(Hordijk 1991; Vecchio and Collins 1982). This effect iscalled tension-stiffening, which is generally acknowledged tobe attributed to the interfacial bond stress between theconcrete and reinforcing steel. Therefore, it can be concludedthat the effect of interfacial bond stress-slip is implicitlytaken into account by a tension-stiffening model (Rots1988). For RC members with well-distributed reinforcement,the average post-cracking tensile stress-strain behavior ofconcrete can be modeled as follows (Collins and Mitchell 1987)

(1)

where σt and εt are the concrete stress and strain in tension;εcr is the concrete cracking strain associated with thecracking stress, fcr (fcr is assumed to be equal to 0.33 ,where f ′c is the uniaxial compressive strength of concrete at28 days). For RC members such as bent caps with concentratedlongitudinal reinforcement, however, the effect of local

σtfcr

1 500εt+-------------------------- εt εcr>,=

f ′c

Suraphong Powanusorn is a Structural Engineer with Thai Nippon Steel Engineeringand Construction Co. Ltd. in Chachuengsao, Thailand. He received his PhD in civilengineering from Texas A&M University, College Station, Tex.; his MS in civilengineering from the University of New South Wales, Australia; and his BS fromChulalongkorn University, Bangkok, Thailand.

Joseph M. Bracci is a Professor and Head of the Construction, Geotechnical, andStructural Engineering Division in the Zachry Department of Civil Engineering atTexas A&M University. He received his PhD from the State University of New York atBuffalo, Buffalo, N.Y. His research interests include experimental testing, analyticalmodeling, and performance-based design of structures.

Fig. 2—Parametric study on effect of shrinkage.

ACI Structural Journal/September-October 2006 749

bond-slip can pose difficulties such that the averageapproach used by tension-stiffening may cause large errorsin numerical simulations (Rots 1988).

RESEARCH SIGNIFICANCEThe results in a companion paper (Powanusorn and Bracci

2006) showed that the direct application of the MCFT led toan overestimation of the post-cracking stiffness of the RCbent cap members. This paper shows that the overestimationis caused by the use of tension stiffening to implicitly takeinto account the interfacial slip between the concrete andreinforcement. Although the use of bond-slip constitutivemodels proposed in the available literature leads to animprovement on the load-deformation behavior, the post-cracking stiffness of the RC bent cap specimens remainssomewhat overestimated. Based on a parametric study bycurve-fitting the overall response from 16 bent cap testspecimens, a new bond-slip relationship is proposed formembers with lumped reinforcement and that are prone toshear deformations (small shear span-depth ratios).

FEM MODEL FOR REINFORCED CONCRETE BENT CAPS USING EXPLICIT BOND-SLIP MODEL

To justify the proposition by Rots (1988), parametric studieson the effect of interfacial bond-slip were performed in thiswork. In this approach, the effect of bond-slip was modeledexplicitly through the use of nonlinear spring elements usingthe program ABAQUS©. Early research on finite elementmethod (FEM) modeling of RC members by Ngo and Scordelis(1967) adopted the same approach to take into account theeffect of slip between the concrete and reinforcing steel. Inessence, this method separates the concrete and reinforcingsteel elements through the use of different nodes, eventhough the nodes may share the same geometric locations at theinterfacial zone. Fictitious spring elements were then assignedto simulate the effect of interfacial normal contact andtangential slip as shown in Fig. 3. The stiffness normal to theinterface represents the dowel action between concrete andreinforcing steel (Rots 1988), while the stiffness parallel tothe interface represents the interfacial slip.

In general, both the normal and tangential stiffness of thespring element should be correctly identified. The effect ofthe dowel action between the concrete and reinforcing steel,however, is complicated and highly variable. Pruijssers (1988)indicated that experimental results on the effect of dowelaction is relatively scattered and can vary by several ordersof magnitude. Research in the past on FEM modeling of theinterfacial bond-slip effect on the overall performance of RCmembers usually assumed that the stiffness in the directionnormal to the slip interface was perfectly rigid (Rots 1988).This assumption was also used in this research. Therefore,only the effect of tangential slip was considered in theexplicit bond-slip models in this work.

The mechanical properties of the spring elements are crucialto simulate the slip between the concrete and reinforcementinterface. Eligehausen et al. (1983) conducted an experimentalprogram to determine a constitutive model for interfacial slipbetween the concrete and reinforcement. They concludedthat the bond stress-slip under monotonic loading dependson several factors such as bar diameters, type and rib areaof deformed bars adopted, concrete strength, restrainingreinforcement, confinement, loading rate, and positions ofbars during casting. These results served as the basis for themodeling of the concrete-reinforcement interface and were

adopted in the CEB-FIP “Model Code” (1990) for bond-slipmodeling as follows

(2)

where τ is the calculated bond stress (MPa); s is the interfacialslip between the concrete and reinforcement (mm); τmax isthe maximum bond stress = 2.5 (Mpa); τf is the bondstress at failure = 0.4τmax (MPa); s1, s2, s3 are constants = 1.0,3.0, and 10.5 mm, respectively. Figure 4 shows the bondstress-interfacial slip model proposed by the CEB-FIBmodel code (1990).

Shima et al. (1987) performed experimental studies onbond between reinforcing steel and concrete. They concludedthat the bond stress-slip relationship generally depends onthe boundary conditions and should not be regarded as aunique material property. However, when the effect of strainin the reinforcement is additionally incorporated to form a bondstress as a function of the slip and strain in the reinforcement,a unique relation was found and can be treated as a materialproperty. The bond stress-slip-strain relationship proposedby Shima et al. (1987) is

(3)

τ τmaxss1

----⎝ ⎠⎛ ⎞ 0.4

s s1<,=

τmax s1 s s2< <,=

τmaxτmax τf–( )s3 s2–( )

------------------------- s s2–( ) s2 s s3< <,–=

τf s s3>,=

f ′c

τ0.73 1 5S+( )ln( )3

f ′c

1 105ε+--------------------------------------------------=

Fig. 3—Interface modeling with spring element.

Fig. 4—Interfacial bond-slip model (CEB-FIP 1990).

750 ACI Structural Journal/September-October 2006

can also occur between the concrete and this skin reinforcement.However, the amount of skin reinforcement is relativelysmall and the slip between the concrete and skin reinforcementshould not significantly affect the overall load-deformationresponse. Therefore, the skin reinforcement was neglected inthis work.

The FEM mesh, applied loading, and boundary conditionsof the RC bent cap model are shown in Fig. 1 and 6. In theimplicit bond model, the post-cracking stress-strain relationshipof concrete in the longitudinal reinforcement region, asshown in Fig. 6(a), is modeled using Eq. (1).

Three major changes were made for the explicit bondmodel: (1) change of the node numbering system along theconcrete-reinforcement interface; (2) introduction of springelements; and (3) change of concrete constitutive model inprincipal tension directions. Because the effect of interfacialbond-slip is now taken into account by an explicit bond slipmodel, only tension-softening of concrete after crackingwas considered. Therefore, the post-cracking stress-strainrelationship of concrete in tension as proposed by Hordjik(1991) was used for all concrete elements, as shown in Fig. 6(b).This expression is described by the tensile stress-crack widthrelationship of concrete as given by

(5)

where wc is the crack opening at the complete release ofstress (wc = 5.14GF/fcr); GF is the fracture energy of concreterequired to create a unit area of stress free crack, which isequal to the area under the tensile stress and crack width(GF = 0.000025fcr) curve; w is the crack opening associatedwith the concrete is tension; and c1 and c2 are the materialconstants which equal 3.0 and 6.93, respectively. The crackopening displacement (w) is a product of the cracking strainand the length of the localized zone, which is equal to thecharacteristic length of the element in the FEM application.Cracking strain is obtained from the concept of decompositionof the total strain into the concrete elastic strain and crackingstrain as shown in Fig. 7.

Because stiffness and stress for spring elements inABAQUS© are calculated on the basis of relative displacementbetween two connecting nodes, the application of the CEB-

σt

fcr

----- 1 c1wwc

------⎝ ⎠⎛ ⎞ 3

+⎩ ⎭⎨ ⎬⎧ ⎫

c2wwc

------–⎝ ⎠⎛ ⎞exp=

wwc

------ 1 c13+( ) c2–( )exp–

where τ is the calculated bond stress (MPa); S is a nondimen-sionalized parameter (= 1000s/D); s is displacement of thebars at the concerned point measured relative to a fixed pointin the concrete (not interfacial slip between concrete andreinforcing bar) (mm); D is the bar diameter (mm); and ε isthe reinforcement strain.

Shima et al. (1987) also concluded that the bond stress-slip relationship only exists under the limited condition ofsufficient bar embedment. The bond stress-slip relationshipin this case can be represented as

(4)

where S is a nondimensionalized parameter (= s/D).Figure 5 shows the bond stress-slip model proposed by

Shima et al. (1987).For sake of comparison, two-dimensional FEM analyses

of the RC bent caps tested by Young et al. (2002) wereperformed using both the implicit bond model (tension-stiffening) and explicit bond model between the concreteand the main longitudinal reinforcement using the springelements as defined in Eq. (2) and (4). Because the bent capspecimens typically have skin reinforcement, interfacial slip

τ 0.9 f ′c

23---

1 e 40S0.6

––⎝ ⎠⎛ ⎞=

Fig. 5—Interfacial bond-slip model (Shima et al. 1987).

Fig. 6—Zoning in reinforced concrete bent caps accordingto post-cracking stress-strain curve. Fig. 7—Strain decomposition of total strain.

ACI Structural Journal/September-October 2006 751

FIP Model can be applied directly using the default springelement. However, slip in the Shima et al. (1987) model isdefined as the slip of reinforcement measured relative to afixed point in the concrete. Therefore, a separate FEM codewas developed specifically for this purpose. The program iscapable of performing a nonlinear analysis for two-dimensionalRC membranes subjected to in-plane loading using theproposed constitutive relationship with the introduction ofspring elements where stiffness and stress are defined solelyby the displacement (or strain) of the reinforcement.

For concrete in compression, the confined model in thecompanion paper by Powanusorn and Bracci (2006) is usedalong with the same assumptions of the MCFT.

Results using CEB-FIP Model Code (1990)and Shima et al. (1987) bond-slip model

Figure 8 shows the comparison between the predictedload-deformation curves for RC bent cap Specimens 1A, 1B,2A, and 2B (Young et al. 2002 and Bracci et al. 2000) usingthe implicit (tension-stiffening) model and explicit CEB-FIP(1990) and Shima et al. (1987) models for the interfacialbond-slip between the concrete and reinforcement. Thefigure shows that the use of an explicit bond model yieldssuperior results beyond the first cracking compared with theimplicit bond model as the simulated response of RC bentcaps consistently lies closer to the experimental response.The difference in the predicted member strength for cracking,first yielding of the longitudinal reinforcement, and ultimatefor the implicit and explicit bond models is insignificant.However, the predicted post-cracking stiffness of the explicitbond models better correlates with the experimental results.

PROPOSED BOND-SLIP MODELResults in the previous sections show that the application

of the CEB-FIP and Shima et al. bond-slip models led to

improved predictions of the load-deformation behavior forthe RC bent cap specimens. The predicted first cracking andultimate strengths of the RC bent caps were also in goodagreement with the results obtained in the experimentalprogram. In addition, the incorporation of the explicit bond-slip model between the concrete and reinforcement led to asimilar post-cracking stiffness. In spite of this, thepredicted post-cracking deformations remained somewhatunderestimated, as shown in Fig. 8. The CEB-FIP model forthe concrete and reinforcement interface was derived basedon pull-out tests of a single bar in a concrete block. Therefore,the direct application of the model may not be representative ofthe interfacial slip between the concrete and longitudinalreinforcing steel in typical RC bent caps where multiplenumbers of large diameter reinforcing steel are concentratedfor bending resistance. Following an argument proposed byShima et al. (1987), the bond stress-slip relationship onlyexists under limited conditions with sufficient embedment.Consequently, it could be hypothesized that the embedmentof main longitudinal reinforcement may be adequate fordeveloping the full strength of the reinforcement, butinadequate for ensuring the bond stress-slip relationship toexist. In addition, the effect of shear cracking in memberswith small shear span ratios, as with RC bent caps, maysomewhat deteriorate the bond-slip stiffness. Therefore,parametric studies were performed to determine an appropriatebond-slip model to correlate with the response of the same16 RC bent cap specimens. The study showed that the slopeof the post-cracking load-deformation curve of the RC bentcaps depends upon the initial slope of the bond stress-slipmodel. Based on curve fitting, the following constitutiverelationship for the bond stress-slip between the concrete andreinforcement interface was determined

Fig. 8—Simulated results using explicit bond-slip models.

752 ACI Structural Journal/September-October 2006

(6)

= τf , s > s3

Essentially, the curve is a modification of the CEB-FIPmodel by decreasing the initial slope. Figure 9 shows thebond stress-slip curve proposed for the RC bent caps.

Figure 10 shows the comparison between the experimentalresults and simulated response of the RC bent caps using theimplicit bond model, explicit CEB-FIP bond model, explicitShima et al. (1987) bond model, and the proposed model.The figure clearly indicates that the proposed bond-slipmodel leads to a better improvement in the prediction of theload-deformation response of the RC bent cap specimensprone to shear deformations.

τ τmaxss2

----⎝ ⎠⎛ ⎞ s s2<,=

τmaxτmax τf–( )s3 s2–( )

------------------------- s s2–( ) s2 s s3< <,–=

SUMMARY AND CONCLUSIONSIn a companion paper by Powanusorn and Bracci (2006),

the direct application of the MCFT using an implicit bond-slip model for the concrete and reinforcement interfacethrough tension-stiffening led to an overestimation of post-cracking stiffness in RC members prone to shear deformations,regardless of the incorporation of confinement due to thetransverse reinforcement. The overestimation of stiffness ledto the underestimation of deformation, which is related to theoverall member cracking and magnitude of crack widthsunder loading, particularly at service loading. Parametricstudies showed that the overestimation was not caused by achange in the constitutive relationship of concrete thatincorporates the effect of confinement. In fact, the effect ofconfinement was only mobilized at higher levels of load asthe analytical predictions of the load-displacement responsewere virtually the same before the first reinforcement yieldingfor models with and without confinement. The effect of thebase curves for the confined and unconfined concrete stress-strain relationships in compression (Mander et al. [1988]model and Hognestad parabola [Vecchio and Collins 1982],respectively) on the predicted load-deformation was alsonegligible. Additional parametric studies on the effect ofshrinkage through a pre-strain concept led to better correlationwith experimental behavior. However, it did not provide thecorrect mechanism as the slope of the load-deformationrelationship after initial cracking remained unchanged.

A remedy to improve the analytical model was proposedin this paper by the direct incorporation of an interfacialbond-slip representation between the concrete and the mainlongitudinal reinforcing steel. It was shown that, by usingexplicit bond-link element models to simulate the interfacebetween the concrete and reinforcement, the analyticalprediction of the load-deformation relationship wasimproved as the stiffness, particularly in the post-crackingFig. 9—Proposed bond-slip model.

Fig. 10—Response using proposed bond-slip model.

ACI Structural Journal/September-October 2006 753

range, had a better fit with the experimental results.However, numerical simulations of the explicit bond-linkelements using the bond stress-slip relationships normallyproposed in the literature did not lead to significantimprovements in the predicted load-deformation responsein the RC bent caps, as opposed to its good performancewhen flexural deformations are predominant. Better resultswere obtained by decreasing the initial stiffness of the bondstress-slip relationship as proposed in this work. In reality,the decrease in bond stress-slip stiffness for the concrete-reinforcement interface in RC bent caps may be justifiedbecause most experiments on interfacial bond-slip betweenthe concrete and reinforcing steel were conducted using pull-out tests of a single bar in a block of concrete. For RC bentcap applications, multiple numbers of large diameterreinforcing bars are typically arranged in a single layer orpossibly multiple layers. The effect of early splitting cracksbetween the bars may somewhat alter the bond-slip stiffness.In addition, the effect of inclined cracks due to the shearaction in RC bent caps can also lead to bond stiffnessdeterioration. Experimental results reported in the literaturealso show large differences in bond stress-slip relationships.Some even suggest that the bond stress-slip relationshipshould not be treated as a unique material property. Based ona parametric study by curve-fitting the overall response from16 bent cap test specimens, a new bond-slip relationship isproposed for members with lumped reinforcement and thatare prone to shear deformations. Results show that theproposed model better correlates with the experimental load-deformation response in the 16 RC bent cap test specimens,while still providing an accurate prediction of member strength.

ACKNOWLEDGMENTSFunding for this research was provided by the National Science Foundation

under Grant No. CMS. 9733959, the Texas Department of Transportation(Project 0-1851), and the Department of Civil Engineering of Texas A&MUniversity, College Station, Tex. This support is gratefully acknowledged. Anyopinions, findings, and conclusions or recommendations expressed in thismaterial are those of the authors and do not necessarily reflect the view ofthe sponsors.

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RC Bent Caps,” Research Report 1851-1, Texas Transportation Institute,Texas A&M University, College Station, Tex.

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