Fatigue and Overloading Behavior of Steel–Concrete ... · Fatigue and Overloading Behavior of...

Fatigue and Overloading Behavior of Steel–ConcreteComposite Flexural Members Strengthened with High

Modulus CFRP MaterialsM. Dawood1; S. Rizkalla2; and E. Sumner3

Abstract: Due to corrosion and the continuous demand to increase traffic loads, there is a need for an effective system which can be usedto repair and/or strengthen steel bridges and structures. This paper describes an experimental program, recently completed, to investigatethe fundamental behavior of steel–concrete composite scaled bridge beams strengthened with new high modulus carbon fiber-reinforcedpolymer �HM CFRP� materials. The behavior of the beams under overloading conditions and fatigue loading conditions was studied aswell as the possible presence of shear lag at the interface of the steel surface and the CFRP strengthening material. The test results arecompared to an analytical model based on the fundamental principles of equilibrium and compatibility, to predict the behavior of thestrengthened steel–concrete composite beams. Based on the findings of this research work, combined with other work in the literature, adesign guideline is proposed for the use of HM CFRP for strengthening the steel flexural members typically used for bridges andstructures.

DOI: 10.1061/�ASCE�1090-0268�2007�11:6�659�

CE Database subject headings: Fatigue; Composite materials; Fiber reinforced polymers; Flexure; Beams; Bridges.

Introduction

The use of fiber-reinforced polymer �FRP� materials has becomea common practice for the repair and strengthening of concretestructures and bridges. Due to the success of this technique, sev-eral researchers have also investigated the use of externallybonded carbon FRP �CFRP� materials for the repair and strength-ening of steel bridges and structures. A number of different ap-proaches have been investigated to assess the effectiveness ofusing CFRP materials for rehabilitation of steel bridge girdersincluding repair of naturally deteriorated girders �Mertz andGillespie 1996�, repair of overloaded girders �Sen et al. 2001�,strengthening of undamaged girders �Tavakkolizadeh and Saadat-manesh 2003c�, and repair of girders with simulated corrosiondamage �Al-Saidy et al. 2004�. Other research has been conductedto study the fatigue durability of CFRP strengthening systems�Miller et al. 2001�.

Early research focused on the use of conventional modulusCFRP materials to repair naturally corroded bridge girders �Mertz

1Graduate Research Assistant, Constructed Facilities Laboratory,North Carolina State Univ., 2414 Campus Shore Dr., Campus Box 7533,Raleigh, NC 27695-7533.

2Distinguished Professor of Civil Engineering and Construction,Constructed Facilities Laboratory, North Carolina State Univ., 2414Campus Shore Dr., Campus Box 7533, Raleigh, NC 27695-7533.

3Assistant Professor, Constructed Facilities Laboratory, NorthCarolina State Univ., 2414 Campus Shore Dr., Campus Box 7533,Raleigh, NC 27695-7533.

Note. Discussion open until May 1, 2008. Separate discussions mustbe submitted for individual papers. To extend the closing date by onemonth, a written request must be filed with the ASCE Managing Editor.The manuscript for this paper was submitted for review and possiblepublication on February 14, 2006; approved on December 16, 2006. Thispaper is part of the Journal of Composites for Construction, Vol. 11, No.
6, December 1, 2007. ©ASCE, ISSN 1090-0268/2007/6-659–669/$25.00.
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and Gillespie 1996�. The research findings indicated that CFRPmaterials can be effectively used to restore the stiffness and flex-ural capacity of the damaged girders to levels comparable to thoseof the undamaged girders.

Researchers have also investigated the use of conventionalCFRP materials to repair steel–concrete composite bridge girderswhich were damaged due to severe overloading conditions �Senet al. 2001�. The CFRP strengthening system helped to increasethe nominal capacity of the beams by up to 52%. The presence ofthe CFRP also substantially increased the yield load and postelas-tic stiffness of the strengthened beams.

In another study, three undamaged steel–concrete compositebeams were strengthened with one, three, and five layers of CFRPstrips, respectively �Tavakkolizadeh and Saadatmanesh 2003c�.The CFRP materials increased the nominal capacity of thestrengthened beams by up to 76%, however, the increase of theelastic stiffness was minimal. In a related study, the tension flangeof three other steel–concrete composite beams were notched witha 1.3 mm wide notch at midspan to simulate 25, 50, and 100%loss of the area of the tension flange �Tavakkolizadeh and Saadat-manesh 2003b�. The repair restored the elastic stiffness and nomi-nal capacity of the girders to levels comparable to the undamagedbeams and helped in reducing the residual deflections due to over-loading conditions.

Other researchers have simulated corrosion damage by remov-ing a uniform portion of the tension flange along the entire lengthof the girders �Al-Saidy et al. 2004�. CFRP materials were sub-sequently used to repair the girders. The technique restored thelost strength of the damaged beams to levels higher than those ofthe undamaged girders. However, only 50% of the lost stiffness ofthe beams was recovered.

Investigations on the fatigue durability of steel beamsstrengthened with CFRP materials have been limited.Tavakkolizadeh and Saadatmanesh �2003a� demonstrated that
installation of externally bonded CFRP patches can reduce crack
OR CONSTRUCTION © ASCE / NOVEMBER/DECEMBER 2007 / 659

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propagation rates and increase the fatigue life of cracked steelmembers. Prestressing CFRP patches prior to installation can helppromote crack-closure effects and further extend the fatigue lifeof cracked steel members �Bassetti et al. 2000�. The fatigue du-rability of naturally corroded steel bridge girders, which wererepaired with CFRP materials, has been shown to be at least equalto that of many typical steel details which are commonly used incurrent bridge construction �Miller et al. 2001�.

The majority of the previous research has focused on the useof conventional modulus CFRP materials for the repair of steelbridge members. Although substantial strength increases havebeen achieved, typically a large amount of CFRP materials wasrequired to achieve an increase of the elastic stiffness of thebeams. This is due to the relatively low modulus of elasticity ofthe CFRP as compared to steel and also possibly due to the pres-ence of shear-lag effects between the steel beam and the CFRPmaterials �Tavakkolizadeh and Saadatmanesh 2003c�.

Recently, high modulus CFRP materials have become com-mercially available which have a modulus of elasticity approxi-mately twice that of conventional steel. The effectiveness of usinghigh modular �HM� CFRP materials to repair steel bridge girderswas demonstrated by testing three large-scale steel–concrete com-posite beams strengthened with different configurations of HMCFRP materials �Schnerch 2005�. The elastic stiffness and nomi-nal moment capacity of the beams were increased by up to 36 and45%, respectively. The testing demonstrated that prestressing theHM CFRP strips prior to installation on the steel beam increasedthe efficiency of utilization of the CFRP. Test results indicatedthat prestressing of the HM CFRP required only half the amountof prestressed laminates that was required for a similar beamstrengthened with unstressed CFRP laminates to achieve a similarincrease of the stiffness. The use of prestressed laminates alsohelped to maintain the original ductility of the unstrengthenedmember.

This paper presents the findings of an experimental investiga-tion, recently completed, to study the behavior of steel–concretecomposite beams strengthened with HM CFRP materials and sub-jected to overloading and fatigue loading conditions. The researchexamined also, the possible presence of shear lag at the interfacebetween the steel surface and the CFRP materials. The paper alsoprovides an analytical model, based on equilibrium and compat-ibility principles, to predict the response of steel and steel–concrete composite flexural members strengthened with CFRPmaterials. A detailed description of the research program pre-sented in this paper is given in Dawood �2005�. Based on theresearch findings and the available literature review, a guideline isproposed which can be used by practitioners to design the re-quired HM CFRP strengthening system for a given steel–concretecomposite beam.

HM CFRP Strengthening System

The carbon fiber-reinforced polymer materials used in this studyconsist of pitch-based carbon fibers pultruded into 4 mm thick,100 mm wide laminates. The modulus of elasticity and ulti-mate strain of the strips reported by the manufacturer were460,000 MPa and 0.00334, respectively. The reported ultimatestrain was lower than that measured in the experimental programreported in this paper. The laminates had a fiber volume fractionof 70% and were fabricated with a glass fiber peel ply on bothfaces to minimize the need for surface preparation of the compos-
ite material. The strips were bonded to the tension flange of the
660 / JOURNAL OF COMPOSITES FOR CONSTRUCTION © ASCE / NOVE


steel beams using a two part epoxy adhesive with a fast hardener.This adhesive was selected from among six adhesives consideredin the same research program �Schnerch 2005�. The tension flangeof the steel beam was grit blasted immediately prior to installationof the strengthening system to remove any rust and mill scalefrom the surface. The surface was subsequently cleaned by airblowing and solvent wiping. After the CFRP strips were installeda wooden clamping system was applied for at least 12 h until theadhesive had thoroughly set. The adhesive was allowed to curefor at least one week prior to testing.

Experimental Program

The experimental program consisted of seven steel–concrete com-posite beams, five of which were strengthened with full-lengthHM CFRP strips, to study the behavior of the proposed HMCFRP strengthening system under the effect of overloading andfatigue loading conditions. In the first phase three beams weretested to study the behavior of the strengthening system underoverloading conditions. The three beams tested in the secondphase were used to study the behavior under fatigue loading con-ditions and to investigate the durability of the strengthening sys-tem. The effect of the adhesive thickness on the fatigue behaviorwas also examined. In the third phase, the seventh beam wastested to examine the shear-lag phenomenon at the interface of thesteel surface and the CFRP materials. The strengthened beams,tested in the first and second phase, were also used to investigatethe possible presence of shear-lag phenomenon. The tested beamswere designed to represent scaled steel–concrete compositebeams which are typically used for highway bridge construction.The cross section of the tested beams is shown schematically inFig. 1. The beams were strengthened with different reinforcementratios, �, of HM CFRP materials and tested in a four point bend-ing configuration as shown schematically in Figs. 2�a and b�.

A detailed description of the three phases of the experimentalprogram is presented in Table 1. A total of three beams weretested to investigate the behavior under overloading conditions.Two of the test beams were strengthened with two different levelsof CFRP to investigate the effect of the CFRP reinforcement ratioon the behavior of the beams. A third unstrengthened beam wastested to serve as a control beam for the overloading study. Allthree of the beams were unloaded and reloaded at various loadlevels to simulate the effect of severe overloading conditions.

The objective of the fatigue study was to verify the fatiguedurability of the strengthened beams and to assess the effect of

Fig. 1. Cross section of a typical test beam

the bond preparation on the fatigue durability of the strengthening

MBER/DECEMBER 2007


system. Three additional beams were tested. Two of the beamswere strengthened with the same amount of CFRP materials,however, using different bonding techniques. The first beam wasstrengthened using the standard bonding procedure described pre-viously. The second beam was strengthened using a modifiedbonding technique which included increasing the thickness of theadhesive layer which was applied in conjunction with a primer

Table 1. Test Matrix for the Three Phases of the Experimental Program

Beam

Reinforcementratioa, �

�%�

Adhesivethickness, ta

�mm�

Overloading

ST-CONT 0 N/A

OVL-1 4.3 0.1

OVL-2 8.6 0.1

Fatigue

FAT-CONT 0 N/A

FAT-1 4.3 0.1

FAT-1bb 4.3 1.0

Shear lag

SHL 8.6 0.1

Note: N/A�not applicable.aDefined as the ratio of the cross-sectional area of the CFRP strengtheningbeam.b

Fig. 2. Beam test set

Included the use of a silane adhesion promoter.



coat of a silane adhesion promoter. The third beam remained un-strengthened and was used as a control beam for the fatigue study.All three beams were subjected to three million fatigue loadingcycles and the load was cycled at a frequency of 3 Hz. The mini-mum applied load used for the cycled loading, Pmin, was selectedto be equivalent to 30% of the calculated yield load of the un-strengthened beams to simulate the effect of the sustained dead-

Concretestrength, fc�

�mPa� Loading

44 Unload/reload

44 Unload/reload

44 Unload/reload

34 Fatigue: Pmin=50 kN, �P=50 kN



44 Monotonic

nting for the fiber volume fraction to the cross-sectional area of the steel

schematic; �b� actual

, accou

up �a�



load for a typical bridge structure. The maximum load applied,Pmax, for the unstrengthened beam, was selected to be equivalentto 60% of the calculated yield load to simulate the combinedeffect of dead load and live load. The maximum load for the twostrengthened beams, Pmax, however, was selected to be equivalentto 60% of the calculated increased yield load of the strengthenedbeams. The resulting load range, �P, also simulated an increaseof 20% of the allowable live-load level in comparison to theunstrengthened beam.

To simulate the actual behavior of a typical strengthened high-way bridge, the two strengthened beams that were tested in thefatigue study were subjected to a sustained simulated dead loadprior to installation of the HM CFRP strengthening system. Thesimulated dead load was applied using an independent loadingsystem as shown in Fig. 3. Prior to installation of the CFRP, thesimulated dead load of 50 kN was applied by tightening the nutsagainst the load cells on the threaded rods. The simulated deadload was sustained on the beams during installation of the CFRPstrips and also throughout the curing process of the adhesive.After the adhesive cured, the load was transferred from the inde-pendent dead-load system to the hydraulic actuator and thefatigue loading program was commenced.

The seventh beam, tested in the third phase, was tested undermonotonic loading conditions up to failure to investigate theshear-lag phenomenon independent of the effect of overloading orfatigue loading conditions. The strain measurements of the fourstrengthened beams, tested in the first and second phases, werealso used to examine the shear-lag phenomenon.

The tensile yield strength and modulus of elasticity of the steelbeams were determined by standard coupon tests and were foundto be 380 and 200,000 MPa, respectively. The compressivestrength of the concrete, used for the concrete deck slabs for theseven test beams, was determined from standard cylinder testsafter 28 days. The measured concrete cylinder strengths for thedeck slabs used for the different test beams are given in Table 1.

All of the test beams were instrumented to measure deflectionsat midspan and at the support locations. All of the test beams werealso instrumented to measure strain at several depths along themidspan cross-section. The two strengthened beams which were

Fig. 3. Independent dead-load apparatus

tested in the fatigue study, were also instrumented to measure



strain at the quarter-span cross section. The measured strains wereused to construct the strain profiles for the strengthened beams toinvestigate the shear-lag phenomenon at the interface between thesteel surface and the CFRP materials.

Experimental Results

This section presents and discusses the test results of each of thethree phases considered in the experimental program and summa-rizes the relevant research findings.

Overloading Study

The load–deflection relationships of the three beams that weretested to study the overloading behavior of the strengthenedbeams are presented in Fig. 4. The behavior of the control beam,Beam ST-CONT, is given in Fig. 4�a�, whereas the behavior ofthe other two beams, strengthened with 4.3 and 8.6% reinforce-ment ratios of HM CFRP, are given in Figs. 4�b and c�, respec-tively. All three beams were unloaded and reloaded at variousloading stages to simulate the effect of overloading conditions.

In general, the load–deflection behavior of the three beamswas essentially linear up to yielding of the steel. Prior to yieldingof the steel all three of the tested beams exhibited minimal re-sidual deflections upon removal of the applied load. Reloadingresulted in minimal hysteresis in all cases. After yielding of thesteel, the unstrengthened beam exhibited a significant increase ofthe measured residual deflection, as shown in Fig. 4�a�, whereasthe two strengthened beams continued to exhibit minimal residualdeflections up to rupture of the CFRP. A typical rupture failure ofthe HM CFRP laminates is shown in Fig. 4�d�. After rupture ofthe CFRP occurred, the load–deflection response of the strength-ened beams followed a similar trend to that measured for theunstrengthened beam. The tests indicate that the nominal capacityof the unstrengthened beam, ST-CONT, was governed by crush-ing of the concrete while the nominal capacity for the twostrengthened beams, OVL-1 and OVL-2 was governed by ruptureof the CFRP.

The increases of the elastic stiffness, yield load and nominalstrength of the two strengthened beams are presented in Table 2.The elastic stiffness, yield load and nominal capacity of thebeams were increased by 46, 85, and 66%, respectively, using thehigher reinforcement ratio. Inspection of Table 2 indicates thatdoubling the CFRP reinforcement ratio, from 4.3 to 8.6%, ap-proximately doubled the elastic stiffness increase of the beams.Doubling the reinforcing ratio also approximately tripled the in-crease of the measured yield load and nominal capacity of thestrengthened beams. This demonstrates that increasing the rein-forcement ratio increases the efficiency of the CFRP material.

In addition to the increase of the stiffness and strength, use ofthe HM CFRP materials also helped to reduce the residual deflec-tion of the strengthened beams due to possible overloading con-ditions of the beams. To evaluate the effectiveness of the HMCFRP strengthening system, each of the three beams was un-loaded at a load level of 175 kN to study the behavior underpossible overloading conditions. This load is equivalent to theallowable service load for the beam strengthened with the higherHM CFRP reinforcement ratio of 8.6% and induced a strain levelof 60% of the yield strain of the steel, �y, as determined from thecoupon tests. The average measured strain at the steel tensionflange at this load level was 2.5 �y, 1.0 �y, and 0.6 �y for Beams
ST-CONT, OVL-1, and OVL-2, respectively. The beams were
MBER/DECEMBER 2007


unloaded to a load level of 45 kN which simulates an equivalentsustained load acting on a typical bridge after an overloadingevent due to the effect of self-weight and superimposed deadload. The plastic residual deflection, at the 45 kN load level forBeams OVL-1 and OVL-2 were, respectively, 20 and 15% of themeasured residual deflection of Beam ST-CONT. Consequently,under severe overloading conditions, an unstrengthened beammay require replacement, whereas a strengthened beam may re-main in excellent service condition.

Fatigue Study

Three beams were tested in the fatigue study. Beams FAT-1 and

Fig. 4. Load–deflection behavior of the three overloading test beam

FAT-1b were strengthened with 4.3% reinforcement ratio of



Table 2. Comparison of the Overloading Beams

Beam

Reinforcementratio, �

�%�

Stiffnessincrease

�%�

Yield loadincrease

�%�

Capacityincrease

�%�

ST-CONT 0 N/A N/A N/A

OVL-1 4.3 27 32 20

OVL-2 8.6 46 85 66

s �a� ST CONT; �b� OVL-1; �c� OVL-2; and �d� typical rupture failure

Note: N/A�not applicable.



CFRP using two different bonding techniques, whereas BeamFAT-CONT remained unstrengthened to serve as a control beamfor the fatigue study. The two strengthened beams were testedunder an equivalent load to simulate a 20% increase of theapplied live load as compared to the unstrengthened beam. Allthree beams sustained a 3�106 cycle fatigue loading course with-out exhibiting any indication of failure. The degradation ofthe stiffness and mean deflection of the three beams throughoutthe 3�106 cycle loading course are shown in Figs. 5�a and b�,respectively. The stiffnesses and mean deflections presented inFig. 5 are normalized with respect to the measured initial valuesat the beginning of the fatigue loading program.

All three of the tested beams exhibited a minimal degradationof the elastic stiffness of less than 5% throughout the three mil-lion fatigue loading cycles as shown in Fig. 5�a�. However, theunstrengthened beam, FAT-CONT, exhibited a nearly 30% in-crease of the mean deflection due to the applied fatigue cycles.This behavior was most likely due to the fatigue-creep behaviorof the concrete deck slab. Both of the strengthened beams exhib-ited superior performance with a maximum increase of the mea-sured mean deflection of 10%. The observed degradation of thetwo strengthened beams throughout the 3�106 fatigue cycles wassimilar. This indicates that neither the bonding procedure nor theadhesive thickness affected the fatigue behavior of the strength-ening system.

After the completion of the fatigue program, the three beamswere loaded monotonically to failure. The load–deflection behav-ior of the beams followed a similar trend to the observed load–deflection envelope of the three beams that were tested in theoverloading study. The nominal capacity of the two strengthenedbeams, FAT-1 and FAT-1b, was governed by rupture of the CFRPat a load of 250 kN. After rupture of the CFRP, the load–deflection behavior of the two beams followed a similar trendto the load–deflection behavior of the unstrengthened beam,FAT-CONT. Crushing of the concrete for all three beams occurred

Fig. 5. Degradation of �a� stiffness; �b� mean deflection for thefatigue beams

at a measured load of between 200 and 215 kN. The findings of



the fatigue study demonstrate that the strengthened beams cansustain the specified increase of the live load level for the selectedHM CFRP reinforcement ratio while maintaining a level of dura-bility, which was comparable to that of the unstrengthened beam.

Shear-Lag Study

One additional beam, SHL, was tested to investigate the possiblepresence of a shear-lag phenomenon at the interface of the steelsurface and the CFRP materials under monotonic loading condi-tions. The beam was strengthened with 8.6% reinforcement ratioof HM CFRP. The load–deflection behavior of Beam SHL wasessentially the same as the load–deflection envelope of BeamOVL-2, shown in Fig. 4�c�, which was strengthened with thesame reinforcement ratio of HM CFRP.

The measured strain profiles at midspan of Beams SHL andOVL-2, immediately prior to rupture of the HM CFRP material,are shown in Fig. 6. The measured strain profiles for both beamsindicate a slight discontinuity of the strain profile at the interfaceof the bottom surface of the steel tension flange and the CFRPmaterial. However, the opposite sign of the discontinuity suggeststhat the discontinuity is not due to the presence of a shear lageffect. The measured discontinuity is likely due to the effect ofresidual stresses in the steel beam during the manufacturing pro-cess or due to possible local instability and lateral movement ofthe tension flange of the steel beam during the test. The presenceof these effects was confirmed by independent strain measure-ments at different locations along the steel tension flange of thestrengthened and unstrengthened test beams. The measured strainprofiles for the remaining three strengthened test beams, OVL-1,FAT-1, and FAT-1b, were essentially linear and exhibited minimaldiscontinuities between the steel and the CFRP. The findings ofthe shear-lag study indicate that the effect of shear-lag is negli-gible and the plane sections remain plane assumption is appropri-ate for the analysis of the strengthened beams.

Analytical Model

The analytical model proposed to predict the load–deflection be-havior of the strengthened steel–concrete composite beams isbased on equilibrium and compatibility. The model considers thenonlinear material characteristics of the steel and the concrete andassumes linear-elastic behavior for the CFRP materials. The pro-cedure is described briefly in the following and is presented indetail elsewhere �Dawood 2005; Schnerch 2005; Schnerch et al.

Fig. 6. Strain profiles for beam SHL and OVL-2 ��=8.6% �

2006�.

MBER/DECEMBER 2007


The moment–curvature behavior for a given cross section isdetermined based on a selected strain at the top level of the com-pression flange and iteration of the neutral axis depth. For a givenstrain at the top surface of the concrete deck, and an assumedneutral axis depth, the strain at any level in the cross section canbe calculated using an assumed linear strain profile. The knownmaterial characteristics can be used to calculate the stress distri-bution throughout the cross section. The internal forces are cal-culated by integration of the stress profile. The neutral axis depthcan then be determined through iteration until horizontal forceequilibrium is satisfied and the corresponding moment and curva-ture of the section can be calculated for the given strain level. Thestrain at the top of the section is incremented to establish thecomplete moment–curvature relationship of the section. For agiven loading and support configuration the load–deflection be-havior of the beam can be determined by integration of the cur-vature profile using any commonly accepted method.

The nominal capacity of the strengthened section is limited byrupture of the CFRP which occurs when the strain at the level ofthe CFRP approaches the maximum value. After rupture of theCFRP the behavior of the beam can be described by consideringthe unstrengthened section up to crushing of the concrete deckslab. The model assumes that the capacity of the adhesive joint isadequate to develop the full tensile capacity of the CFRP materi-als and, consequently, debonding is not considered as a possiblemode of failure. An independent analytical model which can beused to determine the shear and normal bond stresses in the ad-hesive joint of a strengthened beam is presented in a separatepaper by Schnerch �2005�.

Validation of the Analytical Model

The accuracy of the analytical model was verified by comparingthe predicted load–deflection response to the measured valuesobtained from the experimental program. The material proper-ties to be input into the analytical model were determined bytesting of representative material samples. The load–deflectionresponse of the strengthened test beams was predicted andcompared to the measured values obtained from the experimentalprogram.

The material properties of the concrete deck slabs for the fivebeams were determined by testing representative concrete cylin-ders. The complete stress–strain relationship of the cylinders wasmeasured and a best fit curve to the measured data was estab-lished using the equation presented in Fig. 7 �Collins and Mitchell

Fig. 7. Concrete material properties

1997�, where fc�stress in the concrete corresponding to a strain,



�; �c��strain corresponding to the peak concrete stress, fc�;n�curve fitting factor; and k�postpeak decay factor. The mea-sured stress–strain relationships for the cylinder tests, as well asthe best fit curves for all three batches of concrete are presented inFig. 7. The material characteristics used for the concrete materialmodel are presented in Table 3. The longitudinal steel reinforce-ment in the concrete slab was modeled using an elastic–plasticrelationship with an elastic modulus of 200,000 MPa and a yieldstrength of 400 MPa.

The modulus of elasticity and yield strength of the structuralsteel W sections were determined from representative coupontests as 200,000 and 380 MPa, as discussed previously. However,all of the beams that were tested in the experimental programexhibited an earlier deviation from the elastic behavior due to thepresence of residual stresses which was not observed in the cou-pon tests. A trilinear material model was used to account for thegradual yielding of the steel in the beam tests due to the presenceof residual stresses as shown in Fig. 8 �Englekirk 1994�. Theproportional limit strain, �p, for the steel was determined from themeasured strain at the tension flange of the steel beams that weretested in the experimental program. The measured load–strain re-lationship at the tension flange of the beams became nonlinear ata measured strain of approximately 0.0016. Consequently, thisvalue was selected as the proportional limit strain for the materialmodel.

The HM CFRP laminates were modeled as a linear–elasticmaterial to failure using the elastic modulus of 460,000 MPa re-ported by the manufacturer and the average measured strain atrupture of the CFRP strips of 0.0037 from the beam tests.

The predicted and measured load–deflection responses basedon the proposed model and the measured values for BeamsOVl-1, OVL-2, FAT-1, and FAT-1b are compared in Fig. 9. In-spection of Fig. 9 indicates that the analytical model closely pre-dicts the load–deflection behavior of the strengthened beams prior

Table 3. Coefficients for the Concrete Material Model

Coefficient Batch 1 Batch 2 Batch 3

Peak strength, fc� �mPa� 44 34 58

Strain at peak, �c� 0.0035 0.0035 0.0038

Fitting factor, n 4.77 2.84 4.25

Post peak factor, k 1.13 1.22 1.92

Ultimate strain, �cu 0.0045 0.0049 0.0043

Fig. 8. Steel material properties



to rupture of the CFRP. The predicted response of the unstrength-ened beams closely matches the measured behavior after ruptureof the HM CFRP laminates. The measured and predicted nominalcapacity and elastic stiffness increase for each of the five beamsare given in Table 4. In all cases the analytical model accuratelypredicted the nominal capacity and elastic stiffness increase of thestrengthened beams to within 10% of the measured values.

The analytical model was also used to predict the nominalmoment capacity of the tested beams for a number of differentreinforcement ratios of CFRP up to 40% to establish practicallimits for the amount of strengthening which can be applied to agiven cross section. The relationship between the reinforcementratio and the nominal moment capacity of the strengthened beamsis presented in Fig. 10 for the specific cross section considered inthe current test program. The test results of the five strengthenedbeams that were tested in the experimental program are also plot-ted for reference purposes. From the Fig. 11, it can be seen thatthe relationship is essentially trilinear and Fig. 11 can be sepa-rated into three distinct regions. The first region includes rein-forcement ratios up to 1.5%, which corresponds to installing a100 mm wide �0.5 mm thick CFRP strip on the tension flange ofthe steel beam. This represents a very underreinforced section for

Fig. 9. Model verification �a� OVL-2 ��=8.6% �, �b� OVL

which rupture of the CFRP occurs prior to achieving the nominal



strength of the unstrengthened section, Mn,U. Within this regioninstallation of the CFRP does not increase the nominal capacity ofthe section. As such, this represents a practical lower limit ofeffectiveness for the allowable amount CFRP strengthening whichshould be applied to the beam.

For reinforcement ratios from 1.5 to 20% the nominal capacityof the section is governed by rupture of the CFRP prior to crush-ing of the concrete. Increasing the reinforcement ratio within this

Table 4. Comparison of Measured and Predicted Nominal Capacities andElastic Stiffness

Nominal capacity�kN�

Stiffness increase�%�

Beam Measured Predicted Measured Predicted

OVL-1 259 270 27 27

OVL-2 357 366 46 48

SHL 358 366 N/Ac 48

FAT-1 250 264 40 32

FAT-1b 252 272 35 26c

4.3% �, �c� FAT-1 ��=4.3% �, and �d� FAT-1b ��=4.3% �
-1 ��=
Unstrengthened stiffness of beam SHL was not measured.

MBER/DECEMBER 2007


region results in a corresponding increase of the nominal capacityof the strengthened section, Mn,S up to 2.6 times the nominalcapacity of the unstrengthened member. All of the tested beamsfall within this region as indicated in Fig. 10. The failure of thesection by rupture of the CFRP in this region indicates full utili-zation of the capacity of the CFRP materials.

The third region includes sections with a reinforcement ratioof CFRP greater than 20%. This corresponds to installing a100 mm wide �7 mm thick CFRP strip on the tension flange ofthe beam. In this region failure of the section occurs due to crush-ing of the concrete prior to rupture of the CFRP. The slight in-crease of the strength in this region is mainly due to the shift ofthe neutral axis by increasing the amount of CFRP applied to thebeam. This represents a practical upper limit for the reinforcementof the cross section in this study. From Fig. 10 it can be seen thatincreasing the reinforcement ratio beyond this limit does not sig-nificantly increase the nominal capacity of the section indicatinginefficient utilization of the CFRP strengthening materials.

Although the relationship shown in Fig. 10 and the limits dis-cussed previously are for the specific beam cross-section consid-ered in this study, a similar behavior can be expected for mosttypical bridge girders which consist of a relatively slender steel-

Fig. 10. Effect of reinforcement ratio on nominal moment capacity

Fig. 11. Load levels and moment–c



section and a typical reinforced concrete deck. Similar limits canbe easily established for any steel–concrete composite beam con-figuration using the presented analytical model.

Design Guidelines

Based on the findings of this research program a series of designguidelines have been developed and proposed for the design ofHM CFRP strengthening for steel–concrete composite beams. Adetailed description of the proposed flexural design procedures isgiven by Schnerch et al. �2006�.

The design procedure requires that the increase of live load fora steel–concrete composite beam strengthened with HM CFRPmaterials should satisfy three criteria. These three criteria areshown in Fig. 11 with respect to the moment–curvature responseof a typical strengthened beam. Due to the presence of the addi-tional layer of HM CFRP material, the yield moment of thestrengthened beam, MY,S, is greater than the yield moment of thesame beam prior to strengthening, MY,U. This was verified by thefindings of several experimental studies �Dawood 2005; Schnerch2005�. It should be noted that the increase of the yield momentdue to installation of the HM CFRP strengthening system ishighly dependent on the level of the dead load acting on themember prior to installation of the strengthening. To ensure thatthe strengthened beam remains elastic under service loading con-ditions, the total applied moment acting on the strengthened sec-tion, including the effect of dead load, MD, and the increased liveload, ML, should not exceed 60% of the increased yield momentof the strengthened section. To satisfy the strength limit state, thetotal factored moment based on the appropriate dead-load andlive-load factors, �D and �L, respectively, should not exceed theultimate moment capacity of the strengthened section, MU,S. Also,to ensure that the structure remains safe in the case of possibleloss of the strengthening system, the total applied moment, in-cluding the effect of dead-load and the increased live load shouldnot exceed the residual nominal moment capacity of the un-strengthened section, Mn,U. The fatigue life of the strengthenedmember under the effect of the increased live load level should bechecked to be within the allowable stress range specified by theapplicable design codes. The findings of the fatigue study dem-onstrate that the fatigue durability of the strengthening system

re behavior for a strengthened beam
urvatu


¯

under an increased live load inducing a stress range at the tensionflange of the steel beam of 30% of the yield strength of the steelwas comparable to that of an unstrengthened beam which wastested using the same stress range.

Although the nominal behavior of the member can be used topredict the behavior under service loading conditions, the designultimate capacity should incorporate suitable reduction factorsto ensure that the member remains safe. Due to the statisticaluncertainty of the measured ultimate capacity of the HM CFRPmaterials, the mean strength of the CFRP reported by the manu-

facturer, f̄FRP,u, should be reduced by 3 times the standard devia-tion, �, when calculating the ultimate capacity of the strengthenedsection �ACI 2002�. To account for possible environmental deg-radation of the CFRP materials, an environmental degradationfactor, CE should also be implemented �ACI 2002�. Therefore, thedesign strength of the HM CFRP material can be calculated as

fFRP,u = CE� f̄FRP,u − 3�� 1�

Based on the current guidelines of the American Concrete Insti-tute it is proposed that an environmental degradation factor of0.85 be considered for CFRP materials under outdoor exposureconditions �ACI 2002�.

The design failure strain of the CFRP material, �FRP,u can becalculated using the calculated design strength of the CFRP andthe average elastic modulus, EFRP, reported by the manufacturer.

The nominal capacity of a steel–concrete composite beamstrengthened with high modulus CFRP materials is typically gov-erned by rupture of the CFRP materials which occurs in a sudden,brittle manner without significant warning. To account for thebrittle nature of failure, a strength reduction factor, , of 0.75 isrecommended. This reduction factor is consistent with the reduc-tion used in the American Institute of Steel Construction LRFDSpecification �2001� for rupture type limit states. The designultimate capacity of the strengthened beam, MU,S should thus becalculated as Mn,S.

Conclusions

This paper presents details of an experimental program which wasundertaken to investigate the fundamental behavior of steel–concrete composite beams strengthened using high modulusCFRP materials. The findings of the experimental program pro-vide comprehensive evidence that HM CFRP materials can beused to increase the elastic stiffness, yield load, and nominal ca-pacity of steel flexural members which are typically used for mosthighway bridge structures. The presence of the CFRP helps toreduce the residual deflection due to overloading conditionswhich can help reduce or eliminate the need for repair or replace-ment of a structure. The tested strengthened beams where able tosustain 3�106 loading cycles with a 20% increase of the simu-lated live load level. The beams exhibited similar performance toa control beam which was tested at a lower loading range. Fur-ther, using thicker adhesive and a silane adhesion promoter didnot appear to affect the fatigue behavior of the strengthening sys-tem. Based on the measured strain profiles of the five strength-ened beams which were investigated in the shear-lag study, theeffect of shear lag between the steel beam and the CFRP materialsis minimal.

An analytical model is also presented which is based on a
moment–curvature analysis and satisfies the conditions of equilib-


rium and compatibility. The model accurately predicted the load–deflection response, the nominal capacity and the elastic stiffnessincrease of the tested beams.

Based on the findings of the research program a series of de-sign guidelines are presented which can be used to design therequired HM CFRP strengthening for a steel–concrete compositebeam. The allowable live-load increase for a strengthened beamshould satisfy three conditions. Particularly

MD + ML 0.6MY,S

�DMD + �LML MU,S

MD + ML Mn,U

The findings of this research demonstrate that externally bondedHM CFRP materials represent an effective strengthening systemfor steel–concrete composite highway bridge girders.

Acknowledgments

The writers would like to acknowledge the support provided bythe National Science Foundation �NSF� Industry/University Co-operative Research Center �I/UCRC� for the Repair of Buildingsand Bridges with Composites �RB2C� and the support providedby Mitsubishi Chemical FP America Inc.

Notation

The following symbols are used in this paper:CE � environmental reduction factor;fc � concrete stress;fc� � peak concrete strength;

fFRP,u � design strength of FRP material;

fFRP,u � mean nominal strength of FRP as reported bymanufacturer;

k � postpeak decay factor;MD � moment due to applied dead load;ML � moment due to applied live load;

Mn,S � nominal moment capacity of a strengthened section;Mn,U � nominal moment capacity of an unstrengthened

section;MU,S � factored ultimate moment of a strengthened section;MU,U � factored ultimate moment of an unstrengthened

section;MY,S � yield moment of a strengthened section;MY,U � yield moment of an unstrengthened section;

n � curve fitting factor;Pmax � maximum load in a fatigue cycle;Pmin � minimum load in a fatigue cycle;

ta � adhesive thickness;�D � dead load factor;�P � fatigue load range;

� � strain;�L � live load factor;�c� � concrete strain corresponding to peak concrete

stress;�cu � ultimate concrete strain;

�FRP,u � design failure strain of FRP material;�p � steel proportional limit strain;
�y � steel yield strain;
MBER/DECEMBER 2007


� � reinforcement ratio of FRP;� � standard deviation; and � strength reduction factor.

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