effect of bond degradation on fire resistance of frp-strengthened reinforced concrete beams
TRANSCRIPT
Composites: Part B 42 (2011) 226–237
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Composites: Part B
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Effect of bond degradation on fire resistance of FRP-strengthened reinforcedconcrete beams
A. Ahmed, V.K.R. Kodur ⇑Department of Civil and Environmental Engineering, 3546 Engineering Building, Michigan State University, East Lansing, MI 48824-1226, United States
a r t i c l e i n f o a b s t r a c t
Article history:Received 7 May 2010Received in revised form 27 September 2010Accepted 3 November 2010Available online 17 November 2010
Keywords:B. DebondingB. DelaminationB. Fiber/matrix bondC. Numerical analysisFRP-strengthened concrete beams
1359-8368/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.compositesb.2010.11.004
⇑ Corresponding author. Tel.: +1 517 353 9813; faxE-mail address: [email protected] (V.K.R. Kodur)
FRP-strengthened reinforced concrete (RC) members experience significant loss of strength and stiffnessproperties when exposed to fire. At elevated temperatures, the rate of loss of such properties is influencedconsiderably by the bond degradation at the FRP–concrete interface. This paper presents a numericalapproach for modeling the bond degradation in fire exposed FRP-strengthened RC beams. The numericalprocedure is incorporated into a macroscopic finite element model which is capable of accounting hightemperature material properties, different fire scenarios, and failure limit states in evaluating fireresponse of FRP-strengthened RC beams. The validity of the model is established by comparing predic-tions from the program with data from full scale fire resistance tests on FRP-strengthened RC beams.The validated model is applied to evaluate the effect of bond degradation on fire response of FRP-strengthened beams. Results from the analysis indicate that significant bond degradation occurs closeto glass transition temperature of the adhesive leading to initiation of FRP delamination. The time atwhich bond degradation occurs depend on the fire insulation thickness and glass transition temperatureof the adhesive. However, variation of adhesive thickness does not significantly influence fire resistanceof FRP-strengthened RC beams.
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1. Introduction
In recent years, fiber reinforced polymers (FRP) are findingincreasing applications in repair, rehabilitation and strengtheningof reinforced concrete (RC) structural members. The increased loadcarrying capacity of such FRP-strengthened structures primarilydepends on the effectiveness of bond between FRP and concretesubstrate that is highly influenced by the properties of adhesive[1]. At room temperature, the effect of bond characteristics ondebonding failure of FRP-strengthened RC beams has been wellstudied in the literature. Based on these studies, bond–slip modelshave been proposed to account for load–slip at ambient conditions[2–9]. When FRP-strengthened members are exposed to fire, bondat FRP–concrete interface degrades due to increasing temperature.The term ‘‘FRP–concrete interface’’ in this paper, refers to adhesiveadjacent to concrete substrate that bonds FRP with concrete andany deterioration in adhesive properties resulting from tempera-ture, leads to relative slip between FRP and concrete substrate. Clo-ser to glass transition temperature (Tg), the thermo-mechanicalproperties (strength and stiffness) of adhesive degrade consider-ably and this initiates debonding of FRP. Previous studies clearlyshow that the bonding material (adhesive) soften at temperatures
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close to Tg and this leads to significant reduction in tensile strengthand elastic modulus as illustrated in Fig. 1 [10]. Gluguru reported a20% reduction in shear strength for high temperature epoxy and a70% for general purpose epoxy, when the temperature reachesabout 80 �C [11].
The bond at FRP–concrete interface is influenced by a number offactors such as type of FRP reinforcement, type of adhesive and itsthickness, compressive strength of concrete, moisture, surfacepreparation (roughness), workmanship, and temperature level[12]. While the effect of many of these factors have been studiedin the literature [4,13–15], there is little information on the influ-ence of temperature on bond degradation. This bond at interfaceis critical for transfer of forces from concrete to FRP. When thetemperatures of FRP/adhesive reaches Tg, bond properties (shearand bond strength) of adhesive deteriorate considerably and thisintroduces slip at the interface. This slip reduces the ability ofadhesive to transfer forces efficiently, ultimately leading to deb-onding of FRP composite as illustrated schematically for an FRP-strengthened RC beam in Fig. 2. Previous research has indicatedthat Tg is likely to be a critical factor in the event of fire [12].Therefore, load carrying capacity of FRP-strengthened structuralmembers under fire conditions is primarily influenced by ther-mo-mechanical properties (mainly Tg) of the adhesive.
Guidelines for design of FRP-strengthened RC structures atroom temperature are available in codes and standards. However,
Fig. 1. Schematic sketch for variation of elastic modulus and tensile strength ofadhesive [10].
Fig. 2. Schematic sketch showing debonding of FRP at elevated temperature (a)beam elevation (b) development of shear stresses at interface of FRP–concrete (c)slip at the interface (d) debonding at the end of FRP reinforcement.
A. Ahmed, V.K.R. Kodur / Composites: Part B 42 (2011) 226–237 227
there are no specific guidelines for design under fire conditions. Asan example, ACI 440.2R-08 [16] guidelines assumes no contribu-tion from FRP to the load carrying capacity of strengthened mem-bers in the event of fire. Most of the previous research studies onfire resistance of FRP-strengthened member assumed a perfectbond up to glass transition temperature and a complete debonding,thereafter. Currently available numerical models does not accountfor temperature induced bond degradation in the fire resistanceanalysis. This paper presents a numerical procedure to model thetemperature induced bond degradation at FRP–concrete interface.This procedure is implemented to a macroscopic finite elementmodel that is capable of tracing the fire response of FRP-RC beams.
This model is applied to carry out parametric studies to quantifyeffect of bond on the overall fire performance of FRP-strengthenedRC beams.
2. State-of-the-art review
A large number of studies, both experimental and theoretical,have been undertaken to study bond degradation at betweenFRP–concrete interface at ambient temperature. Results from thesestudies have generated bond strength models and also quantifiedinfluence of various factors on bond strength degradation. Someof the proposed models are based on empirical relationships, whileothers take into consideration fracture mechanics principles toevaluate bond strength [17–23].
Limited studies have been conducted in the literature on theeffect of temperature on bond between FRP–concrete interface.Tadeu and Branco [24] studied the influence of temperature onbond between externally bonded steel plates and concrete by test-ing concrete specimens of 150 � 100 � 100 mm with a gluing areaof 100 mm long and 80 mm wide. The specimens were tested indouble-lap shear at five selected temperatures (20, 30, 60, 90 and120 �C). Based on these tests, authors reported significant reduc-tion in bond strength with temperature; a 90% reduction at 120 �C.
Blontrock et al. [25] conducted double-lap shear test on CFRP-strengthened concrete prisms 150 � 150 � 800 mm separated bya thin metal plate. The specimens were subjected to direct tensileload at four temperature levels of 20, 40, 55 and 70 �C. The tests con-ducted at 40 and 55 �C showed an increase in failure load by 41% and24% respectively, however, the failure load decreased by about 19%(compared to maximum load at 20 �C) at 70 �C (close to Tg).
Klamer et al. [26] investigated the influence of temperature ondebonding behavior of externally bonded CFRP through two differ-ent test setups namely: double-lap shear test and small scale threepoint bending test at five temperatures (�10, 20, 50, 60 and 75 �C).Results indicated an increase in failure load by about 10% for spec-imens tested at 50 �C. However, a further increase in temperatureto 75 �C resulted in 27% decrease in failure load. A similar trendwas not observed in three point bending test.
Klamer et al. [27] also tested four full scale FRP-strengthened RCbeams at 20, 50 and 70 �C to investigate influence of temperatureon FRP debonding mechanism. Test results indicated that the typeof failure and the failure load at room temperature was similar tothat at 50 �C, however, at 70 �C failure loads reduced considerably.Therefore, the authors concluded that the contribution of FRP tostrength capacity can be ignored when temperatures at FRP–concrete interface reach Tg.
The effect of service temperature (50, 65 and 80 �C) on bondstrength was studied by Leone et al. [28]. The test specimens(150 � 150 � 800 mm) were strengthened with CFRP and GFRPhand layup sheets and tested under double-lap shear test procedure.The experimental investigation showed a decrease in maximumbond strength for temperatures above Tg of adhesive. At 80 �C, thebond strength in CFRP and GFRP sheets, and CFRP laminate droppedby about 54%, 72% and 25% respectively. Data from these tests indi-cate that strain level along FRP reinforcement and initial transferlength for a given load increases with rise in temperature.
Wu et al. [29] studied the effect of temperature on bond behav-ior between FRP sheet and concrete. The specimens (100 �100 � 450 mm) were tested at temperature levels ranging from26 to 60 �C using ordinary and thermo-resisting epoxies. Basedon tests data, the study concluded that close to Tg, debondingfracture energy (Gf) decreases while length (Le) required to achieveeffective bond increases. It was also observed that failure load andelastic modulus decrease with temperature.
Gamage et al. [30] investigated bond characteristics ofCFRP plated concrete blocks (130 � 130 � 300 mm) at elevated
228 A. Ahmed, V.K.R. Kodur / Composites: Part B 42 (2011) 226–237
temperatures. The authors conducted two series of shear tests; firstseries of eleven specimens without any insulation, and second ser-ies of two specimens with 50 mm thick insulation. The test datashowed that bond strength is independent of bonded length ofFRP when exposed to elevated temperatures. The un-insulated testspecimens experienced loss of bond after 5–6 min of fire exposuretime that indicated the necessity for fire protection (insulation) tomaintain effective bond between FRP and concrete at elevatedtemperatures.
The experimental study conducted by Camata et al. [12] and DiTomasso et al. [31] on bond behavior at elevated temperaturesshowed degradation of bond properties at temperatures close toglass transition temperature (Tg).
A closed form solution to determine interfacial shear stressesand normal stresses for a prismatic section due to thermal expan-sion while assuming elastic behavior, was presented by Denton[32]. The results indicated peak shear stress values near to theend of the FRP plate reducing non-linearly towards the mid-spanof the beam. Numerical results also showed that for FRP plates,use of tapered end configuration significantly reduces the peakinterfacial shear stress.
The above review clearly illustrates that bond degradation oc-curs in FRP-strengthened concrete members at high temperatures.Most of these studies were conducted on small scale test speci-mens and data on full scale FRP-strengthened members is limited.The state-of-the-art review also indicates that bond at FRP–con-crete interface is a weak link at higher temperatures since concreteand steel properties do not degrade much up to 400 �C [33].
3. Evaluating strain (eslip) due to bond–slip
In FRP-strengthened RC members, the binding material (adhe-sive) provides load path for transfer of stresses from concrete sub-strate to FRP reinforcement. At temperatures beyond Tg, bondproperties (shear and bond strength) deteriorate considerablyand this introduces a slip at bond interface. Due to this bond–slip,adhesive loses its ability to effectively transfer forces between con-crete and FRP and this result in FRP developing only partial tensilestresses as compared to a perfect bond case where full stresses inFRP can effectively be utilized. With increasing slip, the bond dete-
Fig. 3. Development of shear stresses and
riorates considerably and ultimately leads to debonding of FRP.Thus, bond degradation with temperature is to be properlyaccounted for reliable assessment of fire resistance in FRP-strengthened RC members.
In FRP-strengthened members, FRP terminates at a distancefrom the support. Concentration of shear stresses, which mainlycontribute in transfer of forces from concrete to FRP, is substantialnear edges of FRP reinforcement. Previous studies have shown thatthis high shear stress concentration is a major cause of FRP deb-onding. Fig. 3 schematically shows development of shear stressesin a beam segment of FRP-strengthened RC beam and relatedbond–slip at FRP–concrete interface. Thus, variation of these shearstresses with temperature can be used to derive an expression forcomputing bond–slip at FRP–concrete interface. This expressionwill account for changing material properties of adhesive (shearstiffness) with temperature. The assumptions made in deriving thisexpression are; shear stresses are invariant across adhesive thick-ness, stress distribution is independent of flexural cracks in con-crete, and curvature at beam soffit and FRP is to be the same.The beam is idealized into a number of segments along its length.For a small elemental length ‘‘dx’’ of the adhesive (see Fig. 3c), dis-placement (du) due to slip is given by:
du ¼ sG
tg ð1Þ
where s is the shear stress, G is the shear modulus and tg is adhesivethickness.
For each beam segment i, average shear stress si at the FRP–concrete interface can be expressed as (refer Fig. 3):
si ¼Pfrpðiþ1Þ � PfrpðiÞ
Li � bð2Þ
where Pfrp(i) is force in FRP reinforcement for segment i, Li is lengthof segment i, and b is the width of the beam.
With increasing temperature due to fire, the adhesive softensand experiences a significant reduction in its shear modulus (G).This softening effect results in a relative slip (dslip) between FRPcomposite and concrete. Slip in a segment i can be calculated as(refer to Fig. 3c):
ipðiÞ
¼ ci
� tg
ð3
bond–slip in a beam segment.
dsl
Þ
A. Ahmed, V.K.R. Kodur / Composites: Part B 42 (2011) 226–237 229
where tg is adhesive thickness and ci is the shear strain in segment igiven by:
ci ¼si
Gð4Þ
Substituting ci in Eq. (3), relative slip (dslip) in a beam segmentcan be expressed as:
dslipðiÞ ¼Pfrpðiþ1Þ � PfrpðiÞ
Li � b� 1
G� tg ð5Þ
Knowing dslip, the relative strain due to slip can be established as:
eslipðiÞ ¼change in length
original segment length¼
dslipðiÞ
Li
¼Pfrpðiþ1Þ � PfrpðiÞ
L2i � b
� 1G� tg ð6Þ
In Eq. (6), bond–slip (eslip) depends on shear modulus of adhe-sive (that decreases with temperature) as well as force in FRP (Pfrp)which in turn depends on temperature, curvature and strain in FRP.The bond–slip (eslip) in each beam segment can be calculated at anyfire exposure time using Eq. (6). The variation of bond–slip is afunction of distance from FRP plate ends. As schematically shownin Fig. 4, peak bond–slip occurs near FRP plate end and varies expo-nentially towards center of the beam. The beam segment with peakbond–slip represents critical segment of the FRP-strengthenedbeam since delamination of FRP initiates at this segment. For sim-plification, bond–slip evaluated in critical segment can be assumedconsistent in all beam segments, for a given time step.
Under fire conditions, FRP only develops partial tensile strengthdue to bond–slip. Therefore, in computing effective mechanicalstrain in FRP, strain due to bond–slip (eslip) is to be subtracted fromthe total strain. This effective mechanical strain, which takes intoconsideration bond degradation, can be used to calculate stressand tensile force in FRP. The effect of temperature induced bond–slip is significant when the temperature at FRP–concrete interfaceexceeds Tg.
Fig. 4. Schematic interfac
4. Numerical model
The above approach to account for bond–slip has been incorpo-rated into a fire resistance model, which was initially developed toevaluate fire response of FRP-strengthened RC beams by assuminga perfect between FRP and concrete [34]. This fire resistance modeltakes into account high temperature properties of constitutivematerials to generate moment–curvature (M � j) relationshipsfor different beam segments at various time steps. These timedependant M � j relationships are utilized to trace the responseof FRP-strengthened RC beam in the entire range up to collapse un-der fire conditions.
In the analysis, the total fire exposure time is divided into num-ber of time steps and at each time step, response of the beam istraced through the following steps:
� Establishing temperatures due to fire.� Conducting heat transfer analysis to determine temperature
distribution in segmental cross section.� Calculating the slip (eslip) at the interface of FRP and concrete.� Generating moment curvature (M � j) relationships for each
beam segment at various time steps and performing beam anal-ysis to compute internal forces and deflections in the FRP-strengthened RC beam.
The beam is idealized by dividing it into a number of segmentsalong its length (refer to Fig. 3b) and the mid-section of each seg-ment is assumed to represent the overall behavior of the segment.This mid-section is further discretized into a number of elements(see Fig. 4b). A finer mesh is used for insulation (3 � 3 mm) andFRP (6 � 3 mm) since these elements are in close proximity to firezone and are also highly sensitive to temperature rise. In the mod-el, the beam is assumed to be exposed to fire from three sideswhile ambient conditions are assumed to prevail on the top sideto represent the presence of slab. Fire temperatures are establishedfrom known time–temperature curves for standard or any other
ial shear stress distribution.
230 A. Ahmed, V.K.R. Kodur / Composites: Part B 42 (2011) 226–237
specified design fire scenario. Then, at each time step, temperaturedistribution in the beam cross section is established through ther-mal analysis utilizing high temperature thermal properties of con-stitutive materials. The procedure for undertaking thermalanalysis, including governing heat transfer equations, is given inReference [35].
The computed cross sectional temperatures form input tostrength analysis wherein time dependant M � j relationshipsare generated for each beam segment. Under fire conditions, eachelement of concrete, steel and FRP are subjected to different strainsand all these strains have to be included to assess effectivemechanical strain. At a given fire exposure time, the mechanicalstrains are computed as:
ecmec ¼ ec
t � ecth � ec
cr � ectr ðfor concreteÞ ð7Þ
esmec ¼ es
t � esth � es
cr ðfor steelÞ ð8Þ
efrpmec ¼ efrp
t � efrpth � efrp
cr þ ebi þ eslip ðfor FRPÞ ð9Þ
where et = total strain, eth = thermal strain, emec = mechanical strain,ecr = creep strain, etr = transient strain, ebi = initial strain at the soffitof the beam at the time of retrofitting with FRP and eslip = slip at theinterface of FRP and concrete. The superscripts ’c’, ’s’ and ’frp’ repre-sents concrete, steel rebar and FRP respectively.
In Eqs. (7)–(9), at a time step, a total strain (et) in each elementof concrete, FRP and rebar can be computed for an assumed value
Fig. 5. Discretization of beam for analysis and
of strain at top most fiber in concrete (ec) and curvature (j) by fol-lowing expression (see Fig. 5a):
et ¼ ec þ jy ð10Þ
where et = total strain, ec = strain in top most fiber in concrete,j = curvature and y = distance from uppermost fiber in concrete tocenter of element
In Eqs. (7)–(9), creep strains for both concrete and steel, andtransient strain in concrete, which depend on time, temperatureand stress levels, are computed based on the models proposed byHarmathy [36,37], and Anderberg and Thelandersson [38], respec-tively. For FRP, creep strain is negligible and is not accounted for inthe analysis since fiber direction coincides with loading directionof the strengthened beam [39]. Initial strain (ebi) in FRP is evaluatedbased on dead loads at the time of retrofitting, while bond–slip(eslip) at the interface of FRP–concrete is computed using proposedapproach in Eq. (6).
With this approach all strains components in Eqs. (7)–(9), ex-cept mechanical strain efrp
mec
� �are known and thus efrp
mec can be eval-uated. Knowing mechanical strain, stresses in each of the concrete,steel rebar and FRP elements can be obtained through temperaturedependent stress–strain relationships for these materials. Knowingthe stresses, force in concrete, steel and FRP can be calculated.
At each time step, the computed forces are used to check forceequilibrium. As schematically shown in Fig. 5a, for an assumed to-tal strain at the top layer of concrete ðec
t Þ, curvature (j) is iterated
relationship for idealized segment.
Fig. 6. Normalized thermal conductivity of FRP and insulation as a function oftemperature.
Fig. 7. Normalized thermal capacity of FRP and insulation with varyingtemperature.
A. Ahmed, V.K.R. Kodur / Composites: Part B 42 (2011) 226–237 231
until force equilibrium is satisfied. This iterative procedure is re-peated till equilibrium, compatibility and convergence criterionare satisfied. Once these conditions are satisfied, moment and cur-vature corresponding to that strain is computed. Through this ap-proach, various points on the moment–curvature curve aregenerated for each time step.
Following the generation of M � j relationships, an iterativeprocedure described by Cambell and Kodur [40] is employed toevaluate deflections of the beam at each time step. The beam anal-ysis starts under a unit applied load using initial rigidity (EIo) andthe moment and corresponding curvature in each beam segmentis determined. The segment that has the maximum moment is se-lected as the critical (key) segment of the beam. Then, a target cur-vature in the key beam segment is selected on pre-generatedM � j curve. Utilizing unit load analysis, a scaling factor is evalu-ated by dividing the target curvature with unit load curvature inthe key segment. The unit load curvatures in all beam segmentsare scaled by multiplying them with the by this scaling factor. Aniterative procedure, illustrated in Fig. 5, is employed till conver-gence of secant rigidity within a certain tolerance is achieved. Oncetolerance is achieved, the above procedure is repeated for next as-sumed target curvature [41]. After each iteration procedure, loadrequired to attain target curvature (key segment) is computedand stored. To compute the actual curvatures and deflections inthe beam, applied load is interpolated between these stored values.
In the above procedure, stiffness matrix and the loading vectorare computed for each longitudinal segment and assembled in theform of a nonlinear global stiffness equation, and solved to com-pute deflections at that time step:
½Kg �½d� ¼ ½P� ð11Þ
where Kg = global stiffness matrix, d = nodal displacements,P = Pf + Ps where Pf = equivalent load vector due to applied loadingand Ps = equivalent nodal vector due to P � d effect.
The model generates various output parameters, such as crosssectional temperatures, stresses, strains, deflections and momentcapacity for each time increment. These parameters are checkedagainst pre-designated failure criterion, which include thermaland structural considerations. The time increment continues untilone of the limiting criteria is reached. At this time step, the beamis said to have failed. The time duration to reach this failure pointis the fire resistance of the beam.
In the model, any or all of the following limiting criteria can beapplied to evaluate failure of the FRP-strengthened RC beam:
� The moment due to applied load exceeds the strength capacityof the beam.� The temperature in reinforcing steel (tension reinforcement)
exceeds 593 �C.� The deflection of the beam exceeds L/20, where L is the length of
the beam, at any fire exposure time.� The rate of deflection exceeds the limit L2/9000d (mm/min)
where L is the length of the beam (mm); and d, effective depthof the beam (mm).� The temperature in FRP layer exceeds glass transition tempera-
ture (Tg) of FRP.
It should be noted that the user has the option to specify any (orall) of the five limit states to define failure.
4.1. High temperature material properties
For modeling the response of FRP-strengthened beams, hightemperature properties of concrete, steel, FRP, adhesive and insula-tion are required. These properties include thermal, mechanicaland deformation properties which vary as a function of tempera-
ture. In literature, there is reliable data on high temperature prop-erties of concrete and steel. However, knowledge is limited on hightemperature properties of FRP, adhesive and insulation. For con-crete and steel, the properties suggested by ASCE Manual [42]and for FRP and insulation, semi-empirical relationships suggestedby Bisby [43], have been incorporated into the model. These hightemperature relationships for thermal and mechanical are pre-sented in Appendix A. Accordingly, temperature dependantstress–strain curves for FRP are linear elastic till ultimate rupturestrain.
Figs. 6 and 7 show normalized thermal conductivity and ther-mal capacity for FRP and insulation (vermiculite–gypsum) as afunction of temperature. It can be seen that there is a considerablereduction in thermal conductivity of FRP with increasing tempera-ture. The plateau in thermal capacity of FRP in the range of 340–510 �C is due to additional heat absorbed for decomposition ofthe resin [44]. For insulation the thermal conductivity decreasesup to 200 �C, remains nearly constant till 500 �C and then increaseswith temperature. The peak for thermal capacity of insulation is atabout 100 �C (shown in Fig. 7) and is due to evaporation of trappedwater that consumes most of the heat energy.
In externally bonded FRP-strengthened RC members, mechani-cal properties of adhesive, which provides load path for transfer ofstresses between FRP and concrete substrate, degrade significantlywith temperature. The reduced stiffness of adhesive at elevatedtemperature (close to Tg) has softening effect that initiatesbond–slip. Therefore, to account for bond–slip, variation of shearmodulus (G) of adhesive with temperature is needed to computebond–slip (eslip) at FRP–concrete interface utilizing Eq. (6). Bondstress–slip curves presented by Leone et al. [28] have been in-cluded in the model. These curves provide data for variation of
Fig. 8. Variation of adhesive shear modulus versus temperature.
Table 1Summary of properties for FRP-strengthened RC beams used in the fire resistance ana
Property Beam I
Description Tested by Blontrock et al. [45]Cross Section (mm) 200 � 300Length (m) 3.15Reinforcement Top bars 2 / 10 mm
Bottom bars 2 / 16 mmf0c (N/mm2) 57.5fy (N/mm2) 591Applied total load 2 � 40.6 (kN)Concrete cover thickness (mm) 25Aggregate type SiliceousFRP type Sika carbodur S1012FRP thickness (mm) 1.2FRP ultimate tensile strength (kN/mm2) 2.8Modulus of elasticity FRP (kN/mm2) 165Rupture strain of FRP (mm/mm) 1.7%Insulation thickness (mm) 25Insulation type Promatect – H
232 A. Ahmed, V.K.R. Kodur / Composites: Part B 42 (2011) 226–237
Fig. 9. Measured and predicted temperatures at the interface of FRP–concrete andcorner rebar for Beam I.
Fig. 10. Measured and predicted deflection as a function of fire exposure time forBeam I.
shear modulus (G) with temperature. Fig. 8 shows the variation ofshear modulus as function of temperature. It can be noticed thatshear modulus reduces consistently with increasing temperatureand thus significantly influence the bond performance.
5. Model validation
The above described fire resistance model is verified by compar-ing predictions from the model with measured test data on FRP-strengthened RC beams. As highlighted in state-of-the-art reviewsection, there is limited test data that accounted for fire inducedbond degradation in FRP-strengthened RC members. The twobeams selected for validation, designated as Beams I and II, weretested by Blontrock et al. [45] and Ahmed and Kodur [46]. The geo-metric properties of the beams as well as material properties ofconcrete, steel, CFRP and insulation are given in Table 1.
Beam I is 200 � 300 mm in cross section and 3 m in span length.The beams had two 10 mm and 16 mm rebars as compression andtensile reinforcement respectively. The beam was strengthenedwith 1.2 mm thick and 100 mm wide CFRP laminates, and wasinsulated with Promatect-H type fire protection. The beam had25 mm of insulation thickness at the beam soffit, and an additional12 mm insulation thickness extending on both sides of the beamup to a height of 105 mm (measured from the soffit insulationthickness). Beam II is of 254 mm width, 406 mm depth and3.96 m span length. The flexural strength of Beam II was enhancedby installing two CFRP sheets of 2 mm thick and 203 mm widthand spray-applied with Tyfo� WR Advance Fire Protection (AFP)system. The insulation layout comprised of 25 mm at the bottom
lysis.
Be
Te253.92 /3 /52452 �54CaCF298951.025Ty
surface extending 100 mm on the two sides of the beam (refer toRef. [46]).
Both the beams were analyzed with the above describednumerical model and results from analysis are compared withmeasured test data in Figs. 9–12. For the analysis, the high temper-ature material properties as discussed above were used. Fig. 9shows the comparison of predicted and measured temperaturefor Beam I in steel reinforcement and at the interface of FRP–con-crete, respectively. A good agreement between the predicted and
am II Beam III
sted by Ahmed and Kodur [46] Typical FRP-strengthened RC beam [48]4 � 406 380 � 6106 6.713 mm 2 / 15.8 mm19 mm 4 / 25 mm
380 414
70 (kN) 60 (kN/m)40
rbonate CarbonateRP (Tyfo� SCH-41) CFRP
36 2450.8 176% 1.41%
20fo� WR AFP system Vermiculite–gypsum (VG)
Fig. 11. Measured and predicted temperatures for FRP-RC Beam II.
Fig. 12. Measured and predicted deflections for FRP-RC Beam II.
A. Ahmed, V.K.R. Kodur / Composites: Part B 42 (2011) 226–237 233
measured values can be seen in entire range of fire exposure. Pre-dicted and measured deflections at mid-span of FRP-strengthenedRC beam (Beam I) are compared in Fig. 10. Results from analysisindicate that debonding of FRP occurs at 30 min of fire exposuretime that is slightly higher than that reported by Blontrock et al.(at 26 min when the temperature at the interface was 52.1 �C i.e.,less than measured Tg = 62 �C). This variation in predictions maybe due to slight differences in bond properties used in the modelas compared to the actual properties of tested beam. In early stagesof fire exposure, the response of the beam is relatively stiff (lowerdeflections) which can be attributed to high strength and stiffnessproperties of bonded FRP. When the temperature at FRP–concreteinterface exceeds Tg, a slight jump in the time–deflection curve canbe observed that indicates debonding of FRP. After FRP debonds,the beam experience high magnitude of stresses as compared toan un-strengthened RC beam and this result in an increase indeflection rate with early strength failure (reduced fire resistance)as shown in Fig. 10. The deflection predicted by the model beforeand after composite action between FRP and concrete was lost,matches closely with measured test data.
Fig. 11 provides a comparison of temperatures at FRP/concrete(FRP/C) and FRP/insulation (FRP/insulation) interfaces, and at threedifferent locations (TC5, TC6 and TC9) in the beam cross section forBeam II [46]. TC5 represent temperature in compression reinforce-ment, TC6 represent corner rebar temperature (flexural reinforce-ment) while TC9 is middepth of beam cross section (203 mm), asshown in Fig. 11a. The model predicts temperature fairly well incompression and flexural reinforcement as well as at the middepthof the beam cross section (refer to Fig. 11a). For first 35 min of fireexposure time, the predicted temperature at FRP/insulation andFRP/concrete interfaces matches well with the measured data, as
shown in Fig. 11b. Beyond this point, the model predictions doesnot match well with measured temperatures since a portion ofinsulation fell off when FRP delaminated around 38 min and themodel could not account for falling-off of insulation [46]. The pre-dicted and measured mid-span deflection of FRP-RC beam (BeamII) is compared in Fig. 12. There is a good agreement betweenmeasured and predicted deflections for the entire duration of thetest. Compared to measured time of FRP debonding which isaround 20 min, the model predicts it to be about 25 min. This var-iation can be attributed to the discrepancy between measured andpredicted temperatures at interface of FRP as discussed above.Overall, the model provides reasonable estimates of temperatureat different locations of beam cross section and deflections matchfairly well with measured data.
The above comparison indicate that the model is capable of trac-ing overall thermal and structural response of FRP-strengthenedbeams, including the effect of fire induced bond degradation on fireresistance.
6. Effect of bond degradation on fire resistance
To illustrate the effect of bond degradation at FRP–concreteinterface on fire response, a case study has been carried out on aFRP-strengthened RC beam, designated as Beam III. The analysiswas carried out for three cases namely; with perfect bond, withtemperature induced bond degradation and with a plain RC beam(with and without externally applied insulation). The properties ofthe beam used in the analysis are summarized in Table 1. The RCbeam is strengthened with 2 mm thick CFRP laminate and has20 mm thick insulation at the beam soffit extending on two sidesof the beam up to 105 mm height (measured from the soffit insu-lation thickness). The beam is analyzed under ASTM E119 standardfire exposure. For structural analysis, the beam is loaded with 60kN/mm (52% load ratio, which is defined as the ratio of appliedloading at the time of fire to capacity at room temperature). Theanalysis is carried out using the above described model and fireresistance is evaluated based on four failure criteria as describedabove. The results are presented in Figs. 13–19.
Fig. 13 shows a comparison of time–deflection response for twocases of FRP-strengthened RC beams, namely; with a perfect bond,with temperature induced bond–slip, and two cases of un-strength-ened RC beams, namely with and without externally applied fireprotection. In early stages of fire exposure, the response of bothstrengthened beams (with and without accounting for bonddegradation) is stiffer as compared to un-strengthened RC beamdue to high strength and stiffness properties provided by FRPcomposite. For the un-strengthened RC beam, the rate of deflectionis much higher since mechanical properties of concrete and steel
Fig. 13. Deflection of beams as function of fire exposure time.
Fig. 14. Ultimate tensile strength of CFRP as a function of temperature.
Fig. 15. Temperature variation at the interface of FRP–concrete interface as afunction of fire exposure time.
Fig. 16. Moment capacity of FRP-strengthened and RC beam as function of fireexposure time.
Fig. 17. Variation of interfacial shear stress as a function of fire exposure time.
Fig. 18. Slip distribution for mid-span of the beam as a function of fire exposuretime.
234 A. Ahmed, V.K.R. Kodur / Composites: Part B 42 (2011) 226–237
degrade faster in the absence of any external fire protection. Forstrengthened beam with a perfect bond, the response of the beamis stiffer for entire duration of fire exposure as compared to theFRP-RC beam that accounts for bond degradation. This is becauseoverall behavior of the beam (deflection) primarily depends on hightemperature properties of FRP. From Fig. 14, which illustrates thevariation of tensile strength of FRP with temperature, it can be seenthat FRP strength reduces significantly when the temperature rangeis beyond 300–400 �C. Therefore, the strength and stiffness proper-ties of FRP are not much affected for the duration of fire exposuretime since insulation works efficiently in keeping FRP temperatures
sufficiently low. This results in relatively low deflections in FRP-RCbeam with a perfect bond. This analysis also illustrates thatbehavior of the FRP-strengthened RC beam predicted with a perfectbond is not realistic.
For the case of FRP-strengthened beam, where slip is accountedfor in the analysis, it can be noticed from Fig. 13 that debonding ofFRP occurred at around 40 min. This can be attributed to the loss ofbond when the temperature reaches glass transition temperatureof the adhesive (Tg of adhesive is 81 �C). An examining of resultsfrom thermal analysis indicated that temperature at the interface
Fig. 19. Effect of adhesive thickness on slip at FRP–concrete interface as function offire exposure time.
A. Ahmed, V.K.R. Kodur / Composites: Part B 42 (2011) 226–237 235
of FRP–concrete (Tfrp–concrete) reached 83 �C at about 40 min (seeFig. 15). It can be seen from the results presented in Fig. 13 thatthe effect of slip starts around 25 min into fire exposureðTfrp—concrete was around 46 �CÞ and full debonding occurred around40 min when temperature at the bond interface exceeds Tg. At thisstage, stiffness of the beam decreases significantly, leading to in-crease in deflections at a faster rate. However, rate of increase indeflection in this FRP-strengthened RC beam and un-strengthenedinsulated RC beam is much slower than that in RC beam (no insu-lation) which is mainly due to beneficial effect of insulation thatslows the temperature rise in steel reinforcement leading to aslower stiffness degradation.
For initial 20–30 min of fire exposure, the behavior of un-strengthened insulated RC beam is similar to that of RC beam withno external fire protection. This is because in absence of anystrengthening in these beams, flexural steel reinforcement thatmainly contribute to moment capacity, maintains its full strengthdue to slower rebar temperature increase resulting from effectiveprotection provided by the concrete cover. In later stages withincreasing temperatures, fire insulation continues to protect theun-strengthened insulated RC beam, while non-insulated RC beamloses much of its strength and stiffness in the absence of externallyapplied fire protection. This leads to rapid increase in deflections inun-insulated RC beam, as shown in Fig. 13. It can also be noticedthat after FRP fully debonds, the deflections in FRP-strengthenedRC beam and insulated un-strengthened RC beam closely match.This is because, after debonding, FRP does not contribute towardscapacity of the beam and the steel rebars are the one that carrytensile forces. Thus, FRP-strengthened RC beam behaves similarto un-strengthened insulated RC beam.
Effect of slip on strength of FRP-strengthened RC beams isillustrated in Fig. 16 where the variation of moment capacity isplotted as a function of time for two cases of the FRP-strengthenedRC beam. In both cases, the behavior of the beams is identical forearly stages of fire exposure (up to 20 min) where there is slight in-crease in moment capacity of the beams followed by reduction. Atroom temperature, the behavior of an externally bonded FRP-strengthened beam is stiffer due to applied FRP reinforcementand this result in a non uniform distribution of curvature alongthe beam length for a given applied loading (minimal towardsthe supports). Therefore, full capacity of FRP reinforcement atbeam soffit is not utilized. With increasing fire temperatures, con-crete on two sides of the beam (upper zone) which is directlyexposed to heat flux in absence of any fire protection, starts to loseits strength and stiffness and this introduces more ductility in thebeam (curvature increases with time). At this stage, the strain dis-tribution along FRP reinforcement is more uniform. This uniformstrain distribution results in an increase in tensile force in FRP
which leads to a slight increase in moment capacity. However,with further increasing temperature at FRP–concrete interface,properties of FRP and the adhesive starts to degrade and this re-duces the moment capacity of the FRP-strengthened beam.
The adhesive loses its strength and stiffness with temperature,and composite action between FRP and concrete is lost when thetemperature approaches glass transition temperature. At thispoint, results show an abrupt decrease in the moment capacityof FRP-strengthened beam that accounts for bond degradation.However, for FRP-strengthened beam with a perfect bond, themoment capacity of the beam decreases almost linearly sincestrength and stiffness of FRP degrade with temperature.
The variation of interfacial shear stress and strain (bond–slip)distribution over half the span of the beam for various fire exposuretimes is presented in Figs. 17 and 18. It can be noticed that the peakinterfacial shear stress and strain (eslip) occurs in the vicinity of FRPtermination zones (edges) and are relatively more uniformly distrib-uted in portions away from plate ends. As expected, shear stressespredicted at the FRP end are zero and matches the free surface stresscondition. As the temperature at interface increases with fire expo-sure time, the maximum interfacial shear stress and correspondingstrain (eslip) also increase towards plate end. These increasing shearstresses contribute to debonding of FRP when its magnitude exceedsdecreasing shear capacity of the adhesive with temperature. Also,with increase in temperature, strain distribution along bondedlength of FRP becomes more uniform which can be attributed toreduction in stiffness of the adhesive with temperature. As the tem-perature reaches close to glass transition temperature, magnitude ofpeak strains increases significantly in FRP end zones just prior to FRPdelamination as shown in the Fig. 18. These trends in shear stress andstrains (eslip) distribution predicted by the model closely follow thetrends from test results conducted by Denton, and Klamer et al.[32,47].
From the above analysis, it can be concluded that the strengthand stiffness of the adhesive reduces considerably at temperaturesclose to glass transition temperature. This results in peak shearstress and strain (eslip) concentration near the end of FRP compositethat ultimately contribute to initiation of FRP debonding.
7. Effect of adhesive thickness on bond degradation
To study the effect of adhesive thickness on temperature in-duced debonding of FRP, an FRP-strengthened RC beam was ana-lyzed for varying thickness of adhesive from 1 to 4 mm. Thebeam had same characteristics as that of Beam III. Fig. 19 showsthe deflection–time curves for the four cases of insulation thick-nesses and for the case of fully bonded FRP beam. Results fromthe analysis indicate that up to first 20 min of fire exposure, thereis no noticeable effect of adhesive thickness on time–deflection re-sponse. Beyond 20 min when debonding starts to occur, insulationthickness has minor influence on the deflections. For an increasedadhesive thickness, bond–slip starts to occur in an earlier fire expo-sure time and as a consequence, the beam deforms slightly more.However, irrespective of adhesive thickness, beam experiencessimilar deflection after debonding of FRP. Therefore, adhesive layerthickness does not have significant effect on bond degradation andfire resistance of FRP-strengthened RC beam.
8. Effect of insulation thickness on bond degradation
From above study, it clear that the bond degradation is a functionof temperature at the FRP–concrete interface. The interface temper-ature depends on the insulation thickness. To investigate effect ofinsulation schemes on bond degradation of FRP-strengthened RCbeams, beam designated as Beam III, has been analyzed with
Fig. 20. Effect of insulation thickness on time to reach Tg.
236 A. Ahmed, V.K.R. Kodur / Composites: Part B 42 (2011) 226–237
varying insulation thicknesses. The dimensions and material prop-erties of the beams are tabulated in Table 1. The beam (Beam III)is provided with supplement insulation of varying thicknesses andconfiguration schemes. On the sides of the beam, the insulationthickness (20 mm) and application depth (105 mm) is kept consis-tent. However, insulation thickness at the beam soffit was variedto be 15, 25, 40, and 50 mm, respectively. The analysis was carriedout by exposing the beams to the standard ASTM E119 fire fromthree sides. The applied load ratio on the beam was kept constantat 52% for all the cases. Time to reach glass transition temperature(Tg) of the adhesive was determined.
Fig. 20 shows effect of insulation thickness on time to reachglass transition temperature of the adhesive. As expected, time toreach Tg increases with increasing insulation thickness. An increasein insulation thickness from 15 to 40 mm enhances time to reachTg by about 70 min. This can be attributed to the low thermal con-ductivity of the fire insulation that helps to keep temperatures lowat the FRP–concrete interface. This study shows that for FRP-strengthened structural members, where reaching Tg is criticalfor structural performance, provision of external fire protectionof appropriate thickness is necessary. Numerical models, like theone discussed in this paper, will help practitioners to arrive atoptimum fire insulation scheme for a given fire resistanceapplication.
9. Conclusions
Based on the information presented, the following conclusionscan be drawn:
� FRP-strengthened beams experience significant degradation inmoment capacity and stiffness when the temperature at FRP–concrete interface exceeds glass transition temperature.� FRP-strengthened RC beam protected with insulation, attains
lower deflection under fire conditions as compared to an un-strengthened RC beam, due to beneficial effect of external insu-lation that slows the temperature rise and strength loss in steelreinforcement.� Adhesive thickness does not have significant influence on bond
properties and thus the fire resistance of FRP-strengthened RCbeam is not influenced by adhesive thickness.� In fire design of FRP-strengthened RC beams, it is conservative
to assume that debonding of FRP occurs at Tg. An insulatedFRP-strengthened RC beam even after debonding exhibits betterfire performance (higher strength capacity, fire resistance andlower deflections) than an un-strengthened RC beam.
� In computing moment capacity of a fire exposed insulated FRP-strengthened RC beam, a perfect bond can be assumed till tem-perature at FRP–concrete interface (adhesive) reaches Tg.Beyond Tg, FRP contribution can be taken as zero towards themoment capacity.
Acknowledgments
The research presented in this paper is supported by the Na-tional Science Foundation (Grant No. CMMI 0855820) and Michi-gan State University through Strategic Partnership Grant (AwardNo. SPG 71-4434). Any opinions, findings, and conclusions or rec-ommendations expressed in this paper are those of the authorsand do not necessarily reflect the views of the sponsors.
Appendix A
High temperature properties of carbon/epoxy (CFRP) [43].Thermal conductivity (kw,T).
Temperature range (Tw) is �C
Thermal conductivity (kw,T)in W/m�C0 6 Tw 6 500
kw;T ¼ 1:4þ �1:1500 � Tw500 6 Tw 6 650
kw;T ¼ 1:4þ �0:1150 � ðTw � 500ÞTw P 650
kw,T = 0.2Specific heat (Cw,T).
Temperature range (Tw) is �C
Specific heat (Cw,T) is kJ/kg �C0 6 Tw 6 325
Cw;T ¼ 1:25þ 0:95325 � ðTwÞ325 6 Tw 6 343
Cw;T ¼ 2:2þ 2:818 � ðTw � 325Þ343 6 Tw 6 510
Cw;T ¼ 5:0þ �0:15167 � ðTw � 343Þ510 6 Tw 6 538
Cw;T ¼ 4:85þ �3:5928 � ðTw � 510Þ538 6 Tw 6 3316
Cw;T ¼ 1:265þ 1:3852778 � ðTw � 538ÞTw P 3316
Cw,T = 0Density (qw,T).
Temperature range (Tw) is �C
Density (qw,T)is g/cm30 6 Tw 6 510
qw,T = 1.6 510 6 Tw 6 538 qw;T ¼ 1:6þ �0:3528 � ðTw � 510Þ
538 6 Tw 6 1200 qw,T = 1.25Tensile strength (fcom,T) in MPa.
fcom;T ¼ fcom1� ar
2tanh½�brðTw � crÞ� þ
1þ ar
2
� �
Elastic Modulus, ðEcom;TÞ in MPa.
Ecom;T ¼ Ecom1� aE
2tanh½�bEðTw � cEÞ� þ
1þ aE
2
� �
where ar ¼ 0:1; br ¼ 5:83e� 3; cr ¼ 339:54; aE ¼ 0:05;bE ¼ 8:68e� 3; cE ¼ 367:41
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