Fibre reinforced polymer composite bars for thestructural concrete slabs of a Public Works andGovernment Services Canada parking garage

Brahim Benmokrane, Ehab El-Salakawy, Zoubir Cherrak, and Allan Wiseman

Abstract: Public Works and Government Services Canada (PWGSC) is currently undertaking the reconstruction of theinterior structural slabs of the Laurier–Taché parking garage (Hull, Quebec). An agreement between PWGSC and theUniversité de Sherbrooke was reached to use fibre reinforced polymer (FRP) reinforcement technology in some demon-stration areas of the Laurier–Taché parking garage. Based on this agreement, three different designs using carbon andglass FRP bars were carried out in collaboration with the project consultant. These designs were made according toCAN/CSA-S806-02, Design and Construction of Building Components with Fibre-Reinforced-Polymers. To verify thedesign, it was agreed to conduct laboratory testing on full-scale slab prototypes of the proposed designs. This paperpresents the results of the experimental tests where six full-sized one-way slabs were constructed and tested. The slabswere 3100 mm long × 1000 mm wide × 150 mm deep and were tested under four-point bending. The test results alongwith a comparison to the predictions of CAN/CSA-S806-02 Code and ACI 440.1R-03 design guidelines are presented.Recommendations for design of FRP-reinforced concrete slabs are also given.

Key words: concrete slabs, parking garages, FRP bars, flexural behaviour, cracking, deflection.

Résumé : Travaux publics et Services gouvernementaux Canada (TPSGC) entreprend présentement la reconstructiondes dalles structurales intérieures du garage Laurier Taché (Hull, Québec, Canada). Une entente entre TPSGC etl’Université de Sherbrooke a été conclue permettant l’utilisation de la technologie d’armature en FRP dans certaineszones de démonstration du garage Laurier Taché. Selon cette entente, trois différentes conceptions utilisant des tigesFRP à la fibre carbone et de verre ont été effectuées en collaboration avec le consultant responsable du projet. Cesconceptions ont été réalisées conformément à la norme CAN/CSA-S806-02 « Règles de calcul et de construction descomposants contenant des polymères renforcés de fibres ». Afin de vérifier la conception, il a été décidé d’effectuerdes essais en laboratoire sur des prototypes de dalles à pleine échelle selon les conceptions proposées. Le présent ar-ticle présente les résultats des essais expérimentaux dans lesquels six dalles unidirectionnelles à pleine échelle ont étéconstruites et mises à l’épreuve. Les dalles mesuraient 3100 mm × 1000 mm × 150 mm (long. × larg. × prof.) et ontété mises à l’épreuve de flexion sous une presse à quatre points. Les résultats des essais sont présentés, de mêmequ’une comparaison avec les prévisions de la norme CAN/CSA-S806-02 et les lignes directrices de conception de lanorme ACI 440.1R-03. Des recommandations pour la conception des dalles de béton armés de tiges FRP sont égale-ment présentées.

Mots clés : dalles en béton, garage, tiges FRP, comportement en flexion, fissuration, flexion.

[Traduit par la Rédaction] Benmokrane et al. 748

Introduction

Fibre reinforced polymer (FRP) rods are used as rein-forcement for concrete structures in which the corrosion ofsteel reinforcement has typically led to significant deteriora-tion and rehabilitation needs. The noncorrosive nature of the

FRP rods is beneficial for improved durability. Thus, PublicWorks and Government Services Canada (PWGSC) decidedto use the FRP technology in the reconstruction of the inte-rior structural slabs of the Laurier–Taché parking garage.However, the relatively low modulus of FRP composites, es-pecially glass FRP (GFRP), compared with steel reduces the

Can. J. Civ. Eng. 31: 732–748 (2004) doi: 10.1139/L04-049 © 2004 NRC Canada

732

Received 1 December 2003. Revision accepted 12 May 2004. Published on the NRC Research Press Web site at http://cjce.nrc.caon 1 October 2004.

B. Benmokrane,1 E. El-Salakawy, and Z. Cherrak. Department of Civil Engineering, University of Sherbrooke, Sherbrooke, QCJ1K 2R6, Canada.A. Wiseman. Public Works and Government Services of Canada, Hull, QC, and Department of Civil Engineering, University ofSherbrooke, Sherbrooke, QC J1K 2R6, Canada.

Written discussion of this article is welcomed and will be received by the Editor until 28 February 2005.

1Corresponding author (e-mail: Brahim.Benmokrane@USherbrooke.ca).

serviceability performance of the flexural members. Havingthe same ultimate capacity, FRP-reinforced members willhave larger deflections and crack widths than steel-reinforced members. Accordingly, in most cases, service-ability requirements govern the design of FRP-reinforcedconcrete members (Matthys and Taerwe 1995; Michaluk etal. 1998; Alkhrdaji et al. 2000; El-Salakawy et al. 2003a; El-Salakawy and Benmokrane 2003).

Several codes and design guidelines for concrete struc-tures reinforced with FRP composite bars have been recentlypublished: CAN/CSA-S6-00 (CSA 2000), ISIS-M03-01(ISIS Canada 2001), ACI 440.1R-03 (ACI 2003), includingthe new Canadian code, Design and Construction of Build-ing Components with Fibre Reinforced Polymers(CAN/CSA-S806-02 (CAS 2002)). Based on these codesand design guidelines, several field applications, especiallyconcrete bridges, have been recently carried out in NorthAmerica using FRP composite bars as reinforcement for theconcrete deck slabs (Steffen et al. 2001; El-Salakawy andBenmokrane 2003; Benmokrane et al. 2003). In the con-structed bridges, different FRP reinforcement types, ratios,and configurations were used based on flexural behaviour ofthe concrete deck slab and different serviceability criteria.However, to date, no field applications for building and es-pecially parking structures have been carried out.

This paper investigates the flexural behaviour and service-ability performance of one-way concrete slabs reinforcedwith FRP composite bars (glass and carbon) and premanu-factured carbon FRP grids (CFRP), which were designed toreplace the interior structural slabs of the Laurier–Tachéparking garage (Hull, Quebec).

Laurier–Taché parking garage

The Laurier–Taché parking garage, located in Hull (Que-bec), consists of three wings, Maisonneuve Wing, Laurier–Taché East Wing, and Laurier–Taché West Wing, as shownin Fig. 1. The two newest wings have three levels, whileMaisonneuve Wing has only two levels. This garage, whichwas originally constructed in the early 1970s, is a skeletalbuilding made of reinforced concrete columns, beams, andslabs. As a result of corrosion of the steel reinforcement, thestructural concrete slabs of this parking garage suffered fromthe partial or total loss of steel reinforcement and spalling ofconcrete cover at several locations, as shown in Fig. 2. ThePWGSC decided to rehabilitate this parking garage by re-placing all structural slabs without damaging the other struc-tural elements (beams and columns). In addition, somedamaged beams and columns will be repaired. This recon-struction is being carried out in three phases over a period of3 years. Phase I includes Maisonneuve Wing (2001–2003)and is scheduled to commence in the spring of 2004. TheUniversité de Sherbrooke in collaboration with the PWGSCdesign team established a location within the garage to usethe FRP composites as embedded reinforcement for the re-construction of some designated slabs located in the firstfloor level on Laurier–Taché East Wing. The work includesthe design of structural concrete slabs reinforced with FRPbars, preparation of specifications and construction details,laboratory testing of full-scale slabs of the proposed designs,

instrumentation, and monitoring. The objectives of this pro-ject are:• to build more durable and maintenance-free concrete

structures. Building more durable long-lasting structureswill advance the commitment of the Canadian FederalGovernment to sustainability and reduction of green housegas emission

• to implement FRP reinforcing bar technology in parkinggarages

• to evaluate long-term performance of FRP under serviceand environmental conditions

• to compare the in-service behaviour of FRP with that ofsteel

• to validate and (or) improve the design codes and guide-lines

• to enhance the confidence of using FRP as concrete rein-forcement based on the real-life monitoring informationBased on the pouring sequence suggested by the project

consultant, different types of FRP composites are to be usedto reinforce the slabs between axis LT18 to LT28 and LTB toLTC (about 1000 m2) as shown in Fig. 3. The slabs betweenaxis LT28 to LT30 and LTA to LTB (about 160 m2) are to bereinforced with conventional steel as a control area. It shouldbe mentioned that based on the construction details and thefield test results of the FRP-reinforced concrete slabs, otherareas of the parking garage may be reinforced with FRPbars.

Three different designs were proposed by the researchpersonnel at the Université de Sherbrooke and approved bythe project consultant. These designs were made accordingto CAN/CSA-S413-94 (CSA 1997) for parking structuresand CAN/CSA-S806-02 (CSA 2002) for design and con-struction of building components with fibre reinforced poly-mers that include:• glass FRP bars (both top and bottom mats)• carbon FRP bars (both top and bottom mats)• glass FRP bars for top mat and carbon FRP bars for bot-

tom matIn addition, the proposed designs took into account the

concerns raised by the project design team regarding the firerating of 2 h as specified by CAN/CSA-S413-94. On page169 of the CSA S806-02 Code, it is stated that “… the fireresistance of FRP-reinforced concrete slabs depends on thecritical temperature of FRP reinforcement, the thickness ofthe concrete cover, and the type of aggregate in the concretemix. The critical temperature is defined as the temperature atwhich the reinforcement loses enough of its strength (typi-cally 50%) that the applied load can no longer be sup-ported.” Based on Figures T1 to T8 provided by the Code,for 2-h fire rating, approximately 80 mm of concrete cover isneeded (Figure T6, page 175) for the 150-mm thick slab. Incase of a fire from one side of the slab, and provided that theconcrete cover on that side of the slab is only 30 mm, theFRP reinforcement on that side will be completely lost be-fore 2 h. However, applying the aforementioned concept andassuming that the FRP reinforcement on the other side, awayfrom the fire, will be capable, by itself, of carrying thewhole applied load for more than 2 h, establishes a safe de-sign of the slab. As the concrete cover for the FRP main re-inforcement on the other side of the fire is at least 101 mm,

© 2004 NRC Canada

Benmokrane et al. 733

which is greater than the required 80 mm, the slab will havemore than 2-h fire rating.

The design calculations using carbon FRP bars and takinginto account the fire rating of 2 h are given in Appendix A. InAppendix A, in the case of fire on the top of the slab, it is as-sumed that the top reinforcement mat will be totally lost andno moment can be transferred across the supporting beams.Consequently the slab panel will be simply supported on thebeams over a span of 4.0 m, which will result in a bendingmoment of 26.58 kN·m in the bottom layer. However, in thecase of fire on the bottom side of the slab, it is assumed thatthe bottom reinforcement mat will be totally lost and a majorcrack will be developed at the middle of the slab panel. Con-sequently the slab panel will be divided into two parts. Eachis a cantilever of 2.0-m length hanging from the two adjacentpanels, which resulted in a bending moment of 43.08 kN·m inthe top layer. These developed moments can be safely carriedby a single layer of FRP reinforcement.

Figure 4 shows the carbon FRP reinforcement (carbonFRP bar No. 10) details in the Laurier–Taché parking ga-rage. The design calculations using glass FRP bars (top andbottom mats), and glass FRP bars (top mat) and carbon FRPbars (bottom mat), can be found elsewhere (El-Salakawy etal. 2003b).

Laboratory experimental program

Material propertiesThe slabs were constructed using normal-weight ready-

mixed concrete with an average targeted concrete compres-sive strength of 35 MPa similar to the one that will be usedin the field. However, the obtained 28-d compressive strength,from compressive tests that were performed on three150 mm × 300 mm cylinders from each concrete batch, var-ied between 37 and 40 MPa. The properties of the CFRP andGFRP bars and grids as well as steel bars that were used inreinforcing the slabs are listed in Table 1. Figure 5 shows aphotograph of the reinforcing bars used in the slabs.

Test prototypesA total of six full-sized one-way slab prototypes were

constructed and tested to failure. The slabs were 3100 mmlong × 1000 mm wide × 150 mm deep. The six slab proto-types included three slabs reinforced with carbon and glassFRP bars (S-CCB, S-GGB, and S-CGB), one slab with car-bon FRP rods (S-CCR), one with premanufactured carbonFRP grids (S-CCG), and one control slab reinforced withconventional steel bars. Five of these slabs were identical tothe proposed design of the structural slabs of the Laurier–

© 2004 NRC Canada

734 Can. J. Civ. Eng. Vol. 31, 2004

Fig. 1. General layout of Laurier–Taché parking garage.

Taché parking garage, whereas the remaining slab (S-CCR)represents a repair work that was done a few years ago tosome of the structural slabs of the same parking structure.

The designations of the slabs can be explained as follows.The first character, S, denotes the slab and the last characterdenotes the type of FRP bar, B for bar, G for grid, and R forrod. The second and third characters denote the type of FRPfibre, C for carbon and G for glass in the bottom and topmats, respectively. Table 2 gives full details of the reinforce-ment configuration. Also, Fig. 6 shows the dimensions andreinforcement details of the slab prototypes.

The balanced reinforcement ratio, ρfb, of a concrete sec-tion is the reinforcement ratio at which a simultaneous rup-ture of FRP bars (yielding for steel) and crushing ofconcrete occur. The FRP-reinforced test slabs were designedsuch that the actual reinforcement ratio is equal to or greaterthan the balanced reinforcement ratio, ρfb, which is given inSection 8.2.1 of ACI 440.1R-03 as

[1] ρ β εε1fb

c

fu

f cu

f cu fu

0.85= ′+

ff

EE f

© 2004 NRC Canada

Benmokrane et al. 735

Fig. 2. Corrosion of steel reinforcement in the concrete structural slabs: (a) Laurier–Taché parking garage, (b) partial and completeloss of steel reinforcement.

In the Canadian code CAN/CSA-S806-02 (Clause 8.2.1), itis specified that the FRP-reinforced concrete section shallbe over-reinforced (ρ ρf fb≥ ). As it can be seen in Table 2,all FRP-reinforced slabs satisfy this condition except slabS-CCG, reinforced with carbon grids, which was under-

reinforced. However, according to the same code(CAN/CSA S806-02, Clause 5.1.2), the reinforcement con-figuration of slab S-CCG can be accepted if proven by ex-periment that it satisfies both serviceability and strengthrequirements.

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736 Can. J. Civ. Eng. Vol. 31, 2004

Fig. 3. Reinforcement details and cross-section of the FRP-reinforced area: (a) details of FRP reinforcement, (b) cross section ofLaurier–Taché parking garage.

InstrumentationElectrical resistance strain gauges were used to measure

tensile strains in the reinforcing bars and compressive strainsin the concrete. These gauges were glued on several loca-tions across the slab width at the midspan section. Themidspan deflection was measured using two linearly varyingdisplacement transformers (LVDTs) fastened at each side ofthe slab. Two high-accuracy LVDTs (0.001 mm) were alsoinstalled at positions of first cracks to measure crack widths.A data acquisition module monitored by a computer wasused to record the readings of the strain gauges, LVDTs, andthe load cells.

Test set-up and procedureThe slabs were tested under four-point bending over a

simply supported clear span of 2500 mm and a shear span of1000 mm, as shown in Fig. 7. The load was monotonicallyapplied at a stroke-controlled rate of 2.0 mm/min to achievefailure in 30–40 min. The loading was stopped when the firsttwo cracks appeared and the initial crack widths were mea-sured with the aid of a hand-held 50× microscope, then thetwo high-accuracy LVDTs were installed to measure crackwidth electronically. During loading, the formation of crackson the sides of the slabs were also marked and recorded.

It should be noted that the slab prototypes were testedover a clear simple span of 2.5 mm while the actual struc-tural slabs of Laurier–Taché parking garage are continuouslysupported over an effective span of 3.6 m. The continuity ofthe slabs results in redistribution of the top and bottom mo-ments, especially at high loads. However, this will not affectthe flexural behaviour comparison to actual slabs, except fordeflection values, as all test results are analyzed based onthe applied moment (section analysis) at relatively low loadlevels compared with the ultimate capacity of the slabs. Thevalidation of comparison to deflection values (based onmember analysis) will be discussed in details in the follow-ing section.

Test results

Test results will be presented in terms of deflection,cracking, strains in reinforcing bars and concrete, ultimatecapacity, deformability, and mode of failure. The test resultsare analyzed and compared at the two design load levels,service (14.5 kN·m) and ultimate (20.2 kN·m), according toCAN/CSA-S413-94 Parking Structures (CSA 1997) asshown in Appendix A. The test results presented are consis-tent with previous work that was done by the authors andother researchers (El-Salakawy et al. 2003a; El-Salakawyand Benmokrane 2003; Michaluk et al. 1998).

Deflection characteristicsFigure 8 shows the midspan deflection versus applied mo-

ments for the tested slabs. For the control steel-reinforcedslab (S-ST), the load-deflection curve was trilinear withyielding plateau. For FRP-reinforced slabs, the load–deflectioncurve was bilinear. The first part up to the cracking moment(Mcr = 9.5 to 10.3 kN·m — the moment due to the ownweight of the slab, 2.7 kN·m, was not included) was similarto the control slab representing the behaviour of the un-cracked slab utilizing the gross inertia of the concrete crosssection, while the second part represents the cracked slabwith reduced inertia.

The maximum midspan deflection in an elastic membercan be expressed as (Wang and Salmon 1985)

[2] δ β= aser

c e

M lE I

2

( )

where βa is a coefficient that depends on the degree of fixityat supports, the variation of the moment of inertia along thespan, and the distribution of loading.

For the case of a continuous one-way slab with more thanthree equal spans under uniformly distributed loads, the

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Benmokrane et al. 737

Fig. 4. Area reinforced with carbon FRP bars (No. 10): (a) planview, (b) elevation view.

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738 Can. J. Civ. Eng. Vol. 31, 2004

Reinforcement type Bar No.Diameter(mm)

Area(mm2)

Modulus ofelasticity (GPa)

Tensile strength(MPa)

Ultimatestrain (%)

Bars CFRP 10 9.50 71 114 1535 1.2010 9.50 71 45 775 1.70

GFRP 16 15.90 198 45 755 1.70Carbon FRP rods 8 8.00 49 155 2800 1.40Carbon FRP grids C10 8 × 4.9 39.2 100 1200 1.55Steel 10M 11.30 100 200 fy = 465 εy = 0.2

Table 1. Properties of reinforcing bars

Fig. 5. Fibre reinforced polymer and steel reinforcement used in the tested slabs.

Strong direction Weak direction

Slab ρact (%) ρact/ρfb Top Bottom Top Bottom

S-CCB 0.49 1.49 No. 10@125 carbon bar No. 10@125 carbon bar No. 10@300 carbon bar No. 10@300 carbon barS-GGB 1.77 3.2 No. 16@100 glass bar No. 16@100 glass bar No. 10@200 glass bar No. 10@200 glass barS-CGB 0.49 1.49 No. 16@100 glass bar No. 10@125 carbon bar No. 10@200 glass bar No. 10@200 glass barS-CCR 0.42 2.53 No. 8@125 carbon rod No. 8@125 carbon rod No. 8@300 carbon rod No. 8@300 carbon rodS-CCG 0.34 0.69 (C10) 100 × 200 mm

carbon grids(C10) 100 × 200 mm

carbon gridsS-ST 0.9 0.2 No. 10M@150 steel No. 10M@150 steel No. 10M@150 steel No. 10M@150 steel

Table 2. Details of slab reinforcement.

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Benmokrane et al. 739

Fig. 6. Test specimens: (a) Slab S-GGB (Configuration 1), (b) Slab S-CCB (Configuration 2), (c) Slab S-CGB (Configuration 3),(d) Slab S-CCR (Configuration 4), (e) Slab S-CCG (Configuration 5), and (f) Slab S-ST (Configuration 6).

maximum deflection is expected to be in the first panel(span) with a zero moment at the end support. In this case,the value of βa is 1/12.16 (using the values of M+ve = 0.077wl2 and M–ve = 0.107w l2 (CPCA 1995)). Thus, the maximumdeflection of the actual slabs (span of 3.6 m) in the parkingstructure can be given by

[3] δfieldser

c e

112.16

3.6= ME I

( )( )

2

For the case of a simply supported one-way slab undertwo equal concentrated loads applying at a shear span of 0.4l(test set-up), the value of βa is 1/10.17. Thus, for the samevalue of applied moment, Mser, the maximum deflection ofthe tested slabs (span of 2.5 m) in the laboratory can begiven by

[4] δexpser

c e

110.17

.5= ME I

( )( )2 2

and

[5] δ δ δexp

2

2 field field12.16 (2.5)10.17 (3.6)

0.576= ××

=

At service load level, the allowable deflection limit by Cana-dian Code (CAN/CSA-S806-02) should not exceed

[6] δfieldspan360

3600360

10 mm≤ = =

Substituting eq. [5] into eq. [6]

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740 Can. J. Civ. Eng. Vol. 31, 2004

Fig. 7. Test set-up: (a) schematic drawing, (b) photograph.

Fig. 8. Moment-deflection relationship.

[7] δexp ≤ 0.576 × 10.0 = 5.76 mm

Thus, the allowable deflection for the laboratory-tested slabs(simply supported span of 2.5 m) is 5.76 mm. As listed inTable 3, at service load level (14.2 kN·m), the measured de-flection for the tested slabs varied between 1.90 mm (S-ST)and 4.7 mm (S-CCG), which is less than the allowable codelimits.

For the sake of comparison, at service load level, the ra-tios of the measured deflection for slabs S-CCB, S-GGB, S-CGB, S-CCR, and S-CCG reinforced with FRP compositesto that of the control slab, S-ST, reinforced with steel were1.82, 1.65, 1.78, 1.78, and 2.47, respectively.

Measured deflections at service and failure load levels aregiven in Table 3. It can be noted from Table 3 that the ratioof the measured deflections at failure to those at service loadlevel ranges between 17 and 21, which indicates the amplewarning that the FRP-reinforced slabs would give beforefailure. This will be further explained in the following sec-tion of this paper dealing with deformability.

CrackingFor all slabs crack formation was initiated at a moment,

Mcr, of 12 to 13 kN·m. The experimental values of the crack-ing moments, listed in Table 4, included the moment due tothe own weight of the slab (2.7 kN·m).

Cracks in the pure bending zone (the middle 500 mm)were vertical cracks perpendicular to the direction of themaximum principal stress induced by pure moment. Cracksoutside the pure bending zone (shear span of 1000 mm oneach side) started similarly to flexural cracks, but as the loadwas increased shear stress become more dominant and in-duced inclined cracks. Figures 9 and 10 show schematicdrawings of the crack patterns for the tested slabs at twoload stages: service and failure.

It can be noted that at service load level the number ofcracks developed in FRP-reinforced slabs was in the rangeof 6 (slab S-GGB) to 8 (slab S-CCG), while this numberwas in the range of 12 (slab S-GGB) to 16 (slab S-CGB) atfailure. In addition, the crack penetration depth and spacingat service load level were in the range of 40–80 and 175–120 mm (S-GGB and S-CCG), respectively. These valueswere 110–130 and 65–43 mm (S-GGB and S-CCG), respec-tively, at failure (see Table 4). Figure 11 shows the finalcrack patterns of the tested slabs at failure. In other words,the ratios of number of cracks, crack penetration depth, andcrack spacing at failure to those at service load level were inthe range of 2, 1.5 to 2, and 0.3 to 0.4, respectively. This is

also a good indication of the ample warning that the FRP-reinforced slabs would give before failure.

For crack width measurements, Fig. 12 shows the varia-tion of the maximum measured crack width against the ap-plied moment for the tested slabs. For slabs reinforced withFRP bars, the crack width varies linearly with the load up tofailure. The measured crack widths ranged between 0.1(S-ST) and 0.34 mm (S-CCG), which is less than the allow-able code limits of 0.5 mm (ACI 2003).

For cracking control, the new Canadian Code (CAN/CSA-S806-02) introduced a parameter, z

[8] zEE

k f d A= s

fb f c

3

The parameter z should not exceed 45 000 N/mm for interiorexposure and 38 000 N/mm for exterior exposure when FRPreinforcement is used. Table 4 gives the z values for thetested slabs based on the actual measured strains in the rein-forcing bars at service load level of 14.2 kN·m. These z val-ues ranged between 8 775 (S-ST) and 18 589 (S-CCG),which are below the allowable code limit of 38 000 N/mm.

Strains in reinforcement and concreteFigure 13 shows the measured midspan strains in rein-

forcement as well as in concrete versus the applied moment.For the five slabs reinforced with FRP bars, it can be notedthat the strains vary linearly with the increased load up tofailure and the maximum measured strains (10 400 to 11 955microstrain) were less than the ultimate strains of the FRPmaterials except for slab S-CCG (reinforced with carbonFRP grid), which failed by rupture of FRP grids (14 700microstrain). This was expected, since slab S-CCG was un-der-reinforced. The maximum measured compressive strainsin concrete at failure ranged between 3230 and 3710microstrain for all tested slabs.

As listed in Table 3, at service load level of 14.2 kN·m,the maximum measured strains in FRP bars varied between998 (S-CCB) and 1262 microstrain (S-CCG), which are lessthan 2000 microstrain.

According to ISIS Canada Design Manual (ISIS Canada2001), if the measured strain in FRP reinforcement at ser-vice load level is below 2000 microstrain, it means that theconcrete member would satisfy the serviceability limits.

Furthermore, creep-rupture is a well-known phenomenonfor FRP material that is addressed by FRP design codes andguidelines (CAN/CSA S806-02, ACI 440.1R-03) throughlimiting the stress level in FRP bars under sustained loads.

© 2004 NRC Canada

Benmokrane et al. 741

Deflection (mm)Strain in reinforcement(microstrain)

Strain in concrete(microstrain)

SlabFailure moment(kN·m) Service Failure Service Failure Service Failure

Deformabilityfactor Mode of failure

S-CCB 75 3.51 56.1 1082 10 400 486 3280 19 Crushing of concreteS-GGB 91 3.11 65.8 1020 11 955 425 3710 13 Crushing of concreteS-CGB 76 3.39 57.0 1028 10 860 522 3270 18 Crushing of concreteS-CCR 85 3.38 60.0 998 10 430 648 3300 18 Crushing of concreteS-CCG 67 4.70 79.5 1262 14 700 665 3230 14 Rupture of gridsS-ST 55 1.90 57.6 611 11 230 249 3860 N/A Steel yielding

Table 3. Summary of the test results.

According to ACI 440.1R-03, these stress limits depend onthe type of fibre used and are 0.2, 0.3, and 0.55 of ffu forglass, aramid, and carbon FRP, respectively, underunfactored sustained loads. However, in CAN/CSA S806-02, these stress limits were defined only for glass FRP bars(0.3ffu under factored sustained loads). In the case of theglass FRP-reinforced slab, the calculated stress due to thefactored sustained load of 8.97 kN·m (the sustained load isdefined by ACI 440.1R-03 as dead load + 20% of the liveload) is approximately 118 MPa (0.156ffu) in the glass FRPbars, which is well below the code allowable limits of 0.3ffu(CAN/CSA S806-02). The experimentally measured strainfor the slab reinforced with glass FRP bars, S-GGB, at aload level equal to the sustained load (Msus = 8.97 kN·m)was 655 microstrain, as shown in Fig. 13. This strain would

cause a stress equal to 72.1 MPa in the GFRP bars, which iseven less than the calculated value.

For the control slabs reinforced with steel (S-ST), a typi-cal steel-yielding plateau was obtained with a maximummeasured strain of approximately 11 230 microstrain. Aftersteel yielding, the compression strains in concrete increased(3500 microstrain), resulting in failure by concrete crushing.

Ultimate capacity and mode of failureFour slabs reinforced with FRP bars failed by the crushing

of concrete in compression, whereas the control steel-reinforced slab S-ST and the slab reinforced with carbongrids S-CCG failed by steel yielding and FRP rupture, re-spectively, followed by crushing of concrete. These resultswere expected because the two slabs S-ST and S-CCG were

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742 Can. J. Civ. Eng. Vol. 31, 2004

Cracking moment(kN·m)

Crack width(mm)

Crack depth(mm)

Crack spacing(mm)

Slab

E A

E Af f

s s Theor. Exper.*1st crackwidth (mm) Service Failure Service Failure Service Failure

z(N/mm)

S-CCB 0.50 13.6 12.0 0.16 0.24 1.63 45 120 165 60 17 504S-GGB 0.63 13.6 13.0 0.12 0.18 2.15 40 110 175 65 16 181S-CGB 0.50 13.6 12.2 0.17 0.24 1.77 50 125 170 65 16 631S-CCR 0.50 14.2 12.4 0.16 0.21 1.97 47 118 140 45 15 227S-CCG 0.30 14.2 12.8 0.22 0.34 2.21 80 130 120 43 18 589S-ST 1.00 13.6 12.7 0.06 0.10 1.54 25 120 210 70 8 775

*Taking into account the moment due to the own weight of the slab.

Table 4. Summary of cracking distribution for the tested slabs.

Fig. 9. Cracks pattern for the tested slabs at service load level. Fig. 10. Cracks pattern for the tested slabs at failure.

© 2004 NRC Canada

Benmokrane et al. 743

Fig

.11

.P

hoto

grap

hof

the

fina

lcr

ack

patt

erns

atfa

ilur

e.

under-reinforced and the remaining four slabs were over-reinforced. In addition, all slabs reinforced with FRP rein-forcement showed an increase of the ultimate carryingcapacity of 22–65% compared with the control slab, S-ST.Failure moments for the tested slabs are listed in Table 3.

DeformabilityDuctility of a reinforced concrete element provides a mea-

sure of the energy absorption capability. Ductility of con-crete members reinforced with steel bars is defined as theratio of deflection or curvature values at ultimate to those atyielding of steel. As there is no yielding point for FRP com-posite bars, a parameter for comparing the ductility behav-iour of FRP-reinforced beams with that of steel-reinforcedones has been developed by Jaeger et al. (1995); it is re-ferred to as the J-factor or deformability factor. This factorcan be defined as the ratio of energy absorption (area underthe moment–curvature curve) at ultimate strength level to theenergy absorption at service level. In other words, it is calcu-lated as the product of the ratio of the moment at ultimate,Mult, to the moment at a certain service condition, Mc, calledthe strength factor, and the ratio of the curvature at ultimate,ψult, to curvature at the same service condition, ψc, calledthe curvature factor.

[9] JMM

= ult

c

ult

c

ψψ

The service condition is defined as the upper limit of elasticbehaviour of concrete, which was taken corresponding toεc = 0.001. This approach is adopted by the Canadian High-way Bridge Design Code, Standard CAN/CSA-S6-00 (CSA2000), which requires a J-factor exceeding 4 for rectangularsections. The values of the deformability factor using theabove approach are listed in Table 3. For all tested slabs, theJ-factor is well above the CAN/CSA-S6-00 Code limit of 4(for rectangular sections). The higher the J-factor values, themore ample warning the FRP-reinforced concrete membergives before failure. In other words, the J-factor indicatesthe number of cracks and amount of deflection the FRP-reinforced concrete member will exhibit through load historyfrom service to failure conditions.

Conclusions and recommendations

Public Works and Government Services Canada has de-cided to investigate the use of FRP composite bars and gridsin reinforcing a demonstration area of the structural concreteslabs of a parking garage in Hull (Quebec). This paper pres-ents the proposed design and the laboratory test results ofslab prototypes using different FRP reinforcement types andconfigurations. Based on the experimental test results, thefollowing conclusions can be drawn:(a) The load carrying capacity of concrete slabs reinforced

with composite FRP bars (carbon and glass) was higherthan the control slab reinforced with steel (22%–65%)satisfying the same strength and serviceability require-ments. In addition, the slabs reinforced with FRP barsfailed by concrete crushing, while the control slab andthe slab reinforced with carbon grids failed by steelyielding and rupture, respectively, followed by concretecrushing.

(b) At service load level, the calculated cracking control pa-rameter, z, based on actual measured strains and themaximum measured crack width were below the allow-able limits of 38 000 N/mm and 0.5 mm, respectively(CSA 2002; ACI 2003).

(c) At service load level, the maximum measured deflec-tions for all tested slabs were below the allowable limitsof span/360 (CSA 2002).

(d) The values of the deformability factor, J, for the fiveconcrete slabs reinforced with FRP reinforcement werein the range of 14 to 19, which are more than threetimes the minimum (4 for rectangular sections) requiredby the Canadian Highway Bridge Design Code (CSA2000).

(e) The ratios of measured deflections, number of cracks,crack penetration depth, and crack spacing at failure tothose at service load level were in the range of 17 to 21,2, 1.5 to 2, and 0.3 to 0.4, respectively. This, along withthe values of the deformability factor, indicates the am-ple warning that the FRP-reinforced slabs would givebefore failure.

Test results showed that all FRP reinforcement configura-tions satisfied both serviceability and strength requirements ofthe available codes and design guidelines (CAN/CSA-S806-02 (CSA 2002); CAN/CSA-S6-00 (CSA 2000); ISIS-M03-01(ISIS Canada 2001); ACI 440.1R-03 (ACI 2003)) for concretestructures reinforced with FRP reinforcement. The proposed

© 2004 NRC Canada

744 Can. J. Civ. Eng. Vol. 31, 2004

Fig. 12. Moment – crack width relationship.

Fig. 13. Moment–strain relationship.

design configurations for the reconstruction of the structuralslabs of the Laurier–Taché parking garage can be consideredadequate. Based on this work, PWGSC is planning to incor-porate the use of FRP into sections of the structural slabs andto monitor the performance over several years.

It is worth mentioning that the slab reinforced with thepremanufactured carbon FRP grids was under-reinforced,which is not in agreement with Clause 8.2.1 of CAN/CSAS806-02 (CSA 2002). However, based on the experimentalresults, the reinforcement configuration of slab S-CCG canbe accepted (CAN/CSA S806-02, Clause 5.1.2).

Acknowledgements

The authors would like to thank David Harmer, HarmerPodolak Engineering Consultants Inc. (Ottawa, Ontario) forhis collaboration in this project. The authors would like alsoto acknowledge François Ntacorigira, technician at the CivilEngineering Department, Université de Sherbrooke for thehelp received from him during different stages of fabricationof test slabs and testing.

References

ACI. 2003. Guide for the design and construction of concrete rein-forced with FRP bars (ACI 440.1R-03). ACI Committee 440,American Concrete Institute, Farmington Hills, Mich.

Alkhrdaji, T., Ombres, L., and Nanni, A. 2000. Flexural behaviourof one-way concrete slabs reinforced with deformed GFRP bars.Proceedings of the 3rd Conference on Advanced Composite Ma-terials in Bridges and Structures, Ottawa, Ont., pp. 217–224.

Benmokrane, B., El-Salakawy, E.F., and Desgagné, G. 2003. Con-struction, testing, and monitoring of three FRP reinforced con-crete bridges in North America. Proceedings of the 6thInternational Symposium on Fibre Reinforced Polymer (FRP)Reinforcement for Concrete Structures (FRPRCS-6), NationalUniversity of Singapore, Singapore, Vol. 2, pp. 1311–1320.

CPCA. 1995. Concrete design handbook. Canadian Portland Ce-ment Association, Ottawa, Ont.

CSA. 1997. Parking structures. Standard CAN/CSA-S413-94, Ca-nadian Standards Association, Toronto, Ont.

CSA. 2000. Canadian highway bridge design code (CHBDC). Stan-dard CAN/CSA-S6-00, Canadian Standards Association, Toronto,Ont.

CSA. 2002. Design and construction of building components withfibre reinforced polymers. Standard CAN/CSA S806-02, Cana-dian Standards Association, Toronto, Ont.

El-Salakawy, E.F., and Benmokrane, B. 2003. Design and testingof a highway concrete bridge deck reinforced with glass andcarbon FRP bars. In Field applications of FRP reinforcement:case studies. American Concrete Institute, Farmington Hills, De-troit, Mich., ACI Special Publication SP-215-2, pp. 26–48.

El-Salakawy, E.F., Kassem, C., and Benmokrane, B. 2003a. Flex-ural behaviour of concrete bridge deck slabs reinforced withFRP composite bars. Proceedings of the 6th International Sym-posium on Fibre Reinforced Polymer (FRP) Reinforcement forConcrete Structures (FRPRCS-6), National University of Singa-pore, Singapore, Vol. 2, pp. 1291–1300.

El-Salakawy, E.F., Cherrak, Z., and Benmokrane, B. 2003b. FRP re-inforcing bars for concrete slabs of Laurier Taché parking garage:design and laboratory test results. Final Technical Report, Re-search contract No. EN336-020283/001/55. Submitted to PublicWorks and Government Services Canada, July. Gatineau, Que.

Jaeger, G.L., Tadros, G., and Mufti, A.A. 1995. Balanced section,ductility and deformability in concrete with FRP reinforcement. In-dustry Centre for Computer-Aided Engineering, Technical Univer-sity of Nova Scotia, Halifax, N.S. Research Report No. 2-1995.

ISIS Canada. 2001. Reinforcing concrete structures with fibre rein-forced polymers (ISIS-M03-01). The Canadian Network of Cen-tres of Excellence on Intelligent Sensing for InnovativeStructures, ISIS Canada, University of Winnipeg, Man.

Matthys, S., and Taerwe, L. 1995. Loading tests on concrete slabsreinforced with FRP grids. Proceedings of the 2nd InternationalRILEM Symposium: Non-metallic (FRP) Reinforcement for Con-crete Structures, Ghent, Belgium, August. Edited by L. Taerwe.pp. 287–297.

Michaluk, R., Rizkalla, S., Tadros, G., and Benmokrane, B. 1998.Flexural behaviour of one-way concrete slabs reinforced with fi-bre reinforced plastic reinforcements. ACI Structural Journal,95: 145–157.

Steffen, R.E., Trunfio, J.P., and Bowman, M.M. 2001. Performanceof a bridge deck reinforced with CFRP grids in Rollinsford,New Hampshire, USA. Proceedings of the FRP Composites inConstructions, Porto, Portugal, May. Edited by Figueiras et al.pp. 671–676.

Wang, C-K., and Salmon, C.G. 1985. Reinforced concrete design.4th ed. Harper & Row Publishers Inc., New York, N.Y.

List of symbols

A effective tension area of concrete surrounding the maintension reinforcement with its centroid coincides withthe reinforcement, divided by the number of bars (mm2)

db nominal diameter of the bar (mm)Ec modulus of elasticity of concrete (GPa)Ef modulus of elasticity of FRP bar (GPa)Es modulus of elasticity of steel (GPa)fc′ compressive strength of concrete (MPa)ff stress in FRP reinforcement at specified loads, calcu-

lated by elastic cracked section theory (MPa)ffu ultimate tensile strength of FRP reinforcing bars (MPa)J deformability factorIe effective moment of inertia of the beam section (mm4)kb bond-dependent coefficient

l span of the slab (m)Mc moment at a service condition such that εc = 0.001 (kN·m)

Mcr cracking moment (kN·m)Mser moment under service load conditions (kN.m)Msus moment under sustained load conditions (kN.m)Mult moment at ultimate condition (kN·m)

M+ve maximum moment in the slab between supports (kN.m)M-ve maximum moment over supports (kN.m)

w uniformly distributed load on the slab (kN/m2)z cracking control parameterβ1 a factor taken as 0.85 for concrete strength fc′ ≤ 28 MPa.

For strength >28 MPa, this factor is reduced continuouslyat a rate of 0.05 per each 7 MPa of strength in excess of28 MPa, but is not taken less than 0.65

βa coefficient depending on the degree of fixicity at supportsδ maximum midspan deflection in an elastic member (mm)

δexp maximum deflection of the experimentally tested slabsunder four-point bending set-up (mm)

δfield maximum deflection of actual continuous parking ga-rage slabs under uniformly distributed dead loads andconcentrated wheel loads (mm)

© 2004 NRC Canada

Benmokrane et al. 745

εc strain in the concreteεcu the maximum usable compressive strain in the concreteεfu ultimate tensile strain of FRP reinforcing barsρf actual reinforcement ratio calculated assuming the effec-

tive depth of the slab to be the distance between the top

of the slab and the centroid of the lower reinforcementin the main (considered) direction

ρfb reinforcement ratio at balanced strain conditionψ c curvature at a service condition such that εc = 0.001ψ ult curvature at ultimate condition

Appendix A. Design example: Design of the structural slabs of the Laurier–Taché parkinggarage using carbon FRP bars, based on CAN/CSA-S413-94 (CSA 1997) and CAN/CSA-S806-02 (CSA 2002)

Geometry and loading dataThe structural system consists of one-way slabs continuous over prestressed concrete girders:

Concrete and carbon fibre reinforced polymer material properties

Design moments in the deck slab

According to ACI 440.1R-03 (ACI 2003), the sustained load is considered as the dead load plus 20% of the live loads.Thus, the factored sustained moment, Msus, is given by

Msus = factored Md+ve + 0.2 × factored Ml

+ve = 6.20 + 0.2 × 13.86 = 8.97 kN·m

Also, the cracking moment is given by

Mf I

hcr

r g43.66 2.813

0.15= = × × × −2 2 10

© 2004 NRC Canada

746 Can. J. Civ. Eng. Vol. 31, 2004

Service dead load, wds 4.03 kN/m2

Service midspan moment (Mds+ve ) 0.077wds l2 = 0.077 × 4.03 × (4.00)2 = 4.96 kN·m

Service over support moment (Mdsve− ) 0.121wds l2 = 0.121 × 4.03 × (4.00)2 = 7.80 kN·m

Factored dead load, wd 1.25 × 4.03 = 5.04 kN/m2 (NRC, Clause 4.1.3.2),Factored midspan moment, Md

+ve 6.20 kN·m and factored over support moment, Mdve− = 9.75 kN·m

Service wheel load, Pws 11.0 kN (NBC, Table 4.1.6.10)Service midspan moment (M ls

+ve ) 0.210l Ps = 9.24 kN·mService over support moment (M ls

ve− ) 0.181l Ps = 7.96 kN·mFactored wheel load, Pw 1.5 × 11.0 = 16.50 kN (NRC, Clause 4.1.3.2),Factored midspan moment, M l

+ve 13.86 kN·m and factored over support moment, M lve− = 11.95 kN·m

The total design midspan service moment, M s+ve 4.96 + 9.24 = 14.20 kN·m (Bottom moment)

The total design over support service moment, M sve− 7.80 + 7.96 = 15.76 kN·m (Top moment)

The total design midspan factored moment, Mu+ve 6.20 + 13.86 = 20.06 kN·m (Bottom moment)

The total design over support factored moment, Muve− 9.75 + 11.95 = 21.70 kN·m (Top moment)

Slab thickness 150 mmAverage spacing between girders (span of slabs) 4.00 mWidth of concrete girders 0.60 mClear concrete cover top and bottom) 30 mmOwn weight of wearing surface 0.50 kN/m2

Uniformly distributed service live loads 2.40 kN/m2 (NBC, Table 4.1.6.3), orService wheel load 11.0 kN (NBC, Table 4.1.6.10)

Specified compressive strength of concrete, fc′ 35 MPaUltimate tensile strength, fu,ave 1535 ± 45 MPaGuaranteed tensile strength, f*fu (guaranteed) 1535 – 3 × 45 = 1400 MPaUltimate tensile strain, εfu 0.012Modulus of elasticity, Ef 115 GPaBar diameter, db 9.5 mmBar area, Af 71 mm2

where

Ibh

g0.15

m= = × = ×3 3

4 4

121

122 813 10

( ). –

and

f fr cu0.6 0.6= = =λ 35 3 55. MPa (CSA 2002, Clause 8.5.4)

Mf I

hcr

r g43.66 2.813

0.1513.75 kN m= = × × × = ⋅

−2 2 10

Ultimate limit state: Based on CSA 2002 (Section 8.4)Try No. 3 at 125 mm (568 mm2/m)

Effective depth:

d = 115 mm

α1 = 0.85 – 0.0015fc′ = 0.8

β1 = 0.97 – 0.0025fc′ = 0.88

φfAf ff = α1φc fc′ab

0.75 × 568 × (115 000 × εf) = 0.8 × 0.6 × 35 × (0.88 × c) × 1000 � c = 2916.05εf

and

c/0.0035 = 115/(0.0035 + εf) � c × (0.0035 + εf) = (0.0035 × 115)

εf = 0.010128, ff = 1164.74 MPa < 1400 MPa � the section is over-reinforced

c = 29.53 mm and a = 0.88 × 29.53 = 25.99 mm

cd=

+7

7 2000εfu

c/d = 29.53/115 = 0.257 > 7/(7 + 2000 × 0.012) = 0.226 OK

Mu = α1φc fc′ab(d – a/2) = 0.8 × 0.6 × 35 × 1000 × 25.99(115 – 25.99/2)

= 44.54 kN·m > 21.70 kN·m > 1.5Mcr = 1.5 × 13.75 = 20.62 kN·m OK

Serviceability limit state: Based on CSA 2002 (Section 8.3)

DeflectionThe total design service moment Ms

+ve = 14.20 kN·m(Bottom moment)

Cracked section properties

nEE

E

ff

f

c

f

c

4.31= =′= × =

4500

115 10

4500 35

3

and

ρf71

115 1250.494%=

×=

k p n p n p n= + −2 2f f f f f f( )

= +2(0.00494)(4.31) 0.00494(4.31)[ ]2

– . ( . ) .0 00494 4 31 0 19=

Ibd

k n A d kcr f f m= + − = ×3

3 2 2 5 4

31 2 5644 10( ) . –

Reduction coefficient for deflection βd using recom-mended value α b = 0 5.

β αd bf

s

0.5= +

= +

=E

E1

115200

1 0 7875.

( )IMM

IMM

Iecr

ag

cr

acr=

+ −

3 3

1β

Ie13.7514.20

(0.7875)(0.00028125)=

3

+ −

× −1 25644 103

13.7514.20

5( . ) = 19.28 × 10–5 m4

© 2004 NRC Canada

Benmokrane et al. 747

δ = =× ×

M lE I

ser

c e

2(14.20)(4.0)12.16 0.

2

612 16 27 10. ( ) ( )( 0001928)�

δ = 3 23. mm

Limitation l/360 = 3600/360 = 10 mm OK

CrackingThe maximum design service moment, Ms

–ve = 15.76 kN·m(Top moment)

fM

A dk

fser

f4

15.76

5.9166 0.1150.19

=−

=

× × × −−13

10 13

247 36

35

== =

.

( – )

MPa

mmcd h d

Ad b= = =2 2 35 1000

88750 2c

Number of barsmm

( )( )

β = −−

= −−

=h kdd kd

0.150 0.19(0.115)0.115 0.19(0.115)

1.375

Bond coefficient kb = 1.2Crack control parameter z: (8.3.1.1. CSA/S806-02)

zEE

k f d A= ≤s

fb f c 38 0003

z = 200115

1.2)(247.36 35)(8750( ) ( )3

z = 34 796 N/mm

Crack control parameter, z ≤ 38 000 N/mm(exterior exposure) OK

Design for 2 h fire ratingThe available clear concrete cover to the side far away

from fire, dc, is given by

dc = 150 – 30 – 2 × 9.5 = 101 mm

Design moments and capacityIn case of fire on the top of the slab, it is assumed that the

top reinforcement mat will be totally lost and no moment canbe transferred across the supporting beams. Consequently theslab panel will be simply supported on the beams over a spanof 4.0 m.

The factored moment

= + =w l P l w ld w d2 28 4 0 125/ / . + 0 251. Pw

= × × + × ×0 125 5 04 4 0 2 0 25 4 0 16 5. . ( . ) . . .

= 26 58. kN·m

In case of fire on the bottom side of the slab, it is assumedthat the bottom reinforcement mat will be totally lost and a

major crack will be developed at the middle of the slabpanel. Consequently the slab panel will be divided into twoparts each is an overhang (2.0 m) from the adjacent panel.However, in the worst case, which is unlikely to occur ow-ing to the continuity of the top reinforcement, a concentrated(wheel load) can be carried by only one overhang (cantile-ver):

The factored moment

= +w l l P ld w( / ) ( / ) ( ) ( / )2 4 2

= +0 125 0 52. .w l l Pd w

= × ×0 125 5 04 4 0 2. . ( . )

+ × × =0 5 4 0 16 5 43 08. . . . kN·m

The ultimate capacity as calculated above

= 44.54 kN·m > 43.08 kN·m > 26.58 kN·m OK

References

ACI. 2003. Guide for the design and construction of concrete rein-forced with FRP bars (ACI 440.1R-03). ACI Committee 440,American Concrete Institute, Farmington Hills, Mich.

CSA. 1997. Parking structures. Standard CAN/CSA-S413-94, Ca-nadian Standards Association, Toronto, Ont.

CSA. 2002. Design and construction of building components withfibre reinforced polymers. Standard CAN/CSA S806-02, Cana-dian Standards Association, Toronto, Ont.

NRC. 1995. National building code of Canada. NBC 95. NationalResearch Council of Canada, Ottawa, Ont.

List of symbolsb width of the slab strip under consideration (mm)d effective depth of tensile reinforcement (mm)

Ec modulus of elasticity of concrete (GPa)Es modulus of elasticity of steel (GPa)ff stress in FRP reinforcement at service load level, calcu-

lated by elastic cracked section theory (MPa)fr modulus of rupture of concrete (MPa)h height of the slab cross section (mm)

Icr moment of inertia of the cracked section of the slab strip(mm4)

Ie effective moment of inertia of the slab strip section (mm4)Ig moment of inertia of the gross section of the slab strip

under consideration (mm4)l span of the slab (m)

Ma applied moment (kN·m)α1 ratio of average stress in rectangular compression block

to the specified concrete strengthβ1 ratio of depth of rectangular compression block to depth

of the neutral axisεf strain in FRP tensile reinforcementρf actual reinforcement ratio calculated assuming the effec-

tive depth of the slab to be the distance between the topof the slab and the centroid of the lower reinforcementin the main (considered) direction

© 2004 NRC Canada

748 Can. J. Civ. Eng. Vol. 31, 2004