Assessment of Eurocode-like design equations for the shearcapacity of FRP RC members

Raffaello Fico *, Andrea Prota 1, Gaetano Manfredi 2

Department of Structural Engineering, University of Naples Federico II, Via Claudio 21, 80125 Naples, Italy

Received 20 April 2007; received in revised form 8 October 2007; accepted 17 October 2007Available online 6 November 2007

Abstract

Fibre reinforced polymer (FRP) bars represent an interesting alternative to conventional steel as internal reinforcement of reinforcedconcrete (RC) members where some properties such as durability, magnetic transparency, insulation, are of primary concern. The presentpaper focuses on the assessment of Eurocode-like design equations for the evaluation of the shear strength of FRP RC members, as pro-posed by the guidelines of the Italian Research Council CNR-DT 203 [CNR-DT 203/2006. Guide for the design and construction ofconcrete structures reinforced with fiber-reinforced polymer bars. National Research Council, Rome, Italy; 2006]. Both the concreteand the FRP stirrups contributions to shear are taken into account: the new equations derived with reference to Eurocode equationsfor shear of steel RC members are verified through comparison with the equations given by ACI, CSA and JSCE guidelines, consideringa large database of members with and without shear reinforcement failed in shear.� 2007 Elsevier Ltd. All rights reserved.

Keywords: A. Reinforced concrete; A. FRP; C. Analysis; Shear

1. Introduction

FRP has much potential as longitudinal reinforcementin concrete structures exposed to reinforcement corrosionand stressed primarily in bending. Bridge decks, footings,floor slabs, soft eyes applications and wall type structuresare some examples of such structural components.

Most of the current design provisions which have beendeveloped for the design of FRP-reinforced concrete mem-bers follow the approach of conventional reinforced con-crete design methods, using the well-known Vc + Vs

format to compute the shear resistance of RC members,although the specific manners in which they derive the con-tribution of concrete Vc may differ considerably, whereasthe steel contribution Vs is determined similarly.

For steel-RC members, the Joint ASCE-ACI Committee445 ([1]) assessed that the quantity Vc can be considered asa combination of five mechanisms activated after the for-mation of diagonal cracks:

(1) shear stresses in uncracked compressed concrete;(2) aggregate interlock;(3) dowel action of the longitudinal reinforcing bars;(4) arch action; and(5) residual tensile stresses transmitted directly across the

cracks.

All of these mechanisms provided by conventional steelRC elements are expected to be affected when using FRPreinforcement due to larger strains that are generally mobi-lized in the latter. They are discussed in turn in the following.

The contribution of the uncracked concrete in RCmembers depends mainly on the concrete strength, f 0

c ,and on the depth of the uncracked zone, which is functionof the longitudinal reinforcement properties. In steel RCelements the neutral axis depth decreases rapidly during

1359-8368/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compositesb.2007.10.007

* Corresponding author. Tel.: +39 081 7683663; fax: +39 081 7683484.E-mail addresses: ficoraf@unina.it (R. Fico), aprota@unina.it

(A. Prota), gamanfre@unina.it (G. Manfredi).1 Tel.: +39 081 7683534; fax: +39 081 7683491.2 Tel.: +39 081 7683486; fax: +39 081 7683491.

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Available online at www.sciencedirect.com

Composites: Part B 39 (2008) 792–806

yielding, thus reducing the area of concrete in compres-sion, whereas in FRP RC members the area of concreteunder compression is considerably smaller than that devel-oped in similar steel RC sections already at relatively lowload levels. As the strain in the bars increases, however,the compression area does not decrease further as is thecase for steel ([2,3]).

The aggregate mechanical interlock allows the sheartransfer across a crack in the tensile zone; its magnitudeis estimated to range between 33% and 50% of the shearcapacity of uncracked concrete ([4]), although these per-centages reduce when the crack width increases ([5]); theaggregate interlock is function of:

the crack roughness, which depends on the maximumaggregate size;the crack width, which depends on the reinforcementstiffness; andthe concrete strength.

Higher strain values and a smaller reinforcement ratiorequired to sustain a given load in FRP with respect tosteel, together with a lower stiffness, reduce the total stiff-ness of the element and thus larger deflections and widercracks are attained; a smaller amount of shear force istherefore expected to be carried by aggregate interlock inFRP-reinforced members.

Nomenclature

a shear spanAf area of FRP reinforcementAfv area of FRP shear reinforcement within

spacing s

bw width of the webc neutral axis depthd distance from extreme compression fibre to cen-

troid of tension reinforcementdb equivalent diameter of barsEc modulus of elasticity of concreteEf guaranteed modulus of elasticity of tensile FRP

reinforcementEfw guaranteed modulus of elasticity of shear FRP

reinforcementEs modulus of elasticity of steelf 0c specified compressive strength of concreteffb strength of a bent portion of FRP barffd design tensile strength of FRPffr reduced tensile strength of FRP for shear de-

sign, defined as 0.5ffdffu ultimate tensile strength of FRPffv tensile strength of FRP for shear design, taken as

the smallest of the design tensile strength, ffu, thestrength of the bent portion of the FRP stirrups,ffb, or the stress corresponding to 0.004 Æ Ef

h member depthk ratio of depth of neutral axis to reinforcement

depthkd coefficient depending on d

M maximum moment to occur at the sectionnf ratio of modulus of elasticity of FRP bars to

modulus of elasticity of concreterb internal radius of bend in shear FRP reinforce-

mentV factored shear force at the section under consid-

eration corresponding to the load combinationcausing maximum moment to occur at the sec-tion

Vc nominal shear strength provided by concretewith steel flexural reinforcement

Vc,f nominal shear strength provided by concretewith FRP flexural reinforcement

Vexp experimental shear strength of membersVf shear resistance provided by FRP stirrupsVn nominal shear strengthVpred predicted shear strength of membersVRd shear resistance of a member (Eurocode 2)VRd,c design shear resistance provided by concrete

when steel reinforcement is used (Eurocode 2)VRd,ct design shear resistance provided by concrete

when FRP reinforcement is used (Eurocode 2)VRd,f design shear resistance provided by FRP stir-

rups (Eurocode 2)VRd,max maximum design shear force sustained, limited

by crushing of a compression strut.Vu factored shear force at sectionef,lim limit strain of FRP stirrupsefw design value of shear reinforcement strain at

ULScb member factor (JSCE)cc strength safety factor for concrete (JSCE and

Eurocode 2)cf strength safety factor for FRP (CNR DT 203)cf,U partial factor accounting for bending effects of

FRP stirrupsk factor to account for concrete density/ strength safety factor for FRP reinforcement

(ACI 440.1R-06)/c resistance factor for concrete (CSA S806-02)/f resistance factor for FRP reinforcement (CSA

S806-02)qf tensile FRP reinforcement ratioqfw shear FRP reinforcement ratioqs steel reinforcement ratiosRd design shear stress per unit area

R. Fico et al. / Composites: Part B 39 (2008) 792–806 793

The dowel action refers to the shear force resistingtransverse displacement between two parts of a structuralelement split by a crack that is bridged by the reinforce-ment; therefore, dowel contribution strongly depends onthe transverse stiffness and strength of the reinforcement([6]). Experimental tests carried out by Tottori and Wakui[7] show that the dowel capacity of members using FRPreinforcement is about 70% of those using reinforcing steel;it has been suggested ([8]) that the load carried by dowelaction of the reinforcement across a crack is negligible insteel-reinforced elements; with FRP reinforcement, whichhas a low transverse stiffness and strength, an even smallerload will be carried by dowel action ([9]). Hence, whenFRP reinforcement is used as flexural reinforcement thedowel contribution can be neglected ([10]).

The arch action occurs in the uncracked concrete nearthe end of elements where the shear span to depth ratio(a/d ratio) is less than 2.5 ([1]). The shift in the resistancemechanism from the so-called beam action to the archaction can substantially increase the shear resistance of amember because shear resistance by arch action is depen-dent on the effective compressive strength rather than theshear strength of concrete and on the strength and properanchorage of the longitudinal reinforcement. With properanchorage, the FRP reinforcement can resist high tensileforces and can serve as tie for the arch; therefore, the archmechanism may substantially contribute to the shear resis-tance of FRP-reinforced members ([6]).

The residual tension in cracked concrete has been foundto be present for crack widths smaller than 0.15 mm ([1]);since generally wider cracks are observed in FRP RC mem-bers, this contribution to the shear resistance can beneglected.

Therefore, it is critical that an accurate assessment ofconcrete contribution to the shear strength of membersreinforced with FRP bars as flexural reinforcement, Vc, isperformed.

Test results have shown that the shear strength of FRPRC beams is significantly lower than that predicted usingequations developed for steel reinforcement ([11]; [12]);therefore, it is definitely recognized that existing shearstrength equations related to steel-RC members should bemodified to be suitable for FRP RC members, accountingfor the different mechanical properties of FRP compared tosteel reinforcement.

This is the approach taken herein to extend the equationgiven by Eurocode 2 [13] for the shear capacity of steel RCmembers to the case of FRP RC members. A modified for-mula accounting for the concrete contribution to shearcapacity of FRP RC elements has been derived; this expres-sion has been included in the lately issued guidelines of theItalian Research Council CNR-DT 203 [14].

The equation reported by Eurocode 2 [13] accountingfor the concrete contribution to shear was taken intoaccount rather than that proposed in the last version ofEurocode 2 [15], being the 1992 equation included in sev-eral national codes and widely used by designers, therefore,

the Eurocode 2 [13] approach was deemed more suitable tolet professionals becoming accustomed to the new designguidelines.

As for the shear reinforcement, its role can be summa-rized as follows ([16]):

enabling the transfer of tensile actions across inclinedshear cracks;confining the compression-zone concrete, thus increas-ing the shear capacity;enclosing the flexural reinforcement, thus preventingdowel-splitting of the concrete and promotingthe dowel-rupture of FRP reinforcement.

The contribution of the shear reinforcement to the shearcapacity depends on the maximum stress that the reinforce-ment can attain. In the case of steel reinforcement it isassumed that steel overcomes the yielding strain and thenthe maximum stress (yielding stress) can be evaluated with-out exact assessment of the maximum strain; in the case ofFRP transverse reinforcement, which is linear elastic up tofailure, it is important to define the maximum strain toassess the stress in FRP transverse reinforcement. Further-more, FRP reinforcement needs large strains to develop itsfull tensile strength, but in the bent zones such strengthcannot be attained due to its anisotropic properties: thestrength reduction is attributed to the residual stress con-centration, hence minimum values for the bend radius arerecommended by all the existing provisions. Increasing ten-dency of shear force carried by shear reinforcement afterdiagonal cracks seems to be predictable by the truss anal-ogy ([7]) as shown in the equations reported by the maindesign provisions; however, technical question marks existover its applicability ([17]). The same approach has beenadopted herein to derive an equation accounting for thecontribution of the FRP shear reinforcement to shearcapacity of FRP RC elements; this expression has also beenincluded in the CNR-DT 203/2006 [14].

2. Review of current design provisions

Findings from experimental investigations on concretemembers longitudinally reinforced with carbon (C) andglass (G) FRP bars and with no shear reinforcement showthat the shear strength reduction experienced by such ele-ments when compared to those reinforced with the sameamount of steel reinforcement is mainly due to the lowermodulus of elasticity. Such investigations also reveal thatthe axial stiffness of the reinforcing bars is a key parameterwhen evaluating the concrete shear strength of flexuralmembers reinforced with FRP bars. Most of the currentinternational design provisions developed methods to com-pute Vc that are based on these findings.

As for the shear reinforcement, the main code proposalsfor FRP reinforcement assume an effective stirrup strainfor use in the truss analogy ([18]). The original intentionof the ‘‘allowable strain’’ concept ([19]) was to limit the

794 R. Fico et al. / Composites: Part B 39 (2008) 792–806

stirrup strain so that the crack width at failure was similarto that in steel-reinforced concrete, thus allowing the full‘‘concrete contribution’’ to be developed ([16]).

This section summarizes the design equations to com-pute both Vc and Vf as recommended by the AmericanConcrete Institute ([20]), by the Canadian Standard Asso-ciation ([21]), and by the Japanese Society of Civil Engi-neers ([22]).

2.1. ACI 440.1R-06 design guidelines

The ACI 440.1R bases the design of cross sections sub-ject to shear on the same approach used by the ACI 318-02([23]): /Vn P Vu, where / is the strength safety factor, Vu

is the factored shear force at the section considered, and Vn

is the nominal shear strength, computed as the sum of theshear resistance provided by concrete, Vc, and the FRPshear reinforcement, Vf.

As for the computation of Vc, a new design method wasproposed by Tureyen and Frosh [24] and adopted by theACI 440.1R-06 [20]; according to this method Vc can beevaluated as follows

V c ¼ 2

5k

ffiffiffiffif 0c

pbwd; ð1Þ

where k ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2qfnf þ ðqfnfÞ2

q� qfnf , qf being the flexural

FRP reinforcement ratio, and nf = Ef/Ec, where Ef andEc are the modulus of elasticity of FRP reinforcementand concrete, respectively; f 0

c is the specified compressivestrength of concrete; bw is the web width; and d is the dis-tance from the compression fibre to the centroid of themain tensile reinforcement.

Eq. (1) accounts for the axial stiffness of the FRP rein-forcement through the neutral axis depth, c = kd, whichis a function of the reinforcement ratio, qf, and the modu-lar ratio, nf. This equation has been shown to provide a rea-sonable factor of safety for FRP-reinforced specimensacross the range of reinforcement ratios and concretestrengths tested to-date ([25]). Eq. (1) may be rewritten inthe following way:

V c ¼ 12

5k1

6

ffiffiffiffif 0c

pbwd: ð2Þ

This form of the equation indicates that Eq. (1) is simplythe ACI 318 [23] shear equation for steel reinforcement,modified by the factor 12/5k which accounts for the axialstiffness of the FRP reinforcement ([20]).

The ACI 318 [23] method used to calculate the shearcontribution of steel stirrups is applied also when usingFRP as shear reinforcement. The shear resistance providedby FRP stirrups perpendicular to the axis of the member,Vf, is derived as follows:

V f ¼ Afvffvds

; ð3Þ

where Afv is the amount of FRP shear reinforcement withinstirrups spacing s, ffv is the tensile strength of FRP for

shear design, taken as the smallest of the design tensilestrength ffd, the stress corresponding to 0.004 Æ Ef, or thestrength of the bent portion of the FRP stirrups ffb, com-puted as

ffb ¼ 0:05rbdb

þ 0:30

� �ffd; ð4Þ

where rb and db are the internal radius and the equivalentdiameter of bent bar, respectively.

As it is for equation given for Vf in ACI 318 [23], Eq. (3)is based on a modified truss analogy. The truss analogyassumes that the total shear is carried by the shear rein-forcement. Yet, according to findings on both non-pre-stressed and prestressed members it is now recognizedthat the shear reinforcement needs to be designed to carryonly the shear exceeding that which causes inclined crack-ing, provided that the diagonal members in the truss areassumed to be inclined at 45 deg ([23]).

2.2. CAN/CSA-S806_02 design guidelines

The traditional Vc + Vf philosophy is also used by theCanadian Standard Association ([21]). Two cases are iden-tified therein:

members longitudinally reinforced with FRP using steelstirrups; andmembers with longitudinal and transverse FRPreinforcement.

Only the latter case will be discussed herein. The CSAS806-02 gives the following expression to compute Vc, forsections having either the minimum amount of transversereinforcement required or d < 300 mm

V c ¼ 0:035k/c f 0cqfEf

VM

d� �1

3

bwd; ð5Þ

where k accounts for concrete density (set equal to 1 here-in); /c is the resistance factor for concrete; V and M are thefactored shear force and moment at the section of interest,

such thatVM

d 6 1:0; moreover, Vc needs not be taken as

less than 0:1k/c

ffiffiffiffif 0c

pbwd nor shall it exceed 0:2k/c

ffiffiffiffif 0c

pbwd.

The computation of Vc slightly differs from theapproach followed by the Canadian guidelines for steel,CSA A23.3-94 ([26]), where

V c;s ¼ 0:2k/c

ffiffiffiffif 0c

pbwd: ð6Þ

Thus, according to the Canadian approach, the contribu-tion of concrete to the shear resistance when using steel isan upper bound for Vc.

For sections with d > 300 mm and with no transverseshear reinforcement or less than the minimum amountrequired, Vc is calculated using

V c ¼ 130

1000þ d

� �k/c

ffiffiffiffif 0c

pbwd P 0:08k/c

ffiffiffiffif 0c

pbwd: ð7Þ

R. Fico et al. / Composites: Part B 39 (2008) 792–806 795

The latter equation is derived from the corresponding for-mula given for steel reinforced sections multiplied by 0.5;this coefficient replaces the term

ffiffiffiffiffiffiffiffiffiffiffiffiEf=Es

p(Es being the

modulus of elasticity of the steel reinforcement), whenconsidering Ef = 50 GPa and Es = 200 GPa. Therefore,Eq. (7) represents the lower bound for concrete contribu-tion to the shear strength of FRP-reinforced concrete mem-bers regardless of the type of reinforcing bars ([27]).

For members with FRP flexural and shear reinforce-ment, the value of Vf shall be calculated as:

V f ¼ 0:4/fAfvffuds

; ð8Þ

where /f is the resistance factor for FRP reinforcementequal to 0.75, and ffu is the characteristic strength ofFRP shear reinforcement.

2.3. JSCE design guidelines

According to the Japan Society of Civil Engineers rec-ommendations for design and construction of concretestructures using continuous fibre reinforcing materials([22]), the design shear capacity of FRP RC elements canbe computed adopting the same principles as for the designof steel RC, using the equation Vud = Vc,f + Vf, where

V c;f ¼ bdbpbnfvcdbwd=cb; ð9Þwhere bd ¼

ffiffiffiffiffiffiffiffi1=d4

p6 1:5; bp ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi100qfEf=Es

3p

6 1:5; bn ¼ 1in this study where no axial forces are taken into account;fvcd ¼ 0:2

ffiffiffiffiffiffiffiffiffiffif 0c=cc

3p

6 0:72 N=mm2, cc being the concrete safetyfactor, set equal to 1.3 when f 0

c < 50 N=mm2, if not cc =1.5; cb is a member factor generally set equal to 1.3 atthe ULS.

The design shear capacity given by shear reinforcementshall be computed as

V f ¼ AfvEfwefws

z=cb; ð10Þ

where Efw is the modulus of elasticity of shear reinforce-ment, z = d/1.15, cb is the member factor generally setequal to 1.15 at the ULS, and efw is the design value ofshear reinforcement strain in ULS, obtained fromffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

h0:3

� ��1=10 f 0c

cc

qfEf

qfwEfw

s� 10�4; ð11Þ

where h is the member depth, qfw is the reinforcement ratioof shear reinforcement (qfw = Afv/bws).

When Efwefw is greater than ffbd, defined as the designvalue for the strength of the stirrup bent portion (equalto ffbd = ffb/cmfb, ffb being defined in Eq. (4) and cmfb gen-erally set as 1.3), ffbd is substituted for Efwefw.

Eq. (10) is equivalent to the corresponding Japaneseequation for steel RC after taking into account the differentnature of the reinforcement by substituting the yield stressof steel with the product Efwefw.

2.4. Italian guidelines

In compliance with the Eurocode 2 approach ([13]), theCNR-DT 203 [14] distinguishes two different cases forshear, namely for members not requiring and requiringshear reinforcement.

In the former case, at ULS the design shear strength of amember reinforced with longitudinal FRP reinforcementcan be evaluated as the minimum of the design shear resis-tance provided by concrete, VRd,ct, and the design value ofthe maximum shear force which can be sustained by themember before crushing of the compression strut, VRd,max.

As for the derivation of VRd,ct, the new formula pre-sented is a modified version of the Eurocode 2 shear equa-tion recommended for conventional steel RC members,which is (disregarding the axial forces term)

V Rd;c ¼ sRdkdð1:2þ 40qsÞbwd; ð12Þ

where VRd,c is the design shear resistance provided byconcrete when longitudinal steel reinforcement is used;sRd is the design shear stress per unit area, defined as0.25fctk0.05/cc, fctk0.05 being the characteristic tensilestrength of concrete (5% fractile); cc is the strength safetyfactor for concrete (cc = 1.6); kd is a factor taken equalto j1j in members where more than 50% of the bottomreinforcement is interrupted; if not, it will be kd =j(1.6 � d) P 1j (with d in meters); qs is the geometrical per-centage of longitudinal reinforcement and cannot exceedthe value 0.02.

A calibration has been conducted by the CNR DT 203Task Group to modify Eq. (12) and extend it to FRP RCmembers; the following expression for VRd,ct has beenproposed

V Rd;ct ¼ 1:3Ef

Es

� �1=2

V Rd;c; ð13Þ

where qf replaces qs and can not be less than 0.01 nor ex-ceed 0.02; moreover, the limitation 1.3 Æ (Ef/ Es)

1/2 6 1 shallbe satisfied; the coefficient 1.3 was determined after thecomparison with experimental data reported in the follow-ing section.

The rationale behind the above formula was based onthe objective of developing a reliable and simple equationhaving a structure which practitioners are familiar with.Once a full comprehension will be reached about howmuch the different mechanisms change their contributioncompared to the case of steel reinforcement, then it willbe appropriate to propose an updated equation in whichweighted safety factors are specifically applied to each termof Eq. (12). The assessment analysis of Eq. (13) is reportedin the following section.

When considering members requiring shear reinforce-ment, the ultimate design shear strength of a member rein-forced with longitudinal FRP reinforcement and FRPstirrups can be evaluated as the minimum between VRd,ct +VRd,f and VRd,max, where VRd,ct and VRd,max are the same

796 R. Fico et al. / Composites: Part B 39 (2008) 792–806

quantities introduced before, and VRd,f is the contributionof FRP stirrups, computed in compliance with the trussanalogy as

V Rd;f ¼ Afvffrds

; ð14Þ

where ffr is the so-called reduced tensile strength of FRPfor shear design, defined as ffd/cf,U, ffd being the design ten-sile strength of FRP reinforcement, computed dividing thecharacteristic value by the strength safety factor for FRP(cf = 1.5), and cf,U being the partial factor which further re-duces the design tensile strength of FRP reinforcement toaccount for the bending effect; cf,U shall be set equal to

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

0.0025 0.005 0.0075 0.01 0.0125 0.015 0.0175 0.02 0.0225 0.025 0.0275 0.03

Reinforcement ratio of reinforcing FRP bars. ρf

Vex

p /V

pred

CSA S-802

CNR-DT 203

ACI 440.1R

JSCE

Fig. 1. Comparison of Eq. (13) with major design provisions (w/o saf. factors).

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0.0025 0.005 0.0075 0.01 0.0125 0.015 0.0175 0.02 0.0225 0.025 0.0275 0.03

Reinforcement ratio of reinforcing FRP bars. ρf

Vex

p/V

pred

CSA S-802

CNR-DT 203

ACI 440.1R

JSCE

Fig. 2. Comparison of Eq. (13) with major design provisions (w/ saf. factors).

Table 1Comparison of Eq. (13) with major design provisions

Vexp/Vpred

CNR DT 203 ACI 440.1R CSA S806 JSCE

w/osaf.fact.

w/saf.fact.

w/osaf.fact.

w/saf.fact.

w/osaf.fact.

w/saf.fact.

w/osaf.fact.

w/saf.fact.

Mean 1.05 1.69 2.02 2.69 1.50 2.51 1.51 2.14St. dev. 0.31 0.49 0.61 0.82 0.51 0.86 0.48 0.68Coeff.

ofvar.(%)

29 30 34 32

R. Fico et al. / Composites: Part B 39 (2008) 792–806 797

– 2 when no specific experimental tests are performed,provided that the bend radius is not less than six timesthe equivalent diameter, db;

– the ratio of the straight FRP bar strength to the bentFRP portion design strength, in all other cases.

Similarly to ACI Eq. (3), CSA Eq. (8), and JSCE Eq.(10). Eq. (14) depends on the amount of FRP shear rein-forcement, on the distance from the compression fibre tothe centroid of the main tensile reinforcement, on the stir-rups spacing and on the design tensile strength of the FRPshear reinforcement. A comparison of the four formula-tions is reported hereafter.

3. Comparison between experimental results and codespredictions

3.1. Members without shear reinforcement

To verify Eq. (13), a database composed of test resultsrelated to 88 tested beams and one way slabs withoutFRP stirrups ([28], [7], [29], [30], [31], [32], [33], [34], [35],[36], [37], [24], [38], [39], [40], [41], [42]) was used for com-parisons, as given in Table 6; test results where prematurefailure occurred were disregarded ([43]).

Six specimens were reinforced with aramid FRP bars, 32specimens reinforced with carbon FRP, and 50 specimensreinforced using glass FRP bars. All specimens failed inshear. The concrete compressive strength, f 0

c , rangedbetween 22.7 and 50.0 MPa (specimens with f 0

c > 50MPawere neglected not being typical of FRP RC members).The reinforcement ratio of tensile FRP bars, qf, rangedbetween 0.0025 and 0.03; however, since CNR-DT 203 pre-scribes a minimum qf equal to 0.01 for members that donot require shear reinforcement, experimental points belowthis threshold (dashed line in Figs. 1 and 2) were not con-

sidered for the sake of the comparison. The effective depth,d, ranged between 150 and 970 mm, and the shear span todepth ratio, a/d, ranged between 1.78 and 6.50.

The predictions from Eq. (13) were compared with thevalues derived using Eqs. (1), (7) and (9). Table 1 reportsthe mean, the standard deviation and the coefficient of var-iation relating the ratio of the shear resistance attainedexperimentally, Vexp, to the corresponding analytical valuederived according to each of the four considered guidelines,Vpred, both with and without safety factors. It can be seenthat the CNR-DT 203 equation has the least mean valuesof both Vexp/Vpred (i.e., 1.05, w/o safety factor) and coeffi-cient of variation (i.e., 29%). Fig. 1 shows that the trendline of CNR-DT 203 equation is similar to that of CSAS-802 equation, regarded together with the Japaneseequation as the most reliable. For the CNR-DT 203equation when considering the material safety factors allthe values Vexp/Vpred remained greater than unity((Vexp/Vpred)ave = 1.69), as shown in Fig. 2; therefore, Eq.(13) can be deemed adequately conservative as well. Hence,Eq. (13) is found to be reliable for predicting the concretecontribution to the shear capacity of FRP RC members.

Table 2Comparison of Eq. (14) with major design provisions

Vexp/Vpred

CNR DT 203 ACI 440.1R CSA S806 JSCE

w/osaf.fact.

w/saf.fact.

w/osaf.fact.

w/saf.fact.

w/osaf.fact.

w/saf.fact.

w/osaf.fact.

w/saf.fact.

Mean 0.83 1.28 1.63 2.18 1.08 1.58 2.66 3.68St. dev. 0.27 0.42 0.69 0.92 0.39 0.60 1.13 1.57Coeff.

ofvar.(%)

32 33 42 42 36 38 43 43

0

100

200

300

400

500

600

700

800

0 100 200 300 400 500 600 700Vexp [kN]

Vpr

ed[k

N]

CNR DT 203

ACI '06

CSA

JSCE

UNSAFE

SAFE

Fig. 3. Comparison of Eq. (14) with major design provisions (w/o saf. factors).

798 R. Fico et al. / Composites: Part B 39 (2008) 792–806

3.2. Members with shear reinforcement

To verify Eq. (14), a database composed of test resultsrelated to 85 tested beams reinforced with FRP stirrups

and failed in shear (shear tension, shear compression orflexural shear failure) was collected from experimental pro-grams carried out by Nagasaka et al. [28], Tottori andWakui [7], Maruyama and Zhao [44], [45], Nakamura

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 20 40 60 80 100 120 140 160

E f [GPa]

f fu/f

fben

d

Fig. 4. Straight to bend strength ratio vs modulus of elasticity of FRP bars.

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10 12 14

d b [mm]

fu/ f

ffb

end

Fig. 5. Straight to bend strength ratio vs diameter of FRP bars.

Table 3Comparison of Eq. (14) with Eqs. (15) and (3)

Vexp/Vpred

CNR DT 203 ACI 440.1R

cf,U = 2 cf,U = ffd/ffb

w/o saf. fact. w/ saf. fact. w/o saf. fact. w/ saf. fact. w/o saf. fact. w/ saf. fact.

qmax = 1% qmax = 1% qmax = 1%

Mean 0.64 0.97 1.03 0.56 0.85 0.89 1.22 1.62 1.71St. dev. 0.23 0.36 0.31 0.28 0.44 0.40 0.55 0.74 0.66Coeff. of var. 37% 37% 30% 51% 52% 44% 46% 46% 39%

R. Fico et al. / Composites: Part B 39 (2008) 792–806 799

and Higai [29], Zhao et al. [30], Vijay et al. [31], Duranovicet al. [33], Shehata et al. [46], Alsayed et al. [47], and White-head and Ibell [48], as given in Table 7; such database wasthe basis for comparison of Eq. (14) with Eqs. (3), (8) and(10), although results reported by Whitehead and Ibell [48]were not considered for comparison since all specimens hadf 0c > 50 MPa. Only specimens with both longitudinal andtransverse FRP reinforcement were investigated. None ofthe tested specimens was disregarded depending on theshape of stirrups: specimens having closed loops or helicalshaped stirrups made either of bars or square rods wereused for comparisons; in some of the beams having helicalstirrups the helixes were placed only along the top of beam,in such cases the depth of the helixes rather than the effec-tive depth was used in calculations. Moreover, for beamswith circular helixes, according to the relevant researchersthe assumption of considering an effective diameterreduced by 30% with respect to the nominal diameter valuewas made to account for the reduced tie action. In caseswhere no specifications on the internal radius of stirrupsbend, rb, were provided in the literature source, the mini-mum value rb = 3db suggested by Ehsani et al. [49] wasconsidered.

Twenty-one specimens were reinforced with aramidFRP stirrups, 37 specimens had carbon FRP stirrups, 23specimens were reinforced using glass FRP stirrups, andfour specimens had hybrid (carbon and glass) FRP stir-rups. The ultimate tensile strength of FRP shear reinforce-ment, ffu (corresponding to the characteristic value in bothJSCE and CNR-DT 203) ranged between 400 and2040 MPa (environmental factors assigned by both ACI440.1R-06 [20] and CNR-DT 203 [14] accounting for dura-

bility issues in the FRP reinforcement were set equal to theunity); Afv ranged between 9 and 346 mm2; qfw rangedbetween 0.04% and 1.50%; d ranged between 100 and750 mm, and s ranged between 20 and 200 mm. It is under-lined that specimens tested by Nagasaka et al. [28] had aconsiderably high amount of shear FRP reinforcement(qfw = 0.5% in six specimens, 1.0% in 10 specimens and1.5% in eight specimens).

0

100

200

300

400

500

600

700

800

900

0 100 200 300 400 500 600 700 800 900

Vexp [kN]

Vpr

ed [

kN]

CNR DT 203 - gamma = 2

CNR DT 203 - gamma = ffd / ffb

ACI 440.1R-06

UNSAFE

SAFE

Fig. 6. Comparison of Eq. (15) with Eqs. (3) and (14).

Table 4Proposed values for the limit strain of FRP stirrups

Type of fiber ef,lim

CFRP 0.0035AFRP 0.0070GFRP 0.0085

Table 5Influence of limit strain of FRP stirrups on CNR DT 203 and ACI 440.1Requations

Vexp/Vpred

CNR DT 203 ACI 440.1R

cf,U = 2 ef,lim * Ef 0.004 * Ef ef,lim * Ef

w/osaf.fact.

w/saf.fact.

w/osaf.fact.

w/saf.fact.

w/osaf.fact.

w/saf.fact.

w/osaf.fact.

w/saf.fact.

Mean 0.83 1.28 1.03 1.60 1.63 2.18 1.43 1.90St. dev. 0.27 0.42 0.31 0.48 0.69 0.92 0.52 0.70Coeff.

ofvar.(%)

32 33 30 30 42 42 37 37

800 R. Fico et al. / Composites: Part B 39 (2008) 792–806

Table 6Database for FRP RC members without shear reinforcement

Reference f 0c (MPa) bw (mm) d (mm) qf Ef (GPa) Type Vexp (kN)

Nagasaka et al. [28] 34.1 250 265 0.019 56 AFRP 11322.9 250 265 0.019 56 AFRP 83

Tottori and Wakui [7] 44.6 200 325 0.007 137 CFRP 9844.5 200 325 0.007 137 CFRP 12345.0 200 325 0.007 137 CFRP 11846.9 200 325 0.009 192 CFRP 14746.9 200 325 0.009 192 CFRP 9346.9 200 325 0.009 192 CFRP 7846.9 200 325 0.009 58 CFRP 15246.9 200 325 0.009 58 CFRP 6246.9 200 325 0.009 58 CFRP 47

Nakamura and Higai [29] 22.7 300 150 0.013 29 GFRP 3327.8 300 150 0.018 29 GFRP 36

Zhao et al [30] 34.3 150 250 0.015 105 CFRP 4534.3 150 250 0.030 105 CFRP 4634.3 150 250 0.023 105 CFRP 41

Vijay et al. [31] 44.8 150 265 0.014 54 GFRP 4531 150 265 0.006 54 GFRP 45

Mizukawa et al. [32] 34.7 200 260 0.013 130 CFRP 62

Duranovic et al. [33] 38.1 150 210 0.013 45 AFRP 2632.9 150 210 0.013 45 AFRP 22

Swamy and Aburawi [34] 34.0 254 222 0.016 34 GFRP 39

Deitz et al. [35] 28.6 305 158 0.007 40 GFRP 2730.1 305 158 0.007 40 GFRP 2827 305 158 0.007 40 GFRP 2928.2 305 158 0.007 40 GFRP 2930.8 305 158 0.007 40 GFRP 28

Yost et al. [36] 36.3 229 225 0.011 40 GFRP 3936.3 229 225 0.011 40 GFRP 3936.3 229 225 0.011 40 GFRP 3736.3 178 225 0.014 40 GFRP 2836.3 178 225 0.014 40 GFRP 3536.3 178 225 0.014 40 GFRP 3236.3 229 225 0.017 40 GFRP 4036.3 229 225 0.017 40 GFRP 4936.3 229 225 0.017 40 GFRP 4536.3 279 225 0.018 40 GFRP 4436.3 279 225 0.018 40 GFRP 4636.3 279 225 0.018 40 GFRP 4636.3 254 224 0.021 40 GFRP 3836.3 254 224 0.021 40 GFRP 5136.3 254 224 0.021 40 GFRP 4736.3 229 224 0.023 40 GFRP 4436.3 229 224 0.023 40 GFRP 4236.3 229 224 0.023 40 GFRP 41

Alkhrdaji et al. [37] 24.1 178 279 0.023 40 GFRP 5324.1 178 287 0.008 40 GFRP 3624.1 178 287 0.013 40 GFRP 40

Tureyen and Frosh [24] 39.7 457 360 0.010 41 GFRP 10839.9 457 360 0.010 38 GFRP 9540.3 457 360 0.010 47 AFRP 11542.3 457 360 0.019 41 GFRP 13742.5 457 360 0.019 38 GFRP 15342.6 457 360 0.019 47 AFRP 177

(continued on next page)

R. Fico et al. / Composites: Part B 39 (2008) 792–806 801

The predictions from Eq. (14) were compared with thevalues derived using Eqs. (3), (8), and (10). Table 2 reportsthe ratio of the shear resistance attained experimentally,Vexp, to the corresponding analytical values derivedaccording to each of the four considered guidelines, Vpred

(both Vexp and Vpred are meant to be the total strength ofthe tested specimens).

The CNR-DT 203 equation proves to give the least(Vexp/Vpred)ave both with and without safety factors, i.e.,0.83 and 1.28, respectively, and the least coefficients of var-iation, i.e., 32% and 33%, respectively (see Table 5; two dif-ferent values of coefficient of variation were derived forequations where two different material factors are present,namely concrete and FRP safety factors); Fig. 3 shows thecalculated ultimate shear strength based on the four equa-tions (each with all safety factors set equal to 1) versus thatmeasured; the comparison between experimental resultsand predictions given by CNR-DT 203, ACI 440.1R-06and CSA S-802 equations points out that there are somevery unconservative results which are related to the testdata by Nagasaka et al. [28] (see upper portion of

Fig. 3). The authors believe that this discrepancy couldbe due to the fact that only part of the high percentageof shear reinforcement is effectively contributing to theshear capacity of the members.

In such cases Vexp/Vpred was found to be lower thanunity even when considering safety factors for all the equa-tions except for the JSCE equation (which converselyseems rather conservative); again, this is particularly occur-ring for the experimental results reported by Nagasakaet al. [28]. This aspect is better investigated hereafter.

3.3. Influence of bent strength of stirrups and shear

reinforcement ratio

The available literature data found in the first stage forthe bend strength of FRP induced the CNR DT 203 TaskGroup to set an upper bound value of cf,U = ffd/ffb = 2.Later more data were retrieved ([28], [29], [31], [50]), andthen it is now possible to investigate the influence of thestrength reduction of stirrups due to the bend based on awider number of data.

Table 6 (continued)

Reference f 0c (MPa) bw (mm) d (mm) qf Ef (GPa) Type Vexp (kN)

Tariq and Newhook [38] 37.3 160 346 0.007 42 GFRP 5537.3 160 346 0.007 42 GFRP 6443.2 160 346 0.011 42 GFRP 4343.2 160 346 0.011 42 GFRP 4634.1 160 325 0.015 42 GFRP 4934.1 160 325 0.015 42 GFRP 4537.3 130 310 0.007 120 CFRP 4937.3 130 310 0.007 120 CFRP 4643.2 130 310 0.011 120 CFRP 4843.2 130 310 0.011 120 CFRP 5334.1 130 310 0.015 120 CFRP 5634.1 130 310 0.015 120 CFRP 58

Lubell et al. [39] 40.0 450 970 0.005 40 GFRP 136

Razaqpur et al. [40] 40.5 200 225 0.003 145 CFRP 3649.0 200 225 0.005 145 CFRP 4740.5 200 225 0.006 145 CFRP 4740.5 200 225 0.009 145 CFRP 4340.5 200 225 0.005 145 CFRP 9640.5 200 225 0.005 145 CFRP 4740.5 200 225 0.005 145 CFRP 38

El Sayed et al. [27] 40.0 1000 165 0.004 114 CFRP 14040.0 1000 165 0.008 114 CFRP 16740.0 1000 161 0.012 114 CFRP 19040.0 1000 162 0.009 40 GFRP 11340.0 1000 159 0.017 40 GFRP 14240.0 1000 162 0.017 40 GFRP 16340.0 1000 159 0.024 40 GFRP 16340.0 1000 154 0.026 40 GFRP 168

El Sayed et al. [42] 50.0 250 326 0.009 130 CFRP 7850.0 250 326 0.009 40 GFRP 7144.6 250 326 0.012 130 CFRP 10444.6 250 326 0.012 40 GFRP 6043.6 250 326 0.017 130 CFRP 12543.6 250 326 0.017 40 GFRP 78

802 R. Fico et al. / Composites: Part B 39 (2008) 792–806

Table 7Database for FRP RC members with shear reinforcement

Reference Geometric data Concrete Longitudinal reinforcement Shear reinforcement Vexp (kN)

b (mm) d (mm) a/d f 0c (MPa) Type qf (%) Et (GPa) Type qfw (%) Et (GPa)

Tottori and Wakui [7] 200 325 3.2 44.4 CFRP 0.70 137 GFRP 0.15 40 103200 325 3.2 44.7 CFRP 0.70 137 GFRP 0.15 40 106200 325 3.2 44.9 CFRP 0.70 137 AFRP 0.07 69 85200 325 2.2 44.6 CFRP 0.70 137 CFRP 0.07 110 162200 325 3.2 44.8 CFRP 0.70 137 CFRP 0.07 110 83200 325 4.3 44.6 CFRP 0.70 137 CFRP 0.07 110 74200 325 3.2 45.0 CFRP 0.70 137 CFRP 0.04 144 98200 325 3.2 44.7 CFRP 0.70 140 CFRP 0.06 137 108200 325 3.2 44.7 CFRP 0.70 140 CFRP 0.10 137 157200 325 3.2 39.4 CFRP 0.70 140 AFRP 0.12 58 103200 325 3.2 39.4 AFRP 0.92 58 AFRP 0.09 58 83200 325 3.2 39.4 AFRP 0.92 58 AFRP 0.13 58 98200 325 3.2 39.4 AFRP 0.92 58 AFRP 0.23 58 132200 325 3.2 39.4 AFRP 0.92 58 AFRP 0.12 58 107200 325 3.2 39.4 AFRP 0.92 58 AFRP 0.12 58 78200 325 3.2 39.4 AFRP 0.92 58 CFRP 0.04 137 86150 250 2.5 35.5 CFRP 0.55 94 CFRP 0.12 94 58150 250 2.5 37.6 CFRP 0.55 94 CFRP 0.24 94 82150 250 2.5 34.3 CFRP 1.05 94 CFRP 0.12 94 71150 250 2.5 34.2 CFRP 2.11 94 CFRP 0.12 94 81300 500 2.5 31.9 CFRP 0.53 94 CFRP 0.06 94 160150 260 3.1 42.2 AFRP 3.08 63 AFRP 0.13 53 60

Nagasaka et al. [28] 250 253 1.2 29.5 AFRP 1.90 56 CFRP 0.50 115 251250 253 1.2 34.7 AFRP 1.90 56 CFRP 1.00 115 317250 253 1.2 33.5 AFRP 1.90 56 CFRP 1.50 115 366250 253 1.8 29.5 AFRP 1.90 56 CFRP 0.50 115 208250 253 1.8 29.5 AFRP 1.90 56 CFRP 1.00 115 282250 253 1.8 29.5 AFRP 1.90 56 CFRP 1.50 115 288250 253 2.4 33.5 AFRP 1.90 56 CFRP 0.50 115 162250 253 2.4 33.5 AFRP 1.90 56 CFRP 1.00 115 234250 253 1.8 34.1 AFRP 1.90 56 AFRP 0.50 62 205250 253 1.8 35.4 AFRP 1.90 56 AFRP 1.00 62 277250 253 1.8 34.1 AFRP 1.90 56 HFRP 0.50 45 173250 253 1.8 34.1 AFRP 1.90 56 HFRP 1.00 45 248250 253 1.8 35.4 AFRP 1.90 56 GFRP 0.50 47 179250 253 1.8 36.7 AFRP 1.90 56 GFRP 1.00 47 233250 253 1.8 24.0 AFRP 1.90 56 CFRP 1.00 115 211250 253 1.8 23.0 AFRP 1.90 56 CFRP 1.50 115 226250 253 2.4 24.8 AFRP 1.90 56 CFRP 1.00 115 186250 253 2.4 23.4 AFRP 1.90 56 CFRP 1.50 115 195250 253 1.8 23.0 AFRP 1.90 56 AFRP 1.00 62 194250 253 1.8 23.0 AFRP 1.90 56 AFRP 1.50 62 207250 253 1.8 24.0 AFRP 1.90 56 HFRP 1.00 45 194250 253 1.8 24.0 AFRP 1.90 56 HFRP 1.50 45 216250 253 1.8 40.3 AFRP 1.90 56 CFRP 1.50 115 298250 253 2.4 40.0 AFRP 1.90 56 CFRP 1.50 115 231

Vijay et al. [31] 150 265 1.9 44.8 AFRP 1.43 54 AFRP 0.93 54 127150 265 1.9 44.8 AFRP 1.43 54 AFRP 0.62 54 115150 265 1.9 31.0 AFRP 0.64 54 AFRP 0.93 54 123150 265 1.9 31.0 AFRP 0.64 54 AFRP 0.62 54 123

Maruyama and Zhao [44] 150 250 2.5 36.2 CFRP 0.55 94 CFRP 0.12 94 59150 250 2.5 38.3 CFRP 0.55 94 CFRP 0.24 94 84150 250 2.5 35.0 CFRP 1.05 94 CFRP 0.12 94 73150 250 2.5 33.1 CFRP 1.10 94 CFRP 0.24 94 89150 250 2.5 31.3 CFRP 1.39 94 CFRP 0.24 94 95150 250 2.5 30.5 CFRP 2.11 94 CFRP 0.24 94 120150 250 2.5 30.5 CFRP 2.11 94 CFRP 0.18 94 86150 250 2.5 31.3 CFRP 2.11 94 CFRP 0.15 94 75150 250 2.5 34.9 CFRP 2.11 94 CFRP 0.12 94 83

(continued on next page)

R. Fico et al. / Composites: Part B 39 (2008) 792–806 803

For 32 out of 85 shear tested beams the ratio ffd/ffb wasprovided by the relevant authors; 26 extra values werereported by Shehata et al. [50] from tests carried out to spe-cifically study the bend effect on the strength ofFRP stirrups.In Fig. 4, the overall 58 values ffd/ffb versus Ef are depicted,showing the great scattering of results; similar outcomes areattained when considering db in lieu of Ef (see Fig. 5).

Eq. (14) modified by replacing cf,U = 2 with the experi-mental value of ffd/ffb can be considered:

V f ¼ Afvffdds

ffbffd

: ð15Þ

The 32 shear tested specimens where ffd/ffb was availablewere used for comparison of Eq. (15) with CNR DT 203Eq. (14) and ACI Eq. (3) (only the American equationwas considered as reference for comparison with the Italianequation because it has a slightly different approach, lim-ited predominantly by the maximum strain rather thanby the strength of stirrup bent portion). Table 3 reportsthe mean, the standard deviation and the coefficient of var-iation of Vexp/Vpred relating each of the three equations,both with and without safety factors; Fig. 6 shows thetrend of Vexp versus Vpred, derived with the three equations.The results show that Eq. (3), where the minimum value forffv always corresponded to 0.004Ef (the value 0.004 is justi-fied as the strain that prevents degradation of aggregate

interlock and corresponding concrete shear, Priestleyet al. [51]), gives better predictions than Eqs. (14) and(15); besides, better outcomes are derived for Eq. (14) thanEq. (15), which greatly overestimates the shear capacitywhen ffd/ffb is lower than 1.8 (that is when the bendstrength of the bar approaches that of the straight portion)and gives more scattered predictions, as expected; similarlyto what was observed for Fig. 3, also the most unconserva-tive predictions in Fig. 6 are related to the experiments con-ducted by Nagasaka et al. [28].

Therefore, it can be concluded that the strength of stir-rups bent portion seems not to be a significant factor affect-ing the FRP stirrups contribution to shear; this resultbecomes more evident when the bend strength of stirrupapproaches that of the straight portion and justifies the lar-ger inaccuracy of some analytical results ([28]). Such con-clusion is in agreement with the results of shear testscarried out by Nagasaka et al. [28], where the average stressof FRP stirrups across a critical crack obtained from thestrain gage readings was measured to be only half of thebreaking strength of bent portions. According to the find-ings of Nagasaka et al. [28], the values reported in Table 4are suggested as limit strains, ef,lim, depending on the typeof stirrup fiber; such values were used in replacement of0.004 given by ACI 440.1R-06 [20] in Eq. (3), while inEq. (14) ffr was replaced by ef, lim Æ Ef, thus yielding

Table 7 (continued)

Reference Geometric data Concrete Longitudinal reinforcement Shear reinforcement Vexp (kN)

b (mm) d (mm) a/d f 0c (MPa) Type qf (%) Et (GPa) Type qfw (%) Et (GPa)

Nakamura and Higai[29]

200 250 3.0 35.4 GFRP 1.61 29 GFRP 0.35 31 83200 250 3.0 33.4 GFRP 1.61 29 GFRP 0.35 31 100200 250 3.0 35.2 GFRP 1.61 29 GFRP 0.18 31 56200 250 3.0 35.2 GFRP 1.61 29 GFRP 0.18 31 66

Zhao et al. [30] 150 250 3.0 34.3 CFRP 3.02 105 GFRP 0.42 39 113150 250 3.0 34.3 CFRP 3.02 105 CFRP 0.42 100 126150 250 3.0 34.3 CFRP 2.27 105 GFRP 0.42 39 116150 250 2.0 34.3 CFRP 1.51 105 GFRP 0.42 39 123150 250 4.0 34.3 CFRP 1.51 105 GFRP 0.42 39 73

Maruyama and Zhao[45]

150 250 2.5 34.0 CFRP 1.07 100 GFRP 0.43 30 110150 250 2.5 34.0 CFRP 1.07 100 GFRP 0.43 30 107150 250 2.5 34.0 CFRP 1.07 100 GFRP 0.43 30 148150 250 2.5 34.0 CFRP 1.07 100 GFRP 0.43 30 131300 500 2.5 29.5 CFRP 1.07 100 GFRP 0.86 30 370450 750 2.5 29.5 CFRP 1.07 100 GFRP 1.28 30 590

Alsayed et al. [47] 200 310 3.2 29.5 GFRP 1.37 36 GFRP 0.21 42 69200 309 2.4 29.6 GFRP 1.28 43 GFRP 0.40 42 109

Duranovic et al. [33] 150 230 3.3 33.0 GFRP 1.31 45 GFRP 0.35 45 49150 230 2.2 33.0 GFRP 1.31 45 GFRP 0.35 45 67

Shehata et al. [50] 135 470 3.2 50.0 CFRP 1.25 137 CFRP 0.29 137 305135 470 3.2 50.0 CFRP 1.25 137 GFRP 1.07 41 305

Whitehead and Ibell[48]

110 100 3.1 55.61 AFRP 0.32 60 AFRP 0.40 60 45110 200 3.1 63.91 AFRP 0.32 60 AFRP 0.19 60 51110 100 3.1 55.61 AFRP 0.32 60 AFRP 0.40 60 53110 100 3.1 58.1 AFRP 0.32 60 AFRP 0.80 60 55110 200 3.1 58.1 AFRP 0.32 60 AFRP 0.29 60 60

804 R. Fico et al. / Composites: Part B 39 (2008) 792–806

V f ¼ Afvef ;limEfds

: ð16Þ

Table 5 shows that the two modified equations seem to givebetter predictions than corresponding Eqs. (3) and (16) (thecomparison was based on the total group of shear testedbeams, i.e., 85 experimental results).

In addition, Nagasaka et al. [28] pointed out that forstirrup ratios qfw over 1% the increase rate of shear capac-ity greatly reduces; if this remark is accounted for in Eqs.(3) and (14) by limiting qfw to 1%, better predictions areattained for the referred equations in terms of both meanand coefficient of variation (see Table 3).

4. Conclusions

The paper presents an assessment of Eurocode-likedesign equations for predicting the shear strength of FRPRC members, which have been included in the lately issuedCNR-DT 203 2006 guidelines of the Italian ResearchCouncil. The new expressions for the concrete and FRPstirrups contributions to the shear strength of FRP RCmembers have been compared with the correspondingAmerican, Canadian and Japanese provisions using a largeexperimental database. The following conclusions can bedrawn:

(1) The equation proposed by the CNR DT 203 account-ing for the concrete contribution to the shearstrength, Vc, gives accurate predictions and can beconservatively used by practitioners.

(2) For shear reinforced members, the strength of stir-rups bent portion seems not to be a significant factoraffecting the FRP stirrups contribution to shear; thisis confirmed by experimental results where the effec-tive strain measured in the stirrups across criticalcracks governed the shear failure, namely 0.0035 forCFRP stirrups, 0.007 for AFRP stirrups and 0.0085for GFRP stirrups. Moreover, in many shear testedmembers when the bend strength of stirrupapproaches that of the straight portion the shearcapacity did not increase as expected.

(3) The equation proposed by the CNR DT 203 account-ing for the stirrups contribution to the shear strengthseems to give rather good results; nevertheless, thecf,U factor accounting for bending effects of stirrupsshould be replaced by a term accounting for the limitstrain not governed by rupture of bent portion.

(4) Increasing the stirrup ratio qfw over 1% seems not toincrease the shear capacity; when settingqfw,max = 1% more reliable predictions are attained.

(5) Work is in progress to perform a probabilistic cali-bration of the material factor for FRP bars as wellas to better understand the influence of FRP barproperties on different mechanisms contributing tothe concrete strength. The outcomes of this researchplan will be used to optimize the proposed equations

to determine safety factors with different weightdepending on each mechanism.

Acknowledgements

The authors would like to acknowledge the support ofthe Center of Excellence on Structural Composites forInnovative Construction. The work presented herein hasbeen part of the activities of the Technical Committee thathas developed the CNR DT 203/2006 guidelines; theauthors would like to thank the Chair of the Committee,Prof. Luigi Ascione, for his supervision and coordination.

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