Experimental study and code predictions of fibre reinforced polymerreinforced concrete (FRP RC) tensile members

M. Baena ⇑, A. Turon, Ll. Torres, C. Miàs

Analysis and Advanced Materials for Structural Design (AMADE), Polytechnic School, University of Girona, Campus Montilivi s/n, 17071 Girona, Spain

a r t i c l e i n f o

Article history:

Available online 15 April 2011

Keywords:

Reinforced concrete

Fibre reinforced polymer bars

Tension stiffening

Tensile behaviour

Bond

a b s t r a c t

Due to their different mechanical properties, cracking and deformability behaviour of FRP reinforced con-

crete (FRP RC) members is quite different from traditional steel reinforced concrete (SRC) having great

incidence on their serviceability design. This paper presents and discusses the results of an experimental

programme concerning concrete tension members reinforced with glass fibre reinforced polymer (GFRP)

bars. The main aim of the study is to evaluate the response of GFRP reinforced concrete (GFRP RC) tension

members in terms of cracking and deformations. The results show the dependence of load-deformation

response and crack spacing on the reinforcement ratio. The experimental results are compared to predic-

tion models from codes and guidelines (ACI and Eurocode 2) and the suitability of the different

approaches for predicting the behaviour of tensile members is analysed and discussed.

Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Corrosion of steel reinforcement in aggressive environments

can cause considerable damage in reinforced concrete structures,

reducing their service life and increasing the costs of maintenance,

repair or replacement. The use of fibre reinforced polymer (FRP) as

reinforcement in concrete structures offers an alternative to over-

come the corrosion-related problems.

Due to their different mechanical properties, the behaviour of

FRP reinforced concrete (FRP RC) members is quite different from

traditional steel reinforced concrete (SRC). Because of the lower

stiffness of FRP bars compared to steel, deformations and crack

widths at service loads are usually larger for GFRP RC than for

SRC. Therefore, their prediction plays an important role in the

design of GFRP RC flexural elements, which is often governed by

the serviceability limit states [1]. In this sense, the study of the

interaction between FRP reinforcement and concrete is essential

for predicting deformations in FRP reinforced concrete [2].

Although the bond behaviour and the tension stiffening effect

(contribution to stiffness of tensioned concrete between cracks)

are quite well defined for traditional SRC structures, this is not

the case for innovative FRP RC structures, as the parameters

involved are numerous and their influence on the physical phe-

nomenon is not clear. Consequently, the direct extension of SRC

code formulations to FRP RC may not be straightforward.

A number of experimental programmes have been conducted to

assess the influence of the different mechanical properties of FRP

bars on the deformability and cracking (i.e. crack spacing, crack

width and deflections) of FRP RC flexural elements [3–8]. The

tension stiffening effect, which results from the bond interaction

between reinforcement and concrete, is also included in most of

the cited references. However, although the tension stiffening

effect is characteristic of tensioned concrete, fewer studies have

focussed on FRP RC tensile members [9–11].

This paper presents and discusses the results of a research

programme on GFRP RC members tested in tension. The tensile

members were reinforced with helically wrapped sand-coated

GFRP rebars. The rectangular specimens had different reinforce-

ment ratios combining different section sizes and reinforcement

diameters. Details of the tensile behaviour along with results of

the cracking analysis are presented. The experimental results of

load-deformation, crack width and crack spacing are compared

with guidelines and code predictions. Finally, the suitability of

the prediction models is analysed.

2. Experimental programme

2.1. Test programme

The experimental programme consisted of testing GFRP RC ele-

ments axially loaded in tension in order to investigate the post-

cracking response of reinforced concrete. All the GFRP RC ties were

1300 mm long, with 50 mm debonded length on either side giving

an effective bond length of 1200 mm. Three GFRP bar diameters

and two concrete square section sizes were used. One reinforcing

bar was placed in the centre of the cross section. Six specimens

were manufactured, each with different reinforcement ratios by

0263-8223/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compstruct.2011.04.012

⇑ Corresponding author. Tel.: +34 972419517; fax: +34 972418098.

E-mail address: marta.baena@udg.edu (M. Baena).

Composite Structures 93 (2011) 2511–2520

Contents lists available at ScienceDirect

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journal homepage: www.elsevier .com/locate /compstruct

combining different diameters and sectional dimensions, as shown

in Table 1.

The specimens designated as 19-170-N and 16-170-3 N in Table

1 correspond to a second part of the programme focussed on

obtaining specific results for numerical simulation in which bars

were internally strain gauged and several notches were created

to induce cracking at specific locations. Therefore, the results

obtained from these two specimens are used for the load-

deformation response only and not for cracking behaviour.

A specially designed gripping system was used to apply the load

without damaging the rebar. It consisted of drilled-through

threaded-bars housing the rebar and an epoxy-based resin bonding

the rebar to the housing bar. Load was applied at the ends of the

protruding bars by means of a hydraulic jack at one end of each

specimen, and a rigid frame connected to the other end of the spec-

imen, as shown in Fig. 1. The load was applied in a displacement

control mode and an automatic data acquisition system was used

to collect the data. The tests were stopped whenever a new crack

appeared at the concrete surface; at each stop, the evolution of

cracks and strains was recorded. Crack widths were measured with

an optical magnifier to within an accuracy of 0.05 mm. A linear

variable differential transducer (LVDT) was used to measure the

member deformation. Additionally, member strains were mea-

sured at the height of reinforcement by means of a mechanical

extensometer with a gauge length of 150 mm between Demec

points; both the LVDT and the mechanical extensometer measured

and recorded deformations along the 1200 mm bond length.

2.2. Materials

The GFRP reinforcing bars, from different batches delivered at

different times, and all manufactured by Hughes Brothers Inc.

(Aslan 100), were helically wrapped with sand-coated surfaces

(Fig. 2). Bare bar tensile tests were performed to characterise both

the normal and strain-gauged reinforcing bars, using a servo-

hydraulic testing machine with a capacity of 600 kN. Displacement

control mode was selected and load was applied to the bar at a rate

of 0.08 mm/s until failure. The load was measured with the elec-

tronic load cell of the testing machine while an axial extensometer

with a gauge length of 100 mm was used to capture the displace-

ment. Normalised tests were conducted to determine the cross-

sectional areas of the rebars, according to ACI 440.3R-04 [12] and

CSA S806-02 [13]. Mean values of mechanical and geometrical

properties, as well as the resulting reinforcement ratios are shown

in Table 2.

Ready-mix concrete, with a maximum aggregate size of 20 mm

and a target compressive strength of 50 MPa, was used to cast the

specimens. Due to the limited capacity of the laboratory, the exper-

imental campaign was conducted in three stages at three different

times.

Control cylinders with a nominal diameter of 150 mm and a

height of 300 mm were match-cured and tested at the same time

as the specimens. The compressive strength and the modulus of

Table 1

Geometric characteristics of specimens.

Specimen Nominal diameter,

dn (mm)

Cross-section size

(mm)

Concrete

mix

13-170 12.7 170 C1

16-170 15.9 170 C3

19-170 19.1 170 C2

16-110 15.9 110 C2

19-170-N 19.1 170 C2

16-170-3 N 15.9 170 C3

Fig. 1. GFRP RC tensile test setup (units in mm).

Fig. 2. GFRP rebars used in the experimental programme.

Table 2

Geometrical and mechanical properties of GFRP rebars.

Specimen Nominal

diameter,

dn (mm)

Experimental

diameter,

db (mm)

Reinforcement

ratio, q (%)

Tensile

strength,

ffu (MPa)

Axial

stiffness

ErAr (kN)

13-170 12.7 13.7 0.51 770 5540

16-170 15.9 16.9 0.71 1030 9362

19-170 19.1 19.1 1.00 637 11,680

16-110 15.9 16.1 1.69 751 7900

19-170-N 19.1 21.4 1.25 535 14,727

16-170-3 N 15.9 19.1 1.00 917 10,087

2512 M. Baena et al. / Composite Structures 93 (2011) 2511–2520

elasticity were tested according to UNE-EN 12390-3 [14] and ASTM

C 469 [15] standards, respectively. The composition and mechani-

cal properties of the concrete are summarised in Table 3.

3. Test results and data analysis

In this section the experimental results of the present study on

GFRP RC tensile tests are presented. Details on the tensile behav-

iour, along with results on the cracking analysis of concrete ele-

ments reinforced with GFRP rebars are given.

3.1. Tensile behaviour

3.1.1. Experimental response

The load-member strain curves (P–em) measured during the

experimental tests are shown in Fig. 3. Member strain has been

computed as the continuously recorded member elongation, d,

measured with the LVDT and the mechanical extensometer be-

tween Demec points, over the bond length L (i.e. 1200 mm). Good

agreement is observed in Fig. 3 for the two measurements in each

tie.

The tension response of a RC member can be defined by three

different regions. An initial linear branch with a steep slope, corre-

sponding to the uncracked condition of the tie, is detected in the

so-called pre-crack stage. When the cracking load, Pcrack, is reached,

the cracking stage begins and a drop in the slope is observed, due

to the progressive cracking of the tie. Finally, the cracking process

stabilizes and the post-cracking stage starts, with a monotonic in-

crease until failure.

Previous studies show that cracking resistance and deformation

of RC members could be affected by the shrinkage generated dur-

ing the curing process [16,17]. Although the influence of shrinkage

on the deformation behaviour of RC ties was not within the scope

of this work, its possible effects on the results have been evaluated.

Hence, using the humidity and temperature readings taken during

curing, Model Code 90 [18] predictions of shrinkage strains, esh,were made and are presented in Table 4. The reinforcement

embedded in the concrete provides restraints to concrete shrink-

age, leading to compressive stress in the reinforcement and tensile

stress in the concrete (see Fig. 4). Therefore, the two main effects of

the shrinkage on the final response of the RC tie are the initial

shortening of the member, em,i, and the lower cracking load (since

concrete is under an initial tensile load, hereafter referred to as

Padd). These variables can be computed as:

em;i ¼ esh=ð1þ nqÞ ð1Þ

Padd ¼ eshEFRPAFRP ð2Þ

where n is the modular ratio, q is the reinforcement ratio, EFRP is the

modulus of elasticity of the FRP bar, and AFRP is the FRP reinforcing

area.

Because the shrinkage strain values were small, the specimens

were tested early (at the age of 28 days), and the modulus of elas-

ticity of the reinforcement was low, small influence of shrinkage

was expected. The estimated initial shortening, em,i, and the addi-

tional initial load that should be added to the measured load dur-

ing testing, Padd, are shown in Table 4.

Initial member shortening resulting from shrinkage effects is ta-

ken into account when representing the member tensile behaviour

(Fig. 3) by offsetting the bare bar response with the shortening va-

lue, em,i, presented in Table 4. The largest initial shortening corre-

sponds to specimen 16-110, although its influence is barely

detected with respect to the global response.

3.1.2. Comparison with guidelines and code provisions

The experimental evolution of RC tie mean strain with load is

compared with theoretical predictions based on Eurocode 2, ACI

224 and Model Code 90 in Fig. 5. According to Eurocode 2-92

[19] provisions, the mean reinforcement strain at a certain applied

load reads

em ¼ e1rcr

rs

� �2

þ e2 1ÿ b1b2

rcr

rs

� �2" #

ð3Þ

where b1 stands for the bond characteristics of the internal reinforc-

ing bars (1 for ribbed and 0.5 for smooth bars), b2 represents the

loading type (1 for first loading and 0.5 for repeated or sustained

loading), rcr is the tensile stress in the reinforcing bar at the cracked

section when the first crack occurs (rcr = Pcrack/As), rs is the stress in

the reinforcing bar at the cracked section at the actual load (rs = P/

As), and e1 and e2 are the strains calculated for the uncracked and

the fully cracked section, respectively. While Eq. (3) was proposed

for steel RC structures, predictions for FRP RC members can be com-

puted if an adequate value for the bond quality coefficient, b1, is as-

sumed. Although the current version of Eurocode 2 (Eurocode 2-04

[20]) proposes essentially the same equation, the coefficient

accounting for bond influence, b1, has been removed. Therefore

the equation from the previous version is considered to be more

adequate for the present study.

According to the ACI approach, the mean member strain of a

tensile member can be computed as em = PL/EcAe, where Ec is the

modulus of elasticity of concrete and L and Ae are the length and

the effective cross-sectional area of the reinforced tension mem-

ber. To be consistent with ACI 318.05 [21] based on Branson’s

equation [22] for SRC flexural members, ACI 224.2R-92 [23] pro-

poses an expression for the effective cross-sectional area of SRC

tensile elements, Ae, that varies gradually from the gross sectional

area, Ag, to the cracked cross-sectional area, Acr, as load increases

beyond the cracking point:

Ae ¼ Ag

Pcrack

P

� �3

þ Acr 1ÿPcrack

P

� �3" #

6 Ag ð4Þ

In ACI 440.1R-06 [24], for FRP RC flexural elements, a reduction

coefficient, bd, which depends on the balanced reinforcement ratio,

is used to modify Branson’s equation and adapt it to the FRP char-

acteristics. However, no reference is made in these guidelines to

tensile members. The balanced reinforcement ratio defined in ACI

440.1R-06 [24] cannot be computed in RC tensile elements. There-

fore, in order to study the tensile behaviour of FRP RC tension

members some authors have calibrated their own experimental

coefficient [9], whilst others have introduced the expression for

Table 3

Composition of concrete and mechanical properties.

Component Units C1

mix

C2

mix

C3

mix

Water kg/m3 160 150 160

Cement 42.5 kg/m3 450 450 400

Fine aggregate kg/m3 775 775 825

Coarse 12 aggregate kg/m3 250 250 250

Coarse 20 aggregate kg/m3 700 70 700

Super plasticiser Sika

Viscocrete 5920

% cement

weight

1.1 1.0 1.0

Super plasticiser Sikament 90P % cement

weight

– – 0.6

Super plasticiser Sikament 290 % cement

weight

0.72 0.60 –

Mechanical properties

Compressive strength, fc MPa 48.1 56.2 46.6

Elasticity Modulus, Ec MPa 27,315 33,275 34,514

M. Baena et al. / Composite Structures 93 (2011) 2511–2520 2513

bd proposed in the previous guidelines, ACI 440.1R-03 [11,25], with

the final expression for the effective cross-sectional area being:

Ae ¼ Agbd

Pcrack

P

� �3

þ Acr 1ÿPcrack

P

� �3" #

6 Ag ð5Þ

where bd computes the differences in reinforcement characteristics

bd ¼ 0:5EFRP

Esteel

þ 1

� �

ð6Þ

The tension stiffening effect, responsible for increasing the post-

cracking stiffness of the RC tension member, is taken into account

in Model Code 90 [18] by modifying the stress–strain relationship

of embedded reinforcement:

em ¼

e1 uncracked stagee2 ÿ

btðrsÿrsr1ÞþðrsrnÿrsÞ

ðrsrnÿrsr1Þðesr2 ÿ esr1Þ crack formation phase

e2 ÿ btðesr2 ÿ esr1Þ stabilized cracking

8

<

:

ð7Þ

where esr1 and esr2 are the reinforcement strains for uncracked and

cracked sections, respectively, when the first crack has formed. rsr1

and rsrn are the reinforcement stresses in the crack, when the first

and last cracks have formed, respectively, and bt is a factor for rein-

0 0.005 0.01 0.0150

60

120

180

Member Mean Strain εm

Ax

ial

Load P

(kN

)

13-170 ρ =0.51%13mm bare barMechanical extensometer

(a)

0 0.0045 0.009 0.0135 0.0180

50

100

150

200

Member Mean Strain εm

Ax

ial

Load P

(kN

)

16-170 ρ =0.71%16mm bare barMechanical extensometer

(b)

0 0.005 0.01 0.0150

60

120

180

Member Mean Strain εm

Ax

ial

Load

P (

kN

)

19-170 ρ =1.00%19mm bare barMechanical extensometer

(c)

0 0.0045 0.009 0.0135 0.0180

50

100

150

200

Member Mean Strain εm

Ax

ial

Load P

(kN

)

16-110 ρ =1.69%16mm bare barMechanical extensometer

(d)

0 0.005 0.01 0.0150

60

120

180

Member Mean Strain εm

Axia

l L

oad

P (

kN

)

19-170-N ρ =1.25%19-N bare barMechanical extensometer

(e)

0 0.005 0.01 0.0150

60

120

180

Member Mean Strain εm

Axia

l L

oad

P (

kN

)

16-170-3N ρ =1.00%16-N bare barMechanical extensometer

(f)

Fig. 3. Experimental load-member mean strain curves.

Table 4

Predictions of shrinkage strains, esh, RC tie initial shortening, em,i, and additional load,

Padd.

Specimen fcm (MPa) RH (%) esha (le) em,i (le) Padd (N)

13-170 48.1 60 ÿ99 ÿ98 499

16-170 46.6 52 ÿ111 ÿ110 1058

19-170 56.2 45 ÿ87 ÿ86 1017

16-110 56.2 45 ÿ130 ÿ127 1023

19-170-N 56.2 45 ÿ87 ÿ86 1017

16-170-3 N 46.6 52 ÿ111 ÿ110 1058

a According to Model Code 90 [18].

2514 M. Baena et al. / Composite Structures 93 (2011) 2511–2520

forcement strain along the transmission length reading 0.4 for pure

tension. According to Model Code 90 [18], the reinforcement stress

at the last crack may be taken as rsrn = 1.3 rsr1.According to Eq. (3), the differences in mechanical properties

between FRP and steel reinforcement can be accounted for in Euro-

code 2-92 with a correct assumption of the bond quality coefficient

b1. For instance, in the experimental programme presented in [9], a

very close to that proposed for smooth steel rebars global b1 value

(i.e. b1 = 0.5) was found; however, the authors observed that a lar-

ger number of tests was needed to be analysed. In the present

study, with no specific data available for the rebar used, extreme

values of b1 = 0.5 and b1 = 1 have been assumed to validate the

Eurocode 2-92 proposal (see Fig. 5). In the verification of ACI

224/440, Eqs. (5) and (6) have been used.

As shown in Fig. 5, the prediction of member deformation using

Eq. (5) clearly underestimates the strain of the FRP RC specimen as

a consequence of an overestimation of the member stiffness, as re-

ported in previous studies [3,9]. The underestimation of computed

deflections for FRP RC flexural elements observed by others

[4,5,7,8,10,11] is also linked with the overestimation of the tension

stiffening effect obtained with the direct use of Branson’s

approach.

In contrast, experimental load-deformation curves fall within

Eurocode 2-92 predictions, with conservative predictions when

b1 = 0.5.

3.2. Crack formation and stabilized cracking phase

The initial linear branch with a steep slope visible in the load-

member strain relationship (Fig. 3) corresponded to the uncracked

condition of the tensile members. Once cracking load, Pcrack, was

reached, the first transversal crack appeared. From that moment,

and due to the increments in the applied load, a progressive trans-

verse cracking of the ties where q = 0.51%, 0.71% and 1.69% was ob-

served. However, for the tension member with q = 1.00%, as load

was increased beyond the cracking load, a combination of trans-

verse and splitting cracking took place. The zigzag line observed

in the crack formation phase is the result of the displacement con-

trol mode chosen to conduct the tests. Finally, once the cracking

process stabilized, no more new cracks appeared and only the

opening of the existing ones could be observed. The final crack pat-

terns of the specimens are shown in Fig. 6, with cracks numbered

according to appearance order and crack spacing measurements

taken at the height of the reinforcement.

The experimental values of the ratio of crack stabilization load

to first cracking load, Psta/Pcrack, are presented in Fig. 7 (for the

non-notched elements). In contrast to the simplified proposal of

a constant ratio of 1.3 in Model Code 90, a dependence on the rein-

forcement ratio is found. In Table 5, the experimental data illus-

trated in Fig. 7 is presented.

3.3. Crack spacing

3.3.1. Experimental results

The crack stabilization phase is reached when crack spacing be-

tween two existing cracks, sr, is not large enough for a new crack to

form. Therefore, minimum crack spacing, sr0, can be defined as the

closest point to an existing crack at which the concrete tensile

strength has been reached. Hence, a new crack can form if srP 2

sr0, whereas if sr < sr0, no more cracks can be formed. Therefore,

crack spacing is expected to vary between sr,min = sr0 and

sr,max = 2sr0, while average crack spacing could be defined as

srm = 1.5sr0. According to these equalities, maximum-to-average

and minimum-to-average crack spacing ratios could be expressed

as sr,max/srm = 1.33 and sr,min/srm = 0.67. It should be mentioned that,

values for these maximum-to-average and minimum-to-average

crack spacing ratios proposed in the literature for flexural elements

range from 1.33 to 1.54 and from 0.67 to 0.77, respectively [26,27].

In Table 6 experimental results on crack spacing measurements,

taken at the height of the reinforcement once stabilized cracking

was reached, are presented. The experimental average crack spac-

ing is defined as the ratio of the distance between the most external

transverse cracks formed during the test to the quantity (nc ÿ 1),

where nc is the number of transverse cracks. In Fig. 8 experimental

values of the ratios sr,max/srm and sr,max/srm, computed for each tie in

the crack stabilization phase, are shown. The ratios vs. average

crack spacing are presented. Although a trend line cannot be drawn,

the mean values of the ratios are presented with a horizontal

dashed line (sr,max/srm = 1.53, sr,min/srm = 0.58). The experimental

mean value of sr,max/srm obtained in the tests falls within the

above reported range [26,27], while the experimental mean value

of sr,min/srm is slightly lower than the values of the reported range.

3.3.2. Comparison with code provisions

The experimental average crack spacing, srm, can be compared

with Eurocode 2 predictions. The Eurocode 2-92 [19] proposal for

average crack spacing predictions at the stabilized stage describes

the influence of reinforcement size and reinforcement ratio as:

srm ¼ 50þ 0:25k1k2db

qeff

ð8Þ

where the bond coefficient, k1, is 0.8 for ribbed and 1.6 for smooth

steel bars, the loading type coefficient, k2, is 0.5 for flexural and 1 for

tensile loading, and qeff is the ratio of internal reinforcement to the

effective area of concrete in tension (total area for members in ten-

sion). In Eurocode 2-04 [20], the maximum crack spacing can be ob-

tained with:

sr;max ¼ 3:4c þ 0:425k1k2db

qeff

ð9Þ

In Eqs. (8) and (9), the first term accounts for the influence of

concrete cover on crack spacing. Eq. (8) implicitly assumes a cover

value of 25 mm, whereas in Eq. (9) the cover influence is explicitly

included.

As in Eqs. (3), (8), and (9) can be adapted to FRP RC structures,

by adjustment of the bond coefficient (k1). The Eurocode 2 provi-

sions for crack spacing are compared with the experimental results

in Table 7. Although good bond behaviour of FRP bars was consid-

ered in the provisions, assuming k1 = 0.8, the comparison of the

predicted and experimental results shows a clear overestimation

of crack spacing.

εsh

εm,iPadd

Shrinkage

compensated

response

P

εm

Pcr

idealized

origin

Bare bar response

Fig. 4. Shrinkage compensated response (after Bischoff [16]).

M. Baena et al. / Composite Structures 93 (2011) 2511–2520 2515

Following the Eurocode 2 approach, the experimental average

crack spacing is presented in Fig. 9 as a function of db/qeff. Based

on the experimental results for average crack spacing obtained in

this study, a linear relationship is adjusted to describe their

dependence:

srm ¼ 20:8þ 0:0835db

qeff

ð10Þ

A clear dependence on the ratio db/qeff is observed, although the

value of the origin ordinate of Eq. (10) does not fit with either of

the two Eurocode 2 proposals when the covers of the tested spec-

imens are taken into account. Therefore, the role that the concrete

cover plays on the crack spacing of RC members with large cover

(as those of the present study) differs from that of RC flexural

members, where smaller concrete covers are usually found.

3.4. Crack width

3.4.1. Experimental results

Crack width measurements taken at the height of the reinforce-

ment are presented in this section. In Table 8 maximum, minimum

and average crack widths measured during the crack formation

phase are shown. As these measurements were taken whenever a

new crack appeared during the test, the load level at the time of

measurement was taken and the number of cracks at that load is

also reported. The loads shown in Table 8 correspond to the valley

points in Fig. 3 when the crack width was measured. It should be

noted that the evolution of the average crack width depends on

the number of cracks that formed at a certain load. In this sense,

for those cases where more than one crack appears at a certain load

value, the increase in reinforcement strain is distributed over the

0 0.005 0.01 0.0150

60

120

180

Member Mean Strain εm

Ax

ial

Lo

ad

P (

kN

)

13-17013 bare barEC2-92 β

1=0.5

EC2-92 β1=1

ACI 224/440MC90

(a)

0 0.0045 0.009 0.0135 0.0180

50

100

150

200

Member Mean Strain εm

Axia

l L

oad

P (

kN

)

16-17016 bare barEC2-92 β

1=0.5

EC2-92 β1=1

ACI 224/440MC90

(b)

0 0.005 0.01 0.0150

60

120

180

Member Mean Strain εm

Ax

ial

Lo

ad

P (

kN

)

19-17019mm bare barEC2-92 β

1=0.5

EC2-92 β1=1

ACI 224/440MC90

(c)

0 0.0045 0.009 0.0135 0.0180

50

100

150

200

Member Mean Strain εm

Ax

ial

Load

P (

kN

)

16-11016 bare barEC2-92 β

1=0.5

EC2-92 β1=1

ACI 224/440MC90

(d)

0 0.005 0.01 0.0150

60

120

180

Member Mean Strain εm

Axia

l L

oad P

(kN

)

19-170-N

19N bare barEC2-92 β

1=0.5

EC2-92 β1=1

ACI 224/440

MC90

(e)

0 0.005 0.01 0.0150

60

120

180

Member Mean Strain εm

Axia

l L

oad P

(kN

)

16-170-3N

16N bare barEC2-92 β1=0.5

EC2-92 β1=1

ACI 224/440

MC90

(f)

Fig. 5. Comparison between experimental curves and EC2-92 [19], ACI 224/440 (Eq. (5)) and MC90 [18] predictions.

2516 M. Baena et al. / Composite Structures 93 (2011) 2511–2520

newly formed cracks, so the average crack width may not necessar-

ily increase during the crack formation phase.

In Fig. 10, the experimental maximum and minimum crack

widths are plotted as a function of experimental average crack

width. Although some scatter is found in the experimental results,

a linear trend of the maximum and minimum crack width with the

average crack width is observed.

3.4.2. Comparison with guidelines and code provisions

The experimental crack width data can be compared with pre-

dictions using ACI 224 and Eurocode 2. ACI 224 [23], for steel ten-

sile RC structures, proposes an empirical formula to directly

evaluate the maximum crack width in fully cracked tensile mem-

bers without evaluating crack spacing:

wmax ¼ 0:0145rs

ffiffiffiffiffiffiffiffi

dcA3p

� 10ÿ3 ð11Þ

where rs is the stress in the steel reinforcement at the cracked sec-

tion, dc is the distance from the centre of bar to the extreme tension

fibre and A is the area of concrete symmetric with the reinforcing

steel divided by the number of reinforcing bars. A large variability

in maximum crack width for tensile members is recognised in

[23], and therefore variations of up to 30% are expected. Moreover,

no extension of Eq. (11) to FRP RC ties has been proposed.

Fig. 6. Final crack pattern.

0 0.5 1 1.5 20

0.5

1

1.5

2

Reinforcement ratio, ρ (%)

Pst

a/P

cra

ck

MC90 proposal: 1.3

Fig. 7. Ratio of crack stabilization to first cracking load.

Table 5

Experimental data on the crack formation phase.

Specimen First cracking

load, Pcrack (kN)

Crack

stabilization load,

Psta (kN)

Psta/

Pcrack

Number of

transverse

cracks, nc

13-170 50.6 60.8 1.20 4

16-170 74.6 85.0 1.14 6

19-170 60.9 100.8 1.65 9

16-110 28.4 49.7 1.75 8

Table 6

Experimental maximum, minimum and average crack spacing at stabilized cracking

phase.

Specimen q (%) sr,max,exp (mm) sr,min,exp (mm) srm,exp (mm)

13-170 0.51 280.33 170.56 264.96

16-170 0.71 288.42 198.60 227.75

19-170 1.00 176.12 77.29 113.27

16-110 1.69 232.11 60.73 123.34

19-170-N 1.25 250.24 82.67 132.03

M. Baena et al. / Composite Structures 93 (2011) 2511–2520 2517

In contrast to the provisions for RC tensile members, equations

originally derived for steel RC beams have been extended for use in

FRP RC flexural members in ACI 440.1R-03 [25]. In these guide-

lines, a modification of the well-known Gergely–Lutz equation

[28] is proposed to calculate the crack width:

w ¼ 2:2akbrFRP

EFRP

ffiffiffiffiffiffiffiffi

dcA3p

ð12Þ

where a is the ratio of the distance from the neutral axis to the ex-

treme tension fibre to the distance from the neutral axis to the cen-

tre of tensile reinforcement, rFRP is the stress in the FRP reinforcing

bar at the cracked section, EFRP is the modulus of elasticity of the

reinforcing bar and kb is a coefficient accounting for the degree of

bond between the FRP bar and the surrounding concrete. According

to the ACI 440.1R-03 [25] provisions, kb can vary from 0.71 to 1.83,

with a proposed design value of 1.2 for those cases where no data

are available for a given bar.

ACI 440.1R-06 [24] proposes a crack width formulation based

on a physical model, rather than an empirically derived one [29].

Following this approach, the maximum crack width may be calcu-

lated from:

w ¼ 2ffEf

bkb

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

d2c þ

s

2

� �2r

ð13Þ

where ff is the reinforcement stress, Ef is the reinforcement modulus

of elasticity, b is the ratio of (i) the distance between the neutral

axis and the tension face to (ii) the distance between the neutral

axis and the centroid of reinforcement (assumed to be 1 in this

case), dc is the thickness of cover, s is the bar spacing and kb is a

bond quality coefficient. For those cases where no data are avail-

able, a value of kb = 1.4 is recommended.

The Eurocode 2-92 [19] proposal for characteristic crack width

is derived from average crack width, through the coefficient bk.

Therefore, the characteristic crack width is a function of the

product of average crack spacing, srm, and relative average strain

of reinforcement, esm,r, and reads:

wk ¼ bksrmesm;r ð14Þ

where srm is described through Eq. (8), bk may be taken as 1.7 for

load induced cracking, and esm is defined as:

esm;r ¼ e2 1ÿ b1b2

rcr

rs

� �2" #

ð15Þ

In Eurocode 2-04 [20] a different form of the equations is

adopted and characteristic crack width is defined as the product

of maximum crack spacing and the difference between the mean

strain of steel and concrete between cracks:

wk ¼ sr;maxðesm ÿ ecmÞ ð16Þ

where sr,max is described through Eq. (9) and the difference in mate-

rials’ strains between cracks is described as:

esm ÿ ecm ¼ es ÿ ktfctmAc;eff

EsAs

þfctmEc

� �

ð17Þ

where fctm is the mean tensile strength of concrete, Es and Ec are the

modulus of elasticity of reinforcement and concrete, respectively, As

is the reinforcing area, Ac,eff is the effective area of concrete in ten-

sion, es is the strain in the reinforcing bar at the cracked section at

the actual load (es = PL/EsAs) and kt, a factor that depends on the

duration of the load, is 0.6 for short term loading and 0.4 for long

term loading. In contrast to the provisions of Eurocode 2–92 [19],

in this new provision the reinforcing bar surface type is implicitly

included in the calculation of the term (esm ÿ ecm), with a coefficient

of 1 relating to high bond bars. Also, the coefficient bk of Eurocode

2-92 (see Eq. (14)) in the new version is implicitly included in Eq.

(9).

The experimental maximum crack width, wmax,exp, is compared

to ACI provisions in Fig. 11. The lack of a specific coefficient in ACI

224 [23] to account for the differences in bond behaviour of FRP RC

0 50 100 150 200 250 3000

0.5

1

1.5

2

Average crack spacing, srm

(mm)

Cra

ck s

pacin

g r

ati

os

sr,max

/srm

sr,min

/srm

1.53

0.58

Fig. 8. Ratios of maximum-to-average and minimum-to-average crack spacing vs.

average crack spacing.

Table 7

Maximum and average crack spacing provisions.

Specimen Average crack spacing Maximum crack spacing

srm,exp (mm) sarm (mm) sarm/srm,exp sr,max,exp (mm) sbr,max (mm) sbr,max/sr,max,exp

13-170 264.96 586.00 2.21 280.33 1176.86 4.19

16-170 227.75 486.00 2.13 288.42 1001.47 3.47

19-170 113.27 434.50 3.83 176.12 910.11 5.17

16-110 123.34 241.26 1.96 232.11 484.76 2.09

a Estimated value according to Eurocode 2-1992, Eq. (8).b Estimated value according to Eurocode 2-2004, Eq. (9).

0 1000 2000 30000

50

100

150

200

250

300

db/ρ

eff (mm)

Avera

ge c

rack

sp

acin

g, s

rm (

mm

)

srm

=20.8+0.0835 db/ρ

eff

Fig. 9. Average crack spacing vs. db/qeff with proposed lineal adjustment.

2518 M. Baena et al. / Composite Structures 93 (2011) 2511–2520

ties compared to steel, underestimates the crack width prediction.

However, despite being developed for predicting crack width in

flexural FRP RC members, accurate predictions of maximum crack

width in GFRP RC ties are obtained using ACI 440.1R-03 [25], and

ACI 440.1R-06 [24] with minimal differences between them. The

agreement obtained with provisions of flexural guidelines is better

than with those of direct tensile elements and can be attributed to

their proper adaptation to FRP RC structures. Based on the assump-

tion of crack width being proportional to the strain in the rein-

forcement rather than the stress [30], ACI 440 [24,25] introduces

the elastic modulus of FRP reinforcement in the crack width pre-

diction formula (Eqs. (12) and (13)).

Both versions of Eurocode 2 [19,20] examined in this paper de-

fine a dependence of crack width on crack spacing (see Eqs. (14)

and (16)) and use the k1 bond coefficient to represent the influence

of bond strength. In Fig. 12 comparison between average experi-

mental crack width at different load levels and code provisions is

presented for the two limiting values (i.e. for k1 = 0.8 and

k1 = 1.6). For comparison purposes, the characteristic values from

Eq. (16) [20] have been divided by bk = 1.7 and transformed into

average values.

As in the case of crack spacing predictions, there is a clear over-

estimation of crack width, even when the bond coefficient for high

bond bars is considered (k1 = 0.8). The accuracy of Eurocode 2 crack

width predictions relies on the effectiveness of the code to predict

crack spacing. However, crack spacing predictions have been

shown to overestimate the experimental values. Therefore, a sec-

ond comparison between new predictions and experimental read-

ings is presented in Fig. 13. In these new predictions, average crack

spacing has been computed with Eq. (10). An improvement in code

predictions has been obtained and therefore the crack width code

formulas (Eqs. (14) and (16)) are proven to be valid, although con-

tingent on crack spacing provisions.

Table 8

Experimental values of maximum, average and minimum crack width after each crack

formation.

Specimen Measurement

load P (kN)

Number of

cracks, nc

wmax,exp

(mm)

wm,exp

(mm)

wmin,exp

(mm)

13-170 42.82 1 1.00 1.00 1.00

49.90 2 1.50 1.30 1.10

52.41 3 2.10 1.67 1.00

53.84 4 2.20 1.95 1.80

16-170 57.47 1 1.50 1.50 1.50

60.04 4 1.70 0.95 0.50

63.18 5 1.70 1.08 0.50

85.12 6 2.30 1.05 0.20

19-170 54.91 1 0.80 0.80 0.80

61.53 2 2.00 1.25 0.50

62.84 6 1.70 0.82 0.30

100.23 9 2.20 0.98 0.30

16-110 25.15 1 0.40 0.40 0.40

31.68 2 0.80 0.75 0.70

36.08 3 1.60 0.94 0.40

37.76 5 1.10 0.64 0.20

46.18 6 1.60 0.94 0.20

87.69 8 3.00 1.51 0.30

0 0.5 1 1.5 2 2.50

1

2

3

4

5

Experimental mean crack width, wm,exp

(mm)

Max

imum

and m

inim

um

cra

ck w

idth

wmax,exp

wmin,exp

Fig. 10. Maximum and minimum crack width vs. average crack width.

0 1 2 3 4 5 60

1

2

3

4

5

6

Experimental maximum crack width, wmax,exp

(mm)

Pre

dic

tion

s on

cra

ck w

idth

, wm

ax (

mm

)

ACI 224.2R-92

ACI 440.1R-03

ACI 440.1R-06

Fig. 11. Comparison between experimental and ACI [23–25] provisions of maxi-

mum crack width.

0 5 10 150

5

10

15

Experimental average crack width, wm,exp

(mm)

Pre

dic

tio

ns

on

cra

ck

wid

th, w

m (

mm

)

EC2-92 k1=0.8

EC2-92 k1=1.6

EC2-04 k1=0.8

EC2-04 k1=1.6

Fig. 12. Comparison between experimental and Eurocode 2 [19,20] provisions of

mean crack width using k1 bond coefficient limits.

0 1 2 3 40

1

2

3

4

Experimental average crack width, wm,exp

(mm)

Pre

dic

tio

ns

on

cra

ck

wid

th, w

m (

mm

)

EC2-92 β1=0.5

EC2-92 β1=1

EC2-04

Fig. 13. Comparison between experimental and Eurocode 2 [19,20] provisions of

mean crack width, using proposed Eq. (10).

M. Baena et al. / Composite Structures 93 (2011) 2511–2520 2519

4. Conclusions

The tests results of an experimental programme on GFRP RC ties

have been presented and discussed in this paper. Their tensile

behaviour is compared to the ACI 224 and Eurocode 2 proposals.

Clear overestimation of member stiffness is found in ACI 224.2R

predictions, even when the reduction factor first introduced for

ACI FRP RC flexural guidelines (ACI 440.1R-03) is adapted to ACI

tensile provisions (ACI 224). The different theoretical background

of Eurocode 2 provides more accurate predictions.

However, Eurocode 2 provisions of crack spacing do not provide

accurate results when applied to GFRP RC tension members. In this

sense, the dependence of crack spacing on the ratio of rebar diam-

eter over reinforcement ratio is confirmed by experimental results.

The additional dependence on the concrete cover proposed in

Eurocode 2 does not seem directly applicable to RC tensile mem-

bers as those of the present study. Consequently, the role that

the concrete cover plays on the crack spacing differs from that of

RC flexural members, where smaller concrete covers are usually

found. Based on the limited experimental tests conducted in this

study, an equation that describes the relationship between crack

spacing and the ratio of rebar diameter over reinforcement ratio

is proposed.

Despite being developed to predict crack width in flexural FRP

RC members, accurate predictions of maximum crack width in

GFRP RC ties are obtained using both ACI 440.1R-03 and ACI

440.1R-06.

Direct application of Eurocode 2 provisions on crack width

clearly overestimates experimental values. The poor accuracy is re-

lated to inaccurate predictions on crack spacing. A substantial

improvement in Eurocode 2 crack width prediction is obtained

when the crack spacing proposal presented in this paper is

considered.

Acknowledgements

The authors gratefully acknowledge the support provided by

the Spanish Government (Ministerio de Educación y Ciencia), Project

Ref. BIA2007-60222. The first author also acknowledges the sup-

port from the Generalitat de Catalunya for an FI pre-doctoral grant.

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