Flexural Behaviour of Concrete Beams Reinforced with Carbon FRP Composite Bars

Flexural Behaviour of Concrete Beams ReinforcedWith GFRP Bars

L. Ascione, G. Mancusi and S. Spadea

Department of Civil Engineering, University of Salerno, Via Ponte don Melillo, 84084 – Fisciano (SA) Italy

ABSTRACT: The paper presents some of the results from a large experimental program undertaken

at the Department of Civil Engineering of Salerno University. The static behaviour under service

conditions of concrete beams reinforced with GFRP (Glass Fibre-Reinforced Polymer) as well as

CFRP (Carbon Fibre-Reinforced Polymer) bars and stirrups is examined. Within the whole

experimental program concerning forty beams, two different concrete strengths and two different

percentages of reinforcement are taken into consideration. The final aim is to investigate both

deflections at midspan and crack widths. Moreover, the ultimate behaviour up to failure is also

investigated. A part of this experimental program, concerning ten prototypes reinforced with GFRP

bars, is here presented and discussed. Finally, comparisons with analytical predictions given by CNR-

DT 203/2006 are also shown.

KEY WORDS: CNR-DT 203/2006, crack width, deflection, GFRP bars.

NOMENCLATURE

b cross section width

h cross section depth

d effective dept (distance from internal tensile

bars to the top of the section)

L beam span

La shear span

F single external force according to the four point

bending scheme

Deff effective diameter of FRP bar

DN nominal diameter of FRP bar

A0f amount of reinforcement (FRP) in compression

Af amount of reinforcement (FRP) in tension

Ec compressive Young modulus of concrete (eval-

uated according to [22])

Ef tensile Young modulus of FRP bars

fmax tensile strength of FRP bars

Rcm cubic compressive strength of concrete (mean

value)

Rck cubic compressive strength of concrete (fractile

5%)

fcfm tensile strength of concrete under flexure

(mean value evaluated according to [22])

Fcr cracking limit, referred to the external force F

Fu ultimate limit, referred to the external force F

Mcr bending moment at midspan corresponding to

cracking limit

Mu bending moment at midspan span correspond-

ing to ultimate limit

I1 moment of inertia of un-cracked cross section

I2 moment of inertia of the cracked cross section

f deflection of members

wk characteristic cracks width

srm average distance between cracks

Introduction

Over the last few years the use of FRP (Fibre-Rein-

forced Polymer) bars as internal reinforcement for

concrete structures has been sustained and particu-

larly encouraged in the international technical and

research community and specific technical instruc-

tions and guidelines have been published. Japan has

been one of the forerunners and drew up the first

design guidelines in 1996, subsequently translated

into English 1 year later [1]. Further guidelines were

published in Canada in 1996 [2], followed by those

published by ACI in 2000 and revised in 2006 [3].

More recently technical documents dealing with the

designing and execution of FRP concrete construc-

tions have been published in Europe [4] and in Italy

[5].

Despite the numerous advantages exhibited by

concrete structures reinforced with FRP bars,

there are still many issues demanding further

� 2010 Blackwell Publishing Ltd j Strain (2010) 46, 460–469460 doi: 10.1111/j.1475-1305.2009.00662.x

investigation. The predictive models, the design for-

mulae developed over the years for structures rein-

forced with steel bars, cannot be directly applied to

FRP bars reinforced beams. It is worth considering the

different constitutive behaviour of the FRP bars

[6–10]. With respect to steel bars, FRP bars behave

linearly elastic up to failure, with quite different

stiffness and resistance values. Moreover, concrete

members reinforced with FRP bars very often exhibit

a lower post-cracking bending stiffness. Conse-

quently, the designing phase is substantially gov-

erned by limitations on serviceability (displacements

and crack width). These aspects are strictly connected

when it is considered that the kinematics of these

members depends on the inertia of the cross-section

that is influenced by the cracking phenomenon. On

the other side it is well known that the crack width

increases depending on the deformability of the

reinforcing internal bars.

The classical formulation in evaluating the

moment of inertia of concrete beams reinforced

with steel bars systematically results in excessive

errors in the case of FRP reinforced beams. This

produces an underestimation of the expected dis-

placements. In order to take into account the dif-

ferent behaviour in constitutive law as well as in

bonding to concrete of the composite bars, the

formulae have to be modified, introducing some

appropriate coefficients, which need to be experi-

mentally validated [11–21].

This work aims to give a contribution to the

design procedures of FRP reinforced beams by a

comparison between a large experimental database

and theoretical predictions, both at service and

ultimate conditions.

Experimental Program

The experimental tests presented here concern ten

concrete beams reinforced with GFRP bars and

stirrups. They have been grouped into two sets,

each relating to a different strength of concrete.

Each set is composed of five identical specimens

cast in place with the same concrete mixture and

tested according to a four point bending scheme.

The cross-section of the specimens is rectangular:

b = 150 mm · h = 200 mm; the total length is

equal to 2300 mm; the span, L, is equal to

2000 mm; the ratio between shear span and effec-

tive depth, La/d, is equal to 4.12. Details of the

specimens are reported in Figure 1.

An additional thirty specimens were fabricated and

will be tested in subsequent phases. They differ from

the previous ones with regard to the amount of ten-

sile reinforcing area and/or the type of FRP internal

Figure 1: Test specimen: geometry, reinforcement detail and test scheme

� 2010 Blackwell Publishing Ltd j Strain (2010) 46, 460–469doi: 10.1111/j.1475-1305.2009.00662.x 461

L. Ascione, G. Mancusi and S. Spadea : Flexural Behaviour of GFRP RC Members

reinforcement (GFRP/CFRP). Two different casting

phases have been performed: in the first, concerning

sets I, II, V, VI, a C20/25 concrete was used, in the

second, relative to sets III, IV, VII, VIII, a C28/35

concrete was used. Figure 2 shows the reinforcing

cage of the specimen in the formwork.

For each phase, 15 cubic concrete samples

(150 mm · 150 mm · 150 mm) were tested under

compression. Tensile tests on reinforcing bars (Fig-

ure 3) were carried out too, in order to determine

their mechanical characteristics.

The mechanical properties taken into consideration

within the whole experimental program are given in

Table 1, where the symbol ‘*’denotes the specimens

already tested and discussed in this paper. FRP

mechanical properties are based on experimental test

carried out at Milan Polytechnic University, within the

activity of the same research project [23]. With regards

to tensile strength of CFRP bars, the nominal value

furnished by the producer was reported.

Instrumentation, Test Setup and Loading

Each beam was instrumented by electric strain gauges

(SGs) as well as Linear Variable Differential Trans-

ducers (LVDTs), as shown in Figure 4. Five strain

gauges were bonded to the concrete faces at midspan

section (SG1, SG2, SG3, SG4, SG5). Furthermore,

three displacement transducers (V1, V2, V3) were

installed: one at midspan section and two other ones

at distance La=2 from each support. Another group of

four LVDTs (H1, H2, H3 and H4) were applied to the

concrete front face.

The above described equipment is introduced with

the following purposes:

• Five strain gauges (SG1-SG5), placed in the mid-

span section, are utilised to evaluate the flexural

curvature before cracking. The flexural curvature

is also calculated by data acquired from LVDTs

H1 and H3.Figure 2: Specimens before casting

Figure 3: Reinforcing bars: GFRP (Deff = 10 mm – DN = 10 mm) and CFRP (Deff = 12 mm – DN = 10 mm)

Table 1: Mechanical properties of specimens

Set

Concrete Rebars

Class

Ec

[Mpa]

Rcm

[Mpa]

Rck

[Mpa]

fcfm

[Mpa] GFRPCFRP

Ef

[Mpa]

fmax

[Mpa]

A0f[mm2]

Af

[mm2]

I* C20/25 27086 24.1 22.4 2.53 Glass 46 000 970 2/7 2/10

II C20/25 27086 24.1 22.4 2.53 Glass 46 000 970 2/7 5/10

III* C28/35 29490 32.0 30.1 3.08 Glass 46 000 970 2/7 2/10

IV C28/35 29490 32.0 30.1 3.08 Glass 46 000 970 2/7 5/10

V C20/25 27086 24.1 22.4 2.53 Carbon 115 000 2000 2/7 2/10

VI C20/25 27086 24.1 22.4 2.53 Carbon 115 000 2000 2/7 5/10

VII C28/35 29490 32.0 30.1 3.08 Carbon 115 000 2000 2/7 2/10

VIII C28/35 29490 32.0 30.1 3.08 Carbon 115 000 2000 2/7 5/10

*Specimens already tested and discussed.


Flexural Behaviour of GFRP RC Members : L. Ascione, G. Mancusi and S. Spadea

• Once cracks have occurred, the flexural curvature

is evaluated only by means of LVDTs H1 and H3.

• Moreover, vertical LVDTs V1, V2 and V3 are uti-

lised to evaluate the deflections of the beam over

its whole length.

• Finally three horizontal LVDTs (H2, H3, H4) are

utilised to evaluate the crack width.

The tests were performed at Structural Engineering

Laboratory of the University of Salerno. The experi-

mental setup includes (Figure 5):

• reaction frame for vertical loads,

• servo-controlled hydraulic actuator,

• 350 kN load cell.

The load was gradually increased up to failure. All

sensors (strain gauges, LVDTs, load cell) were

recorded by an automatic data acquisition system

(Vishay System 5000; Vishay Electronic GmbH, Selb,

Germany) connected to a computer.

Results and Discussion

The experimental results regarding ten beam speci-

mens are presented to highlight the peculiar features

of concrete members reinforced with GFRP bars and

stirrups. Comparison between experimental evidence

and theoretical predictions are also shown. With

regards to the latter, predictions have been estab-

lished using force equilibrium equations and strain

compatibility, by assuming the following hypothe-

ses:

• plane section preservation;

• perfect reinforcement-concrete bonding;

• no shear deformations.

Moreover, in order to compare the experimental

values, partial factors and environmental conversion

factors (see the design formulae given in [5]) have

been assumed unitary.

With regard to the theoretical value of cracking

load level, the following assumptions have been

introduced:

• concrete behaviour is linear elastic, with a ratio

between tensile to compressive Young modulus

equal to 0.50;

• concrete tensile strength is equal to fcfm, evaluated

according to the Italian code [22] (fcfm = 1.2 Æ fctm

where fctm ¼ 0:3 � f 2=3ck – unit strength N/mm2).

In Table 2, both experimental and theoretical values

of the cracking load level are summarised. Experi-

mental values are easily determined analyzing the

Load-Displacement curves and detecting the point

where the loss in term of secant stiffness is more than

10% of the initial tangent stiffness.

As expected, Table 2 confirms the low reliability of

the analytical prediction of the initial cracking load

level Fcr.

Figure 5: Testing setup

Figure 4: Instrumentation

Table 2: Initial cracking load (unit load: kN)

Set Test 1 Test 2 Test 3 Test 4 Test 5 Mean value Fcr

I 4.74 3.52 4.55 3.81 3.56 4.04 4.40

III 3.35 2.71 4.88 3.09 4.00 3.61 5.34



In addition, the ultimate load has been evaluated

as follows:

• the concrete contribution has been accounted by

means of the equivalent rectangular stress-block;

• tensile concrete contribution has been neglected;

• compressive FRP bars have not been considered, as

suggested in [5];

In Table 3 the experimental values of failure loads are

presented. Comparisons with theoretical values for

both flexure and shear failure are also shown.

The average experimental ultimate load is, in both

cases, very close to the theoretically predicted one.

However, though the specimens were pre-designed

for a flexural collapse (rupture due to concrete

crashing), measured values of compressive deforma-

tion in concrete at the collapse are normally far from

ones expected. Moreover the actual failure mode has,

in many cases, similarities with a brittle one

(Figure 6). A great discordance between CNR-DT 203

and ACI 440 shear failure load formulae is found, due

to the strain limitation for FRP stirrups introduced in

the latter. It is worth noting that the latter prediction

seems to work better.

In Figure 7(A)–(E) an analysis of cracking phe-

nomenon up to failure of specimens is reported with

reference to Set I.

In Figure 8(A) and (B) bending moment versus

experimental flexural curvature response is shown for

beams (both set I and set III are referred to).

As it is easy to observe, the pre-cracking behav-

iour is clearly separated from the post-cracking

response: the moment-curvature relationship in

post-cracking state is quite linear, no relevant

tension stiffening contributions appeared in these

specimens.

In view of these considerations, a conservative

theoretical moment curvature relation can be repre-

sented through a tri-linear curve depending only on

three parameters, to be calculated according with the

aforementioned assumptions:

• cracking moment, Mcr;

• flexural stiffness of un-cracked cross section, EI1;

• flexural stiffness of totally cracked cross section,

EI2;

The idealised curves shown in Figure 9(A) and (B) still

represent bending moment versus experimental cur-

vature. Each curve, which refers to a single test, has

been obtained by the corresponding one shown in

Figure 8(A) and (B) by means of two linear regres-

sions, without any interdependency, respectively

based on the experimental data concerning the pre-

cracking behaviour and the post-cracked response. In

the same figures the theoretical relationships

between bending moment and curvature are shown.

As it can be seen, the actual flexural stiffness is

always lower than that predicted by theoretical for-

mulae when the reinforcement is made of GFRP bars,

though the totally cracked cross section was consid-

ered. It is to be remarked, however, that the experi-

mental curvatures evaluated by means of LVDT signals

may be affected by the short LVDT gauge-length

compared to the average distance between cracks.

Deflections

The Document CNR-DT 203/2006 [5] suggests dif-

ferent procedures for evaluating deflection in FRP

reinforced members.

The classical integration of moment curvature

diagram may be computed with non-linear analysis

by taking into account both cracking and tension

stiffening concrete.

Figure 6: A typical rupture pattern

Table 3: Failure load (unit load: kN)

Set Test 1 Test 2 Test 3 Test 4 Test 5 Mean value Fflexure* Fshear* Fshear**

I 21.15 20.06 20.98 19.98 20.10 20.45 19.81 64.74 25.04

III 21.64 23.34 26.01 23.76 22.79 23.51 23.64 68.44 25.58

*, CNR-DT 203/2006; **, ACI 440.



(A)

(B)

(C)

(D)

(E)

80

24

20 20

6

7

7 7 7

14

30 30

30 30 20

35 39 38

9 15 13

37 35

30

35 30

25 35 30

15 15

15 15

15 25 11 11 11

7 7 7 7

20

20

35 35 35

26 30

30

35 35 35

35

30 23

20

20 20

20

26

8

8 8

8 8

8

8

8 14

11

11

11

11 11 11 11 11

11

11

11

11

11

11 10

10

10 10

10

10 20 20

7

7

8

8 8 8

915

6 12

16 29

8

8 8

19 19

19

19 19 19

35

12

36 25

25

30 8 25

25 25 25

10

10

10 10

25 25

25 9 9 16

16

16 20

20

38 35 35 25

25

25 25

6

6

6

6 8 6

15

15

15

15 15

17 17

17

17

17

19

19

19

9

9

9

9

9 9

9 9 9

9

32

32

7

7 7

7

7

31 19 24

24 24

9 15

15 15

15 15

20

20

6 6 9 9 9 9

20 20 9 9

39 10

11 20

20 14 12 13 37

19 15 10 37

37 19 13

A B C

A B C

A B C

A B C

A B C

A B C

A B C

A B C

A B C

A B C

Front

Front

Front

Front

Front

Back

Back

Back

Back

Back

15 12 14 10 37

24

20 20

60

40

20

0

80

60

40

20

0

80

60

40

20

0

80

60

40

20

0

80

60

40

20

0

Figure 7: Cracking patterns (A) specimen I.1, (B) specimen I.2, (C) specimen I.3, (D) specimen I.4, (E) specimen I.5



A simplified formulation is derived from the one

proposed in Eurocode 2 for traditional reinforced

concrete members:

f ¼ f1b1b2

Mcr

Mmax

� �m

þ f2 1� b1b2

Mcr

Mmax

� �m� �(1)

where

• terms f1 and f2 are, respectively, the theoretical

deflection of un-cracked and totally-cracked sec-

tion;

• parameters b1 and b2 account for bond properties

of FRP bars and load duration, respectively;

• exponent m is a coefficient to be set equal to 2.00

[5].

Moreover appendix E of [5] reports a procedure to be

used by the manufacturer of the bars to determine

FRP bar-concrete bond in order to accurately evaluate

deflections. It substantially consists of calibrating the

exponent m on the basis of the comparison between

analytical and experimental results – evaluated over

the range between 20% and 60% of ultimate load –

setting coefficient b1 and b2 unity and using an

appropriate statistical analysis.

In this work the calibration of exponent m has been

carried out using data experimentally obtained and

adopting two possible statistic procedures. A minimi-

zation of standard error, e1, and mean error, e2, was

executed separately on data related to Set I and Set III,

as well as on the entire population of data.

e1 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

n

Xn

i¼1

fðexpÞi � f

ðthÞi

� �2

fðthÞi

� �2

vuuuut ; (2)

e2 ¼1

n

Xn

i¼1

fðexpÞi � f

ðthÞi

fðthÞi

: (3)

The statistical results obtained lead to the finding

that for the peculiar bond property of GFRP bars

used, the coefficient best fitting experimental data is

equal to 1.50.

Additionally, the rational procedure proposed by

Razaqpur et al. [15], consisting on the integration of a

tri-linear moment-curvature relation without taking

into consideration tension stiffening effects, is taken

in consideration. In case of a four point bending

scheme the expression, given in [15], results:

f ¼ f2 �FL3

3EcI21� I2

I1

� �L�

L

� �3" #

(4)

(A)

(B)

Figure 8: Bending moment versus experimental flexural cur-

vature (A) (set I), (B) (set III)

(A)

(B)

Figure 9: Idealized bending moment versus experimental

flexural curvature (A) (set I), (B) (set III)



where L* = 2Mcr/F represents the extension over

which the beam is un-cracked.

In Figure 10(A) and (B) the experimental mid-span

displacements versus the total applied load, 2F, are

shown with reference to specimens of set I and set III.

Moreover, three analytical predictions, evaluated only

in the post-cracked phase, are depicted:

• curve a corresponds to the predicting formula

given in Equation (1), where b1 = 0.50, b2 = 1.00,

m = 2.00;

• curve b corresponds to the same formula, where

b1 = 1.00, b2 = 1.00, m = 1.50;

• curve c corresponds to Equation (4).

All the analytical models are in good agreement with

the experimental data with conservative predictions.

The model b, based on the assumption of unitary

values of b1, b2 and the calibration of exponent m,

gives the curve of best fit with the experimental data.

Crack Width and Distance Between Cracks

According toCNR-DT203/2006 [5], bothcharacteristic

crack width, wk, and average distance between cracks,

srm, have been evaluated over the range between 20%

and 60% of the ultimate load. Figure 11(A) and (B)

illustrates a comparison between experimental values

of crack width and the theoretical values wk.

In Table 4 both experimental and theoretical values

of theaveragedistancebetweencracksaresummarised.

Experimental data seem to assess the reliability of

the predicting formula proposed in [5] for crack width,

though a comparison with characteristic values is

done in Figures 11. On the other hand the theoretical

prediction of average distance between cracks is defi-

nitely high if compared with the experimental values.

The result is that cracking phenomenon experi-

mentally observed is, generally, more relevant than

the one predicted.

Conclusions

A large experimental program on the mechanical

behaviour of concrete members with FRP internal

reinforcement is still under development at the

(A)

(B)

Figure 10: Total applied load (2F) versus mid-span deflection,

experimental data and analytical predictions (A) (Set I), (B) (Set

III)

(A)

(B)

Figure 11: Bending moment versus crack width, experimental

data and analytical predictions (A) (Set I), (B) (Set III)

Table 4: Average distance between cracks (unit length: mm)

Set Test 1 Test 2 Test 3 Test 4 Test 5 Mean value Srm

I 143 118 105 108 110 117 193

III 112 110 100 110 133 112 193



Department of Civil Engineering of Salerno Univer-

sity. A part of this research, which has been recently

completed, was presented and discussed. The results

obtained by the authors show the main features of

the behaviour of such members.

• The predicting formula proposed by CNR-DT 203

for evaluating shear failure load seems to largely

overestimate the actual strength of FRP rein-

forced members. This point requires further

investigation in order to improve the reliability

of the design approach.

• The moment-curvature relation of FRP reinforced

members is basically linear in both the pre-

cracked and post-cracked phases, no relevant

tension stiffening contributions appear.

• Experimental results substantially assess the reli-

ability of the predicting formulae proposed in [5]

for both deflections and crack width.

• The procedure of calibration of the exponent m

seems to be consistent and could be enlarged to

other experimental data, to be obtained in sub-

sequent tests.

• Neglecting effects of tension stiffening in calcu-

lating the deflection of flexural members leads to

results in good accordance with experimental

data.

• Cracking phenomenon experimentally observed is

more relevant than the one predictable according

with [5].

Subsequent experimental tests will be useful for

analyzing these topics in members with different

characteristics. More investigation is also required in

order to better predict the actual failure mode. With

this aim, the experimental response of concrete

beams reinforced with steel bars and/or stirrups is

going to be investigated by the authors in order to

compare their mechanical behaviour with that one

here investigated, both at service and ultimate con-

ditions.

ACKNOWLEDGEMENTS

This research is a part of a main national research project

[23] financially supported by Italian Ministry of Research

whose contribution is gratefully acknowledged.

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Flexural Behaviour of Concrete Beams Reinforced with Carbon FRP Composite Bars

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