Flexural Behaviour of MRBC Beams

Composite Structures 74 (2006) 163–174

www.elsevier.com/locate/compstruct

Flexural behaviour of MRBC beams (multi-reinforcing barsconcrete beams), promoting the use of FRHPC

A. Si-Larbi, E. Ferrier *, P. Hamelin

Laboratoire Mecanique, materiaux and structures, Universite Claude Bernard, Lyon I, 82 bd Niels Bohr,

Domaine scientifique de la Doua, 69622 Villeurbanne Cedex, France

Available online 6 June 2005

Abstract

High performance concrete reinforced by short metallic fibers has been recently developed. These materials are of particular

interest for civil engineering thanks to their high compression performance and to their enhanced durability. The addition of short

metallic fibers provides the opportunity to obtain a more ductile material with more resistance to tension. Nevertheless, the use of

reinforcement is still necessary for structural applications [1]. This paper presents results obtained on SFRHP concrete beams using

mixed steel–CFRP rebar.

Five beams with steel rebar or mixed CFRP–steel reinforcement were designed according to Eurocode 2. The goal is to optimize

the reinforced concrete (RC) beam design by combining different reinforcement types in order to use the fiber reinforced HPC most

efficiently. The first beam specimen uses a non-fibrous HPC and constitutes a reference for comparison. The tests carried out upon

an FRHPC beam and reinforced by steel reinforcing bars allow the assessment of the short fiber�s effect against the bending and the

shearing stresses. It is shown that the presence of short metallic fibers in the concrete does in fact contribute to the equilibrium of the

beam. The sum of the internal moments in the tensile zone is increased by 10%.

For the last three beams, the effect of incorporating carbon fiber reinforced polymer rebar mixed with usual steel reinforcement is

studied. It is shown that beams using mixed CFRP–steel rebar are able to achieve a bending stiffness comparable to the beams rein-

forced by traditional steel reinforcement (in the elastic stage). A 50% increase in the failure load is observed.

� 2005 Elsevier Ltd. All rights reserved.

Keywords: Reinforced concrete beam; High performance concrete; Mixed reinforcement; CFRP rebar; Composites structures

1. Introduction

The objective of this study is to highlight the possibil-

ity of using short metallic fiber reinforced high perfor-mance concretes (FRHPC) in beams that are

reinforced by steel-composite multi-reinforcing bars.

First the main properties of high performance concrete

are defined. It is then possible to identify the main differ-

ences existing between standard concretes and high per-

formance concretes, justifying the material

combinations used in this study.

0263-8223/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compstruct.2005.04.001

* Corresponding author. Tel.: +33 472 692 130; fax: +33 478 946 906.

E-mail address: [email protected] (E. Ferrier).

1.1. High performance concretes

HPC are made in similar conditions to that of stan-

dard concretes, but with smaller quantities of water(water/cement ratio ranging from 0.2 to 0.3), this makes

it possible to obtain concrete compression strengths

ranging from 100 to 150 MPa. In order to maintain

good workability, large quantities of admixtures are

used. This type of concrete constitutes a family of mate-

rials with performances that vary according to the man-

ufacturing method. There are many possibilities for the

formulation of the HPC. In every mix the main constit-uents are aggregates, cement, silica fume and super

plasticizers. The different aggregates are subjected to a

rigorous selection process aimed at optimizing the

mailto:[email protected]

Nomenclature

AS1 steel rebars area (mm2)

AS2 CFRP rebars area (mm2)Es steel rebars Young�s modulus (MPa)

Ef CFRP Young�s modulus (MPa)

h height of the crack (mm)

W0 maximal opening of the crack under an incre-

ment of loading (mm)

bw, h basis and height of the area (mm)

Msd moment applied on the beam (kN m)

Mc moment undertaken by concrete (kN m)Ms1 moment undertaken by tense reinforcement

(steel) (kN m)

Ms2 moment undertaken by tense reinforcement

(CFRP) (kN m)

Mf moment undertaken by short metallic fibers

(kN m)P applied load (N)

z neutral axis position (mm)

zu neutral axis position (mm)

a crack length ratio of beam depth

� strains (m/m)

x cracks opening (mm)

rc compressive stress in concrete (MPa)

rf tense stress in concrete (MPa)v curvature

164 A. Si-Larbi et al. / Composite Structures 74 (2006) 163–174

granular mixture�s homogeneity [2]. A thermal treat-

ment or the application of pressure during the aging

phase, can allow the modulation of concrete quality

according to the project needs [3]. However, this study

is limited to the study to HPC set without any thermal

treatment.

1.2. High performance concrete (HPC) mechanical

behaviour

The modifications that create high performance con-

crete significantly affect the material behavior. The

stress–strain relationship is linear until stresses peak.

The concrete modulus of elasticity is increased by 30%

compared with a standard concrete. From a practical

standpoint, the plastic strain is insignificant when com-pared with the ultimate strain, thus, it is noted that

the strain at the ultimate stress is a less important

parameter for HPC than for a standard concrete. The

tensile strength increases less than the compression

strength (Table 1). The ratio between the compressive

strengths and tensile characteristic strengths decrease

by a twentieth, whereas, the ration is of 1/10 concerning

the standard concretes. However, in some cases the ten-sile strength reaches 6 MPa. The addition of 2% short

metallic fibers (10 mm in length) to these cementeous

Table 1

Comparison between several concrete properties

Concrete Compressive strength Tensile stren

Usual concrete R R/10

High performance concrete with

superplasticizer

2R R/10

High performance concrete with

superplasticizer and silica fume

3–5R R/15

Ultra high performance concrete with

superplasticizer and silica fume

6–20R R/20

matrices allows the concrete to obtain better mechanical

characteristics and significantly modifies the post-peak

behavior. The addition of fibers produces a material

with greater tensile properties (higher than 10 MPa)

and more ductile bending behavior. This material ductil-

ity is the consequence of fibers bridging the macro and

micro-cracks in the cementeous matrix highlighted by

many studies [4]. In other words, short metallic fiberscan modify both tensile strength and provide ductility.

1.3. The use of HPC in the case of beams

High performance concretes are most often applied

within the civil engineering field in the cases of archi-

tectural elements (front panels, street fixtures, or spe-

cific structures [5] and prestressed structures [6]. Theuse of short fiber reinforced high performance con-

crete allows the suppression of the shear steel reinforc-

ing bars. Whereas, the high cost of prestress

associated with both the material and the complex

process, limits the promotion of such structures. In

order to reduce the cost, it is necessary to look for un-

ique technical solutions such as non-prestressed steel

reinforced concrete. Concerning HPC beams, earlystudies outline the performance and the limits of these

structures:

gth Workability with slump test Durability Water/cement ratio

6–8 cm 1 0.5

15 cm 1–50 0.4

23 cm 1–500 0.25–0.32

>23 cm >1000 0.06–0.18*

A. Si-Larbi et al. / Composite Structures 74 (2006) 163–174 165

– first, the addition of metallic fibers allows the reduc-

tion or even the removal of all the transverse reinforc-

ing bars [7];

– the performance gains are significant;

– on the other hand, the tests on the ‘‘over rein-

forced’’ HPC beams [8,9] (steel rebar ratio higherthan 4%) failed by concrete crushing in the

compression zone resulting in a brittle structure

failure.

By decreasing the steel reinforcement ratio, one can

obtain a ductile failure by steel yielding, but with a low

compression level in the concrete (about 40% of the

ultimate strain of the concrete in compression). Thisdoes not take full advantage of the improved proper-

ties of HPC. The development of this new type of con-

crete for reinforced concrete structures requires,

therefore, an optimised design. The design goal is the

achievement of ‘‘ductile’’ structures that reach a signif-

icant level of strain in the compression zone at failure.

For this purpose, it is necessary to use a material with

higher tensile properties than steel, such as high resis-tance CFRP reinforcement. These reinforcing bars con-

structed by pultrusion of carbon fiber combined with

epoxy matrices have very high mechanical properties

such as their stiffness level (160 GPa) and their tensile

strength (2500 MPa). The drawback of CFRP rein-

forcement is their brittle mechanical behaviour. This

behaviour does not correspond to the desired mechan-

ical behaviour of a ductile reinforced concrete beam.But, through the combination of CFRP and steel rein-

forcement this required mechanical behavior can be

achieved.

The structural element designed this way, have a duc-

tile, and therefore, a safe behaviour. The addition of

short metallic fibers to the HPC allows the removal of

all the transverse hoops and contributes to a reduction

in the structural production costs.

Table 2

Ultra high performance concrete mix proportioning

Material Quantities (kg/m3)

Water 195

Cement 705

Silica fume 230

Sand 1010

Quartz sand 210

Super-plasticizer 45.6

Ratio water/cement (W/C) 0.21

Metallic fibers 290

2. Research significance

The tests on beams carried out in this study de-

scribe the possibility of using high performance fiber

reinforced concretes for reinforced concrete structures.

The main assumptions of steel reinforced concretedesign may be applied. First, it is shown that

CFRP–steel mixed rebars are able to maintain a bend-

ing stiffness comparable to the beams reinforced by

traditional steel reinforcement. A 50% increase in the

failure load is observed. Second, it is shown that the

presence of the metallic fibers contributes significantly

to internal section equilibrium. Finally, the results of

this study confirm the potential of this type ofstructure.

3. Experimental program

3.1. The considered method for optimization

In order to optimize the behaviour of fibrous HPC

beams reinforced by mixed reinforcement, it is necessaryto identify the mechanical behaviour of these structures

and compare it to that of standard reinforced concrete

beams. In order to isolate the influence of the material

combinations from possible geometry, it is decided, first,

to define a HPC beam reinforced by steel reinforcing

bars. Then, a HPC beam reinforced by short metallic fi-

bers is tested to identify the fiber�s influence upon the

structural behaviour. The remaining portion of the test-ing program aims to introduce the mixed reinforcement

notion with the objective of evaluating the efficiency of

this combination. The purpose of this program is identi-

fication of the multi-reinforcing bars concrete beam

behaviour by combining the materials properties with

section geometries.

Moreover, the crack bridging by short metallic fibers

effect is particularly studied with regard to both normaland shear stresses. Furthermore, the modifications to

structural behaviour caused by the use of mixed steel-

composite reinforcing bars are examined.

The performance level of MRBRC beams is assessed

through the analysis of the ultimate behaviour (load

gains, failure mechanisms, etc.) and the moment-curva-

ture response of the structure. The variation in bending

stiffness and internal moment equilibrium due to the useof different materials is studied.

3.2. Properties of high performance concrete

Lafarge defines the HPC considered for this study

(Table 2). The whole manufacturing process was carried

out by Lafarge�s Central Research Laboratory teams.

The concrete was cast in steel molds in three layersand was internally and externally vibrated. Uniaxial

compression tests were conducted on 12 test cylinders

resulting from two distinct mixing. The results are sum-

marized in Table 3.

Table 3

Compression concrete test results

Beam 1 (non-RFa) Beam 2 (RFa) Beams 3–5 (RFa)

Force (kN) Strength (MPa) Force (kN) Strength (MPa) Force (kN) Strength (MPa)

Sample 1 537 139.5 520 135.1 603 142

Sample 2 560 145.5 532 138.2 597 141

Sample 3 515 133.8 540 140.3 619 146

Sample 4 565 146.8 525 136.4 600 141

Sample 5 549 142.7 – – 625 147

Sample 6 560 145.5 – – 590 139

Average (MPa) 142 ± 5 137.5 ± 2 143 ± 3

a Reinforced fibers.

Uniti in mm

150

250

3000As = 3.35%

10 esp 100 mmA

A

Beam 1

Beam 2, 3 and 4

150

250

3000As= 3.35 % (Beam 2)As= 3.02 % (Beam 3)

Unity in mm

B

B


3.3. Mechanical properties of the reinforcement

The elastic modulus and average yield strength of the

steel reinforcement are, respectively, 210 GPa and

550 MPa. The elastic modulus and average ultimate

strength of the CFRP reinforcement are, respectively,

160 GPa and 2500 MPa (see Fig. 1).

3.4. Beam characteristics

The beams were designed according to Eurocode 2.

The resulting dimensions are shown in (Fig. 2) The de-

sign required failure of the steel/composite rebar and a

structural dead load of 200 kN, loaded in four-point

bending, which corresponds to an ultimate moment of

fc28 =R

Ft28 =T

E

Fig. 1. Mechanical law behavior of concrete.

2 6

4 20

150

5020

303020

3040

180

2 6

4 20

2 6

2 25

2 10

CFRP rebars

Steel rebars

180

70

2 252 10

150

170

7070

150

130

Beam 4 Beam 5

Beam 1 Beam 2 Beam 3

2 25 2 10

Fig. 2. Beams description.

115 kN m. The beams had a span of 3 m. Four

20 mm-diameter steel reinforcing bars were necessary

for beams 1 and 2. Two 25 mm-diameter steel rebar were

mixed with two 10 mm CFRP rebars for beams 3, 4 and

5.

250

3000

*strains gauges bonded on the lower part of the framework

3 m

Strains gauges*

Deflection sensors

700

Displacement measuring deviceFour bending point

150

Fig. 3. Experimental device.


According to Rilem recommendations [10], the shear

resistance has been verified using a concrete tensile

strength of 10 MPa.The first beam is tested in order to verify the design

and to identify the bending behavior of the HPC

beams. The second beam is HPFRC, and was tested

to evaluate the contribution of the short metallic fi-

bers. In this case, no shear stirrups were used. The last

three beams are tested in order to observe the effi-

ciency of CFRP rebars. The fourth beam had a re-

duced concrete area in the compression region (Fig.2) in order to increase the compressive stress level in

the concrete and, as a consequence of equilibrium,

the tensile stress in the rebar. The last beam corre-

sponds to an optimised area according to beam

performance.

3.5. Instrumentation of the beams

Electrical gauges of 120 X and 10 mm gauge length

were bonded on the concrete and on the longitudinal

steel to the right of the center of the beam (Fig. 3). These

measurement points give the opportunity to analyse the

changes in the strains of the concrete upper fiber and

tensile steel according to the loading. A 100 mm LVDT

displacement sensor was placed at mid-span to measure

the deflection. For each load level, the values of the dis-placement and strain gauges are recorded. The tests are

carried out to failure.

Table 4

Beam tests result

Cracking load (kN) Yielding load (kN) Failure load

Beam 1 20.3 183 199

Beam 2 24.7 153 173

Beam 3 27.8 201 270

Beam 4 15.0 180 200

Beam 5 26.7 173 260

4. Experimental investigation

Table 4 gives data for the obtained test results. They

are analysed and compared successively by taking into

consideration, first, the deflection evolution at the centre

of each beam, then by comparing the strains of theupper fiber and the tensile steel. Navier�s strain diagram

allows calculation of the curvature and the neutral axis

position. The last section concerns the study of failure

modes of each beam. For each part, a comparison of dif-

ferent mechanical behaviours is performed.

4.1. Evolution of the mid-span displacement

The set of load–deflection curves does not show sig-

nificant differences during the loading. In fact, the

deflection evolution corresponds to the usual three

stages of reinforced concrete structure behaviour. The

first stage consists of the response of the non-cracked

beam. The second stage follows cracking of the beam.

In this stage, the crack reduces the moment of inertia

and, therefore, the bending stiffness. The last stage ofbehaviour corresponds to the tensile longitudinal steel

yielding. For beams 3, 4 and 5 (mixed reinforcement),

it is important to note that the third stage of behavior

is modified. The applied load upon the structure in-

creases until failure. The first stage corresponds to the

elastic behaviour without any cracks. In the second

stage the cracking decreases the moment of inertia and

therefore the bending stiffness of the beam. The laststage of the curves corresponds to the yielding of the

tensile longitudinal reinforcement. The yielding of the

steel reinforcement occurs while the CFRP rebars

remain elastic; they bear additional loads. The stress–

strain curve analysis confirms, afterwards, this observa-

tion. A load gain of de 50% is, therefore, observed for

beams 3 and 5. The use of the mixed steel-composite

reinforcing bars allows the beams to obtain a behavioursimilar to strain hardening (see Fig. 4).

4.2. Evolution of strains

Fig. 5 represents the strain evolution of the upper

fiber and the lower reinforcing bars due to the applied

loading. Table 5 gives the strains in the materials at

loads corresponding to tensile cracking of the concrete,steel yielding, and failure.

(kN) Mid-span deflection (mm) Failure mode

31.0 Tensile rebars

34.8 Tensile rebars

51 Tensile rebars

32.3 Concrete in compression

56 Tensile rebars

0

50

100

150

200

250

300

0 10 20 30 40 50 60

Mid span displacement (mm)

Lo

ad (

kN)

Beam 1Beam 2Beam 3Beam 4Beam 5

Beam 2

Beam 4

Beam 3

Beam 1

Beam 5

Fig. 4. Evolution of mid-span deflection as a function of loading.

0

50

100

150

200

250

300

-3500 -1500 500 2500 4500 6500 8500 10500 12500 14500

Strain (µm/m)

Lo

ad (

kN)

Beam 1 steel rebars Beam 1 Beam 2 steel rebars Beam 2Beam 3 steel rebars Beam 3 CFRP rebars Beam 3 Beam 4 steel rebarsBeam 4 CFRP rebars Beam 4 Beam 5 Beam 5 steel rebarsBeam 5 CFRP rebars

5

strain gauges

strain gauges

Beam 3Beam 3

Beam 1Beam 1

Beam 2

Beam 4Beam 4

Beam 2

Beam 5Beam 5

Beam 5

Fig. 5. Evolution of material strain during the loading.


The load–strain curves of Fig. 5 illustrate the behav-

iour per unit length until failure for the concrete and

steel. It is also important to note that for beams 1, 3

and 5, the ultimate strain in the steel is higher than a

conventional strain of 10& considered by the standard.

For example, for beam 1, a strain of 14& has been re-

corded prior to tensile steel failure. It is also important

to note that for beam 3, the stress–strain response showsa strain hardening behaviour. This allows an increase in

the moment supported by the beam. Regarding the

strains of the extreme compression fiber in the concrete,

there is a significant difference between the fiber rein-

forced high performance concrete of beam 2 and the

non-reinforced HPC of beam 3. In fact, at equal load,

the upper fiber strain level is higher for the FRHPC

(beam 2) than for HPC (Fig. 5). This difference is most

likely explained by a structural effect (neutral axis posi-

tion, section equilibrium) combined with a modification

of the material behavior in the tensile part of the beam

due to the short metallic fiber reinforced concrete. The

use of Navier diagrams confirms, this observation. In

order to analyse the behaviour differences between the

different beams, it is important to calculate the evolutionof the position of the neutral axis (see Fig. 6).

4.3. Navier�s diagrams—position of neutral axis

In a compressed member, measurements from dis-

placement sensors give the length variation and, there-

fore, the strains at many points. The strain

Fig. 6. Calculated curvature.

Table 5

Beams materials strain values for several level of loading

Beam 1 Beam 2 Beam 3 Beam 4 Beam 5

Upper strain value (lm/m)

Cracking �233 �254 �212 �229 �236

Yielding �1540 �2310 �1810 �2780 �1990

Failure �2470 �3260 �3160 �3400 �3470

Rebars strains (lm/m)

Cracking 200 287 160 147 382

Yielding 2850 2870 2910 2820 2930

Failure 14600 12500 13500 3540 13100


measurements from the extreme compressive fiber and

reinforcing bars allow for the development of Navier

diagrams. These diagrams provide the opportunity to

determine the bending curvature and the position of

the neutral axis according to the applied load.

A comparison of the bending of the upper and lower

parts of the beam allows for the verification of the

assumptions that initially plane sections remain so andthat there is no sliding between the two levels of rein-

forcement and the concrete. In fact, it is possible to cal-

culate the curvature and the neutral axis position using

relation 1 and 2 (Fig. 7).

v ¼ etopfiber

ðh� zuÞð1Þ

zu ¼ �1

v� eþ h ð2Þ

With v the curvature and zu the position of the neutral

axis compared to the top of the beam, h the height ofthe beam, and e strain of the top fiber.

The neutral axis position (zu)) and the bending value

(v) are, thus, obtained from the diagrams plotted for

each load (Fig. 8a–d). The experimental strain plot is

linear through the depth of the beam, confirming that

the beam shows ideal bending behaviour. For each

beam, the bending is identical in the compressive and

tensile regions of the beam, verifying that the classichypotheses of perfect bond between concrete and rein-

forcement are not thrown into doubt when the mixed

reinforcing bars (steel–CFRP) or short metallic fiber

HPC are used.

The curvature of beam 2 follows that of beams 1 and

3 up to 30 kN m (corresponding to 52.2 kN). Above this

value the curvature of the FRHPC (beam 2) increases

more rapidly than that of the HPC beams without short

metallic fibers and of the HPFRC beams with mixedreinforcement (beams 3–5). This can be explained by

the low position (lower than in the other cases) of the

neutral axis of beam 2 denoted by zu (zu, Fig. 8). This

position stabilizes rapidly at about 146 mm for the first

HPRC beam. This phenomenon is due to the brittle con-

crete behavior in tension, which allows cracks to grow

quickly. In this situation, the equilibrium of the beam

is ensured by the steel reinforcement and the concretecompressive zone. The behaviours of Beams 2, 3, 4

and 5 differ from that of beam 1. The behaviour of the

tensed FRHP concrete is more ductile; the crack propa-

gation is controlled by short metallic fibers and rein-

forcement rebars and the neutral axis position is

modified. The neutral axis position stabilizes itself to a

position of 166 mm when the value of the load is

70 kN. The metallic fibers are therefore particularly effi-cient and contribute to the lowering of the neutral axis

position. Their effect on the flexural bending behaviour

of the beam will be analysed next. It is important to

highlight that the ultimate loads achieved in testing fit

with the design value for beam 1, however, they are

lower in the cases of the HPFRC beams. The conventional

0

50

100

150

200

250

-1.5 -1

Beam 1 Beam 2

Beam 3 Beam 4

Beam 5

-0.5 0 0.5 1

strain (m/m)

Bea

m d

epth

(mm

)

510 daN1000 daN2500 daN3000 daN4500 daN5000 daN5500 daN6000 daN7000 daN8000 daN9000 daN10000 daN11000 daN12000 daN13000 daN14000 daN15000 daN

(a)

0

50

100

150

200

250

-2 -1.5 -1 -0.5 0 0.5

Strain (m/m)

Bea

ms

dep

th (

mm

) 510 daN

1010 daN

2500 daN

3000 daN

4470 daN

5000 daN

6000 daN

11900 daN

7000 daN

9000 daN

10100 daN

13000 daN

14000 daN

(b)

0

50

100

150

200

250

-1.5 -1 -0.5 0 0.5 1 1.5

Strain (m/m)

Bea

ms

dep

th [

mm

]

2805607701000150020002500300035004000500060007000800090001000011000120001300014000150001700018000

(c)

0

50

100

150

200

250

-1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3

Strain (m/m)

Bea

m d

epth

[m

m]

2805607701000150020002500300035004000500060007000800090001000011000120001300014000150001700018000

(d)

0

50

100

150

200

250

-3000 -2500 -2000 -1500 -1000 -500 0

Strain (μm/m)

Bea

m d

etp

h (

mm

)

10 kN20 kN40 kN100 kN80 kN100 kN120 kN140 kN160 kN180 kN220 kN

(e)

Fig. 7. Navier diagram.


equilibrium of the section should be reconsidered. In-deed, the position of the calculated neutral axis does

not take into account the tensile behaviour of the

short-fiber reinforced concrete, which modifies the posi-

tion of the neutral axis.

4.4. Failure mode and cracking pattern of the beams

Beam 1 exhibits behaviour that is quasi linear with ashort ductility; its failure results from the yielding of the

steel rebar. The actual compressive stress at the top con-

crete fiber is about 50% of the ultimate compressive con-crete stress. During loading, regularly spaced vertical

cracks are observed for beam 1. On the contrary Beam

2 does not present any shear cracking pattern. A high

number of cracks do not reach the position of the tensile

steel (Fig. 9c and d). The location of the cracks, confirms

that the position of the neutral axis is lower than for

beam 1. The number of cracks with a smaller spacing

(3–5 cm) is higher. The failure occurs in the tensile zonefollowing the appearance of one macro crack at mid-

span in the central zone of constant moment. This

Fig. 8. Neutral axis position in function of loading.

Fig. 9. Evolution of beam cracking.


macro crack occurs when the lower level of reinforce-

ment fails. In this case, the concrete strain reaches

80% of its ultimate value.

The reinforcement failure causes a drop in load until

a value of 100 kN, where the load is maintained under

the crack-bridging effect of the metallic fibers. The test

is then interrupted. The same observations are made

for beam 3, with the crack height corresponding to ahigher neutral axis position. The crack number is larger

than for the beam 1 but crack openings are smaller. The

area decrease in the compressive zone for beam 4 makes

it possible to obtain a concrete compressive failure of the

beam.

In this case, HPFRC is able to achieve its maximum

level of performance. It is then possible to look for an

optimised area in which compressive failure of the con-crete and yielding of the reinforcement occur simulta-

neously. This is obtained with beam 5. In conclusion,

the ductility and the failure mode of the HPFRC beam

can be tailored by a suitable design (reinforcement ratio,

geometry. . .).

5. Analysis

5.1. Influence of the mixed reinforcement

As mentioned before, the behaviour of beams 2–5

are different. For beams 3 and 5, in comparison with

beam 1, the yield load is 30% higher and the failure

load is increased by 50% and the neutral axis position

shifts upward by 25 mm. These modifications are essen-

tially the consequence of the use of mixed reinforcingbars.


In order to understand the origin of these changes, it

is necessary to compare the tensile reinforcement sec-

tions of each beam.

The variation of the neutral axis position between

beams 2 and 3 can be understood by the difference in

the reinforcement ratio of the tensile reinforcing bars.The reinforcement area of beams 1 and 2 is

1256.6 mm2 (4 HA 20) for an equivalent trussing area

of 1101.07 mm2 (equivalent section with a steel–compos-

ite Young�s modulus equivalence coefficient of 4) for

beams 3, 4 and 5. This results in an effective decrease

of the tensile reinforcement ratio of 12.4%. The tensile

area of the section is reduced. Thus to satisfy equilib-

rium, the neutral axis is shifted toward the top of thebeam The compression concrete is then less stressed

allowing for the reduction of the upper fiber strains at

equal loads.

Moreover, the tensile strength of the lower level

CFRP reinforcement in the mixed reinforced beams

(210) is approximately 1900 MPa compared to

570 MPa for the steel rebar of beams 1 and 2. When

the upper level reinforcement of the beam is yielded,the CFRP bars continue to show resistance, thus,

increasing the section resisting moment. The failure load

is therefore increased by 50%.

It is therefore possible to conclude that the interac-

tion between CFRP and steel reinforcement allows for

significant modification of the structural behaviour by

increasing the ductility, the range of pseudo-elastic

behaviour and the failure load.

5.2. Influence of the short metallic fibers on the beam

mechanical behavior

This experimental study allowed for confirmation

that sections that are plane remain so during bending.

The strain distribution is linear through the entire depth

of the beam. Due to the almost elastic character of theHPC, a triangular distribution of stresses is considered

for the compressive zone (Fig. 10). The tensile stresses

are divided between the steel and concrete. The distribu-

tion of the fiber reinforced tensile concrete stresses com-

plies with technical and scientific documents of the

εc σcbw

d1

d2

h

z

zu

εs

As2

As1

z

σf

zu

α.hFAs1

FAs2

Fig. 10. Strain and stress distribution in an FRHPC beam.

AFGC [10]. The reinforced concrete section is balanced

if the sum of internal forces is equal to zero. The force

taken by the FRHRPC can be calculated using Eq.

(3). The external moments must be equal to the sum

of the compression concrete moment (Mc), tensile rein-

forcement steel moment (Ms1 and Ms2) and fiber mo-ments (Mf).

N f ¼ N c þ N s1 þ N s2 ð3Þ

M sd ¼ M c þM s1 þM f þM s2 ð4ÞFor every value of loading and increment of curva-

ture, knowledge of the constitutive law of the concrete

in compression, makes it possible to calculate the corre-

sponding moment (Mc).

M c ¼ bw �Z zu

0

rcðzÞ � dz ¼ bw �Z zu

0

EðrcÞ � v � z2 � dz

¼ bw � v �Z zu

0

EðrcÞ � z2 � dz ð5Þ

Knowing the experimental curvature and the materialstress–strain relation, it is possible to calculate, for each

value of loading, applying an iterative calculation pro-

cess (Fig. 11), the corresponding values of the internal

moments relating to the equilibrium of the section

(Eqs. (6)–(8); Fig. 12).

M s1 ¼ As1 � rs1 � ðd1 � zÞ ¼ As1 � EsðrsÞ � es1 � ðd1 � zÞ

¼ As1 � EsðrsÞ � v � ðd1 � zÞ2 ð6Þ

M s2 ¼ As2 � rs2 � ðd2 � zÞ ¼ As2 � EsðrsÞ � es2 � ðd2 � zÞ

¼ As2 � EsðrsÞ � v � ðd2 � zÞ2 ð7Þ

The moment undertaken by the short fiber reinforced

concrete is calculated using an expression proposed by

Rilem recommendations [10] (Eq. (8)).

M f ¼ bw �Z h

h�zu

rfðzÞ � dz

¼ ða � hÞ2bw

w0

�Z w0

0

rfð1� wÞ � dw� �

ð8Þ

with a the height of the crack, w0 the maximum openingof the crack under an increment of loading, b, h the

Mf = f(P)

Msd(P)

zu = f(P) χ = f(P)

Mc MS1 MS2

)( 21 sscsdf MMMMM ++=

σs1 = f(P) σs2 = f(P)

P

Fig. 11. Internal moment calculation process.

-80

-60

-40

-20

0

20

40

60

80

100

120

0 5000 10000 15000 20000 25000

Load (daN)

Bea

m in

tern

al m

om

ent

(kN

)

Beam 1 concreteBeam 1 steel rebarsBeam 2 steel rebarsBeam 2 concreteBeam 3 steel rebarsBeam 3 concreteBeam 4 steel rebarsBeam 4 concreteBeam 5 concreteBeam 5 rebars

Fig. 12. Internal moment value in function of loading.

0

20

40

60

80

100

120

0 10 20 30 40 50 60

Tense metallic short fibers moment (KN.m)

Bea

m e

xter

nal

mo

men

t (k

N.m

)

Beam 2Beam 3Beam 4Beam 5

Fig. 14. Tense steel fibers concrete moment in function of external

moment.


width and height of the beam, rf the tensile stress in the

concrete.

Calculating the moment taken by the fibers requires

knowledge of crack opening values (w), and tractionstress developed in the tensile concrete (rf).

It is also possible to calculate, for every increment of

loading, this value by subtracting from the external mo-

ment the sum of internal moments, that is to say

M f ¼ M sd � ðM c þM s1 þM s2Þ ð9ÞIndeed, the sum of the total internal moments is equal

to the external moments for the beam in FRHPC (Fig.

13). This difference corresponds to the value of the mo-

ment undertaken by the short metallic fibers (see Fig.

14).

It is important to observe the linear increase in the

moment corresponding to progressive cracking of the

0

20

40

60

80

100

120

0 20 40 60 80 100 120

Beam internal moment (KN.m)

Bea

m e

xter

nal

mo

men

t (K

N.m

)

Beam 1

Beam 2

Beam 3

Beam 4

Beam 5

Fig. 13. External moment in function of internal moment.

concrete. The significant differences between the two

curves (beams 2 and 3) are explained by the difference

of the neutral axis position, in the case of beam 3, the

lever arm of the equivalent stress carried by the tensile

fiber reinforced concrete is larger, the moment it car-

ries is thus higher. On the other hand, a difference also

exists in the ultimate moment carried by the beams.

Beam 2 reaches a maximum value of 200 kN m whenthe steel yields, the crack opening depends therefore

only on the fibers. Whereas, for beam 3, the fibrous

CFRP reinforcing bars (non-yielding material) control

the crack opening, and the moment taken by the fibers

continues to increase (Fig. 13). The cracking mecha-

nisms are different. It is important to keep in mind

that the moment taken by the fibers acting in tension

represents, at the failure, 10% of the applied momentvalue.


6. Conclusion

The tests on beams carried out in this study describe

the possibility of using high performance fiber rein-

forced concretes for reinforced concrete structures.

The main assumptions of steel reinforced concrete de-sign may be applied to this kind of structure.

First, it is shown that CFRP–steel mixed rebars (in

the elastic stage) are able to maintain a bending stiffness

comparable to the beams reinforced by traditional steel

reinforcement. A 50% increase in the failure load is

observed.

Second, it is shown that the presence of the metallic

fibers contributes significantly to internal section equi-librium, the fibrous concrete contributing 10% the sum

of internal moments from the tensile region. The tensile

stress taken by the fibers lowers the neutral axis posi-

tion. The lever arm of the force taken by the steel rebar

is smaller whereas, the moment undertaken by the con-

crete in compression is increased. Moreover, it is impor-

tant to notice that the metallic fibers allow for the

exclusion of all transverse reinforcement in the shearzone.

Finally, the results of this study confirm the

potential of this type of structure. In fact, using a

standard concrete (fc28 = 40 MPa), a section of

190 · 315 mm2 is needed in order to reach an ultimate

moment of 115 kN m (beams 1, 2 and 4) and a section

of 210 · 350 mm2 in order to reach 150 kN m (beam

3). The use of the fiber reinforced HPC in associationwith mixed steel/CFRP reinforcing bars allows for the

reduction of structural weight by 48%. The material

performance allows design with optimized sections

that show improved performance and lighter

weight.

Acknowledgments

The authors would like to thanks the Lafarge socie-

ties (LCR) and Etandex for their technical support

and the supplies of the materials having permitted to

achieve this program of research.

References

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Flexural Behaviour of MRBC Beams

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