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Flexural behaviour of MRBC beams
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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
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
166 A. Si-Larbi et al. / Composite Structures 74 (2006) 163–174
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.
A. Si-Larbi et al. / Composite Structures 74 (2006) 163–174 167
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.
168 A. Si-Larbi et al. / Composite Structures 74 (2006) 163–174
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
A. Si-Larbi et al. / Composite Structures 74 (2006) 163–174 169
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.
170 A. Si-Larbi et al. / Composite Structures 74 (2006) 163–174
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.
A. Si-Larbi et al. / Composite Structures 74 (2006) 163–174 171
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.
172 A. Si-Larbi et al. / Composite Structures 74 (2006) 163–174
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.
A. Si-Larbi et al. / Composite Structures 74 (2006) 163–174 173
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.
174 A. Si-Larbi et al. / Composite Structures 74 (2006) 163–174
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.
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