EFFECT OF ANALYTICAL AND EXPERIMENTAL BOND SLIP CURVES ON SHEAR
BEHAVIOR OF CIRCULAR RC BEAMS STRENGTHENING BY CFRP BARS
Kobe University Student Member ○Mamy A. RABOTOVAO
Kobe University Regular Member Tomohiro Miki
1. Introduction
In an aggressive environment, the lifespan of steel reinforced concrete members is limited due to the corrosion ofsteel reinforcements. Fiber reinforced polymer (FRP) rebars can be considered as an alternative solution to that matter
since their non-corrosiveness, high tensile strength, lightness, fatigue resistance and small creep deformation. However theforce transfer between FRP rebars and concrete is still ambiguous since the lack of research regarding the bond slip between
FRP bars and concrete. This article presents the effect of analytical bond slip curves which take into consideration the
deformed shape of CFRP bars, on the behavior of Circular cross-sectionnal CFRP reinforced concrete (RC) beams.
2. Analytical program(1) Representative model for pull-out test
This representative model for pull-out test, shown in Fig.1, istargeted for experimental results performed by Solyum et al.
(2020). It takes into consideration two different shape of deformed
CFRP rebars namely ribbed bar and dented bar, as shown in Fig.1.
For the FE analysis, CFRP bar is modeled with an elastic modelcharacterized by a moduls of elasticity of 141,000 N/mm2.
Regarding constituve models for concrete, an ideal models are
considered for both compressive behavior and tensile behavior.
The compressive strength and tensile strength of concrete are 36
N/mm2 and 2.5 N/mm2 respectively. Based on parametric analysis,
the shear stiffness and normal stiffness moduli of the interface
element between concrete and CFRP bar are 0.005 N/mm3 and 5
N/mm3, respectively.
(2) Circular cross sectionnal CFRP RC beam under shear
This part of the analysis, shown in Fig.2, consists of circularbeams reinforced with CFRP bars. Each specimen was 3000 mm
in length with a diameter of 500 mm. Moreover, each specimen issimply supported over a length span of 2400 mm. The parabollic
model with a compressive strength of 38 N/mm2 is considered forthe compresive behavior of concrete. on the other hand, the tensile
behavior of concrete is represented with the Hordjick model. Thetensile strength of concrete was 2.5 N/mm2 and the tensile fracture
enrgy was 0.1 N/mm. Regarding the CFRP bars and spirals, thelinear elastic model was used.
3. Results(1) Bond slip curves
Fig.3 presents different bond slip curves used for the analysis.
Analytical bond slip curves of dented bar and ribbed bar arecharacterized by a uniform post-peak curve in both cases.
However, the initial stiffnesses of those analytical bond slip curves
are 336 N/mm3 and 13 N/mm3 for ribbed model and dented modelrespectively. Their bond strengths are 8.27 N/mm2 and 7.90
N/mm2 respectively. In contrast to those analytical bond slip
curves, a fitted bond slip curve of sand coating surface based on
experimental results is also considered. It is characterized by aninitial stiffness of 88 N/mm3 and a bond strength of 12.865 N/mm2.
Moreover, this sand coating bond slip curve presents a post
softening part.
Apart from those three models, a perfect bond model is also
associated to one specimen. A perfect bond model is defined as noFigure 1: Representative model for pull-out test

Figure 2: CFRP RC beam under shear

Figure 3: Bond slip curves

Keywords: CFRP RC beam, bond slip, circular cross-section, interface element, surface characteristics
Contact address: 1-1 Rokkodai, Nada, Kobe 657-8501, Japan, Tel: +81-78-803-6094

slip occurs between CFRP reinforcing bars and concrete. Somehow
those materials are merged perfectly and adopted the samebehavior.
(2) Load carrying capacity of CFRP RC beams
As shown in Fig. 4, in case of BC100, analytical specimens
present a lower load carrying capacity at a larger deflection thanexperimental specimen. This leads to a lower flexural stiffnesses of
those latter ones.
Perfect bond model and sand coated bond model lead to thehighest load carrying capacity among analytical specimens. On theother hand, ribbed model presents a little drop in term of load
carrying capacity if compared to Perfect and sand coated bondmodels. And dented model leads to the lowest load carrying
capacity among all analytical specimens.

Figure 4: Effect of bond slip curves on the load
carrying capacity of BC100

4. Discussion on the cracking pattern of each specimen atPmax
Fig. 5 shows the different cracking pattern of each specimen
at Pmax for BC100. Ecw1 is the maximum crack width in theprincipal direction.
Ribbed bar and perfect bond models present similar cracking
patterns expect the fact that diagonal cracks are more concentrated
for perfect bond model. However, ribbed bond model shows very
few flexural cracks if compared to ribbed model and perfectmodel, leading to steep diagonal crack. This steep diagonal crack
can be the effect of a lower initial stiffness leading to larger slip
and impairing the contribution of reinforcements leading to abrittle failure.
Sand coated bond model presents the highest bond strength,
its cracking pattern show some flexural cracks and someconcentrated diagonal cracks. However, if compared to ribbed
model Ecw1 of sand coated model is lower. It confirms that thisspecimen shows more resistance than other specimens except
perfect bond RC beams. That can be the effect of bond strength
which is somehow dominant than initial stiffness regarding theforce transfer between concrete and reinforcements.
5. ConclusionsThe main finding of this investigation can be summarized asfollows:(1) Deformed surface characteristics leads to bond slip curves
with a uniform post-peak. However, post peak curve does notaffect the affect the behavior of CFRP RC beams. Bondstrength and initial stiffness are the prevalent parameters that
Figure 5: Cracking patterns for BC100 - Pmax
decide the strength of CFRP RC beams.
(2) Regarding the force transfer between concrete andreinforcements which ensure the resistance of a specimen after apparition of diagonal cracks, bond strength issomehow dominant over initial stiffness.
(3) Adjustment is needed regarding the normal and shear stiffnesses moduli of analytical bond slip curves since it tends
to underestimate totally the load bearing capacity of CFRP RC beams. Moreover, those shear and normal stiffnesses
moduli lead when associated with the surface characteristics of CFRP bars lead to a low bond strength if compared
to experimental results.
References
1) Sandor Solyom, György L. Balázs. (2020): Bond of FRP bars with different surface characteristics, Construction andBuilding Materials 264-119839.
2) Mohamed HM, Ali AH, Benmokrane B. (2017) Behavior of circular concrete members reinforced with carbon-FRPbars and spirals under shear. J Compos Construct, 21(2): 04016090.
3) Baena M, Torres L, Turon A and Barris C (2009): Experimental study of bond behavior between concrete and FRP bars
using a pull-out test. Composites Part B: Engineering 40(8): 784–79.