INVISTIGATING
THE EFFECTS OF FRP BARS ON THE SEISMIC BEHAVIOR OF REINFORCED CONCRETE COUPLING
BEAMS
Mojtaba Fallahi
Islamic Azad University of Ahar, Iran, Islamic Republic of
E-mail: m_fallahi64@yahoo.com
Sajjad Sayyar Roudsari
North Carolina A&T State University, United States
E-mail: ssayyarroudsari@aggies.ncat.edu
Taher M Abu-Lebdeh
North Carolina A&T State University, United States
E-mail: taher@ncat.edu
Florian Ion T. Petrescu
Bucharest Polytechnic University,Romania
E-mail: fitpetrescu@gmail.com
Submission: 16/05/2019
Revision: 20/05/2019
Accept: 30/07/2019
ABSTRACT
Sometimes, it is
necessary to install regular openings like windows or doors in the shear walls.
Such openings require special reinforcement. There are several methods for
reinforcing deep beams, one of which is the use of fiber reinforced polymer
bars. In this study, an experimental work on a coupled shear wall has been used
to mode the system by using finite element method with ABAQUS software. The
finite element model was established based on part of the experimental study
and verified with the other parts of the experimental results. The comparison
shows good agreement. In the study, three different types of fiber reinforced
polymer bars were considered in improving the mechanical and structural
behavior of RC coupling beams. Results of the finite element analysis showed
the superiority of the CFRP bars in improving seismic behavior of the coupled
shear wall comparing to GFRP and BFRP.
Keywords: FRP bars ; seismic behavior; coupling
beams; ABAQUS software; shear walls
1. INTRODUCTION
Reinforced
concrete shear wall system is one of the most common lateral load-bearing
systems. It is suitable for seismic loadings. However, it is necessary to
install regular openings for windows or doors in shear walls in accordance with
architectural considerations and in such cases, reinforced concrete coupling
beam is used. The coupling beam, which is an important member in the
performance and formation of the coupled shear walls, may be restored and
strengthened for various reasons.
There
are several methods for reinforcing such beams, one of which is the use of
fiber reinforced polymer bars (FRP). It should be noted that FRP bars have high
strength-to-weight ratio, but low elastic modulus. It has linear deformation
until rupture, leading to brittle failure. Further, concrete members reinforced
with FRP exhibit larger deflections and crack widths comparing to steel
reinforced concrete structures (GE et al., 2019).
In
recent years, several numerical and experimental studies have been conducted on
coupling beams of reinforced concrete coupled shear walls. For instance,
Reazpour et al. (REZAPOUR; GHASSEMIEH, 2018) used
Multiple-Vertical-Line-Element-Model (MVLEM) to analyze several types of
macroscopic models of coupled concrete shear walls. Their results indicated
that the macroscopic wall with moderate connection stiffness has acceptable
consistency in terms of static and dynamic responses of the microscopic model.
Ding
et al (2018) developed an analytical model for seismic simulation of reinforced
concrete coupled shear walls. They proposed new mixed beam-shell model for the
seismic analysis of reinforced concrete coupled walls with sufficient
efficiency and accuracy on the platform of general finite element software MSC.
Marc. Faridani and Capsoni (2017) assessed coupled shear walls (CSWs) equipped
with passive damping systems using the damped continuum models developed as
Coupled-Two-Beams (CTB).
His
work showed that the developed CTB systems with the shear damping model are
suitable tools for the dynamic analysis, and for the preliminary design of CSWs
equipped with velocity-dependent dampers. Cheng, Fikri and Chen (2015)
conducted experimental investigation on two approximately half-scale four-story
coupled shear wall specimens. The walls were subjected to both gravity and
reversals lateral displacement. They concluded that a ductile coupling beam
design does not guarantee a ductile behavior of the coupled shear wall system.
On
an attempt to investigate the effect of coupled shear walls on the seismic
response of tall buildings, Faridani and Capsoni (2016) investigated the
effects of viscous damping mechanisms on structural characteristics in coupled
shear walls. They addressed energy dissipation mechanisms to investigate the
effects of the internal and external viscous damping on structural
characteristics in coupled shear walls.
A
discrete Reference Beam (RB) was first proposed and a Distributed Internal
Viscous Damping (DIVD), composed by bending and shear mechanisms, was defined.
Their results revealed that the bending and shear damping are somehow efficient
where the linear classical damping is incapable to be always a proper
mechanism.
Based
on previous researches, several methods have been proposed to strengthen RC
members. One of these methods is the attachment of advanced composites, such as
glass fiber reinforced plastic (GFRP) and carbon fiber reinforced plastic
(CFRP), to the tension side of the members (SU; ZHU, 2005).
Although,
these composites are generally capable of increasing both the ductility and the
load capacity but are prone to peeling and delamination under shear stresses
and deboning under cyclic loading. On the other hand, an effective method of
replacing steel bars with composite bars have shown considerable strength
against corrosion. It is widely used in offshore concrete structures that
exposed to salty corrosive water. Cai, Wang and Wang (2017) conducted
experimental study on an innovative concrete building column which are
longitudinally reinforced with both steel bars and fiber-reinforced polymer
(FRP) composite bars.
Despite
the various studies on evaluating the seismic behavior of RC coupling beams,
there are little researches on the effect of composite bars on the seismic
performance of such beams. The aim of this study is to develop a finite element
model to investigate the effect of composite bars on the seismic performance of
coupling beams in terms of ductility, stiffness and overall strength.
2. MATERIALS AND METHODS: FINITE ELEMENT MODEL DEVELOPMENT
In
this study, the experimental work of Su and Zhu (2005) and Zaidi et al. (2017)
were utilized to model a coupled shear wall using finite element method with
ABAQUS software. The configuration of the model is illustrated in figure 1.
Material properties of concrete, reinforcing steel, and fiber reinforcement
polymer are shown in tables 1 and 2.
|
|
|
Figure 1:
Configuration and reinforcement details of model (SU; ZHU, 2005)
Table
1: Material properties
|
Material |
ID |
|
|
|
Concrete |
CB |
50.2 |
43.9 |
|
Steel |
|
|
Young’s modolous |
|
Steel bar |
R8 |
462.7 |
212000 |
|
Steel bar |
T10 |
571.0 |
211000 |
|
Steel bar |
T12 |
529.3 |
207000 |
|
Steel bar |
T16 |
549.2 |
210000 |
|
Steel bar |
T20 |
504.1 |
203000 |
Table 2: Physical and Mechanical properties of fiber reinforcement polymer
|
Property |
Glass Fiber |
Carbon Fiber |
Aramid Fiber |
|
Elasticity modulus along Fiber
(GPa) |
35-60 |
100-580 |
40-125 |
|
Tensile strength (MPa) |
450-1600 |
600-3500 |
1000-2500 |
|
Ultimate failure strain,
%. |
1.2-3.7 |
0.5-1.7 |
1.9-4.4 |
The
ABAQUS finite element software was used in the modeling. In the modeling
process, C3D8R, T3D2 and B31 element types were chosen for concrete, stirrups
and longitudinal bars respectively. C3D8R (Figure 2) is a continuum element
with reduced integration and hourglass control and capable of simulating
concrete cracking in tension and crushing in compression.
Figure 2: C3D8R
element type
T3D2
is a two-node, 3-dimensional truss element used in two and three dimensions to
model slender, line-like structures that support only axial loading along the
element. No moments or forces perpendicular to the centerline is supported. B31
is a linear 3-dimensional beam element which does not allow for transverse
shear deformation. In this element, plane sections initially normal to the
beam's axis remain plane (if there is no warping) and normal to the beam axis.
The
ABAQUS finite element model of the considered configuration is illustrated in
figure 3. Further, in this study, concrete damage plasticity model was used to
simulate concrete behavior. The material model is a continuum, plasticity
based, damaged model for concrete. Damaged plasticity is assumed to
characterize the uniaxial tensile and compressive response of concrete as shown
in Figure 4.
Figure 3: Finite
element model
(a)
(b)
Figure 4: Concrete damaged plasticity model. (a): Tension behavior associated with tension stiffening;
(b): Compressive behavior associated with compression hardening
Source: ABAQUS (2014)
It
is assumed that the uniaxial tension stress-strain relationship is linearly
elastic until failure stress ft0 is reached. Beyond the state of the
failure stress, the stress-strain response is designed by softening
characteristic (Figure 4a). Under uniaxial compression, the response is linear
up to the initial yield fc0. After attaining the ultimate stress FCU
in the plastic zone, the response of concrete is characterized by the stress
hardening followed by strain softening (Figure 4b). Therefore, concrete stresses determined to
unload from any point on the strain are:
(1)
(2)
Where Ec is the modulus
of elasticity of concrete. The effective tensile and compressive cohesion
stresses of concrete which determine the size of the failure surface are
estimated as:
(3)
(4)
The post-failure behavior of the reinforced concrete can
be expressed by means of the post-failure stress as a function of cracking
strain εtck and εcck which are
defined as the total strain minus the elastic strain corresponding to the
undamaged material. The tension stiffening data are given in terms of the
cracking strains. When unloading data are available, programming automatically
converts the cracking strain values to plastic strain values using the
following relationships (ABAQUS, 2014).
(5)
(6)
3. VERIFICATION OF THE PROPOSED FINITE ELEMENT MODEL
In
this study, the finite element model was established based on the experimental
study carried out by Su and Zhu in (2005). Figure 5
shows the test setup and loading sequence. Loading was applied by a 500 KN
actuator located at the top end with the line of action passing through the
beam’s center. To simulate the real situation, in which the wall’s piers at the
two ends of a coupling beam remain parallel under deflections, a parallel
mechanism was installed to connect the upper rigid arm with the lower
structural steel beam fixed at the floor (SU; ZHU, 2005).
Source:
Su; Zhu (2005)
The
results of the finite element numerical analysis based on the above procedure
are compared with the shear force-chord rotation angle of the experimental
specimen and shown in Fig. 6. According to Figure 6, there is an acceptable
agreement between experimental and numerical model. The proposed finite element
model is capable of predicting the actual response of the structure accurately.
Also, it can be seen from the curves that the numerical model is to some extent
stiffer than the experimental model, which is an obvious consequence of the
finite element method.
Figure 6: Comparison of shear force-chord rotation
curves for experimental and numerical models
4. PRPOSED STRENGHENING METHOD AND RESULTS
Due to the brittle failure modes of
concrete, various strengthening methods have been proposed by researchers.
These methods can increase the ductility and seismic performance of the
structures considerably. In this study, three types of fiber reinforced polymer
were used to replace steel reinforcement in order to improve both the mechanical
and structural behaviour of RC coupling beams.
The Physical-mechanical properties
of FRP used in this study as a reinforcing material are presented in Table 2.
In this study, one control model and six different finite element model have
been considered based on the strengthening procedures. Table 3 shows the
properties of finite element models based on strengthening method.
Table
3: Numerical Specimens Specification
|
SPECIMEN ID |
Method of strengthening |
Type of Fiber |
Bar diameter (mm) |
|
control |
- |
- |
- |
|
CFRP-T |
Coupling
beam |
CFRP |
20 |
|
CFRP-L |
Whole
model |
CFRP |
12,16,20 |
|
GFRP-T |
Coupling
beam |
GFRP |
20 |
|
GFRP-L |
Whole
model |
GFRP |
12,16,20 |
|
BFRP-T |
Coupling
beam |
BFRP |
20 |
|
BFRP-L |
Whole
model |
BFRP |
12,16,20 |
Results
of the finite element analysis are presented in form of load- displacement and
load-chord rotation in Figures 7 and 8. Figures 7(a) and 8 shows load-rotation
and load-displacement curves for the situation in which the longitudinal bars
of the coupling beam are replaced with glass, carbon, and aramid composite bars.
It is obvious that the CFRP bars show the best ability in enhancing the load
carrying capacity of the coupled shear wall comparing to FRP bars.
By
contrast, the GFRP and BFRP bars cause small reduction in the load carrying
capacity of the coupling beam in comparison to steel bars. The results of
replacing longitudinal bars in the entire structure (coupling beam and shear
wall) (Figure 7 b) is approximately similar to Figure 7 a. Comparison between
equivalent plastic strain of two specimens is presented in Figure 9 (a, b).
As
can be seen, the development of plastic strain in CFRP-T specimen is
considerably higher than BFRP-T which this is due to better performance and
efficiency of CFRP bars in comparison with BFRP (The higher the amount of
yielded elements, the greater the energy dissipation of the system).
(a) Results for utilizing FRP bars in coupling
beam
(b) Results for utilizing
FRP bars in whole model
Figure 7: Comparison of FEM
shear force-chord rotation curves
(a) results for utilizing FRP bars in coupling
beam
(b) results for utilizing FRP bars in whole
model
Figure 8: Comparison of FEM
Shear Force-Displacement Curves
|
|
|
(a)
equivalent plastic strain in CFRP-T (b)
equivalent plastic strain in BFRP-T
Figure 9:
Comparison Between Equivalent Plastic Strain of two Specimens
5. DISCUSSION
In
order to evaluate the seismic performance of the FRP coupled shear walls,
parameters such as response reduction factor, ductility, energy absorption and
initial stiffness need to be determined. In this study, the values were
determined following Newmark and hall (NEWMARK; HALL, 1982).
Results
of these parameters are presented later in this section. Further, it is known
that the inelastic behavior of structures is usually incorporated in the design
by dividing the elastic spectra by a reduction factor, R, reducing the spectrum
from its original elastic demand level to a design level. Structural ductility
and overstrength capacity are the crucial constituent in defining the response
reduction factor. According to Patel and his co-researchers (PATEL; AMIN;
PATEL, 2014), The response reduction factor can be expressed by equation 7:
(7)
In
which RS, Rμ, and RR
are the overstrength factor, ductility factor and redundancy factor
respectively. According to Petrescu and his co-workers (PETRESCU et al., 2017)
and Patel, Amin and Patel (2014) these reduction factors can be calculated
using equation 8 and Figure 10.
(8)
Figure 10: Bilinear curve of the response reduction
factor
Source: Patel,
Amin and Patel (2014)
The
initial stiffness and energy absorption can also be calculated using bilinear
curves. In this study, a MATLAB code was developed to simulate the bilinear
envelopes and to calculate the mentioned parameters. Figures 11 and 12
illustrate the derived bilinear envelopes of pushover curve for both steel and
CFRP-L. Furthermore, values of the initial stiffness, ductility, seismic
(response reduction) factor and energy absorption for all 7 specimens were
calculated and the results are shown in Figures 13 to 16. It is clearly obvious
from Figure 13 that CFRP-T specimen has shown the highest initial stiffness
among the other specimens.
Figure 11: bilinear envelope for
steel Figure 12: bilinear envelope for BFRP-L
Figure 13: Comparison
of initial stiffness Figure 14: Comparison
of a seismic factor
|
|
|
Figure
15: Comparison of ductility stiffness Figure 16: Comparison of energy absorption
As
shown in the above figures, the difference between the stiffness of CFRP-T and
GFRP-T is significant because. The stiffness of GFRP-T plunged to about half of
its initial value. The pattern for seismic factor is approximately the same,
however the maximum seismic factor is assigned to CFRP-T at 15.36, while the
seismic factor of GFRP-T is 6.68 and the minimum amount has been calculated for
BFRP-L at 2.67. Regarding ductility, despite the maximum obtained for CFRP-T
but the difference between CFRP-T and GFRP-T decreased noteworthy. Further, the
energy absorption of all specimens (Fig 15) is somehow close to each other.
CFRP-T has the maximum energy absorption at 6.26E+6.
6. CONCLUSIONS
From the results
obtained by the Finite Element models, the following conclusions can be drawn:
1- Comparing the
results of the numerical analysis with the experimental test indicate that
there is an acceptable agreement between experimental and numerical results,
and thus the finite element model is capable of accurately predicting the
actual response of the structure.
2. results of
finite element analysis showed that FRP bars positively changed the structural
response of RC coupling beams in terms of initial stiffness, ductility, and
energy dissipation characteristics.
3. Comparing
between the specimens in term of seismic parameters indicated that
strengthening of coupling beam with FRP bars has a better seismic response than
that for the whole structure.
4. Result of the
finite element analysis showed that CFRP has the highest impact in improving
seismic behaviour of the coupled shear wall rather than GFRP and BFRP.
5. Based on the
results, CFRP bars increased the ductility, seismic factor, stiffness, and
energy absorption of the coupled shear wall by about 124%, 227%, 314%, and 18%
respectively. And the results for GFRP bars is 56%, 88%, 42% and -2%
respectively.
6. Unlike CFRP
and GFRP, BFRP bars have some aggravating effect on the seismic performance of
the wall.
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