Engineering, Technology & Applied Science Research Vol. 7, No. 6, 2017, 2147-2155 2147
www.etasr.com Askarizadeh and Mohammadizadeh: Numerical Analysis of Carbon Fiber Reinforced Plastic (CFRP) …
Numerical Analysis of Carbon Fiber Reinforced
Plastic (CFRP) Shear Walls and Steel Strips under
Cyclic Loads Using Finite Element Method
Nahid Askarizadeh
Department of Civil Engineering
Faculty of Engineering
Bandar Abbas Branch
Islamic Azad University
Bandar Abbas, Iran
Mohammad Reza Mohammadizadeh
Department of Civil Engineering
Faculty of Engineering
Hormozgan University
Bandar Abbas, Iran
Abstract—Reinforced concrete shear walls are the main elements
of resistance against lateral loads in reinforced concrete
structures. These walls should not only provide sufficient
resistance but also provide sufficient ductility in order to avoid
brittle fracture, particularly under strong seismic loads.
However, many reinforced concrete shear walls need to be
stabilized and reinforced due to various reasons such as changes
in requirements of seismic regulations, weaknesses in design and
execution, passage of time, damaging environmental factors,
patch of rebar in plastic hinges and in some cases failures and
weaknesses caused by previous earthquakes or explosion loads.
Recently, Fiber Reinforced Polymer (FRP) components have
been extensively and successfully used in seismic improvement.
This study reinforces FRP reinforced concrete shear walls and
steel strips. CFRP and steel strips are evaluated by different yield
and ultimate strength. Numerical and experimental studies are
done on walls with scale 1/2. These walls are exposed to cyclic
loading. Hysteresis curves of force, drift and strain of FRP strips
are reviewed in order to compare results of numerical work and
laboratory results. Both numerical and laboratory results show
that CFRP and steel strips increase resistance, capacity and
ductility of the structure.
Keywords-numerical analysis; shear wall; FRP; lateral load;
ABAQUS
I. INTRODUCTION
Polymer coatings used to improve concrete structures were
first developed in 1980 in Europe and Japan. In Europe, FRP
systems were used as an alternative to steel plates. Connection
of steel plates to tensile part of concrete members by epoxy
resins is a common durable method to enhance bending
strength of these members. Steel plates are corroded and their
corrosion leads to the collapse of steel plates with concrete.
Moreover, they are difficult to install, because they are
installed by heavy machinery. Thus, scientists tended to replace
steel coatings by FRP materials. With almost 20% of the
weight of steel coatings, FRP is approximately 8 to 10 times
more resistant than steel. One of the problems with system
structural calculations is the difficulty of computer modeling in
the form of finite element. Moreover, variation in effective
parameters on behavior of these structures challenges
laboratory methods due to high cost and time. Numerical
methods also require a correct understanding of non-linear
behavior of reinforced concrete and FRP [1]. This study
develops suitable structural models and models non-linear
behavior of concrete, reinforcement and FRP.
II. PROBLEM DESCRIPTION
A. Concrete Damage Plasticity
The most important step in numerical modeling of
reinforced concrete structures is the determination of concrete’s
nonlinear behavior. In the finite element software ABAQUS,
nonlinear behavior of brittle materials can be defined through
three models: 1) smeared cracking, 2) brittle cracking and 3)
concrete damage plasticity [2]. Concrete damage model is the
only model which can be used in both static and dynamic
analysis. In this model, it is assumed that tensile cracking and
compressive crushing are two main aspects of concrete failure
mechanism. In modeling brittle material cracking under cyclic
loading (alternating tension and compression), stiffness
recovery is allowed during reciprocating loads [3]. In plastic
damage model, elimination of elements and cracking are not
allowed during analysis due to the lack of failure criterion,
however, this model is able to predict location and direction of
cracks.
B. Interpretation of Moment - Curvature Curve for
Reinforced Concrete Shear Wall Section
Unlike the simplicity in design and construction of
reinforced concrete shear walls, the real response of these
elements is rather complex. Overall behavior of walls is
influenced by bending, shear and axial responses. Wall sections
are against compressive axial forces caused by gravity loads
and their own weight. Axial pressure acting on the wall is
estimated at 20% of product of concrete compressive strength,
fc΄, in Ag (gross concrete cross section) [4]. Authors in [4]
described the moment-curvature relationship in walls of high-
rise buildings against a unidirectional load. When bending
moment is applied on the wall section, initial response of the
wall is linear elastic with initial flexural stiffness. Cracking
Engineering, Technology & Applied Science Research Vol. 7, No. 6, 2017, 2147-2155 2148
www.etasr.com Askarizadeh and Mohammadizadeh: Numerical Analysis of Carbon Fiber Reinforced Plastic (CFRP) …
occurs when moment exceeds initial elasticity and flexural
stiffness is reduced by growth of the first crack and start of
additional cracks. Slope of this phase results from
approximately parallel response of flexural stiffness of the
cracked and deformed section. Further increase in the applied
moment leads to the weakening of steel and the section's
capacity. It is thus considered essential to use non-linear
analysis and theories of plasticity to simulate behavior of
reinforced concrete shear wall.
Uniaxial stress-strain relationship of concrete under
pressure and tension is an important parameter in importing
concrete damage plasticity model to the software. To do this,
the Hognestad curve is used. Equations (1) and (2) are used to
import compressive stress of concrete versus compressive
strain to the software. In these equations, ε0 is the
corresponding strain to maximum stress. For specimens of
which ε0 is unknown, this study uses the value 0.002, which is
a rational value for conventional concretes [5]. In (2), ''cf is
maximum stress in concrete element. The ks factor can be
considered as portrayed in Table I [5] for concretes with
cylindrical compressive strength. Descending branch of the
modified Hognestad curve is linear which extends from ''0 c, f
to ''cε , 0.85fu . εu corresponds to ultimate corresponding strain
to compressive failure of concrete, which has been reported
from 0.003 to higher than 0.005. This study considers 0.0038.
'' 2
0 0
2
( )c cc cf f
(1)
'' ' c s cf k f (2)
TABLE I. kS VALUES IN HOGNESTAD CURVE
'
cf (MPA) 15 20 25 30 >35
s k 1 0.97 0.95 0.93 0.92
C. Stress-Strain Under Tension by Using ABAQUS-
Suggested Equation
Concrete alone cannot tolerate tensile stresses and its tensile
strength is low (7%-11% of compressive strength). Steel rebar
is usually used to compensate these problems. Concrete tensile
response begins with cracking and its expansion. Thus,
concrete behavior cannot be evaluated by considering tensile
strain. Instead, the crack should be evaluated. The concrete
response under pressure is linear until it reaches its tensile
strength which is associated with very fine cracks. The increase
in loading decreases resistance and expands cracks to fracture
under ultimate strain [6-7]. A straight line is usually used for
softening part of tensile curve. Moreover, tensile strength and
ultimate strain are calculated by following equations [8-10]:
' '0.33 t cf f (3)
* 0.001 (4)
In periodic loading, stiffness decreases and cracks after
each cycle emerge. Unlike compressive cracks, these cracks are
completely obvious and open [6]. The curves presented for the
static scenario are in fact pushover curves of maximum stresses
under periodic loading.
D. Damage Parameter
The slope of unloading curve is lower than the slope of the
elastic curve in the softening part, which indicates damage. The
reduced initial stiffness is shown by dt and dc (stiffness decline
under tension, and stiffness decline under pressure
respectively). It is assumed that these two variables are
functions of plastic strain, temperature and other field variables
[3].
, , 0 1plt t t i td d f d (5)
, , 0 1plc c c i cd d f d (6)
where, cε
pl and plt are corresponding plastic strains
under pressure and tension, θ is the temperature, and fi is
the field variable. In fact, concrete damage is determined by dt
and dc in uniaxial stress-strain curves. These damage variables
are expressed as follows:
, 01 t cE d E (7)
where E is the damaged module of elasticity, E0 is
undamaged module of elasticity. It is important to select
properties of damage, because excessive damage values have
unsuitable effect on convergence rate.
E. Behavior of Reinforcements
There are many stress-strain models in finite element
software. This study uses a bilinear elastoplastic model for
reinforcement. In ABAQUS, longitudinal and transverse
reinforcements are modeled by two-node truss element T3D2
which is only able to tolerate axial force and acts separately
from concrete.
F. Stiffness Recovery in ABAQUS
Stiffness recovery is an important discussion in the
mechanical response of concrete in periodic loading. In
ABAQUS, the user can directly import the stiffness recovery
factors, wt and wc. In the majority of quasi-brittle materials
such as concrete reflect improvement of compressive stiffness
resulting from closure of cracks when loading shifts from
tension to compression. On the other hand, tensile stiffness is
not recovered by this shift after formation of microcracks under
concrete crushing. This behavior which is related to wt=0 and
wc=1 is default in ABAQUS.
Engineering, Technology & Applied Science Research Vol. 7, No. 6, 2017, 2147-2155 2149
www.etasr.com Askarizadeh and Mohammadizadeh: Numerical Analysis of Carbon Fiber Reinforced Plastic (CFRP) …
III. SPECIMENS
A. Reinforced concrete shear walls specimens
Group A: Five specimens of CFRP reinforced concrete
shear walls tested by authors in [11] at scale of ½ are modeled
in different arrangements of CFRP in ABAQUS. All specimens
are 1000 mm in length, 100 mm in width and 1500 mm in
height. All specimens are exposed to cyclic loading with drift
control. Group B: Three specimens of CFRP reinforced
concrete shear walls tested in [12] are modeled in different
arrangements of CFRP in ABAQUS. All specimens are 1200
mm in length, 80 mm in width and 1045 mm in height. All
specimens are exposed to cyclic loading with drift control and
48 kN compressive axial force and two axial forces, one
compressive and the other tensile, in a distance which forms
couple on top of the wall, as shown in (8) and (9).
24 1.115A CF F (8)
, 01 t cE d E (9)
Group C: Four specimens of steel strip reinforced concrete
shear walls tested in [13] at scale of ½ are modeled in different
arrangements of steel strips in ABAQUS. All specimens are
1000 mm in length, 100 mm in width and 1500 mm in height.
All specimens are exposed to cyclic loading with drift control
B. Specifications of materials
Group A: specimen 1 which is unreinforced is selected as
reference specimen. Four other specimens are determined
(Specimen 2, Specimen 3, Specimen 4 and Specimen 5). All
four reinforced specimens have a layer reinforced by CFRP
strips [11]. Group B: CW which is unreinforced is selected as
reference specimen. Two other specimens are determined
(RW1 and RW2). All two reinforced specimens have a layer
reinforced by CFRP strips [2]. Group C: specimen 1 which is
unreinforced is selected as reference. Three other specimens
are determined (Specimen 2, Specimen 3 and Specimen 4). All
three reinforced specimens have a layer reinforced by steel
strips [13]. Table II shows 28-day resistance of concrete in all
specimens. Table III shows yield and ultimate strength of rebar
used in this experiment. Values of shear modulus (G) are given
in Tables IV and V.
IV. RESULTS
A. Group A
Figure 1 shows the force-drift hysteresis curve of numerical
analysis for Group A specimens under cyclic load [11]. Figure
3 shows the strain-force hysteresis curve of CFRP materials in
numerical analysis for Group A Specimens under cyclic load.
Table VI lists the experimental results and compares them to
numerical results related to maximum strain. As shown, the
numerical analysis is consistent with the experimental results.
TABLE II. SPECIFICATIONS OF SPECIMENS
Group A: Five specimens of CFRP reinforced concrete shear walls
Specimen5 Specimen4 Specimen3 Specimen2 Specimen1
15.6 15.9 15 15.7 15.5 'cf (MPa)
A combination of mesh and
horizontal and parallel strips at
the top and bottom of specimen
A combination of X-shaped,
horizontal and parallel strips at the
top and bottom of specimen
An X-shaped
layer
Horizontal and
parallel strips -
Fiber
arrangement
Group B: Three specimens of CFRP reinforced concrete shear walls
RW2 RW1 CW
37 37 45 'cf (MPa)
A crossed and a wrapping layer at the top
and bottom of wall
A vertical C-shaped layer in
side edges and a wrapping
layer around the wall
- Fiber arrangement
Group C: Four specimens of steel strip reinforced concrete shear walls
Specimen 4 Specimen 3 Specimen 2 Specimen 1
18.5 17.8 18.2 15.5 'cf (MPa)
A combination of horizontal
and vertical strips
Horizontal and parallel
strips A X-shaped layer -
Arrangement of steel
strips
TABLE III. SPECIFICATIONS OF REINFORCEMENTS
Group A: CFRP reinforced concrete shear walls
Ultimate strength (MPa) Yield strength (MPa) Reinforcement diameter (mm)
420 325 6
522 430 10
515 428 12
520 425 16
Group B: CFRP reinforced concrete shear walls
Ultimate strength (MPa) Yield strength (MPa) Reinforcement diameter (mm)
550 450 10
720 620 6
Group C: Steel strip reinforced concrete shear walls tested
Ultimate strength (MPa) Yield strength (MPa) Reinforcement diameter (mm)
Engineering, Technology & Applied Science Research Vol. 7, No. 6, 2017, 2147-2155 2150
www.etasr.com Askarizadeh and Mohammadizadeh: Numerical Analysis of Carbon Fiber Reinforced Plastic (CFRP) …
420 325 6
522 430 10
520 425 16
Fig. 1. Force-drift hysteresis curve under cyclic load, Group A, Specimens 1-5 a) experimental b) numerical
TABLE IV. SPECIFICATIONS OF CFRP
Group A: CFRP reinforced concrete shear walls
Ultimate strain (%) Ultimate tensile stress (MPa) Modulus of elasticity (MPa) Thickness (mm) Fiber
1.7 4100 231000 0.12 CFRP
Group B: CFRP reinforced concrete shear walls
Ultimate strain (%) Ultimate tensile stress (MPa) Modulus of elasticity (MPa) Thickness (mm) Fiber
1.6 3790 230 0.175 CFRP
Engineering, Technology & Applied Science Research Vol. 7, No. 6, 2017, 2147-2155 2151
www.etasr.com Askarizadeh and Mohammadizadeh: Numerical Analysis of Carbon Fiber Reinforced Plastic (CFRP) …
Group C: Steel strip reinforced concrete shear walls
Ultimate strength (MPa) Yield strength (MPa) Thickness (mm) Steel strips
470 340 2.5
TABLE V. INPUT PARAMETERS FOR MODELING FIBERS IN ABAQUS
Group A: CFRP reinforced concrete shear walls
2 3G 1 3G 1 2G 2 3N u 1 3N u
1 2N u 3
E 2E 1E Thickness Layer Fiber
9625 9625 96250 0.2 0.2 0.2 23100 23100 231000 0.12 1 CFRP
Group B: CFRP reinforced concrete shear walls
2 3G 1 3G 1 2G 2 3N u 1 3N u 1 2N u 3E 2E 1E Thickness Layer Fiber
9583 9583 95833 0.2 0.2 0.2 23000 23000 230000 0.12 1 CFRP
Group C: Steel strip reinforced concrete shear walls
Ultimate strength (MPa) Yield strength (MPa) Thickness (mm) Steel strips
470 340 2.5
Fig. 2. Push comparison of hysteresis curves of experimental results and numerical analysis (Group A)
TABLE VI. GROUP A: COMPARISON OF MAXIMUM FORCE
Num/ Exp Num Exp
Specimen Pull
(KN)
Push
(KN)
Pull
(KN)
Push
(KN)
Pull
(KN)
Push
(KN)
0.99 0.97 149.55 136.072 151.33 140 Specimen1
1.05 0.91 267.57 225.62 254.72 250 Specimen2
1.02 0.95 234.63 204.55 230.22 215 Specimen3
1 1.05 239 273.69 238 260 Specimen4
1.11 0.99 272.3 248.5 245 250 Specimen5
TABLE VII. GROUP A: MAXIMUM CFRP STRAIN
Num/Exp Exp Num Specimen
- - - Specimen1
0.97 0.0075 0.0073 Specimen2
0.89 0.0095 0.0085 Specimen3
0.97 0.0088 0.0085 Specimen4
0.96 0.0083 0.008 Specimen5
B. Group B
Figure 4 shows the force-drift hysteresis curve for Group B:
CW, RW1 and RW2 under cyclic load [12] (Table VII). Figure
5 compares push of force-drift hysteresis curves of specimens
under cyclic load resulting from experimental
numerical analysis. Table VIII lists experimental results and
compares them to numerical analysis related to maximum
forced obtained in reciprocating cycles. As shown, the
numerical analysis for Group B specimens is consistent with
the experimental results. Figure 4 shows the strain-force
hysteresis curve of CFRP materials in numerical analysis for
RW1 and RW2 under cyclic load. Table IX compares the
experimental and the numerical results which are shown to be
consistent.
Engineering, Technology & Applied Science Research Vol. 7, No. 6, 2017, 2147-2155 2152
www.etasr.com Askarizadeh and Mohammadizadeh: Numerical Analysis of Carbon Fiber Reinforced Plastic (CFRP) …
Fig. 3. Strain-force curve of CFRP in Group A, Spesimens 1-5 a) experimental b) numerical
TABLE VIII. GROUP B: COMPARISON OF MAXIMUM FORCE
Num/ Exp Num Exp Specimen Pull (KN) Push (KN) Pull (KN) Push (KN) Pull (KN) Push (KN)
1.075 1.04 64.52 62.53 60 60 CW
1.01 1.06 111.63 117.53 110 110 RW1
1.11 1.14 100.33 107.82 90 94 RW2
TABLE IX. GROUP B: MAXIMUM CFRP STRAIN
Num/Exp Exp Num Specimen
1.04 5100 5300 RW1
0.93 4300 4000 RW2
Engineering, Technology & Applied Science Research Vol. 7, No. 6, 2017, 2147-2155 2153
www.etasr.com Askarizadeh and Mohammadizadeh: Numerical Analysis of Carbon Fiber Reinforced Plastic (CFRP) …
Fig. 4. Force-drift hysteresis curve under cyclic load, Group B, a) experimental b) numerical
Fig. 5. Push comparison of hysteresis curves of experimental results and numerical analysis for Group B specimens.
(a) (b)
Fig. 6. Strain-force curve of CFRP in Group B, Specimens RW1 and RW2 a) experimental b) numerical
Engineering, Technology & Applied Science Research Vol. 7, No. 6, 2017, 2147-2155 2154
www.etasr.com Askarizadeh and Mohammadizadeh: Numerical Analysis of Carbon Fiber Reinforced Plastic (CFRP) …
C. Group C
Figure 7 shows force-drift hysteresis curve for Group C
specimens under cyclic load [13]. Figure 8 compares the
experimental and numerical push of force-drift hysteresis
curves. Table X lists the experimental results and compares
them to numerical analysis related to maximum forced
obtained in reciprocating cycles. As shown numerical analysis
results are consistent with the experimental results.
TABLE X. COMPARISON OF MAXIMUM FORCE
Num/ Exp Num Exp
Specimen Pull
(KN)
Push
(KN)
Pull
(KN)
Push
(KN)
Pull
(KN)
Push
(KN)
1 0.94 150 131.9 150 140 Specimen1
1.04 1.004 254.07 239.15 245 238 Specimen2
1.03 0.99 225.99 219.12 220 222 Specimen3
1.09 0.96 228.65 215.73 208 225 Specimen4
Fig. 7. Force-drift hysteresis curve under cyclic load, Group C – Specimens 1-4 a) experimental b) numerical
Engineering, Technology & Applied Science Research Vol. 7, No. 6, 2017, 2147-2155 2155
www.etasr.com Askarizadeh and Mohammadizadeh: Numerical Analysis of Carbon Fiber Reinforced Plastic (CFRP) …
Fig. 8. Push comparison of hysteresis curves of experimental results and numerical analysis (Group C)
V. CONCLUSION
Close results of numerical analysis and experiments on
specimens before and after FRP reinforcement indicate that
numerical modeling can be used as a scientific and inexpensive
tool for analyzing the cyclic behavior of unreinforced and FRP
reinforced concrete shear walls. Both numerical and
experimental results showed that reinforcement of reinforced
concrete shear walls, which have shear weakness under seismic
loads by FRP coating, is a suitable solution for increasing their
resistance. Adjustment of reinforced strips was effective on
cyclic behavior of reinforced shear walls and failure mode. To
compensate shear weakness of reinforced concrete shear walls,
it is better to use horizontal strips along transverse
reinforcements on both sides of the wall. To compensate
bending weakness of reinforced concrete shear walls, FRP
plates are installed vertically along the height of shear wall
parallel to longitudinal reinforcements. In general, results show
that shear positions of fibers concentrated on edges increase
bending and shear strength of the wall. Both numerical and
experimental results show that FRP materials increase ultimate
strength related to reinforced walls compared to unreinforced
ones.
REFERENCES
[1] A. Kheroddin, H. Naderpour, “Nonlinear Finite Element Analysis of
R/C Shear Walls Retrofitted Using Externally Bonded Steel Plate and
FRP Sheets”, 1st International Structural Specialty Conference, pp. 23-
26, 2006
[2] S. Soroshnia, H. Najafi, M. Mamaghani, M. Mehrvand, The Most
Complete Practical Reference of ABAQUS, 2nd ed., Negarandeh
Danesh, 2014
[3] Dassault Systemes, Abaqus Analysis User’s Manual, Version 6-10,
Dassault Systemes Simulia Corp., 2011
[4] I. M. M. Ahmed, Linear and Nonlinear Flexural Stiffness Models for
Concrete Walls in High-Rise Buildings, PhD Thesis, University of
British Columbia, 2000
[5] D. Mostofinejad, Reinforced concrete structures, 12th ed, Arkaneh
Danesh, 2010
[6] A. Saedi-Darian, H. Bahram Pour, H. Arabzadeh, ABAQUS Software
Comprehensive Guide, Angizeh, 2011
[7] J. Lee, G. L. Fenves, “Plastic-Damage Model for Cyclic Loading of
Concrete Structures”, Journal of Engineering Mechanics, Vol. 124, No.
8, pp. 892-900, 1998
[8] H. T. Hu, F. M. Lin, Y. Y. Jan, “Nonlinear finite element analysis of
reinforced concrete beams strengthened by fiber-reinforced plastics”,
Composite Structure, Vol. 63, No. 3-4, pp. 271-281, 2004
[9] A. A. Tasnimi, “Strength and deformation of mid-rise shear walls under
load reversal”, Engineering Structures, Vol. 22, No. 4, pp. 311-322,
2000
[10] J. H. Thomsen, J. W. Wallace, “Displacement-Based Design of Slender
Reinforced Concrete Structural Walls-Experimental Verification”,
Journal of Structural Engineering, Vol. 130, No. 4, pp. 618-630, 2004
[11] S. Altin, O. Anil, Y. Kopraman, M. Emin Kara, “Hysteretic behavior of
RC shear walls strengthened with CFRP strips”, Composites Part B:
Engineering, Vol. 44, No. 1, pp. 321-329, 2013
[12] H. El-Sokkary, K. Galal, “Seismic Behavior of RC Shear Walls
Strengthened with Fiber-Reinforced Polymer”, Journal of Composites
for Construction, Vol. 17, No. 5, pp. 603-613, 2013
[13] S. Altin, Y. Kopraman, M. Baran, “Strengthening of RC walls using
externally bonding of steel strips”, Engineering Structures, Vol. 49 pp.
686–695, 2013