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Concrete columns confined by fiber composite wrapsunder combined axial and cyclic lateral loads
Azadeh Parvin *, Wei Wang
Department of Civil Engineering, The University of Toledo, Toledo, OH 43606-3390, USA
Abstract
This paper presents nonlinear finite element analysis of fiber reinforced polymer (FRP) jacketed reinforced concrete columns
under combined axial and cyclic lateral loadings. Large-scale control and FRP-wrapped reinforced concrete columns (762 mm in
diameter and 4978 mm in height) were modeled using the nonlinear finite element analysis software MARCe. The models were
capable of allowing for the degradation of the stiffness under cyclic loading. The finite element analysis results indicated that re-
inforced concrete columns externally wrapped with the FRP fabric in the potential plastic hinge location at the bottom of the
column showed significant improvement in both strength and ductility capacities, and the FRP jacket could be used to delay the
degradation of the stiffness of reinforced concrete columns.
� 2002 Elsevier Science Ltd. All rights reserved.
Keywords: Fiber composites; Concrete; Jacketed columns; Cyclic loading; Ductility; Stiffness degradation; Finite element analysis
1. Introduction
When reinforced concrete columns are subjected to
seismic loading, the large lateral cyclic earthquake forcewill degrade the concrete and the reinforcing bar very
quickly, and the columns will fail prematurely. Investi-
gations of bridge failures during the recent earthquakes,
such as the 1987 Whittier, 1989 Loma Prieta, 1994
Northridge, and 1995 Kobe show that inadequate lat-
eral reinforcement and insufficient lap length of the
starter bars are among the major catastrophic causes of
failure [1–3]. The seismic loads can induce large mo-ments and lateral forces to the bridge columns. This will
result in large shear forces in the columns, which are
resisted mainly through the lateral reinforcement.
Properly detailed lateral reinforcement can also prevent
the sudden loss of bond and buckling of the longitudinal
rebars. Many existing bridge columns are designed using
elastic analysis methods along with much smaller
earthquake forces compared to current design codes.The lateral reinforcement in these bridge columns are
poorly detailed, which results in unreliable flexural ca-
pacity, insufficient shear strength, and low strength at
the footing-column joints. There is an urgent need to
upgrade these deficient bridge columns to meet the
current design standards in seismic regions. Steel jac-keting has been extensively used in the state of Cali-
fornia, USA, to retrofit the bridge columns and has been
proven to be very efficient to increase the strength and
ductility of the columns [4]. In the meantime, researchers
and practitioners are looking for innovative approaches
to improve the retrofit of deteriorating bridges. One
approach is by the use of fiber-reinforced polymer
(FRP), which offers ease of handling and speed of in-stallation, durability, resistance to corrosion, and high
strength-to-weight ratio among many other properties
compared to steel, in particular.
Recent research on one-fifth scale reinforced concrete
bridge columns by Saadatmanesh et al. [5,6] shows that
the FRP jacket can also be used to enhance the per-
formance of the reinforced concrete bridge columns
under constant axial load and lateral cyclic loading.Their research concluded that the FRP jacket is very
effective in preventing the columns from bond failure or
longitudinal bar buckling. In another experimental
study by the same researchers [7], reinforced concrete
columns that were damaged by earthquake were re-
paired using FRP wraps. Their findings indicated that
this repair technique increased displacement ductility
* Corresponding author. Tel.: +1-419-530-8134; fax: +1-419-530-
8116.
E-mail address: [email protected] (A. Parvin).
0263-8223/02/$ - see front matter � 2002 Elsevier Science Ltd. All rights reserved.
PII: S0263-8223 (02 )00163-0
Composite Structures 58 (2002) 539–549
www.elsevier.com/locate/compstruct
and strength of repaired columns. Seible et al. [8] vali-
dated the design of seismic carbon fiber retrofitted re-
inforced concrete columns through large-scale bridge
column experiments and determined that carbon fiberjackets provide the desired inelastic design deformation
capacity levels as good as steel shell jacketing. Xiao and
Ma [9] investigated a prefabricated composite jacketing
system for retrofitting reinforced concrete columns with
lap-spliced rebars. They concluded that the FRP jacket
was able to delay the premature brittle failure of the
columns due to the bond deterioration of the lap-spliced
rebars.Samaan et al. [10] proposed a simple analytical con-
finement model to predict the response of FRP-confined
concrete. They validated this analytical model through
their own experiment as well as experiments by others
and observed good correlation between the analytical
predictions and experimental results. Spoelstra and
Monti [11] presented a uniaxial analytical model for
FRP-confined concrete. Their study pointed out thedifferences in behaviors of concrete elements confined
with a variety of wraps such as fiberglass or carbon fiber.
They derived relations between axial and lateral strains
to trace the state of strain or to detect its failure. Xiao
and Wu [12] experimentally investigated the effect
of compressive strength and confinement modulus of
confined concrete, which they concluded as the most
influential parameters affecting the behavior of FRP-confined concrete. They also proposed a simple bilinear
stress–strain model for confined concrete, which they
claimed to compare well with experimental results from
previous studies by other researchers. Rochette and
Labossiere [13] tested the behavior of small rectangular
and square columns confined by aramid and carbon fi-
ber sheets. Their study showed that the ductility and
strength of the concrete column subjected to axial loadhad increased. Their study was limited to experimenta-
tion on rectangular or square columns subjected to
monotonic uniaxial compression loading and did not
consider lateral cyclic load. Parvin and Wang [14] in-
vestigated the behavior of FRP-jacketed square concrete
columns under eccentric loading experimentally and
numerically. Their results showed that the strength and
ductility of concrete FRP-jacketed columns under ec-centric loading can greatly increase and that the strain
gradient decreases the retrofit efficiency of the FRP
jacket for concrete columns. As a result, when designing
FRP-jacketed columns under eccentric loading, a
smaller enhancement factor should be used. Their study
involved nonlinear finite element analysis while being
limited to square short columns subjected to eccentric
loadings. Mirmiran et al. [15] developed a nonlinear fi-nite element model using nonassociative Drucker–Pra-
ger plasticity to account for confined concrete (circular
and square cross-sections). They studied the effect of
corner radius of square concrete sections on stress
concentration. Their model however did not allow
strength or stiffness degradation. They suggested, under
the cyclic load, a kinetic hardening rule may be more
appropriate to model stiffness degradation.Most of the studies performed on FRP-jacketed col-
umns in the reported literature concentrate on either
experimental and/or analytical models. Consequently,
there appears to be relatively few finite element analysis
studies of FRP-jacketed reinforced concrete columns,
which take into account material and geometric nonlin-
earities, and stiffness degradation of materials, while
utilizing large-scale complex models. This study fills inthis perceived void in literature by proposing a highly
complex nonlinear finite element analysis model for a
large-scale FRP-jacketed column to study its behavior
under combined axial and cyclic lateral loadings with the
capability of allowing the stiffness degradation for con-
crete behavior. A successful outcome for the proposed
study would significantly reduce dependency on costly
and time consuming experimental analysis of large-scaleFRP-jacketed reinforced concrete columns while main-
taining a high degree of predictive capacity for the nu-
merical models in terms of exposing the behavioral
characteristics of the physical columns themselves.
2. Finite element analysis of FRP-jacketed columns
In the following sections, the material modeling ofconcrete and FRP, as well as case studies for control and
FRP-jacketed reinforced concrete column models under
combined axial and monotonic lateral loads, or com-
bined axial and cyclic lateral loads are described. Four
case studies are presented. In the first and second case
studies, behaviors of the control reinforced concrete
column and the FRP-jacketed reinforced concrete col-
umn under combined axial and monotonic lateral loadswere investigated. In the third and the fourth cases, the
same control reinforced concrete column and the FRP-
jacketed reinforced concrete column were studied under
combined axial and cyclic lateral loads. For those cases
with monotonic lateral load, initially the load corre-
sponding to the yielding of the rebar in the column was
determined. Then, this value was used to control the
cyclic lateral load steps. The load versus displacementresponse of control columns under each loading condi-
tion were compared to the FRP-jacketed reinforced
concrete columns under the same loading condition to
study the effect of the FRP jackets used as external re-
inforcement for columns.
2.1. Finite element model of FRP-jacketed concrete
column
The nonlinear finite element analysis software
MARCe (MARC K7.2/Mentat 3.2) was used to model
540 A. Parvin, W. Wang / Composite Structures 58 (2002) 539–549
the FRP-jacketed concrete columns [16]. The nonlin-
earities incorporated in the model include the material
property and the structure geometry. The concrete
model was three-dimensional eight-node solid brick el-ements and required 1176 elements in total. The non-
linear behavior of the confined concrete material was
simulated by employing the Mohr–Coulomb yield cri-
teria combined with the isotropic hardening rule. The
Mohr–Coulomb yield criteria is a reasonable choice
since, the concrete can flow like a ductile material under
high triaxial compression, and the deviatory failure or
‘‘yield’’ stress in concrete depends on the hydrostaticpressure. The deviatoric yield function is a function of
the hydrostatic stress, which is defined as:
f ¼ aðr1 þ r2 þ r3Þ
þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi16½ðr1 � r2Þ2 þ ðr2 � r3Þ2 þ ðr3 � r1Þ2�
q� K ¼ 0;
ð1Þ
where r1, r2, and r3 represent the principal stresses in
the concrete, coefficient a depends on the angle of in-
ternal friction and cohesion, and coefficient K depends
on the angle of internal friction of concrete. The steelrebars were modeled by 224 three-dimensional truss el-
ements.
As described by the generalized Hook law, the FRP
materials demonstrate a linear elastic behavior until
failure. In this study, the FRP is considered to be an
orthotropic material. The three principle material di-
rections (direction 1 along the fiber direction and di-
rections 2 and 3 perpendicular to the fiber direction) areorthogonal to each other. The stress–strain relation is
given as:
ri ¼ Dijej for i; j ¼ 1; 2; . . . ; 6; ð2Þ
where the components of tensor Dij, are defined as fol-
lows, while noting that zero components are not in-
cluded:
D11 ¼ ð1 � m223Þ½ð1 þ m23Þð1 � m23 � 2m12m21Þ��1E11;
D22 ¼ ð1 � m12m21Þ½ð1 þ m23Þð1 � m23 � 2m12m21Þ��1E22;
D12 ¼ m21ð1 þ m23Þ½ð1 þ m23Þð1 � m23 � 2m12m21Þ��1E11;
D23 ¼ ðm23 þ m12m21Þ½ð1 þ m23Þð1 � m23 � 2m12m21Þ��1E22;
D44 ¼ ð1 � m23 � 2m12m21Þ½ð1 þ m23Þð1 � m23 � 2m12m21Þ��1E22=2; and
D55 ¼ G12;
ð3Þ
where E11 is the modulus of elasticity for the FRP jacket
along the fiber direction; E22 is the modulus of elasticityfor the FRP jacket perpendicular to the fiber direction;
G12 is the shear modulus for the FRP jacket; and m12, m21,
m23 are Poisson�s ratios for the FRP jacket. The FRP
jacket was modeled as a single layer and by 224 three-
dimensional thin-shell elements. Different element
thicknesses were assigned based on if the jacket con-
sisted of one or multi-layer FRP fabrics.
Simulation of the bonding force between the concrete
column surface and FRP jacket was realized through the
‘‘Glue’’ sub-option of the ‘‘Contact’’ option in
MARCe. The separating force between the concreteand the FRP jacket was given a large value in order to
assume perfect bonding.
2.2. Case 1––control reinforced concrete column under
monotonic lateral loading
A reinforced concrete column that is 762 mm (30 in.)
in diameter and 4978 mm (196 in.) in height was mod-
eled. The reinforcement ratio of this column was about
2.5%. The bottom of the column was fixed. A uniform
axial load of 2.76 MPa (400 psi) and a lateral load of 345
KN (77,563 pounds) were applied at the top of thecolumn (Fig. 1). The concrete column was modeled
by 1176 three-dimensional solid brick elements. The
strength of the concrete was 27.6 MPa (4000 psi), while
the modulus of elasticity and the Poisson�s ratio were
20.69 Gpa (3 � 106 psi) and 0.17, respectively. The
longitudinal rebars in the columns were modeled by 224
three-dimensional truss elements. The strength of the
rebar was 413.7 MPa (60,000 psi) with the modulus ofelasticity of 206.9 Gpa (3 � 107 psi) and the Poisson�sratio of 0.3. Concrete and steel materials were isotropic.
Cracking was taken into account. The critical tensile
strength of concrete was 4.83 MPa (700 psi) with the
Fig. 1. Large-scale control reinforced concrete column.
A. Parvin, W. Wang / Composite Structures 58 (2002) 539–549 541
softening modulus and the crushing strain of 2.52 Kpa
(365 psi) and 0.003, respectively. The monotonous lat-
eral load of 345 KN (77,563 pounds) was added to 101
nodes on the top of the column as external point load
within 48 load increments along the global Y direction.
Fig. 2 illustrates the load–displacement curve for the
node 267 on top of the column. At load increment 48,
which was when the external load at each node reached3.42 KN (769 pounds), the column failed completely.
Checking the strain distribution at the bottom of col-
umn, it was found that the load increment 46 corre-
sponded to the yielding point of the rebar. At this point,
the axial strain in the rebar exceeded 0.002. When the
steel rebar yielded, the largest compressive strain in the
concrete was 0.0021. Further larger loading leads
the concrete to crush quickly. The lateral displacementat the yielding point of the rebar was 44.7 mm (1.76 in.).
This value is used to control the lateral loading steps in
the cyclic lateral loading.
2.3. Case 2––FRP-jacketed reinforced concrete column
under monotonic lateral loading
The large-scale reinforced concrete column given in
Fig. 1 was wrapped with the FRP jacket at the bottom
height of the column. The jacket was E-glass FRP with
fibers along the two perpendicular directions. The
thickness of the jacket was 5.08 mm (0.2 in.) with a
height of 1778 mm (70 in.) (Fig. 3).
The concrete and rebar were modeled as in the pre-
vious case of column without FRP. The FRP jacket was
modeled by 224 three-dimensional thin shell elements.
The FRP was assumed orthotropic elastic material with
the modulus of elasticity along the fiber direction of 48.2Gpa (7 � 106 psi), the Poisson�s ratio of 0.24, and ulti-
mate strain of 0.02, which was used to predict the failure
of the structure.
The lateral monotonic load of 629 KN (141,412
pounds) was applied to 101 nodes at the top of the
column as external point load within 28 load increments
along the global Y direction. A uniform concentric axial
load of 2.76 MPa (400 psi) was also added on the top ofthe column. Fig. 4 presents the load–displacement curve
for node 267 in the global Y direction.
The rebar yielded at about load increment 20.
Checking the axial strain value of the rebar at the bot-
tom of the column shows the axial strain of the rebar is
0.002 at the load increment 19. The strain distribution in
the FRP jacket indicated that the FRP failed in the
longitudinal direction. At load increment 28, the largesttensile strain along the longitudinal direction was 0.0178
and the largest tensile strain along the circumferential
direction was only about 0.005.
Fig. 2. Load–displacement curve of large-scale control reinforced concrete column under monotonic lateral load.
542 A. Parvin, W. Wang / Composite Structures 58 (2002) 539–549
2.4. Case 3––control reinforced concrete column under
cyclic lateral loading
A reinforced concrete column without FRP jacketunder cyclic lateral load was modeled as the control
column. The finite element model of this column was
exactly the same as the one under monotonic loading in
case 1. The only difference is that the lateral load was
applied cyclically. The lateral displacement of 44.7 mm
(1.76 in.), which corresponded to the yielding of the
rebar, was used to control the loading steps. For the
control reinforced concrete column, this displacementrequired the external lateral load at each node to be 3.29
KN (740 pounds). The load factors for the entire load-
ing process are listed in Fig. 5. These factors were de-
rived based on making the maximum lateral
displacement at the end of each loading loop to be 1, 1.5,
2, and 3 times the critical lateral displacement 44.7 mm
(1.76 in.) for the first, second, third and fourth loading
loops, respectively.The lateral displacement and external load at the
node 267 was used to construct the hysteresis loops for
the structure (Fig. 6). The total lateral load should be
the value at the node times the number of top element
nodes (101). In order to make this graph comparable to
the hysteresis loops of the FRP-jacketed reinforcedFig. 3. Large-scale FRP-jacketed reinforced concrete column.
Fig. 4. Load–displacement curve of large-scale FRP-jacketed reinforced concrete column under monotonic lateral load.
A. Parvin, W. Wang / Composite Structures 58 (2002) 539–549 543
Fig. 5. Lateral load factor for large-scale control reinforced concrete column.
Fig. 6. Load–displacement response of large-scale control reinforced concrete column under cyclic loading.
544 A. Parvin, W. Wang / Composite Structures 58 (2002) 539–549
concrete column under cyclic lateral loading, it was
plotted with the same scale as the hysteresis loop of the
FRP-jacketed reinforced concrete column.
At load increment 74 (fourth hysteresis loop), theconcrete crushed and the structure failed completely.
The stiffness of the reinforced concrete column degraded
with the external cyclic loading as it can be seen from the
change in the slope of each hysteresis loop.
2.5. Case 4––FRP-jacketed reinforced concrete column
under cyclic lateral loading
The FRP-jacketed reinforced concrete column under
cyclic lateral loading had the same model as the one
under monotonic lateral loading in case 1. The yield
displacement of 44.7 mm (1.76 in.) was used to controlthe lateral loading. For the column with the FRP jacket,
this displacement controlled the external lateral load at
each node to be 3.47 KN (780 pounds). The load factors
for the entire loading process are listed in Fig. 7. These
factors are based on making the maximum lateral dis-
placements at the end of each loading cycle to be ap-
proximately 1, 2, 3, 4 and 5 times the critical lateral
displacement (44.7 mm) for the first, second, third,fourth, and fifth loading cycles, respectively.
Fig. 8 shows the load–displacement curve for the
node 267. At load increment 130 (fifth cycle), the FRP
jacket reached its maximum tensile strain and the col-
umn failed. Because of the confinement of the FRP
jacket, the stiffness of reinforced concrete column did
not degrade significantly compared to the one without
the FRP jacket as it can be observed by the change inthe slope in each hysteresis loop. Additionally, from
Figs. 6 and 8, it can be concluded that under lateral
cyclic load, the FRP-jacketed concrete column strength
and ductility had increased significantly compared to the
control concrete column, before cyclic capacity degra-
dation in the neighborhood of third hysteresis loop in
Fig. 6 (about 70% increase in strength and 203% in-
crease in lateral displacement).
2.6. Assessment of validity for proposed numerical models
Validation of the proposed numerical models of theconcrete columns through comparison with similar
columns employed in laboratory experiments as re-
ported in the recent literature will be presented in this
section. Ideally, full-scale laboratory experimentation
would be desirable to validate the proposed numerical
models of columns. However, in the absence of such
experimentation due to constraints imposed by limited
availability of well-equipped laboratory infrastructure,which can facilitate large-scale experimentation, it is still
possible to make reasonably good observations per-
taining to validity of the proposed numerical models.
This validation would be based on comparing the
Fig. 7. Lateral load factor for large-scale FRP-jacketed reinforced concrete column.
A. Parvin, W. Wang / Composite Structures 58 (2002) 539–549 545
response envelopes for proposed numerical models of
control and FRP-jacketed columns with those of other
‘‘similar’’ columns, for which scaled-down laboratoryexperimentations were reported in the literature.
Initially, it will be established that columns chosen
from the literature for correlating load–displacement
envelopes are ‘‘similar’’ to the columns for which the
numerical models were proposed in this study. Differ-
ences between columns subjected to experimentation in
the literature and the ones under study in this paper will
be noted with the anticipation that load–displacementcurves will project nonidentical (due to these differences)
but correlated behavior (due to similarities). Finally,
reasonable level of correlation among load–displace-
ment envelopes for the two experimentally tested col-
umns, reported in literature, and the finite element
analysis models of control and FRP-jacketed-columns,
proposed in this study, will be noted.
Two noteworthy experimental investigations thathave been carried out on circular FRP-jacketed rein-
forced concrete columns subjected to combined axial
and cyclic lateral loads were reported in recent literature
[7,9]. Both of these experimental studies are based on
scaled-down models. The experimental study by Saa-
datmanesh et al. [7] involved one-fifth scale FRP-
wrapped reinforced concrete columns. Overall height of
the test units was 2413 mm (95 in.). The column had the
height (from the center of the pins where the cyclic loadwas applied to the top of footing) of 1892 mm (72 in.)
and the cross-section diameter of 305 mm (12 in.) with
the concrete strength of 36.5 MPa (5297 psi), the lon-
gitudinal steel rebar ratio of 2.48%, and steel yield stress
of 358 MPa (51,959 psi). The unidirectional E-glass FRP
jacket tensile strength and tensile modulus were 532
MPa (77,213 psi) and 17,755 MPa (2577 ksi), respec-
tively. The jacket consisted of six layers with 0.8 mm(0.03 in.) thickness per layer in the form of a strap with
151 mm (6 in.) width and was placed butt-to-butt along
the height of the column up to 635 mm (25 in.) from the
top surface of footing. A constant axial load of 445 KN
(100 kips) was applied on top of the column. The lateral
cyclic load was modeled as a combination of load con-
trol and displacement control phases.
In another experimental investigation [9], half-scalecolumns with 2440 mm (96 in.) in height and 610 mm (24
in.) in diameter with longitudinal steel ratio of 2% of the
gross area of column section were employed. The yield
strength of the steel rebar was 414 MPa (60,000 psi). The
compressive strength of the concrete was 44.8 MPa (6500
psi). Elastic modulus and ultimate strength for the uni-
Fig. 8. Load–displacement response of large-scale FRP-jacketed reinforced concrete column under cyclic loading.
546 A. Parvin, W. Wang / Composite Structures 58 (2002) 539–549
directional glass fiber composites were 48,300 MPa (7000
ksi) and 552 MPa (80,116 psi), respectively, and the
wrapped portion of the column had a height of 1220 mm
(48 in.). The wraps consisted of four layers, 3.2 mm (0.12in.) thickness per layer, for 610 mm (24 in.) high from the
bottom of footing and the remaining 610 mm (24 in.)
portion of the wrapped section consisted of three layers
for this case of retrofitted column. The applied concen-
trated load was 712 KN (160 kips). The sequence of
lateral load was controlled by displacement increment,
which was based on the reference ductility index.
The finite element analysis presented in this studyinvolves larger column sizes: full-size models with the
height of 4978 mm (196 in.) and the diameter of 762 mm
(30 in.), larger axial loading of 1258 KN (283 kips), and
larger lateral cyclic loading than experimental analyses
performed by other researchers described above. The
column had the concrete strength of 27.6 MPa (4000
psi), the rebar yield strength of 414 MPa (60,000 psi)
with reinforcement ratio of 2.5%. Thickness of the E-glass FRP jacket was 5.08 mm (0.2 in.) with a height of
1778 mm (70 in.) from the bottom of column. The
modulus of elasticity along the fiber direction had a
value of 48.2 Gpa (7 � 106 psi). The ultimate strain for
the FRP was 0.02. A uniform axial load of 2.76 MPa
(400 psi) and a lateral load of 345 KN (77,563 pounds)
were applied at the top of the column.
Next, load versus displacement curves of the columnsinvestigated by two experimental studies in the literature
[7,9] and the columns, for which finite element analysis
models were proposed in this study, will be observed and
compared to expose the degree of behavior correlation
among them while noting the differences between the
same.
In the experimental study performed by Saadatm-
anesh et al. [7], the measured maximum lateral load andthe corresponding lateral displacement for one config-
uration of the FRP-wrapped circular column with con-
tinuous longitudinal bars were 72 KN (16.2 kips) and
110 mm (4.33 in.), respectively, versus the value of 60
KN (13.5 kips) and 70 mm (2.75 in.) for the control
model (after that the control column experienced stiff-
ness degradation). This leads to an increase of 20% in
lateral load and 57% in lateral displacement for theFRP-jacketed column.
In the experimental investigation by Xiao and Ma [9],
the maximum lateral load and corresponding lateral
displacement for control model were 231 KN (52 kips)
and 13 mm (0.51 in.), respectively (after that the column
experienced stiffness degradation). The retrofitted FRP-
jacketed column with 4-layer wrapping exhibited maxi-
mum lateral load and lateral displacement values of 300KN (67.56 kips) and 85 mm (3.35 in.), respectively (after
that the column started degrading gradually). This re-
sults in an increase of 30% in lateral load and 554% in
lateral displacement.
In the finite element analysis presented in this study,
the control column maximum lateral load and corre-
sponding lateral displacement were 337 KN (75.7 kips)
and 58 mm (2.28 in.), respectively (after that the columnstarted degrading gradually). The FRP-wrapped con-
crete column lateral load and lateral displacement were
573 KN (128.76 kips) and 176 mm (6.93 in.), respec-
tively. Therefore, an increase of 70% in lateral load and
203% in lateral displacement were observed for the
FRP-jacketed column under combined axial and cyclic
lateral loading.
In general, response profile of the finite elementanalysis model of FRP-jacketed reinforced concrete
column under combined axial and cyclic lateral loadings
as exhibited by the hysteresis loops in Fig. 6 for the
control column and Fig. 8 for FRP-jacketed column
correlates to those observed in the experiments by other
two studies, namely Fig. 13(a) for control column and
Fig. 13(b) for wrapped column in [7] and Fig. 6(a) for
as-built column and Fig. 6(b) for retrofitted column in[9]. For all three studies, FRP-wrapped columns per-
formed extremely well under combined axial and cyclic
lateral loadings compared to control columns with
considerable enhancement in the response to cyclic loads
clearly observable. The lateral strength and ductility of
wrapped columns increased compared to the control
columns, which means significant improvement in the
hysteresis loops of lateral load versus lateral displace-ment of jacketed columns. Furthermore, results of fi-
nite element analysis for the proposed column model
were in good agreement with those of experimental
analysis on the circular column with continuous longi-
tudinal rebars [7] on the basis of not showing stiff-
ness degradation or pinching of hysteresis loops for
the FRP-jacketed columns. Test results [9] on retrofit-
ted column exposed no stiffness degradation as wellexcept, during the last few hysteresis loops, a gradual
yet insignificant degradation was observed. The grad-
ual degradation at large displacements was most
likely due to bond slip in the lap-spliced longitudinal
bars.
As expected, variations in slenderness ratio and ri-
gidity of columns as well as magnitude of loadings, for
the three studies being compared, likely induced a rangeof percent improvement values in lateral load carrying
capacity and lateral displacement. Specifically, there is
20–70% increase in lateral load carrying capacity and
57–554% increase in lateral displacement capacity. This
variation in percent improvement can easily materialize
due to imposed requirements to emphasize the increase
of either flexural strength or ductility or both for repair
and rehabilitation, while noting that for structuralframes subjected to earthquake loads, both strength and
ductility should be taken into account. For example, one
way to increase the ductility of the column is by in-
creasing the number of wraps. One of two experimental
A. Parvin, W. Wang / Composite Structures 58 (2002) 539–549 547
studies [9] reported substantially more increase in the
lateral displacement compared to lateral displacement
increases in the other two studies. This difference in
increases might have been due to the fact that the FRPjacket was approximately two and half times thicker
than those of other two studies. These observations
based on a comparative assessment of two experimen-
tal studies and the finite element analysis in this
paper suggest that the proposed numerical models
are reasonably accurate and provides expected re-
sponse envelopes for the load–displacement curves of
columns.The proposed finite element analysis models of the
columns is poised to provide the engineering community
the opportunity to simulate high-resolution response of
structural systems at significantly reduced cost and time
compared to experimental analysis of large-scale FRP-
jacketed reinforced concrete columns: in most cases,
full-scale experimentation is not feasible due to limited
resources and unavailability of large laboratory facilitiesand equipments.
3. Conclusions
The necessity to understand the principles and be-
havior of FRP-wrapped structural systems is vital in
order to design systems with high performance and
predictable behavior. The proposed finite element
analysis study will unable the engineers to foresee the
behavior of the structure before construction.
Finite element study of large-scale FRP-jacketed re-inforced concrete columns under combined axial and
cyclic lateral loadings results in the following observa-
tions:
• Reinforced concrete columns externally wrapped
with the FRP fabric in the potential plastic hinge lo-
cation showed significant improvement in both
strength and ductility capacities. Under monotoniclateral loading, the lateral displacement of the FRP-
jacketed column could be four times as large as that
of the column without the FRP jacket, and the
strength of the column increased about 80%. Under
cyclic lateral loading, the lateral displacement of the
FRP-jacketed column could be two times as large
as that of the column without the FRP jacket, and
the strength of the column increased about 70%.• The FRP jacket could be used to delay the degrada-
tion of the stiffness of the reinforced concrete col-
umns. Under lateral cyclic loading, the stiffness of
the unjacketed column decreased rapidly after the lat-
eral displacement reached 1.5 times the yielding dis-
placement. For the FRP-jacketed column, there was
no significant stiffness degradation observed through-
out the complete loading process.
• Due to the confinement by the FRP jacket at the crit-
ical section, the failure of the column, the failure
mode of the reinforced concrete columns had chan-
ged. The failure of the unjacketed columns initiatedfrom the crushing of the concrete at a relatively
low compressive strain of 0.003. The failure of the
jacketed columns was due to the failure of the FRP
jacket. When the FRP jacket failed, the concrete
crushed simultaneously. The crushing strain for con-
fined concrete can be very large (much greater than
0.003) depending on the type of the FRP jacket.
• The proposed numerical full-scale column modelswere reasonably accurate and provided expected re-
sponse profiles or envelopes which clearly revealed
the gain in strength and ductility of the FRP-jacketed
columns as observed by other experimental studies on
scaled-down columns.
Although the presented finite element analysis studies
were restricted to a particular column configuration, theresults nonetheless provided valuable insight into the
mechanisms governing the behavior of FRP-confined
reinforced concrete columns subjected to combined axial
and lateral cyclic loads. Extension of the results pre-
sented here to other columns with different size, geom-
etry, loading conditions, and types of FRP wraps will
require further research.
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