marc mentat rc

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

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mail to: [email protected]

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.


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.


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.


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.


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.


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


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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