modelling of circular concrete columns with cfrp sheets ... · modelling of circular concrete...

Bauhaus Summer School in Forecast Engineering: Global Climate change and the challenge for built environment

17-29 August 2014, Weimar, Germany

Modelling of circular concrete columns with CFRP sheets under

monotonic loads by ATENA-3D

ALRAYES, Omar

Institute of Structural Mechanics, Bauhaus-Universität Weimar, Germany.

KÄSEBERG, Stefen

Department of Civil Engineering and Architecture Leipzig, Germany.

Abstract

Over the last years, performance based design has become acceptable in abnormal events assessment

of structures. Therefore, using this design method, performance of existing and retrofitted

reinforcement concrete (RC) buildings can be evaluated using nonlinear analysis. In this case, the

performance of a fiber reinforced polymer (FRP)-retrofitted column is assessed under monitoring

loading and the result is compared with unstrengthened ones. The results are examined and compared

with models reported in literature such as Teng and Lam model ( Teng, et al., 2007). The reliability of

the model is assessed through comparison with experiment results that were done in Institut für

Betonbau (IFB), Leipzig in 2009. The comparison shows that within the practical range of the

confinement model variables, the ATENA analytical model is in very good agreement with the

empirically model (Vladimír, et al., 2012). This model is based on smeared crack method in order to

develop a nonlinear finite element method that describes the behavior of the plasticity and mechanical

damage of the material. Also,

The number of structures in the world continues to increase, as does their average age. The need for

increased maintenance is inevitable. Complete replacement is likely to become an increasing financial

burden and is certainly a waste of natural resources if upgrading is a viable alternative. Therefore,

maintenance, strengthening and monitoring of existing buildings have become more important. The

way in which FRP composite material as carbon fiber reinforced polymer (CFRP) can apply in

strengthening structures like buildings and bridges is illustrated in EUROCOMP Design Code

(December 2004) and ACI committee 440 (Technical committee document 440. 2R-02, 2002). The

predictions are confirmed as confinement efficiency depends on the strength of both concrete and

confinement, the shape of cross section, lateral ties hoop and fiber orientation.

1. Introduction

1.1. CFRP Confinement

The repair of deteriorated, damaged and substandard civil infrastructure has become one of the

important issues for civil engineers worldwide. The rehabilitation of existing structures is fast

growing; as a matter of fact, especially in developed countries, which completed most of their

infrastructure in the middle period of the last century. Furthermore, structures which were built after

World War II had little attention paid to durability issues

Numerous experiments since the 1980s have demonstrated the effectiveness of CFRP composites for

confining RC columns such as (De Lorenzis, et al., 2005). The increase of the load-carrying capacity

of columns being reinforced with Textile Reinforced Concrete (TRC) is partly achieved by the

additional concrete cover. But then it is also decisively caused by the confinement effect of the textile

reinforcement.

ALRAYES, Omar, KÄSEBERG, Stefen / FE 2014 2

An important application of fiber-reinforced polymer composites is to provide confinement to RC

columns to enhance their load-carrying capacity and ductility. This method of strengthening is based

on the well-known phenomenon that the axial compressive strength and ultimate axial compressive

strain of concrete can be significantly increased through lateral confinement.

Various methods have been used to achieve confinement to columns using CFRP composites. In situ

CFRP wrapping has been the most commonly used technique, in which unidirectional fiber sheets or

woven fabric sheets are impregnated with polymeric resins and wrapped around columns in a wet lay-

up process, with the main fibers orientated in the hoop direction. In addition, filament winding and

prefabricated CFRP jackets have also been used. The filament winding technique uses continuous

fiber strands instead of sheets/straps so that winding can be achieved automatically by means of a

computer-controlled winding machine. When prefabricated CFRP jackets are used, the jackets are

fabricated in half circles or half rectangles and circles with a slit or in continuous rolls, so that they can

be opened up and placed around columns.

Figure 1. Confining action of CFRP jacket under Axial Load

Regardless of the type of FRP jacket used, any vertical joint in the FRP jacket should include an

adequate overlap to ensure that failure of the joint will not precede failure of the jacket away from the

joint when subjected to hoop tension. In the strengthening of rectangular columns, the sharp corners of

the columns should be rounded to reduce the detrimental effect of the sharp corners on the tensile

strength of the FRP, and to enhance the effectiveness of confinement.

The confinement of concrete with FRP is based on a well-understood mechanism and denoted in

Figure 1. When the concrete is subject to axial compression, it expands laterally. This expansion is

resisted by the FRP jacket, which provides a confining pressure to the concrete. Eventual failure

occurs when the FRP jacket ruptures as a result of tensile stresses in the hoop direction. Concrete in a

circular jacket is uniformly confined, while concrete in a jacket of any other sectional shape is non-

uniformly confined. Most existing studies of FRP-confined concrete have been concerned with

uniformly confined concrete by testing FRP-confined circular concrete specimens (lam, et al., 2003b).

The FRP confinement action is passive. It arises as a result of the lateral expansion of the concrete

core under an axial load (LAM , et al., 2003). The confining reinforcement develops a tensile stress

balanced by pressures reacting against the concrete lateral expansion. FRP displays an elastic behavior

up to failure and therefore exerts a continuously increasing confining action. Failure normally results

by tensile rupture of the FRP. Hence, the confined concrete strength is closely related to the tensile

rupture strain of the FRP on the confined element. Experimental evidence shows that this failure strain

is usually lower than the ultimate strain obtained by standard tensile testing of the FRP sheet.

1.2. Proposed Model

Many researchers carry out a lot of embedded test and research work in confined concrete specimens.

They investigated the mechanical behavior of large number of experimental test, and discussed the

results by their models. Such as Lam and Teng model (LAM , et al., 2003), Richart model (Richart,

11

1 - 1


1994), Samaan and Mirmiran model (Samaan, et al., 1998), Mander moel (Mander, et al., 1998), and

Teng and Lam model ( Teng, et al., 2007).

Lam and Teng model is built on results from a parametric study using an accurate analysis-oriented

stress-strain model for FRP-confined concrete. This model allow the effects of confinement stiffness

and the jacket strain capacity to be separately reflected and accounts for the effect of confinement

stiffness explicitly instead of having it reflected only through the confinement ratio. The test database

used in the model based on key features.

For ease of discussion, three basic ratios are first defined: the confinement ratio (

), the confinement

stiffness ratio ( ); with sufficiently confined concrete ( ) illustrated in figure 2 and equation

2 also, the strain ratio ( ). The mathematical expressions of these three ratios are as follows:

(

)

Figure 2. Schematic of stress strain model ( ( Teng, et al., 2007))

Where, is the confining pressure provided by the FRP jacket when it fails by rupture due to hoop

tensile stresses (i.e. the maximum confining pressure possible with the jacket), is the elastic

Axia

l S

tress

𝜎𝑐

Axial Strain

Unconfined

> 0.01


modulus of FRP in the hoop direction, t is the thickness of the FRP jacket, is the hoop rupture

strain of the FRP jacket and D is the diameter of the confined concrete cylinder.

The confinement ratio is a commonly used parameter in the existing literature. The confinement

stiffness ratio represents the stiffness of the FRP jacket relative to that of the concrete core. The strain

ratio is a measure of the strain capacity of the FRP jacket. The confinement ratio is equal to the

product of the other two ratios. Based on Lam and Teng (2003) and on the interoperation of the test

results database, the following improved equation for the ultimate axial strain of FRP confined

concrete is proposed and showed in figure 2:

The compressive strength equation was refined on a combined experimental and analytical basis.

Parametric study was conducted using the refined version (Jiang and Teng 2007) of the analysis-

oriented stress-strain model for FRP-confined concrete. The equation (5) illustrates the axial stress

when it reaches ( ):

A careful examination of the present tests data showed that the second portion of all the experimental

axial stress-lateral strain curves intercepts the axial stress axis at a stress value which is very close to

the unconfined concrete strength when this portion is approximated by a best-fit straight line. The

slope of this straight line is (k), as proposed:

The new ultimate strain and compressive strength equations account for the effects of confinement

stiffness and jacket strain capacity separately and provide close predictions of test results. The

modified model of Lam and Teng’s model provide much closer predictions of test stress-strain curves

than the other models. And, it is suitable for direct use in practical design and for inclusion in design

cods/specifications. Also, this model is more compatible with current experiments data that are

compared.

1.3. Numerical Analysis

Finite element method (FEM) is a numerical technique to find approximate solutions for boundary

value problems, for partial differential equations and also for integral equations. These differential

equations are solved by either eliminating the differential equations completely or by rendering these

differential equations into ordinary differential equations which are then numerically integrated using

standard techniques. FEM is a good choice for solving partial differential equations over complex

domains.

The technique of FE Method is described by: discretizing the continuum, selecting interpolation

functions, finding and assembling the material properties to obtain the system equations, imposing the

boundary conditions, solving the system equations, and making additional computations if desired.


In fact, the nonlinear fracture models based on the numerical approach are relatively more involved in

the computations as ATENA program. For this reason, probably, the fracture models based on the

modified linear elastic fracture mechanics may bridge the gap between the computational efficiency

and the model predictive capability of results; because, they are relatively more computationally

efficient, but have limited capacity to predict the fracture parameters.

FEM is well suited for superimposition of material models for the constituent parts of a composite

material. Advanced constitutive models implemented in the finite element system ATENA serve as

rational tools to explain the behaviour of connection between steel and concrete. Nonlinear simulation

using the models in ATENA can be efficiently used to support and extend experimental investigations

and to predict behaviour of structures and structural details. Several constitutive models covering these

effects are implemented in the computer code ATENA, which is a finite element package designed for

computer simulation of concrete structures. The graphical user interface in ATENA provides an

efficient and powerful environment for solving many anchoring problems. ATENA enables virtual

testing of structures using computers, which is the present trend in the research and development.

Because of material properties play an important role in modeling of structural elements, each material

inside the program is defined; concrete is represented by solid brick element, reinforcement by bar

elements and FRP by shell elements.

2. Materials and Methods

2.1. Experiment Data Base

The test database used in the present study (i.e., the present test database) has been reported for the

assessment of analysis oriented stress strain models. The study is divided the database of many tests

on concrete cylinders to four groups’ results. Table 1 illustrate the specimens’ geometry with (150

mm) diameter and (300 mm) height for all specimens and steel detailing for both unconfined and

confined groups. Also, figure 3 and figure 4 showed the cross section details, CFRP layer thickness

(T) and steel bars distributions. The mechanical priority of concrete material as concrete strength (i.e.,

the compressive strength) is with concrete class C35/37. All these tests were recently conducted

under standardized test conditions at HTWK University for applied science-Leipzig by the writers’

group.

Table 1. Specimen grouping and basic parameters

PC: Plain concrete, RC: Reinforcement concrete, CFRP: Carbon fibre reinforced polyethylene.

Also, the material properties for the concrete and steel that used in lab are inserted in table 2. Same specimens after the tests were retrofitted with FRP sheets in the damage area to restore their strengths. Four types of specimens were constructed with different detailing; two were unconfined and the other two confined. The monitoring load had been applied using Quasi-static testing technique. CFRP wrapping was used for retrofitting of damaged specimens with epoxy resin.

The test procedure that made in laboratory to get the test database is summarized as: the FRP jackets

were formed via the wet lay-up process and had hoop fibers only, for each batch of concrete, three

No. Group

Name

Specimen Group Specimen

Size (mm)

Longitudinal

Reinforcement

Stirrups CFRP

T. (mm)

1 Z0 Unconfined PC 300*150 ------ ------ ------

2 Z 6/10 Unconfined RC 300*150 6 T 8 T 6 /100mm ------

2 Z 6/5 Unconfined RC 300*150 6 T 8 T 6 /50mm ------

3 Z0 CFK Confined PC with CFRP 300*150 ------ ------ 2*0.11

4 Z 6/10CFK Confined RC with CFRP 300*150 6 T 8 T 6 /100mm 2*0.11

4 Z 6/5 CFK Confined RC with CFRP 300*150 6 T 8 T 6 /50mm 2*0.11


plain concrete cylinders were tested as control specimens to determine the average values of the

unconfined concrete strength and the corresponding axial strain .

Figure 3. Reinforcement detailing and cross section details of unconfined specimen

Figure 4. Reinforcement detailing and cross section details of confined specimen

Table 2. Material Properties

Strength classes of normal concrete C: C35/37

Cylinder compressive strength

Initial elastic modulus 29 GPa

Poisson’s ratio = 0.2

Tensile Strength

Reinforcement bars

Compressive strength

Initial elastic modulus 200 GPa


Also, for each specimen was tested in Figure 5, the behaviour of the load-displacement curve and

cracks pattern were controlled. Table 1, Figure 3 and Figure 4 show the cross section of cylinder

specimens included the longitudinal bars and stirrups that are used. Also, table 2 shows the material

properties that are used.

(a)

(b)

Figure 5. (a) CFRP Confined RC specimen (b) unconfined RC specimen; test loading are appeared.

Finally, the CFRP jackets hoop fibers with two layers of unidirectional, woven carbon fiber fabric for

confined specimens are used. The material property of this kind of carbon fiber (SikaWrap-200c)

shows in table 3.

Table 3. Carbon fiber material property

2.2. Numerical Method

The program ATENA offers a variety of material models for different materials and purposes. The

most important material models in ATENA for RC structure are damage model for concrete and

reinforcement based on smeared crack method. This advanced model considers all the important

aspects of real material behaviour in tension and compression as well the CFRP material modeling is

also considered.

This model which is determined for nonlinear finite element analysis of structures, used ATENA offer

tools specially designed for computer simulation of concrete and reinforced concrete structural

behavior. ATENA program system consists of a solution core and several user interfaces. The solution

core offers capabilities for variety of structural analysis tasks, such as: stress and failure analysis,

transport of heat and humidity, time dependent problems (creep, dynamics), and their interactions.

Technical Data

Fiber type High strength carbon fibers

Fiber orientation 0° (unidirectional)

Areal weight 200 g/m2 ± 5 %

Fiber Density 1.80 g/cm3

Fabric design thickness 0.11 mm (based on total carbon content

Tensile strength of fibers 3´900 N/mm2 (nominal)

Tensile E-Modulus of fibers 230´000 N/mm2 (nominal)

Construction Warp: Carbon fibers (98 % of total areal weight)

Weft: Thermoplastic heat-set fibers (2 % of total areal weight)

Fabric length/roll Fabric width 300/600 mm

Shelf life 2 years from date of production


Solution core offers a wide range of 2D and 3D continuum models, libraries of finite elements,

material models and solution methods. User interfaces are specialized on certain functions and thus

one user interface need not necessarily provide access to all features of ATENA solution core. This

limitation is made on order to maintain a transparent and user friendly user environment in all specific

applications of ATENA.

ATENA 3D program is designed for 3D nonlinear analysis of solids with special tools for reinforced

concrete structures. However, structures from other materials, such as soils, metals etc. can be treated

as well. The program has three main functions; pre-processing, run and post-processing. The pre-

processing step includes input of geometrical objects (concrete, reinforcement, interfaces, etc.),

loading and boundary conditions, meshing and solution parameters. Also, the analysis procedure

makes possible a real time monitoring of results during calculations, and the last step, post-processing,

it accesses to a wide range of graphical and numerical results.

2.3. FEM Modeling of cylinder specimens in ATENA

Element geometric modeling of concrete has been done using 3D solid brick element with 8 up to 20

nodes in ATENA. The 3D solid brick elements having three degree of freedom at each node:

translations in the nodal x, y and z directions. This is an isoperimetric element integrated by Gauss

integration at integration points. This element is capable of plastic deformation, cracking in three

orthogonal directions, and crushing. The most important aspect of this element is the treatment of non-

linear material properties.

Reinforcement modeling could be discrete or smeared. In our work, a discrete modeling of

reinforcement has been done. The reinforcement has been modeled using bar elements in ATENA.

Reinforcement steel is a 3D bar element, which has three degrees of freedom at each node; translations

in the nodal x, y and z direction. Bar element is a uniaxial tension-compression element. The stress is

assumed to be uniform over the entire element. Also plasticity, creep, swelling, large deflection, and

stress-stiffening capabilities are included in the element.

The FRP modeling can be done as a 3D shell element in ATENA. The Ahmad shell element

implemented in ATENA, is described in ATENA theory manual. The present Ahmad element belongs

to group of shell element formulation that is based on 3D elements concept. It can be used to model

thin as well as thick shell or plate structures.

There are many methods to model the fiber material. A better option is to model the CFs as discrete

bars at/near the concrete surface (Vladimír, et al., 2012). About 2 bars per element (with the area

corresponding to the total CF cross section area per the concrete element width) should be enough.

However, it is not possible to capture debonding/delamination with this modeling. Another

recommended option is to use shell elements to model the wraps. Then, the user can model the

interface between the concrete and the wrap using contact elements.

The method, in this research, of how carbon fiber wraps strengthening in ATENA model is built on

the linear relation between the elastic modulus of the CFRP material and the thickness of the CFRP

layer. In fact, the thickness of CFRP layer is modeled as (10 mm) with elastic modulus (5060 MPa),

but in real the thickness of the CFRP layer is (2*0.11 mm) with elastic modulus (230000 MPa), the

material proprieties of the CFRP material is shown in Table 4.

Table 4. CFRP Material Properties modeling

Material Type (ATENA) 3D Elastic Isotropic

Elastic modulus E 5060 MPa

Poisson’s ratio ν 0.3 -

Material Type (Lab) 3D Elastic Isotropic

Elastic modulus E 230000 MPa

Poisson’s ratio ν 0.3 -


The steel plates and the resin material properties of the models are considered. The function of the

steel plate in the ATENA is for support and for loading. The property of steel plate is the same as the

reinforcement bar yield strength. And for resin material perfect connection material is proposed as

epoxy material properties that used in lab tests.

3. Results and Discussion

In pre-processing window the model is built and the processing steps are performed by create the

geometry of FE model as shown in Figure 6. Then the material properties are assigned to the various

elements of each cylinder specimens. After that, the structural element boundaries are come, various

supports, loadings, FRP and monitoring points are defined in Figure 6. Also, the finite element

meshing parameters are given and meshing of the model is generated accordingly. Various analysis

steps are defined. The FE non-linear analysis is done in Run window.

The FE non-linear static analysis calculates the effects of steady loading conditions on a structure. A

static analysis can, however, include steady inertia loads (such as gravity and rotational velocity), and

time-varying loads that can be approximated as static equivalent. Static analysis is used to determine

the displacements, stresses, strains, and forces in structures or components by loads.

When the FE nonlinear static analysis is completed the, the results are shown in third part of the

ATENA i.e. Post processing. The stress- strain values at every step, crack pattern and cracks

propagation at every step shown help in to analyse the behaviour of the elements at every step of load

deflection.

(a) (b) (c)

Figure 6. (a) FE mesh of unconfined specimen; (b) Monitoring points of specimens; (c) FE mesh of confined

specimen

3.1.Unconfined Plain Concrete Columns

Load deflection curve for unconfined specimen has been plotted in Figure 7. It can be observed from

Figure 7 that the structure behaved linearly elastic up to the value of load around100 kN at 0.1 mm. At

this point the minor cracks started to get generated at the specimen. After this point there is a slight

curvature in the plot and load started increasing with the deflection increments. When the load reached

to the value of 521 kN, the graph depicted non-linearity in its behavior and the maximum load taken

by cylindrical specimen is 690 kN at deflection of 0.9 mm. Subsequently, deflection started increasing

without any significant increment in load; it has reached to the value of 0.7 mm with the load value

around 600 KN. As the analysis continued, the load carrying capacity decreased progressively.

Further, the load has been found to be 220 kN at the deflection of 2 mm.


Figure 7. Load-Displacement curves of unconfined plain concrete cylinders

Results of analytical modeling are compared with Experimental Results of Unconfined plain concrete

specimen, the results vary but the behavior remains almost same. The analytical results vary due to

actual experimental conditions and conditions of fixed end. The modeling parameters are constant for

the analytical specimen but for actual specimen some parameters are different. The same model for

concrete has been modeled but the actual behavior may not resemble exactly the same. Considerable

increase in strength of around 12% was shown by experimental modeling. In figure 7, there are four

developments of fracture zones. At the first zone, the initial stiffness in ATENA model is not the same

as in lab data because of the boundary conditions (supports, loads, symmetry planes, etc.), the E-

modulus, and reinforcement ratio differences. At the second zone, the main difference is in the peak

point position. In fact, the main reason of gap between lab results and analytical data is meshing size

of the element. At the third and fourth zones, the cracking and material yielding are different because

of the material definition at ATENA program database. Also, neglecting shrinkage effect of relaxation

concrete material affects the behaviour of stress-strain curve under monitoring loading. The same

discussion for unconfined reinforcement concrete specimens with different ties spacing is proposed.

3.2. CFRP Confined Reinforced Concrete Columns

The load and deflection for a confined specimen has been depicted through Figure 8. It can be

observed from this plot that the load-deformation behavior is the same as for unconfined specimen.

The structure behaved linearly elastic up to the value of load around 228 kN at 0.15 mm. At this point

the minor cracks started to get generated at the confined specimen. After this point there is a slight

curvature in the plot and load started increasing with the deflection increments. When the load reached

to the value of 858 kN, the graph depicted non-linearity in its behavior with deflection of 1 mm.

Subsequently deflection started increasing without any significant increment in load; it has reached to

the value of 3 mm with the load value of 1170 kN. The maximum value of load has been observed to

be 1540 kN at deflection of 4.78 mm.

In Figure 8, at the first zone, the initial stiffness in ATENA model is nearly the same as in lab data

because of the boundary conditions (supports, loads, symmetry planes, etc.), the E-modulus, and

reinforcement ratio differences. At the second zone, the behavior of ATENA curve is approximately

the same. At the third and fourth zones, the cracking and reinforcement yielding (and eventually, other

nonlinearities) developed. We see that the ATENA model at this zone not similar in lab curves and

this because of the material definition at ATENA program database. Finally, the same behavior of

0

100

200

300

400

500

600

700

800

900

0.0 0.5 1.0 1.5 2.0 2.5

ATENA

LAB-S1

LAB-S2

LAB-S3

Displacement [mm]

Co

mp

ress

ive

axia

l L

oad

[k

N]


ATENA curve can be predicted if the first elastic zone is shifted. Also, some differences will be made

because of relatively common source of differences is neglecting shrinkage effect. The same

discussion for unconfined reinforcement concrete specimens with different ties spacing is proposed.

Figure 8. Load-Displacement curves of confined Reinforcement concrete cylinders with stirrups spacing

S1= 10 cm

3.3.Extension to the behaviour of concrete under fatigue loading

Because of the traditional approach that used to describe damaged caused by static load is not

applicable for fatigue loading so it is thus necessary to modify the traditional formulation of these

models (Alliche, 2004). To describe fatigue degradation of concrete material, the concept of damage

mechanics is denoted as (Papa, 1993) model. This model is based on strain damage theory and

assumed that degradation of material is mainly due to nucleation and growth of the micro cracks.

Some numerical simulation was created by (Alliche, 2004) and show that strain can be divided into

three stages of degradation with different percentage under fatigue load. In experimental fatigue

behaviour for concrete material the increasing of damage is described as extension of pre-existing

cracks until the stable state is reached and it will be the first stage. Then the second stage start with

nucleation of new cracks and creep. Finally, the instable crack propagation leading to failure as third

stage. Also, during fatigue test the indication of damage occurring in the material is the decrease of the

Young modulus. In order to check the validity of previous model and parameters, experimental results

are proposed from (Kim, et al., 1996) on concrete specimens subjected to compressive fatigue loading.

Some indications of fatigue results obtained from (Alliche, 2004) study is denoted in table 5. The

experimental evolution of axial strain showed in figure 9 and compared with damage analytical model

of (Alliche, 2004) model. The model based on damage theory described the material degradation

under fatigue loading and uses tensorial damage (Dragon, et al., 2000) parameters in conjunction with

fatigue damage evolution.

Table 5. Fatigue results

Compressive

Strength (Mpa)

Young’s

Modulus

(Mpa)

Maximum

Stress

(Mpa)

Fatigue

cycles

80 38000 63 4284

0

200

400

600

800

1000

1200

1400

1600

1800

0 1 2 3 4 5 6

ATENA

LAB-S1

LAB-S2

LAB-S3

Displacement [mm]

Com

pre

ssiv

e ax

ial

Load

[kN

]


The comparison which obtained showed also good agreement with experimental results and the

validity of the damage model under axial load. Furthermore, several phenomenon observed in fatigue

test: the progressive stiffness decay during fatigue loading, three stages of strain during fatigue life and

accumulation of permanent strains under constant amplitude fatigue load.

Figure 9. Comparison between experimental and computed axial strain evolution for one fatigue test (Alliche,

2004)

These results will be used later in a new study related to the development of the model in case of

strengthening system with CFRP sheets under fatigue loading. The study will investigate the fatigue

performance of RC concrete material and fiber reinforced concrete. These authors developed some

damage models incorporating fiber reinforced concrete enhanced sensitivity of fatigue.

4. Conclusion

The four types of concrete cylinders before and after confined them by FRP jackets were tested to

study the fundamental stress–strain behavior of confined concrete. In this progress the test results and

analysis declared the behavior of CFRP concrete cylinders. Based on the results of this study, the

following conclusions can be drawn: significant increase in strength and ductility of concrete can be

achieved by CFRP composite jackets, the confinement modulus and the confinement strength of the

composite jacket have been identified as the two critical parameters in describing the system

confinement effectiveness. Also, the ultimate confined concrete which is determined by the rupture of

the composite jacket (rupture strain), is much lower than the rupture strain obtained from flat tensile

coupon samples which refined constitutive model of concrete confined by FRP. In addition to

validation model, the results of cyclic tests of compressive fatigue load for unconfined specimens

show the demand of applying such test to CFRP specimens in terms of extending fatigue service life.

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Number of cycles N

3

2.8

2.4

2.2

2

1.8

1.6

2.6

(10-3

)

Axia

l S

trai

n

Experiment

Analytical Alliche 2004


Furthermore, this study is important because of the whole procedure is guided to economic view of the

lab experiments. The progress is summarized with prediction the post behavior of the confined

concrete circular columns with two layers of Carbon fiber polymer material by studying the most

parameters that affect the behavior of the composite material. Then create a finite element model with

ATENA program simulate the experimental one. This progress will save a lot of experiment material

and also save time in the future.

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