Parameters Affecting the Behavior of Reinforced Concrete Wrapped With CFRP Sheet

1 Parameters Affecting the Behavior of Reinforced Concrete Wrapped With CFRP Sheet Azad A. Mohammed and Yassamin K. Faiud Department of Civil Engineering , Department of Civil Engineering College of Engineering , University of Sulaimani College of Engineering , University of Duhok E-mail: azadkadr@yahoo.com , Abstract In this paper the behaviors of strength and deformation of short reinforced concrete column specimens wrapped with CFRP were studied through testing 48 cylindrical specimens under axial loading. The role of parameters of CFRP wrap layers and arrangement, concrete strength , main steel reinforcement , lateral reinforcement and specimen slenderness ratio was studied. Results indicated that due to wrapping with CFRP layers the state of confined concrete occurs and the properties of strength and deformation are modified considerably. The ultimate load percentage was found to vary from 123% to 280% of that of unconfined specimens. The ductility of reinforced concrete specimens was found to be increased considerably as a result of wrapping. The effect of wrapping was found to be important in the case of concrete of lower strength and poorly reinforced with both main bars and lateral reinforcements. In order to obtain higher load capacity of wrapped high strength concrete it should be reinforced highly with both types of reinforcements. In general the parameters influencing the behavior reinforced concrete confined with CFRP sheets are: number of layers, replacing layers with strips, concrete compressive strength, main bars, lateral reinforcement, and specimens slenderness ratio. An analytical model was proposed for calculating ultimate load capacity and load-strain relationship for reinforced NSC and HSC confined with CFRP sheets. The predictions were found to be accurate, and the ratio of test / calculated ultimate load was found to be 1.0043 for NSC and 1.0033 for HSC.


1-Introduction
Strengthening of reinforced concrete received considerable emphasis throughout the world and the issue of upgrading existing civil engineering infrastructures took a great deal of importance compared with new constructions. Many techniques and procedures for strengthening of the structural member are adopted where the level of strengthening depends on strength and deformation demands of the members. The strengthening in particular is important to increase the live-load capacity e.g. of a building that changes its use from residential to commercial [ 13 ]. Problems related to using steel plate for strengthening led to an alternative solution which is the use of Fiber Reinforced Polymer composites commonly known as FRP's. Fiber-wrapping technology was first used in practice for concrete chimneys in Japan; this concept then was extended to retrofit concrete columns [ 3 ]. Strengthening using fibers has been widely used for both bridges and buildings and for concrete surfaces in tension and compression. This scheme has also a beneficial effect in seismic region by enhancing ductility and increasing shear strength to the extent that brittle shear failure is converted to a ductile one [ 15 ].
Lin and Chen [10 ] found that the strength of confined normal strength concrete cylinders increased in direct proportions by the increase in composites layer number. Ilki et al [ 8 ] showed that for very low strength concrete there is a significant increase in compressive strength. Test results obtained by Lam and Teng [ 9 ] indicate that insufficient confined cylinders behave like the unconfined ones with similar failure pattern and a slight or almost no increase in the peak compressive stress. Harries and Kharel [6 ] and Esfahani and Kianoush [ 4 ] found that there is an increase in compressive strength and ductility of the wrapped cylinders due to confinement effect imposing a more ductile stress-strain behavior as compared to unconfined one. Tests by Park et al [ 12 ] indicated that wrapping concrete with strips instead of full wrapping lead to CFRP fracture mode of failure and the applied load was higher when the spacing between CFRP strips reduces and exhibits larger ductility. They also found that the differences in cylinders height have no significance on effectiveness of CFRP reinforcement. Test results by Berthete et al [2] indicated a significant increase in strength and ductility but the confinement efficiency decreased when the compressive strength of the specimens increased. Also they found that when the confinement level is high, there will be more enhancements in structural ductility. Tamuzs et al [ 16 ] noticed that the existing of steel bars help in increasing the rigidity and stress level of concrete cylinders where the steel bars lead to a uniform increase in stress. They also found the presence or absence of reinforcing bar does not change the second portion characteristic of the deformation diagram of wrapped specimens.
Most of the studies were conducted on plain concrete having compressive strength ranges from 20 to 30 MPa and there are few number of researches clarifying the effect of reinforcement on the behavior of confined concrete. Because of the widespread use of high strength concrete in building structures, it is important to study the mutual combined influence and interaction when using high strength concrete with steel reinforcement and CFRP sheets wrapping on the behavior of confined concrete. The experimental work presented in this paper included testing cylindrical concrete specimens reinforced with steel bars provided both axially and laterally and wrapped with CFRP laminate. A comparative study was carried out to illustrate the role of important parameters affecting the strength and deformation of reinforced concrete wrapped with CFRP sheets.

2-1 Materials:
Ordinary Portland cement [Type I ] was used in the tests for producing both NSC and HSC mixes. Natural river sand was used as fine aggregate of (2.71) specific gravity at saturated surface dry condition and fineness modulus equal to 2.78. Natural river gravel and crushed gravel of maximum aggregate size equal to 12 mm were used. Results of sieve analysis indicated that the grading conforms to ASTM C33-03 [ 1 ] specifications limits. The specific gravity for the aggregates used were 2.74 and 2.68 with dry bulk density of 1860 kg / m 3 and 1740 kg / m 3 for natural gravel and crushed gravel, respectively. High range water reducer of Sika®Viscocrete®-20 Gold ( liquid ) [(type G) according to ASTM C494/C 494M-05a ] of constant dosage equal to 2.5% by cement weight was used for preparing HSC mixes. CFRP of SikaWrap®-230C type was used for the purpose of wrapping specimens which is a unidirectional woven carbon fiber fabric having the following properties: elastic modulus is 238 GPa, tensile strength is 4300 MPa, and ultimate tensile strain is 1.8%. For bonding CFRP sheets to the concrete adhesive epoxy of Sikadur ® -330 type was used which consisted of two component impregnation resin on epoxy resin base, mixed together in a ratio equal to (1: 4). All concrete specimens were reinforced with longitudinal compression reinforcement consisting of two types of hot-rolled deformed bars of 10 mm and 16 mm diameter. Deformed bars of 6 mm diameter were used as transverse reinforcement in a shape of ties and spiral. Concrete cover equal to 15 mm was provided. Table ( 1 ) shows the properties of the steel bars used.

Mix Proportion:
Thirteen trial mixes were prepared to get the optimum mix proportion for HSC of cube compressive strength equal to 80 MPa and the mix was found to be 1:1.2:1.8 ( cement :sand : gravel , by weight ). For NSC mix design was carried out to obtain a concrete of compressive strength equal to 45 MPa and the mix proportion was found to be 1:1.6:2.

Molds:
According to the dimensions of the specimens two types of mould were used in the present study. The first one was the standard cylindrical metal mold of 152 × 304.8 mm dimensions. For specimens of larger length a height was equal to 750 mm in which three standard cylinders were connected together by the mean of welding. Spacers were used to omit the extra space and to obtain a height equal to 750 mm.

Casting and Curing:
The steel reinforcement cage was put in the center of the cylindrical mould after omitting a bottom concrete cover equal to about 15 mm by putting a small amount of mix, then the mixture was poured in four layers each layer was compacted 25 strikes using 18mm diameter standard steel road as recommended for compacting plain concrete in ASTM C470/c 470M-03a specification. [ 1 ] Later a further compaction was made by striking the molds gently with a rubber hammer to exclude the remained air bubbles. The top surface of the concrete then finished by the mean of trowel and the specimens were left inside the mold for 24 hours to harden. After remolding the specimens were put in a water tank inside the laboratory to cure with a temperature kept to be (25± 3 Cº). At the end of curing, the specimens were removed from the water tank and left in the laboratory to dry for 14 days before wrapping with carbon fiber reinforced polymer (CFRP) sheets.

Wrapping Procedure:
After drying, the surface of all specimens intended to be wrapped by CFRP sheets was well cleaned by a steel brush to remove any dirt and dust. After brushing process which was done accurately and homogenously, the surface of specimens was cleaned again and prepared to be covered with the epoxy material, then CFRP layer was cut and prepared according to the surface area to be wrapped. The preparation of CFRP sheets is followed by painting cylinders faces with epoxy carefully using soft paint brush. It was made sure that the epoxy was equally and homogenously distributed at a constant thickness over the whole surface of the specimens. The process of providing epoxy was followed by pasting CFRP sheets on each specimen carefully and according to the variables requirements of each specimen. A steel roller was used in order to distribute the epoxy on the CFRP layer to allow for good impregnation and to ensure that all entrapped air bubbles disappeared. After wrapping the specimens were left to cure within 7 days according to manufacturer's recommendation.

Capping procedures:
Before testing, all the specimens were capped according to the recommendation of ASTM C617-03 specification. [ 1 ] The capping process is important to ensure a plane surface in order to distribute the load uniformly. For capping, gypsum paste was prepared; the dry gypsum was sieved on No.16 sieve to remove the deleterious substances. The steel base for capping device was filled with gypsum paste and the specimen was put on its inverted position and left for 30 minutes. After gypsum hardening the specimens were taken from the steel base and the extra portions of gypsum at the sides of the cylinders were removed.

Test Measurements and Instrumentation:
The cylinders were tested and loaded to failure under increasing compressive load using the computerized testing machine of type (Walter + Bai AG/ Switzerland / 08 -2003). The maximum capacity of the machine is 3000 kN. The rate of loading was constant and kept to be 0.3 MPa/sec for control specimens and 0.5 MPa/sec for wrapped ones. The load applied continuously without shock or impact till failure of the specimen. All measurements of axial and lateral deformations were recorded using a digital video recorder, to obtain accurate data especially near failure in which the deformation value is high and using the classical method via stopping the machine and taking the results leads to significant errors. Figure ( 1 ) shows the arrangement of the specimen at testing indicates the measurement units. For each concrete mix batch two cubes of 150 mm dimension were tested, and the cube compressive strength was taken as the average of the two values. Later, cylinder compressive strength was calculated by multiplying the value of cube compressive by 0.8 for normal strength concrete as proposed by Neville and Brooks [ 11 ] and by 0.88 as suggested by Yi et al [ 19 ] for HSC.

Details of Test Specimens:
According to the tested variables a total of 48 cylindrical specimens were prepared. The variable attempted to be studied in the present work are : (a) number of CFRP layer, (b) effect of replacing sheets with strips of CFRP, (c) amount of main reinforcement, (d) amount of lateral reinforcement, (e) concrete compressive strength, (f) type of lateral reinforcements, and (g) specimen height. Figures ( 3 ) and ( 4 ) show the dimensions and reinforcement details of the two types of specimens. The detail of specimens can be seen in the tables. The first item of the specimen's code is the type of concrete, N for normal strength and H for high strength concrete, the second item is the specimen height; it is either 300 mm or 750 mm. The third item is the longitudinal or main reinforcement which is 10 mm diameter or 16 mm diameter, the forth item is the type and the spacing between the lateral reinforcement, T is used for ties and S for spiral, 70 and 40 are spacing between ties in mm. The last item is the arrangement of CFRP layers, C for control specimens without confinement while W is for wrapped specimens, the number beside W represent number of layers and P is for specimens wrapped with strips provided at the outer layer of CFRP sheet. The distance between strips and their width were constant and equal to 35 and 50 mm, respectively. According to the number of main bars provided to the specimens, the longitudinal compression reinforcement ratios were equal to 2.59% and 4.04%. It should be pointed out that to prevent failure of the end of specimens near the test machine platens and to ensure failure in the central zone of the specimens extra strips of 50mm were provided at ends of all specimens.

Concrete Strain Measurements:
The lateral strain in specimens was measured by using two dial gauges with accuracy equal to 0.01 mm displacement, placed at 180 o apart, attached and located to the mid-height of each specimen. They were placed on an especially fabricated metal base with adjustable and moveable metal arms to control the required position as illustrated in Figure ( 2 ). To measure axial displacement, one dial gauge was placed with accuracy equal to 0.01 mms displacement, attached to the cylinder by especially manufactured metal ring and located at the top third part of the cylinder. The axial strain was obtained by dividing the displacement by the gauge length ( 230 mm for small specimens and 590 mm for large specimens ) and the lateral strain was obtained by dividing the average reading of the two dial gauges by the specimen's diameter.

3-1 Ultimate Load Capacity of Wrapped Concrete:
As a result of wrapping, a state of confined concrete usually occurs and accordingly the behavior of concrete becomes different in strength and deformation compared with plain concrete. Tables ( 2 ) ( 3 ) and ( 4 ) contain the results of ultimate load capacity of wrapped and unwrapped control specimens. The Tables also contain the percentages of ultimate load for wrapped to that of control specimens. Compressive strength of confined concrete ( f' cc ) also calculated and shown in the tables. The compressive strength of confined concrete was obtained by calculating the load resisted by the concrete divided by the net concrete area. The load resisted by the confined concrete ( Pc ) is the total load ( P u ) minus the load resisted by the axial steel reinforcement ( P s ). The later load value is obtained by multiplying the yield stress of steel by the steel area. Figure ( 5 ) shows the variation of ultimate load percentage with the number of layers of CFRP for Group (1), (2), (4) and (5) specimens. For normal strength concrete specimens the percentages are 179%, 245% and 280% for specimens wrapped with one, two and three layers, respectively. While for high strength concrete the percentages of ultimate load are smaller and equal to 123%, 146%, and 168% for one, two and three layers of CFRP, respectively. Therefore, the effect of wrapping reinforced concrete with CFRP is more important for the case of NSC compared with HSC. It is observed from Figure ( 5 ) that the response of ultimate load with the number of layers for HSC is linear, while that of NSC slightly deviates from linearity especially when the number of layers is more than two layers.  (4) and (5) specimens. Such specimens were reinforced laterally with Ø 6 mm ties at 40 mm spacing, instead of 70 mm spacing. The percentages of the ultimate load for wrapped NSC specimens are 199%, 274% for one and two layers, respectively and equal to 137% and 181% for one and two layers, respectively for HSC specimens. For NSC the ratio is higher by 62% using one layer of CFRP and higher by 93% using two layers. Such ratios for Group (1) and (2) (4), (5), (6) and (7) Specimens Therefore, the difference between the percentage of ultimate load capacity of wrapped NSC and HSC is only marginal due to the change of spacing between lateral reinforcement. It is obvious from the results of Figure ( 5 ) that the percentage of ultimate load usually increases when the spacing between ties reduces especially for larger number of CRFP layer. Therefore to obtain higher load capacity especially for larger number of CFRP wrapped concrete attention must be offered to the arrangement of lateral ties because such type of reinforcement besides the wrapping with CFRP have a significant effect of buckling and collapse of concrete where the change of spacing between the ties from 70 mm to 40 mm will increase the load capacity of wrapped concrete by a ratio of 14% to 35 % regardless the effect of concrete strength. Results of ultimate load of Group (3) specimens are shown in Table ( 2 ) and in Figure ( 6 ). The percentages of ultimate load are 156%, 195% and 223% for one, two and three layers of CFRP layers, respectively. Accordingly, there is an increase in the percentage of ultimate load varied from 23% to 55% as a result of using spiral instead of ties in the concrete wrapped with CFRP. In general, both types of lateral reinforcement and spacing between them are considered important factors in concrete after it confined with CFRP layers regardless of the number of layers provided, and the compressive strength of unconfined concrete. The best arrangement is the spiral type of lateral reinforcement with smaller spacing between rounds as far as possible. Table ( 4 ) and ( 5 ) contain test results and ultimate load capacity for wrapped specimens reinforced with four Ø 16 mm bars. In Group (6) and (7) specimens of the ratio of main bars which is equal to 0.0443 are nearly two times higher than that provided by Group (1) and (2) specimens. The percentage of the ultimate load for the wrapped HSC specimens are 151%, 188%   (8) and 212% for one, two and three layers of CFRP, respectively. For NSC, such ratio is 183%, 214 % and 267% for one, two and three layers, respectively. The difference between these values are 32%, 26 % and 55%, which are smaller than that of Group (1) and (2) specimens which are 56%, 99% and 112% for one, two and three layers respectively. Therefore, the difference in the ultimate load capacity of wrapped concrete with CFRP between HSC and NSC reduces when the amount of main bars increases. Accordingly, using HSC confined with CFRP sheets is more suitable for the case of concrete section which contains high amount of main bars.  From Figure ( 7 ), one can observe that changing the amount of main bars from 6 Ø 10 mm to 4 Ø16 mm has a slight effect on the percentages of load capacity of the wrapped NSC specimens where the percentages varied from 1% to 31% difference between Group (1) and (6) compared to percentages of 13 % to 44% between Group (2) and (7) where there is a positive effect in the change in the amount of main bar on the load capacity of the wrapped HSC. Therefore the performance of HSC to be wrapped with CFRP sheets is better when the amount of main bars is high. Table ( 4 ) contains the results of ultimate load and percentages of the ultimate load for Group (8) and (9) specimens. Figure ( 8 ) shows the variation of the ultimate load percentages with the number of layers. The percentages of the ultimate load are 180% and 213% for one and two layers of CFRP for those specimens made from NSC. For HSC specimens, the percentages are 164% and 218%. Therefore the difference between these values for the two types of concrete is not important because the difference between the two groups varied from 5% to 16%. According to the data of Figure ( 8 ), there are no important differences between the percentages of ultimate load for Group (6) and Group (8) specimens, the differences are (1% to 3%). Therefore, reducing the spacing between ties from 70 mm to 40 mm has no effect on the percentages of ultimate load of NSC reinforced specimens with a large amount of main reinforcement and wrapped with CFRP sheets, and slightly affects that of HSC [ 13% to 30% ]. Comparison between results of Figure ( 5 ) and ( 8 ) indicates that the combined effect of spacing between ties and concrete strength is important only for the concrete reinforced lightly with main bars. Table ( 4 ) shows the results of the ultimate load and the percentages for the Group (10) and (11) specimens. Figure ( 9 ) shows the variation of percentage of ultimate load for Group ( 7 ), ( 8 ) , ( 10 ) and ( 11 ) specimens. Percentages of the ultimate load for NSC specimens are 166% and 239% for one and two layers of CFRP, respectively. For HSC specimens, the percentages are 144% and 167%. Again, the percentages of the ultimate load are higher for NSC. In general, the percentage of the ultimate load is reduced as a result of increase in the height of wrapped reinforced concrete specimens but the change is not large and it ranges between 17% to 25% for NSC and 7% to 21% for HSC specimens. Figure ( 10 ) shows the variation of the ultimate load from those specimens partially wrapped and fully wrapped with CFRP sheets. Instead of the outer layer provided in fully wrapped specimens, strips are provided in partially wrapped specimens. Figure ( 11 ) shows the variation of the percentages of the ultimate load for partially and fully wrapped specimens. Comparing the two figures indicates the similarity between the two figures leading to a decision that the discussion of the results based on the percentage of the ultimate load (as done in the previous paragraphs) is true for the case of ultimate load capacity of wrapped specimens. Results of Table ( 2 ) and Figure ( 11 ) indicate that replacing the outer layer in a specimen wrapped with two CFRP layers with strips will reduce the percentages of the ultimate load from 245% to 205% (reduction by 40%). For specimen wrapped with three layers, such replacements lead to reduction from 280% to 258% (reduction by 22%). Different behavior can be observed from HSC specimens of Group (2) that is if the last layer of CFRP is replaced with strips, the percentage of ultimate load is changed by 1% only in one specimen and not changed in the other specimen (remains 168%). Therefore, there is a chance to replace the outer layer of CFRP with strips of CFRP without reducing the ultimate load capacity of HSC, but the change from outer layer to strip lead to reducing the ultimate load by about 22% to 40% in NSC .

Dilation Ratio of Fiber Wrapped Reinforced Specimens:
The dilation ratio presents a good indication for the lateral damage that can happen to the column geometry due to access loading. The most important result obtained is the large ratios of dilation for all unwrapped control specimens compared to the wrapped ones indicating the important influence of CFRP wrapping on reducing, to a large extent, the dilation ratios. From the test results data of Tables (3), (4), and (5), one can notice the reduction of dilation ratio as a result of wrapping with CFRP sheets. It is inversely proportional to high confinement; where for almost specimens confined by three layers of CFRP compared to one and two layers wrapping of Group (1), (2), (7) minimum values of dilation ratios were obtained. The same thing can be said for two layers wrapped specimens compared to one layer of Group (4), (8), (9) and (11). With expectance of Group (3), (5), (6) and (10) there was a small difference noticed in the dilation ratio which may be due to improper bonding of CFRP layers and the difference in the readings of dial gauges.

Load-Strain Relationships of Wrapped Reinforced Concrete Specimens:
Figures ( 12 ) through ( 22 ) show the compressive loadaxial strain and lateral strain relationships obtained from tests for all groups of specimens. From Figure ( 12 ) one can find that replacing the outer layer of CFRP with strips does not affect the maximum axial and lateral strains compared with improving the ultimate load capacity. Comparison between Figure ( 12 ) and ( 13 ) indicates that both the maximum axial and lateral deformations are in general lower for HSC specimens compared with NSC ones. Nearly, the same observation can be noticed in Figure (17) and (18) specimens [Group (6) and Group (7) ] indicating that there is no significant influence of main longitudinal bars on such behavior. The difference between the two maximum deformations as affected by the concrete compressive strength particularly can be considered as another property of the confined concrete. Such property can be added to another properties of concrete confined with FRP sheets that does not change with the existence of main longitudinal steel bars. With regard to the effect of specimen height, it is shown from the comparison between

Modes of Failure:
The failure pattern of HSC specimens is governed by an explosive and sudden failure manner accompanied by well crushing of concrete after rupturing the CFRP sheets. Figure( 23 ) show a view of the failure modes for some of tested specimens. For specimens with high number of CFRP layers (two layers and strips, and three layers), well damaged specimens with extensive fractures are observed associated with local buckling of the longitudinal bars and damage of the ties and spirals of Groups (1), (2) and (3). However, this phenomenon is less observed in the case of heavy reinforced specimens of Groups (6) and (7). In low ratios of confinement by CFRP wraps (one layer), light to medium crushing of concrete was observed. In the case of Group (3) with spiral lateral reinforcement, the damaged specimens are noticed by separating the outer layer of concrete cover bonded with CFRP wraps from the inner core of concrete. For specimens with small ties spacing of Groups (4) and (5), the rapture of CFRP and crushing of concrete can be defined within 14-18 cm at the middle part and the appearance of steel is noticed. This is not the case in the higher steel ratios of Groups (8) and (9) where smaller failure areas were observed

4-Analsis and Modeling
An attempt was made to provide an analytical model for calculating the compressive loadstrain relationship of the reinforced concrete confined with CFRP sheets. For this purpose, some models proposed earlier were adjusted to include the effect of axial and lateral reinforcement in addition to the effect of confinement on concrete strength. Parameters of peak compressive stress and ultimate compressive strength and their corresponding strains were calculated for constructing the whole load-strain relationship. Accordingly, the load-strain relationship for the case of short reinforced concrete column wrapped with CFRP can be obtained.

Basic Properties of CFRP
Based on the test results of tensile stress and deformation of composite CFRP-epoxy material obtained by Zangana [20], the properties of different layers of CFRP are shown in Table  (5), such properties are used later in the analysis of the reinforced concrete confined by CFRP wraps. Note that both the tensile strength and elastic modulus are reduced with the increase in layers number of CFRP sheets because of the increase in the amount of the epoxy adhesive of lower strength and elastic modulus compared with CFRP material.  [20] No. of layer

Idealized Form of Stress-Strain Relationship
Different forms of idealized stress-strain relationship were used by researchers. In this analytical procedure the well-known relationship given by Hognestad [ 7 ] to describe the ascending portion of stress-strain curve for unconfined concrete of the following form is used in which f c is the composite stress in general and f′ cp is the peak compressive stress and ε′ cp is the corresponding strain. The parameters of the stress-strain relationship are illustrated in Figure  (

4-3 Parameters of the First Portion of Stress-Strain Curve
The following relationship proposed by Richart et al [ 14 ] is considered as the main source for calculating the confined stress of concrete and later used (with modifications) by many researchers for calculating the strength of the concrete confined with steel and FRP composites.

Figure (24) Idealized Form of Stress-Strain Relationship for FRP-Confined Concrete
In which f′ cp is the peak compressive stress of the confined concrete, f′ co is the compressive stress of the unconfined concrete. f ℓ ′ is the lateral pressure, k is a constant. For concrete members reinforced with lateral ties or spirals and confined with CFRP sheets Eq. ( 2 )  Lateral confinement pressure due to lateral steel, hoop or spiral f ℓs can be calculated as follows [ 5 ] ( 14 ) in which ρ cc is the steel ratio relative to the confined concrete core measured to the outside of hoop, x and y are the larger and smaller dimensions of rectangular steel hoops, respectively. For calculating the strain at peak confined stress (f′ cp ), ε′ cp the relationship given by Toutanji [ 17 ]  in which ε ℓo is the yield strain of transverse steel hoop obtained by dividing the yield stress of transverse steel f yt by the elastic modulus of steel or 0.002 if no confinement by steel hoops or spirals are available. ε o is the strain corresponding to peak compressive stress of unconfined concrete and approximately equal to 0.002 [ 5 ]. Equations (3) and (15) then substituted into Eq.(1) for calculating the stress-strain relationship of the first portion of the whole relationship.

4-4 Parameters of the Second Portion of Stress-Strain Curve
As pointed out by many researchers due to the elastic behavior of FRP material till rupture, the second portion of the compressive stress-strain relationship of FRP confined concrete is linear (a straight line) between the peak stress-strain ( f′ cp , ε′ cp ) and the ultimate stress-strain ( f′ cu , ε′ cu ) points.
For calculating the value of f′ cu , a regression analysis was carried out based on the obtained test data. A nonlinear equation of the following form was found to be useful for predicting the dependent variable from the independent variable observations Regression analysis was carried out separately for NSC and HSC confined specimens to calculate the constants a and b. Statistical analysis was carried out using SPSS program to define the most suitable description for the test variable. Figure

Calculation of Load-Strain Relationship
To calculate the ultimate load of the concrete specimens the following relationship is used where f′ cu, cal is the ultimate strength calculated by using Eq. (18) and Eq. (19). A c is the net concrete area of the specimen and it can be calculated as follows where A s is the area of longitudinal steel bar used, Ø 10 mm or Ø 16 mm, in which P s is the load carried by steel and can be obtained by using the form Ps = fys × As Where ε o is the ultimate strain of unconfined concrete and can be taken equal to 0.0038. From the foregoing calculation steps the complete axial load-deformation relationship can be drawn.
specimens the ratio is equal to 1.0033, indicating the acceptable range of the model predication values.

5-Conclusion
From the present research work, the important conclusions may be drawn and summarized as follows 1-As a result of wrapping with CFRP sheets, a state of confinement occurred and accordingly the behavior of concrete becomes different compared with plain concrete. Different ratios in improving the strength characteristics were found for NSC and HSC specimens. The effect of wrapping with CFRP is more clear for the case of NSC. 2-In general, the ratio of ultimate load varied from 123% to 280% and the ultimate load capacity of wrapped specimens varied from 1315.9 kN to 2891.7 kN. Unlike that of NSC specimens a proportional increase in the percentages of ultimate load of HSC with the increase in CFRP layers up to three layers was observed. 3-Change of the ratio of the main bars from 0.0259 to 0.044 has less effect on the percentages of ultimate load capacity of wrapped NSC specimens. Oppositely, the effect is noticeable in HSC specimens where the performance is improved with a ratio varied from 13 % to 44% compared to a ratio equal to 1 % to 31% for NSC. The effect of reducing ties spacing only important in the case of confined HSC specimens. There is an increase in the percentage of ultimate load varied from 23% to 55% as a result of using spiral instead of ties in the HSC specimens. The difference in the ultimate load capacity of wrapped concrete with CFRP between HSC and NSC was found to reduce when the amount of main bars are increased. 4-The role of changing the height of concrete member on the ultimate load capacity after wrapping with CFRP is not significant. The change of the specimen height does not affect the axial deformation but influences the lateral deformation and the dilation ratio. 5-Replacing the outer layer in the specimen wrapped with CFRP layers with strips will reduce the percentages of ultimate load for NSC with ratios varied from 22% to 40% and no reduction was found for HSC specimens. 6-The ductility of the wrapped specimens was improved as a result of strengthening with CFRP sheets, where the behavior changes to more ductile behavior. The comparison of the loaddeformation relationships indicated that both the maximum axial and lateral deformations are in general lower for HSC specimens compared with NSC and the influence of main reinforcement on such behavior is not important. 7-An analytical model was proposed for calculating ultimate load capacity and load-strain relationship for reinforced NSC and HSC confined with CFRP sheets. The model predictions were found to be reasonably accurate, and the ratio of test / calculated ultimate load was found to be 1.0043 for NSC and 1.0033 for HSC.