Analytical Review on Eccentric Axial Compression Behavior of Short and Slender Circular RC Columns Strengthened Using CFRP

Although reinforced concrete (RC) columns subjected to combined axial compression and flexural loads (i.e., eccentric load) are the most common structural members used in practice, research on FRP-confined circular RC columns subjected to eccentric axial compression has been very limited. More specifically, the available eccentric-loading models were mainly based on existing concentric stress–strain models of FRP-confined unreinforced concrete columns of small scale. The strength and ductility of FRP-strengthened slender circular RC columns predicted using these models showed significant errors. In light of such demand to date, this paper presents a stress–strain model for FRP-confined circular reinforced concrete (RC) columns under eccentric axial compression. The model is mainly based on observations of tests and results reported in the technical literature, in which 207 results of FRP-confined circular unreinforced and reinforced concrete columns were carefully studied and analyzed. A model for the axial-flexural interaction of FRP-confined concrete is also provided. Based on a full parametric analysis, a simple formula of the slenderness limit for FRP-strengthened RC columns is further provided. The proposed model considers the effects of key parameters such as longitudinal and hoop steel reinforcement, level of FRP hoop confinement, slenderness ratio, presence of longitudinal FRP wraps, and varying eccentricity ratio. The accuracy of the proposed model is finally validated through comparisons made between the predictions and the compiled test results.


Introduction
The building industry plays a significant role in the development of human history. There are various building materials, such as structural materials, decorative materials, and some special materials, that have significantly contributed to the development of the building industry. Structural materials include metal, bamboo, wood, concrete, stone, cement, brick, plastics, ceramics, glass, and composite materials; decorative materials include various coatings, paints, glass with special effects, etc.; special materials refer to waterproof, fire-retardant, heat insulation, etc (i.e., [1]).
With the development of material science and technology, polymer materials exhibit a potential role in the building industry due to their excellent properties compared with inorganic materials. Building polymers commonly used in the construction industry include polyethylene (PE), polyvinyl chloride (PVC), polymethyl methacrylate (PMMA), polyester resin (PR), polystyrene (PS), polypropylene (PP), phenolic resin (PF), and organic silicon resin (OSR). By adding these polymers into traditional building materials, such as concrete and mortar, polymer-based building materials have great benefits when used in construction engineering. Compared with cement concrete, it provides good mechanical strength, Test results Wu and Jiang [32] Model Al-Nimry and Soman [26] (C1-S1-1V1C-B) Axial stress (MPa) Axial strain (mm/mm) Al-Nimry and Soman [26] (C2-S1-1V2C-A) Siddiqui et al. [30] (STR1-600) Axial stress (MPa) Axial strain (mm/mm) Wang et al. [31] (C2H0L2M) Figure 1. Stress-strain response for FRP-confined columns of small and large scales obtained using Wu and Jiang's [32] model for FRP-confined concrete cylinders.

Experimental Tests
To develop a stress-strain model and also to test the accuracy of the proposed model, a test database of 207 concentrically and eccentrically loaded FRP-confined unreinforced and reinforced concrete columns with different slenderness ratios and material properties (i.e., internal steel ties) was compiled from the literature [23,[25][26][27][28][29][30][31][32]57]. The database covers unconfined concrete compressive strength between 21.2 MPa and 59 MPa. All specimens  [32] model for FRP-confined concrete cylinders.

Experimental Tests
To develop a stress-strain model and also to test the accuracy of the proposed model, a test database of 207 concentrically and eccentrically loaded FRP-confined unreinforced and reinforced concrete columns with different slenderness ratios and material properties (i.e., internal steel ties) was compiled from the literature [23,[25][26][27][28][29][30][31][32]57]. The database covers Polymers 2021, 13, 2763 6 of 32 unconfined concrete compressive strength between 21.2 MPa and 59 MPa. All specimens were reinforced with longitudinal and hoop steel bars except those of Jiang et al. [29], Wang et al. [31], Wu and Jiang [32], and few specimens from Wang et al. [23]. All specimens were also strengthened using FRP wraps except for some specimens reported by Al-Nimry and Rabadi [25], Al-Nimry and Soman [26], and Fitzwilliam and Bisby [28], which were reinforced using lateral and longitudinal FRP sheets. To consider the important effects of column slenderness, the column diameter ranges from 150 mm to 305 mm and the height is from 300 to 1200 mm (i.e., kl/r = 8-32). Table A1 displays a summary of the tests.
Expressions to predict the peak axial strength were derived by utilizing the results of tests from [23,[25][26][27][28][29][30][31][32]57]. The expressions of the corresponding axial strains were mainly based on the results of Wang et al. [23], Al-Nimry and Soman [26], and Fitzwillian and Bisby [28] due to the limited stress-strain responses in the studied literature. Moreover, the lateral deflection model of Section 6 was derived based on results from [26][27][28][29]. To compare the accuracy of the different components of the present model with that of existing models, the models from [34,[39][40][41]47,48] were also assessed against the peak strength and strain. Furthermore, the complete stress-strain response was compared previously with the Wu and Jiang [32] model using results of specimens from [26,[30][31][32][33], whereas the model of this paper was validated later against the results of the published literature. Finally, the moment interaction diagram was assessed using only the results of Al-Nimry and Rabadi [25] and compared with the existing models [32,34,55].

Effect of Confinement by FRP Wraps
The lateral confinement resulting from the use of FRP wraps to a circular column section is a significant parameter for calculating the peak axial stress and corresponding strain of complete stress-strain response of FRP-confined concrete. The confinement by the FRP hoop wraps is considered using a dimensionless parameter described by Equation (1): where E f is the elastic modulus of FRP wraps (MPa); n f is the number of layers of FRP hoop wraps; t f is the nominal thickness of an FRP hoop sheet (mm); D is the diameter of a circular section (mm); ε fu is the ultimate tensile strain of FRP resulted from flat coupon tests (mm/mm); f c ' is the unconfined concrete cylinder strength (MPa).

Effect of Longitudinal FRP Wraps
Tests on the behavior of FRP-wrapped concrete columns have confirmed that using only FRP hoop wraps had a minor effect on the flexural resistance while using longitudinal FRP wraps combined with FRP hoop wraps resulting in significant enhancements in their flexural capacities (e.g., [25,26]). In the study of Siddiqui et al. [30], tests on circular RC columns of different heights (i.e., l = 600, 900, 1200 mm) were conducted to study the effect of FRP hoop and longitudinal fibers on the column behavior. It was found in particular that the axial and flexural capacities of slender columns are shared by the longitudinal fibers and that their contributions to the load-carrying capacities of columns with the heights of 900 and 1200 mm are more significant than the shorter ones. The significant efficiency of the longitudinal FRP fibers to slender columns is also reported in Ref. [28], in which the longitudinal FRP sheets do not enhance the performance of concrete cylinders, since these members experience compressive material failure rather than flexural failure. To account for the effect of the longitudinal fibers, the following parameter is introduced (Equation (2)): where n f,v is the number of longitudinal layers of FRP sheets.

Effect of Internal Steel Reinforcement r
Tests on FRP-confined RC columns have revealed a contribution made by the internal hoop reinforcement to the peak strength and strain enhancements (e.g., [23,24,26,[58][59][60]), and this contribution is found to be influenced by the amount of FRP wrap, column section size, and slenderness ratio. For example, the effect of internal hoop steel confinement is found to be minimal for columns with an adequate amount of FRP confinement (e.g., Wang et al. [23]). In their study, it has been also found that the effectiveness of FRP reduces as the section size is increased. Among the existing FRP confinement models under eccentric loading as presented in Tables A2 and A3, one can find the model of Hu et al. [41] that only addresses the effect of the varying slenderness ratios on the effectiveness of FRP confinement. However, the effect of steel confinement is neglected. Therefore, two dimensionless parameters that are relative to the compressive strength of unconfined concrete to consider the effects of steel confinement (λ hs ) and the longitudinal reinforcing steel bars (λ vs ) are provided as: where f yh and f yl are the yield strengths of the hoop and longitudinal reinforcing steel bars (MPa), respectively; ]ρ hs and ρ vs are the ratios of the hoop and longitudinal steel bars, respectively; d hs is the diameter of the hoop bar (mm); D c is the diameter of the concrete core measured to the outside of the hoop bars (mm) (as shown in Figure 2); s is the center-to-center vertical spacing of hoop bars (mm). The final coefficient k v is used herein to quantify the effectiveness of hoop steel confinement in the vertical direction between the hoop reinforcing bars. For concrete columns confined with circular hoop bars, k v is given in Equation (6) (Mander et al. [60]): where s' is the clear spacing between the hoop steel bars (see Figure 2); ρ cc is the ratio between the area of longitudinal steel reinforcement to the area of the concrete core, and it can be determined as ρcc = π(D c /2) 2 − ρ vs A g , in which A g (mm 2 ) is the total cross sectional area of the column.

Peak Axial Strength and Strain
The peak strength, fcc ' , and strain, ɛcc, are two significant requirements for a stressstrain response of FRP-confined concrete. Existing tests on FRP-confined RC columns revealed that fcc ' and ɛcc are influenced by the level of internal steel confinement, longitudinal and hoop FRP sheets, eccentric load ratio, and slenderness ratio. The ratio of hoop steel reinforcement has a significant effect on the ductility enhancement rather than on the

Peak Axial Strength and Strain
The peak strength, f cc ' , and strain, ε cc , are two significant requirements for a stressstrain response of FRP-confined concrete. Existing tests on FRP-confined RC columns revealed that f cc ' and ε cc are influenced by the level of internal steel confinement, longitudinal and hoop FRP sheets, eccentric load ratio, and slenderness ratio. The ratio of hoop steel reinforcement has a significant effect on the ductility enhancement rather than on the strength enhancement resulting from the FRP confinement [26,61]. For accurate modeling, two expressions (i.e., Equations (7) and (8)) with different ranges of longitudinal and hoop steel reinforcement ratios are provided. Equation (7) was calibrated using all eccentric loading tests, whereas Equation (8) was expanded to consider the concentric tests compiled from Wang et al. [23] and Kaeseberg et al. [57]. The expressions had an averaged correlation coefficient (R 2 ) of about 93.7% and were based on the analysis of all 207 specimens summarized in Table A1: where l is column height (mm); e is loading eccentricity (mm); δ URC and δ CRC (dimensionless coefficients) are strength gains of unwrapped and FRP-wrapped RC columns, respectively. The resulting values of B The proposed peak strength model is applicable for FRP-confined unreinforced columns, FRP-confined RC columns, and unwrapped RC columns. The accuracy of the proposed and existing expressions is assessed by the average absolute error (AAE). Predictions given by the proposed expressions and those of the models [39,40,47,48] are compared with the test results in Figure 3. It is seen that the existing models for tests with slenderness ratios ranging from 7.9 to 17.0 overestimate the results by 11.4% (AAE = 29.3). Moreover, the direct use of these models leads to significant errors in predicting the tested peak strength of FRP-confined slender RC columns. In a range of higher slenderness ratios ranging from 23.7 to 32, the experimental results are overestimated by 45.6% (almost increased by four times as compared with the smaller range of slenderness, kl/r ≤ 17). The ratio between the analytical results given by the new model and the results equal 101% with an AAE value of about 7.2, whereas the ratio between the analytical results from the existing models and the results is equal to 128.5% with an AAE value of about 38.7. Finally, it can be concluded that the present model agrees best with the test results.
peak strength of FRP-confined slender RC columns. In a range of higher slenderness ratios ranging from 23.7 to 32, the experimental results are overestimated by 45.6% (almost increased by four times as compared with the smaller range of slenderness, kl/r ≤ 17). The ratio between the analytical results given by the new model and the results equal 101% with an AAE value of about 7.2, whereas the ratio between the analytical results from the existing models and the results is equal to 128.5% with an AAE value of about 38.7. Finally, it can be concluded that the present model agrees best with the test results. Similar to the model given in Equation (9), an expression for the peak strain ɛcc accounting for the effects of key parameters is provided in Equation (11), in which the correlation coefficients are 91.9 and 88.7% for the first and second parts of the expression, respectively: Similar to the model given in Equation (9), an expression for the peak strain ε cc accounting for the effects of key parameters is provided in Equation (11), in which the correlation coefficients are 91.9 and 88.7% for the first and second parts of the expression, respectively: where CZ indicates that the proposed expression can predict the maximum confined strain in the compression zone of the cross-section, whereas CZ and TZ refer to the ultimate strain in compression and tension section sides, respectively; ε co is the compressive strain corresponding to the peak strength of unconfined concrete and is taken to be 0.002. In the present model, the (ε cc /ε co ) con ratio was determined from the concentrically loaded model of Wang et al. [23], as provided in Equations (12)- (14). The model proposed for the ultimate strain is also applicable for FRP-confined unreinforced columns, FRP-confined RC columns, and unwrapped RC columns. Predictions given by the proposed Equation (11) and those of the models [34,39,41,47,48] are compared with the tested strains in Figure 4. Among the presented models, the proposed model has the best correlation between the analytical and experimental results. In addition, the error of the proposed model is insignificant when compared with those of the existing models: where f lf and f ls (MPa) are the lateral confinement pressures provided by the FRP wrap and internal steel reinforcement, respectively; ε fe is the actual rupture strain of the FRP wrap and is considered to be equal to 0.8 times the ε fu value [23].
strain in the compression zone of the cross-section, whereas CZ and TZ refer to the ulti-mate strain in compression and tension section sides, respectively; ɛco is the compressive strain corresponding to the peak strength of unconfined concrete and is taken to be 0.002. In the present model, the (ɛcc/ɛco)con ratio was determined from the concentrically loaded model of Wang et al. [23], as provided in Equations (12)- (14). The model proposed for the ultimate strain is also applicable for FRP-confined unreinforced columns, FRP-confined RC columns, and unwrapped RC columns. Predictions given by the proposed Equation (11) and those of the models [34,39,41,47,48] are compared with the tested strains in Figure 4. Among the presented models, the proposed model has the best correlation between the analytical and experimental results. In addition, the error of the proposed model is insignificant when compared with those of the existing models: where flf and fls (MPa) are the lateral confinement pressures provided by the FRP wrap and internal steel reinforcement, respectively; ɛfe is the actual rupture strain of the FRP wrap and is considered to be equal to 0.8 times the ɛfu value [23].

Analytical Prediction of Slenderness Limit
To propose a slenderness limit for FRP-confined RC columns, a total of 32 specimens were designed and analyzed. The control specimen as provided in Figure 5 was selected from [26] for the present parametric study. The amount of longitudinal steel reinforcement and the spacing of the hoop bars were kept the same. The key parameters that are considered were varying amount of hoop and longitudinal FRP (i.e., n f = 1, 2, n f,v = 0, 1, 2, 4), slenderness ratio (i.e., kl/r = 8-44), eccentricity ratio (i.e., e/D = 0.1-1.0), and strength of unconfined concrete (i.e., f c ' = 30-60 MPa). For example, the symbol S8 in S8L2V4C60S12.1 and its number represent the specimen code of a particular category. The following letter L and its number refer to the number of layers of FRP hoop wraps, whereas V4 refers to the number of layers of FRP longitudinal wraps. The term C60 refers to the concrete type. Finally, the last symbol, S, and the number following it refer to the slenderness ratio. In Figure 6, the results of the proposed model (Equation (9)) are provided, and the regressed formula indicates that the slenderness limit is dependent on the test variables (i.e., FRP confinement ratio), as already confirmed by Pan et al. [62] based on tests on FRP-confined slender RC columns under concentric loading. The slenderness limit is found to be equal to 12.8 (on average). This highlights that designers should apply FRP strengthening in longitudinal direction to ensure that slender CFRP wrapped columns can exhibit improvements in their load-carrying capacity and lateral deformation responses.
derness ratio (i.e., kl/r = 8-44), eccentricity ratio (i.e., e/D = 0.1-1.0), and strength of unconfined concrete (i.e., fc ' = 30-60 MPa). For example, the symbol S8 in S8L2V4C60S12.1 and its number represent the specimen code of a particular category. The following letter L and its number refer to the number of layers of FRP hoop wraps, whereas V4 refers to the number of layers of FRP longitudinal wraps. The term C60 refers to the concrete type. Finally, the last symbol, S, and the number following it refer to the slenderness ratio. In Figure 6, the results of the proposed model (Equation (9)) are provided, and the regressed formula indicates that the slenderness limit is dependent on the test variables (i.e., FRP confinement ratio), as already confirmed by Pan et al. [62] based on tests on FRP-confined slender RC columns under concentric loading. The slenderness limit is found to be equal to 12.8 (on average). This highlights that designers should apply FRP strengthening in longitudinal direction to ensure that slender CFRP wrapped columns can exhibit improvements in their load-carrying capacity and lateral deformation responses.  S1L1V0C50S8.72 S1L2V0C50S12.3 S1L1V1C50S9.48 S1L2V2C50S13.1 S1L1V0C60S7.98 S1L2V0C60S10.8 S1L1V1C60S8.65 S1L2V2C60S11.6  derness ratio (i.e., kl/r = 8-44), eccentricity ratio (i.e., e/D = 0.1-1.0), and strength of unconfined concrete (i.e., fc ' = 30-60 MPa). For example, the symbol S8 in S8L2V4C60S12.1 and its number represent the specimen code of a particular category. The following letter L and its number refer to the number of layers of FRP hoop wraps, whereas V4 refers to the number of layers of FRP longitudinal wraps. The term C60 refers to the concrete type. Finally, the last symbol, S, and the number following it refer to the slenderness ratio. In Figure 6, the results of the proposed model (Equation (9)) are provided, and the regressed formula indicates that the slenderness limit is dependent on the test variables (i.e., FRP confinement ratio), as already confirmed by Pan et al. [62] based on tests on FRP-confined slender RC columns under concentric loading. The slenderness limit is found to be equal to 12.8 (on average). This highlights that designers should apply FRP strengthening in longitudinal direction to ensure that slender CFRP wrapped columns can exhibit improvements in their load-carrying capacity and lateral deformation responses.  S1L1V0C50S8.72 S1L2V0C50S12.3 S1L1V1C50S9.48 S1L2V2C50S13.1 S1L1V0C60S7.98 S1L2V0C60S10.8 S1L1V1C60S8.65 S1L2V2C60S11.6    [63], De Lorenzis and Tepfers [64], Siddiqui et al. [30], and the present analysis. The chart demonstrates that the slenderness limit values provided by all the investigators, including the present, are less than those of the ACI [65] for the unwrapped RC columns (i.e., kl/r = 22). This is attributed to the fact that reductions in strengths of FRP-wrapped columns are higher than those of the unwrapped columns, and that the slenderness effects are more significant for FRP-wrapped columns with higher confinement levels (e.g., [27,28,30]). Generally, it is interesting to report that the averaged result, kl/r = 12.8 (see Figure 8), is typical of the averaged result from other models (Figure 7). The satisfactory agreement obtained from these comparisons confirms the accuracy of the present model, and that the effect of the slenderness on column response with different levels of FRP confinement should be accurately estimated.
higher than those of the unwrapped columns, and that the slenderness effects are more significant for FRP-wrapped columns with higher confinement levels (e.g., [27,28,30]). Generally, it is interesting to report that the averaged result, kl/r = 12.8 (see Figure 8), is typical of the averaged result from other models (Figure 7). The satisfactory agreement obtained from these comparisons confirms the accuracy of the present model, and that the effect of the slenderness on column response with different levels of FRP confinement should be accurately estimated.
J i a n g a n d T e n g

13.2
Selenderness ratio, kl/r 7.8 Figure 7. A comparison between models of slenderness limit.  significant for FRP-wrapped columns with higher confinement levels (e.g., [27,28,30]). Generally, it is interesting to report that the averaged result, kl/r = 12.8 (see Figure 8), is typical of the averaged result from other models (Figure 7). The satisfactory agreement obtained from these comparisons confirms the accuracy of the present model, and that the effect of the slenderness on column response with different levels of FRP confinement should be accurately estimated.
J i a n g a n d T e n g

Minimum Amount of FRP for Adequate Confinement
A confined column needs a minimum amount of FRP wraps for sufficient confinement [66][67][68][69]. In this case, if the axial load δ CRC (Equation (9)) is greater than one, the resulting threshold represents the sufficiently confined concrete. Based on an analytical paper by Pham and Hadi [66] on FRP-confined circular and non-circular columns under concentric compression, the minimum limit of effective confinement pressure ratio is proposed to be 0.15.
The response between the effective confining pressure ratio and the confined axial load ratio is given in Figure 8. Based on an averaged curve, when δ CRC is equal to 1, then the f lf /f c ' ratio is about 0.22, and such a threshold is larger than that of FRP-confined circular columns under concentric loading due to the reduced effects caused by the eccentric loads. Refer to the discussions of Section 4.2: the results of Figure 8 also confirm that longitudinal FRP sheets for columns under small eccentric ratios are not effective and they can provide greater strength enhancements for slender columns under large eccentricity (e.g., [70,71]).

Complete Stress-Strain Model
According to Ref. [23], A design-oriented stress-strain model for circular unreinforced and reinforced columns strengthened with FRP wraps is presented as follows: where x = ε c /ε co and y = f c /f c ' ; ε c and f c are assumed levels of longitudinal axial strain and stress, respectively. The coefficient A, which can be determined from the boundary condition dσ c /dε c = E c at ε c = 0, is provided as follows: where E c = 4736 f c (MPa) [72] is the elastic modulus of unconfined concrete; E co = f c ' /ε co (MPa) is the secant modulus at the peak stress of unconfined concrete.
where X = ε cc /ε co and Y = f cc /f c ' . The parameter r in Equation (17) is of significant importance because it controls the overall shape of the stress-strain curve. From two different methodologies of analysis conducted on 64 stress-strain test responses reported by two independent research groups [23,26], the shape factor r can be obtained twice for each curve. This rounded analysis reveals that the factor r is related to the lateral confinement provided by the internal steel confinement and external FRP wraps, as well as the contribution made by the longitudinal FRP sheets. Based on these observations, the following model r is proposed and the regressed results are in Figure 9; note that the expressions are calibrated based on specimens of a small range of eccentricity due to the very limited availability of eccentric stress-strain curves of FRP-confined circular RC columns.
where the coefficients B 6.1 , B 6.2 , B 6.3 , B 6.4 , B 6.5 , B 6.6 in Equation (18) where the coefficients B6.1, B6.2, B6.3, B6.4, B6.5, B6.6 in Equation (18) Figure 10 shows clear comparisons between theoretical stress-strain responses versus tested responses of selected specimens reported in Table A1. The comparisons are from the axial stress and strain data which could be extracted from their original papers. There are no comparisons with results from other tests due to the limited eccentrically loaded responses; however, an additional three concentrically loaded specimens selected from the tests of Lam et al. [73], Wang and Wu [74], and Benzaid et al. [75] to the tests summarized in Table A1 are introduced to calibrate the model. Generally, an inspection of the comparisons demonstrates that the proposed model can capture well the major features of the curve. The shape of stress-strain curves that are well described also reflects the performance and accuracy of the model.   Table A1. The comparisons are from the axial stress and strain data which could be extracted from their original papers. There are no comparisons with results from other tests due to the limited eccentrically loaded responses; however, an additional three concentrically loaded specimens selected from the tests of Lam et al. [73], Wang and Wu [74], and Benzaid et al. [75] to the tests summarized in Table A1 are introduced to calibrate the model. Generally, an inspection of the comparisons demonstrates that the proposed model can capture well the major features of the curve. The shape of stress-strain curves that are well described also reflects the performance and accuracy of the model.

Background
Only limited research focusing on the axial load-bending moment response is available for FRP-confined columns (e.g., [25,27,28]). Based on the study provided by Al-Nimry and Al-Rabadi [25], the P-M values of an axial load-bending moment response are calculated using the conventional sectional analysis and considering linear strain variation in the concrete section. While neglecting the contribution of concrete in tension, the concrete in the compression zone is divided into eight equal-width segments (Ref. Figure 11). The concrete strain ɛci at the centroid of ith segment is determined using linear trigonometry and the stress fci is then calculated using the FRP-confined concrete stress-strain models in Table A2. Assuming a perfect bond between concrete and steel bars, strains in the steel bars were equal to the strains in the adjacent concrete. The tensile and compressive stresses of the steel bars are considered negative and positive in signs, respectively. The force and moment equilibrium expressions are provided as follows:

Background
Only limited research focusing on the axial load-bending moment response is available for FRP-confined columns (e.g., [25,27,28]). Based on the study provided by Al-Nimry and Al-Rabadi [25], the P-M values of an axial load-bending moment response are calculated using the conventional sectional analysis and considering linear strain variation in the concrete section. While neglecting the contribution of concrete in tension, the concrete in the compression zone is divided into eight equal-width segments (Ref. Figure 11). The concrete strain ε ci at the centroid of ith segment is determined using linear trigonometry and the stress f ci is then calculated using the FRP-confined concrete stress-strain models in Table A2. Assuming a perfect bond between concrete and steel bars, strains in the steel bars were equal to the strains in the adjacent concrete. The tensile and compressive stresses of the steel bars are considered negative and positive in signs, respectively. The force and moment equilibrium expressions are provided as follows: where A ci is the ith concrete segment area; f ci is the stress at the centroid of the ith concrete segment; A s1 to A s4 are section areas of a single reinforcing steel bar (A s1 and A s4 correspond to a single bar, whereas A s2 and A s3 are the areas of 2 reinforcing bars); f s1 to f s4 are the corresponding stress results of the steel bars. The term S ci is the distance between the column centroid and the center of the segment I, and S 1 to S 4 are the distances between the column centroid and the steel reinforcement bars 1 to 4, respectively. The effect of using longitudinal FRP wraps on the column response is also introduced into the above two expressions, in which A v is the area of longitudinal FRP wraps and is calculated using the geometric properties of a circular segment, f FRP is the ultimate tensile strength of FRP wraps, and z is the distance between the column's centroid and the centroid of FRP composites.

M A f S A f S A f S A f S A f S A f z
where Aci is the ith concrete segment area; fci is the stress at the centroid of the ith concrete segment; As1 to As4 are section areas of a single reinforcing steel bar (As1 and As4 correspond to a single bar, whereas As2 and As3 are the areas of 2 reinforcing bars); fs1 to fs4 are the corresponding stress results of the steel bars. The term Sci is the distance between the column centroid and the center of the segment I, and S1 to S4 are the distances between the column centroid and the steel reinforcement bars 1 to 4, respectively. The effect of using longitudinal FRP wraps on the column response is also introduced into the above two expressions, in which Av is the area of longitudinal FRP wraps and is calculated using the geometric properties of a circular segment, fFRP is the ultimate tensile strength of FRP wraps, and z is the distance between the column's centroid and the centroid of FRP composites.

Performance of Proposed and Existing P-M Models
The P-M interaction responses using the newly proposed expressions (Equations (21) and (22)) are shown in Figure 12. The predicted responses obtained using the conventional sectional method in conjunction with the models provided by Lam and Teng [34], Wu and Jiang [32], and Lin and Teng [55] are also provided and assessed. A summary of these models can be found in Table A3. The confined column strength under pure compressive loading was obtained from Nu = 0.85fcc ' (Ag − Ast) + fyAst, where the column was considered as unconfined in the case of lower load levels (Nu ≤ 0.1fc ' Ag), and its strength in pure flexure was obtained accordingly. The comparisons included analytical and test P-M responses with different wrapping systems. In Figure 12a, the averaged results of specimens confined with hoop FRP sheets were provided ( [25] and Table A1), whereas the averaged results of specimens reinforced with longitudinal and hoop FRP sheets were provided in Figure 12b. The evaluation reveals that the models of FRP-confined unreinforced concrete cylinders have major shortcomings. The predicted results underestimated the tested responses significantly. As noted, before, one reason is the high effectiveness provided by the longitudinal FRP sheets at higher load levels for slender columns when additional

Performance of Proposed and Existing P-M Models
The P-M interaction responses using the newly proposed expressions (Equations (21) and (22)) are shown in Figure 12. The predicted responses obtained using the conventional sectional method in conjunction with the models provided by Lam and Teng [34], Wu and Jiang [32], and Lin and Teng [55] are also provided and assessed. A summary of these models can be found in Table A3. The confined column strength under pure compressive loading was obtained from N u = 0.85f cc where the column was considered as unconfined in the case of lower load levels (N u ≤ 0.1f c ' A g ), and its strength in pure flexure was obtained accordingly. The comparisons included analytical and test P-M responses with different wrapping systems. In Figure 12a, the averaged results of specimens confined with hoop FRP sheets were provided ( [25] and Table A1), whereas the averaged results of specimens reinforced with longitudinal and hoop FRP sheets were provided in Figure 12b. The evaluation reveals that the models of FRP-confined unreinforced concrete cylinders have major shortcomings. The predicted results underestimated the tested responses significantly. As noted, before, one reason is the high effectiveness provided by the longitudinal FRP sheets at higher load levels for slender columns when additional moments are developed, and they can greatly enhance the flexural rigidity resistance under combined axial and flexural loads [28]. Generally, the present model exhibits a much better performance in simulating the P-M responses of tested specimens: where the results of parameters moments are developed, and they can greatly enhance the flexural rigidity resistance under combined axial and flexural loads [28]. Generally, the present model exhibits a much better performance in simulating the P-M responses of tested specimens: where the results of parameters B8. 1

Conclusions and Future Research
Based on analytical investigation of a comprehensive database of eccentrically loaded short and slender circular RC columns of varying slenderness ratios and FRP wrapping systems, the following conclusions are drawn as follows: 1. None of the existing design codes and models, among them the GB 50608 [47] and Concrete Society [48], provide accurate predictions for the peak strength and strain, and due to the large test data and parameters studied in the present paper, this finding contradicts a recent conclusion made by Xing et al. [76]. 2. The slenderness limit is proposed to be dependent on the FRP confinement level, and the averaged result from the presented model matches well with the averaged results by Jiang and Teng [63], De Lorenzis, and Tepfers [64], and Siddiqui et al. [30]. 3. A design-oriented stress-strain model was newly developed using a database of 207 FRP-confined plain and RC columns under different loading conditions. The model parameters included longitudinal and hoop steel reinforcement ratio, amount of FRP hoop wraps, presence of longitudinal FRP sheets, slenderness ratio, eccentric loading ratio, column section's size, and compressive strength of unconfined concrete. 4. Based on a parametric investigation by the model, the sufficiently confined concrete threshold under eccentric loads was proposed to be 0.22, which is larger than that of Pham and Hadi. [66], since the test database employed in their study mostly contains results of small-scale circular specimens under concentric loading. 5. For slender columns, significantly underestimated predictions of the P-M responses were obtained using both the existing concentric and eccentric stress-strain models of FRP-confined concrete cylinders. However, good agreement between the

Conclusions and Future Research
Based on analytical investigation of a comprehensive database of eccentrically loaded short and slender circular RC columns of varying slenderness ratios and FRP wrapping systems, the following conclusions are drawn as follows: 1.
None of the existing design codes and models, among them the GB 50608 [47] and Concrete Society [48], provide accurate predictions for the peak strength and strain, and due to the large test data and parameters studied in the present paper, this finding contradicts a recent conclusion made by Xing et al. [76].

2.
The slenderness limit is proposed to be dependent on the FRP confinement level, and the averaged result from the presented model matches well with the averaged results by Jiang and Teng [63], De Lorenzis, and Tepfers [64], and Siddiqui et al. [30].

3.
A design-oriented stress-strain model was newly developed using a database of 207 FRP-confined plain and RC columns under different loading conditions. The model parameters included longitudinal and hoop steel reinforcement ratio, amount of FRP hoop wraps, presence of longitudinal FRP sheets, slenderness ratio, eccentric loading ratio, column section's size, and compressive strength of unconfined concrete.

4.
Based on a parametric investigation by the model, the sufficiently confined concrete threshold under eccentric loads was proposed to be 0.22, which is larger than that of Pham and Hadi. [66], since the test database employed in their study mostly contains results of small-scale circular specimens under concentric loading.

5.
For slender columns, significantly underestimated predictions of the P-M responses were obtained using both the existing concentric and eccentric stress-strain models of FRP-confined concrete cylinders. However, good agreement between the proposed predictions and tested responses was found, confirming that the model can simulate slender RC columns experiencing greater flexural resistance when strengthened with lateral and longitudinal FRP sheets. Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.
Appendix A  Table A2. Summary of existing confined stress and corresponding strain models.

For Confined Stress For Confined Strain Model Parameters
GB 50608 (GB2010) [47] f cc,con = f c + 3.5 D (mm) diameter of a circularcolumn section n f,v total number of FRP wraps in the longitudinal direction l (mm) column height N u (KN) maximum load capacity