Advances in Technology Innovation, vol. x, no. x, 20xx, pp. xx-xx Strength Prediction of Rectangular FRP-Reinforced Concrete Columns Under Eccentric Loading Nam Nguyen Van1, Hiep Dang Vu2, Duy Nguyen Phan1,* 1Faculty of Civil Engineering, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam 2Faculty of Civil Engineering, Hanoi Architectural University, Hanoi City, Vietnam Received 09 May 2025; received in revised form 31 August 2025; accepted 24 September 2025 DOI: https://doi.org/10.46604/aiti.2025.15124 Abstract This study aims to develop an analytical model for evaluating the load-carrying capacity of rectangular fiber- reinforced polymer (FRP) reinforced concrete columns under eccentric loading. In the proposed model, the contribution of FRP bars in compression is considered, with their compressive strength estimated as a fraction of tensile strength. Meanwhile, the effects of confinement, tension stiffening, and second-order effects are conservatively neglected. Two main failure modes, namely concrete crushing and FRP rupture, are distinguished by the balanced failure condition. This model applies strain compatibility with the plane section and constitutive laws to derive stress-strain distributions across the cross-section. Then, the model is validated against 91 experimental results covering diverse sections, strengths, and eccentricities (e/h = 0.1-1.0), showing high accuracy (mean: 0.932; RMSE: 0.154; COV: 22.9%; SD: 0.145; r: 0.84) and outperforming ACI CODE-440.11. Analysis results also show that compressive FRP reinforcement contributed between 0.94% and 22.3% to the column strength. Keywords: FRP, concrete column, eccentricity, analytical method 1. Introduction Steel-reinforced concrete (RC) structures are extensively used in buildings, transportation infrastructure, including roads and railways, hydraulic structures, and marine applications due to their many advantages. However, steel corrosion in harsh environments reduces the durability and lifespan of RC structures. Fiber-Reinforced Polymer (FRP) reinforcement for concrete structures has been under development since the 1960s and has gradually become a viable alternative to traditional steel reinforcement in specific environments, owing to its high tensile strength, corrosion resistance, electromagnetic neutrality, electrical insulation, and high strength-to-weight ratio [1]. Common FRP rebar types include carbon FRP (CFRP), basalt FRP (BFRP), aramid FRP (AFRP), and glass FRP (GFRP) [1-2]. Despite these advantages, FRP-RC structures have not yet been widely adopted worldwide due to several limitations: only a few countries have developed design standards; the structural behavior of FRP-RC is not fully understood; theoretical models are still being improved; and the cost of FRP bars remains relatively high. As a result, research on FRP-RC structures continues to attract significant attention. Unlike traditional steel reinforcement, which exhibits good tensile and compressive strength as well as a high modulus of elasticity, FRP reinforcement has significantly lower compressive strength compared to its tensile capacity. It also has a lower elastic modulus and behaves in a brittle manner without yielding. As a result, the structural behavior and design methodology of FRP-RC columns differ markedly from those of conventional RC columns. Consequently, the study of the behavior of FRP- RC columns has attracted considerable interest from researchers worldwide [3]. * Corresponding author. E-mail address: nguyenphanduy@iuh.edu.vn Advances in Technology Innovation, vol. x, no. x, 20xx, pp. xx-xx 2 Although most existing research on FRP-RC columns focuses on axial loading, real-world conditions rarely involve pure axial forces. Eccentricity arising from load misalignment, second-order effects, or construction imperfections leads to significant moment-axial interaction, which is especially critical in FRP-RC columns due to the linear-elastic behavior of FRP bars. In contrast, concentrically loaded FRP-RC columns have been more extensively studied, and their behavior is relatively simple and, in many aspects, analogous to that of conventional steel-RC columns. Several analytical models have been proposed for such cases, often adapting existing design formulas developed for concentrically loaded steel-RC columns [4]. However, under eccentric loading, FRP-RC columns exhibit more complex nonlinear behavior due to cracking, lack of yielding, and tension-compression interactions, which necessitate a dedicated modeling approach to ensure accurate predictions and safe design. Studies show that FRP-RC columns exhibit distinct behavior compared to steel-RC columns under eccentric compression, primarily due to linear-elastic behavior and lower modulus of elasticity of FRP reinforcement [5]. Unlike steel-RC columns, which display ductile yielding, FRP-RC columns show brittle failure after peak load due to the absence of a yield point [6]. GFRP- and BFRP-RC columns have 17-30% lower capacities than steel RC columns, whereas CFRP-RC columns have a load-carrying capacity averaging 7% lower load-carrying capacity [4, 7]. FRP-RC columns experience larger longitudinal deformations but smaller crack widths. In terms of failure modes, FRP-RC columns predominantly fail by concrete crushing under concentric and low-eccentricity loading, often accompanied by cover spalling or bar kinking [4]. At moderate eccentricities, failure transitions to compression-dominated or flexural-compression modes, with flexural cracking and gradual concrete degradation [8]. High-eccentricity loading results in flexural-tension failure with tension-side cracks and excessive deformations [9]. Research indicates that the compressive strength of FRP bars ranges from 10% to 86% of their tensile strength, depending on the fiber type [10]. While the compressive modulus of elasticity of FRP reinforcement is relatively close to its tensile modulus (with a ratio between 0.97 and 1.20) [3, 10], the much lower compressive strength significantly limits its effectiveness in compressive members such as columns. Studies indicate that increasing the FRP reinforcement ratio in FRP-RC columns from 1% to 3.8% enhances load-carrying capacity by 5-35%, particularly at high eccentricities [9, 11]. An increase in FRP reinforcement ratio also enhances flexural stiffness and reduces post-peak decay [9]. Despite their limited compressive strength, FRP bars still contribute meaningfully to the load-carrying capacity of FRP-RC columns: approximately 3-15% for GFRP, 6- 19% for CFRP, and around 11% for BFRP, compared to 6.5-36% for steel reinforcement [4, 8]. As a result, many authors recommend accounting for the contribution of compressive FRP reinforcement in design methods [3, 12]. Similar to steel-RC columns, the load-carrying capacity of FRP-RC columns under eccentric compression depends on several factors, including material characteristics, longitudinal reinforcement ratio, eccentricity, slenderness, and confinement effect of transverse reinforcement. Slenderness amplifies second-order effects (P-Δ effect) in FRP-RC, resulting in greater strength degradation and larger deformations compared to steel-RC columns [5, 13]. Short FRP-RC columns (slenderness ratio ≤ 18) show minimal second-order effects (4-10% of total moment), allowing simplified design without considering these effects [8]. However, slender FRP-RC columns require careful consideration of second-order effects [7]. Transverse reinforcement, such as GFRP or CFRP ties and spirals, enhances confinement and prevents longitudinal bar buckling [14-15]. Reducing tie spacing improves ductility, confinement, and residual strength, and can also shift the failure mode of the column from brittle to more ductile behavior [14-16]. Tightly spaced ties tend to cause failure by concrete crushing or rupture of transverse reinforcement, whereas wider tie spacing often leads to longitudinal bar buckling [14]. Current design codes like ACI 440.1R-15 [17], ACI CODE-440.11-22 [18], CSA S806:2012:R2017 [19], and SP 295.1325800.2017 [20] utilize equilibrium equations and strain compatibility principles, along with an equivalent concrete stress block, to calculate the axial load-carrying capacity of eccentrically loaded FRP-RC columns. In these methods, the contribution of FRP bars located in the compression zone is commonly neglected and is not considered in the load-carrying Advances in Technology Innovation, vol. x, no. x, 20xx, pp. xx-xx 3 mechanism. While this assumption simplifies design and ensures safety, it often results in conservative predictions and underestimation of the actual structural capacity [4, 15]. To address this, many researchers have proposed alternative methods for calculating the load-carrying capacity of FRP-RC columns under eccentric compression. Sharbatdar [1] developed a plane section analysis method, validated through experiments on CFRP-RC columns, focusing on concrete crushing as the primary failure mode. Choo et al. [5] employed numerical integration to derive axial load-moment- curvature relationships, accounting for slenderness effects and recommending a reduced slenderness ratio (17 vs. 22) for non- sway frames. Zadeh and Nanni [21] adapted ACI 318-11 principles, using strain compatibility and force equilibrium to construct interaction diagrams for GFRP-RC columns. Elchalakani et al. [15] modified AS 3600, integrating Mander’s confinement model and GFRP properties to develop moment-axial load interaction diagrams. Tarawneh and Majdalaweyh [12] used sectional analysis with the Response-2000 software to investigate the load-carrying capacity of FRP-RC columns, achieving high accuracy (reliability index >3.5). Almomani et al. [11] employed Gene Expression Programming to develop predictive models for FRP-RC columns, accounting for eccentricity and slenderness. The P-Δ effect has also been addressed in several studies. Choo [5], Xue [13], and Hamid [7] all proposed analytical methods, with Xue modifying ACI 318-11’s moment magnifier method, and Hamid implementing an iterative second-order analysis. Although various analytical methods have been proposed to account for the contribution of compressive FRP reinforcement in evaluating the load-carrying capacity of eccentrically loaded FRP-RC columns, these approaches remain incomplete. Most existing methods focus primarily on failure modes governed by concrete crushing in the compression zone, without clearly distinguishing among different possible failure mechanisms. In addition, they often rely on simplified assumptions, such as employing an equivalent rectangular stress block for concrete, which can limit both their accuracy and practical applicability. To address this gap, this paper proposes an analytical method for evaluating the load-carrying capacity of eccentrically loaded FRP-RC columns, incorporating material constitutive laws and accounting for all theoretically potential failure modes. To achieve this, the following aspects are addressed: (1) Classification of failure modes of FRP-RC columns under eccentric compression and development of corresponding strain and stress distribution across the cross-section for each failure mode (2) Formulation of internal force equilibrium equations for each failure mode and construction of a computational flowchart (3) Validation of the analytical model using experimental data from previous studies and comparison of the proposed method’s accuracy with calculations based on ACI CODE-440.11. The subsequent sections of the paper are organized as follows: Section 2 presents the analytical method for evaluating the load-carrying capacity of the column along with the computational flowchart; Section 3 discusses model validation; and Section 4 concludes the study and offers recommendations for future research on FRP-RC columns under eccentric loading. 2. Analytical Model Development In this section, an analytical model is proposed to predict the load-carrying capacity of rectangular FRP-reinforced concrete columns under eccentric compression. The model incorporates strain compatibility, force equilibrium, and material constitutive laws to capture all potential failure modes and accounts for the compressive contribution of FRP rebars. Compared with conventional design methods, it provides more realistic and less conservative predictions. 2.1 Fundamental assumptions for calculations and constitutive laws of materials Under eccentric compression, the column's cross-section is conventionally divided into two zones: the zone on the side of the applied force, which undergoes higher compressive stress, is referred to as the "compression zone"; the opposite zone, which experiences lower compressive stress or tension, is referred to as the "tension zone". The analytical method is developed based on the following assumptions: the plane section remains plane; the bond resistance between the concrete and FRP rebars Advances in Technology Innovation, vol. x, no. x, 20xx, pp. xx-xx 4 is constant; the strain compatibility and force equilibrium are satisfied; the maximum compressive strain of concrete (εcu) is 0.0035; the tensile resistance of concrete is ignored due to concrete's low tensile strength and the presence of cracks. Also, it should be emphasized that the present model is limited to short-term analysis of short FRP-RC columns under eccentric compression. It does not account for P–Δ effects, confinement effects, softening behavior of concrete, or time-dependent phenomena such as creep, shrinkage, and load duration. To accurately assess the behavior of concrete, a simplified bilinear stress–strain relationship for compression, as defined in SP 63.13330.2018 [22], was adopted (Fig. 1 (a)). Meanwhile, a linear stress-strain relationship is used for FRP reinforcement under both compression and tension (Fig. 1 (b)). The contribution of FRP reinforcement in compression is considered in the calculations, with its compressive strength (ffcu) defined as a fraction of its tensile strength (ffu): fcu f fuf f , where βf is a coefficient representing the compressive-to-tensile strength ratio of the FRP rebar. , 1, c c red c red f E     ; ,c c c redE  fcu f fuf f (a) Concrete (b) FRP rebar Fig. 1 Constitutive laws of materials 2.2 Analytical formulation for the balanced failure mode (a) Cross-section (b) Balanced failure mode (c) Failure mode governed by concrete crushing (d) Failure mode governed by FRP rupture Fig. 2 Cross-section geometry, strain, and stress distributions on the normal section for various failure modes Studies have shown that the failure of eccentrically loaded FRP-RC columns can occur either in the tension zone - due to rupture of the FRP bars, or in the compression zone, where concrete crushing takes place while the FRP remains intact [5, 14, 21]. To distinguish between these two failure modes, a balanced failure condition is established. In this case, failure occurs simultaneously in both the tension and compression zones. Specifically, when the tensile strain in the FRP bars and the Advances in Technology Innovation, vol. x, no. x, 20xx, pp. xx-xx 5 compressive strain in the extreme concrete fiber both reach their ultimate limits at the same time. Fig. 2 illustrates the cross- section geometry, the corresponding strain and stress distributions for all possible failure modes, derived based on the material constitutive laws (Fig. 1) and the strain compatibility condition. The height of the compression zone under balanced failure condition (cb) is determined based on Fig. 2 (b) as cu b fu cu d c      (1) where d is the effective depth, and εfu denotes the ultimate tensile strain of FRP rebar. The resultant forces in the concrete compression zone C1 and C2 can be found by 1 1 1 2 cC bc f  (2) 2 2 cC bc f  (3) where b is the width of cross-section, β denotes the conversion factor from cylinder to prism compressive strength, and f'c represents the cylinder compressive strength of concrete. In addition, c1 and c2 are the heights of the compressive concrete stress blocks, show in Fig. 2 (b), they can be computed by 1 bc c  (4)  2 1bc c   (5) where α is the coefficient determined by 1, 1, 1 1 cu c red c red        (6) where εc1,red is the limiting strain value at the transition between the elastic range and the horizontal plateau in the bilinear stress-strain diagram according to SP 63.13330.2018 [22], εc1,red = 0.0015. The strain (εfc) and the corresponding resultant force (Cf) in the FRP rebar located in the compression zone are calculated by b fc cu b c a c     (7) b f fc f cu f b c a C A E c     (8) where Afc and Ef denote the total area of FRP rebar in the concrete compression zone and its elastic modulus, respectively; a' is the distance from the centroid of the compressive reinforcement to the extreme compression face of the section. Advances in Technology Innovation, vol. x, no. x, 20xx, pp. xx-xx 6 The resultant force in tensile FRP rebar can be expressed as f fu fT f A (9) where Af denotes the total area of FRP rebar located in the concrete tension zone or in the less compressed region (in case of full-section compression). The internal equilibrium of axial force and bending moment is expressed by Eqs. (10) - (11), respectively: 1 2b f fP C C C T   (10) 1 1 2 2b c c f fc f fM C Z C Z C Z T Z    (11) where Zc1, Zc2, Zfc, and Zf represent the lever arms associated with the resultant forces C1, C2, Cf, and Tf, respectively (Fig. 2 (b)). When calculating moments about an axis that passes through the centroid axis and is perpendicular to the bending plane, these values are calculated as 1 1 2 2 3 c ch Z c   (12)  2 20.5cZ h c  (13) 2 fc h Z a  (14) 2 f h Z a  (15) The eccentricity of the axial force in the case of balanced failure is determined by b b b M e P  (16) Based on the compression zone height or eccentricity at the balanced failure condition, the failure mode of the column is classified as follows: if c ≥ cb or eexp ≤ eb , failure initiates in the concrete compression zone; conversely, if c < cb or eexp > eb, the column fails due to rupture of the tensile FRP reinforcement, where e is the eccentricity induced by external loading. 2.3 Analytical formulation for the failure mode governed by concrete crushing The concrete crushing failure mode in the compression zone is the predominant failure mode for FRP-RC columns subjected to eccentric compression. This failure mode is observed in nearly all experimental research results. Failure occurs when the compressive strain in concrete (on the loaded edge) reaches its ultimate value εcu (Fig. 2 (c)). The tensile (εf) and compressive strains (εfc) in FRP rebars are determined by f cu fu d c c      (17) Advances in Technology Innovation, vol. x, no. x, 20xx, pp. xx-xx 7 fc cu fcu c a c        (18) where c represents the depth of the compression zone of the cross-section, and εfcu denotes the ultimate compressive strain of FRP rebars. The resultant tensile force (Tf) and compressive force (Cf) in the FRP reinforcement are determined by f f f cu d c T E A c    (19) f f f f cu c a C E A c     (20) The resultant force in the concrete compression zones C1 and C2 can be found by 11 1 2 ccC b f  (21) 2 2 cC bc f  (22) where c1 and c2 are the heights of the compressive concrete stress blocks, as shown in Fig. 2 (c), and can be computed by 1c c (23) 2 (1 )c c  (24) The internal equilibrium of axial force and bending moment is expressed, respectively, by 1 2 f fP C C C T   (25) 1 1 2 2c c f fc f fM C Z C Z C Z T Z    (26) where the lever arms Zc1, Zc2, Zfc, and Zf are determined by Eqs. (12) - (15). The eccentricity of the axial force is determined by M e P  (27) 2.4. Analytical formulation for the failure mode governed by FRP rupture In the case of failure due to FRP rupture, the tensile strain in the FRP reinforcement reaches its ultimate limit. Based on the strain distribution diagram for this failure mode (Fig. 2 (d)), the strain values in the materials are determined with respect to the depth of the compression zone. Advances in Technology Innovation, vol. x, no. x, 20xx, pp. xx-xx 8 The strain and resultant force in the FRP rebar located in the compression zone can be determined by ( ) fu fc c a d c      (28) f fc f f fC E A  (29) The resultant force in FRP rebar located in the tension zone can be computed by f fu fT f A (30) Maximum strain in the outermost compressed concrete fiber can be found by fu c c d c     (31) The resultant force in the compressed concrete area is determined based on the strain in the outermost compressed fiber. When 1,c c red  , the stress distribution in the concrete compression zone is split into two regions, as illustrated in Fig. 2 (d). Accordingly, the heights c1 and c2 of these zones, along with their respective resultant forces C1 and C2, are calculated by 1, 1 ( ) c red fu c d c     (32) 2 1c c c  (33) 1 1 1 2 cC bc f  (34) 2 2cC f bc  (35) The load-carrying capacity of the column is determined using the axial force and moment equilibrium Eqs. (25) - (26), with the lever arms in Eq. (26) calculated based on Eqs. (12) - (15). When 1,c c red  , due to the small compressive strain in the concrete, the stress in the compression zone follows a triangular distribution. As a result, resultant force C2 equals zero, and C1 is calculated by 1 1 2 c credC bc E (36) where Ec,red denotes the reduced deformation modulus of compressive concrete. The internal equilibriums of axial force and bending moment are expressed by Eqs. (25) - (26), respectively. The lever arms Zfc and Zf in Eq. (26) are calculated based on Eqs. (14) - (15), while the lever arm Zc1 is calculated by 1 2 3 c h c Z   (37) Advances in Technology Innovation, vol. x, no. x, 20xx, pp. xx-xx 9 The eccentricity of the axial force for this failure mode is determined in the same manner as for the failure mode governed by concrete crushing, that is, according to Eq. (27). 2.5. Calculation flowchart The theoretical load-carrying capacity of an eccentrically loaded FRP-RC column is determined through the following procedure: First, the failure mode is identified based on the comparison between the balanced eccentricity (eb) and the applied eccentricity (eexp). Next, an iterative calculation process is carried out: for each assumed value of the compression zone height (c), the corresponding force components (C1, C2, Cf, and Tf) and their respective lever arms (Zc1, Zc2, Zfc, and Zf) are calculated. These values are then used to determine the axial force (P), bending moment (M), and theoretical eccentricity (e). The iteration continues until the theoretical eccentricity (e) closely matches the experimental eccentricity. At this point, the corresponding P and M values represent the theoretical load-carrying capacity of the column. The calculation flowchart is illustrated in Fig. 3. Fig. 3 Flowchart for calculating the load-carrying capacity of FRP-RC columns under eccentric loading 3. Model Validation To validate the proposed model, a dataset of 91 rectangular-section FRP-RC columns subjected to eccentric axial compression was compiled from 16 different sources [1, 4, 6-9, 14, 16, 23-30]. These experimental specimens were sourced from reputable peer-reviewed journals published between 2003 and 2024. A summary of the key parameters is presented in Table 1, with complete descriptions provided in the Appendix. The dataset exhibits a wide variation in geometry, material properties, and loading conditions, enabling comprehensive validation across different structural configurations. Column dimensions (length: 780 - 2000 mm; width and height: 150 - 405 mm) indicate a broad range of slenderness ratios (λ = 13.23 - 39.35), which significantly influence stability under eccentric loading. The reinforcement types include GFRP, CFRP, and BFRP, with total reinforcement ratios (ρft) ranging from 0.38% to 3.88%. These variations affect the stiffness and ductility of the columns. The eccentricity ratio (e/h = 0.096 - 1.0) captures a spectrum from nearly concentric to highly eccentric loading. The concrete compressive strength (f′c = 27.73 - 47.3 MPa) spans from normal-strength to moderately Advances in Technology Innovation, vol. x, no. x, 20xx, pp. xx-xx 10 high-strength concrete, affecting confinement behavior and strain compatibility, especially in failure modes involving concrete crushing or FRP bar instability. The wide-ranging properties presented in the dataset not only validate the model’s robustness but also provide insights into how geometric and material parameters influence column behavior under eccentric axial compression. Table 1 Summary of experimental parameters of the tested columns collected from previous studies Year l, mm b, mm h, mm λ Rebar ρft, % ffu, MPa Ef, GPa e/h f'c, MPa 2003- 2025 780- 2000 150- 405 150- 405 13.23- 39.35 GFRP CFRP BFRP 0.38- 3.88 347.5- 2550 32.67- 151 0.096- 1.0 27.73- 47.3 As previously mentioned, the ratio of compressive to tensile strength of FRP reinforcement varies over a wide range. Therefore, to verify the model, a conservative reduction factor of βf = 0.3 is adopted, in line with recommendations from previous studies [3]. Additionally, the compressive strength of cubic concrete samples was converted to cylindrical sample strength using a factor of 0.893. Beyond being verified against experimental data, the proposed model was also compared with theoretical outcomes derived from the ACI CODE-440.11 [18] (PACI, PACI,nor), which neglects the compressive contribution of FRP reinforcement. The Appendix details the load-carrying capacity of the experimental columns as predicted by both the proposed method and ACI CODE-440.11. Fig. 4 compares the normalized load-carrying capacities predicted by the proposed model and those calculated using the ACI CODE-440.11 standard. The proposed model shows slightly better alignment with experimental data. (a) Proposed model (b) ACI CODE-440.11 Fig. 4 Comparison between theoretical and experimental normalized load-carrying capacity, and possible error distribution histograms The statistical comparison in Table 2 demonstrates that the proposed method provides improved accuracy over ACI CODE-440.11 in predicting the behavior of FRP-RC columns under eccentric compression. Specifically, the proposed model yields a mean value of 0.932, closer to the experimental results than the ACI CODE-440.11's 0.896. Its Pearson correlation coefficient (r) of 0.84 also slightly exceeds the ACI’s 0.83, indicating enhanced consistency in predictions. While the coefficient of variation (COV) and standard deviation (SD) are comparable between the two approaches, the proposed model shows a modest but meaningful improvement in estimating the load-carrying capacity. It is also worth noting that a compressive strength reduction factor of βf = 0.3 was adopted in the verification process, representing a conservative 0 0.25 0.5 0.75 1 0 0.25 0.5 0.75 1 P p ro p ,n o r. Pexp,nor. 0 0.25 0.5 0.75 1 0 0.25 0.5 0.75 1 P A C I, n o r. Pexp,nor. Advances in Technology Innovation, vol. x, no. x, 20xx, pp. xx-xx 11 assumption. In practice, the compressive strength of FRP bars may be higher; therefore, the accuracy of the proposed model could further improve and align more closely with the experimental results. Overall, the proposed method offers a more accurate and reliable alternative for the design of FRP-RC columns subjected to eccentric loading. Table 2 Statistical comparison of theoretical against experimental results Method Pprop.nor/Pexp.nor RMSE COV, % SD r Proposed 0.932 0.154 22.9 0.145 0.84 ACI CODE-440.11 0.896 0.161 22.7 0.148 0.83 In addition to the comparative statistical metrics mentioned earlier, the reliability of the computational method is further assessed through the ratio Pprop.nor/Pexp.nor for key parameters affecting the load-carrying capacity of eccentrically compressed FRP-RC columns. These parameters include concrete strength, slenderness ratio, eccentricity ratio e/h, elastic modulus of FRP rebar, strength of FRP rebar, and reinforcement ratio as shown in Fig. 5. From Fig. 5, it is evident that the predictions yield a nearly flat trend for all variables except the reinforcement ratio (Fig. 5 (f)). In this case, the negative slope indicates an underestimation of the load-carrying capacity. (a) Relation Pprop.nor/Pexp.nor and f’c (b) Relation Pprop.nor/Pexp.nor and λ (c) Relation Pprop.nor/Pexp.nor and e/h (d) Relation Pprop.nor/Pexp.nor and Ef (e) Relation Pprop.nor/Pexp.nor and ffu (f) Relation Pprop.nor/Pexp.nor and ρf Fig. 5 Accuracy of the proposed analytical model in predicting the behavior of FRP-RC columns, under eccentric loading for various structural parameters To assess the contribution of FRP reinforcement to the axial compressive capacity, the relationship between the ratio Cf/Pprop and the compressive reinforcement ratio ρfc is constructed and shown in Fig. 6. It is evident from Fig. 6 that the contribution of FRP bars to the column's load-carrying capacity is substantial and increases progressively with higher reinforcement ratios. Based on the results of 91 tested columns, the contribution of compressive FRP reinforcement ranges from 0.94% to 22.28%, with an average value of 4.25%, corresponding to a variation in ρfc from 0.19% to 1.94%. However, it should be noted that the contribution of FRP reinforcement to axial capacity is not solely governed by the compressive reinforcement ratio, but also significantly influenced by other parameters, such as load eccentricity, tie spacing, material 0 0.5 1 1.5 2 25 30 35 40 45 50 P p ro p ,n o r/ P ex p .n o r. . f'c, MPa 0 0.5 1 1.5 2 10 20 30 40 P p ro p ,n o r/ P ex p .n o r. . λ 0 0.5 1 1.5 2 0 0.25 0.5 0.75 1 P p ro p ,n o r/ P ex p .n o r. . e/h 0 0.5 1 1.5 2 30 65 100 135 170 P p ro p ,n o r/ P ex p .n o r. . Ef, GPa 0 0.5 1 1.5 2 0 700 1400 2100 2800 P p ro p ,n o r/ P ex p .n o r. . ffu, MPa 0 0.5 1 1.5 2 0.0% 0.5% 1.0% 1.5% 2.0% P p ro p ,n o r/ P ex p .n o r. . ρf Advances in Technology Innovation, vol. x, no. x, 20xx, pp. xx-xx 12 properties, and cross-sectional geometry. Fig. 6 Contribution of compressive FRP reinforcement Additionally, the current experimental data on eccentrically loaded FRP-RC columns remain limited in both the number of specimens and the range of test parameters, particularly the degree of eccentricity. Among the 91 specimens compiled from prior studies (see Appendix), eccentricity values range only from 0.096 to 1.0, with no instances of high eccentricity. As a result, failure in these specimens is typically due to concrete crushing in the compression zone, while the FRP reinforcement in the tension zone generally remains intact. Therefore, the analytical model proposed in this study has not been validated for failure modes involving FRP rupture, highlighting a significant research gap. This issue is intended to be addressed in future studies through both experimental testing and numerical simulations. Furthermore, the proposed model does not yet account for key factors affecting column load-carrying capacity, such as longitudinal bending, the role of transverse reinforcement, or random eccentricity. Consequently, discrepancies persist between the theoretical load-carrying capacity predicted by the model and experimental results, which are not yet fully satisfactory. Addressing these challenges will be a primary objective of future research. 4. Conclusions This study developed an analytical model to predict the load-carrying capacity of rectangular FRP-RC columns under eccentric compression. The proposed model is established based on strain compatibility and force equilibrium conditions. It incorporates the specific stress-strain relationships of both concrete and FRP reinforcement and also considers the contribution of compressive FRP rebars to the overall sectional capacity. The model was validated using a database of 91 experimentally tested columns collected from reputable publications. The main findings can be summarized as follows: (1) Two primary failure modes of FRP-RC columns under eccentric compression were identified: concrete crushing and FRP rupture, separated by a balanced failure condition. (2) An analytical approach and a corresponding computational framework were established to estimate the load-carrying capacity across all possible failure modes of FRP-RC columns under eccentric loading. (3) The proposed model demonstrated high predictive accuracy, with a mean predicted-to-experimental strength ratio of 0.932, RMSE = 0.154, COV = 22.9%, SD = 0.145, and correlation coefficient r = 0.84, outperforming ACI CODE-440.11 in most cases. (4) The contribution of compressive FRP reinforcement was found to be significant, enhancing column strength by 0.94% to 22.3%, depending on reinforcement ratio and eccentricity. This finding highlights the importance of including the contribution of compressive FRP rebars in design formulations rather than neglecting them for conservative design. Despite its promising performance, the model remains limited in scope. It does not account for P–Δ effects, confinement from transverse reinforcement, or time-dependent behavior. Furthermore, the current dataset lacks sufficient high-eccentricity columns to validate failure modes governed by FRP rupture. Future research should address these limitations and explore the influence of longitudinal bending and multi-layer FRP reinforcement. These advancements would broaden the applicability ò the model and support its integration into design codes. 0% 6% 12% 18% 24% 0.0% 0.5% 1.0% 1.5% 2.0% C f/ P p ro p . ρfc 0% 6% 12% 18% 24% 0.0% 0.5% 1.0% 1.5% 2.0% C f/ P p r o p . ρfc 0% 6% 12% 18% 24% 0.0% 0.5% 1.0% 1.5% 2.0% C f/P pr op . ρfc Advances in Technology Innovation, vol. x, no. x, 20xx, pp. xx-xx 13 Conflicts of Interest The authors declare no conflict of interest. Notation a Distance from the centroid of the tensile reinforcement (Af) to the outermost tension fiber of the cross-section a' Distance from the centroid of the compressive reinforcement (Afc) to the extreme compression face of the section Af Total area of FRP rebar located in the concrete tension zone or in the less compressed region (in case of full- section compression) Afc Total area of FRP rebar in the concrete compression zone b Width of the cross-section of the column c Depth of the compression zone of the cross-section cb Depth of the compression zone of the cross-section at the balanced failure c1 Depth of the rectangular stress block in the concrete compression zone C1 Resultant compressive force in the concrete compression zone with uniformly distributed stress c2 Depth of the triangular stress block in the concrete compression zone C2 Resultant compressive force in the concrete compression zone with triangularly distributed stress Cf Resultant internal force in FRP rebar in the concrete compression zone d Effective depth of the cross-section of the column e Eccentricity of the axial force Ec, red Reduced the deformation modulus of compressive concrete eexp Experimental eccentricity of the axial force eb Theoretical eccentricity of the axial force at balanced failure mode Ef Elastic modulus of FRP rebar f’c Cylinder compressive strength of concrete ffcu Ultimate compressive strength of FRP rebar ffu Ultimate tensile strength of FRP rebar h Height of the cross-section of the column l Total length of the tested column M Bending moment C.A. Centroid axis N.A. Neutral axis P Axial force Pexp Experimental axial force Pexp. nor Normalized experimental axial force - Pexp.nor = Pexp/(0.85f’cAg) Pprop Axial force obtained from the proposed analytical method Pprop.nor Normalized axial force obtained from the proposed analytical method - Pprop.nor = Pprop/(0.85f’cAg) PACI Axial force calculated according to the ACI CODE-440.11-22 PACI.nor Normalized axial force calculated according to the ACI CODE-440.11-22 Tf Resultant internal force in FRP rebar located in the concrete tension zone or in the less compressed region (in case of full-section compression) Zc1 Lever arm of the compressive force C₁, i.e., the distance from the line of action of C₁ to the centroid axis Zc2 Lever arm of the compressive force C2, i.e., the distance from the line of action of C2 to the centroid axis Zf Lever arm of the tensile force Tf, i.e., the distance from the line of action of Tf to the centroid axis Zfc Lever arm of the compressive force Cf, i.e., the distance from the line of action of Cf to the centroid axis α Coefficient  1 1 1 1 /cu c red c red        β Conversion factor from cylinder to prism compressive strength βf Conversion factor for translating FRP tensile strength to its equivalent compressive strength εc Compressive strain in concrete εc1,red Limiting strain value at the transition between the elastic range and the horizontal plateau in the bilinear reduced stress-strain diagram according to SP 63.13330.2018, εc1, red = 0.0015 εcu Ultimate compressive strain of concrete εf Tensile strain in FRP rebar εfc Compressive strain in FRP rebar εfcu Ultimate compressive strain of FRP rebar εfu Ultimate tensile strain of FRP rebar λ Slenderness ratio of the column σc Compressive stress in concrete ρf Tensile reinforcement ratio ρfc Compressive reinforcement ratio Advances in Technology Innovation, vol. x, no. x, 20xx, pp. xx-xx 14 ρft Total reinforcement ratio, ρft = ρf + ρfc References [1] M. K. Sharbatdar, “Concrete Columns and Beams Reinforced with FRP Bars and Grids under Monotonic and Reversed Cyclic Loading,” Ph.D. dissertation, Department of Civil Engineering, University of Ottawa, Ottawa, 2003. [2] H. Dang Vu and D. N. Phan, “Experimental and Theoretical Analysis of Cracking Moment of Concrete Beams Reinforced with Hybrid Fiber Reinforced Polymer and Steel Rebars,” Advances In Technology Innovation, vol. 6, no. 4, pp. 222-234, 2021. [3] K. Khorramian and P. Sadeghian, “Material Characterization of GFRP Bars in Compression Using a New Test Method,” Journal of Testing and Evaluation, vol. 49, no. 2, pp. 1037-1052, 2021. [4] N. Elmesalami, F. Abed, and A. E. Refai, “Concrete Columns Reinforced with GFRP and BFRP Bars under Concentric and Eccentric Loads: Experimental Testing and Analytical Investigation,” Journal of Composites for Construction, vol. 25, no. 2, article no. 04021003, 2021. [5] C. C. Choo, I. E. Harik, and H. Gesund, “Strength of Rectangular Concrete Columns Reinforced with Fiber-Reinforced Polymer Bars,” ACI Structural Journal, vol. 103, no. 3, pp. 452-459, 2006. [6] L. Sun, M. Wei, and N. Zhang, “Experimental Study on the Behavior of GFRP Reinforced Concrete Columns under Eccentric Axial Load,” Journal of Composites for Construction, vol. 152, pp. 214-225, 2017. [7] F. L. Hamid and A. R. Yousif, “Behavior of Short and Slender RC Columns with BFRP Bars under Axial and Flexural Loads: Experimental and Analytical Investigation,” Journal of Composites for Construction, vol. 28, no. 1, article no. 4465, 2023. [8] M. Guérin, H. M. Mohamed, B. Benmokrane, A. Nanni, and C. K. Shield, “Eccentric Behavior of Full-Scale Reinforced Concrete Columns with Glass Fiber-Reinforced Polymer Bars and Ties,” Structural Journal, vol. 115, no. 2, pp. 489- 499, 2018. [9] M. Guérin, H. M. Mohamed, B. Benmokrane, C. K. Shield, and A. Nanni, “Effect of Glass Fiber-Reinforced Polymer Reinforcement Ratio on Axial-Flexural Strength of Reinforced Concrete Columns,” Structural Journal, vol. 115, no. 4, pp. 1049-1061, 2018. [10] A. S. Hosseini and P. Sadeghian, “Assessing Compressive Properties of GFRP Bars: Novel Test Fixture and Statistical Analysis,” Journal of Composites for Construction, vol. 29, no. 2, p. 04025011, 2025. [11] Y. Almomani, A. Tarawneh, R. Alawadi, Z. N. Taqieddin, Y. Jweihan, and E. Saleh, “Predictive Models of Behavior and Capacity of FRP Reinforced Concrete Columns,” Journal of Applied Engineering Science, vol. 21, no. 1, pp. 143- 156, 2023. [12] A. Tarawneh and S. Majdalaweyh, “Design and Reliability Analysis of FRP-Reinforced Concrete Columns,” Structures, vol. 28, pp. 1580-1588, 2020. [13] W. Xue, F. Peng, and Z. Fang, “Behavior and Design of Slender Rectangular Concrete Columns Longitudinally Reinforced with Fiber-Reinforced Polymer Bars,” ACI Structural Journal, vol. 115, no. 2, pp. 311-322, 2018. [14] M. Elchalakani and G. Ma, “Tests of Glass Fibre Reinforced Polymer Rectangular Concrete Columns Subjected to Concentric and Eccentric Axial Loading,” Engineering Structures, vol. 151, pp. 93-104, 2017. [15] M. Elchalakani, G. Ma, F. Aslani, and W. Duan, “Design of GFRP-Reinforced Rectangular Concrete Columns under Eccentric Axial Loading,” Magazine of Concrete Research, vol. 69, no. 17, pp. 865-877, 2017. [16] Z. S. Othman and A. H. Mohammad, “Behaviour of Eccentric Concrete Columns Reinforced with Carbon Fibre- Reinforced Polymer Bars,” Advances in Civil Engineering, vol. 2019, no. 1, article no. 1769212, 2019. [17] ACI Committee 440, “Guide for the Design and Construction of Structural Concrete Reinforced with FRP Bars,” ACI, Farmington Hills, MI, USA, Rep. 440.1R-15, 2015. [18] Building Code Requirements for Structural Concrete Reinforced with Glass Fiber Reinforced Polymer (GFRP) Bars - Code and Commentary, ACI CODE-440.11-22, 2023. [19] Design and Construction of Building Structures with Fibre-Reinforced Polymers, CSA S806:2012:R2017, 2017. [20] Concrete Structures Reinforced with Fibre-Reinforced Polymer Bars. Design Rules, SP 295.1325800.2017, 2017 [21] H. J. Zadeh and A. Nanni, “Design of RC Columns Using Glass FRP Reinforcement,” Journal of Composites for Construction, vol. 17, no. 3, pp. 294-304, 2013. [22] Concrete and Reinforced Concrete Structures. General Provisions, SP 63.13330.2018, 2019. [23] M. Issa, I. Metwally, and S. Elzeiny, “Performance of Eccentrically Loaded GFRP Reinforced Concrete Columns,” World Journal of Engineerning, vol. 9, no. 1, pp. 71-78, 2012. [24] M. N. S. Hadi and J. Youssef, “Experimental Investigation of GFRP-Reinforced and GFRP-Encased Square Concrete Specimens under Axial and Eccentric Load, and Four-Point Bending Test,” Journal of Composites for Construction, vol. 20, no. 5, article no. 04016020, 2016. [25] A. K. Pour, A. Shirkhani, M. S. Kırgız, and E. N. Farsangi, “Experimental Investigation of GFRP-Reinforced Concrete Columns Made with Waste Aggregates under Concentric and Eccentric Loads,” Structural Concrete, vol. 24, no. 1, pp. 1670-1688, 2022 [26] M. S. Irhayyim, W. A. Aules, and M. M. Jomaa’h, “Structural Behavior of Reinforced Concrete Columns Fully and Partially Reinforced with GFRP Bars Tested under Concentric or Eccentric Compressive Loads,” Diyala Journal of Engineering Sciences, vol. 17, no. 3, pp. 58–77, 2024. Advances in Technology Innovation, vol. x, no. x, 20xx, pp. xx-xx 15 [27] H. G. Fathi, M. K. N. Ghali, A. S. Shanour, and A. N. M. Khater, “Experimental and Analytical Study on Eccentrically Loaded Fiber Concrete Columns Reinforced Longitudinally with GFRP Bars,” Engineering Structures, vol. 312, article no. 118251, 2024. [28] N. S. Mahmoudabadi, A. Bahrami, S. Saghir, A. Ahmad, M. Iqbal, M. Elchalakani, and Y. O. Özkılıç, “Effects of Eccentric Loading on Performance of Concrete Columns Reinforced with Glass Fiber-Reinforced Polymer Bars,” Scientific Reports, vol. 14, no. 1, article no. 1890, 2024. [29] A. S. Hosseini and P. Sadeghian, “Slenderness Effect on GFRP-RC Columns with Square Spirals under Concentric and Eccentric Loading: Experimental and Analytical Study,” Engineering Structures, vol. 334, article no. 120277, 2025. [30] S. A. Emam, O. Amer, A. H. Ali, and H. A. Haggag, “Experimental Investigation on the Compressive Behaviour of GFRP-Reinforced Concrete Short Columns,” Engineering Research Journal, vol. 184, no. 3, pp. 44-58, 2025. Copyright© by the authors. Licensee TAETI, Taiwan. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY-NC) license (https://creativecommons.org/licenses/by-nc/4.0/). Appendix Table A1 Database of tested eccentrically loaded FRP-RC columns Ref. Specimen’s ID Geometry Main reinforcement Conc rete Test results Proposed ACI CODE- 440.11 l, mm b, mm h, mm d, mm λ e/h FRP type Af, mm2 ρft, % ffu, MPa Ef, GPa f'c, MPa Pexp, kN Pexp.nor Pprop Pprop .nor PACI PACI. nor Sharbatdar [1] CFS1 1680 230 230 226 25.4 0.26 CFRP 100.6 0.38 2550 147 47.3 1020 0.48 1077.6 0.51 1053 0.5 CFS2 1680 230 230 226 25.4 0.33 CFRP 100.6 0.38 2550 147 47.3 1000 0.47 875.6 0.41 841.2 0.4 CFS3 1680 230 230 226 25.4 0.26 CFRP 100.6 0.38 2550 147 47.3 1200 0.564 1077.6 0.51 1053 0.5 CFS4 1680 230 230 226 25.4 0.33 CFRP 100.6 0.38 2550 147 47.3 960 0.451 875.6 0.41 841.2 0.4 Issa, et al. [23] GN8 1200 150 150 144 27.8 0.33 GFRP 226.2 2.01 347.5 32.67 27.7 227.1 0.428 228.9 0.43 217.4 0.41 GN13 1200 150 150 144 27.8 0.17 GFRP 226.2 2.01 347.5 32.67 27.7 425.8 0.803 362.6 0.68 353.6 0.67 GM8 1200 150 150 144 27.8 0.33 GFRP 226.2 2.01 347.5 32.67 38.4 535.8 0.731 304.7 0.41 291.3 0.4 Hadi and Youssef [24] RF-25 800 210 210 177 13.2 0.12 GFRP 253.4 1.15 1641 67.9 31 995 0.856 888.6 0.76 879 0.76 RF-50 800 210 210 177 13.2 0.24 GFRP 253.4 1.15 1641 67.9 31 615 0.529 632.5 0.54 615.9 0.53 Elchalakani and Ma [14] G150-25 1200 160 260 228 16 0.1 GFRP 380.1 1.83 708 50 32.75 880.3 0.76 935.4 0.81 930 0.8 G150-45 1200 160 260 228 16 0.17 GFRP 380.1 1.83 708 50 32.75 584.2 0.504 771.7 0.67 753.8 0.65 G75-25 1200 160 260 228 16 0.1 GFRP 380.1 1.83 708 50 32.75 917.2 0.792 935.4 0.81 930 0.8 G75-35 1200 160 260 228 16 0.14 GFRP 380.1 1.83 708 50 32.75 787.8 0.68 856.2 0.74 841.1 0.73 Sun, et al. [6] Z175-1 1000 180 250 225 13.9 0.7 GFRP 235.5 1.05 1103 92.4 29.9 201 0.176 240.7 0.21 225 0.2 Z175-2 1000 180 250 225 13.9 0.7 GFRP 235.5 1.05 1103 92.4 29.9 174 0.152 240.7 0.21 225 0.2 Z175-3 1000 180 250 225 13.9 0.7 GFRP 235.5 1.05 1103 92.4 29.9 181 0.158 240.7 0.21 225 0.2 Z125-1 1000 180 250 225 13.9 0.5 GFRP 235.5 1.05 1103 92.4 29.9 291 0.254 336.6 0.29 316 0.28 Z125-2 1000 180 250 225 13.9 0.5 GFRP 235.5 1.05 1103 92.4 29.9 290 0.253 336.6 0.29 316 0.28 Z125-3 1000 180 250 225 13.9 0.5 GFRP 235.5 1.05 1103 92.4 29.9 347 0.303 336.6 0.29 316 0.28 Z75-1 1000 180 250 225 13.9 0.3 GFRP 235.5 1.05 1103 92.4 29.9 632 0.552 542.1 0.47 516.7 0.45 Z75-2 1000 180 250 225 13.9 0.3 GFRP 235.5 1.05 1103 92.4 29.9 677 0.592 542.1 0.47 516.7 0.45 Z75-3 1000 180 250 225 13.9 0.3 GFRP 235.5 1.05 1103 92.4 29.9 602 0.526 542.1 0.47 516.7 0.45 Guérin, et al. [8] CGA40 2000 405 405 357 17.2 0.1 GFRP 927 1.13 1317 51.3 42.3 4760 0.807 4696.2 0.80 4705.8 0.8 CGA80 2000 405 405 357 17.2 0.2 GFRP 927 1.13 1317 51.3 42.3 3354 0.569 3593.1 0.61 3551.3 0.6 CGA160 2000 405 405 357 17.2 0.4 GFRP 927 1.13 1317 51.3 42.3 1943 0.329 1875.5 0.32 1797.5 0.31 CGA320 2000 405 405 357 17.2 0.79 GFRP 927 1.13 1317 51.3 42.3 745 0.126 813.3 0.14 769.8 0.13 CGB40 2000 405 405 357 17.2 0.1 GFRP 1038 1.27 838 48.2 42.3 4417 0.749 4699.6 0.80 4706.2 0.8 CGB80 2000 405 405 357 17.2 0.2 GFRP 1038 1.27 838 48.2 42.3 3200 0.543 3596.4 0.61 3552.2 0.6 CGB160 2000 405 405 357 17.2 0.4 GFRP 1038 1.27 838 48.2 42.3 1589 0.269 1890.1 0.32 1810.1 0.31 CGB320 2000 405 405 357 17.2 0.79 GFRP 1038 1.27 838 48.2 42.3 645 0.109 826.6 0.14 783.8 0.13 M. Guérin, et al. [9] G1e10 2000 405 405 360 17.2 0.1 GFRP 927 1.13 1317 51.3 42.3 4760 0.807 4695.5 0.80 4707.3 0.8 G1e20 2000 405 405 360 17.2 0.2 GFRP 927 1.13 1317 51.3 42.3 3357 0.569 3595.7 0.61 3552.6 0.6 G1e40 2000 405 405 360 17.2 0.4 GFRP 927 1.13 1317 51.3 42.3 1942 0.329 1883.3 0.32 1803.8 0.31 G1e80 2000 405 405 360 17.2 0.79 GFRP 927 1.13 1317 51.3 42.3 745 0.126 820.7 0.14 774.9 0.13 G2e10 2000 405 405 360 17.2 0.1 GFRP 1236 1.51 1317 51.3 42.3 5028 0.853 4716.5 0.80 4707.3 0.8 G2e20 2000 405 405 360 17.2 0.2 GFRP 1236 1.51 1317 51.3 42.3 3625 0.615 3623.8 0.61 3562.3 0.6 G2e40 2000 405 405 360 17.2 0.4 GFRP 1236 1.51 1317 51.3 42.3 2035 0.345 1969.3 0.33 1881.7 0.32 G2e80 2000 405 405 360 17.2 0.79 GFRP 1236 1.51 1317 51.3 42.3 914 0.155 903 0.15 853.2 0.15 G3e10 2000 405 405 357 17.2 0.1 GFRP 2120 2.58 1122 54.4 42.3 5294 0.898 4787 0.81 4704.5 0.8 G3e20 2000 405 405 357 17.2 0.2 GFRP 2120 2.58 1122 54.4 42.3 3790 0.643 3707.3 0.63 3585.5 0.61 G3e40 2000 405 405 357 17.2 0.4 GFRP 2120 2.58 1122 54.4 42.3 2110 0.358 2157.6 0.37 2042.7 0.35 G3e80 2000 405 405 357 17.2 0.79 GFRP 2120 2.58 1122 54.4 42.3 1008 0.171 1081.8 0.18 1012.5 0.17 Othman and Mohammad [16] C10-T90-E0.5 1500 150 150 124 34.7 0.5 CFRP 157 1.4 2000 150 44.7 258 0.302 249.8 0.29 236.8 0.28 C10-T90-E1.0 1500 150 150 124 34.7 1 CFRP 157 1.4 2000 150 44.7 119 0.139 125.9 0.15 119 0.14 C12-T90-E0.5 1500 150 150 123 34.7 0.5 CFRP 226.2 2.01 2000 145 44.7 262 0.306 265.5 0.31 249.1 0.29 C12-T90-E1.0 1500 150 150 123 34.7 1 CFRP 226.2 2.01 2000 145 44.7 126 0.147 137.6 0.16 129.5 0.15 C16-T90-E0.5 1500 150 150 121 34.7 0.5 CFRP 402.2 3.58 2000 151 44.7 290 0.339 296.8 0.35 268.9 0.32 C16-T90-E1.0 1500 150 150 121 34.7 1 CFRP 402.2 3.58 2000 151 44.7 137 0.16 161.6 0.19 146.8 0.17 Advances in Technology Innovation, vol. x, no. x, 20xx, pp. xx-xx 16 Table A1 Database of tested eccentrically loaded FRP-RC columns (continued) Ref. Specimen’s ID Geometry Main reinforcement Conc rete Test results Proposed ACI CODE- 440.11 l, mm b, mm h, mm d, mm λ e/h FRP type Af, mm2 ρft, % ffu, MPa Ef, GPa f'c, MPa Pexp, kN Pexp.nor Pprop Pprop .nor PACI PACI. nor C12-T140-E0.5 1500 150 150 123 34.7 0.5 CFRP 226.2 2.01 2000 145 44.7 264 0.309 265.5 0.31 249.1 0.29 C12-T140-E1.0 1500 150 150 123 34.7 1 CFRP 226.2 2.01 2000 145 44.7 129 0.151 137.6 0.16 129.5 0.15 C12-T40-E0.5 1500 150 150 123 34.7 0.5 CFRP 226.2 2.01 2000 145 44.7 237.7 0.278 265.5 0.31 249.1 0.29 C12-T40-E1.0 1500 150 150 123 34.7 1 CFRP 226.2 2.01 2000 145 44.7 113 0.132 137.6 0.16 129.5 0.15 Elmesalami, et al. [4] B-16-40* 1100 180 180 135 22 0.22 BFRP 402.1 2.48 1242 49.3 28.4 577 0.738 444.7 0.57 432.7 0.55 B-16-80 1100 180 180 135 22 0.44 BFRP 402.1 2.48 1242 49.3 34.4 347 0.366 270.3 0.29 261.4 0.28 G-16-40* 1100 180 180 135 22 0.22 GFRP 402.1 2.48 785 44.9 28.4 585 0.748 443 0.57 432.4 0.55 G-16-80 1100 180 180 135 22 0.44 GFRP 402.1 2.48 785 44.9 34.4 364 0.384 266.2 0.28 257.8 0.27 B-20-40 1100 180 180 133 22 0.22 BFRP 628.3 3.88 913 45.9 34.4 720 0.76 540.7 0.57 523.6 0.55 B-20-80 1100 180 180 133 22 0.44 BFRP 628.3 3.88 913 45.9 34.4 412 0.435 283.8 0.30 273.8 0.29 Karimi Pour, et al. [25] N-G-60-50 1000 200 200 164 17.4 0.25 GFRP 760.3 3.8 966 39.5 37.3 1378 1.087 677.8 0.53 652.6 0.52 N-G-60-100 1000 200 200 164 17.4 0.5 GFRP 760.3 3.8 966 39.5 36 631.1 0.516 346.5 0.28 329.1 0.27 R-G-60-50 1000 200 200 164 17.4 0.25 GFRP 760.3 3.8 966 39.5 40.5 1532 1.112 732.5 0.53 706.2 0.51 R-G-60-100 1000 200 200 164 17.4 0.5 GFRP 760.3 3.8 966 39.5 40 690 0.507 376.8 0.28 358.1 0.26 N-G-120-50 1000 200 200 164 17.4 0.25 GFRP 760.3 3.8 966 39.5 35 1224 1.028 638.9 0.54 613.1 0.52 N-G-120-100 1000 200 200 164 17.4 0.5 GFRP 760.3 3.8 966 39.5 35 605.4 0.509 339.1 0.28 321.7 0.27 R-G-120-50 1000 200 200 164 17.4 0.25 GFRP 760.3 3.8 966 39.5 39 1311 0.989 706.8 0.53 681.5 0.51 R-G-120-100 1000 200 200 164 17.4 0.5 GFRP 760.3 3.8 966 39.5 39 634.8 0.479 369.3 0.28 350.7 0.26 N-G-180-50 1000 200 200 164 17.4 0.25 GFRP 760.3 3.8 966 39.5 36.2 1108 0.9 659 0.54 633.8 0.52 N-G-180-100 1000 200 200 164 17.4 0.5 GFRP 760.3 3.8 966 39.5 36 592.5 0.484 346.5 0.28 329.1 0.27 R-G-180-50 1000 200 200 164 17.4 0.25 GFRP 760.3 3.8 966 39.5 39.6 1173 0.871 716.9 0.53 691.2 0.51 R-G-180-100 1000 200 200 164 17.4 0.5 GFRP 760.3 3.8 966 39.5 39 634.8 0.479 369.3 0.28 350.7 0.26 Mohammed S. Irhayyim, et al. [26] C1-G 1700 150 150 125 39.4 0.67 GFRP 157.1 1.4 1207 50.3 26.1 131 0.262 95.6 0.19 90.8 0.18 C2-G 1700 150 150 125 39.4 1 GFRP 157.1 1.4 1207 50.3 26.1 61 0.122 62.4 0.13 59.6 0.12 Hamid and Yousif [7] 31-2B10B150-40 1620 210 180 137 31.3 0.22 BFRP 402 2.13 978.6 48.26 38.5 754 0.61 695.5 0.56 683.1 0.55 31-2B10B150-80 1620 210 180 137 31.3 0.44 BFRP 402 2.13 978.6 48.26 38.5 334 0.27 341.4 0.28 330.6 0.27 31-2B10B150-120 1620 210 180 137 31.3 0.67 BFRP 402 2.13 978.6 48.26 38.5 170 0.137 212.2 0.17 205.1 0.17 15-2B10B150-40 780 210 180 137 15.1 0.22 BFRP 402 2.13 978.6 48.26 38.5 772 0.624 695.5 0.56 683.1 0.55 15-2B10B150-80 780 210 180 137 15.1 0.44 BFRP 402 2.13 978.6 48.26 38.5 395 0.319 341.4 0.28 330.6 0.27 15-2B10B150-120 780 210 180 137 15.1 0.67 BFRP 402 2.13 978.6 48.26 38.5 182 0.147 212.2 0.17 205.1 0.17 Fathi, et al. [27] G1 1200 150 150 125 27.8 0.27 GFRP 157 1.40 1000 40 30 335 0.654 251.6 0.49 244.9 0.48 G2 1200 150 150 125 27.8 0.27 GFRP 157 1.40 1000 40 30 328 0.64 251.6 0.49 244.9 0.48 G3 1200 150 150 125 27.8 0.27 GFRP 157 1.40 1000 40 30 320 0.625 251.6 0.49 244.9 0.48 Shakouri Mahmoudabadi, et al. [28] 50-E25 1200 180 180 155 23.1 0.14 GFRP 190 1.17 750 62.5 35 847.5 0.879 697.8 0.72 690.8 0.72 100-E25 1200 180 180 155 23.1 0.14 GFRP 190 1.17 750 62.5 35 792.1 0.822 697.8 0.72 690.8 0.72 50-E75 1200 180 180 155 23.1 0.42 GFRP 190 1.17 750 62.5 35 385.6 0.4 302.2 0.31 289.1 0.3 100-E75 1200 180 180 155 23.1 0.42 GFRP 190 1.17 750 62.5 35 381.9 0.396 302.2 0.31 289.1 0.3 Sadat Hosseini and Sadeghian [29] S20-e15 1220 203 203 170 20.9 0.15 GFRP 595.8 2.89 1020 53.7 32.5 865 0.76 820.1 0.72 790.8 0.7 S40-e15 2440 203 203 170 41.7 0.15 GFRP 595.8 2.89 1020 53.7 32.5 588 0.517 820.1 0.72 790.8 0.7 S40-e30 2440 203 203 170 41.7 0.3 GFRP 595.8 2.89 1020 53.7 32.5 558 0.49 539.7 0.47 512.1 0.45 Emam, et al. [30] SC1 1500 250 250 220 20.8 0.2 GFRP 213.9 0.68 880 53.4 32.4 1018 0.591 1036.4 0.6 1026.9 0.6 SC2 1500 250 300 270 17.4 0.17 GFRP 213.9 0.57 880 53.4 32.4 1321 0.64 1370.6 0.66 1366.6 0.66 SC3 1500 250 350 320 14.9 0.14 GFRP 213.9 0.49 880 53.4 32.4 1731 0.718 1706.1 0.71 1709.2 0.71