Examination of strength reduction factor in CFRP-confined columns under axial compression

Abstract

Keywords: Strength Reduction Factor; Carbon Fiber Reinforced Polymer; First-order Second-moment Approach; Axial load; Column

Introduction

Today, one of the most frequently used method in the field of structural strengthening is to wrap the column with fiber polymers. Fiber polymers act like transverse reinforcement in reinforced concrete columns, causing an increase in the axial load-carrying capacity and ductility of the columns. High strength capacity, high resistance to corrosion, light weight, ease of application, not requiring costly equipment, being applicable to any shape due to its

flexibility, and providing the opportunity to be applied on buildings without distrupting the existing use are among the most important advantages of fiber polymers [1]. One of the main features of engineering design is to provide structural safety by considering economic conditions. The reliability of a structural element can be explained as the probability of continuing its intended use throughout its lifespan. Safety factors were recommended from reliability analysis for the design purposes which ensure structural

*Corresponding author. *E-mail address: noyan@yildiz.edu.tr This paper was recommended for publication in revised form by Editor in Cheif Ahmet Selim Dalkilic Published by Yıldız Technical University Press, İstanbul, Turkey Copyright 2021, Yıldız Technical University. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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safety. Depending on the β, the safety factors are determined and the desired safety level is aimed to be achieved. Reliability and probability of failure are directly related to the risk taken into account in determining the safety factor [2]. In ACI 318-19, the reliability of structural elements are obtained by multiplying the strength values with a strength reduction factor 𝜙 which is less than one. The 𝜙 is used to take into account uncertainties in both the size and strength of the material to reduce possible design equation errors [1]. In the structural reliability, 𝜙 depends on the accepted target reliability index β. β also varies depending on the accepted failure probability pF in the structural design. As per ACI 318-19 code recommendation, β taken into account in determining of the 𝜙 is taken as 3.5, and the failure probability pF corresponding to this value is taken as 2.33×10-4 in the current study. The 𝜙 values in the ACI 318-19 for the axial compression load are different for plain concrete column and both types of transverse reinforcing steels (spiral or tie) in column. In ACI 318-19, the 𝜙 factor is suggested as 0.75 for spiral reinforced concrete columns, 0.65 for tie reinforced concrete columns and 0.60 for plain concrete columns, respectively [1]. ACI 440.2R-17 emphasizes that strength reduction factor for CFRP-confined RC columns under the axial compression load should be used as required by ACI 318-19 [3]. In the literature, a study was investigated to determine the strength reduction factor of axially-loaded CFRPconfined columns by Ozer and Alacali [4]. The factors 𝜙 were determined for CFRP-confined specimens with 21 transverse and longitudinal reinforcement and 38 plain circular columns under axial load collected from literature in this study. Then, these factors were compared those of recommended in the ACI 318-19. In the current study, however, the strength reduction factors for different coefficients of variation were determined by considering the axial compression test data of 298 circular and rectangular column specimens with/out longitudinal reinforcement collected from 18 different papers in the literature by increasing the number of experiments. Then, the obtained factors are been compared to those of recommended in the ACI 318-19. To determine the strength reduction factors, the performance functions were obtained from the equations in ACI 440.2R-17. The first-order second-moment (FOSM) approach, which is one of the probabilistic methods, was utilized to determine these factors and it was assumed that the random variables constituting the performance functions were statistically independent. In other words, the correlation effects between the variables were neglected. The effects on the reduction factors of the columns of the variability in the coefficients of variation of the random variables in performance function of CFRP-confined columns under axial compression load were examined. In order to achieve an acceptable safety level, the coefficients of variation

corresponding to the factors recommended in ACI 318-19 have been determined.

Design Of Cfrp-Confined Reinforced Concrete Column

According to ACI 318-19, the basic requirement in the structural design is expressed as follows: (1) The design strength (𝜙Pn) obtained by multiplying with a factor (𝜙) must be sufficient to satisfy the required strength Pu. The axial load carrying capacities of the fiber polymer-wrapped columns for both types of transverse reinforcing steel (spirals or ties) can be calculated with the following equations according to the ACI 440.2R-17. As seen in Equations (2) and (3), any contribution of lateral reinforcement to the axial compression strength of a reinforced concrete column is not taken into account [3]. For steel spiral reinforcement; (2) For steel-tie reinforcement; (3) where, in above equations, f´cc is compressive strength of FRP-confined concrete, Ag is gross area of concrete section, Ast is total area of longitudinal reinforcement, fy is yield strength of longitudinal reinforcement, 𝜙 is strength reduction factor and Pn is nominal axial compressive strength [3]. The compressive strength of FRP-confined concrete f´cc and the maximum confinement pressure of FRP jacket fl can be written as: (4) (5) where, f´c is the compressive strength of unconfined concrete, κa is the shape factor, n is the number of plies of FRP reinforcement, tf is the nominal thickness of one ply of FRP reinforcement, Ef is the modulus of elasticity of FRP, εfe is the effective strain in FRP reinforcement attained at failure, D is the diameter of circular section or diagonal distance equal to for rectangular section as seen in Figure 1. The shape factor κa in Equation 4 for circular section is taken as 1 [3]. For rectangular section, κa is calculated depending on the effective confinement area Ae. The values of the b, h and Ac seen in Equation 6 are cross-sectional dimensions and area of the column, respectively. (6)

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As shown in Figure 2, according to this proposed model in the ACI 440.2R-17, 𝐸𝑐 represents the modulus of elasticity of concrete, ε´c, ε´t and E2 represent compressive strain corresponding to f´c, transition strain and slope of the linear component of the stress-strain model, respectively. The ultimate axial strain of confined concrete εccu is calculated by Equation 9. In addition, εccu calculated by the Equation 9 should be equal or less than 0.01 to avoid concrete integrity being lost due to excessive cracking as shown in Equation 10 [3]. (9)

Figure 1. Equivalent circular cross section [3]. In Equation 4, "Ψf" is defined as additional reduction factor and taken as 0.95 in ACI 440.2R-17. The εfe in Equation 5 means the strain efficiency factor which is used to consider the premature failure of FRP in relation to the stress concentration regions caused by cracking of concrete as it expands. εfe is as given below in ACI 440.2R-17:

(10) In case εccu calculated by the Equation 9 is greater than 0.01, a new limit value (εccu.new = 0.01) is taken. In this case, (f´cc.new) is recalculated with the following equations. (11)

(7) Various experimental calibrations were realized to determine the strain efficiency factor κε, and the mean value of κε was proposed as 0.586 by Lam and Teng and 0.58 by Harries and Carey [3]. In this study, it was assumed that κε equals to 0.586. In Equation 7, εfu is defined as design rupture strain of FRP reinforcement and calculated by Equation 8. CE in Equation 8 is environmental reduction factor and ACI 440.2R-17 recommends 0.95 for structures exposed to interior environmental conditions. In Equation 8, ε*fu is defined as ultimate rupture strain of CFRP. (8)

(12) The accuracy of the above-mentioned all equations for specimens with unconfined concrete compressive strength of 70 MPa and greater was not been experimentally proven. Also, ACI 440.2R-17 does not recommend for rectangular cross section with side aspect ratios h/b greater than 2.0, or face dimensions b or h exceeding 900 mm. Therefore, the aforementioned specimens are not considered in current study.

Reliability Analysis

Partial Safety Factors As statistical information about the random variables that constitute the performance function is usually limited to the mean values (first-moment) and variances (second-moment). For this reason, reliability equations include terms based on the first and second moment of random variables. In the probabilistic design with the second moment approach, different safety factors can be determined for each design variable. The designs corresponding to different failure surfaces of reduced variables can be represented as follows (Figure 3) [2]: (13)

Figure 2. Stress-strain model for FRP-confined concrete [3].

Using the most probable failure point ( ) on the failure surface, the partial safety factors γi are determined by the following Equation [2].

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Figure 3. Designs corresponding to different failure surfaces [2].

(14) Similarly, the sensitivity coefficient (α*i ) obtained from the most likely failure point (x*i = -α*i β) in the space of reduced variables is given by Equation (15) [2].

the safety factors of the variables corresponding to β. It is supposed that the safety factor γ1 corresponds to 𝜙 calculated according to probabilistic theory. Then, the factors obtained from probabilistic calculations are compared with the values recommended in ACI 318-19. In ACI 318-19, 𝜙 is proposed as 0.75 for axially loaded spiral reinforced concrete columns, 0.65 for other axially-loaded reinforced concrete columns and 0.60 for axially-loaded unreinforced columns. As mentioned in previous sections, the value of the 𝜙 also varies depending on the β. In the literature, β is proposed as 3.5 by Zou and Hong [6], Alqam et al. [7], and Zhou et al. [8]. Mirza [9] suggested the β between 3.0-3.5 in his study on transversely reinforced concrete columns. The β can be considered as a function of the failure probability pF as follows: (19) where Φ-1 is the inverse of the cumulative distribution function. In this study, β taken into account in determining of the 𝜙 is considered as 3.5, and the failure probability corresponding to this value is calculated as pF = 2.33×10-4. Making necessary arrangements in Equation (3), the performance functions were obtained by Equations (20)-(23). For FRP-confined reinforced concrete circular column is as given below: (20)

In Equation 14, the original variables x*i are expressed by the following equation:

For FRP-confined unreinforced circular column is as given below:

(16) By writing Equation 16 instead of x*i in Equation 14, the γi safety factors are; (17) If the distributions of variables that constitute the performance function are not normal or the structure of the performance function is non-linear, iteration is required to reveal x*i. In the case of the lognormal or Type-I asymptotic distributions, these distributions are transformed to equivalent normal distributions [2,5]. Performance Functions The performance function for axially loaded columns is calculated with the following equation; (18) In this study, Pu and Pn represent the axial compressive strengths obtained from the experimental data and equation proposed in ACI 440.2R, respectively. γ1 and γ2 are

(21) For FRP-confined reinforced rectangular column is as given below:

For FRP-confined unreinforced rectangular column is as given below: (23) Coefficients of Variation and Distribution Types of Variables All experimental parameters regarding the CFRPconfined column specimens were modeled as random variables in order to provide a probabilistic analysis. The

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statistical parameters of variables to determine the strength reduction factor were investigated in accordance with the studies available by reviewing the literature and codes. TheVfc´ was taken between 0.1 and 0.2 through the literature depending on the concrete grade. The Vfc´ was suggested 0.11 by Hao et al.[10], 0.16 by Ali [11], 0.12 by Jafari [12], 0.13 by Val et al. [13], 0.15 by Atadero and Karbhari [14], 0.18 by Hong and Zhou [15], 0.2 by Monti and Santini [16], 0.18 by Taki et al. [17], 0.18 by Wieghaus and Atadero [18], 0.18 by Okeil et al. [19], and 0.15 by Ghobarah et al. [20]. In this study, it is used 0.10, 0.12 and 0.15 for Vfc´. The Vfy varies between 0.04 and 0.15. The Vfy was proposed as 0.1 by Ali [11], 0.1 by Jafari [12], 0.1 by Val et al. [13], 0.098 by Hong and Zhou [15], 0.15 by Monti and Santini [16], 0.04 by Kim et al. [21], 0.11 by Ellingwood [22], 0.125 by Taki et al. [17], 0.093 by Wieghaus ve Atadero [18], 0.125 by Okeil et al. [19], 0.05 by Huang et al. [23], 0.098 by Stewart and Attard [24], 0.93-0.107 by Ghobarah et al. [20], and 0.05 by Mestrovic et al. [25]. In this study, it is used 0.10 for Vfy.

The VEf varies between 0.04 and 0.15. The VEf is proposed as 0.2 by Atadero and Karbhari [14], 0.15 by Taki et al. [17] and 0.1 by Wieghaus and Atadero [18]. In this study, it is used 0.10, 0.15 and 0.20 for VEf. The Vε*fu was proposed as 0.022 in literature. The value of Vε*fu was taken 0.2 by Taki et al. [17] and Okeil et al. [19]. In this study, it is used 0.022 for Vε*fu. The Vtf varies between 0.05 and 0.07. The Vtf is proposed as 0.07 by Hao et al. [10], 0.05 by Ali [11], 0.05 by Atadero and Karbhari [14], 010 by Taki et al. [17] and 0.05 by Wieghaus and Atadero [18]. In this study, it is used 0.05 and 0.07 for Vtf . The coefficients of variation of VD, Vb, Vh and Vrc vary between 0.01 and 0.05. The VD is proposed as 0.03 by Hao et al. [10], Wieghaus and Atadero [18] and Okeil et al. [19] and 0.02 by Ghobarah et al. [20]. In this study, it is used 0.03 for the coefficient of variation of VD, Vb, Vh and Vrc. The Vρg was proposed as 0.01 by Hao et al. [10]. Therefore, it is used 0.01 for Vρg in this study. Besides, the probability distribution types of the variables that constitutive the performance function are one of the important factor in the probability theory to determine

Table 1. Coefficients of variation and distribution types of variables Cases

0.05 0.07 0.05 0.07 0.05 0.07 0.05 0.07 0.05 0.07 0.05 0.07 0.05 0.07 0.05 0.07 0.05 0.07 0.05 0.07 0.05 0.07 0.05 0.07 ND*

DT*:Distribution Type, LD*:Lognormal Distribution, ND*:Normal Distribution, T-I AD*: Type I Asymptotic Distribution

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the strength reduction factors. In this regard, according to international statistics, normal distribution for variables such as cross section, proportional expressions, area and perimeter; normal or preferably lognormal distribution for material strength, modulus of elasticity; normal distribution for time-invariant loads; Type-I asymptotic distribution for time varying loads; Type-I or Type-II asymptotic distribution for wind and earthquake loads; For snow loads, Type-I asymptotic or Weibull distributions are used [2]. The distributions of the f´c, fy and Ef variables are considered as log-normal in this study. Normal distribution is used for tf, ρg, D, b, h and rc. Type-I asymtotic distribution is used for the ε*fu and Pu. Table 1 represents the coefficient of variation and distribution type for each variable considered in the present study.

longitudinal reinforcement. 36 specimens are HSC, and the remaining 128 specimens are NSC. CFRP tube was used in 23 of the specimens and the in the remaining 141 specimens was used CFRP jacket. The mechanical and geometrical properties of the circular test specimens are given in Table 2. Moreover, Figure 4 shows frequency distributions of the input variables for circular test specimens.

Experimental Database

In this study, an extensive database of 298 column test specimens of circular and rectangular cross-section, with/ without longitudinal and transverse reinforcement collected from 18 different experimental studies in the literature is taken into account to determine the strength reduction factors. All database includes specimens subjected to monotonic load. Besides, specimens with partial CFRP confinement were not taken into account. The properties of the column test specimens in collected database are given in the following sections. Test Specimens with Circular Cross-section A total of 21 column specimens, collected from 4 different studies, were examined in the group of circular cross-sectional columns CFRP-confined with longitudinal reinforcement. One of specimens in the database is highstrength concrete (HSC), and the remaining 20 specimens are normal-strength concrete (NSC). CFRP jacket was applied in all test specimens. A total of 164 column specimens obtained from 8 different studies are examined in the group of circular columns CFRP-confined without

Test Specimens with Rectangular Cross-section A total of 41 column specimens obtained from 5 different studies were examined in the rectangular cross-sectional column group with longitudinal reinforcement. 3 specimens are HSC, the remaining 38 specimens are NSC. CFRP jacket was applied in all specimens. A total of 72 specimens CFRP-confined obtained from 5 different studies were examined in the rectangular cross-sectional column group without longitudinal reinforcement. 15 of them are HSC and the remaining 57 specimens are NSC. 3 of the test specimens were confined by CFRP tube, the remaining 69 specimens were confined with CFRP jacket. The mechanical and geometrical properties of the rectangular test specimens are summarized in Table 3. Figure 5 shows frequency distributions of the input variables for rectangular test specimens.

Examination Of Strength Reduction Factors

FRP-confined Circular Columns As a result of the probabilistic calculations, it is shown that the (𝜙=0.65) for transversely reinforced columns in ACI 318-19 corresponds to the case “23” (Vfc´ = 0.18, Vtf = 0.05, VEf = 0.20, Vε*fu = 0.022,VD = 0.03, Vρg = 0.010, Vfy = 0.10) for the (β=3.5). The strength reduction factors 𝜙 for each case shown in Table 4a were the means of the values obtained from 21 test data. The reduction factors ranged from 0.607~0.721, and in approximately 62% of the specimens, the reduction factors are lower than the (𝜙=0.65)

Table 2. Mechanical and geometrical properties of the circular test specimens Reference

Nsc-Hsc

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Figure 4. Frequency distributions of the input variables for circular test specimens.

Table 3. Mechanical and geometrical properties of the rectangular test specimens Reference

Nsc-Hsc

value proposed in ACI 318-19 while approximately 38% of the specimens meet the regulations. The value of (𝜙=0.60) proposed for unreinforced/plane columns in ACI 318-19 corresponds to the case “24” (Vfc´ = 0.18, Vtf = 0.05, VEf = 0.20, Vε*fu = 0.022,VD = 0.03, Vρg = 0.010, Vfy = 0.10) for the (β=3.5) as seen in Table 4b. The mean values of the 𝜙 obtained from 164 test data for each case are shown in Table 4b. The reduction factors 𝜙 ranged from 0.596~0.693, and in approximately 46% of the specimens, the values of 𝜙 are lower than the proposed value (𝜙=0.60) in ACI 318-19 while approximately 54% of the specimens meet the regulations [44].

As seen in Table 4, assuming that the coefficients of variation of other variables remain constant, the 𝜙 decreases with the increase of the variation coefficients of the f´c, Ef and tf for the reinforced and unreinforced column specimens. It is seen that the effect of the uncertainty in the concrete strength on 𝜙 for the examined column specimens is higher than those of the other variables. In Figure 6, the variations of the strength reduction factors for 24 different cases have also shown for the reinforced and unreinforced circular test specimens, respectively. According to this distributions, as the coefficients of variation of the variables increase, the strength reduction factors decrease. Namely, the increase in the uncertainty in

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Figure 5. Frequency distributions of the input variables for rectangular test specimens. the structure of the variables causes a decrease in the axial load carrying capacity of the column [44]. In Figure 6a, it is seen that the mean values of the 𝜙 for the reinforced column specimens examined in this study are greater than the value

recommended in ACI 318-19 (𝜙=0.65) for all cases except the 24rd case. As seen in Figure 6b, the mean values of the 𝜙 for the unreinforced column specimens are greater than the value recommended in ACI 318-19 (𝜙=0.60) for all cases.

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Table 4. Strength reduction factors for reinforced and unreinforced circular test specimens

Case 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Case 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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Figure 6. Distributions of strength reduction factor of reinforced and unreinforced circular test specimens [44].

Figure 7. Strength reduction factors versus variables of the reinforced circular columns for case “23” and the target reliability index (β=3.5) [44]. Figures 7 and 8 also present the variations of the strength reduction factors for reinforced and unreinforced columns versus variables constituting the performance function, respectively. When the figures are examined, it could not be

concluded that the increment in the values of the variables increases or decreases the strength reduction factor, due to the limited number of column test specimens examined within the scope of the study.

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Figure 8. Strength reduction factors versus variables of the unreinforced circular columns for case “24” and the target reliability index (β=3.5) [44].

Figure 9. Comparison of the strength reduction factors of NSC-HSC and CFRP-jacket and CFRP-tube unreinforced circular column specimens for all cases [44].

36 high-strength concrete (HSC) ( ) and 128 normal-strength concrete (NSC) ( ) specimens are considered in this study. The values of the 𝜙 obtained by taking this distinction into account are compared in Figure 9a. As seen, for all cases, the mean strength reduction factors of the NSC specimens were greater than those of HSC. Also, 141 CFRP-jacket and 23 CFRP-tube confined column specimens are considered. Figure 9b shows that the value 𝜙 of the specimens confined by CFRP-jacket were greater than those of CFRP-tube columns for all cases.

FRP-confined Rectangular Columns As seen in Table 5a, (𝜙=0.65) proposed for transversely reinforced rectangular columns in ACI 318-19 corresponds to the case “23” for the (β=3.5). The means of the strength reduction factors 𝜙 ​​obtained from 41 test data have shown in Table 5a. The strength reduction factors ranged from 0.624~0.739, and in approximately 63% of the specimens, the 𝜙 is lower than (𝜙=0.65) recommended in ACI 31819 while approximately 37% of the specimens meet the regulations.

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Table 5. Average strength reduction factors for reinforced and unreinforced rectangular test specimens

Case 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Case 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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proposed for unreinforced columns in ACI 318-19 corresponds to the case “20” for (β=3.5) as seen in Table 5b. The strength reduction factors 𝜙 for each case were obtained ​​ from the 72 test data and ranged from 0.560~0.636, and in approximately 33% of the specimens, the reduction factor is lower than the (𝜙=0.60) recommended in ACI 318-19

while approximately 67% of the specimens meet the regulations [44]. As seen in Figure 10a, the mean values of the 𝜙 for the reinforced column specimens examined in this study are greater than the proposed value (𝜙=0.65) in ACI 318-19 for all cases except the 24th case. In Figure 10b, it is seen that the mean values of 𝜙 for the plain column specimens are

Figure 10. Distributions of strength reduction factors for rectangular test specimens [44].

Figure 11. Strength reduction factors versus variables of the reinforced rectangular columns for case “23” and the target reliability index (β=3.5) [44].

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Figure 12. Strength reduction factors versus variables of the unreinforced rectangular columns for case “20” and the target reliability index (β=3.5) [44].

Figure 13. Comparison of the strength reduction factors for NSC and HSC unreinforced rectangular column specimens [44].

Figure 14. Comparison of the mean strength reduction factors for all column specimens [44].

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greater than the proposed value (𝜙=0.60) in ACI 318-19 for all cases except the 21th, 22th, 23rd and 24th case. As Figures 11 and 12 are examined, it could not be concluded that the increase in the values of the variables in rectangular columns, similar to the circular columns, increases or decreases the strength reduction factor. Figure 13 shows a comparison of strength reduction factors for NSC and HSC unreinforced rectangular column specimens. As seen in Figure 13, the mean strength reduction factors 𝜙 of the NSC specimens were greater than those of HSC specimens except in cases 5 and 6. The differences between NSC and HSC columns for cases 5 and 6 are about 0.002. In Figure 14, the mean 𝜙 values for the different columns examined in this study are compared. From the examination of the Figure 14, it is seen that 𝜙 values for FRP-confined unreinforced columns are lower than those of FRP-confined reinforced columns for all cases. In circular and rectangular cross-section columns with longitudinal reinforcement, the 𝜙 is obtained higher than the unreinforced columns, since the effect of longitudinal reinforcement increases the axial capacity of the column. The figure shows the comparison of the calculated mean 𝜙 values for the different columns examined in the study.

Conclusion

This study evaluates the strength reduction factors 𝜙 to provide the target reliability index (β=3.5) of the CFRPconfined circular and rectangular columns under axial compression load. These factors were determined by probabilistic methods for 298 column specimens collected from the literature, according to 24 different coefficients of variation of the variables. Then, obtained factors were compared with ACI 318-19 ones. To provide (β=3.5), the extreme values of coefficients of variation were investigated. The following conclusions can be obtained from the current study: • In all columns, the strength reduction factors are inversely proportional to the coefficients of variation of the variables constitute the performance function. The strength reduction factors are decrease with the increase of the coefficients of variation of the variables. Namely, an increase in the coefficient of variation causes a decrease in the reliability of the column. • Since the effect of reinforcement increases the axial load capacity, the strength reduction factors (𝜙) in the reinforced columns are higher than the coefficients in the unreinforced columns. • In all column specimens, it is observed that the effect on 𝜙 of the uncertainty in the compressive strength of the concrete (Vfc´ ) is the highest compared to other variables. • The strength reduction factors (𝜙) of the (NSC) specimens were obtained higher than those of (HSC) specimens for circular columns. Similarly, the strength reduction factors (𝜙) of the (NSC) specimens for

rectangular columns were found to be higher except for cases 5 and 6. It can be interpreted that since the (HSC) specimens are more brittle materials compared with (NSC), the reduction factors of the (HSC) specimens were obtained smaller than (NSC) ones. However, further research should be conducted to verify the results due to the limited number of test specimens for (HSC) columns. The sensitivity of the results obtained in a probabilistic study is closely related to the adequacy of the database considered in the research. The above-obtained results are only valid for the specimens collected from the literature. For this reason, it is necessary to examine more specimens with different materials and qualities to determine the strength reduction factors more sensitively.

Nomenclature

Ac Cross-sectional area of column (mm2) Ae Effective confinement area Ae (mm2) Ag Gross area of concrete section (mm2) Ast Total area of longitudinal reinforcement (mm2) b Cross-sectional short side dimension of column (mm) CE Environmental reduction factor D Diameter of circular section or diagonal distance of the rectangular section equal to (mm) Ef Modulus of elasticity of FRP reinforcement (MPa) f´c Compressive strength of unconfined concrete (MPa) f´cc Compressive strength of FRP-confined concrete (MPa) fl Maximum confinement pressure of FRP jacket (MPa) Yield strength of longitudinal reinforcement fy (MPa) g(x) Performance function h Cross-sectional long side dimension of column (mm) L Height of compression member (mm) mi Mean value of random variable mNxi Mean value for equivalent normal distribution of xi n Number of plies of FRP reinforcement pF Failure probability Pn Nominal axial compressive strength (kN) Pu Ultimate axial compressive strength (kN) rc Radius of edges of a prismatic cross section confined with FRP (mm) tf Nominal thickness of one ply of FRP reinforcement (mm) Vi Coefficient of variation of random variable xi Random variable Most probable failure point x*i

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Greek symbols α Sensitivity coefficient β Reliability index εccu Ultimate axial strain of confined concrete εfe Effective strain in FRP reinforcement attained at failure ε*fu Ultimate rupture strain of FRP reinforcement εfu Design rupture strain of FRP reinforcement 𝜙 Strength reduction factor γ Safety factor κa Shape factor Efficiency factor for FRP reinforcement in deterκb mination of εccu κε Strain efficiency factor ρg Longitudinal reinforcement ratio σi Standard deviation of random variable σ xi

Standard deviation for equivalent normal distribution of xi Ψf Additional reduction factor

Data Availability Statement

The authors confirm that the data that supports the findings of this study are available within the article. Raw data that support the finding of this study are available from the corresponding author, upon reasonable request

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript

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