CC BY
3Magazine of Civil Engineering. 2024. 17(2). Article No. 12603
Magazine of Civil Engineering issn
2712-8172
journal homepage: http://engstroy.spbstu.ru/
Research article UDC 69.04
DOI: 10.34910/MCE.126.3
Validating the predicted axial strength of FRP-reinforced concrete circular columns
M.Q. Kadhim B , H.F. Hassan
College of Engineering, Mustansiriyah University, Baghdad, Iraq Mmohamedq1992@uomustansiriyah.edu.iq
Keywords: fiber reinforced polymers, axial load, circular columns, spirals, hoops, experimental load
Abstract. Over the last three decades, researchers have significantly contributed to advancing fiber-reinforced polymer (FRP) bars to address corrosion issues in conventional steel reinforcement bars embedded in components of reinforced concrete structures. This research aimed to establish an ideal allowable axial compression load for concrete columns reinforced with FRP using data from previous studies. This article compares and explains the contrasts of several of the most popular FRP codes (ACI, CSA, and JSCE) with one equation proposed in previous research using empirical information gleaned from the literature review. The models' statistical analysis compares theoretical and practical loads, Young's modulus, concrete strength, longitudinal reinforcement ratio, and transverse reinforcement ratio for hoops and spirals. Estimating the effect of FRP longitudinal bars on the applied load carried by FRP-reinforced concrete columns can be done with the help of an empirical equation that uses the compressive strength of concrete to estimate the axial stress of FRP longitudinal bars in concrete columns. Results from the CSA and the ACI were almost similar, and both were superior to those from the JSCE in terms of being ideal, consistent, and safe. The results for modulus of elasticity, concrete compressive strength, and transverse reinforcement ratio for spiral reinforcement were more stable, according to the CSA. In contrast, according to the ACI, results for longitudinal and transverse reinforcement ratios of hoop reinforcement were more stable and secure. Lastly, the previously proposed equation is the best way to determine the transverse reinforcement ratio for hoop reinforcement and the compressive strength of concrete from all codes. In conclusion, the previously proposed equation is the most effective for calculating the transverse reinforcement ratio for hoop reinforcement and compressive strength.
Citation: Kadhim, M.Q., Hassan, H.F. Validating the predicted axial strength of FRP-reinforced concrete circular columns. Magazine of Civil Engineering. 2024. 17(2). Article no. 10.34910/MCE.126.3. DOI: 10.34910/MCE.126.3
1. Introduction
The primary function of a reinforced concrete column is to sustain axial loads with or without bending moments. Due to the corrosion of steel bars, the axial load-carrying capacity of steel bar-reinforced concrete columns decreases over the concrete structures' service life, especially in coastal regions or harsh environments. The cost of rehabilitating and repairing deteriorated concrete structures is significantly high [1]. The literature review found that FRP composites can be used in various civil/structural applications. The FRP composites have various structural forms that can be classified into two main classes: 1) external reinforcement (FRP jacketing) and 2) internal reinforcement (FRP reinforcing bars). There are four common varieties of FRP: aramid (AFRP), basalt (BFRP), glass (GFRP), and carbon (CFRP) fibers, all encased in the polymer [2, 3]. FRP composites, including FRP bars, possess many advantageous characteristics, such as resistance to harsh environmental conditions, lightweight, and high tensile strength [4, 5]. Hence, FRP bars have the potential to replace steel bars and overcome the deterioration of concrete structures associated with the corrosion of steel reinforcement. However, using FRP bars as reinforcement in
© Kadhim, M.Q., Hassan, H.F. 2024. Published by Peter the Great St. Petersburg Polytechnic University.
compression members is still not recommended. This is because the FRP bar's ultimate compressive strength is considerably lower than its ultimate tensile strength [6]. De Luca et al. [7] investigated five square concrete columns subjected to axial load. They concluded that GFRP bars could be used in columns, but their contribution could be ignored when calculating nominal capacity. Moreover, they found that GFRP hoops did not grow longitudinal bars' ultimate capacity but reduced their bend. Kobayashi and Fujisaki [8] conducted experiments with bars made of AFRP, CFRP, and GFRP. The compressive strengths of CFRP, AFRP, and GFRP reinforcement bars were 30-50 %, 10 %, and 30-40 % of their tensile strength, respectively. Deitz et al. [9] conducted compression tests on 45 GFRP bars (15-mm diameter with unbraced lengths varying from 50 to 380 mm). Based on the experiments' outcomes, the average ultimate compressive strength was nearly 50% of the average ultimate tensile strength. However, the compression modulus was about the same as that of tension. Alsayed et al. [10] tested fifteen 450*250*1200 mm concrete columns under concentric axial loads to determine the effect of replacing longitudinal and transverse steel reinforcing bars with an equivalent amount of GFRP reinforcement. GFRP reinforcing bars reduced column axial capacity by 13 %. GFRP hoops reduced axial capacity by 10%, regardless of the longitudinal bar type. Up to 80% of the column's ultimate capacity, replacing steel hoops with GFRP hoops did not affect load deformation. Tobbi et al. [11] and Afifi et al. [12] reported that GFRP and CFRP longitudinal bars can contribute up to 10% and 13%, respectively, to the axial load-carrying capacity of the concrete columns. Hadhood et al. [13] conducted an experimental investigation on the concentric and eccentric behavior of full-scale circular high-strength concrete (HSC) columns reinforced with GFRP bars and spirals. A total of 10 columns were tested under monotonic loading with different eccentricities. The test variables were the eccentricity-to-diameter ratio and the longitudinal-reinforcement ratio. Compression failure in the concrete controlled the ultimate capacity of specimens tested under small eccentric loads. However, a flexural-tension failure initiated in specimens tested under high eccentric loading resulted from excessive axial and lateral deformations and cracks on the tension side until a secondary compression and stability failure occurred due to the concrete's strain limitations. Longitudinal GFRP bars contributed about 5% of the axial load capacity of GFRP-HSC columns. Hadi et al. [14] conducted a study on the use of GFRP bars in HSC. It was observed that the GFRP bar-reinforced HSC specimens sustained a similar axial load under concentric axial compression compared to their steel counterparts, but the efficiency of GFRP bar-reinforced HSC specimens in sustaining axial loads decreased with an increase in the axial load eccentricity. Direct replacement of steel reinforcement with the same amount of GFRP reinforcement in HSC specimens resulted in about 30% less ductility under a concentric axial load. In CAN/CSA S806-12 [15] or ACI 440.1R-15 [16], no theoretical equation was proposed to predict the maximum axial load capacity of FRP bar-reinforced concrete columns. This is because of the variances in the reported ultimate compressive strength of the FRP bars and their contribution as longitudinal reinforcement in concrete columns. However, previous research gave many theoretical equations for predicting the maximum axial loads that FRP bar-reinforced concrete columns could carry. The issue of utilizing FRP as a substitute for traditional reinforcing steel in compression members has yet to be evaluated through available equations and whether these equations can be used for design purposes. As we mentioned, there are available equations, but they have yet to be evaluated through many models. Thus, in this research, we will evaluate the most prominent four equations to determine the validity of their use for design purposes based on a wide range of experimental data collected from previous studies. This statistical analysis predicted the maximum axial load capacity of concrete columns reinforced longitudinally with FRP bars and studied other factors based on many codes and one significant suggested equation from earlier studies.
Table 1. Experimental data of FRP bar reinforced concrete columns taken from available previous research studies.
The Specimen cross-section FRP longitudinal reinforcement FRP transverse reinforcement fc (MPa)
No. specimen reference Specimen Column shape Diamete rs (mm) Type Pfl (%) ffu (MPa) Ef (MPa) Type Pft (%)
1 Pantelides #13GLCT L Circular 254 GFRP bars 1.60 740 43300 GFRP spirals 1.70 36
2 et al. [17] #14GLCT L Circular 254 GFRP bars 1.60 740 43300 GFRP spirals 1.70 36
3 C6V-3H80 Circular 300 CFRP bars 1.00 1899 140000 CFRP spirals 1.50 42.90
4 C10V-3H80 Circular 300 CFRP bars 1.70 1899 140000 CFRP spirals 1.50 42.90
5 Afifi et al. [12] C14V-3H80 Circular 300 CFRP bars 2.40 1899 140000 CFRP spirals 1.50 42.90
6 C10V-2H80 Circular 300 CFRP bars 1.70 1899 140000 CFRP spirals 0.70 42.90
7 C10V-4H80 Circular 300 CFRP bars 1.70 1899 140000 CFRP spirals 2.70 42.90
Specimen cross-section
FRP longitudinal reinforcement
FRP transverse reinforcement
No. specimen reference Specimen Column shape Diamete rs Type Pfl ffu Ef Type Pft J (MPa)
(mm) (%) (MPa) (MPa) (%)
8 C10V-3H40 Circular 300 CFRP bars 1.70 1899 140000 CFRP spirals 3.00 42.90
9 C10V-3H120 Circular 300 CFRP bars 1.70 1899 140000 CFRP spirals 1.00 42.90
10 C10V-2H35 Circular 300 CFRP bars 1.70 1899 140000 CFRP spirals 1.50 42.90
11 C10V-4H145 Circular 300 CFRP bars 1.70 1899 140000 CFRP spirals 1.50 42.90
12 G8V-3H80 Circular 300 GFRP bars 2.20 934 55400 GFRP spirals 1.50 42.90
13 G4V-3H80 Circular 300 GFRP bars 1.10 934 55400 GFRP spirals 1.50 42.90
14 G12V-3H80 Circular 300 GFRP bars 3.20 934 55400 GFRP spirals 1.50 42.90
15 G8V-2H80 Circular 300 GFRP bars 2.20 934 55400 GFRP spirals 0.70 42.90
16 Afifi et al. [18] G8V-4H80 Circular 300 GFRP bars 2.20 934 55400 GFRP spirals 2.70 42.90
17 G8V-3H40 Circular 300 GFRP bars 2.20 934 55400 GFRP spirals 3.00 42.90
18 G8V-3H120 Circular 300 GFRP bars 2.20 934 55400 GFRP spirals 1.00 42.90
19 G8V-2H35 Circular 300 GFRP bars 2.20 934 55400 GFRP spirals 1.50 42.90
20 G8V-4H145 Circular 300 GFRP bars 2.20 934 55400 GFRP spirals 1.50 42.90
21 G2S Circular 300 GFRP bars 2.24 934 55400 GFRP spirals 0.70 42.90
22 G3S Circular 300 GFRP bars 2.24 934 55400 GFRP spirals 1.50 42.90
23 G4S Circular 300 GFRP bars 2.24 934 55400 GFRP spirals 2.70 42.90
24 G3H200 Circular 300 GFRP bars 2.24 934 55400 GFRP hoops 1.50 42.90
25 G3H400 Circular 300 GFRP bars 2.24 934 55400 GFRP hoops 1.50 42.90
26 Mohamed G3H600 Circular 300 GFRP bars 2.24 934 55400 GFRP hoops 1.50 42.90
27 et al. [19] C2S Circular 300 CFRP bars 1.79 1899 140000 CFRP spirals 0.70 42.90
28 C3S Circular 300 CFRP bars 1.79 1899 140000 CFRP spirals 1.50 42.90
29 C4S Circular 300 CFRP bars 1.79 1899 140000 CFRP spirals 2.70 42.90
30 C3H200 Circular 300 CFRP bars 1.79 1899 140000 CFRP hoops 1.50 42.90
31 C3H400 Circular 300 CFRP bars 1.79 1899 140000 CFRP hoops 1.50 42.90
32 C3H600 Circular 300 CFRP bars 1.79 1899 140000 CFRP hoops 1.50 42.90
33 G6-G60 Circular 205 GFRP bars 2.30 1600 66000 GFRP spirals 2.97 37
34 Karim et al. G6-G30 Circular 205 GFRP bars 2.30 1600 66000 GFRP spirals 5.94 37
35 [20] 00-G60 Circular 205 - 0.00 0.00 0.00 GFRP spirals 2.97 37
36 00-G30 Circular 205 - 0.00 0.00 0.00 GFRP spirals 5.94 37
37 C-8-00 Circular 250 GFRP bars 2.43 1184 62600 - - 38
38 GGC-8-H50 Circular 250 GFRP bars 2.43 1184 62600 GFRP hoops 3.13 38
39 Maranan et al. [21] GGC-8-H100 Circular 250 GFRP bars 2.43 1184 62600 GFRP hoops 1.57 38
40 GGC-8-H200 Circular 250 GFRP bars 2.43 1184 62600 GFRP hoops 0.78 38
41 GGC-8-S50 Circular 250 GFRP bars 2.43 1184 62600 GFRP spirals 3.13 38
Specimen cross-section
FRP longitudinal reinforcement
FRP transverse reinforcement
No. specimen reference Specimen Column shape Diamete rs Type Pfl ffu Ef Type Pft J (MPa)
(mm) (%) (MPa) (MPa) (%)
42 GGC-8-S100 Circular 250 GFRP bars 2.43 1184 62600 GFRP spirals 1.57 38
43 GGC-16-H100 Circular 250 GFRP bars 2.43 1184 62600 GFRP hoops 1.57 38
44 GGC-16-S100 Circular 250 GFRP bars 2.43 1184 62600 GFRP spirals 1.57 38
45 Hadi et al. G60E0 Circular 210 GFRP bars 2.19 1190 52000 GFRP spirals 2.94 85
46 [14] G30E0 Circular 210 GFRP bars 2.19 1190 52000 GFRP spirals 5.88 85
47 Hadhood et C1-I Circular 305 GFRP bars 2.18 1289 54900 GFRP spirals 1.44 35
48 al. [22] C1-II Circular 305 GFRP bars 3.27 1289 54900 GFRP spirals 1.44 35
49 C1 Circular 305 GFRP bars 2.19 1449 61800 GFRP spirals 1.17 46.60
50 C2 Circular 305 GFRP bars 2.19 1449 61800 GFRP spirals 1.17 46.60
51 Abdelazim et al. [23] C3 Circular 305 GFRP bars 2.19 1449 61800 GFRP spirals 1.17 46.60
52 C4 Circular 305 GFRP bars 2.19 1449 61800 GFRP spirals 1.17 46.60
53 C5 Circular 305 GFRP bars 2.19 1449 61800 GFRP spirals 1.17 46.60
54 GH75-C Circular 250 GFRP bars 1.57 794 50000 GFRP hoops 1.42 37.66
55 Raza et al. GH150-C Circular 250 GFRP bars 1.57 794 50000 GFRP hoops 0.71 37.66
56 [24] GS38-C Circular 250 GFRP bars 1.57 794 50000 GFRP spirals 2.84 37.66
57 GS75-C Circular 250 GFRP bars 1.57 794 50000 GFRP spirals 1.42 37.66
58 G1 (6G12-G75) Circular 230 GFRP bars 1.63 1113 62300 GFRP spirals 2.20 25.40
59 G6 (6G12-G75) Circular 230 GFRP bars 1.63 1250 61400 GFRP spirals 2.20 25.40
60 El-Gamal and G2 (8G12-G75) Circular 230 GFRP bars 2.17 1113 62300 GFRP spirals 2.20 25.40
61 Alshareeda h [25] G3 (8G16-G75) Circular 230 GFRP bars 3.87 1102 61200 GFRP spirals 2.20 25.40
62 G4 (6G12-G100) Circular 230 GFRP bars 1.63 1113 62300 GFRP spirals 1.65 25.40
63 G5 (6G12-G50) Circular 230 GFRP bars 1.63 1113 62300 GFRP spirals 3.30 25.40
64 G3-120-C Circular 215 GFRP bars 0.55 930 59000 GFRP spirals 0.94 34
65 G4-120-C Circular 215 GFRP bars 0.73 930 59000 GFRP spirals 0.94 34
66 Elchalakani et al. [26] G5-120-C Circular 215 GFRP bars 0.92 930 59000 GFRP spirals 0.94 34
67 G4-40-C Circular 215 GFRP bars 0.73 930 59000 GFRP spirals 2.75 34
68 G4-80-C Circular 215 GFRP bars 0.73 930 59000 GFRP spirals 1.39 34
69 GCP-80S Circular 304 GFRP bars 2.18 1389 52500 GFRP spirals 1.50 40
70 GCP-80S-22 Circular 304 GFRP bars 2.18 1389 52500 GFRP spirals 1.50 40
71 GCP-80S-60 Circular 304 GFRP bars 2.18 1389 52500 GFRP spirals 1.50 40
72 Elhamaymy et al. [27] GCP-40S Circular 304 GFRP bars 2.18 1389 52500 GFRP spirals 3.00 40
73 GCP-40S-22 Circular 304 GFRP bars 2.18 1389 52500 GFRP spirals 3.00 40
74 GCP-40S-60 Circular 304 GFRP bars 2.18 1389 52500 GFRP spirals 3.00 40
75 GCP-120S Circular 304 GFRP bars 2.18 1389 52500 GFRP spirals 1.00 40
Specimen cross-section
FRP longitudinal reinforcement
FRP transverse reinforcement
No. specimen reference Specimen Column shape Diamete rs Type Pfl ffu Ef Type Pft J (MPa)
(mm) (%) (MPa) (MPa) (%)
76 GCP-120S-22 Circular 304 GFRP bars 2.18 1389 52500 GFRP spirals 1.00 40
77 GCP-120S-60 Circular 304 GFRP bars 2.18 1389 52500 GFRP spirals 1.00 40
78 GCP-8O-O Circular 304 GFRP bars 2.18 1389 52500 GFRP hoops 1.50 40
79 GCP-80-O-22 Circular 304 GFRP bars 2.18 1389 52500 GFRP hoops 1.50 40
80 GCP-80-0-60 Circular 304 GFRP bars 2.18 1389 52500 GFRP hoops 1.50 40
81 Bakouregui G-8-0 Circular 305 GFRP bars 2.20 1289 54900 GFRP spirals 1.44 52
82 et al. [28] B-8-0 Circular 305 BFRP bars 2.20 1724 64800 GFRP spirals 1.44 52
83 SC-6G-80 Circular 305 GFRP bars 1.63 1289 54900 GFRP spirals 0.95 34.70
84 Gouda et al. [29] SC-8G-80 Circular 305 GFRP bars 2.18 1289 54900 GFRP spirals 0.95 34.70
85 SC-12G-80 Circular 305 GFRP bars 3.27 1289 54900 GFRP spirals 0.95 34.70
86 fh-f-2 Circular 150 BFRP bars 5.50 1100 50000 BFRP spirals 7.30 65
87 fh-f-4 Circular 150 BFRP bars 5.50 1100 50000 BFRP spirals 3.70 53
88 Tang et al. fh-f-8 Circular 150 BFRP bars 5.50 1100 50000 BFRP spirals 1.80 42
89 [30] fl-f-2 Circular 150 BFRP bars 3.10 1250 50000 BFRP spirals 7.30 55
90 fl-f-4 Circular 150 BFRP bars 3.10 1250 50000 BFRP spirals 3.70 43
91 fl-f-8 Circular 150 BFRP bars 3.10 1250 50000 BFRP spirals 1.80 35
ffu is the ultimate tensile strength of FRP bars. Ef is the modulus of elasticity of FRP bars. f'c is the compressive strength of the concrete.
2. Methods
A collection of 91 FRP RC columns that failed under axial compression was made to study their behavior in axial compression and evaluate the design codes and previously proposed equation [12, 14, 17-30]. Specimens had long and short columns. Data from many studies were clearly reported. However, other calculations used individual parameters to determine parameter values separately. The column results were unaffected. The compression design parameters are summarized in Table 2. The column diameter D was 150-305 mm. Diameter cores Dc range from 104 to 237.2 mm. Column lengths L varied
from 300 mm to 2,500 mm. During the test day, the concrete cylinder strength, f'c, was between 25.4 and
85 MPa. The gross area, Ag was found to be in the range from 17671.46 to 73061.66 mm2 where it was
reported. The longitudinal reinforcement ratio (pft = nx AblAg), where n is the number of longitudinal
reinforcements, Ab is the area of the FRP bar, and Ag is the gross sectional area, was between 0.00 and
5.5 %. The transverse reinforcement ratio (pft = 4 x Aft jDc x s), where A^ is the area of the FRP bar
of transverse reinforcement, Dc is the diameter of the core, and s is the spacing between hoops of reinforcement or the pitch of the spiral reinforcement) ranged from 0.00 to 7.3 %. The longitudinal reinforcement's elasticity modulus, Eft, varied from 0 to 140 GPa. The transverse reinforcement's
elasticity modulus, Eft, varied from 0 to 140 GPa. The longitudinal reinforcement's tensile strength, ffui,
wide-ranging 0 toward 1,899 MPa. Also, the transverse reinforcement's tensile strength is a wide range, fjul, varied from 0 toward 1,899 MPa.
Table 2. Compression design parameters for columns used in the database.
Database
Number of columns -
91
Properties Min Max SD Avg COV (%)
D (mm) 150.00 305.00 46.65 268.25 17.39
Dc (mm) 104.00 237.20 40.21 203.69 19.74
Ag (mm2) 17671.46 73061.66 17790.53 58207.06 30.56
R(mm) 75.00 152.50 23.32 134.13 17.39
L(mm) 300.00 2500.00 403.79 1245.85 32.41
L/R 4.00 16.39 2.55 9.16 27.86
Pft (%) 0.00 5.50 0.89 2.12 41.85
fful (MPa) 0.00 1899.00 393.26 1253.60 31.37
Eft (MPa) 0.00 140000.00 33215.50 68729.67 48.33
Pft (%) 0.00 7.30 1.34 1.98 67.76
fful (MPa) 0.00 1899.00 336.65 1227.52 27.42
Eft (MPa) 0.00 140000.00 27859.66 66413.19 41.95
fC (MPa) 25.40 85.00 9.11 41.08 22.18
Table 3. Comparison between the experimental and theoretical axial load-carrying capacity of FRP bar-reinforced concrete columns available in the previous research studies.
P /P b
o exp.
No. The study Specimen p a exp. Eq. (5) Eq. (5) Eq. (2.1 or 2.2) Eq. (3)
ACI 318-19 CSA A23.3- JSCE 1997 Tobbi et al. [11] d
[31] c 19 [32] c [33]
1 Pantelides et #13GLCTL 1975 0.83 0.83 0.60 0.88
2 al. [17] #14GLCTL 1788 0.91 0.92 0.67 0.97
3 C6V-3H80 2905 0.99 1.01 0.68 1.05
4 C10V-3H80 3013 1.02 1.05 0.66 1.12
5 C14V-3H80 3107 1.05 1.09 0.64 1.19
6 C10V-2H80 2948 1.04 1.07 0.67 1.14
7 Afifi et al. [12] C10V-4H80 3147 0.97 1.00 0.63 1.07
8 C10V-3H40 3070 1.00 1.03 0.65 1.10
9 C10V-3H120 2981 1.03 1.06 0.67 1.13
10 C10V-2H35 3148 0.97 1.00 0.63 1.07
11 C10V-4H145 2941 1.04 1.07 0.67 1.15
12 G8V-3H80 2920 0.95 0.97 0.68 1.04
13 G4V-3H80 2826 0.95 0.96 0.70 0.99
14 G12V-3H80 2998 0.96 0.98 0.66 1.09
15 G8V-2H80 2857 0.97 0.99 0.69 1.06
16 Afifi et al. [18] G8V-4H80 3019 0.92 0.94 0.66 1.01
17 G8V-3H40 2964 0.94 0.95 0.67 1.03
18 G8V-3H120 2804 0.99 1.01 0.71 1.08
19 G8V-2H35 2951 0.94 0.96 0.67 1.03
20 G8V-4H145 2865 0.97 0.99 0.69 1.06
21 G2S 2857 0.97 0.99 0.69 1.06
P /P b
o exp.
No. The study Specimen p a exp. Eq. (5) Eq. (5) Eq. (2.1 or 2.2) Eq. (3)
ACI 318-19 CSA A23.3- JSCE 1997 Tobbi et al. [11] d
[31] c 19 [32] c [33]
22 G3S 2920 0.95 0.97 0.68 1.04
23 G4S 3019 0.92 0.94 0.66 1.01
24 G3H200 2840 0.98 1.00 0.70 1.07
25 G3H400 2871 0.97 0.98 0.69 1.06
26 27 28 Mohamed et al. [19] G3H600 C2S C3S 2935 2948 3013 0.95 1.04 1.02 0.96 1.07 1.05 0.68 0.67 0.66 1.04 1.14 1.12
29 C4S 3147 0.97 1.00 0.63 1.07
30 C3H200 2869 1.07 1.10 0.69 1.18
31 C3H400 2960 1.03 1.06 0.67 1.14
32 C3H600 3008 1.02 1.05 0.66 1.12
33 G6-G60 1425 0.82 0.83 0.56 1.01
34 Karim et al. G6-G30 2041 0.57 0.58 0.39 0.71
35 [20] 00-G60 940 1.10 1.10 0.85 1.10
36 00-G30 1343 0.77 0.77 0.59 0.77
37 GGC-8-00 1772 1.00 1.02 0.69 1.15
38 GGC-8-H50 1791 0.99 1.01 0.68 1.14
39 GGC-8-H100 1981 0.89 0.91 0.62 1.03
40 Maranan et al. GGC-8-H200 1988 0.89 0.91 0.61 1.03
41 [21] GGC-8-S50 1838 0.96 0.98 0.66 1.11
42 GGC-8-S100 2063 0.86 0.88 0.59 0.99
43 GGC-16-H100 1624 1.09 1.11 0.75 1.26
44 GGC-16-S100 1208 1.47 1.50 1.01 1.69
45 Hadi et al. [14] G60E0 2721 0.95 0.96 0.71 1.05
46 G30E0 2593 1.00 1.01 0.74 1.10
47 Hadhood et al. C1-I 2608 0.92 0.93 0.64 1.09
48 [22] C1-II 2670 0.93 0.96 0.63 1.19
49 C1 3535 0.88 0.90 0.63 1.03
50 51 52 Abdelazim et al. [23] 2 3 4 CCC 3490 3453 3359 0.90 0.91 0.93 0.91 0.92 0.95 0.64 0.64 0.66 1.04 1.05 1.08
53 C5 3331 0.94 0.95 0.67 1.09
54 GH75-C 2290.51 0.73 0.73 0.53 0.77
55 Raza et al. [24] GH150-C 1965.8 0.84 0.85 0.61 0.89
56 GS38-C 2678.1 0.62 0.63 0.45 0.66
57 GS75-C 2403.54 0.69 0.70 0.50 0.73
58 G1 (6G12-G75) 1202 0.84 0.86 0.57 0.95
59 60 El-Gamal and AlShareedah [25] G6 (6G12-G75) G2 (8G12-G75) 1166 1536 0.86 0.68 0.88 0.70 0.59 0.45 1.01 0.80
61 G3 (8G16-G75) 1457 0.79 0.83 0.47 1.02
62 G4 (6G12-G100) 1065 0.95 0.97 0.65 1.08
63 G5 (6G12-G50) 1585 0.64 0.65 0.44 0.72
64 G3-120-C 943 1.15 1.16 0.86 1.19
5 6 7 666 Elchalakani et al. [26] G4-120-C G5-120-C G4-40-C 1031 1286 1223 1.06 0.86 0.90 1.07 0.87 0.90 0.78 0.63 0.66 1.11 0.91 0.93
68 G4-80-C 1088 1.01 1.02 0.74 1.05
69 GCP-80S 2850 0.93 0.95 0.67 1.12
70 Elhamaymy et GCP-80S-22 3200 0.83 0.85 0.59 1.00
71 al. [27] GCP-80S-60 3350 0.80 0.81 0.57 0.95
72 GCP-40S 2900 0.92 0.93 0.65 1.10
P /P b
o exp.
No. The study Specimen p a exp. Eq. (5) Eq. (5) Eq. (2.1 or 2.2) Eq. (3)
ACI 318-19 CSA A23.3- JSCE 1997 Tobbi et al. [11] d
[31] c 19 [32] c [33]
73 GCP-40S-22 3100 0.86 0.87 0.61 1.03
74 GCP-40S-60 3450 0.77 0.78 0.55 0.92
75 GCP-120S 2800 0.95 0.97 0.68 1.14
76 GCP-120S-22 3000 0.89 0.90 0.63 1.06
77 GCP-120S-60 3250 0.82 0.83 0.58 0.98
78 GCP-80-O 2700 0.99 1.00 0.70 1.18
79 GCP-80-O-22 3100 0.86 0.87 0.61 1.03
80 GCP-80-0-60 3300 0.81 0.82 0.58 0.97
81 Bakouregui et G-8-0 3530 0.97 0.98 0.70 1.10
82 al. [28] B-8-0 3530 0.98 1.00 0.70 1.17
83 84 Gouda et al. [29] SC-6G-80 SC-8G-80 2550 2700 0.91 0.88 0.92 0.89 0.65 0.61 1.04 1.05
85 SC-12G-80 2890 0.86 0.88 0.57 1.09
86 fh-f-2 1589.63 0.67 0.69 0.47 0.81
87 fh-f-4 1317.76 0.68 0.70 0.46 0.85
88 Tang et al. [30] fh-f-8 908.05 0.82 0.84 0.53 1.07
89 fl-f-2 1127.35 0.78 0.79 0.56 0.92
90 fl-f-4 824.88 0.86 0.87 0.60 1.05
91 fl-f-8 616.12 0.96 0.98 0.66 1.21
Mean 0.92 0.94 0.64 1.04
SD 0.125 0.128 0.089 0.136
COV (%) 13.66 13.74 13.87 13.08
MAPE 10.798 10.122 35.618 10.334
4500.00
4000.00
3500.00
3000.00
2500.00
V
- 2000.00
Q."
1500.00
1000.00
500.00
0.00
P0 = 0.85 f'c{A +• ecoEfAf
fco = u UUJ (ALI 318 - iy [J1J
/ I *
** Kmm,
• vr t* •• • y = 0 9253x
0 •
a
1500
Pe
2000 2500 exp. (KN)
P0 = 0.85f'c<iAc/yb for ties and spirals reinforcement P0 = (0.85/c'dJ4L. + 2.5E..!!r:f ^r),iA.pl.')/yll ...for spirals reinforcemer £„,„, = 2000 x 10"'' and Yb = 1.3 (JSCE 1997 [33])
• •4M mM •
• y = 0.643X R2 = 0.9904
•
C
, (KW)
4500 4000 3500 ■ 3000 ■ ^ 2500
a? 2000 1500 1000 ■ 500 ■ 0
P„ = 0.85 f'C{Ag - Af) + £cr,EfAf
tco - u 11 [¿¿.¡J
MM* ..a*»
r...
• • y = 0.943lx
ft • K" = U. nam
b
0
1500 2000 2500 Pexp. (.KN)
3500 4000
Po = 0. af = 0 B5 f'c{A 35(Tobt ,-Ar) + arfruA f • .
i eiai. Liij)
mat\ fcm.
•
• aMi
¿ft • • • • y = 1.0497X
< • R2 = 0.9901
d
, (KN)
Figure 1. Experimental versus predicted axial load carrying capacity of FRP bar reinforced concrete columns obtained using: a) Eq. (5) (sco = 0.003);
b) Eq. (5) (sco = 0.0035); c) Eq. (2.1 or 2.2) (yb =1.3); and d) Eq. (3) (a f = 0.35).
1.80 1.60 1.40 1.20 1.00
0.80
Q?
0.60 0.40
0.20 0.00
1.80 ■
1.60 ■
1.40 •
1.20 ■
. 1.00 •
^ 0.80 ■ 0?
0.60 . 0.40 • 0.20 • 0.00 •
Pa = 0.85f'c(Ag -Af) + scoEfAf
eCo - u •
•
t!-
R2 = 0.1246 a
20000 40000
60000 80000 100000 120000 140000 160000
Ef (MPa)
P„ = O.SSf'MAc/y p„ = (ohf;„Ac + £sspa = 2000 x 10 ; for ties and spirals reinforcement 2.5EsperspdAslu.)/yb ...for spirals reinforcement -<■ and y„ = 1.3 IJSCE 1997133¡)
4
1.1«. Id ........ ..........«
P
y = 2E-0 R2 = 75-
0.0047 C
1.80
1.60
1.40
1.20
. 1.00 a.
0.80
oP
0.60 0.40 0.20 0.00
1.80 1.60 1.40 1.20 1.00
S-
cC1 0.80 0.60 0.40 0.20 0.00
P„ = 0.85 fc(Aa -Af) + £coEfAf - 19 [32]) •
CO
.f! •
•f • V» 1
12
R2 = 0.1528 b
20000 40000
60000 80000 100000 120000 140000 160000
Ef(MPd)
• PD = 0.85/^C^ - Af) + afffuA{
•
№
.......
I • ••
•< II = 0.0921 d
20000 40000
60000 80000 100000 120000 140000 160000
Ef (MPa)
20000 40000
60000 80000 100000 120000 140000 160000 Ef (MPa)
Figure 2. The relationship between Po / Pexp of the FRP-bar reinforced concrete column
and the modulus of elasticity of the reinforcement Ef. The following equations were used to calculate Po : a) Eq. (5) (sco =0.003), b) Eq. (5), c) Eq. (2.1 or 2.2) (yb =1.3), and
d) Eq. (3) (a f = 0.35).
1.60 1.40 1.20 1.00
ä
0» 0.80 N.
0.60 0.40 0.20 0.00
1.80 1.60 1.40
1.20
.1.00 H
5^0.80 a?
0.60 0.40 0.20 0.00
/>„ = 0 85 f'c{A + ZcoEf V
£c0 — ■ UU3 (ALI jlö-ly [J1J) •
a
• f M\ it .....
1 V t • •
y = 0.0015X + 0.8561
R2 = 0.012 a
1.80
1.60
1.40
1.20
1.00
0^0.80 a?
0.60 0.40 0.20 0.00
P0 = 0 85f'c{Ag-Af)+£coEfAf 10035 (CSA A23.3 - 19 [32]) •
i'hl
1"
t V t • •
R2 0.0106 b
f'c (MPa)
40 50 f'c (MPa)
P„ = 0. Po = (0 ' ! = B5 f'caAc 85f;dAc 2000 X / y: for ties and spirals reinforcement + 2.5fsp£/s,,ayl!,„,)/y„ ...forspirals 10~6 and y„ = 1.3 (JSCE 1997 [33]) reinforcement
• •
1 • • •
V = 0.0016X + 0 5735
R2 = 0.027 C
• p0 = 0.85/ Ar) + a 'ffuAf
af - u.3b [lobbiet al. [Ill)
• •
.....I" • •
• ?
R2 = 0.0082 d
30 40 50
f'c (MPa)
f'c (MPa)
Figure 3. The relationship between Po / Pexp of the FRP bar reinforced concrete column
and the compressive strength of the concrete f'c . Note: Po were calculated using: a) Eq. (5) (s^ =0.003); b) Eq. (5) (s^ =0.0035); c) Eq. (2.1 or 2.2) (Jb =1.3); and
d) Eq. (3) (a f = 0.35).
1.80 1.60 1.40 1.20 1.00
I
0.80
0?
0.60 0.40 0.20 0.00
Po = 0.85f'c(Ag-Af) 8C0 = 0.003 {Ad 318 - + tc0EfAf 19 [31]) •
• .........J::, •• ,........J|.. {
' f •S........................... .............4.............. ... ...j»_
I ■ • • • •
*
y = -0.0382x +0.999 R2 = 0.0734
a
1.80 1.60 1.40 1.20 41.00 ; 0.80 0.60 0.40 0.20 0.00
P„ = 0SSf'c(Ag - Af) + scoEfAf £co = 0.0035 (CSA A233 - 19 [32 •
)
• ................... » ................ ...........
• • :......f fS ........• ' ......j»
4 9 m •
—•-
v = -0.0354X + 1.0103
R2 = 0.06 b
Pfl (%)
P/l(%)
1.80 1.60 1.40 1.20 1.00
I
0.80
o?
0.60 0.40 0.20 0.00
P0 = 0.85 f' cdAc/yb for ties and spirals reinforcement P0 = (0.85 fcdAc + 2.5EspefsTdAspe)/yb ...for spirals reinforcement £ssvd = 2000 x 10"6 and yb = 1-3 (JSCE1997 [33])
•
1 ......«V -...... • n
i • •
R2 = 0.1399 -1- - c
1.60 1.40 1.20 1.00
&
0? 0.80 x
0.60 ■ 0.40 ■ 0.20 ■ 0.00
• Po = 0.85/' c(.Ag-Af) + afffuAf
"f-
—•— • ...........•« • • • m
15
• • •......■(■■% •f*........ • 1
fc • •
y = 0.0043x +1.0312 R2 = 0.0008
d
3
Pf
0
pfl (%)
Figure 4. The relationship between Po / Pexp of the FRP bar reinforced concrete column
and the longitudinal reinforcement ratio pf . Note: Po were found by using: a) Eq. (5) (sco =0.003), b) Eq. (5) (sco =0.0035), c) Eq. (2.1 or 2.2) (yb =1.3), and
d) Eq. (3) (a f = 0.35).
1.S0 1.60 1.40 1.20 1.00
I
^ 0.80 0.60 0.40 0.20 0.00
P0 = 0.85 f'cdAc/Yb forties and spirals reinforcement P0 = (0.85/c'di4c + 2.SESp£fSpdASpe)/Yb —for spirals reinforcement £sspd = 2000 x 10"6 and yb = 1.3 (JSCE 1997 [33])
y = -0.0243x +0.6881 v - 0.0311x + 0 6019
R2 = 0.1341 R = 0.079E
A A
P , A
■P* 6 i S A A A A A
1 A Spirals reinforcement I Hoops reinforcement c
1.80 1.60 1.40 1.20 1.00
o.
5? 0.80 a?
0.60 0.40 0.20 0.00
A Po = 0.85/'c(^ -Af) + c *fffuAf
af = U.3b (Tobbi et al. [llj
/■ A
A \ A J A A
J "a A 1 A A
■ A A A
y = -0 042x +1.1234
R 2 = 0.184 R2 = 0.1285
A Spiral reinforcements ■ Hoops reinforcements d
Pft (%)
Pft (%)
Figure 5. The relationship between Po / Pexp and the transverse reinforcement ratio pft of the FRP bar reinforced concrete column. Note: Po was calculated by using the equations: a) Eq. (5) (sco =0.003), b) Eq. (5) (sco =0.0035), c) Eq. (2.1 or 2.2) (yb =1.3), and
d) Eq. (3) (a f = 0.35).
3. Results and Discussion
3.1. Maximum axial load carrying capacity of reinforced concrete columns
This statistical study looks at theoretical equations to find the maximum axial load-carrying capacity of FRP bar-reinforced concrete columns under pure compression stresses. The previously proposed equations for the maximum axial load-carrying capacity of FRP bar-reinforced concrete columns can be used in future compound structure design codes. This research doesn't address the effect of combined axial and flexural loads on the behavior of FRP bar-reinforced concrete columns. Previous research studies used several equations to predict the maximum axial load-carrying capacity of FRP bar-reinforced concrete columns. It is critical to remember that the concrete's contribution to the analytically computed axial load-carrying capacity of FRP-bar reinforced concrete columns, remains similar in all of the proposed equations. In simpler terms, the differences in analytically derived Po values for FRP bar-reinforced concrete columns are primarily due to the different concepts adopted in different equations for calculating the longitudinal bar contribution (pbar frp ). As was mentioned above, the FRP bar's compressive strength is considerably
lower than its tensile strength and the behavior of the FRP bar under compressive loads differs significantly. Therefore, ACI 440.1R-06 [34] suggests that FRP bars shouldn't be used to reinforce concrete columns longitudinally, and ACI 440.1R-15 [16] makes no recommendations about this. The CAN/CSA S806-12 [15] and JSCE 1997 [33] allow FRP bars to be used to reinforce concrete columns in a main direction. However, CAN/CSA S806-12 and JSCE 1997 [15, 33] say that the contribution of the FRP longitudinal bars should be ignored when estimating the maximum axial load-carrying capacity of FRP bar-reinforced concrete columns. Using the recommendations in CAN/CSA S806-12 and JSCE 1997 [15, 33], Eq. (1) and Eq. (2) can be used to predict the maximum axial load-carrying capacity of FRP bar-reinforced concrete columns.
Po = 085fC(Ag - Af ); (1)
Po = 0.85f'Achh ; (2.1)
Po = (085f'Ae + 2.5EspsfspdAspe^ , (2.2)
where Af is the total cross-sectional area of FRP longitudinal bars, A is the cross-sectional area of concrete (mm2), Ae is the cross-sectional area of concrete surrounded by spiral reinforcement, Aspe is the equivalent cross-sectional area of spiral reinforcement (=ndSpASpjs), dsp is the diameter of the concrete section surrounded by spiral reinforcement, Asp is the cross-sectional area of spiral reinforcement, Esp is the young's modulus of spiral reinforcement (Efu ), sfSpd is the design value for
the strain of spiral reinforcement in the ultimate limit state, which is usually taken to be 2000*10-6, Yb is the member factor, which is generally taken to be 1.3, s is the pitch of spiral reinforcement. Note that JSCE 1997 [33] stated that when the members are subjected to axial compression force, the upper limit of axial compression capacity Po will be calculated using Eq. (2.1) while hoops are used and either Eq. (2.1) or
Eq. (2.2) whatever provides the biggest result, when spiral reinforcement is used. But a lot of research has shown that ignoring the contribution of FRP longitudinal bars in compression, as in Eq. (1-2.2), could cause a big difference between the analytically calculated axial load-carrying capacity of FRP bar reinforced concrete columns and the experimentally obtained value [12, 35, 36]. Consequently, two approaches were considered to compute the contribution of FRP longitudinal bars in the maximum axial load-carrying capacity of FRP bar-reinforced concrete columns. In the first approach, the axial load sustained by FRP
longitudinal bars is calculated using the tensile strength of the FRP bars, af ffuAf (Equation (3)). In the
second approach, the axial load sustained by FRP longitudinal bars is calculated using the axial strain in the FRP bars and the stiffness of the FRP bars, sfEfAf (Eq. (4)).
Po =0.85f'(Ag -Af ) + afffuAf; (3)
Po = 0 85f'( Ag - ) + SfEfAf. (4)
In Eq. (3), the af is a reduction factor that represents the ratio between the strength of the FRP bar
under compression and the strength of the FRP bar under tension. Different values for af were
recommended in the previous studies. Alsayed et al. [10] suggested taking af equal to 0.6. Later, Tobbi
et al. [11] recommended taking af equal to 0.35 based on experimental observations reported in
Kobayashi and Fujisaki [8]. Moreover, af was recommended to be taken equal to 0.35 in Afifi et al. [18] for GFRP bar-reinforced circular concrete columns. Nevertheless, for CFRP bar-reinforced circular concrete columns, Afifi et al. [12] recommended taking af equal to 0.25. In Eq. (4), different values were
also suggested for the axial strain in the FRP longitudinal bars, af, at the maximum axial load-carrying capacity of the concrete columns. Mohamed et al. [19] suggested taking sf equal to 0.002, explaining that this value (s f = 0.002) represents the axial strain in the FRP longitudinal bars at the initiation of the micro-cracks in the plastic stage of the concrete. Nevertheless, Hadi et al. [36] recommended taking s f
equal to 0.003, which represents the ultimate strain of the concrete, scu. It is obvious that different research
studies proposed different equations based on a limited number of experimental data. Therefore, there is no consensus in the previous research studies on a unified equation for predicting the maximum axial load-carrying capacity of FRP bar-reinforced concrete columns, which may also be attributed to the variances in the response of the FRP bars under axial compression. In this study, the axial load sustained by FRP longitudinal bars, Pbar FRp, was predicted based on the stiffness (modulus of elasticity) of the FRP bars because the modulus of elasticity of FRP bars in compression is approximately similar to the modulus of elasticity of FRP bars in tension [7, 9]. Therefore, simply changing the value of the reduction factor af in Eq. (3) might not provide reasonable predictions for the maximum axial load-carrying capacity of FRP bar-reinforced concrete columns. The axial strain in the FRP longitudinal bars sf at the maximum axial load-
carrying capacity of the concrete columns was considered to be equal to the concrete axial strain at peak
stress sco. The concept adopted in this study is consistent with the assumption which states that the axial
strain in the concrete and the axial strain in longitudinal FRP reinforcing bars are equal at any concentric axial load. Consequently, the maximum axial load-carrying capacity of FRP bar-reinforced concrete columns can be predicted using Eq. (5):
Pa =0.85fC(Ag - Af ) + ScoEfAf. (5)
3.2. Evaluation of the proposed and codes equations 3.2.1. Overall performance
In this study, the three code equations were assessed with a proposed equation from a previous study through the analysis of a large set of available experimental data (Table 1). This study examined the equation proposed by Tobbi et al. [8]. Hadi et al. [36] recommended assuming sf equal to scu. The
equation proposed by Hadi et al. [36] was also assessed. First, by taking scu equal to 0.003 as defined in the ACI 318-19 [31 ] standard. Then, by taking scu equal to 0.0035 as defined in the CSA A23.3-19 standard [32]. Table 3 presents the ratios between the analytically predicted and the experimentally obtained axial load carrying capacity (PojPexp ) for the experimentally tested specimens in Table 1. The analytically
predicted axial load carrying capacity, Po, was calculated by either using Eq. (3) by taking af equal to 0.35, as recommended by Tobbi et al. [11], or using Eq. (5), in which the value of sco was taken equal to scu (0.003 or 0.0035, as defined in the ACI 318-19 [31] and CSA A23.3-19 [32], or using Eq. (2.1 and 2.2)
from the JSCE 1997 [33], which depends mostly on the type of transverse reinforcement (hoops or spirals). The most optimal line for each equation is also shown alongside the experimental and theoretical axial load. The same number shows perfect performance. The equation with fewer scatters and better performance is one where the most optimal line and the plotted data are closer to the perfect line. Four
relationships (f', pf, Ef, and pf) are displayed to illustrate the ratio between the experimental axial
load and the theoretical axial load using the selected equations for each tested column. In Table 3, four
different mathematical measurements (Mean value (p), Standard Deviation (SD), Coefficient of Variation
(COV), and the Mean Absolute Percent Error (MAPE)) were used to evaluate the accuracy, consistency, and safety of the equations available according to three codes (ACI 318-19 [31], CSA A23.3-19 [32], and JSCE 1997 [33]) and according to only one proposed in one previous study (Tobbi et al. [11]). Among the
unique values, the Mean value (p) is the midpoint between the wide range of Po. More precise results
can be expected when the mean is closer to unity. The dispersion (variation) in Po values was measured
using the SD. For FRP bar-reinforced concrete specimens, a high SD indicates that the predicted axial load-carrying capacities fall within a wider range of values (less precisely) and a lower value SD indicates the opposite. The COV was then used to evaluate the dispersion of Po values relative to the mean value
as a percentage. As the COV decreases, performance becomes more stable and less variable from the mean. The MAPE is used to compare the accuracy of different equations used to determine the maximum axial load-carrying capacities of FRP-bar reinforced concrete columns. If the MAPE is small, then the equation should yield precise results. The most optimal line's slope indicates how consistently the performance meets or exceeds predictions for the chosen parameter. Table 3 shows a comparison of the experimental axial load-carrying capacity of FRP-bar-reinforced concrete columns to the theoretical value. It was noticed that Eq. (5), in which the contribution of the FRP bars is calculated based on their stiffness, is a more precise and safe way to predict Po than Eq. (3), in which the contribution of the FRP bars is
calculated based on their tensile strength. Eq. (5) is a safer and more reliable way to predict Po than (2.1,
2.2), which uses transverse reinforcement. Possible explanations for this include the fact that despite significant differences between their tensile and compressive strengths, FRP bars have a modulus of elasticity that is nearly identical in tension and compression. Table 3 presents the SD and COV, which are 0.136 and 13.08, respectively, when Po is calculated using Eq. (5), the equation proposed by Tobbi et al.
[11]. This permits more consistent results. However, the lowest MAPE of 10.798 in predicting Po was
achieved by taking the concrete axial strain at peak stress s co = 0.003 in the computation of Pbar frp .
By taking sco equal to 0.0035 when computing Pbar frp, predictions for Po/Pexp with = 0.94, which is
very close to unity and rather secure, but with high SD and COV of 0.128 and 13.74, respectively, were obtained (Fig. 1). As can be seen in Fig. 1, the SD and COV are 0.089 and 13.87, respectively, when using the Eq. (2.1, 2.2) that is available in JSCE is used to calculate Pbar frp, resulting in higher discrepant
values of Po . Thus, Eq. (5) which is available in CSA provides more realistic predictions than do those of
other codes (ACI, JSCE). The axial load-carrying capacity of FRP bar-reinforced concrete columns was taken from previous studies and compared to the axial load-carrying capacity calculated using ACI 318-19 [31] and CSA A23.3-19 [32], respectively in Fig. 1. The JSCE's 1997 [33] equation and Tobbi et al.'s equation [11], were assessed. The slope of the trend line is 0.92 for the ACI, 0.94 for the CSA, 0.64 for the JSCE, and 1.04 for Tobbi. In addition, the axial load was calculated by using CSA and Tobbi equations, and that is more in line with the axial load measured experimentally. ACI, CSA, JSCE, and Tobbi each found a COV for axial load experimental versus a theoretical axial load of 13.66, 13.74, 13.87, and 13.08, respectively. The ACI and JSCE are less precise than the CSA. Finally, when comparing the Tobbi equation to the others that were considered, it was found to be the most precise in predicting the axial load-carrying capacity. Lastly, the performance tests on concrete compression design practices (Table 3) showed that the proposed equation by Tobbi et al. [11] with suitable safety factors had better optimization, followed by the CSA A23.3-19 [32] guidelines, the ACI 318-19 [31] code, and the JSCE 1997 guidelines [33]. The statistical tests yielded consistent results for the SD, COV, MAPE, and mean. The Tobbi et al. [11] design equation and the CSA A23.3-19 [32] guidelines did better than the ACI 318-19 [31 ] code, which had some extreme values because they had fewer conservative values. The JSCE 1997 [33] was not safe and had more conservative points than the other design methods because 97 % of their predictions were dangerous or extremely dangerous. Tobbi et al. [11], CSA A23.3-19 [32], and ACI 318-19 [31] showed better assessment because the PojPexp was less conservative by 9, 19, and 23 %, respectively.
3.2.2. Young's modulus
For solids only, the stress (tension or compression) ratio to strain is known as Young's modulus or the main modulus of elasticity. This linear relationship between stress and strain expresses the extent of
flexibility of the material and explains how the material behaves under the influence of forces. This factor has a major effect on the axial load-carrying capacity of FRP-RC columns. The PojPexp vs the E and the most optimal line trendlines from the database are shown in Fig. 2. As Young's modulus increases, so does the Po/Pexp The most optimal lines for the ACI, CSA, JSCE, and Tobbi have an inclination of 1E-6,
2E-6, 2E-7, and 1E-6, respectively. Therefore, CSA provides greater consistency in terms of E value in terms of safety compared to ACI, JSCE, and Tobbi. The CSA equation can be inferred to be more reliable for FRP types than any of the chosen equations.
3.2.3. Concrete strength
One measure of a material's or structure's durability is its compressive strength, or how well it carries up under compression stresses. The axial load-carrying capacity of FRP-RC columns is significantly impacted by this factor. The PojPexp vs f' and the most optimal line trendline using the proposed and
selected equations are shown in Fig. 3. The Po calculated using Eq. (3) by taking af equal to 0.35 as
recommended by Tobbi et al. [11], using Eq. (5) by taking sco equal to 0.003 as defined in the ACI 318-19
[31] and equal to 0.0035 as defined in the CSA A23.3-19 [32] or calculated using the Eq. (2.1, 2.2) as recommended in JSCE 1997 [33] are shown in Fig. 3. The axial load-carrying capacity for the majority of the FRP bar-reinforced NSC and HSC columns provided in Table 1 is well predicted using an assumption of af equal to 0.35 (Eq. (3)), as suggested by Tobbi et al. [11], as illustrated in Fig. 3a. The performance
indicator PojPexp tends to rise as f' gets higher. The slope of the line that provides the best match has
an inclination of 1.5E-3 for the ACI, 1.5E-3 for the CSA, 1.6E-3 for the JSCE, and 1.4E-3 for the Tobbi. In terms of f safety, the CSA is more reliable than the ACI and the JSCE. The Tobbi also exhibits the
greatest degree of consistency with respect to f'c of any of the chosen equations.
3.2.4. The longitudinal reinforcement ratios
The longitudinal reinforcement ratio, pf, is calculated by dividing the area of the longitudinal
reinforcement by the cross-sectional area of the column. It is a significant factor affecting the axial load-carrying capacity of FRP-RC columns. The fluctuation in PojPexp with longitudinal reinforcement ratio, according to the database, is shown in Fig. 4. As the reinforcement ratio rises, it can be seen that the PojPeXp has a decreasing trend. In addition, the slope of the most optimal line for the ACI, CSA, JSCE,
and Tobbi is -38.2E-3, -35.4E-3, -37.4E-3, and +4.3E-3, respectively. Compared to CSA, JSCE, and Tobbi, ACI points are less crowded and closer to the perfect horizontal line. Consequently, ACI safety is more consistent concerning the pf value than CSA, JSCE, and Tobbi. It may be inferred that the ACI equation
is more consistent for the FRP type than it is for the other equations considered.
3.2.5. Transverse reinforcement ratio 3.2.5.1. Spiral reinforcement ratio
The P,/Pexp vs pft and the most optimal line trendline are shown in Fig. 5. The slope of the most optimal lines is -39.6E-3, -40.8E-3, -24.3E-3, and -4.2E-2 for the ACI, CSA, JSCE, and Tobbi, in that order. As pft increases, Po/Pexp decreases. This suggests that the performance of spiral reinforcement
improves when the distances are increased but within the applicable limits. In addition, the ACI is more consistent regarding p ft safety than the Tobbi and JSCE. Finally, the CSA equation is more consistent
concerning with respect to pft than any of the selected equations.
5.5.2. Hoops reinforcement ratio
The Po/Pexp vs pft and the most optimal line trendline are shown in Fig. 5. For the ACI, CSA,
JSCE, and Tobbi, the slope of the most optimal line is 56.2E-3, 59.3E-3, 31.1 E-3, and 83.8E-2, respectively. Generally, there is a clear increase in Po/Pexp with each increase in the pft. This indicates that hoop
reinforcement gives better performance when the spacings are smaller but within the applicable limits. In addition, the safety of the ACI is more consistent concerning the pft than that of the CSA and JSCE.
Furthermore, the Tobbi outperforms the codes in terms of pj-t consistency. Finally, the behavior of the
most optimal line trendlines for spiral reinforcement is clear that it is the opposite of the behavior of the perfect line for hoops reinforcement. Also, the ACI and the CSA provide better results than the JSCE in general, although Tobbi provides perfect results better than all other codes at least in the hoops reinforcement, and the results are close For the ACI and CSA in spirals reinforcement.
4. Conclusions
An extensive experimental database comprising 91 circular FRP-reinforced concrete columns was utilized to investigate the interrelation of geometry and details of circular FRP-reinforced concrete columns. The axial load-carrying capacity of the experimental database was determined using selected design codes and guidelines with one equation proposed in earlier research, the CSA design code exhibited superior precision compared to JSCE and ACI but less compared with Tobbi. The mean safety factors for JSCE, ACI, CSA, and Tobbi were found to be 0.64, 0.93, 0.94, and 1.04, respectively. JSCE showed less consistency and a significantly more conservative behavior compared to ACI, CSA, and Tobbi while ignoring the contribution of longitudinal bars and ultimate axial strain, which leads to an increase in implementation costs. Key distinctions between FRP-reinforced concrete columns and conventional steel-reinforced concrete columns were considered, such as varying FRP types (Young's modulus: 0-140 GPa), compressive failure due to concrete crushing without yielding FRP reinforcements, and increased deformation experienced by FRP-reinforced concrete columns. To validate the accuracy of the codes and the previously proposed equation, the experimental axial load-carrying capacity was compared with the predicted axial load-carrying capacity using equations for a large experimental database of reinforced concrete circular columns with FRP reinforcements. Tobbi's equation showed good agreement with experimental loads compared to other equations, which can be a good conclusion due to the remarkable complexity in the behavior of FRP bars and the big difference in the behavior of these bars in compression and tension. The analysis investigated the effects of concrete strength, FRP Young's modulus, longitudinal reinforcement ratio, and transverse reinforcement ratio on the results. These results showed the Po/Pexp
of FRP-reinforced concrete columns increases with an increase in the value of the FRP Young's modulus, the longitudinal reinforcement ratio, and the concrete strength, respectively; and Tobbi's equation adequately accounted for the concrete strength and the hoops reinforcement effect. When the type is hoops, Po/Pexp increases as the pft increases, but when the type is spiral, PojPexp decreases as the
pft increases. Finally, Tobbi's equation has the lowest COV compared with all code's equations and the
best average nearing unity. However, MAPE for Tobbi is greater than CSA but less than JSCE and ACI, which require more experimental testing and more exact test measurements.
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Information about authors:
Mohamed Qassim Kadhim, Master of Structural Engineering ORCID: https://orcid.org/0009-0007-0037-6453 E-mail: mohamedq 1992@ uomustansiriyah. edu. iq
Hassan Falah Hassan, PhD
ORCID: https://orcid. org/0000-0003-4610-0560 E-mail: hassanfalah@uomustansiriyah.edu. iq
Received 15.02.2023. Approved after reviewing 19.10.2023. Accepted 22.10.2023.
