Flexural behavior of concrete beams hybrid-reinforced with glass fiber-reinforced polymer,carbon fiber-reinforced polymer,and steel rebars

Abstract

The utilization of fiber-reinforced polymer (FRP) reinforcements in structural design is increasing due to their non-corrosive nature. However, the anisotropic features and linear elastic behavior of FRP rebars have led researchers to explore the use of hybrid combinations of FRP and steel reinforcements. Current codes and guidelines predominantly focus on the design of glass FRP (GFRP) reinforced structural elements, leaving a gap in incorporating the hybrid use of FRP-steel combinations and different types of FRP materials, such as carbon FRP (CFRP). This study conducted experimental investigations on concrete beams reinforced with GFRP, CFRP, and hybrid (GFRP-steel and CFRP-steel in combination) rebars, comparing the results with theoretical models. Ten full-scale beams were tested under monotonic loading. Test results revealed that existing codes overestimate GFRP reinforced beam displacements while underestimating CFRP reinforced beam displacements. A reduction factor is proposed for the effective moment of inertia expression given by ACI 440.11-22 to predict the deflections of CFRP reinforced and hybrid reinforced beams. The experimental data for CFRP and hybrid reinforced concrete beams align well with the predictions calculated using the proposed equations.

Keywords

glass fiber-reinforced polymer carbon fiber-reinforced polymer hybrid steel/fiber-reinforced polymer deflection flexural behavior reinforced concrete beam

Highlights

• Modified I_e equation is proposed for CFRP and hybrid (FRP-steel) RC beams

• Ten full-scale beam specimens are tested under the three-point bending test

• Detailed flexural behavior of the experimental and analytical results is presented

• Codes and guidelines underestimate the midspan displacements of CFRP-RC beams

• Hybrid FRP-steel rebar configuration introduces nonlinearity in load-displacement curve

Introduction

In the last decades, fiber-reinforced polymer (FRP) bars have been a promising alternative to conventional steel rebars due to their better corrosion resistance, high tensile strength-weight ratio, and nonmagnetic nature (ACI 440.1R, 2015). Replacing conventional steel with FRP rebars has been investigated thoroughly (Aiello and Ombres, 2000; Alsayed et al., 2000; Benmokrane et al., 1995; El-Gamal et al., 2011; El-Nemr et al., 2013; El-Sayed et al., 2006; Esmaeili et al., 2020; Junaid et al., 2019; Liang et al., 2023; Ramachandra Murthy et al., 2020; Sarhan and Al-Zwainy, 2022) and several countries and regions developed design guides for FRP reinforced concrete structures, such as Japan (JPCI, 2021; JSCE, 1997), Europe (Fib, 2007, fib, 2023), Canada (CSA 2012; ISIS 2007), and America (ACI 440.1R 2015; ACI 440.11 2022). However, the wide range utilization of FRP reinforcements, particularly as a longitudinal reinforcement, has been rather limited due to their two main drawbacks: linear elastic behavior until rupture and low elasticity modulus. Although the non-corrosive nature of the FRP improves the durability of the reinforced concrete structures, FRP rebars attain their full tensile strength without yielding or hardening, which reduces the ductility of FRP reinforced concrete structures and limits their inelastic behavior (Bencardino et al., 2016; El Refai et al., 2015; Wang and Belarbi, 2011). Therefore, ACI 440.1R-15 (2015) and CSA S806-12 (2012) suggest an over-reinforced design for the glass-FRP (GFRP) reinforced beams to enable the concrete failure before GFRP rupture. Moreover, due to the low elasticity modulus of most commercially available FRP rebars, FRP reinforced concrete beams exhibit larger deflections and wider cracks compared to those reinforced with steel rebars (El-Gamal et al., 2011). To maximize the structural behavior of FRP reinforced concrete beams, researchers proposed methods such as hybridization of different fibrous materials (Elsayed et al., 2011; Harris et al., 1998; Tepfers et al., 1996) or compounding FRP bundles over steel rods (Nanni et al., 1994a, 1994b; Said et al., 2021; Yang et al., 2020). However, application of these proposed hybrid rebars are not widely adopted due to the high complexity in the manufacture process. Some of the relatively practical solutions to improve flexural behavior in terms of ductility and controlling deformability of the FRP reinforced beams are addition of fibers to concrete (Alsayed and Alhozaimy, 1999; Issa et al., 2011; Li and Wang, 2002; Patil et al., 2020; Wang and Belarbi, 2011; Zhu et al., 2018) and using FRP rebars and steel reinforcements in combination (Aiello and Ombres, 2002). With such a hybrid system, steel reinforcement increases the ductility of the beam, while FRP reinforcement maintains the flexural load-carrying capacity (El Refai et al., 2015). Moreover, steel rebars reduce the deformability by decreasing the deformations and crack widths when compared to pure FRP reinforced concrete beams (Aiello and Ombres, 2002).

The hybrid usage of steel and FRP reinforcement has been utilized in recent designs. Qu et al. (2009), Lau and Pam (2010), and Refai et al. (2015) conducted experiments on hybrid (GFRP-steel) reinforced beams, showing that steel reinforcements improved the flexural behavior in terms of ductility and stiffness, as steel has higher stiffness and steel rebars yield before concrete crushing. In addition, Refai et al. (2015) showed that the over-reinforced hybrid beams outperformed their GFRP reinforced counterparts in terms of strength and ductility. Experimental studies on BFRP-steel reinforced beams highlighted the effect of steel reinforcement addition on deformability of the hybrid beams. Ge et al. (2015) found that hybrid (BFRP-steel) reinforced beams exhibited deflection and crack spacing values between those of steel and FRP reinforced beams. Steel-reinforced beams had the least deflection and crack spacing, while FRP-reinforced beams had the most. Akiel et al. (2018) showed that hybrid reinforcement improved the serviceability of the beams with less deflections and smaller crack widths at service load than their counterparts reinforced with BFRP rebars only. Ruan et al. (2020) studied the flexural behavior of GFRP-steel reinforced concrete beams. The ultimate flexural capacity of the hybrid reinforced beam was found to be 5% less (on average) than that of the steel reinforced counterparts. Authors proposed a modification to effective moment of inertia expression given by ACI 440.1R-15 for the prediction of deflections of hybrid reinforced beams.

Another important aspect of hybrid reinforced concrete beams is the ratio between steel and FRP reinforcement. Nguyen et al. (2020a) and Abbas et al. (2022) studied the effect of reinforcement ratios and configurations on the flexural behavior of GFRP and hybrid (GFRP-steel) reinforced concrete beams. Nguyen et al. (2020b) showed that GFRP presence delays the steel yielding with a linear relationship between GFRP reinforcement ratio and steel yielding load. In addition, for the same reinforcement ratios, increasing GFRP reinforcement ratio improves the load-carrying capacity of the hybrid reinforced beams. Abbas et al. (2022) investigated under-reinforced hybrid beams (GFRP-steel) with steel reinforcement ratios to GFRP rebars, varying from 0.5 to 2, showing that the ductility of hybrid reinforced concrete beams increased almost linearly with the increase of the steel ratio. Pang et al. (2016) suggested reinforcement ratio limits to ensure ductile failure of the hybrid reinforced beams and introduced a new ductility index based on deformability and energy absorption capacity. These studies highlight the importance of the balance between the steel and GFRP reinforcement areas on attaining the desired strength and ductility. The effect of the bond-slip relation between the GFRP rebars and concrete (Xingyu et al., 2020) and the effect of bundling on the flexural behavior of hybrid reinforced beams (Sun et al., 2019) are other important aspects for design of hybrid reinforced beams.

Numerical studies on hybrid reinforced beams proposed models for predicting the flexural behavior of hybrid reinforced concrete beams (Bencardino et al., 2016; Kara et al., 2015). However, some numerical models are only suitable for the beams with low and normal reinforcement ratios (Bencardino et al., 2016). Kara et al. (2015) showed that the FRP reinforcement played an important role in the load-carrying capacity of the beams after steel yielding in over-reinforced sections in their parametric study. Kheyroddin and Maleki (2017) proposed a new equation based on the genetic algorithm to estimate the effective moment of inertia of hybrid (FRP-steel) reinforced concrete beams. Mustafa and Hassan (2018) conducted a numerical study using nonlinear finite element analysis on hybrid (GFRP-steel and CFRP-steel) reinforced concrete beams. The authors stated that hybrid CFRP-steel reinforced beams outperformed their GFRP-steel counterparts during crack initiation and propagation. Peng et al. (2023) proposed reliability-based design provisions for hybrid (FRP-steel) reinforced concrete beams.

Existing research demonstrates a wide range of applications of hybrid reinforced concrete beams and various types of FRP rebars. However, current codes and guidelines primarily focus on GFRP rebars, and there is a need to update these regulations to include the hybrid use of FRP-steel combinations and different types of FRP rebars. In pursuit of this goal, this study investigates the flexural performance of hybrid reinforced concrete beams with different FRP rebars, focusing on the effect of FRP type, and FRP rebar size on the deflection and the deformability of the beams. Ten full-scale FRP reinforced concrete beams are tested and the test results of the specimens are presented with the load-displacement curves, failure modes, crack patterns, and concrete strain curves. Experimental results are compared and discussed in detail with the American and Canadian codes and design guidelines and numerical methods proposed by researchers. The novelty of this study lies in proposing a reduction factor for application with the effective moment of inertia expression provided by ACI 440.11-22 (2022) to predict the deflections of CFRP reinforced and hybrid (GFRP-steel and CFRP-steel) reinforced beams.

Experimental program

Test specimens

The details of the specimens are shown in Table 1. The letters S, G, and C represents steel, GFRP, and CFRP reinforcement. The number next to the letters indicates the number of tensile reinforcements. Steel stirrups with a diameter of 8 mm were used, and the concrete cover was 25 mm for all the specimens. Test specimens were divided into two groups regarding the reinforcement diameter and the number of reinforcement bars. In Group I, 12 mm diameter rebars were used, and in Group II, 16 mm diameter rebars were used. Although the numbers of the reinforcements are different in both groups, the reinforcement areas are close to equal.

Table 1.

Details of test specimens.

Group ID	Specimen ID	Tensile reinforcement	$ρ_{s} ρ_{f} ρ_{he}$		$ρ_{sb} ρ_{sb}$	Compression reinforcement (steel)	Steel stirrup diameter and spacing (mm)
Group I	S7-Ø12	7Ø12 steel	0.0088	<	0.0205	2Ø12	Ø8/200
	G7-Ø12	7Ø12 GFRP	0.0088	>	0.0029	2Ø12	Ø8/200
	C7-Ø12	7Ø12 CFRP	0.0088	>	0.0011	2Ø12	Ø8/200
	G4-S3-Ø12	4Ø12 GFRP, 3Ø12 steel	0.0070	>	0.0029	2Ø12	Ø8/200
	C4-S3-Ø12	4Ø12 CFRP, 3Ø12 steel	0.0057	>	0.0011	2Ø12	Ø8/200
Group II	S4-Ø16	4Ø16 steel	0.0090	<	0.0205	2Ø16	Ø8/200
	G4-Ø16	4Ø16 GFRP	0.0090	>	0.0029	2Ø16	Ø8/200
	C4-Ø16	4Ø16 CFRP	0.0090	>	0.0011	2Ø16	Ø8/200
	G2-S2-Ø16	2Ø16 GFRP, 2Ø16 steel	0.0068	>	0.0029	2Ø16	Ø8/200
	C2-S2-Ø16	2Ø16 CFRP, 2Ø16 steel	0.0053	>	0.0011	2Ø16	Ø8/200

Figure 1 shows the dimensions of the specimens. The width and height of the rectangular section and the length of the beam were selected as 250 mm, 400 mm, and 4100 mm, respectively. Cross-section details of Group I and Group II are shown in Figure 2. All specimens were built as over-balanced except the S7-Ø12 and S4-Ø16. ACI 318-19 (2019) (Equation (1) and equation (2)) and ACI 440.1R-15 (2015) (Equation (3) and equation (4)) guides were used for the calculation of balanced reinforcement ratios of steel-reinforced beams and FRP reinforced beams, respectively. Balanced reinforcement ratio for steel and FRP reinforced beams were calculated using equation (2) for $ρ_{s b}$ and equation (4) for $ρ_{f b}$ , respectively. For the hybrid reinforced beams, effective reinforcement ratio which is obtained by strength conversion ratio for steel rebars was calculated with equation (5) for $ρ_{h e}$ and compared with the balanced reinforcement ratio of FRP reinforced beams ( $ρ_{f b}$ ) (El Refai et al., 2015).

ρ_{s} = \frac{A_{s}}{b d}

(1)

ρ_{s b} = 0.85 \frac{f_{c d}}{f_{y d}} k_{1} \frac{0.003}{0.003 + ε_{s d}}, k_{1} = 0.85

(2)

ρ_{f} = \frac{A_{f}}{b d}

(3)

ρ_{f b} = 0.85 β_{1} \frac{f_{c}^{'}}{f_{f u}} \frac{E_{f} ε_{c u}}{E_{f} ε_{c u} + f_{f u}}

(4)

where

β_{1} = 0.85, f_{f u} = C_{e} {f_{f u}}^{*}, f o r G F R P C_{e} = 0.8, f o r C F R P C_{e} = 1

ρ_{h e} = ρ_{s} \frac{f_{y}}{f_{f u}} + ρ_{f}

(5)

Figure 1.

Beam test setup.

Figure 2.

(a) Reinforcement details of Group I and (b) Group II specimens.

Materials

Sand-coated GFRP and CFRP rebars were used as tensile reinforcement. An image of GFRP, CFRP, and steel reinforcements with a nominal diameter of 12 mm and 16 mm is given in Figure 3.

Figure 3.

Reinforcements used in specimens.

The mechanical properties of steel rebars were calculated using nominal cross-sectional areas of 113 and 200 mm² for the 12- and 16-mm diameters, respectively. The tensile tests to determine yield strengths (

f_{y}

) of the steel rebars were conducted according to TS EN ISO 6892-1 (2020) and ASTM E8M-21 (2021), while FRP properties were provided by the manufacturer. Average yield strength of identical five steel rebar specimens were found as 486.2 ± 12.2 MPa and 481.4 ± 8.6 MPa for the 12- and 16-mm diameters, respectively. Mechanical properties of GFRP, CFRP, and steel rebars are given in Table 2.

Table 2.

Mechanical properties of GFRP, CFRP, and steel reinforcements.

Rebar	$f_{u}$ (MPa)	$Е$ (GPa)	$f_{y}$ (MPa)	$Δ$ (%)	$A$ (mm²)	$W_{l i n}$ (gr/m)
Ø12 GFRP^a	1000.00	40	—	2.8	113	200
Ø16 GFRP^a	1000.00	40	—	2.8	200	330
Ø12 CFRP^a	2300.00	130	—	1.8	113	195
Ø16 CFRP^a	2300.00	130	—	1.8	200	340
Ø12 steel^b	702.71	207	485.82	22	113	888
Ø16 steel^b	703.68	207	480.67	24	200	1580

^aobtained from the manufacturer.

^bobtained from experiments.

All specimens were cast on the same day in one batch with normal-weight, ready-mix concrete with specified compressive strength of 25 MPa after 28 days. A concrete admixture with a superplasticizer was used to increase the workability and strength of concrete. Concrete compressive strength was tested on the 7th, 28th and on the test day (120th day on average). The average compressive strength of standard 150 mm × 150 mm x 150 mm cubic specimens tested according to TS EN 206+A2 (2021) on the test days were found as 34.6 MPa ±2.2 MPa, achieving the targeted equivalent cylinder compressive strength of 28.0 MPa.

Test setup

Beam specimens were investigated under a three-point bending test. Figure 1 illustrates the test setup. The middle span displacement was measured with a potentiometric position sensor. The concrete strain at $L / 2$ and $L / 3$ of the span were measured with strain gauges. Four strain gauges were placed in the compression zone at $L / 2$ and $L / 3$ , whereas two strain gauges were placed in the tension zone at $L / 2$ . In total, six strain gauges were placed on the concrete surface for each specimen. Crack patterns of the specimens were mapped throughout the experiments, and the cracks were numbered in order of occurrence (Figure 4).

Figure 4.

Mapping of crack patterns of specimens.

Test results

During the experiments, the applied load, midspan deflections, concrete strains were recorded, and crack patterns were observed. Tests were terminated when the specimens could not carry any more loads, or the load-carrying capacity of the beams suddenly dropped under 10% of the maximum load. A summary of the test results for all beam specimens is presented in Table 3 and Table 4. Table 3 shows initial cracking and ultimate loads with failure modes.

P_{c r E x p}

represents the experimental initial cracking load, and

P_{u}

represents the load-carrying capacity of the beams.

P_{c r P r e d}

represents the predicted initial cracking load according to ACI 440.11-22 (2022).

Table 3.

Initial cracking load, ultimate load and failure modes of specimens.

Group ID	Specimen ID	$P_{crExp}$ (kN)	$P_{crPred}$ (kN)	$\frac{P_{crExp}}{P_{crPred}}$	$P_{u}$ (kN)	$\frac{P_{crExp}}{P_{u}}$	Failure mode
GROUP I	S7-Ø12	39.2	21.9	1.79	140.2	0.28	SY→CC
	G7-Ø12	22.6	21.9	1.03	130.5	0.17	CC
	C7-Ø12	31.4	21.9	1.43	220.0	0.14	CC
	G4-S3-Ø12	25.5	21.9	1.17	137.5	0.19	SY→CC→RR
	C4-S3-Ø12	20.6	21.9	0.94	188.1	0.11	SY→CC
GROUP II	S4-Ø16	31.4	21.9	1.43	154.9	0.20	SY→CC
	G4-Ø16	18.6	21.9	0.85	121.5	0.15	CC
	C4-Ø16	22.6	21.9	1.03	208.2	0.11	CC
	G2-S2-Ø16	17.9	21.9	0.81	134.0	0.13	SY→CC→RR
	C2-S2-Ø16	14.7	21.9	0.64	178.7	0.08	SY→CC

Note: SY = steel yielding; CC = concrete crushing; RR = reinforcement rupture.

Table 4.

Displacements at the Midspan of Specimens.

Group ID	Specimen ID	Midspan Displacement (mm)
Group ID	Specimen ID	$δ_{50 k N}$	$δ_{100 k N}$	$δ_{121.51 k N}$	$δ_{140 k N}$	$δ_{200 k N}$	$δ_{\max}$
GROUP Ⅰ	S7-Ø12	6.4	14.2	17.7	42.1	—	45.1
	G7-Ø12	12.4	33.5	43.3	—	—	47.6
	C7-Ø12	7.9	19.6	24.5	28.6	45.8	54.0
	G4-S3-Ø12	8.0	22.2	33.4	—	—	43.6
	C4-S3-Ø12	7.1	16.9	23.3	29.9	—	61.6
GROUP Ⅱ	S4-Ø16	6.1	13.2	16.2	23.1	—	49.4
	G4-Ø16	15.2	38.6	51.3	—	—	51.3
	C4-Ø16	7.5	19.0	23.5	27.1	42.9	47.5
	G2-S2-Ø16	9.0	21.7	33.3	—	—	42.5
	C2-S2-Ø16	8.5	17.4	22.6	28.6	—	58.9

Note: Highest midspan displacements for each specified loading are shown in bold.

Table 4 shows the midspan displacements of the specimens at different arbitrary intermediate load levels (50 kN, 100 kN). $δ$ represents the midspan displacements at a specific load denoted with the subscripts. $δ_{\max}$ is the midspan displacement at the ultimate load. 121.5 kN is the highest load value that is common in all test specimens. 140 kN and 200 kN load levels are the ultimate loads that CFRP-steel and CFRP reached respectively.

General behavior and failure modes

The results of the experiments along with the observed failure modes are presented in Table 3. Failure modes are denoted as CC (Concrete Crushing), RR (Reinforcement Rupture), and SY (Steel Yielding). These failure modes are listed in the order of their occurrence in the experiments. For specimens solely reinforced with steel rebars (Steel-RC), the sequence of failure modes was SY followed by CC. In contrast, for specimens reinforced exclusively with GFRP (GFRP-RC) and CFRP (CFRP-RC), concrete crushing (CC) was the initial failure mode, consistent with the guidelines outlined in building codes (ACI 440.1R 2015; ACI 318 2019; CSA S806 2012). Both GFRP-RC and CFRP-RC beams ultimately failed due to concrete crushing (CC) (Figure 5).

Figure 5.

Concrete crushing.

In the case of hybrid specimens, SY occurred before CC, followed by RR for GFRP-steel hybrid reinforced beams. A notable observation is that replacing up to 50% of the tensile reinforcement with steel rebars altered the failure mode, causing steel yielding to precede concrete crushing in both GFRP-RC and CFRP-RC specimens. Comparing Group I and Group II specimens, which had different rebar diameters, no significant change in the failure modes was observed. The distinct failure modes observed in the experiments were the result of the different mechanical properties of the rebar materials.

Load-carrying capacity

As anticipated, CFRP-RC beams outperformed GFRP-RC and Steel-RC beams in terms of ultimate load-carrying capacity, primarily due to the significantly higher tensile strength of CFRP, which is 1.30 and 2.27 times greater than that of GFRP and steel, respectively. At the ultimate load levels, hybrid CFRP-steel reinforced beams exhibited the highest midspan displacements. While GFRP-RC beams exhibited the lowest load-carrying capacity, they displayed higher displacements at the same load levels, attributed to their lower flexural stiffness. Comparing hybrid CFRP-steel reinforced specimens to their Steel-RC counterparts, it was observed that steel reinforcement contributed to increased displacement capacity, while CFRP reinforcement improved load-carrying capacity.

According to the test results, using GFRP instead of steel rebars in the same reinforcement area reduced the maximum load-carrying capacity by 6.95% - 21.57% for Group I and Group II, respectively. However, it increased the maximum displacement at ultimate load by 5.66% - 3.91%. In contrast, replacing steel reinforcement with CFRP increased the maximum load-carrying capacity by 56.88% for Group I and 34.40% for Group II, accompanied by an increase (19.74%) in the maximum displacement for Group I and a slight decrease (3.71%) for Group II. As for the hybrid CFRP-steel reinforced beams, replacing nearly half of the CFRP rebars with steel increased the maximum displacement observed at the ultimate load by 14.10% - 24.01%, while the ultimate load-carrying capacity decreased by 14.49% - 14.16% for Group I and Group II, respectively. For the hybrid GFRP-steel reinforced beams, substituting nearly half of the GFRP rebars with steel increased the ultimate load-carrying capacity by 5.38% - 10.26%, while the maximum displacement observed at the ultimate load decreased by 8.40% - 17.22% for Group I and Group II, respectively.

Group I and Group II specimens have the same reinforcement area, with a different number of rebars with different diameters. Based on the test results, increasing the rebar diameter led to a 6.88% and 5.35% reduction in ultimate load for GFRP-RC and CFRP-RC beams, respectively. Simultaneously, it increased the maximum load by 10.48% for Steel-RC beams. Furthermore, an increase in rebar diameter resulted in a 9.49% and 7.68% increase in maximum displacement at the ultimate load for Steel-RC and GFRP-RC beams, respectively, while the displacement for CFRP-RC beams decreased by 11.95%. For the hybrid GFRP-steel and CFRP-steel reinforced beams, an increase in rebar diameter resulted in a decrease in both load-carrying capacity (2.57% and 5.00%) and maximum displacements (2.68% and 4.30%), respectively.

The disparities in load-carrying capacity primarily stem from variations in tensile strength $(f_{u})$ among the reinforcement materials. Notably, CFRP-RC beams outperformed GFRP-RC and Steel-RC beams due to the significantly higher tensile strength of CFRP.

Crack behavior

Analyzing the ratios of initial crack load to maximum load ( $P_{c r E x p} / P_{u}$ ), it was observed that the earliest crack formations occurred in hybrid CFRP-steel reinforced beams, while Steel-RC beams exhibited initial cracking at higher ratios, with values of 0.28 and 0.21 for Group I and Group II, respectively (Table 3). Comparing the predicted initial cracking load (ACI 440.1R 2015; ACI 318 2019) with experimental data, it was evident that hybrid CFRP-steel reinforced beams developed initial cracks earlier than expected, whereas Steel-RC beams experienced delayed initial cracking. The increase in rebar diameter correlated with a decrease in the initial cracking load for all specimens. Consequently, initial cracking occurred later in Group I beams than in Group II beams. The experimental results demonstrated that both the reinforcement diameter and type influenced the initial cracking load. The crack patterns for Group I and Group II specimens are given in Figure 6. Hybrid CFRP-steel and GFRP-steel beams displayed more branching cracks, with smaller crack spacings compared to Steel-RC beams.

Figure 6.

(a) Crack patterns of Group I and (b) Group II specimens.

Load-displacement responses and stress-strain curves

Figure 7 illustrates the load-displacement curves for Group I and Group II specimens, while Figure 8 provides a comparison of Group I specimens with their Group II counterparts. Until the initial cracking load, all specimens displayed similar load-displacement responses. GFRP-RC and CFRP-RC beams exhibited linear elastic behavior until failure, while hybrid GFRP-steel and CFRP-steel reinforced beams displayed some inelastic behavior due to steel yielding occurring before concrete crushing. Moreover, changes in rebar diameter affected the ultimate load and maximum displacements of the specimens, but the overall response remained similar for both Group I and Group II specimens.

Figure 7.

Load midspan displacement curves of Group I (left) and Group II (right).

Figure 8.

Comparison of Group I and Group II load-midspan displacement curves.

As given in Figure 1, each beam specimen instrumented with six strain gages placed on concrete, four on the midspan section (two 30 mm from top and two 30 mm from bottom) and two on the $L / 3$ section (30 mm from the top). The strain graphs in Figure 9 reveal that, as expected, midspan concrete strain in both compression and tension zones approached values of $3000 x 10^{- 6} ε$ and $100 x 10^{- 6} ε$ , respectively. The concrete strain in the L/3 compression zone ranged between $200 x 10^{- 6} ε$ and $1000 x 10^{- 6} ε$ .

Figure 9.

Load Concrete strain values at middle span and L/3.

Discussion

The deflection of an RC flexural member is one of the significant factors that affect its serviceability. Several researchers investigated the deflection behavior of FRP reinforced concrete beams (Bischoff, 2005; Bischoff and Gross, 2011; Dundar et al., 2015; Nguyen et al., 2020a; Kara et al., 2013; Kheyroddin and Maleki, 2017; Mohamed et al., 2017; Mousavi and Esfahani, 2012; Rafi and Nadjai, 2011; Unsal et al., 2017). The load-displacement behavior of RC beams under the static loading is the equation of the relation between the applied load and the flexural stiffness of the beam. There are two stages that define the deflection behavior of the RC beam. The first stage of the load-deflection curve is between the beginning of the loading to the initial crack occurrence, where the maximum service load moment is lower than the cracking moment ( $M_{a} {< M}_{c r}$ ). In this stage, the behavior is controlled by the gross moment of inertia ( $I_{g}$ ) as the moment of inertia equals to $I_{g}$ for the uncracked section. The second stage starts when the maximum service load moment exceeds the cracking moment ( $M_{a} {\geq M}_{c r}$ ), where the stiffness of the beam reduces with the increasing load. Branson (1965) presented an effective moment of inertia ( $I_{e}$ ) representing the gradual transition from the gross moment of inertia ( $I_{g}$ ) to the cracked moment of inertia ( $I_{c r}$ ) to predict the deflection behavior of the beam in the second stage. Branson (1965) equation is found to be under-estimating the deflections of FRP reinforced concrete beams (ACI 440.1R-15, 2015). Bischoff (2005) proposed an alternative section-base model for the effective moment of inertia ( $I_{e}$ ), which is suitable for estimating the deflections of FRP reinforced, and steel-reinforced beams, therefore ACI 440.1R-15 adopted the modified version of Bischoff (2005) equation (ACI 440.1R-15, 2015). In this study, the load-deflection behavior of the tested beams is calculated by using the approaches given by ACI 318-19 (2019), ACI 440.1R-15 (2015), CSA S806-12 (2012), ISIS Canada Design Manual No. 3 (2007), El Refai et al. (2015), Dundar et al. (2015), and Unsal et al. (2017).

ACI 440.1R-15 (2015) suggests using $I_{e}$ given by equation (6) for the effective moment of inertia for FRP reinforced beams. ACI 440.1R-15 (2015) defines $I_{c r}$ with equation (7) where $k$ is the ratio of depth of neutral axis to reinforcement depth (Equation (8)). And $n_{f}$ given by equation (9) is the ratio of modulus of elasticity of FRP rebars to modulus of elasticity of concrete. The factor $γ$ given by equation (10) depends on the boundary conditions and the type of loading (Bischoff, 2005), which is a parameter to account for the variation in stiffness along the length of the member. Equation (11) provided by Bischoff (2005) for simply supported beam subjected to one-point loading is used for calculating the midspan deflections. The only difference between the new code ACI 440.11-22 and ACI 440.1R-15 is given in equation (7).

I_{e} = \{\begin{array}{c} I_{g} & , M_{a} < M_{c r} \\ \frac{I_{c r}}{1 - γ {(\frac{M_{c r}}{M_{a}})}^{2} [1 - \frac{I_{c r}}{I_{g}}]} \leq I_{g} & , M_{a} \geq M_{c r} \end{array}

(6)

I_{e} = \{\begin{array}{c} I_{g} & , M_{a} \leq {0.8 M}_{c r} \\ \frac{I_{c r}}{1 - γ {(\frac{{0.8 M}_{c r}}{M_{a}})}^{2} [1 - \frac{I_{c r}}{I_{g}}]} \leq I_{g} & , M_{a} > {0.8 M}_{c r} \end{array}

(7)

I_{c r} = \frac{b d^{3}}{3} k^{3} + n_{f} A_{f} d^{2} {(1 - k)}^{2}

(8)

k = \sqrt{2 ρ_{f} n_{f} + {(ρ_{f} n_{f})}^{2}} - ρ_{f} n_{f}

(9)

n_{f} = \frac{E_{f}}{E_{c}}

(10)

γ = 3 - 2 (M_{c r} / M_{a})

(11)

δ_{\max} = \frac{P L^{3}}{48 E_{c} I_{e}}

(12)

El Refai et al. (2015) defined the effective reinforcement ratio with equation (5) for hybrid reinforced (FRP-steel) beams. El Refai et al. (2015) proposed equation (13) for calculating the cracked moment of inertia of the hybrid reinforced RC beams including steel reinforcement components in equation (8) given by ACI 440.1R-15 (2015). The researchers redefined the $k$ with equation (14) and included $n_{s}$ (equation (15)) for the ratio of modulus of elasticity of steel rebars to modulus of elasticity of concrete. In this study, the approach is used with the effective moment of inertia equation defined in ACI 440.1R-15 (2015) (equation (6)) to calculate the midspan deflections for the hybrid GFRP-steel and CFRP-steel reinforced specimens.

I_{c r} = \frac{1}{3} b {(k d)}^{3} + (n_{f} A_{f} + n_{s} A_{s}) d^{2} {(1 - k)}^{2}

(13)

k = \sqrt{2 (ρ_{f} n_{f} + ρ_{s} n_{s}) + {(ρ_{f} n_{f} + ρ_{s} n_{s})}^{2}} - (ρ_{f} n_{f} {+ ρ}_{s} n_{s})

(14)

n_{f} = \frac{E_{f}}{E_{c}}; n_{s} = \frac{E_{s}}{E_{c}}

(15)

ISIS Canada (2007) recommends using equation (16) for the effective moment of inertia of FRP reinforced beams. $I_{t}$ is the transformed moment of inertia of the uncracked section of the beam. If gross moment of inertia is used for the uncracked section, the effective moment of inertia given in ISIS Canada becomes the same as the equation ACI 440.1R-15 (2015) recommends by equation (6). Cracked moment of inertia, $I_{c r}$ , is given by equation (8).

I_{e} = \frac{I_{t} I_{c r}}{I_{c r} + (1 - 0.5 {(\frac{M_{c r}}{M_{a}})}^{2}) (I_{t} - I_{c r})}

(16)

CSA S806-12 (2012) provides a maximum deflection equation derived by the curvature integration along the span of a simply supported beam subjected to one-point loading given by equation (17). The moment-curvature relation of FRP reinforced beam is assumed to be trilinear with the slope of three segments $E_{c} I_{g}$ (where $M_{a} {< M}_{c r}$ ), zero (the transition from uncracked to cracked stage), and $E_{c} I_{c r}$ (where $M_{a} {\geq M}_{c r}$ ). Cracked inertia of the beam ( $I_{c r}$ ) is calculated by equation (8). The parameter $η$ is a coefficient given by equation (18) and $L_{g}$ represents the uncracked distance from support.

δ_{\max} = \frac{P L^{3}}{48 E_{c} I_{c r}} [1 - 8 η (\frac{L_{g}}{L})]

(17)

η = (1 - \frac{I_{c r}}{I_{g}})

(18)

The cracking moment was predicted using equation (19), where the concrete modulus of rupture was calculated using equation (20) in accordance with ACI 440.1R-15 (2015) and equation (21) in accordance with CSA S806-12 (2012). The modification factor $λ$ reflects the reduced mechanical properties of lightweight concrete, where ACI 318-19 (2019) suggests using $λ = 1$ for normal weight concrete. $f_{c}^{'}$ represent the specified compressive strength of the concrete and in this study, $f_{c}^{'}$ values were determined experimentally. The parameter $y_{t}$ is the distance from the centroidal axis of the gross section, neglecting reinforcement to tension face.

M_{c r} = \frac{f_{r} I_{g}}{y_{t}}

(19)

f_{r} = 0.62 λ \sqrt{f_{c}^{'}}

(20)

f_{r} = 0.60 λ \sqrt{f_{c}^{'}}

(21)

Dundar et al. (2015) proposed a numerical method for calculation of the displacements of FRP or steel-reinforced RC beams, and Unsal et al. (2017) presented an improved version for RC beams reinforced with a combination of FRP and steel rebars. The effective flexibility of beams at a specific section is calculated by equation (22) and used for determining the flexibility matrix of the member. The proposed method uses the complete moment-curvature relationship obtained from the sectional analysis, where the stress-strain relationships of the concrete and the reinforcement are considered. In this study, a computer program developed by Dundar and his colleagues (Dundar et al., 2015; Unsal et al., 2017) was used to estimate the deflections of the tested specimens. CEB-FIB model was used for concrete in compression.

\frac{1}{E_{c} I_{e}} = \frac{1}{E_{c} I_{c r}} [1 - (1 - \frac{ϕ_{M}}{M}) E_{c} I_{c r}] \leq \frac{1}{E_{c} I_{g}}

(22)

The experimental and predicted deflection behavior of RC beams under applied load is compared in Figure 10. In order to compare the experimental results, the equations for deflection predictions suggested by the regulations and researchers for each reinforcement type were used. In Figure 10, the ultimate load level ( $P_{u}$ ) and service load levels ( ${0.30 \times P}_{u}$ and ${0.67 \times P}_{u}$ (Elgabbas et al., 2016)) were indicated with horizontal lines. $P_{u}$ values were directly taken from the experiments. Ultimate bending moment values at the midspan could be calculated with $M_{u} = P_{u} L / 4 .$ The examined methods showed similar behavior to the experimental results until the load-displacement graphs reached the first cracking load. Although there were minor differences in the experimental results that could be ignored, the load-displacement curves obtained using the equations given in codes and other studies were almost the same for Group I and Group II specimens. This can be explained as the Group I and Group II specimens have the same reinforcement area; also, the equations given by the codes and researchers do not contain a variable for a reinforcement diameter. The method given by Dundar et al.(2015, 2017) approximated the overall behavior most closely to the experimental results until the specimens reach the ultimate load.

Figure 10.

Comparison of load midspan curves with prediction methods.

All predictions for the GFRP reinforced beams had very close results to the experimental behavior. Among these methods, ACI 440.1R.15 and ISIS Canada showed the closest load-displacement behavior for GFRP reinforced beams compared to other methods at service load levels. However, ACI 440.11.22 provided a conservative estimation of the behavior of GFRP reinforced beams compared to ACI 440.1R.15. Besides, all methods under-estimated the flexural behavior of the CFRP reinforced specimens. For hybrid GFRP-steel beams, while El Refai et al. (2015) and Unsal et al. (2017) obtained very similar results to the experimental behavior until the steel yielding point, the method proposed by El Refai et al. deviated from the experimental results after that point. As for hybrid CFRP-steel beams, a similar result was observed with hybrid GFRP-steel beams until the steel yielding point, while both methods deviated from the experimental results after that point.

Prediction of flexural behavior

Current codes and guidelines for FRP reinforced structures do not include CFRP reinforced beams as well as hybrid usage of FRP and steel reinforcements. This section introduces a new approach for estimating flexural behavior of CFRP-RC and hybrid reinforced (GFRP-steel and CFRP-steel) concrete beams. For CFRP-RC beams, the midspan deflections were calculated using the equations given by ACI 440.11-22 and CSA S806-12. For hybrid reinforced beams (GFRP-steel and CFRP-steel), midspan deflections were only calculated using ACI 440.11-22 with only changing the reinforcement ratio calculations using effective reinforcement ratio, $ρ_{h e}$ (equation (5)), which was obtained by strength conversion ratio for steel rebars. This study proposes a reduction factor, κ (equation (23)), for the effective inertia formula, $I_{e}$ , given by ACI 440.11-22, for estimating midspan deflection of beams reinforced with carbon fiber reinforced polymer (CFRP) or hybrid (FRP-steel) rebars. The κ coefficient was computed based on loads ranging from $0.20 P_{u}$ to 0. $80 P_{u}$ , which encompasses both service loads ( $0.30 P_{u} - 0.67 P_{u}$ ) and plastic deformations following steel yielding for the flexural behavior of FRP and hybrid reinforced beams. The coefficients were the values that yield the minimum total summation of squared differences (TSS) in middle span deflection for each load level.

I_{e} = \{\begin{array}{c} {κ \cdot I}_{g} & , M_{a} \leq {0.8 M}_{c r} \\ κ \cdot \frac{I_{c r}}{1 - γ {(\frac{{0.8 M}_{c r}}{M_{a}})}^{2} [1 - \frac{I_{c r}}{I_{g}}]} \leq {κ \cdot I}_{g} & , M_{a} > {0.8 M}_{c r} \end{array}

(23)

The predicted midspan deflections for RC beams reinforced with CFRP, GFRP-steel, and CFRP-steel are shown in Figure 11. The calculated κ factors for CFRP-RC, GFRP-steel, and CFRP-steel beams were 0.7, 0.68, and 0.6, respectively, and were found to agree well with experimental results. In particular, the predicted deflections for CFRP-RC beams closely matched the experimental behavior. On the other hand, it should be noted that the proposed method did not consider steel yielding. Thus, the non-linear $σ - ϵ$ behavior following steel reinforcement yielding affects the accuracy of predicting midspan deflections of hybrid reinforced beams. Although the load-deflection behavior becomes parabolic instead of linear, the predicted results still demonstrated better correlation with experimental results than those obtained from the ACI 440.11-22 formulas.

Figure 11.

Predicted midspan deflections for (a) CFRP reinforced, (b) GFRP-steel Reinforced and (c) CFRP-steel reinforced concrete beams.

Table 5 presents a comparison of experimental to predicted deflection ratios at the service loads of the tested specimens with the proposed methods. Mean, standard deviation, and coefficient of variation of the midspan displacement values were calculated for each method grouped by rebar configuration. The closer the standard deviation value is to zero percent, the more consistent the method is with the experimental results. The coefficient of variation is the ratio of the standard deviation to the mean, which measures the relative variability to the average. The proposed method in this study, which uses a reduction factor, κ (equation (23)), for the effective inertia formula,

I_{e}

, given by ACI 440.11-22, for estimating midspan deflection of beams reinforced with CFRP and hybrid (GFRP-steel and CFRP-steel) rebars showed the closest results with the experiments. ACI 440.11-22 showed the best results for GFRP-RC beams at

0.30 P_{u}

while ACI 440.1R-15 had the best result at

0.67 P_{u}

with an average

δ_{\exp} / δ_{p r e d}

0.91 \pm 0.105

and

0.99 \pm 0.115

, respectively. All methods over-estimated the midspan displacements of GFRP-RC beams. For CFRP-RC and hybrid CFRP-steel beams, equation (23) had the best result at both

0.30 P_{u}

and

0.67 P_{u}

. Equation (23) estimation values for CFRP-RC beams at

0.30 P_{u}

and

0.67 P_{u}

for average

δ_{\exp} / δ_{p r e d}

were

0.92 \pm 0.060

and

0.98 \pm 0.020

, respectively. ACI 440.11-22 under-estimated CFRP-RC beam deflection behavior at both

0.30 P_{u}

and

0.67 P_{u}

with an average

δ_{\exp} / δ_{p r e d}

1.34 \pm 0.065

and

1.40 \pm 0.025

, respectively. For GFRP-steel hybrid beams equation (23) showed the best results at

0.30 P_{u}

while Unsal et al. (2017) had the closest result at

0.67 P_{u}

with an average

δ_{\exp} / δ_{p r e d}

1.06 \pm 0.150

and

1.05 \pm 0.129

, respectively. For CFRP-steel hybrid beams at both

0.30 P_{u}

and

0.67 P_{u}

equation (23) had the closest estimation with an average

δ_{\exp} / δ_{p r e d}

1.03 \pm 0.005

and

1.17 \pm 0.070

, respectively.

Table 5.

Experimental to predicted (δ_exp/δ_pred) midspan displacements of tested beams.

Group ID	Spec. ID	$δ_{\exp} / δ_{p r e d}$ ( $δ_{p r e d}$ mm)
		δ_exp (mm)				ACI-318-19		CSA S806-12		ISIS Canada $I_{e}$		El refai et al		Unsal et al
		121.51kN	0.30M_u	0.67M_u	M_u	0.30M_u	0.67M_u	0.30M_u	0.67M_u	0.30M_u	0.67M_u	0.30M_u	0.67M_u	0.30M_u	0.67M_u
GROUP I	S7-Ø12	17.7	5.24	13.37	45.08	1.30 (4.04)	1.40 (9.58)	—	—	—	—	—	—	1.85 (2.83)	1.39 (9.61)
	G7-Ø12	43.3	7.92	27.63	47.63	—	—	0.58 (13.62)	0.79 (34.99)	1.00 (7.90)	0.90 (30.76)	—	—	0.60 (13.19)	0.78 (35.38)
	C7-Ø12	24.5	12.06	30.37	53.98	—	—	1.26 (9.59)	1.39 (21.89)	1.48 (8.12)	1.44 (21.06)	—	—	1.31 (9.21)	1.31 (23.18)
	G4-S3-Ø12	33.4	6.22	18.98	43.62	—	—	—	—	—	—	1.51 (4.12)	1.37 (13.87)	1.11 (5.60)	0.96 (19.70)
	C4-S3-Ø12	23.3	8.29	24.86	61.59	—	—	—	—	—	—	1.52 (5.47)	1.67 (14.85)	1.36 (6.11)	1.44 (17.25)
GROUP II	S4-Ø16	16.2	5.55	13.75	49.36	1.23 (4.53)	1.30 (10.61)	—	—	—	—	—	—	1.61 (3.46)	1.29 (10.66)
	G4-Ø16	51.3	8.65	29.60	51.29	—	—	0.71 (12.16)	0.91 (32.41)	1.32 (6.56)	1.06 (27.99)	—	—	0.74 (11.63)	0.91 (32.49)
	C4-Ø16	23.5	10.15	27.61	47.53	—	—	1.12 (9.03)	1.33 (20.70)	1.35 (7.52)	1.39 (19.83)	—	—	1.19 (8.51)	1.29 (21.44)
	G2-S2-Ø16	33.3	7.41	17.70	42.46	—	—	—	—	—	—	2.02 (3.67)	1.43 (12.41)	1.56 (4.76)	1.15 (15.44)
	C2-S2-Ø16	22.6	9.07	22.14	58.94	—	—	—	—	—	—	1.83 (4.96)	1.62 (13.68)	1.67 (5.42)	1.45 (15.26)
Steel	Mean					1.26^a	1.35	—	—	—	—	—	—	1.73	1.34^b
	Standard deviation					0.049	0.071	—	—	—	—	—	—	0.174	0.071
	Coeff. of Var. (%)					3.89	5.26	—	—	—	—	—	—	10.06	5.31
GFRP	Mean					—	—	0.65	0.85	1.16	0.98	—	—	0.67	0.85
	Standard deviation					—	—	0.092	0.088	0.223	0.113	—	—	0.101	0.092
	Coeff. of Var. (%)					—	—	14.18	10.29	19.19	11.55	—	—	15.01	10.90
CFRP	Mean					—	—	1.19	1.36	1.42	1.42	—	—	1.25	1.30
	Standard deviation					—	—	0.095	0.038	0.096	0.035	—	—	0.082	0.016
	Coeff. of Var. (%)					—	—	7.96	2.79	6.79	2.50	—	—	6.59	1.24
GFRP-Steel	Mean					—	—	—	—	—	—	1.77	1.40	1.33	1.05^b
	Standard deviation					—	—	—	—	—	—	0.357	0.041	0.315	0.129
	Coeff. of Var. (%)					—	—	—	—	—	—	20.25	2.91	23.60	12.24
CFRP-Steel	Mean					—	—	—	—	—	—	1.67	1.65	1.52	1.45
	Standard deviation					—	—	—	—	—	—	0.220	0.040	0.223	0.006
	Coeff. of Var. (%)					—	—	—	—	—	—	13.19	2.42	14.70	0.43

Group ID	Spec. ID	$δ_{\exp} / δ_{p r e d}$ ( $δ_{p r e d}$ mm)
		δ_exp (mm)				ACI-440.1R-15		ACI-440.11-22		Equation (23) ( $κ = 0.70$ )		Equation (23) ( $κ = 0.60$ )		Equation (23) ( $κ = 0.68$ )
		121.51kN	0.30M_u	0.67M_u	M_u	0.30M_u	0.67M_u	0.30M_u	0.67M_u	0.30M_u	0.67M_u	0.30M_u	0.67M_u	0.30M_u	0.67M_u
GROUP I	S7-Ø12	17.7	5.24	13.37	45.08	—	—	—	—	—	—	—	—	—	—
	G7-Ø12	43.3	7.92	27.63	47.63	1.05 (7.52)	0.91 (30.48)	0.80 (9.89)	0.86 (32.13)	—	—	—	—	—	—
	C7-Ø12	24.5	12.06	30.37	53.98	1.50 (8.02)	1.45 (21.00)	1.40 (8.60)	1.42 (21.32)	0.98 (12.29)	1.00 (30.46)	—	—	—	—
	G4-S3-Ø12	33.4	6.22	18.98	43.62	—	—	—	—	—	—	0.91 (6.86)	0.82 (23.12)	—	—
	C4-S3-Ø12	23.3	8.29	24.86	61.59	—	—	—	—	—	—	—	—	1.03 (8.05)	1.24 (21.84)
GROUP II	S4-Ø16	16.2	5.55	13.75	49.36	—	—	—	—	—	—	—	—	—	—
	G4-Ø16	51.3	8.65	29.60	51.29	1.40 (6.19)	1.07 (27.69)	1.01 (8.54)	1.01 (29.42)	—	—	—	—	—	—
	C4-Ø16	23.5	10.15	27.61	47.53	1.37 (7.42)	1.40 (19.77)	1.27 (8.02)	1.37 (20.11)	0.86 (11.46)	0.96 (28.73)	—	—	—	—
	G2-S2-Ø16	33.3	7.41	17.70	42.46	—	—	—	—	—	—	1.21 (6.12)	0.86 (20.68)	—	—
	C2-S2-Ø16	22.6	9.07	22.14	58.94	—	—	—	—	—	—	—	—	1.02 (7.30)	1.10 (20.12)
Steel	Mean					—	—	—	—	—	—	—	—	—	—
	Standard deviation					—	—	—	—	—	—	—	—	—	—
	Coeff. of Var. (%)					—	—	—	—	—	—	—	—	—	—
GFRP	Mean					1.23	0.99b	0.91a	0.94	—	—	—	—	—	—
	Standard deviation					0.243	0.115	0.105	0.075	—	—	—	—	—	—
	Coeff. of Var. (%)					19.80	11.65	11.54	7.98	—	—	—	—	—	—
CFRP	Mean					1.44	1.42	1.34	1.40	0.92a	0.98b	—	—	—	—
	Standard deviation					0.096	0.035	0.065	0.025	0.060	0.020	—	—	—	—
	Coeff. of Var. (%)					6.70	2.48	4.85	1.79	6.52	2.04	—	—	—	—
GFRP-Steel	Mean					—	—	—	—	—	—	1.06a	0.84	—	—
	Standard deviation					—	—	—	—	—	—	0.150	0.020	—	—
	Coeff. of var. (%)					—	—	—	—	—	—	14.15	2.38	—	—
CFRP-Steel	Mean					—	—	—	—	—	—	—	—	1.03a	1.17b
	Standard deviation					—	—	—	—	—	—	—	—	0.005	0.070
	Coeff. of Var. (%)					—	—	—	—	—	—	—	—	0.49	5.98

^aclosest $δ_{\exp} / δ_{p r e d}$ ratio to 1.00 for 0.30M_u.

^bclosest $δ_{\exp} / δ_{p r e d}$ ratio to 1.00 for 0.67M_u.

Conclusions

Based on the experimental results and prediction models, the following conclusions can be drawn:

1. The maximum load-carrying capacity of CFRP-RC beams were 1.82 and 1.57 times higher than GFRP-RC and Steel-RC beams, respectively.

2. Beams reinforced with GFRP rebars exhibited on average 5% higher midspan displacements and on average 15% lower ultimate load-carrying capacities compared to Steel-RC beams.

3. FRP reinforced beams failed by concrete crushing. The use of a hybrid combination of FRP and steel reinforcement changed the failure mode of FRP reinforced beams. Steel reinforcement yielded before the concrete crushing, similar to the behavior of conventional steel-reinforced beams.

4. The ultimate load-carrying capacity of hybrid GFRP-steel reinforced beams was on average 8% higher than that of GFRP-RC beams, while maximum displacements were on average 13% lower. Conversely, hybrid CFRP-steel beams had 14% lower ultimate load-carrying capacities than CFRP-RC beams, with an average of 19% higher midspan displacements.

5. Since all specimens casted by one batch of concrete, they have same concrete compressive strength; thus, the experimental study demonstrated that the type and diameter of reinforcement influenced the initial cracking load. The initial crack occurred at lower load levels with an increase in rebar diameter across all specimens.

6. The branching of cracks was more prevalent in hybrid specimens than in others, while the spacing between cracks along the span was shorter in hybrid specimens than in Steel-RC beams.

7. ACI 440.11-22 and CSA S806-12 provides better estimates for the displacements of GFRP-RC beams than CFRP-RC beams. However, all methods included in this study (except the proposed method by the authors) overestimated midspan displacements of GFRP-RC beams and underestimated the midspan displacements of CFRP-RC beams. For hybrid reinforced beams, El Refai et al. (2015) and Unsal et al. (2017) methods underestimate the midspan deflections for GFRP-steel and CFRP-steel beams.

8. Equation (23), proposed in this study, showed a good correlation for predicting the flexural behavior of CFRP-RC, hybrid GFRP-steel, and CFRP-steel beams. The reduction factor, κ, proposed for CFRP-RC, GFRP-steel, and CFRP-steel beams are 0.7, 0.68, and 0.6, respectively. Predicted midspan displacements for CFRP-RC well estimates the experimental results with almost no difference. For the hybrid reinforced beams, even though the load-deflection behavior after steel yielding becomes parabolic instead of linear, the predicted results using equation (23) still demonstrate better correlation with experimental results than those from the ACI 440.11-22 formulas.

Footnotes

Acknowledgments

The authors are greateful for the Scientific Research Projects Fund provided by Eskisehir Osmangazi University (Project Number: 201715D32). The authors also would like to express their special thanks and gratitude to Dr Mehmet Canbaz for his generous help with the material tests.

Declaration of conflicting interests

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

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Eskisehir Osmangazi Universitesi; Project Number: 201715D32.

ORCID iD

Meltem Eryilmaz Yildirim

Data Availability Statement

Data will be made available on request.

Appendix

References

Abbas

Abadel

Almusallam

, et al. (2022) Experimental and analytical study of flexural performance of concrete beams reinforced with hybrid of GFRP and steel rebars. Engineering Failure Analysis 138: 106397. DOI: 10.1016/j.engfailanal.2022.106397.

ACI (American Concrete Institute) (2015) Guide for the design and construction of structural concrete reinforced with fiber-reinforced polymer (FRP) bars. Farmington Hills, MI: ACI (American Concrete Institute). DOI: 10.1016/0011-7471(75)90030-3.

ACI (American Concrete Institute) (2022) Building code requirements for structural concrete reinforced with glass fiber-reinforced polymer (GFRP) bars—code and commentary. Farmington Hills, MI: ACI (American Concrete Institute): 11–22.

Aiello

Ombres

(2000) Load-deflection analysis of FRP reinforced concrete flexural members. Journal of Composites for Construction 4(4): 164–171. DOI: 10.1061/(ASCE)1090-0268.

Aiello

Ombres

(2002) Structural performances of concrete beams with hybrid (Fiber-Reinforced polymer-steel) reinforcements. Journal of Composites for Construction 6(2): 133–140. DOI: 10.1061/(ASCE)1090-0268.

Akiel

El-Maaddawy

El Refai

(2018) Serviceability and moment redistribution of continuous concrete members reinforced with hybrid steel-BFRP bars. Construction and Building Materials 175: 672–681. DOI: 10.1016/j.conbuildmat.2018.04.202.

Alsayed

Alhozaimy

(1999) Ductility of concrete beams reinforced with FRP bars and steel fibers. Journal of Composite Materials 33(19): 1792–1806. DOI: 10.1177/002199839903301902.

Alsayed

Al-Salloum

Almusallam

(2000) Performance of glass fiber reinforced plastic bars as a reinforcing material for concrete structures. Composites Part B: Engineering 31(6–7): 555–567. DOI: 10.1016/S1359-8368(99)00049-9.

American Concrete Institute (ACI) (2019) ACI 318-19: Building Code Requirements for Structural Concrete. Farmington Hills, MI: American Concrete Institute (ACI)

10.

ASTM International (2021) Standard Test Methods for Tension Testing of Metallic Materials. West Conshohocken, PA: ASTM. E8/E8M-21.

11.

Bencardino

Condello

Ombres

(2016) Numerical and analytical modeling of concrete beams with steel, FRP and hybrid FRP-steel reinforcements. Composite Structures 140: 53–65. DOI: 10.1016/j.compstruct.2015.12.045.

12.

Benmokrane

Chaallal

Masmoudi

(1995) Glass fibre reinforced plastic (GFRP) rebars for concrete structures. Construction and Building Materials 9(6): 353–364. DOI: 10.1016/0950-0618(95)00048-8.

13.

Bischoff

(2005) Reevaluation of deflection prediction for concrete beams reinforced with steel and fiber reinforced polymer bars. Journal of Structural Engineering 131(5): 752–767.

14.

Bischoff

Gross

(2011) Design approach for calculating deflection of FRP-reinforced concrete. Journal of Composites for Construction 15(4): 490–499. DOI: 10.1061/(ASCE)CC.1943-5614.0000195.

15.

Branson

(1965) Instantaneous and Time-Dependent Deflections of Simple and Continuous Reinforced Concrete Beams. HPR Report No. 7. Alabama: Alabama Highway Department. Available at: https://www.concrete.org/PUBS/JOURNALS/OLJDetails.asp?Home=JP&ID=17002%5Cn, https://www.worldcat.org/title/instantaneous-and-time-dependent-deflections-of-simple-and-continuous-reinforced-concrete-beams/oclc/217079277

16.

CSA (Canadian Standards Association) (2012) Design and Construction of Building Structures with Fibre-Reinforced Polymers. Ontario, Canada: Mississauga. CSA S806-12.

17.

Dundar

Tanrikulu

Frosch

(2015) Prediction of load-deflection behavior of multi-span FRP and steel reinforced concrete beams. Composite Structures 132, 680–693. DOI: 10.1016/j.compstruct.2015.06.018.

18.

El Refai

Abed

Al-Rahmani

(2015) Structural performance and serviceability of concrete beams reinforced with hybrid (GFRP and steel) bars. Construction and Building Materials 96: 518–529. DOI: 10.1016/j.conbuildmat.2015.08.063.

19.

El-Gamal

AbdulRahman

Benmokrane

(2011) Deflection behaviour of concrete beams reinforced with different types of GFRP bars. In: Advances in FRP Composites in Civil Engineering - Proceedings of the 5th International Conference on FRP Composites in Civil Engineering, CICE 2010. 27-29 September, Beijing, China. DOI: 10.1007/978-3-642-17487-2_59

20.

El-Nemr

Ahmed

Benmokrane

(2013) Flexural behavior and serviceability of normal- and high-strength concrete beams reinforced with glass fiber-reinforced polymer bars. ACI Structural Journal 110(6): 1077–1087. DOI: 10.14359/51686162.

21.

El-Sayed

El-Salakawy

Benmokrane

(2006) Shear capacity of high-strength concrete beams reinforced with FRP bars. ACI Structural Journal 103(3): 383–389. DOI: 10.14359/15316.

22.

Elgabbas

Vincent

Ahmed

, et al. (2016) Experimental testing of basalt-fiber-reinforced polymer bars in concrete beams. Composites Part B: Engineering 91: 205–218. DOI: 10.1016/j.compositesb.2016.01.045.

23.

Elsayed

Elhefnawy

Eldaly

, et al. (2011) Hybrid fiber reinforced polymers rebars. Journal of Advanced Materials 43(1): 65–75.

24.

Esmaeili

Eslami

Newhook

, et al. (2020) Performance of GFRP-reinforced concrete beams subjected to high-sustained load and natural aging for 10 years. Journal of Composites for Construction 24(5): 1–14. DOI: 10.1061/(ASCE)CC.1943-5614.0001065.

25.

Fib (2007) Fib Bulletin 40. FRP Reinforcement in RC Structures. Switzerland. The International Federation for Structural Concrete. DOI: 10.35789/fib.BULL.0040.

26.

fib (2023) fib Model Code for Concrete Structures 2020. Switzerland: The International Federation for Structural Concrete.

27.

Zhang

Cao

, et al. (2015) Flexural behaviors of hybrid concrete beams reinforced with BFRP bars and steel bars. Construction and Building Materials 87: 28–37. DOI: 10.1016/j.conbuildmat.2015.03.113.

28.

Harris

Somboonsong

(1998) New ductile hybrid FRP reinforcing bar for concrete structures. Journal of Composites for Construction 2(1): 28–37.

29.

ISIS Canada Research Network (2007) Reinforcing concrete structures with fibre reinforced polymers. Winnipeg, Manitoba, Canada: ISIS Canada: Design Manual No. 3, Version 2, the Canadian Network of Centers of Excellence on Intelligent Sensing for Innovative Structures. Canada: ISIS Canada Research Network

30.

Issa

Metwally

Elzeiny

(2011) Influence of fibers on flexural behavior and ductility of concrete beams reinforced with GFRP Rebars. Engineering Structures 33(5): 1754–1763. DOI: 10.1016/j.engstruct.2011.02.014.

31.

JPCI (2021) Recommendation for Design and Construction of Concrete Structures Using Fiber Reinforced Polymer (FRP). Tokyo: Japan Prestressed Concrete Institute.

32.

JSCE (1997) Machida

(ed) Recommendation for Design and Construction of Concrete Structures Using Continuous Fiber Reinforcing Materials. Tokyo: JSCE.

33.

Junaid

Elbana

Altoubat

, et al. (2019) Experimental study on the effect of matrix on the flexural behavior of beams reinforced with Glass Fiber Reinforced Polymer (GFRP) bars. Composite Structures 222: 110930. DOI: 10.1016/j.compstruct.2019.110930.

34.

Kara

Ashour

Dundar

(2013) Deflection of concrete structures reinforced with FRP bars. Composites Part B: Engineering 44(1): 375–384. DOI: 10.1016/j.compositesb.2012.04.061.

35.

Kara

Ashour

Köroğlu

(2015) Flexural behavior of hybrid FRP/steel reinforced concrete beams. Composite Structures 129: 111–121. DOI: 10.1016/j.compstruct.2015.03.073.

36.

Kheyroddin

Maleki

(2017) Prediction of effective moment of inertia for hybrid FRP-steel reinforced concrete beams using the genetic algorithm. Numerical Methods in Civil Engineering 2(1): 15–23. DOI: 10.29252/nmce.2.1.15.

37.

Lau

Pam

(2010) Experimental study of hybrid FRP reinforced concrete beams. Engineering Structures 32(12): 3857–3865. DOI: 10.1016/j.engstruct.2010.08.028.

38.

Wang

(2002) Flexural behaviors of glass fiber-reinforced polymer (GFRP) reinforced engineered cementitious composite beams. ACI Materials Journal 99(1): 11–21. DOI: 10.14359/11311.

39.

Liang

Peng

Ren

(2023) A state-of-the-art review: shear performance of the concrete beams reinforced with FRP bars. Construction and Building Materials 364: 129996. DOI: 10.1016/j.conbuildmat.2022.129996.

40.

Mohamed

Khattab

Al Hawat

(2017) Numerical study on deflection behaviour of concrete beams reinforced with GFRP bars. IOP Conference Series: Materials Science and Engineering 245: 032065. DOI: 10.1088/1757-899X/245/3/032065.

41.

Mousavi

Esfahani

(2012) Effective moment of inertia prediction of FRP-reinforced concrete beams based on experimental results. Journal of Composites for Construction 16(5): 490–498. DOI: 10.1061/(ASCE)CC.1943-5614.0000284.

42.

Mustafa

SAA

Hassan

(2018) Behavior of concrete beams reinforced with hybrid steel and FRP composites. HBRC Journal 14(3): 300–308. DOI: 10.1016/J.HBRCJ.2017.01.001.

43.

Nanni

Henneke

Okamoto

(1994a) Behaviour of concrete beams with hybrid reinforcement. Construction and Building Materials 8(2): 89–95. DOI: 10.1016/S0950-0618(09)90017-4.

44.

Nanni

Henneke

Okamoto

(1994b) Tensile properties of hybrid rods for concrete reinforcement. Construction and Building Materials 8(1): 27–34. DOI: 10.1016/0950-0618(94)90005-1.

45.

Nguyen

Zhang

Choi

, et al. (2020a) An improved deflection model for FRP RC beams using an artificial intelligence-based approach. Engineering Structures 219: 110793. DOI: 10.1016/j.engstruct.2020.110793.

46.

Nguyen

Dang

(2020b) Performance of concrete beams reinforced with various ratios of hybrid GFRP/steel bars. Civil Engineering Journal 6(9): 1652–1669. DOI: 10.28991/cej-2020-03091572.

47.

Pang

Zhu

, et al. (2016) Design propositions for hybrid FRP-steel reinforced concrete beams. Journal of Composites for Construction 20(4): 04015086. DOI: 10.1061/(ASCE)CC.1943-5614.0000654.

48.

Patil

Chellapandian

Suriya Prakash

(2020) Effectiveness of hybrid fibers on flexural behavior of concrete beams reinforced with glass fiber-reinforced polymer bars. ACI Structural Journal 117(5): 269–282. DOI: 10.14359/51725844.

49.

Peng

Deng

Xue

(2023) Design provisions for flexural strength of hybrid reinforced concrete beams with fiber-reinforced polymer and steel bars. ACI Structural Journal 120(1): 49–60. DOI: 10.14359/51736119.

50.

Zhang

Huang

(2009) Flexural behavior of concrete beams reinforced with hybrid (GFRP and steel) bars. Journal of Composites for Construction 13(5): 350–359. DOI: 10.1061/(asce)cc.1943-5614.0000035.

51.

Rafi

Nadjai

(2011) A suggested model for European code to calculate deflection of FRP reinforced concrete beams. Magazine of Concrete Research 63(3): 197–214. DOI: 10.1680/macr.9.00085.

52.

Ramachandra Murthy

Pukazhendhi

Vishnuvardhan

, et al. (2020) Performance of concrete beams reinforced with GFRP bars under monotonic loading. Structures 27: 1274–1288. DOI: 10.1016/j.istruc.2020.07.020.

53.

Ruan

, et al. (2020) Flexural behavior and serviceability of concrete beams hybrid-reinforced with GFRP bars and steel bars. Composite Structures 235: 111772. DOI: 10.1016/j.compstruct.2019.111772.

54.

Said

Shanour

Mustafa

, et al. (2021) Experimental flexural performance of concrete beams reinforced with an innovative hybrid bars. Engineering Structures 226: 111348. DOI: 10.1016/j.engstruct.2020.111348.

55.

Sarhan

Al-Zwainy

(2022) Analytical investigations of concrete beams reinforced with FRP bars under static loads. Structures 44: 152–158. DOI: 10.1016/j.istruc.2022.07.075.

56.

Sun

Feng

D-C

, et al. (2019) Experimental study on the flexural behavior of concrete beams reinforced with bundled hybrid steel/FRP bars. Engineering Structures 197: 109443. DOI: 10.1016/J.ENGSTRUCT.2019.109443.

57.

Tepfers

Tamužs

Apinis

, et al. (1996) Ductility of nonmetallic hybrid fiber composite reinforcement for concrete. Mechanics of Composite Materials 32(2): 113–121. DOI: 10.1007/BF02254777.

58.

Turkish Standards Institution (2020) Metallic Materials - Tensile Testing - Part 1: Method of Test at Room Temperature (ISO 6892-1:2019). Ankara, Turkey: Turkish Standards Institution.

59.

Turkish Standards Institution (2021) Concrete - Specification, Performance, Production and Conformity. Ankara, Turkey: Turkish Standards Institution.

60.

Unsal

Tokgoz

Cagatay

, et al. (2017) A study on load-deflection behavior of two-span continuous concrete beams reinforced with GFRP and steel bars. Structural Engineering & Mechanics 63(5): 629–637. DOI: 10.12989/sem.2017.63.5.629.

61.

Wang

Belarbi

(2011) Ductility characteristics of fiber-reinforced-concrete beams reinforced with FRP rebars. Construction and Building Materials 25(5): 2391–2401. DOI: 10.1016/j.conbuildmat.2010.11.040.

62.

Xingyu

Yiqing

Jiwang

(2020) Flexural behavior investigation of steel-GFRP hybrid-reinforced concrete beams based on experimental and numerical methods. Engineering Structures 206: 110117. DOI: 10.1016/j.engstruct.2019.110117.

63.

Yang

Sun

, et al. (2020) Experimental study of concrete beams reinforced with hybrid bars (SFCBs and BFRP bars). Materials and Structures 53(4): 77. DOI: 10.1617/s11527-020-01514-8.

64.

Zhu

Cheng

Gao

, et al. (2018) Flexural behavior of partially fiber-reinforced high-strength concrete beams reinforced with FRP bars. Construction and Building Materials 161: 587–597. DOI: 10.1016/j.conbuildmat.2017.12.003.