Introduction

Glass Fiber-Reinforced Polymer (GFRP) bars are a composite material that can be used as reinforcement for concrete structures. GFRP bars have several advantages over conventional steel bars, such as corrosion resistance, high tensile strength, thermal compatibility, electric and magnetic neutrality, thermal insulation, and lightweight (Hassanpour et al., 2022; Kinjawadekar et al., 2023). GFRP bars are a novel solution for durable and sustainable concrete structures. Concrete is one of the world's most widely used construction materials, but it has a significant drawback: it is weak in tension. Concrete is usually reinforced with steel bars to overcome this limitation, which provides tensile strength and ductility. However, steel bars are prone to corrosion, especially in harsh environments exposed to salt, chemicals, and moisture. Corrosion reduces the strength and service life of the reinforced concrete and causes cracking and spalling of the concrete cover, which may compromise the structural integrity and safety. To address this problem, researchers and engineers have developed an alternative reinforcement material: GFRP bars. GFRP bars are made of continuous glass fibres embedded in a polymer resin matrix, which protects them from corrosion and provides a strong bond with concrete. GFRP bars have several benefits over steel bars, such as corrosion resistance, high tensile strength, thermal compatibility, electric and magnetic neutrality, thermal insulation, and lightweight. These properties make GFRP bars suitable for various applications, such as bridges, parking structures, retaining walls, foundations, roads, and slabs, where durability and sustainability are required.

Many experimental flexural behaviour studies were conducted using the GFRP-reinforced bar. The study investigated concrete strength, reinforcement ratio, span-depth ratio and type of FRP bars (Barris et al., 2009; Chitsazan et al., 2010; Dowell et al., 2023; Feng et al., 2018; Kabashi et al., 2020; Kumar & Sundaravadivelu, 2017; Manfredi & Cosenza, 2000; Shamass & Cashell, 2020; Sijavandi et al., 2021; Xiao et al., 2021). Some more research was studied with numerical analysis (Kazemi et al., 2021; Shen et al., 2022), optimum analysis (Kaveh, 2013; Kaveh et al., 2020) and (Ramesh et al., 2021; Xingyu et al., 2020) numerical and experimental study was performed using the GFRP rebars. The ultimate load-carrying capacity is found, and deflection is three times higher than the steel-reinforced concrete beam. Similarly, the ultimate strength of a concrete beam reinforced with sand-coated GFRP bars is 1.4 to 2.0 times greater than that of a steel-reinforced concrete beam (Balendran et al., 2004). (Almahmood et al., 2020) examine the experimental results compared with the ultimate moment prediction of ACI 440.2R-17 and the existing theoretical equations for deflection prediction. It was found that the ACI 440.2R-17 reasonably estimated the moment capacity of both mid-span and middle support sections. (Sirimontree et al., 2021) studied the flexural behaviour, including the load–deflection relationship, the flexural capacity, the stiffness, and the mode of failure, which was investigated under a four-point loading test. The maximum load of the concrete beams reinforced with GFRP bars was higher than those reinforced with steel bars, up to 98%. (Kinjawadekar et al., 2023) studied the various properties of GFRP-reinforced beams to appreciate the applications of GFRP reinforcement in flexural members. Since the GFRP bar has high strength and no yield point, the conventional characterizations of ductility may not be applicable to determine whether GFRP-reinforced concrete components are ductile. Hence, a detailed study is needed to understand the behaviour of such structures.

The main objective of the studies is to increase the structural performance of the beam by using locally available material. The present study was conducted with a GFRP rebar concrete beam with various reinforcement ratios and grades of concrete. The study, including the load–deflection responses, mode of failure and crack width, was compared to the three groups of concrete beams. Numerical analysis, Finite Element Model (FEM), was developed in ANSYS software, and the predicted deflection is compared to the experimental results. The numerical analysis and proposed method give a better correlation to experimental results.

Experimental program

Properties of materials

The concrete beam was studied with three different grades of concrete (30 MPa, 40 MPa, and 50 MPa) and reinforcement ratios (0.75%, 1.02%, and 1.27%), respectively. This study used GFRP rebars (12 mm, 10 mm, and 8 mm) as tension, compression reinforcement and steel rebar (6 mm) for stirrups as shown in Fig. 1(a). The GFRP bars were bought from the Viruksha Composites Manufacturing Pvt Ltd in Telangana. The GFRP rebars were all tested as per the ASTM Standard (ASTM D7205-06) using a 400 kN capacity Universal Testing Machine (UTM), as shown in Fig. 1(b). The stress–strain curve for GFRP bars of 12 mm, 10 mm, and 8 mm diameters and a steel bar of 6 mm diameter, comparison stress–strain curves, is presented in Fig. 1(c). The mechanical properties of concrete compressive strength, GFRP rebars, and steel rebar were determined, and the average results of three samples are reported in Table 1. The physical properties of the materials are reported in Table 2.

Fig. 1
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Details of the GFRP rebars

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Table 1 Specimen designations and concrete strength and material properties of the steel and GFRP bars
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Table 2 Material properties of concrete, steel and GFRP bars
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Preparation of specimens

Three groups of concrete specimens were studied, and their geometric properties are given in Table 3. The GFRP rebar concrete beams were cast with different reinforcement ratios, and their cross sections are shown in Fig. 2(a). The preparation of the specimens consisted of three stages. In the first stage, GFRP rebars (12 mm, 10 mm and 8 mm) with a length of 2500 mm were prepared, and 8 mm steel rebar was provided as two-legged shear reinforcement at 100 mm c/c as shown in Fig. 2(b). In the second stage, the GFRP reinforcement cage was placed on the mould with proper alignment, and then the different grades of concrete were poured into the mould. The concrete was properly compacted with a vibrator to remove the voids. In the third stage, the specimens were kept at room temperature for 24 h. The next day, the specimens were removed from the mould and placed for curing for 28 days.

Table 3 Geometric details of specimens
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Fig. 2
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Geometric information of the specimen

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Test setup

GFRP-reinforced concrete beams were prepared for testing. The beam was tested with a 50 T capacity loading frame. The experimental setup is shown in Fig. 3. The total length of the specimens was 2500 mm, and the effective span of the specimen was 2400 mm. All specimens had one end hinged and the other end supported by rollers, with the support, placed 50 mm from each end. The four-point loading was applied on the beam at L/3 distance of 800 mm from the support condition, and the distance between the loading points was 800 mm. The deflection meter was placed at the mid-span of the beam. The rate of loading was maintained at 0.3 mm/minute in all specimens till failure. Static loading was applied to all beams, and the load increment interval are 2 kN was considered for this experimental study till the failure of the specimens.

Fig. 3
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Experimental setup of the specimen

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Results and discussions

Behaviour of load–deflection

The experimental study examined the load–deflection behaviour of GFRP-reinforced concrete beams and showed three groups of load–deflection curves in Fig. 4. The ultimate load of the group-30, B30-C1, and B30-C2 specimens is higher, and their deflection is lower than that of the B30-C specimens. Similar behaviour was observed in the remaining two groups. The ultimate load increased in the specimens B30-C1 and B30-C2 by 41.59% and 53.54% compared to the B30-C specimens. Similarly, the ultimate load increased in the specimens B40-C1 and B40-C2 by 36.65% and 67.62% compared to the B40-C specimens. Likewise, the ultimate load increased in the specimens B50-C1 and B50-C2 by 32.55% and 62.32% compared to the B50-C specimens. The mid-span deflection of the B30-C1 and B30-C2 specimens was reduced compared to the B30-C specimen. The reason for reducing the deflection was to increase the percentage of reinforcement by 0.75%, 1.03%, and 1.28% for B30-C, B30-C1, and B30-C2 specimens, respectively. To increase the reinforcement ratio, the mid-span deflection of all three groups of specimens was decreased (Kara & Ashour, 2012). Compared to the B40-C specimens, the mid-span deflection of the beams for the B30-C specimens is increased at the ultimate load by the following percentages for each specimen: 7.58% for B30-C and 4.30% for B30-C1, respectively. However, the mid-span deflection of the B30-C2 specimen was reduced by 7.33% compared to that of the B40-C2 specimen. Similarly, when the B50-C specimens were compared to the B40-C specimens, the mid-span deflection of the beams increased at the ultimate load by the following percentages for each specimen: 14.01% for B50-C, 25.80% for B50-C1, and 15.74% for B50-C2.

Fig. 4
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Load–deflection responses of all groups

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Figures 4(a), (b), and (c) represent the load–deflection responses of the three groups of specimens. Figure 4(a) shows that the specimens failed quickly with wide cracks after reaching the ultimate load. Similarly, Figs. 4(b) and (c) illustrate that the GFRP RC beam failed gradually with minor cracks after reaching the ultimate load. The reason for the gradual failure with minor cracks in specimens is to increase the concrete strength and the percentage of steel reinforcement.

Mode of failure

The experimental investigation was conducted, and the mid-span deflection was measured for the all-concrete beams. It was observed that increasing the concrete strength and reinforcement ratio reduced the deflection in the experimental study. Concrete crushing was a common failure mode in the concrete beams, and flexural failure was observed in three specimens, as reported in Table 4. The maximum failure occurred at the bottom of the tension zone of the specimen. The initial, ultimate and failure cracks were observed in the specimens B30-C1 and B30-C2, as shown in Fig. 5. The ductility increased by 13.94% for B30-C2, 27.09% for B40-C1, 70.89% for B40-C2, 28.99% for B50-C1, and 70.83% for B50-C2, compared to that of B30-C1, B40-C1, and B50-C1 specimens, respectively.

Table 4 Test results of specimens
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Fig. 5
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Tested specimens

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Effect of concrete strength and reinforcement ratio on crack width

The compressive strength of concrete and the reinforcement ratio affect the crack width of the concrete beams, as shown in Fig. 6. The initial crack width in the specimens B30-C, B30-C1, and B0-C2 were 0.15, 0.12, and 0.10 mm, respectively, for initial loads of 17.20 kN, 16.30 kN, and 21.40 kN. Compared to the B30-C, B40-C and B50-C specimens, the crack width of the concrete beams is reduced at ultimate load by the following percentages for each specimen: 3.98% for B30-C1, 5.86% for B30-C2, 9.68% for B40-C1, 18.26% for B40-C2, 4.55% for B50-C1 and 6.98% for B50-C2 respectively.

Fig. 6
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Compressive strength-cracks width respect percentages of reinforcement

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Increasing the concrete compressive strength and reinforcement ratio reduces the crack width, as noted in an experimental study shown in Fig. 7. The crack width at the ultimate point for the specimens B30-C, B30-C1, and B30-C2 are 2.35 mm, 2.26 mm, and 2.22 mm, respectively. Similarly, the crack width at the ultimate point for specimens B40-C, B40-C1, and B40-C2 is 1.36 mm, 1.25 mm, and 1.14 mm, respectively. Further crack width at the ultimate load for the specimens B50-C, B50-C1, and B50-C2 is 0.92 mm, 0.86 mm, and 0.82 mm, respectively.

Fig. 7
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Load versus cracks responses of all groups

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Numerical analysis

Finite Element Model (FEM)

The finite element model was developed using the ANSYS software. The Finite Element Analysis (FEA) was conducted to study the flexural behaviour of GFRP reinforced concrete beam. The FEA study included the load–deflection, initial, ultimate and failure load, and maximum deflection. The four-point loading was applied in this study, and the FEM is presented in Fig. 8.

Fig. 8
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3D model of the specimen

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Mesh convergence study

In this study, a mesh convergence study was used to determine the optimal mesh size for a finite element analysis of the beam is depicted in Fig. 9. This can help ensure that the results of the analysis are accurate and reliable. Based on the sensitivity analysis, a mesh size of 30 mm was chosen. This mesh size gives a good correlation and helps to predict the experimental results.

Fig. 9
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Meshing of the specimen

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Comparison of experimental study and numerical analysis load–deflection responses

The numerical analysis was compared with the experimental results reported in Table 5. Most of the concrete beams failed due to concrete crushing and flexural failure. The vertical and shear cracks that appeared at the initial load increased with further load up to the ultimate load. The numerical deflection model of the all-group specimens is illustrated in Fig. 10. The experimental and numerical results were compared, and the ultimate load, failure load, and deflection were depicted in Fig. 11(a) and (b). Figure 12 illustrates the experimental and numerical analysis of the initial and failure cracks. The Coefficient of Variation (CV) was 0.90% for ultimate load and 0.65% for failure load in experimental and numerical analysis, respectively.

Table 5 Comparison between experimental study and numerical analysis
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Fig. 10
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Comparison between experimental study and numerical analysis ultimate load and deflection

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Fig. 11
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Analytical model ultimate deflection responses of the three groups of specimens

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Fig. 12
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Comparison between experimental and analytical failure pattern

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In this study, a 3D model was developed and numerical analysis was performed on GFRP RC beams, including load, deflection, and mode of failure, using ANSYS software. The experimental ultimate load and deflection results were compared to the numerical ultimate load and deflection results presented in Fig. 10, and the comparison showed superior agreement and close correlation. The mean, standard deviation, and coefficient of variation for the ultimate load are 0.99, 0.01, and 0.90, respectively. Similarly, the mean, standard deviation, and coefficient of variation for the ultimate deflection are 0.97, 0.01, and 0.65, respectively.

Analytical study for deflection calculation

Deflection approach for current design codes

The effective moment of inertia is calculated from Branson’s approach using the following Eq. (1). Based on experimental results, Branson’s approach was modified to account for the effect of the moment of inertia (Alsayed et al., 2000). The modified Eq. (2) includes the reduction coefficient, bond properties, and modulus of elasticity of the GFRP rebars (Yost et al., 2003).

$$le = lg\left( {\frac{{M_{c} r}}{{M_{a} }}} \right)^{3} + lcr\left( {1 - \frac{{M_{c} r}}{{M_{a} }}} \right)^{3} \le lg$$
(1)

where:

$${\text{M}}_{{{\text{cr}}}} = \left( {\frac{{f_{r} }}{{f_{rb} }}} \right)$$
$$f_{{\text{r}}} = 0.{6}\sqrt {f^{\prime}_{c} }$$
$$\beta_{{\text{d}}} = \frac{1}{5}\left( {\frac{{\rho_{f} }}{{\rho_{fb} }}} \right) \le 1.0$$
(2)

where le is the effective moment of inertia, lg is the effective moment of inertia of the gross section, and lcr is the effective moment of inertia cracking the transferred concrete area. Mcr, Ma, \(f^{\prime}_c\)and fr are referred to as cracking moment, service moment, compressive strength of concrete and modulus of rupture.

Proposed method

Based on the previous equations, the effective and theoretical moment of inertia is calculated on the Eqs. (3) and (4). The modification factor βd was determined in an actual and balanced ratio is given Eq. (5). Experimental load–deflection data were used to calculate the coefficient of X1 and X2 values.

$$({\text{I}}_{{\text{e}}} )_{{{\text{exp}}}} = \frac{{P_{{{\text{exp}}}} {\text{L}}_{{\text{a}}} }}{{48E_{c} \delta_{\exp } }}\left( {3L^{2} - 4L_{a}^{2} } \right)$$
(3)
$$(le)_{Theo} = \beta_{d} \left( {\frac{{M_{cr} }}{{M_{a} }}} \right)^{3} l_{g} + X_{2} \left. {\left( {1 - \frac{{M_{cr} }}{{M_{a} }}} \right)^{3} } \right)l_{c} r \le lg$$
(4)
$$\beta_{{\text{d}}} = {\text{X}}_{{1}} \left( {\frac{{\rho_{f} }}{{\rho_{fb} }}} \right) \le {1}.0$$
(5)

where: Ec is the modulus of elasticity of the concrete, \(\delta\) is the mid-span deflection of the specimens, and L and La is the total and effective length of the specimen. ρf and ρfb are referred to as actual and balanced reinforcement ratios. βd is the modification factor.

Evaluation of the proposed method

The experimental results were compared to the proposed methods, (ACI 440.1R-06) and (CSA S806-02). The numerical analysis is reported in Table 6. The effective and theoretical moment of inertia was calculated from Eqs. (3) and (4). The experimental mid-span deflection agreed with the proposed method: the mean, standard deviation, and coefficient of variation are 0.98, 0.02, and 2.12%, respectively. Similarly, the numerical analysis also closely correlated with the experimental results: the mean, standard deviation, and coefficient of variation are 0.97, 0.01, and 1.18%, respectively. The mid-span deflection was predicted by ACI 440.1R-06 and CSA S806-02. Their mean values are 1.00 and 0.99. The standard deviation values are 0.04 and 0.05, and the coefficient of variation values are 3.94% and 4.59%, respectively. Based on the experimental codes and proposed mid-span deflection deviation, 10% was observed and is depicted in Fig. 13.

Table 6 Comparison between experimental, codes, proposed method and numerical prediction deflection
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Fig. 13
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Evaluate the experimental, codes, proposed method and numerical deflection of specimens

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Conclusion and recommendation

The study investigated the flexural behaviour of concrete beams reinforced with GFRP bars using experimental, numerical and analytical methods. The experimental tests were performed on beams with three different concrete grades and reinforcement ratios. The numerical and analytical results were validated by comparing them with the experimental deflections. The main conclusions of the study are as follows:

  1. (1)

    The GFRP concrete beams were studied with various grades of concrete (30 MPa, 40 MPa, and 50 MPa) and reinforcement ratios (0.75%, 1.02% and 1.28%), respectively. All GFRP concrete beams failed the same concrete crushing and flexural failure behaviour.

  2. (2)

    The load-carrying capacity of GFRP RC beams was enhanced by increasing the grade of concrete (40 MPa and 50 MPa) and reinforcement ratio (1.02% and 1.28%).

  3. (3)

    Compared to the B30-C, B40-C and B50-C specimens, the crack width of the concrete beams is reduced at ultimate load by the following percentages for each specimen: 3.98% for B30-C1, 5.86% for B30-C2, 9.68% for B40-C1, 18.26% for B40-C2, 4.55% for B50-C1 and 6.98% for B50-C2 respectively.

  4. (4)

    The experimental results were compared to the numerical analysis, and the ultimate and failure load prediction was agreed with the experimental results. The mean, standard deviation and coefficient of variation were 0.99, 0.01, and 0.90% for the ultimate load and 0.98, 0.01, and 0.61% for the failure load respectively.

  5. (5)

    The deflection of the concrete beams was estimated using four different methods: ACI 440.1R, CAS S806, the proposed method, and numerical analysis. The ACI 440.1R and CAS S806 methods did not produce deflections that matched the experimental results. On the other hand, the proposed method and numerical analysis yielded deflections that closely agreed with the experimental results. For these studies, the CV values were 3.94%, 4.59%, 2.12%, and 1.18%, respectively.

The present study examined the flexural behaviour of GFRP bars with three different grades of concrete under four-point loading. Furthermore, research will continue with adding fibres and various loading conditions.