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Abstract

Concrete-filled fiber-reinforced polymer (FRP) tubes (CFFTs) with angle-ply configurations, such as ±55˚ glass-FRP (GFRP) tubes, show highly nonlinear behavior that is not captured by conventional cross-ply tubes. A key challenge has been capturing their failure strains under tension, since large deformations have prevented accurate measurements with conventional instrumentation. This study addresses this challenge by introducing a novel test configuration capable of capturing the tensile response of ±55˚ GFRP tube filled with concrete (±55˚ CFFTs) under pure axial tension. A well-instrumented ±55˚ CFFT beam test was conducted, which recorded ultimate tensile strain of 0.077 mm/mm for the first time. To complement the experiments, nonlinear finite element (FE) models were developed to simulate ±55˚ CFFTs tensile behavior. The models successfully reproduced the nonlinear response with only 3%–4% variance from experimental results. Building on these findings, a design-oriented constitutive tension equation was formulated specifically for ±55˚ GFRP tubes, and an analytical model incorporating this equation was then established to predict the moment capacity of ±55˚ CFFT beams, and validation against multiple experimental beam tests demonstrated strong predictive accuracy (85%–100% agreement in ultimate load and deflection), representing a substantial improvement over existing models.

Keywords

CFFT angle-ply tube nonlinear behavior concrete-filled tube tension flexure

Introduction

Fiber-reinforced polymers (FRPs) have emerged as effective materials in the realm of sustainable infrastructure, owing to their remarkable attributes such as high strength, lightweight, corrosion resistance, and compatibility with concrete core in composite structures (Ahmad et al., 2008b; Ahmed et al., 2024; Allawi et al., 2025; Fam et al., 2003; Fam and Rizkalla, 2001, 2002; Mirmiran and Shahawy, 1996; Qasrawi et al., 2015; Salman and Allawi, 2024, 2025; Shao and Mirmiran, 2005; Yuan and Mirmiran, 2001). Aside from the widely used FRP reinforcing bars and FRP retrofitting systems, the versatile FRP materials find applications across a spectrum of other infrastructural elements, ranging from fender piling and dolphins to light-structural piling, girders, and bridge pier protection (Fam et al., 2003; Fam and Rizkalla, 2003; Helmi et al., 2005). Among FRP based structures, concrete-filled FRP tubes (CFFTs) have garnered substantial attention over the past three decades, with extensive research dedicated to unraveling their fundamental behavior (Alinejad et al., 2022; Fam and Rizkalla, 2002; Gemi et al., 2018; Green et al., 2006; Mirmiran et al., 2000; Mirmiran and Shahawy, 1997; Qasrawi and Fam, 2008; Roy and Sadeghian, 2021; Samaan et al., 1998).

One commercially available configuration, notably featuring glass-FRP (GFRP) with a ±55˚ orientation with respect to the longitudinal axis of the tube, has become prominent in such structural applications. Carroll et al. (1995) examined the rate-dependent behavior of ±55° filament-wound GFRP tubes under biaxial loading, offering insights into the dynamic response of these composite tubes. Bai et al. (1997) presented a micromechanical model of damage initiation and comparing different mechanisms governing the behavior of ±55˚ GFRP tubes, enhancing our understanding of damage mechanisms in these structures. Mirmiran et al. (2000) investigated for the first time the bending behavior of ±55˚ GFRP tubes filled with concrete, referred to hereafter as CFFTs, under 4-point bending. Fam and Rizkalla (2002) studied the flexural behavior of CFFTs of different sizes and laminate structures, providing one of the earliest and most comprehensive data set on their structural performance. Zhu et al. (2006) examined the splicing techniques for precast CFFTs, addressing challenges and providing solutions to ensure structural continuity and integrity in composite members. Ahmad et al. (2008a) investigated the behavior of short and deep CFFT beams, showing how slip governs failure in unreinforced short CFFT beams. The effect of fiber orientation on the nonlinear behavior of angle-ply carbon-FRP (CFRP) composites, which offers insights into material behavior for ±55˚ GFRP tubes, was studied by Sadeghian et al. (2009). Khalifa et al. (2012) characterized the mechanical properties of glass/vinyl ester ±55˚ filament-wound pipes using acoustic emission under axial monotonic loading, providing insights into their failure mechanisms. Zakaib and Fam (2012) studied the flexural performance and moment connection of concrete-filled GFRP tube-encased steel I-sections, showcasing the potential of ±55° GFRP tubes in composite structural applications.

Preliminary cross-sectional analysis by the authors, assuming linear behavior for ±55˚ GFRP tubes in both tension and compression, revealed significant discrepancies—the model predicted a moment capacity of only about 27% of the experimental results. Also, the newly released ACI PRC-440.14-25 guide (American Concrete Institute, 2025) limits one-third of the fibers to be oriented between ±35° relative to the tube’s axial direction, acknowledging the significant non-linear behavior that occurs at higher angles. Additionally, the results of previous studies unveiled a highly ductile, nonlinear behavior in ±55˚ GFRP tubes filled with concrete (±55˚ CFFTs), surpassing that of other CFFT laminate configurations. Although these studies collectively demonstrate the exceptional nonlinear behavior of ±55° CFFTs, a clear understanding of the underlying mechanisms contributing to this behavior remains limited. Subsequent studies conducted by Betts et al. (2019, 2021) further explored the behavior of ±55 hollow tubes under various loads which confirmed the remarkable nonlinear behavior. A new analytical model was then developed to incorporate these nonlinear features in both tension and compression. Although this adjustment brought the CFFT analytical flexural results closer to the experimental findings, the models continue to underestimate flexural strength by a considerable margin. Consequently, the persistent underestimation raised a new hypothesis that the material behavior of ±55 tubes changes significantly in tension when filled with concrete, as opposed to hollow tubes. To evaluate this hypothesis, Khan (2020) introduced a new tension testing configuration for ±55˚ CFFTs, whose results supported the hypothesis. Finite element (FE) modeling has also been employed to simulate the behavior of these specimens under pure tension loads (Jawdhari et al., 2022; Sadat Hosseini and Sadeghian, 2022). In particular, the highly advanced FE model presented by Jawdhari et al. (2022) proposed and indeed demonstrated, the hypothesis of ‘tension-tension’ stiffening of ±55˚ tubes when filled with concrete in which the material gains considerable strength by means of the bi-axial strength phenomenon. The proposed constitutive relation introduced in this study (Jawdhari et al., 2022) helped reduce the gap between theoretical and experimental moment capacity of ±55˚ CFFT members considerably but could not fully close this gap. It became clear that an additional missing component remains unaccounted for in flexural strength of ±55˚ CFFTs. Considering these challenges, revisiting and refining existing models becomes imperative to address this research gap concerning the nonlinear behavior and strengthening effect of ±55˚ tubes when filled with concrete that leads to higher CFFT flexural strength than what all models show.

This study embarks on a comprehensive evaluation of the behavior of ±55˚ CFFTs, unfolding in multiple phases. Both direct tension experimental tests and beam tests were first carried out. Then, nonlinear FE analyses were verified against the experimental results and compensated for their limitations. Building upon the insights gleaned from experimental results and FE analyses, a novel design-oriented equation was formulated to characterize the tensile behavior of ±55˚ GFRP tubes when filled with concrete. Finally, the newly proposed design-oriented equation was integrated into an analytical sectional analysis model aimed at predicting the moment capacity of ±55˚ CFFTs. Leveraging this model, a simplified method was devised to calculate the moment capacity of CFFT beams.

Experimental studies

In this phase, the investigation is focused on two distinct tests: the axial tensile test of ±55˚ CFFTs and the four-point bending test of a ±55˚ CFFT beam. Five CFFTs were manufactured specifically for the purpose of axial tension testing, aiming to gain insights into the tensile behavior of them. Several studies (Ahmad et al., 2008a; Lu and Fam, 2020; Mirmiran et al., 2000; Zakaib and Fam, 2012; Zhu et al., 2006) have investigated the ±55˚ CFFT beams. However, they were unable to record the value of the large ultimate tensile strain of the tube. In this study, a carefully fabricated and instrumented CFFT beam was subjected to a four-point bending test to determine the ultimate tensile strain and the full nonlinear behavior of the ±55˚ CFFT.

CFFT tension test

There are two objectives to carry out the tension tests: first, is to assess the hypothesis of ‘tension-tension’ stiffening of ±55˚ GFRP tubes when filled with concrete by comparing hollow and concrete-filled tubes, and second is to develop an accurate stress-strain curve of concrete-filled ±55˚ GFRP tubes. The first two ±55˚ CFFT tension tests conducted by Khan (2020) resulting in premature failure at one end of the specimens. Several attempts were made to prevent premature failure, leading to the fabrication of three more dumbbell-shaped specimens, as illustrated in Figure 1. All tubes used in this study were manufactured by RPS Composites (Mahone Bay, NS, Canada) using continuous roving electrical and chemical resistance (ECR) glass fibers embedded in a bisphenol-A (BIS-A) vinyl ester resin (Ashland Derakane 411). The tubes featured a fiber volume fraction of 50% and a fiber orientation of ±55° with a tolerance of ±2°. The tube’s properties are listed in Table 1. The ±55˚ GFRP tube used in this study is a commercially available product, and its dimensions are determined by manufacturing standards established for the pipeline industry, particularly based on pressure requirements. Therefore, the specimen geometry in this investigation reflects practical, readily available tube sizes. The third specimen mirrored the dimensions of the first two specimens, measuring 0.6 m in length, while both ends were strengthened using bonded CFRP sheets to mitigate the risk of premature failure (Figure 1(a)). The fourth specimen, 0.9 m in length, incorporated ends reinforced with Basalt-FRP (BFRP) sheets to alleviate stress concentration arising from the substantial difference in modulus of elasticity of CFRP and GFRP (Figure 1(b)). The fifth specimen, with a length of 1.2 m, featured a thin plastic layer at mid-heigh to simulate a crack in the concrete core. This specimen was strengthened at both ends with 10 layers of BFRP and two layers of CFRP (Figure 1(c)).

Figure 1.

Instrumentation of dumbbell-shaped CFFTs: (a) P1050-D76-3; (b) P1050-D76-4; (c) P1050-D76-5; and (d) schematical configuration of the instruments.

Table 1.

Properties of dumbbell-shaped CFFT specimens.

Test #	Specimen name	Nominal pressure rating (kPa)	Inner diameter (mm)	Wall thickness (mm)	Length (mm)	Filament wind layup (˚)	Concrete compressive strength ( $f_{c}^{'}$ )
1	P1050-D76-1	1050	76	3.8	600	[±55]₇	38.56
2	P1050-D76-2	1050	76	3.8	600	[±55]₇	38.56
3	P1050-D76-3	1050	76	3.8	600	[±55]₇	38.56
4	P1050-D76-4	1050	76	3.8	920	[±55]₇	34.55
5	P1050-D76-5	1050	76	3.8	1200	[±55]₇	43.23

To prepare the specimens, one end of the tube was secured with a customized fixture, as shown in Figure 2, while concrete was poured into the tube from the opposite end. The specimens were placed in a moisture room after 24 hours and cured for 28 days. Furthermore, six concrete cylinders (100 × 200 mm) were cast for each dumbbell-shaped CFFT to measure the compressive strength of the concrete core at 28 days and on the actual tension test day. The compressive strength test results of the concrete core for all specimens are presented in Table 1. The customized fixture was engineered to facilitate the tension test as shown in Figure 2. The fixtures were inserted into the tube’s ends and securely fastened with bolts. The two end rods were secured in the grips of a 2 MN Instron testing machine, with the top grip fixed in place while the bottom grip moved downward to apply axial tension to the ±55° CFFT specimens. Two axial strain gauges and two hoop strain gauges were installed on the tubes, along with two displacement-type PI-gauges, as shown in Figure 1(a)–(c), and schematically in Figure 1(d). The PI-gauges were used in all tests since the strain gauges are limited in strain capacity while high ultimate strain was expected for ±55˚ CFFTs. Additionally, a camera was utilized to record all events during the test such as noise and tube discoloration. The tension tests were conducted under displacement control at a loading rate of 2 mm/min.

Figure 2.

Customized fixture for preparing and testing ±55˚ CFFTs in tension.

The test results are presented as load-strain curves along with the failure modes of the specimens in Figures 3 and 4, respectively. Figure 3 presents the load-strain curves all 5 specimens, illustrating a drop in the curves for the first four tests when the applied load approached 60 kN. This drop is attributed to the first crack in the concrete core, which was accompanied by a loud noise. This event did not occur in the fifth test because of the deliberate separation of concrete at mid-height using the plastic sheet. Across all five tests, the curves exhibit bi-linear behavior, with the second slope beginning around 90 kN. This shift in slope is attributed to crack initiation in the tube’s matrix, as evident by rapid discoloration and subtle noises within the tube. Additionally, the strain gauges failed during the first two tests, and no PI-gauge was installed on the first and second specimens. Consequently, the data beyond a load of approximately 100 kN rely on the calibrated stroke measurements of the 2 MN Instron machine. The ultimate loads and corresponding strains were 145.4 kN and 0.032 mm/mm for the first specimen, 139.0 kN and 0.024 mm/mm for the second, 169.4 kN and 0.045 mm/mm for the third, 122.9 kN and 0.030 mm/mm for the fourth, and 152.7 kN and 0.046 mm/mm for the last specimen. Figure 3 also shows the comparison of the filled and hollow tubes tensile behaviour. The outcomes of these tests lend support to the hypothesis of tension-tension stiffening, indicating that the tensile behavior of ±55 GFRP tubes when filled with concrete is significantly enhanced from hollow tubes. However, premature failures prevented the complete acquisition of the load-strain curves for the specimens. The transition zone between the small and large diameters (Figure 2), which required strengthening, proved to be their weak point. In the first and second specimens, failure happened at one end of them due to stress concentration. The failure of the third specimen initiated with debonding between the CFRP and the tube, culminating in the rupture of one end of the tube. The fourth specimen experienced premature failure due to stress concentration at one end, exacerbated by the orientation of BFRP fibers in the hoop direction. In the last specimen, failure ensued as the bolts fastening the tube to the fixture sheared off at one end. These premature failure modes are visually presented in Figure 4(a)–(c), respectively.

Figure 3.

Load-strain curves of the dumbbell-shaped CFFT tensile tests Note: The load-strain curves for Test #1 and Test #2 are based on the findings of Khan (2020), while the load-strain curve for the hollow tube is derived from the study by Betts et al. (2019).

Figure 4.

Premature failure modes of dumbbell-shaped CFFTs: (a) P1050-D76-3; (b) P1050-D76-4; and (c) P1050-D76-5.

CFFT bending test

A CFFT beam, measuring 203 mm in inner diameter and 2 m in length was fabricated. The ±55 GFRP tube, composed of 8 layers of GFRP, was cut to the desired length, secured in a vertical position and filled with concrete, then sealed on the top. The tube’s thickness, as reported by the manufacturer and as shown in Figure 5, was 4.7 mm, including a 0.38 mm liner and a 0.25 mm resin coat, while the structural thickness was 4.07 mm (Betts et al., 2019). The liner protected the filament-wound section from corrosive environments, while the resin coat shielded it from liquids inside the tube. Additionally, six concrete cylinders (100 × 200 mm) were cast to be tested on day 28 and the test day. The compressive strength of the concrete is presented in Table 2. The CFFT beam was equipped with a comprehensive array of measurement instruments, including four linear potentiometers, four string potentiometers, seven longitudinal strain gauges, three hoop strain gauges, and two PI gauges. These instruments are strategically installed on the CFFT beam, facilitating the acquisition of data during the four-points bending test, as shown in Figures 6(a) and (b). The span length for the four-point bending test was 1.5 m, with 0.5 m between the loading points. Span-to-diameter and shear span-to-diameter ratios were carefully selected to balance stability near failure (i.e. achieve manageable rotations at supports under the expected large deflections). Roller supports were positioned at each end and at each loading point.

Figure 5.

Pipe cross section (measurements are provided by manufacturers).

Table 2.

Properties of ±55˚ CFFT beams taken from the literature.

Reference	Specimen ID	Outside diameter (mm)	Thickness (mm)	E_Ten. (GPa)	E_Comp. (GPa)	σ_Ten. (MPa)	σ_Comp. (MPa)	f^’_c (MPa)	Span (mm)	Shear span (mm)
Mirmiran et al. (2000)	T2S3	369.2	6.6	12.6	8.7	71	230	25.9	2286	711
Zhu et al. (2006)	Control	322.2	5.1	12.6	8.7	43.5	71	36.6	1830	610
Ahmad et al. (2008b)	S-4	322	5.1	12.5	8.7	43.5	71	31	1830	644
Zakaib and Fam (2012)	CFFT4	115	5.07	-	-	53	-	35	800	285
Lu and Fam (2020)	F2	142.4	5.4	6.9	6.4	54	122	29	900	300
Current study	C1	213	4.7	10.7	8.3	71	120	37.5	1500	500

Figure 6.

Four-points bending test’s setup: (a) in the laboratory; and (b) schematical drawing.

Deflections were measured using three string pots, placed at mid-span and under the loading points, allowing for the determination of the beam’s deformed shape under varying loads. Tensile strain in the tube could be calculated by analyzing the beam’s deflection curve over the loading history, providing crucial data if stain gauges or PI-gauges failed during the test. For direct strain measurement of the tube, 10 strain gauges and two PI-gauges were employed. Additionally, four linear potentiometers were used to monitor the slip between the concrete core and the tube. To capture the test procedure, noises of the specimen, and various reactions of the beam, three cameras were utilized. The test was conducted under displacement control at a loading rate of 7 mm/min.

As shown in Figure 7, the final tensile strain recorded in the initial test was 0.072 mm/mm. However, premature failure happened because of the instability of one of the supports. To determine the precise ultimate tensile strain, the CFFT beam test was replicated. In the subsequent test, the span was reduced to 1.25 m to address damage observed near one of the supports during the initial test. This adjustment reduced the shear span-to-depth ratio from 2.46 to 1.85, while maintaining a loading points distance of 0.5 m. The failure observed in the second test is identified as tensile failure in the tube, as visually represented in Figure 8. Figure 7 illustrates the moment-tensile strain curves, providing insight into the specimens’ behavior, with these curves selected to account for the different shear span-to-depth ratios in the two tests. The findings indicated that the ultimate tensile strain of ±55˚ CFFT specimens was 0.077 mm/mm. This value is very important as it is the first recorded ultimate tensile strain of a ±55 GFRP tubes filled with concrete. It is also critical to complete the full stress-strain curve of this material.

Figure 7.

Moment-tensile strain curves of the first and second tests on the CFFT beam.

Figure 8.

Failure mode of the CFFT beam.

Finite element modeling

This section presents an FE simulation of the ±55˚ CFFT specimens tested in tension using ABAQUS software and aiming to characterize the tensile behavior of them. Key aspects of the modeling process, including the material properties, boundary conditions, and mesh refinement, are outlined, and the results of the simulation are compared with experimental data to validate the model’s accuracy.

Model parameters

The simulation of the ±55˚ CFFT specimen utilized its symmetrical properties across two planes to optimize computational efficiency by modeling only one-quarter of the specimen. This approach effectively reduced the computational runtime while preserving the accuracy of the analysis. The concrete core was modeled as a solid part with a density of 2400 kg/m³ and an elasticity modulus of 4700 $\sqrt{f_{c}^{'}}$ , where $f_{c}^{'}$ denotes the concrete’s compressive strength. Plasticity behavior of the concrete was defined according to guidelines provided in the ABAQUS Manual (2014). For compressive behavior, the unconfined model proposed by Popovics (1973) was utilized to characterize the stress-strain relationship. The tensile behavior of the concrete was considered linear until it reaches its tensile strength. Upon exceeding the tensile cracking strain, the tension softening effect was incorporated using the model suggested by Collins and Mitchell (1997). Additionally, concrete compression and tension damage were defined as outlined in the ABAQUS Manual (2014). The tube was modeled using the Hashin damage model, with input parameters derived from the study conducted by Betts et al. (2019). The Hashin damage model distinguishes between different failure modes, including fiber tension, fiber compression, matrix tension, and matrix compression. The tube was represented as a laminate comprising 14 layers, identical to the tube used in the tension tests. The total thickness of the tube, including the resin coating and liner, was 3.8 mm, whereas the structural thickness was 3.2 mm. To accurately simulate the strengthened parts at both ends of the specimen, additional layers of CFRP were incorporated to achieve the exact thickness of these reinforcement sections.

Surface-to-surface contact was implemented to describe the interaction between the tube and the concrete core. A penalty friction formulation was employed with a friction coefficient of 0.16 to model tangential contact behavior, while “Hard” contact was utilized to simulate normal contact behavior. The “Hard” contact behavior permits the separation of the two parts without allowing penetration. Additionally, the rigid parts situated at both ends of the model were tied to the tube, mirroring the fastening of steel fixtures to the tube using bolts. Using boundary conditions in the load module, two symmetry planes were established. This allowed for the modeling of one quarter of the specimen. Additionally, one end of the specimen was fully immobilized, while the other end was permitted axial movement. The load was imposed on the rigid part as a displacement-controlled load. All the boundary conditions are depicted in Figure 9(a).

Figure 9.

FE quarter model of dumbbell-shaped CFFTs: (a) boundary conditions; and (b) meshed specimen.

The meshed specimen is also shown in Figure 9(b). A mesh sensitivity analysis was performed to determine the optimal mesh size for the concrete core. The analysis was conducted based on ultimate load and ultimate strain (Figure 10(a)), as well as the first and second slopes of the load-strain curve of the FE models (Figure 10(b)). The coarsest mesh size considered for the concrete core was 10 mm, which was progressively refined by 2.5 mm. The finest mesh, initially set at 2.5 mm, was then increased in increments of 0.5 mm to identify the optimal size, which was determined to be 3.5 mm. The mesh size of the tube has minimal impact on the FE model run time since it is defined as a shell element, which inherently contains fewer elements compared to a three-dimensional (3D) solid element. Therefore, a fine mesh size of 3 mm was selected for the tube. For the part representing the tube, four-node, quadrilateral, stress/displacement shell elements with reduced integration (S4R) were utilized. Meanwhile, continuum, three-dimensional, eight-node, and reduced integration order elements (C3D8R) were employed to mesh the part representing the concrete core.

Figure 10.

Mesh sensitivity analysis based on: (a) ultimate load and ultimate strain; and (b) first and second slop of the load-strain curve.

FE model verification

Various criteria were employed for validation, including comparing the failure mode of the specimen with that of the model and assessing the correspondence between the load-strain curves of both the specimen and the model. As the exact failure mode of the specimen remained uncertain due to premature failures, the decision was made to model the third specimen for several reasons. Notably, the third and fifth specimens were in better condition compared to the other ones, with premature failures occurring at higher loads. Additionally, the premature failure of the fifth specimen resulted from sheared-off bolts. Considering the simplification which can be achieved by excluding bolt representation, the fifth specimen was deemed unsuitable for FE modeling. Therefore, selecting the third specimen for FE modeling was considered the most appropriate choice.

Figure 5(a) illustrates the premature failure mode of the third specimen, occurring at one end due to fiber rupture in a tube section, with visible cracks in the concrete core. Correspondingly, Figures 11(a) and (b) depict the identical failure pattern in the FE model. Figure 11(a) exhibits tube rupture at one end of the tube, consistent with experimental findings, and Figure 11(b) displays cracks in the concrete core, matching well with test observations. Additionally, the concrete core was observed to have crushed at the position of premature failure, a pattern replicated in the model. The second criterion for assessing the validity of the model is comparing the load-strain curves of both the model and the experimental test. This comparison is illustrated in Figure 12. It can be observed that the first drop, associated with the initial crack formation in the concrete core, occurs at approximately 60 kN for both the model and the test. Subsequently, at around 90 kN, both the model and the test exhibited a change in slope, attributed to cracks forming in the matrix of the tube. The ultimate load recorded in the model was 175.1 kN, which closely aligns with the test’s ultimate load of 169.4 kN. Moreover, the ultimate tensile strain observed in the model at the mid-height of the specimen was 0.047 mm/mm, a value close to the 0.045 mm/mm observed in the test. The FE model’s overall behavior aligns well with the experimental test results, as evidenced by the comparison of failure modes and load-strain curves, which show a good correlation between the two.

Figure 11.

FE model results: (a) GFRP tube failure; and (b) concrete tension and compression damage.

Figure 12.

Comparison between the load-strain curve of the CFFT tension test and the FE model.

FE model optimization

Figure 11(a) shows that, based on the FE model results, damage to other parts of the tube remains below 60% when premature failure occurs at one end of the specimen, with the middle section appearing nearly undamaged. To prevent such premature failures, refinement efforts were essential to improve the FE model. One possible reason for the premature failure was stress concentration at the ends of the specimen due to the change in diameter of the GFRP tube. The second reason is because of the coincidence of two weak points where the premature failure happened. The first weak point arises from stress concentration described earlier, while the end of the concrete core represents the second weak point, aligning with the first one. To address the stress concentration, identified as the primary cause of premature failure, a longer transition section was recommended, allowing the strengthened area to gradually increase in thickness. It was also suggested to extend the concrete core length to prevent the alignment of the two weak points. Additionally, increasing the number of CFRP layers at both ends of the tube was advised to strengthen these sections and prevent premature failure, as observed in the fourth tension test. These three enhancements were ultimately incorporated into the primarily FE model to develop a refined version.

Following the FE analysis on the refined model using ABAQUS, the damaged tube, shown just before specimen failure, and its corresponding stress-strain curve are depicted in Figures 13(a) and 12(b), respectively. Figure 13(a) depicts widespread damage across all segments of the tube, indicating close-to-full utilization of its strength. Additionally, the stress-strain curve highlights an ultimate strain of 0.076 mm/mm, mirroring the value obtained in the four-point bending test. Notably, the stress-strain curve generated from the FE analysis on the refined model closely aligns with the trend observed in the experimental test. The absence of premature failure in the tube within the refined model analysis demonstrates the successful capture of its stress-strain behavior under tension when filled with concrete. Another FE model developed to simulate the tensile behaviour of ±55 GFRP tubes filled with concrete had been presented by Jawdhari et al. (2020). That FE model was based on limited data and failed to capture the second slope of the load-strain curve for CFFT under tension. Furthermore, due to the lack of data on the ultimate tensile strain of the ±55 GFRP tube, the FE model by Jawdhari et al. (2020) was unable to predict it accurately. Figure 13(b) compares the load-strain curves of the refined FE model with those of the Jawdhari et al. (2020) model. The ultimate tensile strain predicted by the Jawdhari et al. (2020) FE model is 0.0337 mm/mm, which is approximately half of the value obtained from the four-point bending test and predicted by the refined FE model.

Figure 13.

Refined FE model: (a) Damaged GFRP tube; and (b) Stress-strain curve of the GFRP tube.

A design-oriented equation was proposed based on the experimental tests and refined FE model results to accurately represent the nonlinear stress-strain behavior of the tube when filled with concrete, aiming to facilitate analytical procedures, particularly in calculating the flexural capacity of CFFTs. Both experimental and numerical findings indicate a bi-linear stress-strain curve, characterized by distinct initial and secondary slopes connected by a nonlinear transition zone. To model this behavior, a widely-used format for the confined concrete stress–strain curve was employed, characterized by a single power equation as shown in equation (1).

f (ε) = \frac{(E_{1} - E_{2}) ε}{{[1 + {(\frac{E_{1} - E_{2}}{f_{u} - E_{2} ε_{c u}} ε)}^{n}]}^{\frac{1}{n}}} + E_{2} ε

(1)

In this general expression by Richard and Abbott (1975), which was adopted by many researchers (Jawdhari et al., 2022; Khorramian and Sadeghian, 2021; Samaan et al., 1998),

f

and

ε

denote longitudinal stress and strain;

E_{1}

and

E_{2}

are the initial and secondary moduli;

f_{u}

and

ε_{u}

represent peak stress and strain; and

n

defines the curvature of the transition zone. The resulting curve, based on the Richard-Abbott expression, was fitted to the load-strain curve from the refined FE model to establish a design-oriented equation (i.e., Equation (2)). Figure 13(b) demonstrates the consistency between the stress-strain curve derived from the design-oriented equation and the refined FE model outcomes.

f (ε) = \frac{11250 ε}{{[1 + {(107 ε)}^{4}]}^{\frac{1}{4}}} + 1750 ε

(2)

Analytical modeling

In this section, an analytical study was conducted to evaluate the effectiveness of the newly proposed design-oriented equation. To support this effort, a computational code was developed using MATLAB software to enable precise cross-sectional analysis for predicting the flexural capacity of ±55˚ CFFTs. The code was designed to incorporate key parameters, including material properties and the geometries of the CFFT beams, ensuring accurate prediction of their moment capacity. This analytical approach was validated by applying the model to previously tested CFFTs subjected to four-point bending tests, allowing for a comprehensive comparison between the experimental results and the model’s predictions.

Cross-sectional analysis

Properties of several CFFTs, as detailed in Table 2, served as inputs and defined the geometries of the CFFTs to be incorporated in cross-sectional analysis. A layer-by-layer approach was employed, facilitating the numerical integration of stresses across the cross-sectional area. Figure 14 illustrates both the cross-section and the idealized geometry pertinent to the given problem. $D_{o}$ represents the outside diameter of the tube, and $t$ denotes the thickness of the tube. $D$ signifies the average diameter of the tube, while $n$ indicates the number of fibers dividing the section. Each fiber has a thickness represented by $h_{i}$ , and the depth of the center of each fiber is denoted by $h (i)$ . $L (i)$ represents the length of the tube’s perimeter within each fiber on one side. The angles $φ_{1} (i)$ and $φ_{2} (i)$ are measured in radians and indicate the angles between the vertical centerline of the section and the two radii bounding the length of the arc $L (i)$ , while $φ (i)$ is the angle between the vertical centerline of the section and the radius reaching the perimeter at the level of the mid-thickness of the fiber. Those parameters are mathematically defined as follows:

φ_{1} (i) = \cos^{- 1} [\frac{0.5 D - h (i) + 0.5 h i}{0.5 D}]

(3)

φ_{2} (i) = \cos^{- 1} [\frac{0.5 D - h (i) - 0.5 h i}{0.5 D}]

(4)

φ (i) = \cos^{- 1} [\frac{0.5 D - h (i)}{0.5 D}]

(5)

L (i) = 0.5 D (φ_{2} (i) - φ_{1} (i))

(6)

Figure 14.

The geometry and stress distribution used for the cross-sectional analysis CFFT beams.

Additionally, $B (i)$ represents half of the width of the fiber. $A_{f} (i)$ denotes the area of the tube, while $A_{c} (i)$ represents the area of the concrete core at each fiber. These parameters are defined as follows to determine the areas of the concrete core and the tube, which will be used to calculate tensile and compressive forces.

B (i) = 0.5 D \sin φ (i)

(7)

A_{f} (i) = 2 L (i) t

(8)

A_{c} (i) = 2 B (i) h i - 0.5 A_{f} (i)

(9)

Once the geometry was defined, strain compatibility between the tube and the concrete core was assumed due to the negligible slippage observed between the tube and the concrete core. This conclusion was based on the results from the linear potentiometers attached at both ends of the CFFT beam, as illustrated in Figure 15. Additionally, it was assumed that the plane sections remain planes. These assumptions resulted in a linear strain distribution across the cross-sections of CFFT beams, as illustrated in Figure 14. The stress distribution was determined based on the properties of the involved materials and the linear strain distribution. For the tube under compression, the stress-strain relationship derived from Lu and Fam’s (2020) study was utilized, while the newly proposed design-oriented equation was employed to characterize the tube’s properties under tension. The expression proposed by Richard and Abbott (1975) was incorporated to model the stress-strain curve derived from Lu and Fam’s (2020) study, resulting in the following equation to serve as the constitutive relationship for the tube under compression:

f (ε) = \frac{6500 ε}{{[1 + {(72 ε)}^{4}]}^{\frac{1}{4}}} + 375 ε

(10)

Figure 15.

Load-slip curve of the first bending test.

Regarding the concrete core under compression, it was treated as confined concrete due to the presence of tension in the bottom part of the tube, which caused fibers to be under tension. These tensioned fibers served to confine concrete core on compression side. The fibers in the tensioned section of the tube align nearly axially, while those in compression section align nearly circumferentially. The FRP confined concrete model proposed by Khorramian and Sadeghian (2021) was employed to represent the behavior of the core concrete under compression. That confined model was adopted because the previous FRP confined concrete models assumed a very low ultimate strain for the FRP tubes. However, a study by Bates and Sadeghian (2024) demonstrates that ±55˚ CFFTs can withstand significantly larger strains than conventional cross-ply or near cross-ply FRP tubes filled with concrete. The effect of confinement was considered in the analytical model to calculate the ±55° CFFT beams’ moment capacities. It must also be incorporated into FE models when CFFTs are subjected to axial compression. However, the ±55° CFFT specimens were not modeled under compression in this study; they were modeled under axial tension. Despite the occurrence of cracks on tension side of the core concrete, the tension stiffening effect -wherein the concrete between cracks contributes to stiffness-was accounted for. This was achieved using the model proposed by Collins and Mitchell (1997) to represent the behavior of concrete under tension.

After stress distribution definition across the beam’s section and given that the cross section was divided into multiple fibers, the force in each fiber calculated by multiplying its area by the corresponding stress. The total tension and compression forces were then computed by summing the forces of fibers in the tension and compression zones. Equilibrium between the tension and compression forces was utilized to ascertain the depth of the neutral axis. Finally, the moment capacity of the CFFT was calculated by multiplying the tension or compression force by the distance between them. An analytical model was ultimately developed in MATLAB to incorporate the CFFT section geometries and material constitutive relationships, enabling precise calculation of the moment capacity for CFFT beams.

Analytical model verification

The analytical model was applied across a range of CFFT beams chosen to encompass the different sizes of them, as outlined in Table 1. This section presents the anticipated flexural behavior of CFFTs, specifically focusing on their load-deflection behavior. The first study used for analytical model verification was conducted by Mirmiran et al. (2000). In this study, the GFRP tube consisted of 17 asymmetrically arranged layers with laminae oriented at ±55°, an outer diameter of 369.2 mm, and a thickness of 6.6 mm. The beam’s flexural span measured 2286 mm, and load application was achieved through a hydraulic jack acting on a structural frame. The proposed analytical model was implemented incorporating the properties of the tested beam, and the comparison between the test and analytical results is illustrated in Figure 16(a).

Figure 16.

Comparison of the tests and analytical model results of CFFT beams: (a) Mirmiran et al. (2000) test; (b) Zhu et al. (2006) test; (c) Ahmad et al. (2008a) test; (d) Zakaib and Fam (2012) test; (e) Lu and Fam (2020) test; and (f) Current study four-point bending test.

Although Zhu et al. (2006) primarily aimed to evaluate the feasibility of splicing techniques for precast concrete-filled FRP tubes, a control specimen was tested by them. This control specimen was a ±55˚ CFFT, devoid of any splices, and served as a benchmark for comparison with beams incorporating splices. The properties of the control beam are summarized in Table 1, and they were incorporated into the analytical model to evaluate its accuracy. Figure 16(b) compares the experimental test and analytical model results. Ahmad et al. (2008a) tested 10 specimens, each constructed from a distinct type of GFRP tube with variations in fiber architecture and lamina lay-up. Beam S-4 was composed of a GFRP tube with 17 layers featuring a fiber orientation of ±55°, filled with concrete. The shear span to depth ratio of beam S-4 was 2, with a span measuring 1829 mm. The accuracy of the analytical model is evaluated by comparing the load-deflection curve obtained from the test with that of the analytical model as shown in Figure 16(c).

Zakaib and Fam (2012) assessed the flexural performance and moment connections of two types of CFFTs. The first type involved CFFTs without any steel section reinforcement, while the second type utilized CFFTs encasing steel I section. The specimen chosen for the analytical model verification was beam CFFT4, which did not incorporate a steel section for reinforcement. The beam featured an outer diameter of 115 mm, with a tube wall thickness of 5.07 mm, and a fiber orientation of ±55°. The comparison between the experimental test results and those predicted by the analytical model is illustrated in Figure 16(d).

The last study implemented to evaluate the analytical model was conducted by Lu and Fam (2020). This study conducted an experimental investigation aimed at examining the impact of controlled longitudinal and circumferential linear cuts, comprising up to 22% of the perimeter in length and extending through the full wall thickness, on the flexural strength of the specimens. A total of 12 specimens were tested under four-point bending, including control specimens without any cuts to establish baseline. The second control specimen (F2), consisting of a GFRP tube with 142 mm outer diameter and a thickness of 5.6 mm filled with concrete, was selected to verify the precision of the analytical model. The load-deflection curve obtained from the experimental tests is compared with that derived from the analytical study, as depicted in Figure 16(e). Additional to the literature, the CFFT beam which was tested by the authors of this paper used to validate the analytical model results. The test was conducted to have a complete package of data about CFFTs. The test result is compared with the analytical model result as shown in Figure 16(e).

Analytical modeling results and discussion

The comparative analysis between experimental tests and the analytical model provides valuable insights into the performance of the newly proposed analytical model. In the first three tests conducted by Mirmiran et al. (2000), Zhu et al. (2006), and Ahmad et al. (2008a), the analytical model predicted approximately 85% of the ultimate load and deflection. Notably, the analytical results for the first test exhibited an excellent alignment between the first and second slopes of both test and analytical load-strain curves as shown in Figure 16(a). These slopes correspond to the concrete core and the tube’s behaviors, respectively. However, in the second test, slight disparities between the experimental test and the analytical results emerged due to the reported slippage between concrete core and tube during the test. The slippage impacted the load-deflection curve and contributed to the nearly linear behavior observed in the test load-deflection diagram, which is unusual for ±55˚ CFFTs. To ensure a more accurate comparison between the test and the analytical model results, unaffected by the slippage, a comparison of moment-compressive strain curves was performed. As shown in Figure 17, this comparison demonstrates satisfactory agreement between the test and the analytical model results. In the third test, negligible slippage between concrete core and tube occurred compared to the second test. However, sudden deflection increases between loads of 150 kN to 250 kN is visible in the test load-deflection curve, resulting in discrepancies between the test and the analytical model results. Although load-strain and moment-strain curves could improve comparability, it is important to note that the strain gauges failed before the test was completed, resulting in insufficient data for a full comparison with the analytical model results.

Figure 17.

Comparison of moment-strain curves from Zhu et al. (2006) experimental tests and the analytical model.

There is a disparity between the test and analytical model results for the fourth test (Zakaib and Fam, 2012), marking the only instance where the ultimate load predicted by the analytical model exceeds the experimental value. Notably, the second slope of the load-deflection curve in this test is much smaller compared to the other tests. This discrepancy could be attributed to the test conditions, as the study notes that the tube of the CFFT-4 beam did not reach failure, and the beam continued to deflect significantly until the test became unstable. The load reported for the specimen in the study does not represent its ultimate capacity. This could explain why the analytical model’s predicted ultimate load exceeds the 65 kN value provided in the study. If the test conditions had allowed the specimen to reach failure without becoming unstable, the recorded ultimate load could have been in the range of 80 to 85 kN as calculated by the analytical model. Figures 16(e) and (f) compare the test results from Lu and Fam (2020), as well as those from the authors of this study, with their respective analytical models. The comparisons demonstrate a good agreement between the experimental data and the analytical model’s predictions. The analytical model accurately predicts the ultimate load, achieving approximately 97% of the tests’ ultimate load, indicating a high level of precision. Additionally, the overall trend of the curves—including the first and second slopes, the transition section, as well as the ultimate deflection—closely aligns between the test results and the analytical model. Table 3 provides a summary of the comparisons between the test results and the analytical model predictions.

Table 3.

Comparison of experimental tests, analytical model, and simplified method results.

Reference	Specimen ID	Test Load (kN)	Analytical model		Simplified model
Reference	Specimen ID	Test Load (kN)	Load (kN)	P_uM/P_uT	Load (kN)	P_uM/P_uT
Mirmiran et al. (2000)	T2S3	670	574	0.86	561	0.84
Zhu et al. (2006)	Control	500	411	0.82	415	0.83
Ahmad et al. (2008a)	S-4	472	385	0.82	393	0.83
Zakaib and Fam (2012)	CFFT4	65	80	1.23	85	1.31
Lu and Fam (2020)	F2	135	133	0.99	134	0.99
Current study	C1	200	187	0.94	185	0.93
Average				0.94		0.95
SD				0.14		0.17

The analytical results could not be directly compared with existing international design codes. The newly released ACI PRC-440.14-25 guide (2025) introduces specific limitations on fiber orientation, requiring that at least one-third of the fibers be aligned within ±35° of the tube’s longitudinal axis. In contrast, the Externally Bonded Reinforcement (EBR) provisions of the CEB–fib (Triantafillou et al., 2001) guidance are primarily intended for confinement and strengthening of reinforced concrete members using externally bonded jackets or wraps. These provisions generally assume hoop-oriented fibers to provide confinement pressure and do not offer a design framework for concrete-filled GFRP tubes with angle-ply laminates such as the ±55° configuration. As a result, the present analytical study lies outside the direct scope of these international guidelines.

The implications of these results are particularly significant for both researchers and practitioners involved in the design and evaluation of CFFT structures. The demonstrated accuracy of the analytical model—predicting 85%–100% of the test ultimate loads—suggests that this model can be reliably used in future parametric studies and simulation-based research, reducing the need for extensive physical testing in the early design stages.

Simplified design-oriented method

To propose a simplified method for calculating the moment capacity of ±55˚ CFFTs, the depth of the neutral axis needs to be determined. Based on the test and analytical model results, it was assumed to be a quarter of the outer diameter of the tube. With an ultimate tensile strain of 0.077 mm/mm, the strain distribution across the entire CFFT’s section can be determined, assuming strain compatibility between the tube and the concrete core. To establish stress distribution, the material’s constitutive model must be utilized, considering the FRP confined concrete model for concrete in compression. Tension in the concrete can be disregarded as its impact on results is minimal. For tension in the tube, the newly proposed design-oriented model (i.e., Equation (2)) was employed. Compression in the tube is modeled by the equation derived from Lu and Fam’s (2020) study (i.e., Equation (10)). Finally, the moment capacity of CFFTs can be calculated based on the simplified method. The comparison of experimental tests, analytical model, and simplified design-oriented method results is presented in Table 3, showing a good agreement between the test and the simplified method moment capacities.

The simplified design-oriented method proposed in this study offers clear practical benefits, particularly for the preliminary design validation of ±55 GFRP tube-confined concrete elements. It enables reliable prediction of structural behavior under flexural loading with a high level of confidence. By streamlining the moment capacity calculations into a set of well-defined assumptions and equations, the method is both efficient and accessible, making it suitable for routine use by practicing engineers in design offices.

Conclusions

This study examines the nonlinear behavior of ±55 GFRP tubes filled with concrete through experimental testing, finite element modeling, and analytical modeling. Tension and bending tests were conducted on CFFT specimens, followed by numerical simulations and the development of an analytical model. A simplified design method was also proposed based on the findings. The main conclusions from each phase of the study are as follows:

Under tension, CFFTs showed notable nonlinear behavior, with the concrete core enabling bi-axial tension in the tube. The load-strain curve featured two distinct slopes, reflecting the contributions of the core and the tube. Despite some premature failures, the tests offered important insights into the tensile response of CFFTs. The four-point bending test showed a 7.7% ultimate tensile strain, with about 75% of the tube in tension. This configuration effectively utilized the combined contribution of the tube’s tensile strength and the confined concrete in compression, enhancing the beam’s load-bearing capacity.

• The FE analysis results showed strong agreement with the experimental results, with ultimate load and tensile strain ratios of 1.03 and 1.04, respectively. It accurately captured key behaviors such as concrete core cracking and tube discoloration. The optimized model provided valuable insight into the tensile performance of CFFTs, with failure occurring at mid-span.

• Based on the experimental and refined FE model results, a design-oriented equation was formulated to predict the tensile behavior of the tube when filled with concrete.

• Utilizing the design-oriented equation, an analytical model was developed using MATLAB to predict the flexural behavior of CFFTs, accurately capturing 85%–100% of the experimental moment capacities and deflections by incorporating force equilibrium and strain compatibility.

• A simplified design-oriented method was introduced to calculate the moment capacity of CFFTs. This method, intended for practical engineering applications, produced results that were approximately 85%–100% consistent with the experimental data, making it a useful design tool for engineers.

Footnotes

ORCID iD

Pedram Sadeghian

Author contributions

The manuscript was written through contributions from all authors. All authors have given their approval to the final version of the manuscript.

Funding

The second and third authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by the Natural Sciences and Engineering Research Council of Canada Discovery Grant.

Declaration of conflicting interests

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

Data Availability Statement

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.*

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Nonlinear tensile behavior of ±55˚ concrete-filled GFRP tubes: Experimental and theoretical studies

Abstract

Keywords

Introduction

Experimental studies

CFFT tension test

CFFT bending test

Finite element modeling

Model parameters

FE model verification

FE model optimization

Analytical modeling

Cross-sectional analysis

Analytical model verification

Analytical modeling results and discussion

Simplified design-oriented method

Conclusions

Footnotes

ORCID iD

Author contributions

Funding

Declaration of conflicting interests

Data Availability Statement

References