Experimental investigation on shear behavior of double-row perforated GFRP rib connectors in FRP-concrete hybrid beams

Abstract

Perforated GFRP rib (PFR) connectors have been used in FRP-concrete hybrid beams due to durability and ease of construction. PFR connectors are parallel FRP plates with predrilled holes positioned in the flange of FRP beams. The optimal plate spacing needs to be determined because it affects the shear performance of PFR connectors. 18 push-out tests were conducted to investigate the effect of plate spacing (S_l), penetrating GFRP bar diameter (d), and concrete strength (f_c) on the failure mode, capacity, and shear load-slip (P-S) curves of double-row PFR connectors. Results showed that PFR connectors suffered plate shear failure with the concrete dowel undamaged. Typical P-S curves consisted of micro-slipping and significant-slipping phases. The shear capacity and stiffness of PFR connectors were improved by 33.3% and 45.1%, respectively, by increasing the plate spacing from 1.2 h (where h denotes the plate height) to 3.2 h. The effect of plate spacing on shear capacity and stiffness could be neglected if the ratio (S_l/h) was more than 3.2. Specimens with a larger diameter of penetrating bar and higher concrete strength demonstrated higher capacity and stiffness. An empirical equation based on the maximum stress failure criterion was proposed to estimate the capacity of PFR connectors, considering the plate spacing effect, and verified by available data. Additionally, a description of the P-S curve was developed and calibrated by the experimental results.

Keywords

perforated GFRP rib push-out test plate spacing shear load versus slip curve capacity

Introduction

Steel-concrete composite beams have been widely used in the construction of buildings and bridges due to excellent mechanical properties and rapid construction (Xue et al., 2008b). However, corrosion of structural steel and bars would jeopardize the strength and safety of steel-concrete composite beams, particularly in an aggressive environment (Lehman, 2022). Fiber reinforced polymer (FRP) has become a popular substitute for steel because of its positive qualities, including high strength, light weight, corrosion resistance and relatively lower cost (Hu et al., 2024; Liu et al., 2020; Peng and Xue, 2018; Wang et al., 2021, 2023). A new type of composite beam, FRP-concrete hybrid beam is created by connecting the FRP pultruded profile beam and concrete slab with shear connectors (Zhang et al., 2019). It has excellent properties, such as high strength-to-weight ratio, durability, and rapid construction. Nowadays, the FRP-concrete hybrid beam has been successfully implemented in several bridges, such as the Miyun Bridge (Zou et al., 2020), the first FRP-concrete hybrid bridge in the world, built in 1982 and the San Patricio Bridge, the first FRP-concrete hybrid beam highway bridge constructed in 2004 in the USA (Ulloa et al., 2004; Ziehl et al., 2009).

Ensuring smooth shear transmission between the FRP and concrete components is a major challenge in the design and construction of FRP-concrete hybrid beams (Hu et al., 2023a; Xue et al., 2008a). To address this challenge, several types of shear connectors (Figure 1) have been developed, i.e., epoxy bonding (Correia et al., 2009; Deskovic et al., 1995; Nordin and Taljsten, 2004; Saiidi et al., 1994), stainless steel bolts (Gong et al., 2019; Nguyen et al., 2014; Zou et al., 2018a, 2018b), FRP bolts (El-Hacha and Chen, 2012; Xue et al., 2023), and PFR connectors (Appavuravther et al., 2022; Zhong et al., 2023; Zou et al., 2020; Zuo et al., 2021). Among them, PFR connectors have drawn considerable attentions due to compatibility with FRP profile and rapid installation (Zou et al., 2020). PFR connectors are thin FRP plates with predrilled holes that are embedded in the concrete slab and are attached to the flange of the FRP profile beams in the longitudinal direction (Zou et al., 2016). PFR connectors are particularly suitable for large-span beams (Hollaway, 2010; Zhang et al., 2019).

PFR connectors are arranged in parallel in engineering (Ahn et al., 2010; Wang et al., 2018). Shear resistance of the PFR connectors is achieved by the interaction between the concrete dowel and the predrilled hole (Xiong et al., 2019; Zou et al., 2023). Each concrete dowel in rows and columns transmits unequal shear forces, resulting in a reduction on the shear capacity of the PFR connectors, which forms group connectors effect (Deng et al., 2019). Therefore, the configuration of the predrilled holes and the plate spacing are crucial to the shear performance of the PFR connectors (Tan et al., 2022). Previous research has demonstrated that the effect of predrilled hole configuration could be disregarded if the ratio of hole spacing to hole diameter is greater than 3 (Cho et al., 2012; Oguejiofor and Hosain, 1994). However, further research is needed as the effect of plate spacing on the shear performance of PFR connectors has not been investigated.

Previous research efforts have mostly focused on the shear performance of PFR connectors in a single-row arrangement via push-out tests and theoretical analysis (Européen, 2004; Hu et al., 2024; Huang et al., 2018; Xiong et al., 2019; Zhong et al., 2023; Zou et al., 2016). Test results showed that PFR connectors experienced shear failure of the GFRP plate whether the penetrating bar was applied or not (Huang et al., 2018). Nam et al. (2007) conducted push-out tests on two specimens with single-row PFR connector and observed debonding failure between the connection of PFR connectors and FRP beams, while the concrete dowel remained intact. Zou et al., (2016) compared the shear behavior of single-row PFR connector and steel bolts via eight push-out tests and found that shear failure occurred in the GFRP plate. The shear capacity of PFR connector per predrilled hole was 2.5 times higher than that of steel bolts and the shear stiffness of PFR connector was 10 times greater than that of steel bolts, which indicated that the PFR connector could ensure nearly full composite action in FRP-concrete hybrid beams. Huang et al. (2018) conducted a push-out test on five specimens with single-row PFR connector. The shear capacity of PFR connectors with penetrating bars was 26.9% greater than that of the PFR connectors without penetrating bars. This is attributed to the fact that adding penetrating bars prevented the concrete splitting failure due to the improvement of lateral confinement effect and the reduction of the concrete transverse deformation.

The shear capacity of the single row PFR connector has been predicted by several models (Huang et al., 2018; Nam et al., 2007; Zou et al., 2016). These models were derived from push-out test results that demonstrated shear failure of the GFRP plate when the plate reaches its maximum shear strength under loading. Consequently, researchers such as Huang et al., (2018) and Zou et al., (2016) proposed equations for predicting capacity of PFR connectors, on the basis of the maximum shear stress failure criterion. The position of shear failure was generally thought to be in line with the maximum shear stress. Thus, a crucial factor that needs to be determined in advance is the position of the shear failure on the GFRP plate. Huang et al., (2018) assumed that the shear failure would occur in the middle of the predrilled hole. However, it was discovered that this assumption was not consistent with test results and produced conservative results. (Zou et al., 2016) conducted a finite element analysis on PFR connectors and found that the maximum shear stress was distributed at an angle of 40-60° from the center of predrilled hole section. This angle was approximated to 45° in order to simplify the calculation. If the shear failure of GFRP plate could be effectively avoided by increasing the shear strength of GFRP and the thickness of the plate, the failure of the concrete dowel would determine the capacity of the PFR connectors (Xiong et al., 2019).

The research mentioned above on PFR connectors indicated that:

(1) Research mostly concentrated on shear behavior of single-row PFR connectors, while research on double-row PFR connectors is relatively scarce, resulting in a lack of understanding for the effect of row spacing

(2) There are currently no design recommendations for PFR connectors because of insufficient research and limited experimental data.

To address these issues, this paper presents the results of 18 push-out tests on PFR connectors. The effects of transverse plate spacing, diameter of penetrating GFRP bars, and concrete strength on the shear performance of PFR connectors were investigated. According to the test results, the failure modes, P-S curve and shear behaviors of the PFR connectors were investigated. Additionally, the shear mechanism of FRP connectors was analyzed. Based on experimental findings, a calculation model for the shear capacity of PFR was developed considering the effect of plate spacing, and an equation for the P-S relationship was proposed.

Push-out test

Specimens

Six groups of 18 push-out specimens were examined to determine the shear behavior of PFR connectors. As summarized in Table 1, the variables include the transverse plate spacing, the diameter of penetrating GFRP bars, and the concrete strength. The dimensions of the specimens are shown in Figure 2. The specimens were fabricated in accordance with the standard push-out test specimen in Eurocode 4 (Européen, 2004). Each specimen was symmetrical with a box-shaped GFRP profile beam, two concrete slabs, and PFR connectors. The dimension of the concrete slab was 500 mm × 500 mm × 85 mm, and the configuration of the GFRP profile beam was 160 mm × 260 mm × 5.5 mm × 10 mm (width × height × flange thickness × web thickness) with a length of 500 mm. The dimension of the PFR connector plate was 60 mm × 60 mm × 8 mm (width × height × thickness), and the diameter of the pre-drilled holes was 30 mm. All penetrating GFRP bars were set at the center of the holes. Given the fact that the production of FRP pultruded profile is limited by the mold, PFR connectors and GFRP beams were manufactured independently and later assembled by epoxy bonding.

Table 1.

Parameters of the push-out specimen.

Specimens	Plate arrangement	Plate spacing s_l (mm)	Diameter of GFRP bar d_s (mm)	Concrete
SP-inf-9.5-C50	Single row	—	9.5	C50
DP-70-9.5-C50	Double row	70 (1.2 h)	9.5	C50
DP-120-9.5-C50	Double row	120 (2.0 h)	9.5	C50
DP-190-9.5-C50	Double row	190 (3.2 h)	9.5	C50
DP-70-9.5-C30	Double row	70 (1.2 h)	9.5	C30
DP-70-13.0-C50	Double row	70 (1.2 h)	13.0	C50

Note: SP represents the specimens with a single row PFR connector, DP represents the specimens with double-row PFR connectors, and h represents the plate height of PFR connectors (60 mm).

Each specimen is designated by rows of PFR connectors (SP/DP), plate spacing (s_l), penetrating GFRP bar diameter (d_s), and concrete strength grade as follows: SP/DP-s_l-d_s-C*. For example, specimen DP-70-9.5-C50 includes double-row PFR connectors with 70 mm plate spacing, 9.5 mm penetrating GFRP bars, and C50 concrete.

It is noted that a 150 mm-high concrete stiffener was cast to the loading end to prevent the local buckling of FRP flanges and webs. To reduce the effect of friction on the FRP-concrete interface, lubricant was applied. As shown in Figure 2, the polyfoam was set at the bottom of the PFR connectors to eliminate the resistance of the concrete end-bearing. Epoxy bonding was used to connect the PFR connectors to the GFRP pultruded profile beam.

Material properties

The penetrating bar and structural reinforcement were sand-coated GFRP bars produced by Dextra Group. Table 2 presents their mechanical properties. The PFR connectors and GFRP profile beam were commercial products manufactured by Nanjing Spare Composite Co., Ltd, in China. As reported in Table 3, their mechanical properties were tested in accordance with GB/T 1447-2005 (2005) and GB/T 1448-2005 (2005). The mechanical properties of the concrete were tested according to GB/T 50081-2019 (2019) as listed in Table 4.

Table 2.

Material properties of GFRP bars.

Diameter/mm	Tensile strength f_fu (MPa)	Tensile modulus E_f (GPa)	Shear strength f_fv (MPa)
9.5	910	51.8	152
13.0	860	50.8	143

Table 3.

Mechanical properties of PFR connectors.

Part	Direction	Tensile strength σ_tu (MPa)	Tensile modulus E_tu (GPa)	Compressive strength σ_cu (MPa)	Shear strength τ_xy (MPa)	Shear modulus G_xy (GPa)
Webs	Transverse	112.8	27.1	131.5	68.3	13.1
Webs	Longitudinal	489.7	31.7	230.0	68.3	13.1
Flanges	Longitudinal	698.0	17.4	161.3	-	-

Table 4.

Mechanical properties of concrete.

Concrete grade	Cube compressive strength f_cu (MPa)	Prism compressive strength f_c (MPa)	Tensile strength f_t (MPa)	Elastic modulus E_c (GPa)
C50	51.9	42.4	3.5	39.8
C30	36.7	29.5	3.0	29.2

Test setup

Due to a lack of a standardized method for testing shear connectors used in GFRP-concrete hybrid beams, the push-out test method recommended in Eurocode 4 (2004) (Européen, 2004) was employed to determine the shear behavior of PFR connectors (Huang et al., 2018; Zou et al., 2016). The test setup in the experiments is shown in Figure 3. All specimens were monotonically loaded under a combined force-displacement controlled loading method by a 500 kN hydraulic testing machine. The specimens were under the force controlled with a loading rate of 5 kN/min till 80% of the theoretical ultimate shear capacity, followed by displacement controlled at a rate of 1 mm/min till specimen failure (Xiong et al., 2019). A layer of fine sand was placed on the bottom of the concrete slab and a 20-mm-thick steel plate was positioned above the top of the GFRP profile beam to ensure uniform loading.

Two Linear Variable Differential Transformers (LVDTs), designated D1-D2 with the measuring range of 10 mm, were set on the GFRP beam at the position of holes to continuously detect the relative slips between the GFRP beam and the concrete slab. Thus, the relative slip was determined by the average value of two LVDTs. As shown in Figure 5, the strains in the penetrating GFRP bars were measured by the strain gauges.

Push-out test results

Loading process and failure modes

As shown in Figure 4, all specimens, regardless of the single or double row PFR connectors, suffered shear failure of the GFRP plate along the fiber direction while the concrete dowel remained undamaged. This failure mode aligned with previous studies on the single row of PFR connector (Wang et al., 2015; Xiong et al., 2019; Zou et al., 2016), which indicated that shear failure of the GFRP plate was a typical failure mode. The surface of shearing through the predrilled hole. No obvious phenomenon was observed on the concrete slabs during the loading process. When the failure happened, there was an evident sound indicated tearing of PFR connectors. The shear capacity of PFR connectors is governed by the shear failure of the GFRP plate, and the detailed analysis of this mechanism will be provided in Section (Equations to predict the ultimate shear resistance of PFR connectors). Due to the low thickness and shear strength of the FRP plate, the web of PFR connector would fail prematurely. Therefore, it is important to increase the thickness of the web of PFR connector.

Figure 5 shows that during the initial loading stage, the strain of penetrating bars grew slowly. However, at a subsequent loading stage, the strain increased rapidly, indicating that the penetrating GFRP bar and concrete dowel both contributed to the shear resistance during this phase. A positive value of strain of all GFRP bars indicates all bars were subjected to tension due to the constraint effect imposed by the expansion of the concrete dowel under loading. However, the maximum strains of penetrating GFRP bars were far less than the ultimate strain (17600 με) due to the lower elastic modulus of GFRP.

Shear load versus slip curves

Relative slip between the concrete slab and FRP beam was generated as the load increased. The average shear load per row of the PFR connector was used to evaluate the shear performance due to the specimens with varied rows of PFR connectors. Figure 6 displays the average P-S curves per row of PFR connector. Assuming that each row of PFR in the same specimen undertook equal share of the shear load, the ultimate shear capacity of per PFR connector (P_u) could be calculated by P_u = P_max/n_r, where P_max is the maximum load of specimens and n_r is the rows of PFR connector.

Typical P-S curves of PFR connectors exhibited two distinct phases: the micro-slipping phase (characterized by s ≤ 0.2 mm, P≤(0.5∼0.7) P_u, where s is the slip, P is the shear load per PFR connector held) and the significant-slipping phase (s > 0.2 mm, P>(0.5∼0.7)P_u). The turning point was pointed out in Figure 6. In the micro-slipping phase, the P-S curves demonstrated a linear ascent and the slip was generally less than 0.2 mm. The PFR connector exhibited great shear stiffness. As the load further increased and reached the significant-slipping phase, the P-S curves were in the nonlinear growth stage, indicating a continuous reduction in the shear stiffness of the PFR connector. All P-S curves lacked an evident descent phase due to the sudden failure of the specimens. It should be noted that the P-S curves of DP-190-9.5-C50∼2 and DP-70-13.0-C50∼3 could not be plotted due to the fault of data measurement acquisition. Besides, some discrepancies were observed in the push-out test due to the shear performance of connectors and randomness of PFR connectors shear strength. Thus, in Eurocode 4, three duplicate specimens in a group are needed to evaluate the shear performance of shear connectors.

Static shear behaviors

The shear capacity and shear stiffness are two crucial characteristics that reflect the static shear performance of connectors, which can be determined by the characteristic points of the P-S curves.

The shear capacity of the PFR connector is the maximum shear load that it attained. It is generally equal to the load value corresponding to the top of the P-S curve. Table 5 summarizes the average shear capacity and corresponding slips of the PFR connectors.

Table 5.

Push out test results of PFR Connectors.

Groups	$\bar{P_{u}}$ (kN)	$\bar{S_{u}}$ (mm)	$\bar{k_{s l i p}}$ (kN·mm⁻¹)	Failure mode
SP-inf-9.5-C50	118.74	0.63	229.5	Shear failure of GFRP plate
DP-70-9.5-C50	85.77	0.38	162.1	Shear failure of GFRP plate
DP-120-9.5-C50	88.01	0.54	184.1	Shear failure of GFRP plate
DP-190-9.5-C50	114.36	0.45	235.2	Shear failure of GFRP plate
DP-70-9.5-C30	79.32	0.43	132.6	Shear failure of GFRP plate
DP-70-13-C50	93.61	0.34	227.6	Shear failure of GFRP plate

Notes: $\bar{P_{u}}$ is the average shear load of PFR per group, $\bar{S_{u}}$ is the average slip at the peak load per group; $\bar{k_{s l i p}}$ is the average shear stiffness of a single concrete dowel.

Table 5 lists the outcomes of shear stiffness of PFR connectors. The shear stiffness of the PFR connector which represents the deformation resistance of the connectors, refers to the increment of load generated by the connectors under unit deformation. It is an important characteristic in calculating the overall deflection of the hybrid beam considering the slip effect (Zou et al., 2016). The shear stiffness of the connector is defined as the secant slope of a point on the P-S curves, generally adopted turning point of micro-slipping and slipping phases (Xiong et al., 2019). In this study, the turning point is at a range of 0.5∼0.7 P_u. In the micro-slipping phase, the PFR connector exhibited great shear stiffness and the shear load almost increased linearly with the slip. Therefore, the shear stiffness of PFR connector is assumed to be unchanged in the micro-slipping phase. In order to simplify the calculation, the lower limit (0.5 P_u) was used. The average shear stiffness is defined as the secant slope at the point 0.5 P_u per concrete dowel (Nguyen et al., 2014; Oehlers and Coughlan, 1986), which is given as follows:

k_{slip} = \frac{0.5 P_{u}}{n s_{0.5 P_{u}}}

(1)

where k_slip is the shear stiffness of a single concrete dowel; n is the number of pre-drilled holes in a PFR connector;

s_{0.5 P_{u}}

is the slip at the load of 0.5P_u.

Discussion

Based on the results of the push-out test, the effects of plate spacing, concrete strength, and diameter of penetrating GFRP bar on the shear behavior of PFR connectors are discussed as follows.

Effect of GFRP plate spacing

Figures 7 and 8 reveal the effect of GFRP plate spacing on shear capacity and shear stiffness of specimens with double rows (DP-70-9.5-C50, DP-120-9.5-C50, DP-190-9.5-C50) and single row (SP-inf-9.5-C50) PFR connectors.

The shear capacity and shear stiffness of PFR connectors both increased by increasing the GFRP plate spacing. The shear stiffness approximately linearly increased with the plate spacing increased (Figure 8), gradually approaching the shear stiffness of single row of PFR connector. Compared to specimens with the single-row PFR connector (SP-inf-9.5-C50), the shear capacity of specimens with double-row PFR connector in the plate spacing of 70 mm (DP-70-9.5-C50), 120 mm (DP-120-9.5-C50) and 190 mm (DP-190-9.5-C50) decreased by 27.8%, 25.9%, and 3.7%, respectively. This phenomenon is attributed to the overlapping action zones in the specimens when the plate spacing is small, forming a group plate effect. The difference in average shear capacity and shear stiffness between the DP-190-9.5-C50 and SP-inf-9.5-C50 were within 5%. Accordingly, the group plate effect can be neglected when the plate spacing is over 3.2h (h denotes the height of the GFRP plate).

Effect of concrete strength

The effect of concrete strength on the shear behavior of PFR connectors was evaluated through a comparison of shear strength and stiffness among specimens DP-70-9.5-C50 and DP-70-9.5-C30 as shown in Figures 9 and 10.

Increasing the strength of the concrete is an efficient way to improve the shear capacity and stiffness of PFR connectors. With the concrete strength changing from C30 to C50, the shear capacity increased by 8.1%. This is as a result of the specimens suffering GFRP plate shear failure with the concrete dowel undamaged. Thus, the shear capacity was dominated by the shear strength of the GFRP plate and shear area (Xiong et al., 2019). As a result, concrete strength had less of an impact on PFR’s shear capacity. As concrete strength increased from C30 to C50, PFR’s shear stiffness increased by 22.2%. This is because the concrete’s elastic modulus increased, causing the deformation of the dowel to decrease. Therefore, the slip between the concrete and PFR connector reduced.

Effect of diameter of penetrating GFRP bar

The effect of diameter of penetrating GFRP bar on shear behavior was evaluated by the test results of specimens DP-70-9.5-C50, and DP-70-13-C50, tabulated in Table 5 and Figure 10.

Increasing the diameter of the penetrating bars from 9.5 to 13.0 mm will increase shear capacity of PFR connectors. The shear capacity of specimens with 13.0 mm diameter penetrating GFRP bars was 9.14% larger than that of specimens with 9.5 mm diameter penetrating GFRP bars. The main reason is that by improving the restricted effect of penetrating bars on the deformation of the concrete dowel, a larger diameter of penetrating GFRP bars could enhance the shear resistance of concrete dowels to resist the shear force. However, this effect was left out of the subsequent equations, due to insufficient test data and difficulty in assessing the effect (XUE Weichen et al.).

The shear stiffness of PFR connectors increased as the diameter of the penetrating GFRP bar increased. When the diameter of the penetrating GFRP bar was changed from 9.5 to 13 mm, it was discovered that the shear stiffness of PFR connectors increased by 40.4%.

Equations to predict the ultimate shear resistance of PFR connectors

In this section, empirical equations suggested by several researchers to predict the shear capacity of PFR connectors based on experimental and theoretical analysis are summarized first (Huang et al., 2018; Xiong et al., 2019; Zou et al., 2016). The calculated results of these equations were compared with the experimental results. Then, an equation considering the effects of spacing of the GFRP plate is proposed and validated by the test results.

Existing calculation methods

Nam et al. (2007) proposed equation (2) to predict the shear capacity of the PFR connector considering the contribution of concrete dowel action, the shear resistance of the penetrating GFRP bars, and the friction between the PFR connector and concrete.

V_{Nam} = 2.35 b_{p} l_{p} + 1.66 n π \sqrt{f_{c}^{'}} {(\frac{D}{2})}^{2} + 0.4 A_{v f} f_{fu}

(2)

where b_p is the width of flange of the PFR connector (mm);l_p is the contact length between the PFR flange and concrete;D is the diameter of predrilled hole (mm);f_c’ is the concrete prism compressive strength (MPa);n is the number of predrilled holes;A_vf is the cross-sectional area of penetrating GFRP bar (mm²);f_fu is the tensile strength of GFRP bars (MPa).

It should be noted that equation (2) was based on the assumption of concrete dowel and GFRP bar failure, which was not observed in tests. Thus, it is not suitable for the shear failure of GFRP plate.

As to the shear failure of the GFRP plate, Huang et al. (2018) proposed the shear capacity of PFR connectors based on the maximum shear stress failure criterion. The shear area was assumed to be located at the center of the predrilled holes.

V_{Huang} = τ_{x y} t (l_{p} - n D)

(3)

where t is the thickness of the GFRP plate (mm);

τ_{x y}

is the in-plane shear strength (MPa).

Zou et al. (2016) assumed the maximum compressive stress occurred along the edge of the predrilled hole was at the location of 45° according to the FEM analysis results and suggested an equation as follows:

V_{Wang} = 1.1 τ_{x y} t (l_{p} - 0.7 n D)

(4)

A comparison of the available test results and the calculated results from the above equations is summarized in Table 6. In the case of the specimens with multi-rows PFR connectors, the calculated results of these equations overestimated the shear capacity, and the relevant predictive errors by those equations ranged from −18% to 58%. It should be noted that the shear area of equations (3) and equations (4) does not coincide with the position of the maximum shear stress. Therefore, a more accurate equation should be suggested to calculate the shear capacity of the PFR connectors.

Table 6.

Comparisons between test results and theoretical results.

Literatures	Specimens	S_l (mm)	h (mm)	t (mm)	l_p (mm)	D (mm)	τ_xy (Mpa)	n	V_u,test (kN)	$\frac{V_{Huang}}{V_{u, test}}$	$\frac{V_{Wang}}{V_{u, test}}$	$\frac{V_{cal}}{V_{u, test}}$
Ge, (2009)	LJ1-1	70	40	4	250	20	23	2	17.5	1.29	1.16	0.94
	LJ1-2	70	40	4	250	20	23	2	18.4	1.22	1.1	0.89
	LJ2-1	Single	40	4	250	20	23	2	21.6	1.04	0.94	0.97
	LJ2-2	Single	40	4	250	20	23	2	21.9	1.03	0.93	0.96
	LJ3-2	70	40	4	250	20	23	2	16.9	1.33	1.2	0.98
Zou et al. (2016)	P8	Single	72	6	500	16	25.4	2	87.5	0.92	0.82	0.84
Huang et al. (2018)	TR-H4-R4	Single	80	10	500	35	52	2	333.0	1.03	0.91	0.95
Huang et al. (2018)	TR-H8-R8	Single	80	10	500	35	52	4	295.0	1.07	0.90	1.00
Xue et al. (2022)	SP-inf-13-C50	Single	60	8	250	30	68.3	2	113.9	1.10	1.10	1.03
Xue et al. (2022)	SP-inf-9.5-C30	Single	60	8	250	30	68.3	2	113.4	1.10	1.10	1.04
This paper	DP-70-9.5-C50	70	60	8	250	30	68.3	2	85.8	1.46	1.21	1.00
	DP-120-9.5-C50	120	60	8	250	30	68.3	2	88.0	1.42	1.18	1.09
	DP-190-9.5-C50	190	60	8	250	30	68.3	2	114.4	1.09	0.91	0.96
	DP-70-9.5-C30	70	60	8	250	30	68.3	2	79.3	1.58	1.31	1.08
	DP-70-13-C50	70	60	8	250	30	68.3	2	93.1	1.34	1.11	0.92
	SP-inf-9.5-C50	Single	60	8	250	30	68.3	2	118.7	1.05	0.87	0.99
Average										1.19	1.05	0.98
Standard deviation										0.036	0.022	0.004

Notes: V_u,test is the shearing capacity of PFR connectors; l_p is the length of the GFRP plate(mm); t is the thickness of the GFRP plate (mm); τ_xy is the shear strength of GFRP plate (MPa); D is the diameter of predrilled holes(mm); n is number of predrilled holes.

Calculation methods proposal

As stated in Section 3.1, the strain of the penetrating bar is small during the loading process. Therefore, the shear force transferred from the FRP beam to concrete was primarily through the concrete dowel. Because the capacity of GFRP plate was less than that of the concrete dowel and penetrating bar, shear failure of the plate occurred. This failure mode suggested that the shear stress on the GFRP plate exceed the maximum shear strength. The maximum shear stress failure criterion (equation (5)) was therefore used to determine the PFR connector’s shear capacity.

τ \geq τ_{x y}

(5)

where τ is the shear stress and τ_xy is the shear strength of the GFRP plate.

Referring to (Zou et al., 2016), the exact distribution of contact stress between the concrete dowel and hole boundary can be expressed as the cosine curve distribution theory as shown in Figure 11

{\begin{cases} p (β) = p_{\max} \cos β \\ p_{x} (β) = p (β) \cos β \\ p_{y} (β) = p (β) \sin β \end{cases}

(6)

where β is the angle from the center of the predrilled hole; as shown in Figure 12 p(β) is the contact stress at the location of angle β; p_max is the maximum value of the contact stress; p_x(β) is the component of p(β) along the fiber direction; p_x(β) is the component of p(β) perpendicular to the fiber direction.

The shear failure of the GFRP plate occurred at the location of angle β where the shear stress reached its ultimate shear strength. Thus, the shear capacity of PFR connector could be calculated as equation (7)

V = A_{f} \cdot τ

(7)

A_{f} = (l_{p} - n \cdot D \cdot \cos β) t

(8)

The ultimate shear force F_p could be calculated as equation (9)

F_{p} = 2 t \frac{D}{2} \int_{- \frac{π}{2}}^{β} (p_{\max} \cos^{2} β) d β = \frac{t D p_{\max}}{2} [\frac{1}{2} \sin (2 β) + β + \frac{π}{2}]

(9)

Based on the equilibrium equation of force, the maximum shear stress could be defined as equation (11)

F_{p} = V

(10)

τ = \frac{\frac{D p_{\max}}{2} [\frac{1}{2} \sin (2 β) + β + \frac{π}{2}]}{(l_{p} - n \cdot D \cdot \cos β)}

(11)

The maximum shear force τ is when $d τ / d β = 0$ . Therefore, β equal to 55°.

The ultimate loading for a single row of PFR connectors is obtained using equation (12):

V_{u} = τ_{x y} t (l_{p} - 0.574 n D)

(12)

where l_p (mm) is the length of the GFRP plate; D (mm) is the diameter of holes; t (mm) is the thickness of the GFRP plate; n is the number of predrilled holes.

Equation (12) is independent of the GFRP plate spacing, and it is useful to predict the shear capacity of a single-row PFR connector. For double-row PFR connectors, the shear capacity is significantly affected by the GFRP plate spacing. The data in this study and literatures (Ge, 2009; Zhang, (2018)) are depicted in Figure 13, where reveals the relationship between parameter η and the ratio of S_l/h. The parameter η is defined as the normalized capacity calculated by the ratio of the average shear capacity of the double-row PFR connector to that of the single-row PFR connector. The parameter η increases proportionally with the ratio of S_l/h. Hence, the effect of plate spacing is quantified by equation (13).

η = \frac{{\bar{P}}_{u}}{V_{u}} = {\begin{cases} 0.11 \frac{S_{l}}{h} + 0.65 & \frac{S_{l}}{h} \leq 3.2 \\ 1 & \frac{S_{l}}{h} > 3.2 \end{cases}

(13)

where S_l (mm) is the spacing of the GFRP plate; h (mm) is the height of the GFRP plate.

The ultimate capacity of PFR connector under the GFRP plate shear failure is given as equation (14).

V_{c a l} = η V_{u} = η τ_{x y} t (l_{p} - 0.574 n D)

(14)

Table 6 shows the comparison between the results yielded from equation (14) and the experimental results. Compared with equations (3) and (4), the calculated results of equation (14) are in better agreement with the experiments.

Expression of shear load versus slip curves

The P-S curve of the shear connector is important to evaluate the slip characteristics of PFR connectors. It is indispensable for the ultimate limit state analysis of hybrid beams with partial interaction. Most of the studies on P-S curves have been conducted on steel studs shear connectors in steel-concrete composite beams (Xue et al., 2008a; Yang et al., 2020), and little research was conducted on the expression of P-S curves for PFR connectors. The P-S relationship of PFR connectors has a similar tendency to that of steel studs. It should be further verified whether the equations for P-S curves of studs could be applied to PFR connectors or not. The existing P-S curve models are concluded as follows.

Buttry, (1965) proposed a P-S relationship for steel studs in steel-concrete composite beams as equation (15):

\frac{P}{P_{u}} = \frac{80 S}{1 + 80 S}

(15)

Ollgaard et al. (1971). proposed an empirical formula for the P-S curve of continuously loaded specimens:

\frac{P}{P_{u}} = {(1 - e^{- 18 S})}^{0.4}

(16)

where S in equations (15) and (16) is the average slip (in.).

The P-S curves of the specimens and the curve according to equations (15)∼(16) are shown in Figure 14, in which shows that these equations do not predict the P-S behavior of PFR connectors. Therefore, it is essential to investigate and establish simplified P-S curves for the PFR connectors for accurate analysis of the FRP-concrete hybrid beams.

Based on the push-out test results, the P-S curves of PFR connectors were found to have the same regularity, even though the ultimate load for each specimen was different. Therefore, the P-S curves can be determined by the normalization method and regression analysis method. The P-S relationship was proposed by curve fitting based on the test results, as shown in equation (17).

\frac{P}{P_{u}} = \frac{s}{a + b \cdot s} = \frac{s}{0.15 + 0.70 \cdot s}

(17)

As shown in Figure 14, the results calculated by the proposed formulas are found to be in good agreement with the experimental results. Thus, equation (17) can be used to guide the design of PFR connectors in hybrid beams.

Conclusions

In this paper, a total of 18 push-out tests were conducted to evaluate the shear behavior of double-row PFR connectors and determine the reasonable spacing of the plate. The main conclusions drawn from the study are as follows:

(1) All PFR connectors experienced shear failure of the GFRP plate, while the concrete dowel remained intact.

(2) The measured P-S curves exhibited two phases, including the micro-slipping phase and the significant slipping phase. The turning point between these phases was observed within the range of 0.5-0.7V_u.

(3) The plate spacing-height ratio emerged as the primary influencing factor on the shear capacity and shear stiffness of the PFR connectors. It is suggested to be no less than 3.2 when multi-PFR connectors are used.

(4) Increasing the diameter of the penetrating GFRP bars and the concrete strength, the shear strength and stiffness of PFR connectors increased.

(5) Based on the maximum shear stress failure criterion, the critical shear damaged surface of PFR connectors was determined, and an equation was proposed for calculating the shear capacity of PFR connectors, considering the effect of plate spacing. The P-S model of PFR connectors was provided by curve fitting.

Footnotes

Acknowledgments

The authors would like to appreciate thanks to financial support.

Author contributions

Weichen Xue: Conceptualization, Methodology, Funding acquisition, Writing - review & editing, Validation, Supervision. Dawei Yan: Writing - original draft preparation, Investigation, Formal analysis, Visualization. Yongsheng Wang: Data curation, Resources. Jiafei Jiang: Writing - review & editing, Supervision.

Declaration of competing interest

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 National Key R&D Program of China (Grant No. 2022YFC3801400) and the National Natural Science Foundation of China (Grant No. 52130806).

ORCID iDs

Weichen Xue

Jiafei Jiang

Data availability statement

Data will be made available on request.*

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