Experimental investigation on the cyclic performance of perfobond rib shear connectors

Abstract

The behavior of perfobond rib shear connectors (PBL shear connectors) under monotonic loading has been widely studied. However, the performance of these connectors under cyclic loading is poorly understood and has seldom been investigated. This work presents an experimental study focusing on the cyclic performance of representative PBL shear connectors with passing rebar. Optical fibers were introduced to measure the detailed strain distributions. Results showed that the bearing capacity of these connectors could reduce up to 55.04% when compared with that under monotonic loading. The performance of these connectors differed significantly between the pull and push directions in the cyclic loading process. The concrete cracks, relative slip, and strains were developed earlier and more completely under pull than under push. Furthermore, rapid stiffness degradation, severe cracking and deformation of the concrete dowels were revealed, indicating the rapid failure of the adhesive effect, reduction of both the shear-friction effect and the dowel action of the passing rebars. These factors all contributed to the observed significant cyclic deterioration of the peak load and the slip. Based on this, a modified formula was proposed to consider the reduction effect. Comparisons between the analytical solution and test results validated the formula.

Keywords

composite structures cyclic deterioration cyclic performance cyclic test PBL shear connectors

Introduction

Perfobond rib shear connectors (PBL shear connectors) are extensively adopted in composite structures, owing to their excellent stiffness and ductility, high bearing capacity, outstanding anti-fatigue performance, and high applicability to construction (Higgins and Mitchell, 2001; Machacek and Studnicka, 2002). In recent years, various types of PBL shear connectors (such as I-shaped, 2T-shaped, Y-type, and fiber-reinforced polymer (FRP)) have been proposed and investigated (Costa-Neves et al., 2013; Kim et al., 2017; Zheng et al., 2016; Zou et al., 2016). The existing studies have demonstrated the favorable mechanical performance of these connectors and their considerable potential for use in composite structures.

The mechanical performance of PBL shear connectors under monotonic loading has been extensively investigated, and the load–slip characteristics, shear capacity, and bearing mechanism of these connectors under this loading mode have been revealed. In addition, different equations and analytical models for estimating the bearing capacity of these connectors have been proposed (Gu et al., 2019; Medberry and Shahrooz, 2002). Vianna et al. (2013) performed two series of push-out tests aimed at evaluating the bearing and deformation capacities of PBL shear connectors and formulated an equation through multiple regression analysis. Su et al. (2016) studied the failure mechanism of these connectors and proposed an empirical expression for predicting the corresponding shear capacity. According to these studies, the monotonic static performance of a PBL shear connector is affected by the hole diameter, reinforcement ratio, and material strength. In addition, the bearing mechanism of shear connectors in composite beams differs significantly from those in steel–concrete joints (He et al., 2016; Xiao et al., 2016). Zhao et al. (2018) addressed the contribution of the adhesive effect, shear-friction effect, and dowel action to the bearing capacity of PBL shear connectors. Moreover, the mechanical behavior of grouped PBL shear connectors under monotonic loading has also been studied experimentally and theoretically (Li et al., 2018; Zhang et al., 2017a, 2017b).

In addition, the mechanical performance of shear connectors under repeated loading (especially the high-cycle fatigue resistance of headed shear studs) has attracted the attention of researchers (Hanswille et al., 2007). The low-cycle fatigue performance of studs has also been investigated. The experimental results have indicated that the shear capacity and ultimate slip of the studs decreased by almost 10% and 30%, respectively, due to the accumulated damage (Gattesco and Giuriani, 1996). In addition, the superior anti-fatigue performance of PBL shear connectors, compared with that of headed shear studs, has been repeatedly demonstrated. Additional studies on these connectors have focused on fatigue damage and analytical models for evaluating the accumulated damage (Andrä, 1990; Roberts and Heywood, 1995; Xiao, 2012; Zhang et al., 2018). In particular, Zhang et al. (2014) found that the loading cycle and amplitude had a significant effect on the damage to PBL shear connectors, which shall be more obvious under cyclic loading. Under natural cyclic loads such as strong winds and earthquakes, the connectors will be subjected to rapid alternate shear forces, owing to changes in the bending moment signs (Ciutina and Stratan, 2011). Ciutina and Stratan (2011) investigated the cyclic performance of several shear connector types and reported that the slip capacity and shear resistance of perfobond connectors deteriorated the most under cyclic loading. To assess the shear–slip behavior of PBL shear connectors under cyclic loading, Kisaku and Fujiyama (2017) proposed an empirical model for predicting the unloading and reloading paths of PBL shear connectors without passing rebars. The results of static push-out tests with unloading–reloading cycles were used as the basis for these predictions. However, unlike the representative PBL shear connectors with passing rebars, the connectors considered in these two studies contained no passing rebars. Moreover, the study by Kisaku and Fujiyama (2017) focused only on push load cycling, rather than on a full push–pull cycle. Several studies have recently explored the hysteretic performance of stubby Y-type perfobond rib shear connectors (Kim et al., 2019); this type of PBL shear connectors is, however, not the common type used in engineering practice. The cyclic performance of representative PBL shear connectors has seldom been investigated.

This work focused on the cyclic performance of representative PBL shear connectors used in the steel–concrete joints of practical bridges. The effects of holes perforated in the steel plate and the interfacial condition were investigated via experiments. The detailed strain distributions of the perforated steel plate and the passing rebars measured by optical fibers, and the corresponding load–slip curves, were compared with those obtained from previously conducted monotonic static tests. The performance differed significantly between pull and push during the cyclic loading of these specimens. Significant cyclic deterioration in the strength and the ductility was also observed. The mechanism of deterioration was identified based on these experimental results. Based on the cyclic performance, a modified formula was proposed to consider the reduction effect of both the shear-friction effect and the dowel action of the passing rebars. Comparisons between the calculated results and tested values proved the effectiveness of the formula.

Experimental program

Specimen design

Based on the practical PBL shear connectors in the 3rd Nanjing Yangtze River Bridge (Zhang et al., 2007) and the monotonic static test specimens tested in a previous study (Zhao et al., 2018), the PBL shear connector specimen was designed, as shown in Figure 1. The core part of the cyclic test specimens were the same as the previous monotonic static test specimens (Zhao et al., 2018). The length of the surrounding concrete was extended to 1300 mm and two anchor holes were reserved for anchoring. Small steel pipe segments were added to the end of the passing rebars for optimizing the optical fiber arrangement. The width and the height of the surrounding concrete were 700 and 600 mm, respectively. A steel plate perforated with two holes was placed into the surrounding concrete, and the part of the plate in the concrete had a width of 500 mm, a height of 380 mm, and a thickness of 25 mm. Two passing rebars were passed through the holes. The diameter of each rebar was about one-third of the corresponding hole. All the specimens had the same transverse reinforcement ratio (the ratio of the sectional area of all transverse reinforcement to the area of the perforated steel plate) as that (0.83%) of the standard specimens considered in the previous study. The thickness of the cover layer for the transverse reinforcement was 30 mm. Furthermore, polystyrene strips were located at the end of the steel plate and loading stiffener to eliminate the end-bearing effect.

Figure 1.

Structural details of the PBL shear connector specimen (mm): (a) elevation, (b) A–A, and (c) reinforcement arrangement.

Four specimens were tested. Table 1 summarizes the parameters of the specimens, where the label S60-P10-C50 means the steel plate was perforated with 60 mm holes; the diameter of the transverse reinforcement was 10 mm, and the nominal cubic compression strength of the surrounding concrete was 50 MPa. According to the representative applications in the practical design (Xiao, 2012), this experimental study considered the diameter of the holes in the steel plate and the diameters of the passing rebars as the main parameters. For each specimen, the hole diameter was approximately three times the rebar diameter. For specimen S45-P10-C50u, the “u” indicates that the adhesive effect at the steel–concrete interface was eliminated by the lime paste smeared on the perforated steel plate.

Table 1.

Specimen details.

Specimen	Diameter of holes (passing rebar) (mm)	Diameter of transverse reinforcement (mm)	Nominal concrete strength (MPa)	Ratio of transverse reinforcement (%)	Lime paste
S45-P10-C50u	45 (16)	10	50	0.83	Yes
S45-P10-C50	45 (16)	10	50	0.83	No
S60-P10-C50	60 (20)	10	50	0.83	No
S80-P10-C50	80 (25)	10	50	0.83	No

Material properties

The average cubic compressive strength of the surrounding concrete was 56.30 MPa, which was obtained from tests on 150 × 150 × 150 mm³ concrete cubes after the standard 28-day curing. The age of the concrete during the cyclic loading test was 93 days, and the average cubic compressive strength was 65.02 MPa. For each specimen, the material used for the perforated plates was the Q345B structural steel, and that used for the passing rebars and transverse reinforcement was HRB400 rebar. Table 2 presents the results of the material tests. The average yield strength, ultimate tensile strength, and maximum elongation rate of the Q345B structural steel plates were 416 MPa, 542 MPa, and 24%, respectively. The HRB400 rebar (diameter: 10 mm) had an average yield strength of 464 MPa, ultimate tensile strength of 625 MPa, and elongation rate of 22%. The corresponding values for 16, 20, and 25 mm HRB400 rebar were 460 MPa, 615 MPa, 24%; 458 MPa, 595 MPa, 25%; and 460 MPa, 605 MPa, 21%, respectively.

Table 2.

Material properties of structural steel and rebar.

Material	Thickness/diameter (mm)	Yield strength (MPa)	Ultimate tensile strength (MPa)	Elongation rate (%)
Q345B structural steel	25	416	542	24
HRB400 rebar	10	464	625	22
	16	460	615	24
	20	458	595	25
	25	460	605	21

Loading setup and measuring system

The loading setup was shown in Figure 2(a). The surrounding concrete of the specimen was anchored to the reaction floor. A vertical actuator connected to the bearing plate of the specimen was used to provide the vertical push–pull (cyclic) force. To determine a suitable loading protocol, the first specimen tested (S60-P10-C50) was first loaded at the rate of 5 kN/s to an amplitude of 80 kN with only one cycle, and the force amplitude was increased in intervals of 80 kN until failure. The specimen failed rapidly, indicating an unsuitable loading protocol. Hence, for the other three specimens, the load was adjusted to an amplitude of 40 kN with two cycles at first, and then the force amplitude was increased in intervals of 40 kN until failure, as shown in Figure 2(b). This representative loading protocol, not specific for one structure, could reveal the enveloped capacity of structures under cyclic loading, and recommended by the structural testing specification (Ministry of Housing and Urban-Rural Development of the People’s Republic of China, 2015).

Figure 2.

Loading setup and protocol: (a) loading setup and (b) loading protocol.

The layout of the measuring system was shown in Figure 3(a). The relative slip between the perforated steel plate and the surrounding concrete were monitored by two displacement transducers at the locations of the passing rebars. The two transducers was arranged through two short steel bars that welded to the steel plate sides and extended out from the reserved holes in the surrounding concrete. The other two displacement transducers were used to monitor the displacement at the loading locations. Five strain gauges were placed at each side of the perforated steel plate to monitor the normal stresses out of plane. These strain gauges were embedded in the concrete with their measurement direction perpendicular to the steel plate plane, and one end of the strain gauges were pasted on the plate surface. One strain gauge was placed in the middle of the two holes. Two of the other four were placed 70 mm above the corresponding hole, while the other two were placed 70 mm below. The data from the displacement transducers and the strain gauges were obtained with a frequency of 1 Hz.

Figure 3.

Layout of the measurements (mm): (a) general arrangement, (b) fibers in passing rebar, and (c) fibers in concrete.

Four optical fibers were embedded in the reserved grooves in each plate to measure the vertical strain distributions. The two vertical fibers adjacent to the hole were ∼80 mm away from the hole center. Two pre-stretched optical fibers were placed in the two polished grooves engraved on the passing rebar to monitor the strain in the rebar (Figure 3(b)). Each fiber was protected by epoxy resin and liquid silicon. The strain of the transverse reinforcement in the surrounding concrete was measured by four optical fibers placed along them. The vertical distance of each fiber at the top and bottom to the passing rebars was ∼20 cm (see Figure 3(a) and (c)). The strain distributions were measured at the end of each loading cycle.

Results and discussion

Crack and failure modes

The crack and failure modes of the four specimens (Figures 4 and 5) were almost the same. The cracks appeared first on the edge between the upper and side surfaces, as indicated by the dotted lines in Figure 4. The number of cracks increased and the cracks extended continuously under pull, but almost no cracks formed under push, and those formed during pull loading closed when subjected to push. Cracks inclined from the edge between the upper and side surfaces to the steel structure were formed even under small pull loads, indicating the earlier failure of the adhesive effect at the steel–concrete interface under pulling than under pushing. With increasing loading cycles, the cracks ran through and developed densely at the pull sides. Moreover, the number of vertical cracks formed on the side surface was considerably lower than that formed during monotonic static tests (Su et al., 2016; Xiao et al., 2016; Zhao et al., 2018). This confirmed that the expansion effects induced by the transverse deformation of the surrounding concrete and dilatancy of the concrete dowels were released by the dense cracks at the pull sides. In addition, the perforated steel plate pulled out after the shear-off of the passing rebars, and the concrete on the upper surfaces was quite fragmented.

Figure 4.

Ultimate crack state of each specimen: (a) S45-P10-C50u, (b) S45-P10-C50, (c) S60-P10-C50, and (d) S80-P10-C50.

Figure 5.

Failure modes: (a) shear-off of the passing rebar and (b) scratches on the surfaces of the perforated steel plate.

Each specimen failed, owing to the tensile shear fracture on both the upper and lower sides of the passing rebars, and considerable shear and bending deformations were observed (see Figure 5). The fracture surfaces of the rebars were less smooth and flat than those associated with the monotonic static tests (Zhao et al., 2018). Passing rebars in specimens used lime paste also had only one fracture surface, and severe necking of the passing rebar segments was observed at the other side of the holes, which was the same with the case in the monotonic static tests. Scratches were observed on the surfaces of the perforated steel plate above and under the holes (see Figure 5(b)), but the number of the scratches were considerably less than those in previous monotonic static tests. All of these indicated a significant reduction in the shear-friction effects under cyclic loading.

Load–slip relationship

The load–slip curves of the four specimens are shown in Figure 6. The curve obtained for the monotonic load–slip model associated with static push-out loading proposed by Wang (2015) was plotted for comparison. The performance of each specimen differed considerably between push and pull during the cyclic loading. This resulted from the difference between the boundary conditions associated with these two directions for these PBL shear connectors. The slip in the push direction was substantially smaller than that in the pull direction. Furthermore, the load–slip curves were quite asymmetric, and visible pinching effects were observed, especially for specimen S45-P10-C50u, which experienced a slip of 0.04 mm under the first pull force of 40 kN. The damage occurring in the concrete dowels at this level of slip (Wang 2015) led to an immediate pinching effect, and after that, the slip began to accumulate in the pull direction. While the other specimens did not slip at the first four loading cycles owing to the valid adhesive effect at this time (Zhao et al., 2018). This is verified by the coincidence between the corresponding region of the load–slip curves and the monotonic push-out model. After slipping, the slip accumulated first in the push direction, indicating the effectiveness of shear-friction effects. However, these effects were quickly weakened with the rapid increase of deformation in the pull direction. Subsequently, slip accumulation occurred in the pull direction (rather than in the push direction), and the specimens failed in this direction.

Figure 6.

Load–slip curves of specimens: (a) S45-P10-C50u, (b) S45-P10-C50, (c) S60-P10-C50, and (d) S80-P10-C50.

In contrast to the monotonic model, significant reduction of the stiffness was observed, except in the case of specimen S45-P10-C50u. As previously stated, the adhesive effect on the steel at the steel–concrete interface was valid in the beginning of the cyclic loading process, and it weakened rapidly in a few loading cycles. After that, material damage occurred and accumulated under further cyclic loading, which was earlier and more severe than that in monotonic static loading. Thus, the load–slip behavior of specimens with interfacial adhesion differed significantly between monotonic and cyclic loading. While for S45-P10-C50u, the material damage was caused directly almost at the beginning of both the monotonic and cyclic loading due to the elimination of the interfacial adhesion, thus, the specimen load–slip behavior differed only slightly between these loading modes. Nevertheless, cyclic deterioration was also observed.

Figure 7 shows the envelop curves of the specimens, and Table 3 summarizes the typical performance points. Based on the envelope load–slip curve, the yield point Y is determined as the intersection point of the vertical line through point C and the envelope load–slip curve (Figure 8). Point C is obtained by the intersection of extended line OB and the horizontal line at the peak load, where point B is the intersection point of the tangent line (OA) of the envelope load–slip curve at original and the vertical line through point A. The ultimate slip was defined as the slip occurring when the load decreased to 85% of the peak load (Wang et al., 2019). The ultimate slip and the ductility coefficient (ratio of the ultimate slip to the yield slip) of S45-P10-C50u are absent because measurement failure at the end of the test prevented the recording of this slip value. The curve developed fully under the pull loading process, thus negative performance points were obtained. Significant cyclic deterioration in the load-carrying capacity was observed. The values of the loads at the corresponding points were only ∼0.2–0.5 times the values of the loads for specimens with similar parameters under monotonic static conditions (Zhao et al., 2018). The peak load under monotonic static loading for each specimen was also provided in Table 3 for the quantitative comparison (Zhao et al., 2018). Owing to the cyclic deterioration, the specimen could not achieve its peak load-carrying capacity under static loading. The average reduction ratios of the peak load-carrying capacity values were 53.45% and 19.55% for specimens with and without interfacial adhesion, respectively. However, large ductility coefficients were obtained. The PBL shear connectors still exhibited excellent ductility capacities. As for the initial stiffness, S45-P10-C50u presented smaller values than the other three specimens, owing to the lower slip resistance resulting from elimination of the interfacial adhesion. Furthermore, the shear-friction effect was weakened due to the friction coefficient reduction induced by the lime paste on the perforated steel plate (Zhao et al., 2018).

Figure 7.

Envelope curves of specimens.

Figure 8.

Determination of the yield point (Wang et al., 2019).

Table 3.

Specimen performance points.

Specimen	P_y (kN)	S_y (mm)	P_u (kN)	S_f (mm)	$μ_{D}$	P_s (kN)	R_p
S45-P10-C50u	–204.9	–0.186	–361.2			449.0	19.55%
S45-P10-C50	–230.3	–0.053	–402.7	–9.950	187.74	861.8	53.27%
S60-P10-C50	–232.3	–0.112	–481.2	–13.809	123.29	1070.3	55.04%
S80-P10-C50	–236.4	–0.079	–638.1	–15.013	190.04	1330.3	52.03%

Note: P_y = yield load; S_y = slip at yield load; P_u = peak load under cyclic loading; S_f = ultimate slip; $μ_{D}$ = ductility coefficient; P_s = peak load under monotonic static loading (Zhao et al., 2018); R_p = reduction ratio of the peak load value from static to cyclic.

The secant stiffness degradation is further considered in Figure 9, where the secant stiffness was calculated as the ratio of the load amplitude of the first loading cycle at each loading stage to its corresponding slip. The stiffness values under push loading were substantially larger than those under pull loading. S80-P10-C50 and S60-P10-C50 had similar initial stiffness values, owing possibly to the improper rapid loading of S60-P10-C50. Moreover, the stiffness degraded rapidly with increasing slip, especially for slip of 0–0.1 mm in the push direction and 0–0.2 mm slip in the pull direction, indicative of rapid shear-friction effect weakening as well as damage occurrence and accumulation under cyclic loading. This can be verified by the almost equal stiffness values of S45-P10-C50 and S45-P10-C50u after that. Afterward, the stiffness decreased steadily.

Figure 9.

Stiffness degradation: (a) under pull loading and (b) under push loading.

Normal stresses out of the perforated steel plate plane

Figure 10 present the normal stresses out of the perforated steel plate plane. These curves were plotted by connecting the normal stresses at slip values corresponding to the load amplitude of each loading cycle. All stresses are average values of those from the two opposite surfaces. The strain gauges at the middle locations were damaged and, hence, the average values of the upper and lower locations were adopted as a reference for specimens S60-P10-C50 and S80-P10-C50. In the push direction, compressive normal stresses were first observed in all locations (see Figure 10), owing to the normal constraint effect (Zhao et al., 2018). Subsequently, the perforated steel plate separated from the surrounding concrete due to the cracking and dilatancy of the concrete dowels and, thus the stresses tend to be tensile. In the pull direction, compressive stresses were obtained at the lower locations, except in S60-P10-C50, and tensile stresses were obtained at the upper and middle locations, except in S45-P10-C50u. The rapid loading of S60-P10-C50 may have led to inadequate time for the relevant loading responses such as cracking and dilatancy of the concrete dowels. Thus, changes in the normal stresses may be lagging. The slip occurring in S45-P10-C50u was relatively small, and the thin soft lime paste provided deformable space for the dilatancy of the dowels. Thus, the separation of the steel plate from the surrounding concrete was insufficient for inducing the tensile stresses.

Figure 10.

Normal stresses out of the perforated steel plate plane: (a) S45-P10-C50u, (b) S45-P10-C50, (c) S60-P10-C50, and (d) S80-P10-C50.

Strain distribution in the transverse reinforcement

The strain distribution along the transverse reinforcement was shown in Figure 11, where zero on the abscissa indicates the perforated steel plate center in the transverse direction. Note that “x” – “n” means the nth time of the x kN loading. For example, −600 – 1 means the first round of pulling under 600 kN loading. During the test, tensile deformation was mainly observed in the transverse reinforcement because of the expansion of the concrete dowels. The central segments of the transverse reinforcement at the top underwent slight compressive deformation under large load, indicating substantial bending deformation of this reinforcement. This deformation was attributed to the significant damage of the bonding constraint effect during cyclic loading, as the concrete on the upper location was quite fragmented.

Figure 11.

Strain distributions along the transverse reinforcement in S80-P10-C50: (a) Top1, (b) Top2, (c) Bot1, and (d) Bot2.

The strains of the top transverse reinforcement increased substantially after the first round of −120 kN loading (maximum tensile strain: ∼152 $μ ε$ $(μ ε = 1 0^{- 6})$ ), and the strains increased rapidly after the initial cracking of the concrete. The bonding effect between the transverse reinforcement and the concrete was damaged after concrete cracking, leading to easy deformation of the reinforcement and, in turn, a rapid increase in the strains. While the strains of the bottom transverse reinforcement were quite small below ±200 kN loading, and the values of the strains under corresponding loads were smaller than those at the top. This also demonstrated the easier deformation and greater weakening of the bonding effect at the top (than at the bottom). The strain in the central 40-cm segment (which was wider than the 30-cm range considered in previous tests (Zhao et al., 2018)) increased with increasing load. This indicated that, compared with those occurring during monotonic static loading, (1) more severe cracking and deformation of the concrete dowels and (2) greater weakening of the bonding effect between most sides of the transverse reinforcement and the surrounding concrete (due to the fully reversed loading), occurred during cyclic loading. When the load reached −600 kN, the maximum tensile strain exceeded 1200 $μ ε$ , which was also larger than the strain generated under monotonic static loading.

According to Figure 11, variations in the strains occurred mainly within ±40 cm away from the transverse reinforcement center. The total elongation of the transverse reinforcement was obtained by integral operation on the strains in the central 80-cm range of the transverse reinforcement, which corresponded to the expansion of the concrete dowels in the transverse direction. Figure 12(a) shows the elongation in specimen S80-P10-C50. These curves were plotted by connecting the elongation values at slip values corresponding to the loads in Figure 11. The elongation under push loading differed from that obtained under pull loading. Under push loading, initially, the bottom fiber sustained larger tensile deformation than the top fiber, owing possibly to the internal moment in the surrounding concrete that resulted from the boundary condition, that is, concentrated vertical push force at the center of the top surface and the planar support at the bottom surface, as shown in Figure 12(a). For slip of <0.12 mm, the elongation increased gradually with increasing slip, and then increased sharply when the slip exceeded 0.12 mm, corresponding to the previously mentioned rapid degradation of the stiffness. The elongation of the top then exceeded the elongation of the bottom. This resulted from the fact that the severely fragmented concrete on the upper surfaces was unable to constrain the tensile deformation of the top transverse reinforcement and the top fiber. Under pull loading, significant tensile deformation was observed for all fibers, with the maximum occurring for the top fiber, which may be caused by the internal moment contrary to that under push (Figure 12(a)). Moreover, unlike the elongation occurring under push loading, the elongation increased rapidly from the initial stage, owing possibly to the fact that (as previously stated) deformation is easier in the pull direction.

Figure 12.

Relationship between slip and elongation: (a) in S80-P10-C50 and (b) comparison among specimens.

The average elongations of the transverse reinforcement in the four specimens were compared and similar responses were obtained for all the specimens (see Figure 12(b)). The average elongation increased significantly after a slip of 0.12 mm under push loading, but increased rapidly from the beginning of pull loading. Furthermore, as in the case of previous monotonic static tests, specimens with larger concrete dowels underwent considerably larger elongation, indicating larger transverse expansion, than those with smaller dowels. For specimen S45-P10-C50u, the dowels were damaged in the initial stage of the pull loading, leading to a more rapid increase in the elongation compared with that occurring in specimen S45-P10-C50. This resulted in more damage accumulation and, consequently, more severe transverse expansion in S45-P10-C50u than in S45-P10-C50.

Strain distribution in the passing rebar

The axial-strain and curvature distributions of the passing rebar in S80-P10-C50 under different loading amplitudes are shown in Figure 13, where zero on the abscissa indicates the rebar center. Considerably different trends were observed for push and pull loading. The strains under push loading were relatively small (less than 100 $μ ε$ for loads below 600 kN), whereas the strains under pull loading increased considerably after 200 kN. Considering the curvature, the maximum curvature under push loading occurred mainly in the central segment of the passing rebar. The maximum value (11.3 × 10⁻⁶ mm⁻¹ under 600 kN) is larger than that reported for monotonic static tests at a load of 1100 kN (Zhao et al., 2018). This indicated that, compared with static loading, cyclic loading induced larger deformation. The bearing capacity degraded. Furthermore, the curvature in the central segment was positive and, hence, bending deformation was dominant, whereas the maximum curvature in the pull direction was distributed more discretely along the passing rebar. The maximum value was −22.4 ×10⁻⁶ mm⁻¹ at a load of 600 kN. This value is negative, but positive curvatures were distributed along the rebar, indicative of a substantial bending–shear coupled effect. In addition, unlike the 60-cm-long strain distribution obtained in previous monotonic static tests (Zhao et al., 2018), the strains and the curvature were distributed along almost the full length of the rebar. This was especially true under pull loading, demonstrating that the bonding effect between the passing rebar and the surrounding concrete was significantly damaged, as suggested by the aforementioned quite fragmented concrete.

Figure 13.

Strain distribution and curvature of the passing rebar in S80-P10-C50: (a) axial strains and (b) curvature.

Strain distribution of the perforated steel plate

Figure 14 shows the strain distributions in the perforated steel plate of S80-P10-C50. Zero on the ordinate represents the upper edge of the fiber, and the locations of the holes in the plate is denoted by a dotted line. The plate underwent mainly tension under pull loading and compression under push loading. The strains under pull loading were larger than those under push loading and developed slightly differently with increasing load. Below 200 kN pull loading, the strains of the perforated steel plate were almost linear, owing to the uniform adhesion and shear-friction force considered under monotonic static loading (Zhao et al., 2018). Afterward, the increasing amount of concrete cracking caused by the pull loading resulted in rapid failure of the adhesive effect. The strains increased considerably, especially above 360 kN pull loading. While under push loading, as previously stated, almost no new cracks were observed, and the cracks induced by pull loading became closed during push loading. This led to recovery of the shear-friction effect on the perforated steel plate, and the strains were almost always linear. Under large loads in the push direction, the strains increased quickly in the regions above the holes, and decreased slightly in other regions. This demonstrated that the adhesive effect was further failed, significant shear-friction effect was induced by the dilatancy of the damaged concrete dowels, and dowel action of the passing rebars was gradually strengthened (Zhao et al., 2018). In contrast, under relatively large pull loads, the strains developed in almost the same manner. As previously stated, the bonding effect between the passing rebar and the surrounding concrete was damaged more under pull loading than under push loading. The deformations of the passing rebars were not mainly concentrated in the central segment. Thus, the dowel action effect was reduced and had little impact on the strain distributions in the perforated steel plate.

Figure 14.

Strain distribution in the perforated steel plate of S80-P10-C50: (a) strain of middle optical fiber and (b) strain of side optical fiber.

Estimation of peak bearing capacity

Zhao et al. (2018) proposed a formula incorporating the shear-friction effect and the dowel action of the passing rebars to estimate the ultimate capacity of PBL shear connector under monotonic loading. However, it cannot be directly used in the cyclic loading case due to the reduction of the shear-friction effect and the dowel action. Based on this, a modified formula (equation (1)) was proposed to reflect the reductions, in which the “MPa-mm” unit system was adopted

P_{u} = 0.8 r_{c - m} μ (A_{tr} f_{try} + A_{d} f_{dy}) + 2 nk d^{2} \sqrt{f_{c} f_{dy}}

(1)

where 0.8 is a coefficient considering the variation of materials (Allahyari et al., 2018); $r_{c - m}$ is a reduction factor for the shear-friction effect under cyclic loading; $μ = 0.6$ is the lower boundary of the friction coefficient suggested by ACI-318; $A_{tr}$ is the total area of the transverse reinforcement perpendicular to the perforated steel plate; $f_{try}$ is the yield strength of the transverse reinforcement; $A_{d}$ is the total area of the passing rebars; $f_{dy}$ is the yield strength of the passing rebar; n is the number of the passing rebars in the holes; d is the diameter of the passing rebar; $f_{c}$ is the compressive strength of the concrete; k is an coefficient account for the enhancement of the ultimate dowel force due to shear and kinking deformation of the passing rebars (Zhao et al., 2018), as expressed by equation (2)

k = {\begin{matrix} 2.17 - 0.0011 d^{2} & s > 1.25 d \\ [(1.17 - 0.0011 d^{2}) (s - 0.08 d) / 1.17 d] + 1 & 0.08 d < s \leq 1.25 d \\ 1 & s \leq 0.08 d \end{matrix}

(2)

where s is the ultimate relative slip between the perforated steel plate and the surrounding concrete. It is usually within the range of 0.08d – 1.25d (Zhao et al., 2018)

Note that in the second component of equation (1), the reduction of the dowel action was involved using a coefficient of 1.0 for cyclic loading (Zoubek et al., 2015) instead of 1.27 for monotonic loading (El-Ariss, 2007).

As for the shear-friction strength reduction, the lower-bound shear-friction strength was only $0.25 A_{v} f_{yv}$ (where $A_{v}$ is the area of shear-friction reinforcement, and $f_{yv}$ is the yield strength) under cyclic loading (Baek et al., 2018; Wood, 1990), while ACI-318 and ACI-349 suggest the shear-friction strength $μ A_{v} f_{yv}$ ( $μ$ = 0.6–1.4). The ratio of the lower boundary value 0.416 (=0.25/0.6) can be taken as the simplified reduction factor r_c–m under cyclic loading. It should also be noted that when the adhesive effect at the steel–concrete interface was eliminated, the friction coefficient was reduced to 0.3. The degradation of the shear-friction strength has already been involved in this coefficient reduction. Thus, no further reduction of the shear-friction effect was considered in this case. In general, $r_{c - m} |_{μ = 0.3} = 1$ and $r_{c - m} |_{μ = 0.6} = 0.416$ . Table 4 compares the peak loads from equation (1) with the tested values. The average and maximum relative errors are just −4.06% and −9.93%, respectively, demonstrating the satisfactory accuracy of equation (1).

Table 4.

Comparison between equation (1) and tested peak loads.

Specimen	Calculated P_u (kN)	Tested P_u (kN)	Relative error
S45-P10-C50u	382.3	361.2	–7.31%
S45-P10-C50	362.7	402.7	–9.93%
S60-P10-C50	488.9	481.2	1.6%
S80-P10-C50	634.1	638.1	–0.62%

Further discussion on different cyclic performance between push and pull

According to the aforementioned experimental results, the cyclic performance of the PBL shear connectors differed significantly between push and pull loading, due to the difference between the boundary conditions associated with these loading modes. The mechanism governing this difference is illustrated in Figure 15. Under pull loading, the reaction forces were mainly provided by the contact areas of the anchor beam. The perforated steel plate separated from the surrounding concrete, owing to the transverse expansion of the concrete dowel, and clamping forces were produced in both the transverse reinforcement and passing rebars, as well as from the constraint effect of the surrounding concrete, to restrain the transverse deformation. In the vertical direction, the top surface was free, except for the contact areas between the anchor beam and the specimen and, hence, during pull loading, the specimen was easily deformed in the vertical direction. However, under push loading, the reaction forces were provided by the entire bottom surface. These reaction forces, together with the clamping forces, led to resultant forces that restrained the deformation of the polystyrene. Therefore, in contrast to the case of pull loading, the vertical movements of the PBL shear connectors were restrained under push loading.

Figure 15.

Different boundary conditions in the two directions: (a) under pull and (b) under push.

Conclusion

In this work, the cyclic performance of representative PBL shear connectors used in the steel–concrete joints of practical bridges was investigated through tests. The effects of the hole diameter and the interface between the steel plate and the surrounding concrete were focused. The cyclic performance of the connectors was assessed by measuring the relative slip as well as the strain distribution and development, and compared with the mechanical performance revealed in previously reported monotonic static tests. In addition, the mechanism leading to the significant cyclic deterioration was discussed. Furthermore, a formula, which estimates the overall bearing capacity under cyclic loading, was proposed and validated by the test results. The major findings of this study are summarized as follows:

The performance of these PBL shear connectors differed significantly between pull and push during the cyclic loading process. Compared with that on the push side, the concrete cracked more severely on the pull side and was quite fragmented. This resulted in significant damage of the bonding effect between the top transverse reinforcement and the surrounding concrete, as well as between the passing rebar and the surrounding concrete. Furthermore, the shear-friction effect decreased significantly under cyclic loading.

Owing to the more fragmented concrete and damage of the bonding effect, the length of the passing rebar that sustained visible bending-shear deformation was wider than that observed in monotonic static tests. The dowel action effect of the passing rebar decreased during cyclic loading. In addition, the strain distribution in the perforated steel plate indicates that the adhesive effect between the steel plate and the surrounding concrete failed more rapidly under cyclic loading than under monotonic static loading.

The effect of loading cycle and amplitude on the PBL shear connectors was quite significant under cyclic loading. The bearing capacity of these connectors could reduce up to 55.04% when compared with that under monotonic loading. The significant deterioration in the bearing capacity and the ductility of the PBL shear connectors under cyclic loading resulted from the deterioration of all the three major bearing mechanism components, namely the rapid failure of the adhesive effect, the reduction of both the shear-friction effect and the dowel action of the passing rebars.

A modified formula considering the reduction of both the shear-friction effect and the dowel action effect was proposed for estimating the peak bearing capacity. The small average and maximum relative errors indicated the satisfactory estimation. The PBL shear connectors under cyclic loading need a larger transverse reinforcement ratio or a larger dimension of PBL shear connectors to provide the equal load-carrying capacity with that under monotonic loading.

Footnotes

Acknowledgements

The authors gratefully acknowledge the contribution from Hefei Special Material Technology Limited Company.

Data availability

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

Declaration of conflicting interests

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

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was completed under the support of the Natural Science Foundation of China (grant no. 51708466) and Sichuan Science and Technology Program (grant no. 2019YFH0139).

ORCID iD

Kailai Deng

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