Shear behavior of prefabricated steel–concrete connectors in prefabricated steel–concrete composite beams

Abstract

Stud connectors are widely used to realize the shear connection of steel girders and prefabricated bridge decks in prefabricated steel–concrete composite beams. However, the dense arrangement of stud connectors in the combined bending and shear region makes fabricating prefabricated bridge decks difficult and weakens their integrity. Therefore, a novel prefabricated steel–concrete connector (PSCC) is proposed to accelerate the prefabrication and construction of prefabricated steel–concrete composite bridges. To validate the mechanical properties of PSCC connectors, four groups of 11 static push-out specimens were tested to analyze the effect of interfacial defects and different concrete materials for the shear performance of PSCC connectors. The PSCC connectors have high shear stiffness and ductility. At load levels up to 0.9Pu, the slip values of PSCC connectors range from 6.74 mm to 11.72 mm, which specifies a minimum slip of 6 mm (EC4). The shear capacity of the specimens with 30% and 60% interface defect areas decreased by 0.39% and 8.91%, respectively, compared to the specimens with no interface defects. When the connection layer material was replaced from ordinary concrete to UHPC, the shear capacity of PSCC connectors increased by 39%, and the failure mode shifted from shear failure of studs to shear failure of reinforcements. Moreover, cyclic loading marginally enhanced the shear capacity of PSCC connectors, serving as a safety reserve in practical engineering. Finally, a shear capacity calculation formula for PSCC connectors, derived from finite element analysis and existing formulas, achieved a prediction accuracy within 6.2%.

Introduction

Prefabricated steel–concrete composite beams have gradually become the preferred option for bridge construction by the advantages of low self-weight, high bearing capacity, low environmental impact, high disaster resistance, and high economic efficiency^1,2. Prefabricated steel–concrete composite beams are typically manufactured by fabricating the steel girders and bridge decks in a factory, then transporting them to the site for assembly and installation. To address the engineering requirements for the rapid assembly of steel–concrete composite bridges, optimizing the design of prefabricated shear connectors is a straightforward, reliable, and efficient solution³.

In prefabricated steel–concrete composite beams, shear connectors directly affect mechanical properties and construction mode. The mechanical properties of shear connectors affect the assembly efficiency of composite components^4,5, and change construction process of bridge assembly^6,7,8. The space occupied by connectors in the assembly stage of prefabricated steel–concrete composite beams is low. The resulting space surplus is conducive to reducing the difficulty of assembling prefabricated bridge decks. Prefabricated steel–concrete composite beams mostly adopt cluster studs. Cluster studs have a very high field assembly efficiency, reduces the difficulty of assembly construction and avoids interference with the traffic environment. However, clustered arrangement of stud connectors results in unequal stress distribution between studs, and the stiffness and strength of studs in the densely clustered areas is lower than that of the individual studs. Meanwhile, prefabricated bridge decks need to reserve holes in advance, which weakens the integrity of prefabricated bridge decks⁹. Furthermore, a high level of precision is required during fabrication to prevent the overlap of rebar and studs, thereby increasing the complexity of prefabricated deck production^10,11. To address these deficiencies, Badie et al.¹² and Xu et al.¹³ recommended the use of large diameter stud connectors. The results showed that although large diameter stud connectors improved shear capacity of single stud, the risk of cracking of the concrete deck increased. To avoid the lack of integrity of prefabricated decks and the high difficulty of assembling in the cluster studs, a simple connection construction based on the uniform arrangement of studs was proposed (PSCC connectors)¹⁴. PSCC connectors not only retain the benefits of stud connectors, but also preserve the integrity of prefabricated bridge decks and reduce the difficulty of assembly. The construction of PSCC connectors is shown in Fig. 1. Prefabricated concrete decks equipped with shear connecting steel members (P), studs and side baffles (S) on the flanges of the steel girders. P and S are prefabricated in the factory and transported to the site for assembly. Upon completion, they form an internal connecting cavity, which is subsequently filled with concrete (C) for the connection layer. The connection between the steel girder and the prefabricated bridge decks is finally formed(C). The connecting layer of PSCC connectors is an important medium between the steel girders and prefabricated bridge decks. Therefore, the mechanical properties of the concrete material of the connecting cavity are crucial. UHPC has been widely used in the construction of new and rehabilitated bridges due to its excellent mechanical properties^15,16,17,18 and great bond strength^19,20. Therefore, UHPC is suitable as the connection layer material for PSCC connectors.

Fig. 1

PSCC connectors.

Extensive research has been conducted on the mechanical properties of UHPC applied to stud connectors^{21,22,23,24,25}. Ding et al.²⁶ studied the shear performance of grouped stud connectors (GSCs) in UHPC. Increasing the diameter of studs had a positive effect on the shear performance. Reducing stud spacing had a greater effect on shear resistance, particularly for thin UHPC decks. Yang et al.²⁷ proposed a new UHPC-NSC composite deck system to reduce the cost of UHPC application in bridge construction. Compared to specimens made from conventional concrete, the shear performance of 19 mm and 22 mm diameter studs encased in UHPC increased by 3.8% and 2.2%, respectively. The specimens with studs embedded in UHPC satisfy the ductility requirements (EC4). Zou et al.²⁸ and Guo et al.²⁹ proposed a novel PCSC connection configuration. It avoids the weakening of the deck integrity by the clustered stud connectors, and accelerates the construction of prefabricated steel–concrete composite beams. The results showed that the shear capacity of PCSC connectors increased by 12.27% and the ultimate slip by 47.42% compared to that of clustered studs. The shear capacity of UHPC specimens was increased by 37% compared with that of high strength mortar specimens, and the stiffness of elastic and plastic stages were enhanced by 22% and 42%. Fang et al.³⁰ investigated the shear performance of stud connectors in steel-prefabricated UHPC decks. The results show that the stud diameter and UHPC plate thickness significantly affect the shear performance of the connectors. The casting method has less influence on the shear performance. The arrangement of stud connectors embedded in UHPC in the form of longitudinal and transverse spacing was used as critical values of 5d and 2.5d.

In conclusion, the mechanical properties of UHPC are significantly better than those of ordinary concrete. If conventional structural design is continued, it is usually impossible to fully utilize its excellent mechanical properties and improve assembly efficiency of prefabricated steel–concrete composite beams. The connection layer of the PSCC connector is an important member connecting steel girder and prefabricated decks. UHPC is able to fully bond the two members(Steel girders and prefabricated decks), thus fully utilizing the mechanical properties of the PSCC connector.

New shear connectors maintain the integrity of prefabricated bridge decks and enable rapid construction of assembled composite beams. In this study, mechanical properties of PSCC connectors was verified by monotonic and cyclic loading. Interface defects and connection layer material were taken as the design parameters of PSCC connectors, and push-out tests were carried out to analyze effects of failure modes, load-slip curves, shear stiffness and ductility. Finally, the prediction formula of shear capacity of PSCC connectors was established.

Experimental program

Specimen design

This study designed 11 specimens to evaluate the shear performance of PSCC connectors under different parameters. As shown in Fig. 2, all the specimens are made with the same external dimensions and the studs and shear reinforcements are kept with the same diameter. The overall size of the specimen is 514mm, the size of the precast plate is 400mm, all the structural reinforcement is HRB400, the diameter of the reinforcement is 12mm. Shear connecting steel members are installed in the precast formwork in advance before the prefabricated bridge decks are poured. The shear connecting steel member consists of transverse steel plate, steel plate with small thickness and shear reinforcement. The transverse steel plate is 360mm long, 218mm wide and 4mm thick, and the shear reinforcement is separated into two parts, which are built into the prefabricated bridge decks and the connection layer respectively, with the length of 120mm and 50mm. After the shear reinforcement arrangement is completed, steel plates with small thickness are welded to connect the ends of the shear reinforcement in the same row. The shear reinforcement is HRB400 with 12mm diameter and 170mm length, arranged in four rows and two columns. The transverse and longitudinal spacing of shear reinforcement is 65mm and 100mm respectively. The box-shaped steel element is 50mm × 138mm, the top and bottom steel plate size is 12mm × 182mm, and the two sides of the web plate size is 12mm × 50mm. In the box-shaped steel element on both sides of the welded form to set up side baffle members, the size of the length of 360mm × 40mm × 6mm. In the box-shaped steel element on both sides at the same time set studs connectors, head and shank diameter of 22mm and 13mm, respectively, using three rows and two rows of arrangement, studs transverse and longitudinal spacing of 65mm and 100mm, respectively. Side baffle plate total length of 360mm × 40mm × 6mm.

Fig. 2

Details of Specimen. (unit: mm).

To prevent the shear connecting steel member from slipping downward and crushing the bottom of the prefabricated bridge decks during loading. Therefore, before making prefabricated decks formwork, the lower part will be used to retain 30mm of reserved space using acrylic panels, and after the prefabricated decks are poured, the acrylic panels are taken out to form the reserved space. In order to prevent the overflow of post-cast UHPC through both sides of the side baffle, a rubber water stop strip with a thickness of 2mm is pasted on the top of the side baffle, and extended the length and width of the side baffle was laid. The overall fabrication process is shown in Fig. 3 and Fig. 4. The prefabricated decks and steel beams with attached shear connection steel members are assembled after fabrication. After assembly, the connection cavity is formed in the middle of the prefabricated decks and steel beam. Finally, UHPC is cast to create the connection between the two components.

Fig. 3

Adoption of UHPC specimen fabrication plant.

Fig. 4

Adoption of C50 specimen fabrication plant.

To investigate the effect of bond strength at the interface between the post-cast UHPC layer and the shear connecting steel member on the shear performance of PSCC connectors. Additionally, the effects of UHPC and ordinary concrete materials, with cast-in-place versus post-cast forms, on the shear performance of PSCC connectors were studied. Therefore, the following parameters are considered: the detailed parameters for each group of specimens are shown in Table 1.

Table 1 Grouping of push-out test specimens.

The specimens are classified into three categories, designated by the codes ZC, TK, and XJ, respectively. “ZC” indicates that the interface between the shear connection steel and UHPC is fully bonded. “TK” indicates the existence of deficiencies between the shear connecting steel members and the UHPC interface, respectively, to block 30% and 60% of the rectangular area, the interface blocking using a uniform arrangement, through the transverse steel plate on the transparent thin adhesive to achieve the interface deficiencies, “XJ” indicates that the connection cavity adopts ordinary concrete form to realize the comparison between UHPC and ordinary concrete. Therefore, the transverse steel plate in the shear connecting steel member is not set up, and the shear reinforcement is tied to the surface of the constructional reinforcement in order to realize the formation of an integral connection between the prefabricated bridge decks and the connecting layer.

Material properties

The prefabricated decks are made of C50 concrete and the connection layer is made of Ultra High Performance Concrete (UHPC). For C50 and UHPC materials, three cubic specimens and three prismatic specimens each with dimensions of 150 $\times$ 150 $\times$ 150mm(C50), 100 $\times$ 100 $\times$ 100mm(UHPC), and 150 $\times$ 150 $\times$ 300mm were fabricated to determine the compressive strength ${f}_{c}$ and Young’s modulus ${E}_{c}$ of both materials UHPC material is used to fabricate dogbone shaped members to measure their tensile strength ${f}_{u}$. Box-shaped steel element, shear connecting steel members, and side baffles are made of Q355C grade steel. The prefabricated plate construction reinforcement and shear reinforcement were made of HRB400 reinforcement. The average yield strength ${f}_{y}$, ultimate tensile strength ${f}_{u}$ and Young’s modulus ${E}_{c}$of structural steel and reinforcing were determined by tensile testing. The material property tests were conducted in accordance with "Standard for test methods for mechanical properties on ordinary concrete (GB/T 50,081–2002)"³¹ and "Standard for metallic materials-tensile testing—Part 1: Method of test at room temperature" (GB/T228-2002³²). Table 2 demonstrates the mechanical properties of each material, respectively.

Table 2 Material properties of concrete and steel.

Test setup and measurement system

As shown in Fig. 5, all tests are loaded using a kiloton pressure machine. Once the specimens are in place, fine sand is spread evenly on the bottom of the specimen to ensure uniform loading of the specimen. Four displacement sensors are placed on both sides of the side baffles to measure the relative slip between the steel beams and prefabricated decks. Additionally, two displacement sensors are mounted on the prefabricated decks to measure the relative slip between the connection layer and the prefabricated decks. This is achieved by attaching small steel sheets to the outer extension of the connection layer and analyzing the slip based on the displacement of these steel sheets. The loading form for the push-out test is shown in Fig. 6. The monotonic loading form is used for each group of one and two specimens. Before formal loading, 30% of the ultimate load is loaded three times in advance and destructive loading is carried out after completion. The specimens with UHPC materials are loaded cyclically. After preloading, the specimens are first subjected to 0%−50%−0% for a total of 10 times, followed by 0%−70%−0% for a total of 10 times, and finally monotonic loading until destruction. For the XJ group of specimens, the cyclic loading form is not performed. Crack development is observed and recorded throughout the test.

Fig. 5

Test setup and layout of dial indicator.

Fig. 6

Loading procedure for push-out tests.

Experiment results

Failure modes

In 8 of the 11 specimens, loading is stopped due to shearing of the shear reinforcement. The displacement sensors are close to reaching their limits. The remaining 3 specimens stop loading due to stud shear failure. Table 3 summarizes the main mechanical parameters and failure modes of all specimens. ${P}_{u}$ is the ultimate shear capacity. ${P}_{u,avg}$ is the average ultimate shear capacity of the monotonically loaded specimens. ${K}_{0.2}$ and ${K}_{0.8}$ the cutline shear stiffness corresponding to 0.2 and 0.8 times the ultimate load, respectively. ${S}_{m}$ and ${S}_{0.9Pu}$ represent the slip corresponding to the ultimate load and the slip corresponding to 0.9 ${P}_{u}$, respectively.

Table 3 Experiment results.

Figure 7 shows the form of failure of four groups of typical specimens under monotonic loading. The failure modes of the PSCC connections with UHPC material are all shear reinforcement shear failure. Interfacial slip occurs at the shear connecting steel members (SCSM) and UHPC interface, not at the steel girder and UHPC interface. Cracks in prefabricated concrete panels increase with elevated loads. This is mainly due to the plane bending moment during loading and the splitting of the shear reinforcement embedded in the prefabricated decks. The failure modes of PSCC connectors using plain concrete materials are all stud shear failures. Since the prefabricated decks and connection layer are cast in place, the shear reinforcement is embedded as a whole. Therefore, only the interface between the steel girder and the concrete exists in the ordinary concrete specimen. Therefore, only the interface between the steel girder and the concrete exists in the ordinary concrete specimen, where the interface slip also occurs.

Fig. 7

Deformation state of PSCC connectors after failure.

In order to visualize the form of PSCC connector failure, it is fully separated after the test is completed. From Fig. 7, it is evident that in the specimens from group ZC, TK30, and TK60, the shear reinforcement is completely severed at the base, and the shear surfaces are smooth. However, the top studs of the XJ group specimens are cut off from the root, and the last two rows show downward bending deformation. The concrete layer in the high-pressure stress zone section at the root of the studs is crushed. The parametric difference in the dehiscence rate only between the specimens of groups ZC and TK cannot affect the final failure mode, which is all shear reinforcement shear. The severe damage at the interface between the SCSM and the UHPC is mainly due to the deformation of the shear reinforcement crushing the UHPC layer on the lower side. The whole cast-in-place of the XJ group specimens, on the other hand, does not have the original interface of the connection layer, and thus the failure mode is changed to the conventional form of stud shear failure with a smooth shear surface. The top studs are pulled away from the steel girder as a whole, and the concrete around the roots of the studs is crushed. Although the last two rows are not fully sheared, there is still large deformation.

Due to the cyclic loading setting up resulted in PSCC connectors failure mode conversion. As shown in Fig. 8, the failure mode of specimen ZC-3 is characterized by stud shear failure. Additionally, the interfaces between the steel girder and UHPC, as well as between the baffle plate and UHPC on both sides, experience complete delamination. Friction scratches are clearly observed on the surface of both the steel girder and the UHPC layer, and the three rows of studs are pulled out as a whole after breaking from the root and separating from the UHPC layer together. In addition, compared with the XJ group specimens, the damage area of plain concrete at the root of the studs is much larger than the damage area of UHPC, and there are no obvious splitting cracks. Compared with the former, UHPC also has some integrity. The reason for this is that the side baffle mainly provide part of the shear resistance. Therefore, the studs wrapping in the PSCC connectors is much better than the conventional form of studs connectors. However, the high grade and multiple cyclic loads weaken the restraining force provided by the interface between the two side baffles and the UHPC. The ultimate failure is determined by the strength of the top–bottom interface. The test results show that the top interface outperforms the bottom interface without weakening, and the final failure is stud shear. Compared with the other specimens with shear failure of shear reinforcement, the UHPC of the connection layer transformed from partial cut fracture to overall detachment. It is evident that the bond between the interface between the two side baffles and UHPC of specimen ZC-3 completely failed. In contrast, the side baffles of the other specimens, the steel girder and the UHPC are still connected to each other as a unit.

Fig. 8

Deformation of PSCC connector after failure under cyclic loading.

Load-Slip curves

Figure 9 shows the load-slip curves for all specimens. The slip values are the relative displacements between the steel girder and the prefabricated concrete decks. The relative slip is averaged by a total of four displacement transducers measured on the front and rear sides with the aim of reducing the effect of load eccentricity. The cyclic load test is not carried out for the specimens in group XJ. The primary purpose of the XJ group specimens was to compare the performance of ordinary concrete and UHPC materials, with UHPC still being the preferred choice for the connection layer in practical engineering. When the load is lower than 0.5P_u, the load-slip curves of the specimens using UHPC material are close to the elastic curve. When the load is lower than 0.4P_u, the load-slip curves of specimens using ordinary concrete materials are close to the elastic curve.

Fig. 9

Load-slip curves of push-out specimens.

Once the specimens exceed the elastic stage load, the PSCC connectors enter the plastic stage, where the slope of the curve progressively decreases. The specimens in groups ZC, TK30, and TK60 reach peak load. The slip is more than 3.5 mm. the specimens of group XJ reach the peak load with the slip at 2.2 mm. After all specimens reach the ultimate load, the load decreases slowly and the slip increases rapidly. When the slip reaches 10mm, the load remains above 0.90P_u for the specimens with UHPC material. The specimens with normal concrete material are used and the load is kept above 0.82P_u. The results show that the PSCC connectors have better ductility. For the cyclic loading specimens, during the first level of cycling (0.5P_u), the residual slip of the PSCC connectors after unloading is in the range of approximately 0.05mm-0.1mm. For the secondary cycling process (0.7P_u), the residual slip of the PSCC connectors after unloading is in the range of approximately 0.1mm-0.3mm. The curves of the specimens under cyclic loading maintain essentially the same trend in the loading process as in the unloading process. During cyclic loading, the differences in loading and unloading curves and residuals are mainly related to interface friction, yield strength of shear reinforcement, and yield strength of studs. As the cyclic loading level increases, the deformation of the shear reinforcement and the deformation of the studs in the PSCC connectors gradually increase, as well as the damage of the UHPC in the connection layer will gradually increase. Therefore, there are differences in the cyclic curves of specimens with different interfacial strengths. The residual slip of the specimens with 60% weakened area at the interface between SCSM and UHPC is larger than that of the fully bonded specimens. The difference between the loading and unloading curves is greater for the specimens with 60% interfacial defects. There is no significant difference in the peak load slip of the specimen ZC-3 compared to that of the specimen ZC-1 and specimen ZC-2, indicating that the PSCC connectors still possess excellent ductility after cyclic loading. According to what is stated in EC4³³, when ${S}_{0.9Pu}$ is greater than 6 mm, the connectors can be recognized as ductile connectors and their constructional arrangement can be designed by plastic methods. The PSCC connectors of all specimens in this test meet the requirements.

The curves of the specimens under monotonic and cyclic loading follow similar trends, but the ultimate bearing capacity of the three groups of specimens under cyclic loading increased by 2.3% (ZC), 13.0% (TK30), and 14.2% (TK60), respectively, as compared to the monotonic loading. From the failure diagrams of each specimen in section "Failure modes", it is evident that the transparent thin glue at the interface defects on the prefabricated panel part after chiseling of the specimen of group TK30 has been completely damaged. Moreover, the difference between the ultimate load capacity under monotonic loading between the specimens of group ZC and group TK30 is small only 0.4%. In the failure diagrams, the interface defect and adhesive integrity of the TK60 group are significantly better than those of the TK30 group. The results show that the interface defects of the specimens in the TK30 group do not achieve the desired results. The interfacial weakening for SCSM and UHPC is much less than 30%, while the weakening of interfacial defects for specimens in group TK60 is successful. For all three groups of specimens with cyclic loading the ultimate load of the specimen is increased. The main reason is that the interface between the two sides of the baffle and the UHPC weakened by cyclic loading resulted in the studs not being able to continue to be protected by the side baffle constraints, and the side baffle shear effect disappears. The studs are involved in resisting the loading of the PSCC connectors. Unlike the partial shear connection failure of the PSCC connectors under monotonic loading, the shear reinforcement and the studs resist the shear deformation simultaneously.

According to the load-slip curve characteristics of the connector and the cracking extension of the prefabricated concrete decks. The PSCC connector can be roughly divided into 4 stages, as shown in Fig. 10. Point O is the starting point of the test, and Point A represents the termination of the linear elasticity stage of the PSCC connector (0.4P_u,0.5mm). Point B represents the ultimate load point of the PSCC connector (1P_u,3.5mm), point C represents the ultimate load fluctuation point (1P_u,5.5mm), and point D represents the failure point of the PSCC connector.

Fig. 10

Failure process of PSCC connectors.

“OA” is the elastic stage of the PSCC connectors, and the load-slip curve approximates a linear elastic curve. There are no abnormalities in the specimens during this period, and only a few minor cracks appear at the bottom of the prefabricated decks at the end of this phase. “AB” is the elastic–plastic stage, at this stage, the precast crack gradually extends upward, extends to both sides. The slope of the load-slip curve decreases gradually. When the slip approaches about 3.5 mm, the load is close to the peak. “BC” is in the plastic phase. The specimen intermittently emits loud sounds as the main crack in the prefabricated plate propagates upward and widens. Meanwhile, the load-slip curve is close to horizontal, the PSCC connectors are in an ideal plastic state, the load basically remains stable, but the slip value increases rapidly. “CD” is the failure stage. The cracks in the prefabricated concrete panels have completely penetrated from top to bottom, and a large gap has appeared between the steel girder and the prefabricated decks. This stage indicates that the PSCC connector has sheared. When the slip reaches 12 mm, the load decreases abruptly until it stops. In the normal operating phase, the load on the connector usually does not exceed 0.7 P_u.

Analysis of influencing factor

Interfacial friction between shear connection steel parts and UHPC

Table 3 shows that the ultimate shear capacity of the fully bonded specimen ZC is increased by 0.4% and 9.4% compared to the specimens with 30% (TK30) interfacial defects and 60% (TK60) interfacial defects, respectively. The shear stiffness of PSCC connectors was analyzed in both the elastic and plastic stages, revealing a high overall stiffness in the elastic stage. With the gradual increase of load, the load-slip curve of PSCC connectors changed from inclined to horizontal, and the stiffness of PSCC connectors in the plastic stage is weakened considerably. The stiffness of the fully bonded specimen ZC is increased by 17.4% and 27.7% in the elastic stage and 1.6% and 12.8% in the plastic stage, respectively, compared to the specimens with 30% (TK30) interfacial defects and 60% (TK60) interfacial defects. In terms of the characteristic slip value, the specimens with interfacial defects do not differ significantly from the naturally bonded specimens. Despite the effect of 60% interfacial defects, the PSCC connectors ${S}_{0.9Pu}=9.9mm$ far satisfy the characteristic slip value slip of 6 mm in EC4. The results indicate that 30% interfacial defects have a negligible impact on shear capacity, whereas 60% interfacial defects significantly reduce it. The stiffness difference is pronounced in the elastic stage but less significant in the plastic stage. The main reason is that the interfacial bond in the elastic phase mainly resists the load in the early stage. As the load increases, the interfacial bond fails completely and is converted to shear reinforcement mainly resisting the shear force. Therefore, the shear performance of PSCC connectors with 30% interface defects and fully bonded interface is negligible. The specimen with 60% interface defects has a more substantial weakening in the shear performance and is not negligible. The PSCC connectors applied in the actual engineering should realize the post-cast UHPC in the connection layer of the dense, so as to improve the shear performance, but still allow the existence of 30% of the interface defects in the area.

Connection layer material

From Table 3, the ultimate bearing capacity of the specimen ZC with UHPC material is increased by 39% compared to the ordinary concrete specimen XJ. The shear stiffness increases by 6.6% and 12.1% in the elastic and plastic phases, respectively. When the XJ group of specimens reaches the ultimate load, the slip value is much lower than that of the ZC group of specimens. The PSCC connectors enter the plastic-destruction stage after the load drops to 0.9 P_u. The slip of the XJ group is approximately 50% of that observed in the ZC group. The results show that the UHPC specimens have superior shear performance than the ordinary concrete specimens. It has a significant effect on its shear capacity and shear stiffness, and its ductility capacity is also much stronger than the former. As shown in Fig. 7(g,h), the ordinary concrete specimens exhibit significant crushing around the studs, with extensive damage areas. The UHPC specimens do not show crushing near the root of the studs. The phenomenon indicates that UHPC is able to resist the transverse high splitting force underneath the studs and form a stronger wrapping, which improves the shear performance of the stud connectors.

Effect of cyclic loading

Figure 9 shows the load-slip curves of PSCC connectors under cyclic loading. The trends of the curves under cyclic loading for the three specimens have similarity, while the failure mode of specimen ZC-3 is stud shear failure. When in the cyclic loading stage of class I (0.5P_u), the loading and unloading curves still diverge. The residual slip after each unloading ranges from 0.02 to 0.08 mm, and the total residual slowly superimposes with the number of loadings. After 10 completions, the residual slip is less than 0.08 mm. Despite the differences in the interfacial strength of the three types of specimens, there is no significant difference in the Class I cycle. When in the class II cyclic loading stage (0.7P_u), the difference between the loading and unloading curves of the three specimen cyclic curves increases. The residual slip after each unloading is in the range of 0.08–0.25 mm. Similar to the previous grade, the residual slip is slowly superimposed. After 10 completions, the residual slip is less than 0.25 mm. As shown in Table 4, the residual slip for cyclic loading of Class I is 0.9%−3.05% of the peak slip. The residual slip of class II cyclic loading accounts for 1.99%−5.90% of the peak slip. The residual slips of the 30% interfacial deficiency specimen and 60% interfacial deficiency specimen under Class II cyclic loading increased by 0.53 and 1.26 times, respectively, compared with those of the fully bonded specimens. The results show that under cyclic loading, the nonlinear compression of local concrete and interfacial friction lead to the difference between loading and unloading curves. The interfacial defects weaken the interfacial bond of the PSCC connectors, which results in a much higher residual slip of the interfacially defective specimens than that of the fully bonded specimens after cyclic loading.

Table 4 Slip values of specimens under cyclic loading.

The shear capacity of conventional form stud connectors after cyclic loading usually decreases slightly. In contrast, the ultimate shear capacity of PSCC connectors increased slightly after cyclic loading, by 2.17% (ZC), 11.7% (TK30), and 11.5% (TK60), respectively, for the same parameters. The stiffness in the elastic stage is substantially weakened after cyclic loading compared to monotonic loading, and there is no significant difference in the stiffness in the plastic stage. The reason for this is that the interfacial bond fails almost completely after many cycles of cyclic loading, leading to a weakening of the stiffness. In contrast, the plastic phase resists loading against studs or shear reinforcement, and there is no significant difference in stiffness. After the completion of cyclic loading, the PSCC connectors still have good ductility capacity, which is not significantly different from monotonic loading. The reason for the increase in shear capacity of PSCC connectors under cyclic loading is mainly due to the weakening of the steel-UHPC interface forces at the top, bottom, left and right sides of the connection layer by cyclic loading. For monotonic loading relying on the side baffle to the bottom steel girder and the UHPC interface to the studs, the three sides of the interface bonded together to form a stronger constraint to protect the studs. The SCSM-UHPC interface remains the weakest link, with final failure attributed to the shearing of shear reinforcements. After cyclic loading, the interfacial bond of the PSCC connectors suffers multiple weakening, which ultimately leads to complete failure of the 4-sided interfacial force. The failure mode is determined by the shear strength of shear reinforcement and studs. The shear strength ratio of shear reinforcement and studs at the early stage of specimen design is 1.099, and the former is stronger than the latter, which eventually leads to the change of the failure mode of the specimen ZC-3. There is a small increase in the shear capacity of the PSCC connectors due to the synergistic stressing of the two. Therefore, the elevated shear capacity after cyclic loading can be used as an additional safety reserve in real structures.

Finite element analysis

General

In this study, ABAQUS explicit dynamic analysis is used to simulate the push-out test of PSCC connectors with different parameters. A smoothing step is used in the displacement control to avoid dynamic effects and 1/4 specimen is modeled for computational efficiency. The lateral spacing and vertical spacing of studs and shear reinforcement are arranged according to the experimental design. The finite element model consists of the following parts: base plate, precast concrete panels, shear connecting steel members, studs, steel girder, side baffles, structural reinforcement, and connection layer.

As shown in Fig. 11, precast concrete panels, shear connecting steel members, studs, steel girder, side baffles, and connection layers are simulated using the C3D8R cell type in the mesh region in ABAQUS, which enables effective observation of the shear deformation of the PSCC connectors. The structural reinforcement in the prefabricated concrete panels is simulated using the B31 beam unit. The reason for this is that the structural reinforcement only restrains the prefabricated concrete panels and is not relevant to the factors affecting this test. In order to observe the segmental failure of shear reinforcement and studs in the PSCC connectors. The mesh size is set to 5 mm for the shear reinforcement and studs, 10 mm for the UHPC connection layer, and 15 mm for the prefabricated concrete panels to balance accuracy and computational efficiency. Based on the symmetry of the specimen, symmetry boundary conditions are applied at the symmetry plane of the model. Translational constraints along the x-axis are applied to the x-plane and translational restrictions along the y-axis are applied to the y-plane. Translation and rotation constraints are applied to the bottom surface of the prefabricated concrete panel in all directions.

Fig. 11

Models and meshes for various components.

Structural reinforcement is restrained in prefabricated concrete decks using an embedded form. This form allows the steel nodes to follow the deformation of neighboring concrete nodes with interpolated deformation values. The steel–concrete interface, and the steel-UHPC interface are simulated using the friction form of face-to-face contact with friction coefficients of 0.5 and 0.6, respectively. The analysis process employs displacement control by coupling the degrees of freedom of the upper top surface of the steel girder to a reference point, which is loaded with a displacement of 20 mm.

Material models

Material constitution of steel and structural reinforcement

Figure 12 shows the material properties of steel beams and structural reinforcement set up based on the shown principal model. In this experiment, the steel girder and structural reinforcement, all phases are in the elastic phase. In this constitutive model, the slope of the line represents the modulus of elasticity(${E}_{s}$) followed by the yield stage. ${f}_{y}$ and ${\varepsilon }_{y}$ are the yield stresses and strains of the steel. Design values are taken for each strength using the comparison of material properties experimental results in Table 1³⁴.

Fig. 12

Constitutive relationship of the steel.

Material constitution of concrete and UHPC

(1) Ordinary concrete

The prefabricated decks part of the model is modeled by adopting the concrete damage plasticity model from the ABAQUS material library, CDP model (^28,35). These include concrete compression damage and tensile damage. The model uniaxial tensile and compression curves are shown in Fig. 13. The tensile stress–strain curve consists of two parts, the tensile stress grows with respect to the tensile strain, and cracking occurs when the yield strength ${f}_{t}$ and the corresponding strain ${\varepsilon }_{ck}$ are reached. The compressive stress–strain curve consists of three parts and the rising part can be calculated by Eq. (1)³⁶.

$$\frac{{\sigma_{{\text{c}}} }}{{f_{cm} }} = - (\frac{{k \cdot \eta - \eta^{2} }}{1 + (k - 2) \cdot \eta })$$

(1)

Fig. 13

Material constitution of concrete.

Note: ${\sigma }_{c}$ is the compressive stress. ${f}_{cm}$ is the uniaxial compressive strength of concrete. $k$ is the plasticity constant, which is equal to ${E}_{c}\cdot {\varepsilon }_{cp}/{f}_{cm}$. $\upeta ={\varepsilon }_{c}/{\varepsilon }_{cp}$ is the ratio of strain to peak strain.

The descending phase of the curve is influenced by a number of factors. Therefore, this stage is usually formed by fitting based on experimental data. In Fig. 13(a), $\alpha$ is the ratio of the stress at ultimate strain to the peak stress of concrete. $\upgamma$ is the ratio of the stress at ultimate strain to the peak stress of concrete. The tensile and compressive damage of concrete are defined as Eq. (2) and Eq. (3), respectively, and the model parameters are shown in Table 5³⁷.

$$D_{t} = 1 - f_{ct} /\sigma_{t}$$

(2)

$$D_{c} = 1 - f_{cm} /\sigma_{c}$$

(3)

Table 5 Properties of concrete.

(2) UHPC

The UHPC principal model used in the numerical model is derived from the axial tension principal model proposed by Zhang et al.³⁸ and the axial compression principal model proposed by Yang et al.³⁹. As shown in Fig. 14(a), ${f}_{t}$ is the tensile strength of UHPC. ${\varepsilon }_{ca}= 0.002,{\varepsilon }_{pc}=0.01 ,{w}_{p}=1 ,p=0.95$. As shown in Fig. 14(b), ${f}_{c}$ is the compressive strength of the UHPC cube and ${E}_{c}$ is the initial modulus of elasticity, and each value is established with reference to the test results. The material parameters are shown in Table 6. The Poisson’s ratio of UHPC is 0.2. The damage coefficient D in the CDP model represents the damage evolution process of UHPC, which is calculated by Eq. (4).

$$D = 1 - \sqrt {\frac{\sigma }{{E_{c} \varepsilon }}}$$

(4)

Fig. 14

Material constitution of concrete.

Table 6 Properties of UHPC.

Material constitution of stud and shear reinforcement

The test results show that the steel girder do not yield after the failure of the PSCC connectors and remain in an elastic state. Since both the shear reinforcement and studs yield and fracture, this paper employs a triple-folded principal structure for the shear reinforcement and studs to better simulate real experimental conditions. The experimental data in Table 2 are used for yield strength ${f}_{y}$, ultimate tensile strength ${f}_{u}$, modulus of elasticity ${E}_{s}$, peak strain ${\varepsilon }_{u}=100{\varepsilon }_{y}$. The principal curves are shown in Fig. 15. The shear reinforcement and studs are defined for each of their values based on the test results respectively. ${\varepsilon }_{f1}$ is the strain at fracture and has a value of 0.2 to facilitate the observation of the fracture process of the shear reinforcement and studs. The Poisson’s ratio of the shear reinforcement and stud is 0.3.

Fig. 15

Constitutive relationship of the stud and shear reinforcement.

Validation of numerical simulation model

In Fig. 16, the load-slip curves of the PSCC connectors derived from the finite element analysis are in good agreement with the experimental results. In Table 7, the finite element results show low error in shear capacity calculated by finite elements compared to the average test results. The error is 2.5% for ZC group, 1.2% for TK30 group, 2.5% for TK60 group and 2.4% for XJ group. The shear stiffness of the elastic phase in the finite element is slightly lower than the test results. The reason may be that the friction coefficients at the interface between the transverse steel plates and the UHPC in the modeled shear connecting steel members are lower than the interfacial friction in the tests, which weakens the interfacial bond marginally. The slip values of the PSCC connectors at the ultimate load in the finite element results are not significantly different from the experimental results. In the plastic-failure stage, the load is still higher than 0.9P_u after the slip value of PSCC connectors reaches 6mm, which is in good agreement with the experimental results.

Fig. 16

Comparison of load-slip curves from tests and FE analysis.

Table 7 Comparison of finite element and experimental results.

Failure process analysis

The shear transfer behavior of PSCC connectors is analyzed through a combination of experiments and numerical simulations. However, in the finite element analysis, only the interface slip between the top UHPC and the transverse steel plate (within the connecting steel member) was considered, as this was the main pattern observed in all the test results. Since the specimens with UHPC only change the bond strength at the transverse steel plate-UHPC interface, they do not change the failure mode of the PSCC connectors. Therefore, ZC group is analyzed as a representative. Figure 17 shows the stress distribution of prefabricated concrete panels, connection layer, shear reinforcement, and studs, respectively. When the load reaches 0.5P_u, multiple cracks have appeared at the bottom of the prefabricated decks. In contrast, the internal damage of the UHPC in the connection layer is low, and the damage site only occurs at the localized location of the shear reinforcement. The stress at the bottom of the shear reinforcement reaches 320 MPa, on the contrary the stress at the topmost stud is much lower than the former. When the load reaches 0.8P_u, the prefabricated concrete panel cracking thickens and extends. UHPC damage extends outward from the vicinity of the shear reinforcement towards the stud side. The root stress of the shear reinforcement embedded in the UHPC increases to 450 MPa, while the portion embedded in the precast concrete panel is not significantly stressed. This indicates that the shear reinforcement has locally reached the yield stress and there is still no significant difference in the stud root stress. When the load reaches 1.0 P_u, the damage in the prefabricated decks has penetrated. The damage in the UHPC layer also penetrates from the location of the shear reinforcement holes to the side of the studs, and the extended section shear fracture. All four rows of shear reinforcement reach the ultimate stress of 580 MPa, while the topmost stress of the studs is far from reaching the yield stress. It shows that the reinforcement shear failure, which is consistent with the experimental results.

Fig. 17

Damage evolution of PSCC connectors.

As shown in Fig. 18, the specimen with ordinary concrete exhibits slight damage localized at the root of the studs before reaching 0.5Pu. While the stud stress reaches 340 MPa, the shear reinforcement stress is lower. When the load reaches 0.8P_u, the concrete damage area below the stud root increases. The stud root stress reaches the yield stress of 430MPa, and the shear reinforcement stress increases to 300MPa, which has not yet reached yield. When the load reaches 1.0P_u, the concrete damage in the connection layer gradually increases. The stud root stress has reached the ultimate stress of 480 MPa, while the root stress of the shear reinforcement reaches yielding and large deformation occurs, but does not reach the ultimate stress of 580 MPa.

Fig. 18

Specimens for concrete.

The combination of experimental and finite element results shows that the PSCC connectors with UHPC produce a new interface form (transverse steel plate-UHPC interface) due to the presence of transverse steel plates. The bond at this interface is much lower than that at the steel girder-UHPC interface. As the load increases, slip primarily occurs at the interface between the transverse steel plate and the UHPC, followed by shear failure of the shear reinforcement. As shown in Fig. 19(a), the failure mode of the PSCC connectors using UHPC is shown. For the specimen with ordinary concrete, the precast concrete panel and the connection layer are fully connected at the time of fabrication because there is no additional transverse steel plate member. Therefore, the above interface form doesn’t exist, and the slip mainly occurs at the steel girder-concrete interface, followed by the fracture failure of the studs, as shown in Fig. 19(b). In summary, the shear transfer of the PSCC connectors is as follows: load, steel girder, transverse steel plate-UHPC interface, the connection layer, shear reinforcement, prefabricated concrete decks.

Fig. 19

The failure mode of FEM simulation and test.

Proposed shear-capacity formulae

Based on the above analysis, the shear damage of shear reinforcement fracture is similar to the failure form of conventional stud. Therefore, the shear strength of the reinforcement can be analyzed by referring to the similar calculation method for studs.

The shear strength of studs in EC4 can be calculated by the following Eq. (5):

$$P = 0.8\frac{{A_{s} f_{u} }}{{\gamma_{v} }}$$

(5)

Note:$\gamma_{v} = 1.25$ is the sub-coefficient, $A_{s}$ is the cross sectional area of the stud, $f_{u}$ is the yield strength of the stud.

In JTG/T D64-01–2015⁴⁰, the ultimate shear capacity of a single reinforcement is calculated as Eq. (6):

$$P = 0.7A_{s} f_{u}$$

(6)

Note: $A_{s}$ is the cross sectional area of the reinforcement. $f_{u}$ is the strength of the reinforcement.

According to Sun et al.⁴¹, reinforcement have different forms of failure in shear experiments due to different anchorage lengths on both sides of UHPC and ordinary concrete. The reinforcement shear failure and reinforcement pullout failure are analyzed to derive the effective anchorage lengths and fitted with the coefficients in EC4 to propose the Eq. (7) for the reinforcement shear strength, after a modified calculation method is carried out.

$$P = 0.72A_{s} f_{s}$$

(7)

Note: $A_{s}$ is the cross sectional area of the reinforcement. $f_{s}$ is the strength of the reinforcement.

In PBL connectors with transverse reinforcement, the shear capacity equation is contributed by three main components: the concrete end bearing capacity, the resisting shear force of the transverse reinforcement in the hole, and the shear resistance of the concrete transfer bar. Equation (8), Eq. (9) and Eq. (10) proposed by Oguejiofor⁴², Hosain⁴³, and Ahn⁴⁴ et al.

$$P = 0.59A_{cc} \sqrt {f_{c} } + 1.233A_{tr} f_{y} + 2.871nD^{2} \sqrt {f_{c} }$$

(8)

$$P = 4.5h_{sc} t_{sc} f_{c} + 0.91A_{tr} f_{y} + 3.31nD^{2} \sqrt {f_{c} }$$

(9)

$$P = 3.14h_{sc} t_{sc} f_{c} + 1.21A_{tr} f_{y} + 2.98nD^{2} \sqrt {f_{c} }$$

(10)

Note: $A_{tr}$ is the transverse reinforcement shear area, $f_{y}$ is the ultimate strength of the reinforcement.

From the second term in all three types of equations for the shear capacity provided by the transverse reinforcement, it can be seen that it is similar to that in EC4, with differences only in the correction factor.

It is found that there is a large difference in the mechanical properties between the reinforcement bars embedded with UHPC and the reinforcement bars embedded with NSC. The shear capacity of PSCC connectors in case of shear failure of shear reinforcement is predicted by the above equations respectively.

Figure 20 and Table 8 give the experimental values compared with the theoretical values calculated from each equation. The shear capacity predicted by Eqs. (5) - (10) is the same for different parameters. This is because the shear capacity of the reinforcement in each of the above equations depends mainly on the cross-sectional area and material properties. The calculated values from Eq. (5), Eq. (6) and Eq. (7) are much smaller than the experimental results, and the theoretical load is equivalent to 60% of the experimental load. This indicates that the current design code underestimates the shear capacity of embedded reinforcement in UHPC. The calculated value in Eq. (9) is 80% of the experimental value, also for the consideration of the role of UHPC. Calculations from Eqs. (8) and (10) are closest to the results of shear failure in the PBL, closely matching the stress state and failure mode of the PSCC connectors. The PSCC connectors are still slightly higher than the values calculated by the former formula. The main reason is that the friction between the side baffle and UHPC in the PSCC connectors improves the ultimate shear capacity to a certain extent, while weakening the top interface. Both types of formulas are fitted better, and in the actual project the post-cast UHPC will have defects at the top interface due to natural settlement, and the ultimate bearing capacity of PSCC with different defect areas will have a lower impact.

Fig. 20

Prediction of shear capacity with specific parameters.

Table 8 Shear reinforcement capacity under different empirical formulas.

In summary, although the predicted value of the current code is 60% of the experimental value, it can be taken as a conservative prediction of the shear capacity of PSCC connectors. The correction factors in the Oguejiofor and Ahn^42,44type of formulas, on the other hand, have a good fit to the formula for calculating the PSCC connectors under shear reinforcement fracture. However, in order to get a more accurate fitting coefficient, on this basis it will be used as a correction factor for the shear strength of PSCC connectors reinforcement.

In PSCC connectors, shear reinforcement shear failure has better ductility than stud shear failure by 10% compared to the former. However, the shear capacity of PSCC connectors is reduced by approximately 12%. This is due to the superior ductility of shear reinforcement over studs, while the friction between the side baffle and UHPC still enhances the ultimate shear capacity.

The PSCC connectors are assumed to be in 3 stages under the shear reinforcement failure mode. Stage I top steel—UHPC interface bearing stage, the force at this stage is mainly controlled by the interface bond force. Stage II shear reinforcement bearing stage, with the gradual failure of the top steel-UHPC interface force, the bearing object mainly has the friction bearing between the reinforcement and the side baffle. In the stage III shear reinforcement destruction stage, as the load continues to increase, the shear reinforcement yields one after another until it is completely disconnected.

Interfacial bond, shear reinforcement resistance, and side baffle friction, all three together dominate the shear capacity of PSCC connectors. However, among the three, only the shear reinforcement resistance is the most stable and effective as the reference object of shear capacity. Because the shear reinforcement has high strength in the stress stage and excellent ductility in the yield stage.

In the PSCC push-out specimen, the stress state of the shear reinforcement is complex, which is subjected to shear, bending moment and axial tension. As shown in Fig. 21, the shear reinforcement is subjected to a constraining force perpendicular to the direction of the shear reinforcement on both sides, in addition to the friction between the connection layer UHPC and prefabricated concrete.

Fig. 21

Shear reinforcement force analysis.

The shear reinforcement is subjected to bending, shear, and tension during the loading process, and the composite effect of all three eventually leads to failure. From the finite element analysis, the shear reinforcement is subjected to bending and shear in the early stage, and its upper surface is mainly subjected to tension and its lower surface is mainly subjected to compression. The structural reinforcement produces axial tension due to resisting the lateral deformation of the prefabricated concrete panel, while the shear reinforcement embedded in the UHPC is not only subjected to friction with the UHPC, but also to vertical shear perpendicular to the reinforcement. As the UHPC continuously squeezes the shear reinforcement at the root, a compression zone is formed at its root. As the load increases, the vertical shear force increases, the shear reinforcement continues to slide downward, the concrete area in the compression zone gradually expands, and the stress in the reinforcement gradually increases as the damage to the UHPC in the connection layer increases.

From the above analysis, the formula for calculating the shear capacity of shear reinforcement for PSCC connectors is formulated as follows:

$$P = \lambda A_{s} f_{s}$$

(11)

Note: $A_{s}$ is the cross sectional area of the reinforcement. $f_{s}$ is the strength of the reinforcement.

In order to obtain an effective shear capacity enhancement factor for shear reinforcement, the finite element and experimental results are combined. Firstly, the results of each data are processed by using normalization to avoid the effects arising from different units. This is followed by multiple linear regression analysis using the least squares method. The shear capacity equation based on cross-sectional area is given in Eq. (12), and the equation based on the strength of the reinforcing material is given in Eq. (13) for validation. Comparing the experimental and finite element results with the predicted results, it is evident that both fit well, as shown in Fig. 22.

Fig. 22

Comparison of experimental and predicted results for different parameters.

However, a more rigorous approach will be to conduct the next push-out tests with different strengths and section sizes to assess the shear capacity and to analyze the shear capacity by modifying the shear capacity equation by using probabilistic concepts. By regression analysis of the push-out test results, the equation for the shear bearing capacity of PSCC connectors was obtained as Eq. (11). Based on the combined effect of cross-sectional area and material strength on the shear capacity, λ was determined using the least squares method. In order to more accurately predict the shear bearing capacity equation for the ultimate load, it was further corrected by combining the actual indicators of the defective parameters of the transverse steel-UHPC interface, and the final value of the fitted determination coefficient was obtained as 1.15.

$$P_{1} = 1.0411x + 0.0411$$

(12)

$$P_{2} = 1.4428x + 0.4428$$

(13)

Figure 20 verifies its rationality. From Table 9, it is evident that the fitting results of the fully bonded specimen and the TK30 group are optimal. As for the TK60 specimen after the maximum weakening of the top interface, the load carrying capacity of the PSCC connectors is partially weakened, resulting in a small difference in the ultimate shear capacity. The errors between the calculated results and the experimental results are in the range of −6.2% and 3.3%, with a relative standard deviation of 0.052. In summary, a correction factor of 1.15 is more appropriate for calculating the shear capacity of PSCC connectors.

Table 9 Comparison of test with PSCC connector prediction equations.

Conclusions

The conclusions are as follows:

• (1) This study demonstrates that the load-slip curve of PSCC connectors is similar to that of traditional stud connectors, but with a 42% increase in shear capacity and a 34.3% difference in ultimate slip. Moreover, the PSCC connectors enhance the construction convenience of prefabricated bridges while maintaining the integrity of the prefabricated bridge decks.

• (2) The average shear capacity of UHPC specimens is 39% higher than that of ordinary concrete specimens. The average shear capacity of the fully bonded interface specimens increased by 0.4% and 9.4% than the specimens with different interfacial defects. However, interfacial weakening had less effect on the ductile capacity of the PSCC connectors due to the fact that shear reinforcement possesses better ductility than studs.

• (3) Cyclic loading increases the ultimate load carrying capacity by 2.17% (ZC), 11.7% (TK30), and 11.5% (TK60) compared to monotonically loaded specimens. Residual slips under 0.5 Pu and 0.7 Pu cyclic loading are minimal, ranging from 0.9%−3.05% and 1.99%−5.90%, respectively. Cyclic loading significantly reduces shear stiffness in the elastic stage. The unique side baffle and steel girder wrapping around the studs enhance the interfacial bond, which shows noticeable damage under repeated cyclic loading.

• (4) In UHPC specimens, slip primarily occurs at the interface between the steel shear connection and the UHPC layer, causing fractures at the root of the shear reinforcement while the studs remain elastic. In ordinary concrete specimens, slip is observed at the upper interface between the steel beam and concrete, with fractures extending through the studs, while the shear reinforcement stays elastic.

• (5) The proposed formula, derived from both experimental data and finite element analysis, has demonstrated a strong predictive capability, with a maximum error of only 6.2% when estimating the shear capacity of PSCC connectors.