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Article

Numerical Investigation on the Hysteretic Performance of Self-Centering Precast Steel–Concrete Hybrid Frame

by
Shiqiang Feng
1,*,
Yong Yang
1,2,
Yicong Xue
1 and
Yunlong Yu
1,2
1
School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China
2
Key Lab of Structural Engineering and Earthquake Resistance of the Ministry of Education, Xi’an University of Architecture and Technology, Xi’an 710055, China
*
Author to whom correspondence should be addressed.
Buildings 2024, 14(10), 3202; https://doi.org/10.3390/buildings14103202
Submission received: 31 August 2024 / Revised: 4 October 2024 / Accepted: 7 October 2024 / Published: 8 October 2024
(This article belongs to the Special Issue Earthquake Resistant and Vibration Control of Concrete Structures)
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Abstract

:
To improve the construction performance and seismic resilience of precast reinforced-concrete frame structures, an innovative self-centering precast steel–concrete hybrid frame has been proposed and subjected to cyclic loading tests. In this paper, a comprehensive numerical analysis was conducted to further investigate the frame’s hysteretic behavior. Initially, a numerical model was developed using the finite element software OpenSees. Numerical analyses of two frame specimens were conducted, demonstrating good agreement between the numerical and experimental hysteretic characteristics, thus validating the model’s accuracy. Subsequently, based on the numerical simulations, a quantitative comparison of hysteretic performance between a novel frame and a traditional reinforced-concrete frame of the same scale was performed. While the proposed frame exhibited slightly lower initial stiffness and energy dissipation capacity than the traditional frame, it outperformed in terms of load-carrying capacity and self-centering ability. Finally, parametric analyses were carried out to assess the influence of various design parameters on the hysteretic performance, including friction force in the web frictions devices, initial post-tensioned force of the prefabricated steel–concrete hybrid beams, the steel arm length, and the column longitudinal reinforcement ratio. The results showed that increases in these four parameters improved the load-carrying capacity and initial stiffness of the proposed frame. Additionally, an increase in the friction force, steel arm length, or column longitudinal reinforcement ratio enhanced the frame’s energy dissipation capacity, while an increase in the initial post-tensioned force or a decrease in the friction force enhanced the frame’s self-centering capacity.

1. Introduction

Traditional seismic structures, like traditional cast-in-place reinforced-concrete (RC) frame structures and other conventional structures, cannot recover in the short-term after a moderate earthquake, which causes large residual deformation and significant damage and brings heavy economic losses. Nevertheless, self-centering RC frame structures, as an earthquake resilient structure, have gained significant attention during the past decades [1,2,3]. Compared with the traditional RC frame structures, this novel structure has the characteristics of a low construction cost, a short construction period, life-saving capabilities during an earthquake event, and the ability to restore structural function quickly afterwards.
The “self-centering” concept was first presented by Priestley in the Precast Seismic Structural Systems (PRESSS) program [4,5,6], which began in the early 1990s. Priestley et al. [4] proposed the “hybrid connection”, which was assembled with the precast RC beam and column using the unbonded post-tensioned (PT) tendons through the joint center and the mild steel bars grouted in ducts across the beam–column joint. Studies of a series of beam–column connections and a five-story precast concrete building were conducted using seismic tests and numerical analyses. The results showed that the proposed connection and frame exhibited resilience behavior with negligible residual displacements and mitigated damage. Moreover, the large elastic deformation of the PT tendons can provide self-centering capacity, and the plastic deformation of the mild steel bars can provide an energy dissipation ability.
To further optimize seismic performance for the self-centering RC frame structures, enormous research efforts have been performed in recent decades. In order to avoid concrete crushing at the prestressed crimp area and to improve construction efficiency on site, Wang et al. [7,8] used steel jackets in the contact zone to strengthen the connection interface, while welded steel bars were linked to the beam steel jackets. The cyclic test results indicated that the proposed connection exhibited satisfactory self-centering and energy dissipation capacities. Huang et al. [9,10] also proposed a prefabricated beam–column connection with a novel replaceable artificial controllable plastic hinge to avoid damage of the precast concrete members. Cyclic loading tests and theoretical analysis were conducted on some beam–column connections and frames. The results indicated that the connections and frames exhibited favorable seismic performance. Moreover, the bolted steel angles, as the energy dissipation devices, were placed on the beam–column connection by Lu et al. [11], Cui et al. [12], and Cai et al. [13,14]. A series of shaking table tests were conducted, and the results indicated that the proposed self-centering RC frame showed better construction convenience and resilience performance. However, the buckling of the above metallic energy dissipaters caused a weak energy dissipation capacity. To address this issue, an all-steel bamboo-shaped energy dissipation device without grouting was developed and employed in the self-centering RC frame by Wang et al. [15] and Zhang et al. [16]. The test results showed that, due to the buckling constraint effects in the proposed device, a better and stable energy dissipation capacity was obtained. Furthermore, because of the potential risks of fatigue failures in the metallic energy dissipaters, friction devices were proposed by Morgen et al. [17,18,19]. The dampers were placed on the top and bottom surfaces of the beam ends to provide adjustable and stable energy dissipation when the connection rotated. Nevertheless, the arrangement of large-size dampers outside the connection zone would probably occupy building space and affect the use functionality. Based on this consideration, Guo et al. [20,21], Song et al. [22], and Huang et al. [23,24] proposed the web friction devices (WFDs), used on the beam webs to save building space. Through experimental and computational studies, the results indicated that the self-centering RC frame that applied these devices showed an expected better seismic performance. In summary, previous research has mainly focused on the behavior of self-centering beam-to-column connections of frames with various energy dissipation devices. Additionally, many problems still have not been solved, which are as follows. In construction on site, the complex aerial tension operations of the tendons in the beams were not convenient, and there were security risks. Furthermore, because the connections between the column bases and foundations also adopted the prestressed crimping type in the aforementioned self-centering frames, the redundancy of these structures was insufficient. The collapse of the frame structure has a high possibility of occurring during an earthquake event due to the PT tendons failing suddenly in the beams or columns. Additionally, the simulation approach and design procedure of the self-centering RC frames were not mature.
To address these issues, an innovative self-centering precast steel–concrete hybrid (SPH) frame was proposed by the authors [25]. The configuration of the proposed SPH frame, assembled with the prefabricated steel–concrete hybrid (PH) beams and precast prestressed RC columns using a dry-bolted end-plate connection, is illustrated in Figure 1. The PH beam consists of a precast RC beam component at the beam’s middle and two steel arms at the beam’s ends using the unbonded PT steel tendons and the WFDs. Moreover, considering the performance advantages of the concrete-filled steel tubular column [26,27], to further avoid damage, the square steel tubes were arranged on the outer surface of the column core area at the beam–column connections.
To investigate the seismic resilience of the SPH frame system, a series of experiments were conducted. At the first stage, cyclic tests were performed on five beam–column connection specimens to evaluate the seismic behavior and investigate the effects of the initial PT force of the PT tendons and the friction force in the WFDs [28]. At the second stage, cyclic tests were carried out on three frame specimens [25]; the failure model is illustrated in Figure 2. All of the test results demonstrated that the SPH frame exhibited a typical three-stage cyclic behavior, namely, an elastic stage, a self-centering stage, and an energy dissipation stage. The seismic resilience included avoiding the damage and minimizing the residual deformation, which was observed in the first two stages, and the plastic deformation occurred only in the third stage. The self-centering capacity was mainly provided by the PT tendons employed in the PH beams. Moreover, benefiting from the configuration of the PT tendons in the PH beams, the tensioning of the tendons in the beams on the ground was realized, and the potential issues of aerial tensioning operations in the original self-centering RC frame were avoided. Due to the protection of the prestressed crimping interfaces, namely, the gap opening–closing interfaces, using the steel plates at the precast beam ends, the concrete crushing in the PH beams was restrained. Furthermore, the sequential energy dissipation mechanism was realized through the sliding friction at the WFDs and the successive plastic deformation of both the steel arms and the column foots under heavy loading. Additionally, the conservative seismic concepts, including the rigid connection between the column base and the foundation and the tendons tensioned in each single-span beam, improved the redundancy of the whole frame, which could avoid the collapse of the frame structure when the PT tendons fail during an earthquake.
With few studies on the whole self-centering RC frame structures, the numerical analyses of the proposed SPH frame presented in this paper will gain deeper insights into resilience structures and fill the gaps in the literature. Firstly, a numerical model of the SPH frame was developed based on the Open System for Earthquake Engineering Simulation (OpenSees 3.3.0) computational platform and calibrated based on the results of the physical experiment. Subsequently, the hysteretic behavior of the SPH frame and the same-scale traditional RC frame were quantitatively compared based on the numerical simulation. Finally, the parametric studies of the SPH frame model were conducted and the influences of various parameters were comprehensively investigated. In general, the primary objective of this paper is to further study the hysteretic performance of the SPH frame via the OpenSees platform, building upon the previous limited experimental research.

2. Numerical Modeling and Validation of SPH Frame

2.1. Modeling Method

OpenSees is an open-source finite element simulation platform based on C++, designed for the development of applications to simulate the seismic performance of structural systems. It provides a wealth of modeling tools, including a wide range of general and specific element types as well as material models. A 2D nonlinear numerical model of the SPH frame, as shown in Figure 3, was established using the finite element platform OpenSees to achieve the following targets: (1) to validate the credibility of the modeling approach through comparing simulation results and test results in both the global and local responses of structures, thereby increasing the confidence in the numerical results; (2) to gain deeper insights into the seismic behavior of the SPH frame and enlarge the experimental studies through numerical simulations with different design parameters; and (3) to provide a reference for nonlinear time history analyses and generalize the application of the research outcomes in future research works. Additionally, the following assumptions were made for appropriate simplifications of the numerical model based on the available experimental results: (1) the model involved only in-plane deformation, and the foundation of the specimen was considered a rigid beam; (2) the column fiber elements in the joint panel region were assigned large stiffness due to the restraint effect of the square steel pipe, assuming insignificant elastic deformation occurred in this region [15]; (3) there was no vertical shear slip deformation at the beam–column connection interface between the column and the end plate of the steel arm; and (4) there was also no vertical shear slip deformation at the opening and closing interface between the precast RC beam and steel arm [29].
The boundary constraint conditions of the numerical model were in agreement with those of the test specimen, achieved by constraining in-plane translational and rotational degrees of freedom of nodes, including two column-base connection nodes and two PT tendons anchorage nodes in the foundation beam. The process of modeling and loading was as follows, based on the user manual of OpenSees: establish a simplified macroscopic model composed of lines based on the specimen; set node coordinates; set constraints; set the constitutive relationship of various material models; dissociate the element cross-sections of the main components into fiber-based sections; define the element types; set the output information; define loading protocol; and submit the overall program command. It is worth noting that the loading process of the numerical model was divided into two steps (Figure 3). In the first step, with all of the beam–column connections set only in the Y-direction coupling, the initial prestresses in all the PT tendons which were larger than the design value were set to avoid prestress loss caused by the elastic deformation of components. Then, the first step loading was carried out, i.e., defining the axial loads consistent with the previous test at two column top points and performing the iterative calculations until the calculated initial prestresses of the PT tendons both in both the beams and columns were consistent with the previous test. Subsequently, the command “loadConst -time 0.0” was used, which sets the loads as constant and resets time to be 0.0. In the second step, a supplementary setting was applied to all of the beam–column connections, including the X-direction coupling and rotational stiffness. Finally, the cyclic displacement loading protocol, which is consistent with the actual test loading protocol [25], was applied at the corresponding loading point in the horizontal direction.
The modeling approach was distinguished using the appropriate simplifications applied to the frame, where the individual contributions of each component were meticulously modeled, ensuring that the overall mechanical properties of the structure resulted from the integration of these component-specific contributions. Furthermore, the modeling of the components within the numerical model was based on a rigorous process, with the modeling specifics described below.
Based on the displacement formulation and Gauss–Legendre quadrature rule, the columns, the steel arms, and the precast RC beams of the SPH frame were modeled using the displacement-based beam–column elements with five integration points, considering the spread of plasticity along the elements. As shown in Figure 4, these elements were defined as the fiber cross-sections, and each fiber could be assigned with various material models. The concrete fibers were assigned the concrete01 and the concrete02 material models. The difference was that the constrained concrete fibers, confined by the steel jacket or the stirrups in the precast concrete components, were simulated using concrete02 material model, while the unconstrained concrete fibers at the concrete cover were assigned the concrete01 material model, and do not consider the tensile strength [30]. The longitudinal bars and shaped steel fibers in the precast members were modeled using the steel02 material model, which simulates the isotropic hardening behavior and the Bauschinger effect [31]. A series of elastic beam column elements were used to simulate the contact interface between the steel arm and the precast RC beam, the anchor plates of the PT tendons, and the column panel region of the beam–column connection core, respectively. These elements were assigned large stiffness based on the above rigid assumptions for these regions [32,33].
The PT tendons in the precast columns and PH beams were modeled using the truss elements that considered axial deformation and force. Meanwhile, the steel02 material model was also selected and assigned to these truss elements due to the availability of the “sigInit” command within the steel02 material model, which can be used for the definition of the initial prestress for the PT tendons [34]. At the beam–column bolted connection interface, the “EqualDOF” command was employed to couple the vertical and horizontal degrees of freedom. Meanwhile, the rotational deformation in the core region and above-mentioned interface was modeled using the two node link element assigned with the steel01 material model, and the initial stiffness was calculated based on the component method [35,36].
The opening and closing behavior at the contact interface between the steel arm and the precast concrete beam was simulated with a pair of the zero-length element 1, which were applied to the upper and lower rotation points of that interface, respectively. These elements were assigned with the elastic-perfectly plastic gap (EPPG) material model with the property of uniaxial compression-only and no tension [37]. The force Fp required for the material to reach its plastic state in the model should be assigned as the yield load of the steel arm flange. The initial gap and the hardening ratio of the model should be defined as zero. Meanwhile, the plastic deformation and the accumulated damage of the steel arm flange during the late loading period were simulated through the “damage” command in the material model. The force–displacement relationship of the material model is given in Figure 5. Additionally, the “EqualDOF” command was also employed to couple the vertical degree of freedom between one end node of the precast concrete beam and the corresponding end node of the steel arm, thereby ensuring the assumption of no shear-slip deformation occurring at the interface.
The friction behavior in the WFD was modeled using a zero-length element 2 incorporating with bidirectional plasticity properties [33], and the element was assigned two elastic-perfectly plastic (EPP) material models to simulate friction forces divided into horizontal and vertical directions, respectively. The friction force analysis and the force–displacement relationship were illustrated in Figure 6.

2.2. Validation of the Numerical Model

The numerical simulation was carried out using the aforementioned numerical model. The test results of the specimens SPH-1 and SPH-2 were both used for the validation of the numerical models. The comparison of hysteretic curves and the residual displacement versus the lateral displacement curves between the test results and numerical results is shown in Figure 7. Compared with the test results, the numerical hysteretic curves also presented typical two-stage hysteretic behavior, namely, the self-centering stage and energy dissipation stage. In the first stage, the typical double-flag curves with the minimal residual deformation were exhibited when the drift ratio was less than 2.0%, indicating a clear self-centering capacity. In the second stage, the hysteretic curve became gradually plumper and showed an increase in residual deformation when the displacement angle was larger than 2.0%, indicating an increase in the energy dissipation capacity. Meanwhile, as shown in Figure 7c and Figure 7d, for the above two models, the deviation ratios of the average residual deformation between the simulated and tested results were 8.09% and 9.27%, respectively. Additionally, as the loading displacement increased, there was an increased difference between the numerical and experimental results. The reason was that the numerical model did not consider the concrete crushing and falling at the column foot and anchor retraction of PT tendons in the column. However, the numerical results were generally consistent with the experimental results.
Moreover, as evaluation indicators to analyze the simulation accuracy of the numerical model, the key results, including the average bearing capacity, average initial stiffness, and cumulative energy dissipation, are listed in Table 1. The average bearing capacity and average initial stiffness represented the averages of positive and negative results, and the cumulative energy dissipation was obtained by accumulating the loop area of the first hysteretic loop during each lateral displacement. The average deviation ratios of the above three evaluation indicators were 11.92%, 14.57%, and 1.11%, respectively. Among them, the initial stiffness in the test results of each specimen was less than that in the numerical results. The main reason was that there were many gaps in the real assembled SPH frame, which reduced the stiffness of the overall specimen, and the numerical model could not fully simulate these gaps. However, in general, the above results indicated that the proposed numerical model based on the platform OpenSees was not only able to capture important characteristics of the SPH frame but also offered a good prediction of the hysteretic response for specimens, especially in terms of energy dissipation.
As shown in Figure 8, the test results and the numerical results were compared again, specifically the stress–displacement curves of the PT tendons within two specimen beams and columns, to further verify the accuracy of the numerical model. The stress value of the PT tendons in the beams was calculated from the average stress of the four PT tendons in the specimen beams, as illustrated in Figure 8a,c. The comparison results indicated that the numerical model provided relatively good estimates of the variation tendency of the PT force and prestress loss behavior under cyclic loading. Consequently, the effectiveness of the proposed numerical model was further verified.

3. Performance Comparison between SPH Frame and RC Frame

To compare the seismic performance between the SPH frame and the traditional cast-in-place RC frame, the numerical model of the traditional RC frame, without prestress in either the beam or column members, was developed. It should be noted that the accuracy of the RC frame model‘s calculation results was not verifiable due to the absence of a cyclic test of the RC frame, which was of the same size as the SPH frame. To ensure a certain degree of reliability in the calculation results, the modeling process was based on a case model sourced from OpenSees Wiki [38], ensuring that factors such as structural dimensions, cross-sectional dimensions, the reinforcement ratio within both the column and the beam members, concrete strength, boundary constraints, and loading systems were the same as those in the SPH-1 frame model. Additionally, since the widely used prefabricated RC frame structures generally adopted beam–column connections based on wet connections, their seismic performance was basically equivalent to that of the traditional cast-in-place RC frame structures [39]. Subsequently, the comparison of seismic performance between the SPH frame and the traditional RC frame could also be approximately considered as a comparison between the seismic performance of the SPH frame and the prefabricated RC frame. The hysteretic responses of the numerical model of the SPH frame and the numerical model of the RC frame are compared in Figure 9, and mainly included the comparison of the hysteretic curves, the skeleton curve, the residual deformation curves, and the cumulative energy dissipation curves.
As shown in Figure 9a,b, the hysteretic loops of the RC frame model were much fuller than those of the SPH frame model, and the skeleton curves of the two models all experienced the two-stage growth of rapid load growth and slow load growth. The average peak loads of the SPH frame model and the RC frame model were 768.25 kN and 701.51 kN, respectively. This result indicated that the bearing capacity of the SPH frame was 9.51% higher than that of the RC frame. Additionally, the average initial stiffness of the SPH frame model and the RC frame model was 29.53 kN/mm and 35.10 kN/mm, respectively. This result indicated that the initial stiffness of the SPH frame was 15.87% lower than that of the RC frame. The main reason for the lower initial stiffness of the SPH frame was that the bolted end-plate connection used at the beam–column connection was the typical semi-rigid connection, and any small gap could cause a stiffness reduction.
As depicted in Figure 9c, both the residual deformation curves of the RC frame model and the SPH frame model exhibited a two-stage increasing trend, which was initially slow and then rapid. However, under the same lateral loading displacement, the residual displacement of the RC frame model was larger than that of the SPH frame model, and this difference continued to increase with the increase in lateral loading displacement. According to the criterion that the main structure that experienced an earthquake event could be considered intact and does not need to be repaired when the residual drift ratio is within 0.20% [40,41], the loading displacement corresponding to the residual drift ratio of 0.20% was defined as the boundary drift ratio. The average boundary drift ratios of the SPH frame model and the RC frame model were 1.05% and 1.65%, respectively. This indicates that the boundary drift ratio of the SPH model was 57.14% higher than that of the RC model. Moreover, the average maximum residual drift ratios of the SPH frame model and the RC frame model were 0.84% and 1.60%, respectively. These results indicate that there was a more significant self-centering ability in the SPH frame, and the self-centering capacity of the SPH frame was 47.50% higher than that of the RC frame at the drift ratio of 3.50%.
The cumulative energy dissipation curves of both the RC frame model and the SPH frame model initially displayed a slow rise, followed by a rapid increase in trend (Figure 9d). The two curves were basically equal until the drift ratio reached 1.25%, whereupon the cumulative energy dissipation of the RC frame model gradually exceeded that of the SPH frame model. The final cumulative energy dissipation of the SPH frame model and the RC frame model were 292.57 kN·m and 368.25 kN·m, respectively. This indicated that the energy dissipation capacity of the SPH frame was 20.55% lower than that of the RC frame at the drift ratio of 3.50%. It could be seen that the energy dissipation capacity of the SPH frame was slightly lower compared to the RC frame. The possible reason was that the beam’s hinge energy dissipation of the RC frame was higher than the total of the friction energy dissipation at the WFDs and the plastic deformation energy dissipation of the steel beam flange in the SPH frame beams.
Overall, the initial stiffness and energy dissipation capacity of the SPH frame were slightly lower than those of the RC frame. However, the bearing capacity and, particularly, the self-centering capacity of the SPH frame, were higher than those of the RC frame. This proved that the application of the SPH frame structure was more conducive to the seismic resilience and post-earthquake recovery.

4. Parametric Studies of SPH Frame Model

The parametric studies were aimed at quantitatively investigating the influence of the key design parameters on the hysteretic response of the SPH frame. The numerical model for the Specimen SPH-1, namely model F0, was considered as the reference model for the parametric studies. Based on the preliminary test results of the SPH frame and the mechanism analysis of the beam–column connection [25], the additional parameters are identified and listed in Table 2, including the friction force in the WFDs, the initial PT force of the PH beams, the length of the steel arms, and the longitudinal reinforcement ratio of the columns. The first two parameters had a significant impact on the bending capacity of the pre-compression interface between the steel arm and the precast RC beam, while the latter two parameters had a great influence on the overall lateral resistance capacity of the SPH frame. Additionally, it was important to note that the parametric studies of the numerical simulations were performed by changing a certain parameter, while all of the other parameters of the numerical model remained consistent with the reference model F0.

4.1. Effect of Pretorque in WFDs

Four different pretorques in WFDs (Tw0 = 200 N∙m, 275 N∙m, 500 N∙m, and 800 N∙m) were chosen to investigate the hysteretic performance of the SPH frame. The corresponding friction forces in WFDs were 146.7 kN, 201.7 kN, 366.7 kN, and 586.7 kN, respectively. The hysteretic curves, skeleton curves, residual deformation curves, and cumulative energy dissipation curves obtained under these different parameter values are shown in Figure 10. As illustrated in Figure 10, when the Tw0 was 200 N∙m, 275 N∙m, 500 N∙m, and 800 N∙m, with other design parameters remaining unchanged, some simulated results could be obtained. These results included the peak loads of each frame model, which were 750.91 kN, 768.25 kN, 814.64 kN, and 876.65 kN, respectively; the initial stiffnesses were 28.39 kN/mm, 29.53 kN/mm, 29.58 kN/mm, and 29.60 kN/mm, respectively; the maximum residual deformations were 24.59 mm, 28.69 mm, 39.98 mm, and 47.48 mm, respectively; and the cumulative energy dissipations were 263.33 kN·m, 292.57 kN·m, 373.78 kN·m, and 457.04 kN·m, respectively. These results indicated that the hysteretic curves gradually tended to be full, and the bearing capacity and energy dissipation capacity increased significantly; however, the self-centering capacity decreased significantly with the increasing pretorque of each bolt of the WFDs. The above results were similar to the test results of the corresponding hybrid beam–column connection subjected to the cyclic loading [28]. The main reason was that an increase in the pretorque of each of the bolts resulted in increases in the friction force of the WFDs, meaning that the resistant moment provided by the WFDs in the prestressed crimping connection surface between the end-plate of the precast RC beam and the steel arm was effectively enhanced, which led to an increase in the bearing capacity and energy dissipation capacity and a decrease in the self-centering capacity.

4.2. Effect of Initial PT Force of PH Beams

Three different initial PT forces of the PH beams (Pb0 = 50.00 kN, 102.45 kN, and 150.00 kN) were used to examine the hysteretic performance of the SPH frame, and the corresponding initial prestresses were 357 MPa, 732 MPa, and 1071 MPa, respectively. These values represented 21.5%, 44.1%, and 64.6% of the yield strength of the PT tendons. The hysteretic curves, skeleton curves, residual deformation curves, and cumulative energy dissipation curves obtained under these different parameter values are depicted in Figure 11. As observed from Figure 11, when the Pb0 was 50.00 kN, 102.45 kN, and 150.00 kN with other design parameters remaining unchanged, some simulated results could be obtained, including the peak loads of each frame model, which were 739.05 kN, 768.25 kN, and 778.48 kN, respectively; the initial stiffnesses were 28.09 kN/mm, 29.53 kN/mm, and 30.54 kN/mm, respectively; the maximum residual deformations were 34.89 mm, 28.69 mm, and 27.61 mm, respectively; and the cumulative energy dissipations were 297.37 kN·m, 292.57 kN·m, and 299.04 kN·m, respectively. These results indicated that the bearing capacity, the initial stiffness, and the self-centering capacity of each frame model increased with an increasing initial PT force of the PH beams; however, the influence on the energy dissipating capacity was not obvious. Among them, the increase in the self-centering ability was the most obvious. The main reason was that the resistant moment provided by the PT tendons in the beam–column connection increased with an increase in the initial PT force of the PH beams, which led to the opening deformation at the prestressed crimping connection surface being closed easily.

4.3. Effect of Length of Steel Arms

Three different lengths of the steel arms (Ls = 490 mm, 540 mm, and 590 mm) were used to investigate the hysteretic performance of the SPH frame. The hysteretic curves, skeleton curves, residual deformation curves, and cumulative energy dissipation curves obtained under these different lengths are illustrated in Figure 12. As illustrated in Figure 12, when the length of the steel arm was 490 mm, 540 mm, and 590 mm, with other design parameters remaining unchanged, some simulated results could be obtained, including the peak loads of each frame model, which were 732.26 kN, 768.25 kN, and 810.00 kN, respectively; the initial stiffnesses were 27.22 kN/mm, 29.53 kN/mm, and 29.57 kN/mm, respectively; the maximum residual deformations were 28.30 mm, 28.69 mm, and 29.77 mm, respectively; and the cumulative energy dissipations were 282.39 kN·m, 292.57 kN·m, and 309.43 kN·m, respectively. These results demonstrated that with an increase in the length of the steel arm, the bearing capacity, the initial stiffness, and the energy dissipating capacity of each frame model increased; however, the self-centering capacity decreased. The main reason was that under the same loading displacement, the internal force of the PH beam with the longer steel arms increased more, resulting in an earlier plastic deformation of the steel arm. Therefore, considering the construction cost of the SPH frame, only the space requirements of the slip displacement in the WFD and the anchorage of the PT tendons need to be met in the length design of the steel arms.

4.4. Effect of Longitudinal Reinforcement Ratio of Columns

Four different longitudinal reinforcement ratios of columns (Rc = 7.30%, 4.10%, 2.01%, and 1.03%) were chosen to investigate the hysteretic performance of the SPH frame. The hysteretic curves, skeleton curves, residual deformation curves, and cumulative energy dissipation curves obtained under these different parameter values are shown in Figure 13. As illustrated in Figure 13, when the Rc was 7.30%, 4.10%, 2.01%, and 1.03% with other design parameters remaining unchanged, some simulated results could be obtained, including the peak loads of each frame model, that were 768.25 kN, 650.50 kN, 566.50 kN, and 523.13 kN, respectively; the initial stiffnesses were 29.53 kN/mm, 26.67 kN/mm, 25.01 kN/mm, and 24.86 kN/mm, respectively; the maximum residual deformations were 28.69 mm, 20.22 mm, 12.36 mm, and 9.47 mm, respectively; and the cumulative energy dissipations were 292.57 kN·m, 241.45 kN·m, 196.13 kN·m, and 168.65 kN·m, respectively. The results indicated that with an increase in the longitudinal reinforcement ratios of the columns, the bearing capacity, the initial stiffness, and the energy dissipating capacity of each frame model decreased significantly; however, the self-centering capacity increased. There was a three-stage working mechanism of the original SPH frame, namely, the elastic stage, the self-centering stage, and the energy dissipation stage, with the successively plastic deformation of the steel arm and column foot area. However, with the decrease in the reinforcement ratio of the columns, the plastic hinge at the column foot area occurs earlier than that at the steel arms, resulting in a poor seismic mechanism due to the strong beam and weak column. Therefore, in order to avoid this situation in the seismic design of the SPH frames, the seismic mechanism of the strong column and weak beam should be verified additionally to obtain the appropriate self-centering capacity.

5. Conclusions

To further investigate the hysteretic behavior of the proposed SPH frame, the numerical analyses of the SPH frame were performed using the finite element platform OpenSees (Appendix A). The significant conclusions of this study are summarized as follows.
  • A numerical model for the SPH frame was developed, notably simulating the opening and closing behavior at the prestressed crimping connection between the steel arm and precast beam with a zero-length element based on the EPPG material model, while incorporating damage considerations. A simulation of the two SPH frame specimens was performed, showing that the deviation ratios of the peak load, initial stiffness, cumulative energy dissipation, and average residual deformation were 11.92%, 14.57%, 1.11%, and 8.68%, respectively, validating the effectiveness of the proposed numerical model for SPH frames. Additionally, future research will further improve the calculation accuracy of the model by considering the damage of concrete at the column foot and the prestress loss of the PT tendons in the column. The numerical modeling method could be applied in nonlinear dynamic analysis to further investigate the seismic performance of SPH frames.
  • The hysteretic performance of an SPH frame and a traditional RC frame were quantitatively compared via numerical simulation. Results showed the SPH frame had slightly lower initial stiffness and energy dissipation, but higher bearing and self-centering capacities. Particularly, the SPH frame’s maximum residual deformation was 47.50% lower, demonstrating its advantage in seismic resilience.
  • Parametric studies were performed based on ten SPH frame models, with a focus on four key variables such as the friction force in the WFDs, the initial PT force, the length of steel arms, and the longitudinal reinforcement ratio of columns. The results showed that higher values of these parameters resulted in both an increase in load-carrying capacity and stiffness. An increase in the friction force, the steel arm length, or the column longitudinal reinforcement ratio enhanced the energy dissipation capacity. Additionally, an increase in the initial PT force or a decrease in the friction force improved the self-centering capacity. These results could provide a basis for the seismic design research of the SPH frame.

Author Contributions

Conceptualization, S.F.; methodology, S.F.; software, S.F.; validation, S.F., Y.Y. (Yong Yang), and Y.X.; formal analysis, Y.Y. (Yong Yang) and Y.X.; investigation, S.F. and Y.Y. (Yunlong Yu); resources, S.F.; data curation, S.F.; writing—original draft preparation, S.F.; writing—review and editing, Y.X.; visualization, S.F.; supervision, Y.Y. (Yunlong Yu); project administration, S.F.; funding acquisition, S.F. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Youth Innovation Team Research Project of the Education Department of Shaanxi Province (Grant No. 23JP080) and the National Natural Science Foundation of China (Grant Nos. 52308202 and 52478208). Their financial support is highly appreciated. In addition, the authors of the paper are members of the Youth Innovation Team of Shaanxi Universities.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

Appendix A

To ensure the accuracy and reliability of the proposed numerical model developed in OpenSees, a convergence check was performed by analyzing the lateral force–displacement curves for different numbers of finite-element meshes. The result of this convergence check was shown in Figure A1. As observed in Figure A1, with the increase in the mesh sizes, the lateral force–displacement curves exhibited no obvious change, indicating that the proposed model was insensitive to further mesh refinement.
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Figure A1. Convergence check.
Figure A1. Convergence check.
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Figure 1. Proposed SPH frame.
Figure 1. Proposed SPH frame.
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Figure 2. Failure model and hysteretic curves.
Figure 2. Failure model and hysteretic curves.
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Figure 3. Numerical model of SPH frame.
Figure 3. Numerical model of SPH frame.
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Figure 4. Fiber cross-sections.
Figure 4. Fiber cross-sections.
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Figure 5. EPPG material model.
Figure 5. EPPG material model.
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Figure 6. EPP material model.
Figure 6. EPP material model.
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Figure 7. Comparison diagram of numerical and experimental results.
Figure 7. Comparison diagram of numerical and experimental results.
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Figure 8. Comparison diagram of stress–displacement curves of PT tendons. (a) Stress vs. displacement curves of PT tendons in specimen SPH-1 beams. (b) Stress vs. displacement curves of PT tendons in specimen SPH-1 columns. (c) Stress vs. displacement curves of PT tendons in specimen SPH-2 beams. (d) Stress vs. displacement curves of PT tendons in specimen SPH-2 columns.
Figure 8. Comparison diagram of stress–displacement curves of PT tendons. (a) Stress vs. displacement curves of PT tendons in specimen SPH-1 beams. (b) Stress vs. displacement curves of PT tendons in specimen SPH-1 columns. (c) Stress vs. displacement curves of PT tendons in specimen SPH-2 beams. (d) Stress vs. displacement curves of PT tendons in specimen SPH-2 columns.
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Figure 9. Comparison diagram of hysteretic performance of SPH frame model and RC frame model.
Figure 9. Comparison diagram of hysteretic performance of SPH frame model and RC frame model.
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Figure 10. Performance comparisons of connection with different pretorque at the WFDs.
Figure 10. Performance comparisons of connection with different pretorque at the WFDs.
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Figure 11. Performance comparisons of connection with different initial PT forces in PH beam.
Figure 11. Performance comparisons of connection with different initial PT forces in PH beam.
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Figure 12. Performance comparisons of connection with different steel strengths of steel arm.
Figure 12. Performance comparisons of connection with different steel strengths of steel arm.
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Figure 13. Performance comparisons of connection with different longitudinal reinforcement ratios of column.
Figure 13. Performance comparisons of connection with different longitudinal reinforcement ratios of column.
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Table 1. Comparison table of numerical and experimental results of two specimens.
Table 1. Comparison table of numerical and experimental results of two specimens.
SpecimensClassificationAverage Peak Load
Pk (kN)		Average Initial Stiffness
K0 (kN/mm)		Cumulative Energy Dissipation
Esum (kN·m)
SPH-1Experiment695.8425.51293.54
Simulation768.2529.53292.57
Deviation ratio10.40%15.76%0.33%
SPH-2Experiment725.4926.16550.00
Simulation823.0329.66539.67
Deviation ratio13.44%13.38%1.88%
Average deviation ratio11.92%14.57%1.11%
Table 2. Model parameter analyses scheme.
Table 2. Model parameter analyses scheme.
IDPretorque * at the WFDs Tw0 (N∙m)Initial PT Force of the PH Beams Pb0 (kN)Length of the Steel Arms Ls (mm)Longitudinal Reinforcement Ratio of Columns Rc (%)
F0 275102.455407.30
F1 200102.455407.30
F2500102.455407.30
F3800102.455407.30
F427550.005407.30
F5275150.005407.30
F6275102.454907.30
F7275102.455907.30
F8275102.455404.10
F9275102.455402.01
F10275102.455401.03
* Note: “Pretorque” is the initial pre-tensioned torque of each bolt at the WFDs.
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Feng, S.; Yang, Y.; Xue, Y.; Yu, Y. Numerical Investigation on the Hysteretic Performance of Self-Centering Precast Steel–Concrete Hybrid Frame. Buildings 2024, 14, 3202. https://doi.org/10.3390/buildings14103202

AMA Style

Feng S, Yang Y, Xue Y, Yu Y. Numerical Investigation on the Hysteretic Performance of Self-Centering Precast Steel–Concrete Hybrid Frame. Buildings. 2024; 14(10):3202. https://doi.org/10.3390/buildings14103202

Chicago/Turabian Style

Feng, Shiqiang, Yong Yang, Yicong Xue, and Yunlong Yu. 2024. "Numerical Investigation on the Hysteretic Performance of Self-Centering Precast Steel–Concrete Hybrid Frame" Buildings 14, no. 10: 3202. https://doi.org/10.3390/buildings14103202

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