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Article

Investigation on Seismic Performance of the Fully Assembled Steel Frame Applying Beam-Column Joints with Replaceable Energy-Dissipating Elements

by
Dawei Zhang
1,
Yuanqi Li
2 and
Binhui Huang
1,*
1
Shanghai Pudong Architectural Design & Research Institute Co., Ltd., Shanghai 201206, China
2
College of Civil Engineering, Tongji University, Shanghai 200092, China
*
Author to whom correspondence should be addressed.
Sustainability 2023, 15(6), 5488; https://doi.org/10.3390/su15065488
Submission received: 16 February 2023 / Revised: 13 March 2023 / Accepted: 17 March 2023 / Published: 21 March 2023
(This article belongs to the Section Sustainable Engineering and Science)
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Abstract

:
Based on the application of a beam-column joint with replaceable energy-dissipating elements and hinged beam-column proposed by the author, the seismic performance of a fully assembled steel frame with this joint was investigated in this paper. Through two projects of a traditional steel frame (TSF) and an assembled steel frame applying beam-column joints with replaceable energy-dissipating elements (ASFWREE) and their numerical simulation calculation by SAP2000, the main structural design indicators such as natural vibration period, period ratio, mass participation coefficient, base shear force, inter-story displacement angle, rigid-weight ratio, and shear-weight ratio of two frames under frequent earthquake, and their influence factors were compared and analyzed. By carrying out the elastic–plastic dynamic time–history analysis of two projects under a rare earthquake, the maximum inter-story displacement angle, base shear force, stiffness between floors, maximum vertex displacement, and the occurrence sequence and distribution of plastic hinges of the two items were compared. The results show that the deformation of ASFWREE had the characteristics of the shear deformation of TSF and the deviation of the natural vibration period was less than 5% when the ratio of the linear stiffness of the energy-dissipating element to the steel beam was approximately 0.8, the ratio of horizontal length to span was about 0.25, which was close to the strength grade of the steel beam. The seismic performance under the rare earthquake was close to or higher to that of the TSF, can ensure that the beam and column are not damaged, and the structure does not collapse. The failure mode of the ASFWREE is consistent with the experimental research of the beam-column joints.

1. Introduction

Traditional steel frames (TSF) are favored by many buildings because of their low material consumption, uniformity and high-strength, convenient processing and installation, and excellent seismic performance, especially in high-intensity areas and high-rise buildings [1,2,3]. However, the on-site manual welding and high-altitude operations of the beam-column joints still exist, and the deviation between the construction and the design often causes immeasurable losses to this very important part of the steel frame [3,4,5,6]. Moreover, with the rapid development of urban construction and the continuous improvement in people’s demand for a better life, the construction has stricter requirements on toughness and environment. The application of replaceable energy-consuming components and fully assembled steel frames is a good choice to comply with this development situation.
In order to quickly restore the functions of buildings after an earthquake, the concept of seismic design has begun to shift from preventing structural collapse to recovering structural functions [7]. The concept of restorable function was first proposed by American scholar Bruneau et al. [8] in 2003, and in 2009, the restorable function city was taken as the future cooperative research direction of a seismic structure for the first time at the World Engineering Earthquake Conference. In 2011, Chinese scholar Lv [9] proposed for the first time a recoverable structure, that is, a structure that can quickly return to its function after slight repair or no repair after an earthquake. In 2016, the recoverable function was the theme and served as the core of the next generation of performance-based seismic research at the annual meeting of the Pacific Earthquake Engineering Research Center (PEER) in the United States [10]. In 2017, many scholars conducted special reports on the recoverable functions and discussed the construction and evaluation of their systems from different levels of structure, community, city, and society at the 16th World Conference on Earthquake Engineering with the theme of “Recoverable Functions—New Challenges for Civil Engineering” [11,12,13].
A structure with replaceable components is one of the three main structural forms with recoverable functions (the other two are rocking structures and self-resetting structures) [9], and its application has attracted great attention from many researchers on the beam-column joints of steel frames. Koetaka et al. [14] proposed a beam-column joint with a replaceable Π-shaped damper in 2005. The Π-shaped damper is beneficial to improve the dissipation of energy and self-balancing ability, but the joint exhibits lagging hysteresis behavior. In 2009, Farrokhi et al. [15] put forward a beam-column joint with replaceable perforated cover-plates, which had improved ductility compared with the traditional beam-column joints and effectively avoided brittle failure of the weld, but failed to change fundamentally. Shen et al. [16] proposed a beam-column joint with plastic replaceable connecting-plates. The hysteretic curve of the joints with a replaceable channel steel end-plate was fuller than that with the replaceable webs and bolts, but they reached a certain displacement angle and were subjected to compression-buckling, resulting in a rapid strength reduction. Oh et al. [17,18] proposed a beam-column joint with a replaceable T-shaped damper. The initial stiffness and ultimate strength of the joint were significantly improved, and was easy to replace after an earthquake. However, its hysteretic performance required a large inter-story displacement. The situation was stable, and the influence of the concrete floor slab on the initial stiffness of the structure and the plastic neutral axis position of the steel beam section could not be ignored. Leelataviwat et al. [19,20,21,22,23] proposed a beam-column joint with replaceable knee-support. The strength, stiffness, and seismic performance of the joint were equal to or slightly higher than that of the beam-column joint of the traditional welded rigid frame, but the welded or semi-rigid connection was adopted between the members, and the assembly or design controllability was low. Hsu et al. [24,25] proposed a beam-column joint with a replaceable arc-shaped steel plate damper, which had significantly improved strength, stiffness, and energy-dissipating capacity, but the semi-rigid connection between beams and columns makes it difficult to control the design. Latour et al. [26] proposed a beam-column joint with replaceable frictional energy-dissipating elements at the bottom of the steel beam, which effectively improved the ductility of the joint, but the friction of the energy-dissipating elements was random.
This paper was based on fully assembled joints with replaceable energy-dissipating elements [27,28,29] studied by the author, in which beams were hinged to columns, and additional energy-dissipating elements were added at the joint corners, connected to the column rigidly, and hinged to the beam, as shown in Figure 1. Through two projects of TSF and assembled steel frame applying beam-column joints with replaceable energy-dissipating elements (ASFWREE), the natural vibration period, period ratio, mass participation coefficient, base shear force, inter-story displacement angle, rigid-weight ratio, and shear-weight ratio of two frames under frequent earthquake were compared, and the main structural design indicators and their influence factors were analyzed. In order to evaluate the seismic performance of the ASFWREE, the maximum inter-story displacement angle, base shear force, stiffness between floors, maximum vertex displacement, and the occurrence sequence and distribution of structural plastic hinges were compared by carrying out the elastic–plastic dynamic time–history analysis of two frames under rare earthquakes. In this paper, SAP200 was used for the numerical simulation calculation and analysis. The main problems to be solved are not only the comparison of the natural vibration period and other indicators under frequent earthquakes, but also the maximum vertex displacement and other indicators under rare earthquakes and the order of the plastic hinge. Although ABAQUS is more precise, its calculation cost is high. Therefore, the calculation accuracy of SAP2000 can meet the requirements of this paper. Some researchers have mainly focused on the experiments and numerical simulation of beam-column joints, and the analysis and research on the seismic performance of the structure have not been combined with engineering yet. The main purpose of the research is as follows: (1) Demonstrate the equivalent efficiency of the ASFWREE and the TSF when the ratio of the linear stiffness of the energy-dissipating element to the steel beam is approximately 0.8, the ratio to the span of the steel beam is 0.25 or so, the strength grade to the steel beam and is close and the difference of other members are not obvious; and (2) based on the conclusion parameters obtained from the test and finite element numerical simulation, verify the seismic performance of the ASFWREE to validate the feasibility of its application in engineering.

2. Failure Mechanism of Beam-Column Joints with Replaceable Energy-Dissipating Elements

The failure mode of the beam-column joints with replaceable energy-dissipating elements is obviously different from that of the TSF, and the dissipation of energy mainly comes from the additional elements. Its failure mode goes through the following five stages. (1) When it starts to be subjected to horizontal action, the energy-dissipating elements cooperate with the beams and columns to provide elastic stiffness for the structure, bear the vertical and horizontal load and resist the corresponding deformation. (2) As the horizontal action gradually increases, the deformation of the structure increases, but the deformation rate of the energy-dissipating elements develop faster than other components, and the edge near the end of the steel column begins to yield and enters the energy-dissipating stage. (3) When the horizontal action continues to increase, the edge of the other side of the horizontal section of the energy-dissipating element yields successively and enters the plastic stage to dissipate energy. (4) When the horizontal action increases to a certain stage, the energy-dissipating element yields at the section near the end of the steel column, forming the first plastic hinge, and energy-dissipating behavior is further obvious. (5) When the horizontal action is close to the structural limit load, the other side section of the horizontal section of the energy-dissipating element yields, forming the second plastic hinge. At this point, the energy-dissipating behavior of the energy-dissipating element ends.

3. Engineering Design

3.1. Overview of Projects

This paper designed two engineering cases of TSF and ASFWREE, as shown in Figure 2, Figure 3 and Figure 4, the beam-column rigid connection of TSF and the hinged beam-column connection of ASFWREE, GKZ1 represents the steel columns of the frame, GKL-1 represents the steel beams of the frame, and HNYJ represents the energy-dissipating elements. The two projects were simulated to construct office buildings in a certain area in Shanghai, with a plane grid size of 24.0 m × 18.0 m (length × width), 50-year service life and Class-II safety level. The structural type was a steel frame, with a total of six floors, where the height of the first floor was 3.9 m, the height of the second to sixth floors was 4.2 m, and the total height was 24.9 m. The floors (roofs) were made of steel beams, steel floor slabs, and 100 mm thick cast-in-place concrete. In the calculation of the beam, the combined effect of the floor slab and the steel beam was not considered. The wind and snow load were taken according to the load specification [30], the basic wind pressure was 0.55 kN/m2, and the basic snow pressure was 0.20 kN/m2. The seismic fortification intensity was seven degrees, the design value of basic seismic acceleration was 0.10 g, the design earthquake was grouped into the second, the seismic fortification was classified as Class-B fortification, and the site was classified as Class IV. Under the action of wind load, the structural damping ratio was 0.015; when the earthquake was frequent, the structural damping ratio was 0.04; when the earthquake was rare, the structural damping ratio was 0.05, considering the stiffness of the non-load-bearing infill wall, the reduction factor the seismic influence coefficient of the structural natural vibration period was 0.95. In elastic and elastoplastic analysis, the influence of the second-order effect of gravity was taken into account. The characteristic period under frequent earthquakes was 0.9 s, and the characteristic period under rare earthquakes was 1.1 s. The maximum seismic acceleration used in elastic–plastic dynamic time–history analysis was 200 cm/s2, and the seismic grade of the steel frame was Grade IV.
Steel frame columns, beams, girders, and energy-dissipating elements were all made of Q345B, with a yield strength of 345 MPa, and an ultimate strength of 470 MPa. Young’s modulus was 2.06 × 105 MPa, the Poisson’s ratio was 0.3, and the concrete of the floors (roofs) was C30.

3.2. Structural Design Parameters

According to the distribution of the vertical load, structure layout, span and the condition of supports, etc., the section sizes of the beams and girders were estimated. The columns were evaluated on the basis of the distribution of the vertical and horizontal load, structure layout, slender ratio, and the condition of supports, etc. The estimated member section was input into the software according to the structural layout and material properties, and the two-stage seismic design was adopted, that is, checking the calculation of the strength and deformation of the structural sections under frequent earthquake and the elastic–plastic deformation under rare earthquake to meet the seismic design requirements of “three levels”, that is, the small earthquake is not destroyed, the moderate earthquake is repairable, and the large earthquake is not collapsed. After repeated calculation, analysis, and adjustment, the main components of the TSF and ASFWREE were finally determined, as shown in Table 1 and Table 2.
The loads of the two steel frames were taken according to the actual application conditions.

3.3. Software Selection for Numerical Calculation and Analysis

The numerical calculation and analysis in this paper were mainly used to solve indices such as the natural vibration period under more frequent earthquakes, the maximum vertex displacement under rare earthquakes, and the order of plastic hinges. In the calculation and analysis of SAP2000, the geometric parameters were based on the design requirements of two cases, the physical parameters were based on the selected materials, the steel beams and columns were simulated by frame elements, and the floors were simulated by shell elements. In the calculation and analysis of plastic hinges, the -M2-M3 hinge was used to simulate the steel column, and the M3 hinge was used to simulate the steel beam and energy-dissipating element.
In the numerical simulation, the connections between the energy-dissipating element and the steel column were set as rigid, and the connections with the steel beam were set as a hinge. In the design of the joints, the joint between the energy-dissipating elements and the steel columns should be rechecked and calculated according to the calculated moment, axial force, and shear force, and meet the bearing requirements. The connections between the energy-dissipating elements and the steel beams were calculated according to the calculated axial force and shear force as well as to meet the bearing requirements.

4. Seismic Performance Requirements for the ASFWREE

Based on factors such as seismic fortification category, fortification intensity, site conditions, construction cost, post-earthquake loss, and repair difficulty, the performance target was determined as follows [31]: when subjected to frequent earthquakes, key components, ordinary vertical components, and energy-consuming components are not damaged. In the case of fortification earthquake, the key components and ordinary vertical components were slightly damaged, the energy-consuming components were slightly damaged, some were moderately damaged, and they could only be used after general repair. When suffering from the estimated rare earthquake, the key components will be slightly damaged, some of the ordinary vertical components will be moderately damaged, the energy-consuming components will be moderately damaged, and some of them will be severely damaged. Only after repair or reinforcement can they continue to be used.

5. Model Analysis for Frequent Earthquake

5.1. Parameter Selection Subjected to Frequent Earthquake

The SAP2000 was used for the structural calculation, and both models are shown in Figure 5. The main parameters selected were as follows: The parameters of the ground motion and seismic grades are shown in the overview. The CQC (complete quadratic combination) method was used for the mode combination of seismic action, and the SRSS (square root of the sum of the squares) method was used for the direction combination, the Eigenvalue method was used for modal calculation, and the effective length coefficient of the steel frame column was calculated with the lateral displacement method. When calculating the structural period, the ratio of the story displacement and inter-story displacement angle of the structure, the rigid floor assumption was adopted; when the stress was calculated, the elastic floor assumption was adopted, and the structural damping ratio was taken as 0.04 (0.02 for wind load), and the number of calculated mode shapes was taken as 15.

5.2. Result Comparison Subjected to Frequent Earthquake

The comparison of the main calculation results such as the structural natural vibration period, period ratio, representative value of gravity load, mass participation coefficient, and base shear force between the TSF and ASFWREE is shown in Table 3.
It can be seen from the table that the first three modes and periods of the two models were very reasonable, in which the first was translational in the Y-direction, the second was translational in the X-direction, and the third was torsional. The second period dominated by translation was close to the first, and the mass in both directions was the same, which means that the stiffness in both directions was close, and the structure layout was uniform. The ASFWREE has large natural vibration period and period ratio, which reflects its high rigidity, stronger anti-torsion ability, and reasonable structure layout. Both of the mass participation coefficients were greater than 90%, which met the design requirements of the specification [30,31], which is mainly due to the small torsional impact of the higher-order vibration mode of the ASFWREE. Both of the base shear forces met the design requirements, but there were some differences. The latter was slightly larger, with a maximum of 2.57%, indicating that the participating masses and the seismic influence coefficient of each mode were close to each other.
The comparison of the inter-story displacement angle between the TSF and the ASFWREE is shown in Figure 6. It can be seen from the figure that both the inter-story displacement angles were close, and the change was relatively uniform along the direction of the floor height, but the ASFWREE was slightly smaller, and its stiffness was larger. The stiffness comparison between them is shown in Figure 7, which met the requirements of the seismic code of building, that is, the ratio of the stiffness to the adjacent floor was greater than 0.7, and the ratio to the average value of the stiffness of the adjacent upper three floors was greater than 0.8, indicating that there was no weak layer in both, and the vertical component layout was reasonable.
The floor stiffness-to-weight ratio comparison of the TSF and the ASFWREE is shown in Figure 8. The changes in the height direction were relatively uniform, and all were greater than 10, which met the design requirements.
The comparison of the floor shear-to-weight ratio between the TSF and ASFWREE is shown in Figure 9. It can be concluded from the figure that the rigidity-to-weight ratio of each floor between them was close, and the change along the height direction of the floor was relatively uniform, and was greater than 1.6% of the design requirement, indicating that the structural layout matched the load.
Through the calculation and analysis of the above structures, it can be concluded that the TSF and ASFWREE meet the requirements of elastic seismic design when earthquakes occur frequently, the strength and rigidity of the latter are large, and the capacities of bearing and deformation are slightly dominant.

6. Elastoplastic Dynamic Time–History Analysis

6.1. Overview of Elastoplastic Dynamic Time–History Analysis

The solution of the dynamic balance equation of elastic–plastic dynamic time–history analysis usually adopts the direct integration method based on finite element, that is, the method where the dynamic balance equation is not transformed before the numerical integration. The engineering case in this article adopted the HHT method (α = 0, same as Wilson-θ method).
The elastic–plastic dynamic time–history analysis was based on the assumptions of the planar infinite rigid floor, Rayleigh-damping, synchronous ground motion support, and rigid nodes. The main steps are as follows. (1) Establish a geometric model close to the actual structure and carry out the grid division of the finite element analysis FEA). (2) Select the constitutive relationship that is consistent with the actual application material and apply it to each corresponding unit to determine the mass, damping and stiffness matrix of the structure. (3) Comprehensively consider the peak ground motion, spectrum characteristics and duration, select a certain number of artificial or natural seismic waves, and adjust the corresponding peak value, as the external load input of the dynamic balance equation, define the boundary conditions close to the actual project, and use a reasonable numerical method to solve. (4) After the solution is completed, analyze the resulting data to evaluate the safety and reliability of the structure.

6.2. Establishment of Elastic–Plastic Dynamic Time–History Analysis Model

SAP2000 was used to establish elastic–plastic dynamic time–history analysis models for the TSF and ASFWREE in the paper. The materials used in the structure were mainly Q345B and Q235B. The nonlinear material properties were selected from the material library in SAP2000. The main nonlinear properties were as follows: the hysteresis type was kinematic strengthening, the initial strengthening strain was 0.015, the strain corresponding to the ultimate strength was 0.11, the fracture strain was 0.17, the termination slope (i.e., the ratio of elastic modulus E) was −0.1, and its stress–strain curve is shown in Figure 10. The members were simulated by rod-elements. When conducting nonlinear static analysis, the setting of the main member hinges was as follows: the columns adopted the P-M2-M3 hinge of the default coupling in the American ASCE41-13 standard, the beams adopted the M3 hinge, and the positions were set at 0.1 times of the ends of the member (the total length of the member), The development process of the members from the elastic stage to complete failure, that is, plastic hinge, is shown in Figure 11. In the figure, B is the yield point; IO (immediate occupancy) is the performance level of immediate use; LS (life safety) is the life safety performance level; CP (collapse prevention) is the performance grade of collapse prevention; C is the ultimate bearing capacity of the hinge; D is the residual strength of hinge; E means complete failure.
The damping of the dynamic balance equation of the structure adopts Rayleigh damping, namely, C = αM + βK. In the elastic–plastic dynamic time–history analysis, the damping is constantly changing. In SAP2000, α and β are determined by the damping ratio and the period. The damping ratio is constant at 0.05, and the period adopts two groups, which are 0.9 times the first-order period of the elastic stage and 0.2 times.
According to the specification [31], the maximum value of the acceleration time–history of rare earthquakes is 200 cm/s2, and the corresponding amplitude modulation of the selected seismic waves in the X- and Y-directions was used as the external load input of the dynamic balance equation, and the duration was 30 s.

6.3. Selection Principle of Seismic Wave

The selection of seismic waves mainly involves two key issues, one is the evaluation index including the adjustment of seismic waves; the other is that there are many factors affecting the number of seismic waves selected such as the irregularity of the structure, the structural response, and its seismic performance. At present, the selection principles of seismic waves are mainly based on the seismic information, target spectrum, and seismic intensity index [32,33,34]. According to the selection principle of seismic waves, the seismic waves selected in this paper adopted the method based on the ground motion intensity index, taking the base shear force, vertex displacement, and maximum inter-story displacement of the structure as the main response statistics, and selected three seismic waves, namely, Shanghai artificial wave SHW9 and Taiwan natural waves CHI-CHI_NO_1181 and CHI-CHI_NO_2713, the time–history curve of which is shown in Figure 12, Figure 13 and Figure 14.

6.4. Solution

The elastic–plastic dynamic time–history analysis of the projects adopted the Wilson-θ method in SAP2000.

7. Results of Elastic–Plastic Dynamic Time–History Analysis

In this paper, SAP2000 was used to calculate and analyze the elastoplastic dynamic time–history analysis of the TSF and ASFWREE, and the base shear force, vertex displacement, inter-story displacement angle, maximum vertex displacement, and distribution and development process of plastic hinges were compared under the action of SHW9, CHI-CHI_NO_1181, and CHI-CHI_NO_2713.
The comparison of the dynamic time–history curves of the maximum inter-story shear force and base shear force of the TSF and ASFWREE is shown in Figure 15, Figure 16, Figure 17, Figure 18, Figure 19 and Figure 20.
It can be concluded from Figure 15, Figure 16, Figure 17, Figure 18, Figure 19 and Figure 20 that the change gradient of the maximum shear force between floors in the X- and Y-directions of the ASFWREE was basically the same as that of the TSF under the action of three seismic waves. The variation uniformity of the maximum shear force between floors under CHI-CHI_NO_1181 was better and there was no abrupt change. The main reason is that the basic period was close, and the stiffness and seismic action of both floors were close along the vertical direction. The change of acceleration in the duration was better than the spectrum characteristics of the other two groups of seismic wave under CHI-CHI_NO_1181. Additionally, under the action of three seismic waves, the base shear force in the X- and Y-directions of ASFWREE was basically close to that of TSF, and the maximum difference of the peak value was within 10%. The base shear force of the TSF was larger, mainly because the basic period of ASFWREE and TSF was in the displacement sensitive zone of the design spectrum, the base shear force increased with the increase in the basic period, and the decrease in the ratio of the linear stiffness of the beam to column, while the basic period of the ASFWREE was slightly larger, and the stiffness of the beam-column joints was slightly smaller.
The maximum vertex displacements of the TSF and the ASFWREE are shown in Table 4. The comparison of the dynamic time–history curves of vertex displacement is shown in Figure 21, Figure 22 and Figure 23.
It can be concluded that from the table of the maximum vertex displacement of two frames, the maximum displacement under the action of a natural seismic wave is close to that of an artificial seismic wave, with a maximum difference of 4.02%, mainly because the three selected seismic waves meet the requirements of seismic performance evaluation in a statistical sense. Additionally, the maximum displacement of the two frames was basically close. The TSF was slightly smaller, with a maximum difference of 4.98%. The stiffness degradation was relatively slow. The reduction in the stiffness and strength mainly came from the plastic deformation of the steel beam. However, the linear stiffness of the energy-consuming elements of the ASFWREE was smaller than that of the steel beam, which was easy to yield earlier. The stiffness degradation and the efficiency of energy consumption were obvious.
From Figure 21, Figure 22 and Figure 23 of the time–history curves of the vertex displacements of the two frames, it can be concluded that the curves of the apex displacement of two frames under the three seismic waves had a high degree of agreement, and the maximum difference was within 10%. Under rare earthquakes, the elastic–plastic deformation capacity of the ASFWREE was close to that of the TSF, and the stiffness degradation was basically the same. The stiffness degradation mainly came from the plastic deformation of the energy-dissipating elements, and the development speed was relatively fast.
Table 5 shows the comparison of the maximum inter-story displacement angle between the TSF and ASFWREE.
From the table of the maximum inter-story displacement angles of two frames under three seismic waves, it can be concluded that the weak parts of the floors of two frames were located on the second or third floors, and the second and third floors were relatively close, which was consistent with the main characteristics of the shear deformation of the steel frame under the earthquake; the maximum inter-story displacement angle of the ASFWREE was close to that of the TSF, mainly because the basic period of two frames and the stiffness of the beam-column joints were close, and the degradation of stiffness and strength under the rare earthquake were basically the same.
The comparison of the maximum inter-story displacement angle between the TSF and ASFWREE is shown in Figure 24, Figure 25 and Figure 26.
From the comparison of the inter-story displacement angles of two frames under three seismic waves in Figure 24, Figure 25 and Figure 26, the following can be concluded. (1) The difference between the inter-story displacement angles of the same floor in the X or Y direction of two frames under three seismic waves was small, both of which were less than 15%, mainly due to the regular plane and vertical layout of two frames, and the relatively uniform stiffness distribution; and (2) the inter-story displacement angle of two frames under three seismic waves changed greatly in the second or third floors, and the better the uniformity with the increase in the floors. The main reason is that under rare earthquakes, the plastic deformation of two frames is mainly concentrated in the steel frame beams or energy-dissipating elements at the bottom 1–3 floors.
Under three seismic waves, when the displacement of the apex reached the maximum value in the ASFWREE and TSF, the plastic hinge distribution of the member is shown in Figure 27, Figure 28, Figure 29, Figure 30, Figure 31 and Figure 32, and the plastic hinges of the TSF first appear at the beam end and then at the foot of the columns. According to the results of elastic–plastic dynamic time–history analysis, the plastic hinges of the ASFWREE were mainly distributed in the energy-dissipating elements, and no plastic hinges were found in the rest. The plastic hinge of the ASFWREE only appeared at one or both ends of the energy-dissipating elements, which would ensure the seismic performance requirements of the structure to not collapse under a large earthquake, and the energy-dissipating behavior of the ASFWREE was relatively sufficient.

8. Conclusions

Taking the two cases of the TSF and ASFWREE as research objects, SAP2000 was used for calculation and analysis to compare the performance of load-bearing, deformation, and seismic activity under frequent and rare earthquake action. The main conclusions are as follows:
(1) SAP2000 was used to calculate and analyze the TSF and ASFWREE under a dead load, live load, wind load, and frequent earthquake, and the main parameter indices of design such as natural vibration period, period ratio, mass participation coefficient, base shear force, inter-story displacement angle, rigid-weight ratio, and shear-weight ratio were compared. The results show that the ASFWREE and TSF met the seismic design requirements under frequent earthquake action. The basic natural vibration period and beam-column joint stiffness of the ASFWREE were equivalent to those of the TSF, and the structural deformation had the characteristics of the shear deformation of the TSF. The deviation of the main index such as the natural vibration period was less than 5%; when the ratio of the linear stiffness of the energy-dissipating element to the steel beam was approximately 0.8, the ratio of horizontal length to span was about 0.25, which was close to the strength grade.
(2) Based on the grade C requirements of the seismic performance target, the elastic-plastic calculation and analysis of dynamic time–history of the TSF and ASFWREE were carried out by using SAP2000. One artificial seismic wave (SHW9) and two natural seismic waves (CHI-CHI_NO_1181 and CHI-CHI_NO_2713) were reasonably selected, and the maximum shear force between floors, maximum vertex displacement, maximum inter-story displacement angle, base shear force, and the time–history curve of vertex displacement were compared for two frames. The results show that the seismic performance of the ASFWREE was close to or higher than that of the TSF under rare earthquakes; when the ratio of the linear stiffness of the energy-dissipating element to the steel beam was about 0.8, the ratio of horizontal length to span was about 0.25, the strength grade to the steel beam was close, the maximum shear deviation was within 10%, the maximum peak displacement was within 5%, and the inter-story displacement angle was within 15% compared with the TSF.
(3) The development and distribution of the plastic hinges of two frames shows that the plastic hinges of ASFWREE only appeared at one end or both ends of the energy-dissipating elements, and the steel columns had no plastic hinges all the time, which can ensure that the structure does not collapse under large earthquakes when subjected to rare earthquake action, and was significantly superior to the seismic performance of the TSF.
(4) The development and distribution of plastic hinges of the ASFWREE were consistent with the results of the experimental research.
(5) The assembly of the ASFWREE is realized in the factory, and the construction has no welding, which realizes full-assembled manufacturing and is conducive to environmental protection. The connections between beams and column are hinged, which is more conducive to the design control than the TSF. After earthquake damage, the energy-dissipating components can be replaced quickly to restore their functions, which is conducive to improving the resilience level of the city.

Author Contributions

Conceptualization, D.Z. and Y.L.; Methodology, D.Z. and B.H.; Software, B.H.; Validation, Y.L. and B.H.; Formal analysis, D.Z. and B.H.; Investigation, D.Z. and B.H.; Resources, Y.L. and D.Z.; Data curation, B.H.; Writing—original draft preparation, B.H.; Writing—review and editing, D.Z. and Y.L.; Visualization, B.H.; Supervision, D.Z. and Y.L.; Project administration, Y.L. and D.Z.; Funding acquisition, Y.L. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Natural Science Foundation of China (grant number 51978500) and the APC was granted to the author Binhui Huang.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are contained within the article.

Acknowledgments

The writers gratefully acknowledge the support for this work, which was funded by the National Natural Science Foundation of China (grant no. 51978500).

Conflicts of Interest

The authors declare no conflict of interest.

References

  1. Taranath, B.S. Structural analysis and design of tall buildings. In Steel and Composite Construction; CRC Press: Boca Raton, FL, USA, 2016. [Google Scholar]
  2. Saravanan, M.; Arul Jayachandran, S.; Marimuthu, V.; Prabha, P. Advanced analysis of cyclic behaviour of plane steel frames with semi-rigid connections. Steel Compos. Struct. 2009, 9, 381–395. [Google Scholar] [CrossRef]
  3. Brunesi, E.; Nascimbene, R.; Rassati, G.A. Seismic response of MRFs with partially-restrained bolted beam-to-column connections through FE analyses. J. Constr. Steel Res. 2015, 107, 37–49. [Google Scholar] [CrossRef]
  4. Miller, D.K. Lessons learned from the Northridge earthquake. Eng. Struct. 1998, 20, 249–260. [Google Scholar] [CrossRef]
  5. Popov, E.P.; Yang, T.S.; Chang, S.P. Design of steel MRF connections before and after 1994 Northridge earthquake. Eng. Struct. 1998, 20, 1030–1038. [Google Scholar] [CrossRef]
  6. Nakashima, M.; Inoue, K.; Tada, M. Classification of damage to steel buildings observed in the 1995 Hyogoken-Nanbu earthquake. Eng. Struct. 1998, 20, 271–281. [Google Scholar] [CrossRef]
  7. NIED and NEES Consortium. Report of the Seventh Joint Planning Meeting of NEES/E-Defense Collaborative Research on Earthquake Engineering; University of California: Berkeley, CA, USA, 2010. [Google Scholar]
  8. Bruneau, M.; Chang, S.E.; Eguchi, R.T.; Lee, G.C.; O’Rourke, T.D.; Reinhorn, A.M.; Shinozuka, M.; Tierney, K.; Wallace, W.A.; Von Winterfeldt, D. A framework to quantitatively assess and enhance the seismic resilience of communities. Earthq. Spectra 2003, 19, 733–752. [Google Scholar] [CrossRef] [Green Version]
  9. Lv, X.L.; Chen, Y.; Mao, Y.J. New concept of structural seismic design: Earthquake resilient structures. J. Tongji Univ. Nat. Sci. 2011, 39, 941–948. (In Chinese) [Google Scholar]
  10. Comerio, M.C. Resilience: Next Generation PBEE; University of California: Berkeley, CA, USA, 2016. [Google Scholar]
  11. Qu, Z.; Tamura, K.; Wada, A. Synthetic seismic design strategy for building structures in urban areas. In Proceedings of the 16th World Conference on Earthquake Engineering, 16WCEE, Santiago, Chile, 9–13 January 2017. Paper No. 2686. [Google Scholar]
  12. Ikeda, M.; Asai, K.; Gallardo, R.M. Study on residents’ disaster prevention awareness for tsunami in Valparaíso, Chile. In Proceedings of the 16th World Conference on Earthquake Engineering, 16WCEE, Santiago, Chile, 9–13 January 2017. Paper No. 2671. [Google Scholar]
  13. Mahin, S. Resilience by design: A structural engineering perspective. In Proceedings of the 16th World Conference on Earthquake Engineering, 16WCEE, Santiago, Chile, 9–13 January 2017. [Google Scholar]
  14. Koetaka, Y.; Chusilp, P.; Zhang, Z.; Ando, M.; Suita, K.; Inoue, K.; Uno, N. Mechanical Property of Beam-to-Column Moment Connection with Hysteretic Dampers for Column Weak Axis. Eng. Struct. 2005, 27, 109–117. [Google Scholar] [CrossRef]
  15. Farrokhi, H.; Danesh, F.; Eshghi, S. A modified moment resisting connection for ductile steel frames (Numerical and experimental investigation). J. Constr. Steel Res. 2009, 65, 2040–2049. [Google Scholar] [CrossRef]
  16. Shen, Y.L.; Christopoulos, C.; Mansour, N.; Tremblay, R. Seismic design and performance of steel moment-resisting frames with nonlinear replaceable links. J. Struct. Eng.-ASCE 2011, 137, 1107–1117. [Google Scholar] [CrossRef]
  17. Oh, S.H.; Kim, Y.J.; Ryu, H.S. Seismic Performance of Steel Structures with Slit Dampers. Eng. Struct. 2009, 31, 1997–2008. [Google Scholar] [CrossRef]
  18. Saffari, H.; Hedayat, A.A.; Nejad, M.P. Post-Northridge Connections with Slit Dampers to Enhance Strength and Ductility. J. Constr. Steel Res. 2013, 80, 138–152. [Google Scholar] [CrossRef]
  19. Leelataviwat, S.; Suksan, B.; Srechai, J.; Warnitchai, P. Seismic Design and Behavior of Ductile Knee-braced Moment Frames. Eng. Struct. 2011, 137, 579–588. [Google Scholar] [CrossRef]
  20. Hsu, H.L.; Li, Z.C. Seismic Performance of Steel Frames with Controlled Buckling Mechanisms in Knee Braces. J. Constr. Steel Res. 2015, 107, 50–60. [Google Scholar] [CrossRef]
  21. Shin, J.; Lee, K.; Jeong, S.H.; Lee, J. Probabilistic Performance Assessment of Gravity-Designed Steel Frame Buildings Using Buckling-restrained Knee Braces. J. Constr. Steel Res. 2015, 104, 250–260. [Google Scholar] [CrossRef]
  22. Asghari, A.; Gandomi, A.H. Ductility Reduction Factor and Collapse Mechanism Evaluation of a New Steel Knee Braced Frame. Struct. Infrastruct. Eng. 2016, 12, 17. [Google Scholar] [CrossRef]
  23. Asghari, A.; Saharkhizan, S. Seismic Design and Performance Evaluation of Steel Frames with Knee-element Connections. J. Constr. Steel Res. 2019, 154, 161–176. [Google Scholar] [CrossRef]
  24. Hsu, H.L.; Halim, H. Improving Seismic Performance of Framed Structures with Steel Curved Dampers. Eng. Struct. 2017, 130, 99–111. [Google Scholar] [CrossRef]
  25. Fathizadeh, S.F.; Dehghani, S.; Yang, T.Y.; Vosoughi, A.; Farsangi, E.N.; Hajirasouliha, I. Seismic Performance Assessment of Multi-story Steel Frames with Curved Dampers and Semi-rigid Connections. J. Constr. Steel Res. 2021, 182, 106666. [Google Scholar] [CrossRef]
  26. Latoura, M.; D’Aniellob, M.; Zimbrub, M.; Rizzano, G.; Piluso, V.; Landolfo, R. Removable Friction Dampers for Low-Damage Steel Beam-to-column Joints. Soil Dyn. Earthq. Eng. 2018, 115, 66–81. [Google Scholar] [CrossRef]
  27. Li, Y.Q.; Huang, B.H. Research on load-bearing performance of new fabricated steel structure beam-column joints with energydissipating elements. Structures 2022, 38, 492–501. [Google Scholar] [CrossRef]
  28. Li, Y.Q.; Huang, B.H. Evaluation on seismic performance of beam-column joints of fabricated steel structure with replaceable energy-dissipating elements. Sustainability 2022, 14, 3350. [Google Scholar] [CrossRef]
  29. Huang, B.H.; Li, Y.Q. Research on the seismic performance of beam-column joints of a prefabricated steel structure with additional replaceable energy-dissipating elements. In Proceedings of the 13th Asian-Pacific Conference on Shell and Spatial Structures, Beijing, China, 19–22 September 2022; pp. 3239–3250. [Google Scholar]
  30. GB50009; Load Code for the Design of Building Structures. China Construction Industry Press: Beijing, China, 2012.
  31. JGJ99-2015; Technical Specification for Steel Structure of Tall Building. China Construction Industry Press: Beijing, China, 2016.
  32. GB50011; Code for Seismic Design of Building. China Construction Industry Press: Beijing, China, 2016.
  33. Lervolinoa, I.; Cornell, C.A. Record selection for nonlinear seismic analysis of structures. Earthq. Spectra 2005, 21, 685–713. [Google Scholar]
  34. Tan, Q.; Li, Y.M.; Qin, Y. A spectral intensity index of ground motions for input selection with consideration of higher modes effect for super high-rise buildings. In Proceedings of the 16th World Conference on Earthquake Engineering, Santiago, Chile, 9–13 January 2017. [Google Scholar]
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Figure 1. Beam-column joints with replaceable energy-dissipating elements.
Figure 1. Beam-column joints with replaceable energy-dissipating elements.
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Figure 2. Structural layout plan (unit: mm = 10−3 m).
Figure 2. Structural layout plan (unit: mm = 10−3 m).
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Figure 3. Front elevation of steel frame (TSF on the left, ASFWREE on the right).
Figure 3. Front elevation of steel frame (TSF on the left, ASFWREE on the right).
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Figure 4. Side elevation of steel frame (TSF on the left, ASFWREE on the right).
Figure 4. Side elevation of steel frame (TSF on the left, ASFWREE on the right).
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Figure 5. Three-dimensional model (TSF on the left, ASFWREE on the right).
Figure 5. Three-dimensional model (TSF on the left, ASFWREE on the right).
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Figure 6. Comparison of the inter-story displacement angles in the X-directions and Y-directions.
Figure 6. Comparison of the inter-story displacement angles in the X-directions and Y-directions.
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Figure 7. Comparison of the lateral stiffness in the X-directions and Y-directions.
Figure 7. Comparison of the lateral stiffness in the X-directions and Y-directions.
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Figure 8. Comparison of the rigid-weight ratio of the X-directions and Y-directions.
Figure 8. Comparison of the rigid-weight ratio of the X-directions and Y-directions.
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Figure 9. Comparison of the shear-weight ratio of the X-directions and Y-directions.
Figure 9. Comparison of the shear-weight ratio of the X-directions and Y-directions.
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Figure 10. Stress-strain diagram of steel.
Figure 10. Stress-strain diagram of steel.
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Figure 11. Development history of plastic hinge.
Figure 11. Development history of plastic hinge.
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Figure 12. Acceleration time–history curve of SHW9 in Shanghai.
Figure 12. Acceleration time–history curve of SHW9 in Shanghai.
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Figure 13. Acceleration time–history curve of Chi-Chi_No1181 in Taiwan.
Figure 13. Acceleration time–history curve of Chi-Chi_No1181 in Taiwan.
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Figure 14. Acceleration time–history curve of Chi-Chi_No2713 in Taiwan.
Figure 14. Acceleration time–history curve of Chi-Chi_No2713 in Taiwan.
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Figure 15. Maximum shear force between floors under SHW9.
Figure 15. Maximum shear force between floors under SHW9.
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Figure 16. Time-history curve of the base shear force under SHW9.
Figure 16. Time-history curve of the base shear force under SHW9.
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Figure 17. Maximum shear force between floors under CHI-CHI_NO_1181.
Figure 17. Maximum shear force between floors under CHI-CHI_NO_1181.
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Figure 18. Base shear force time-history curve under CHI-CHI_NO_1181.
Figure 18. Base shear force time-history curve under CHI-CHI_NO_1181.
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Figure 19. Maximum shear force between floors under CHI-CHI_NO_2713.
Figure 19. Maximum shear force between floors under CHI-CHI_NO_2713.
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Figure 20. Base shear force time-history curve under CHI-CHI_NO_2713.
Figure 20. Base shear force time-history curve under CHI-CHI_NO_2713.
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Figure 21. Time–history curve of vertex displacement under SHW9.
Figure 21. Time–history curve of vertex displacement under SHW9.
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Figure 22. Time–history curve of vertex displacement under CHI-CHI_NO_1181.
Figure 22. Time–history curve of vertex displacement under CHI-CHI_NO_1181.
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Figure 23. Time–history curve of vertex displacement under CHI-CHI_NO_2713.
Figure 23. Time–history curve of vertex displacement under CHI-CHI_NO_2713.
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Figure 24. Curve of the inter-story displacement angle under SHW9.
Figure 24. Curve of the inter-story displacement angle under SHW9.
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Figure 25. Curve of the inter-story displacement angle under CHI-CHI_NO_1181.
Figure 25. Curve of the inter-story displacement angle under CHI-CHI_NO_1181.
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Figure 26. Curve of the inter-story displacement angle under CHI-CHI_NO_2713.
Figure 26. Curve of the inter-story displacement angle under CHI-CHI_NO_2713.
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Figure 27. Plastic hinge distribution of the TSF and ASFWREE in the X-direction under SHW9. (TSF on the left, ASFWREE on the right. The following are the same).
Figure 27. Plastic hinge distribution of the TSF and ASFWREE in the X-direction under SHW9. (TSF on the left, ASFWREE on the right. The following are the same).
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Figure 28. Plastic hinge distribution of the TSF and ASFWREE in the Y-direction under SHW9.
Figure 28. Plastic hinge distribution of the TSF and ASFWREE in the Y-direction under SHW9.
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Figure 29. Plastic hinge distribution of the TSF and ASFWREE in the X-direction under CHI-CHI_NO_1181.
Figure 29. Plastic hinge distribution of the TSF and ASFWREE in the X-direction under CHI-CHI_NO_1181.
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Figure 30. Plastic hinge distribution of the TSF and ASFWREE in the Y-direction under CHI-CHI_NO_1181.
Figure 30. Plastic hinge distribution of the TSF and ASFWREE in the Y-direction under CHI-CHI_NO_1181.
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Figure 31. Plastic hinge distribution of the TSF and ASFWREE in the X-direction under CHI-CHI_NO_2713.
Figure 31. Plastic hinge distribution of the TSF and ASFWREE in the X-direction under CHI-CHI_NO_2713.
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Figure 32. Plastic hinge distribution of the TSF and ASFWREE in the Y-direction under CHI-CHI_NO_2713.
Figure 32. Plastic hinge distribution of the TSF and ASFWREE in the Y-direction under CHI-CHI_NO_2713.
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Table
Table 1. Section parameters of the TSF.
Table 1. Section parameters of the TSF.
Structural ElementsSection Size (mm)Section Area (cm2)Section Modulus of Main Axial (cm3)Plastic Section Modulus of Main Axial (cm3)
Columns of floor 1~6□300 × 300 × 20 × 20203.001801.002150.00
Beams of floor 2~6H350 × 250 × 12 × 14109.001320.001487.00
Girders of floor 2~6H300 × 150 × 6.5 × 945.33462.20522.10
Note: All elements were Q345B.
Table
Table 2. Section parameters of the ASFWREE.
Table 2. Section parameters of the ASFWREE.
Structural ElementsSection Size (mm)Section Area (cm2)Section Modulus of Main Axial (cm3)Plastic Section Modulus of Main Axial (cm3)
Columns of floor 1~6□350 × 350 × 20 × 20264.002748.003271.00
Beams of floor 2~6H350 × 250 × 12 × 18137.001728.001938.00
Girders of floor 2~6H300 × 150 × 6.5 × 945.33462.20522.10
Energy-dissipating element□200 × 200 × 10 × 1076.00458.50542.00
Note: The ratio of the linear stiffness of the energy-dissipating element to the steel beam was 0.76 and all elements were Q345B.
Table
Table 3. Comparison of the main calculation results between the TSF and ASFWREE.
Table 3. Comparison of the main calculation results between the TSF and ASFWREE.
ContentsTSFASFWREEComparison (%)
Natural vibration period/sT11.7864 (Y)1.7973 (Y)0.61
T21.7585 (X)1.7538 (X)0.27
T31.5634 (Tortion)1.5337 (Tortion)1.94
Period ratioT3/T10.87520.85332.57
Representative value of gravity load (kN)XY20,011.0320,965.534.77
Mass participation coefficientX0.95920.94621.37
Y0.95850.94551.37
Base shear force (kN)X824.09845.232.57
Y810.16823.671.67
Note: The representative value of gravity load is the sum of 1.0 dead load and 0.5 live load.
Table
Table 4. Maximum vertex displacement of two frames under three seismic waves.
Table 4. Maximum vertex displacement of two frames under three seismic waves.
Seismic WavesTSFASFWREE
Direction X (mm)Direction Y (mm)Direction X (mm)Direction Y (mm)
SHW9241.1263.8253.1262.0
CHI-CHI_NO_1181247.7253.6249.1255.1
CHI-CHI_NO_2713242.3255.4246.1257.7
Table
Table 5. Maximum inter-story displacement angle of two frames under three seismic waves.
Table 5. Maximum inter-story displacement angle of two frames under three seismic waves.
Seismic WavesTSFASFWREE
Direction X Direction YDirection XDirection Y
SHW91/75 (Floor 2)1/66 (Floor 2)1/74 (Floor 3)1/67 (Floor 3)
CHI-CHI_NO_11811/72 (Floor 2)1/71 (Floor 2)1/73 (Floor 3)1/71 (Floor 3)
CHI-CHI_NO_27131/73 (Floor 3)1/76 (Floor 3)1/71 (Floor 3)1/72 (Floor 3)
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Zhang, D.; Li, Y.; Huang, B. Investigation on Seismic Performance of the Fully Assembled Steel Frame Applying Beam-Column Joints with Replaceable Energy-Dissipating Elements. Sustainability 2023, 15, 5488. https://doi.org/10.3390/su15065488

AMA Style

Zhang D, Li Y, Huang B. Investigation on Seismic Performance of the Fully Assembled Steel Frame Applying Beam-Column Joints with Replaceable Energy-Dissipating Elements. Sustainability. 2023; 15(6):5488. https://doi.org/10.3390/su15065488

Chicago/Turabian Style

Zhang, Dawei, Yuanqi Li, and Binhui Huang. 2023. "Investigation on Seismic Performance of the Fully Assembled Steel Frame Applying Beam-Column Joints with Replaceable Energy-Dissipating Elements" Sustainability 15, no. 6: 5488. https://doi.org/10.3390/su15065488

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