# Seismic Performance of CFST Frame-Steel Plate Shear Walls Connected to Beams Only

Authors: Qin Rong; Zhonghui Zhao; Lanhui Guo; Xiaomeng Hou; Li Lin; Hongtao Bi
Journal: Shock and Vibration
 (2021)

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## Abstract

The safety and cost of structures composed of concrete-filled steel tube (CFST) frame-steel plate shear walls (SPSWs) with two-side connections are governed by the seismic performance. The response modification factorR and displacement amplification factor Cd are important seismic performance factors. In this paper, nonlinear seismic responses of 10-story, 15-story, and 20-story CFST frame-SPSWs (CFST-SPSWs) are studied. A nonlinear finite element model which includes both material and geometric nonlinearities is developed using the finite element software OpenSees for this study. The accuracy of model was validated by comparing with experimental results. Nonlinear seismic analysis shows that CFST-SPSWs, in high seismic region, behave in a stable and ductile manner. Also, R and Cd of CFST-SPSWs were evaluated for the structure models using incremental dynamic analysis (IDA), and the average values of 3.17 and 3.05 are recommended, respectively. The recommended R value is greater than the value (2.8) in the “Chinese Code for seismic design of buildings” for composite structures, indicating the code is conservative. The structural periods provided by current code are generally lower than the periods calculated by finite element analysis. Research results show that R and Cd increase with increasing story number, span number, and structural period. Ductility reduction factor Rμ increases with increasing span number and decreasing story number. Overstrength factor Rs increases with increasing story number and decreasing span number.


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## Body

## 1. Introduction

Increasing material strength and deformation properties and using composite structures are two effective methods of improving the seismic performance of building structures [1]. Steel plate shear walls with composite columns and infill plates connected only to beams are important types of composite structures with high seismic performance. Current seismic design methods are primarily based on load-carrying capacity. Currently, in order to ensure structures into inelastic phase, seismic action (horizontal base shear) in design is determined by reducing the elastic seismic force using the response modification factor R for structural seismic acceleration (“moderate earthquake” in Chinese seismic fortification intensity). The R is governed by structural overstrength performance, ductility, and energy dissipation. The structural inelastic degree depends directly on a reduced seismic force, and reduction factor values are concerned with seismic action in design. In the performance-based seismic design method, the inelastic response spectrum is widely applied in the displacement-based design method. In this method, the inelastic response spectrum is obtained by using response modification factor to reduce the elastic response spectrum. Therefore, the structural response modification factor is one of the most crucial parameters in structural seismic design.The structural response modification factor values from various seismic codes around the world are different. In Chinese code, the “General rule for performance-based seismic design of buildings” (CES160 : 2004) [2] (following shorted form is “General rule”) lists some of the structural response modification factors within a structural system; however, the “Code for seismic design of buildings” (GB50011-2010) [3] uses information frequently collected during earthquakes to calculate seismic action. The connotative structural response modification factor is 2.8, which neglects the difference between seismic performance and plastic deformation capacity within the system. Structural response modification factor values in American code were studied and compared with Japanese code by Uang [4] and Whittaker et al. [5]. The reinforced concrete structure designed according to EC8 (Eurocode 8: Design of structures for earthquake resistance) was evaluated in terms of behavior coefficient by Elnashai and Broderick [6], who found that the structural behavior coefficient of European code is conservative. The behavior factor of steel frame structure was analyzed by Kim and Choi [7]. The response modification factors of 20 buckling restrained braced frames (BRBFs) and 30 concentric braced frames (CBFs) were evaluated using Pushover analysis [8]. The response modification factors for CBFs were lower than the BRBF values. The response modification factors for CBFs ranged from 4.10 to 6.10 and ranged from 7 to 22 for BRBFs. The response modification factors of BRBFs with type V, inverted V, diagonal, and split X restrained bracing configurations were calculated using OpenSees software [9]. The response modification factors for BRBFs ranged from 7 to 9.4. The response modification factors of steel moment-resisting frames were calculated using different pushover analysis methods [10]. The response modification factors for steel moment-resisting frames ranged from 3.3 to 3.8, and the maximum difference for response modification factors calculated by adaptive pushover analysis (APA) method and conventional pushover analysis (CPA) method was 16%. The response modification factors of X-braced steel frames with different boundary conditions were calculated using pushover analysis methods using Sap2000 software [11]. The response modification factors for X-braced steel frames ranged from 4.3 to 11. The response modification factors varied with different boundary conditions. The response modification and overstrength factors in moment-resisting steel frames (MRSFs) with added triangular-plate damping and stiffness devices (TADAS) were evaluated using OpenSees software [12]. The response modification factors for MRSFs with TADAS were 15.9, and the factors for MRSFs with TADAS were greater than the MRSFs values. The response modification of steel slit panel-frames was evaluated using pushover analysis and nonlinear incremental dynamic analysis (NIDA) [13]. The response modification factors for steel slit panel-frames ranged from 6.14 to 8.11. The response modification factors calculated using pushover analysis are smaller than those derived from NIDA.Apart from the steel structures [14, 15], the response modification factors of reinforced concrete structures were also investigated [16–19]. The response modification of reinforced concrete frames was evaluated using incremental dynamic analysis (IDA) [20]. The response modification factors R = 6 satisfied the expected safety level-against earthquake-induced collapse. The R = 3 value in current Chinese codes [2] is conservative for RC frames. The seismic behavior and failure mechanism of elevated concrete tanks with shaft and frame staging were evaluated using finite element (FE) modeling [21]. The response modification factors for elevated concrete tanks were 1.5–3, less than the recommended value of 3 by ACI 371R-08 [22]. The values of structural response modification factors for a reinforced concrete frame structure were evaluated based on Indian code by Mondal et al. [23]. The value in Indian code was greater than the actual value, meaning that the code was not safe.Cyclic loading tests on four steel frames assembled with concrete-filled steel tubular (CFST)-bordered composite walls were conducted by Cao et al. [24]. Test results showed that the seismic performance of steel frame was improved by CFST-bordered composite wall. As compared with steel frame, the displacement ductility factor of steel frame CFST-bordered composite wall was reduced from 2.6–3.4 to 1.3–1.8. This is mainly because with the increase in steel ratio, the increase in the damage displacement is lower than that of yield displacement. Five steel-concrete-steel composite shear walls with J hook connectors (SCSSWJ) and boundary CFST columns under cyclic loading were conducted by Yan et al. [25]. Test results showed that the failure mode of SCSSWJs was flexure, which indicated the SCSSWJs exhibit good seismic performance.Recently, our research group conducted seismic behavior tests on steel plate shear walls (SPSWs) and concrete filled steel tube (CFST) columns [26, 27]. The SPSWs exhibited acceptable hysteretic responses under cyclic loading. Literature review shows that the structural response modification factors of reinforced concrete and steel frame structure were studied. However, the research regarding the CFST frame-SPSW response modification factor was limited [28, 29]. To answer this question, the seismic performance of CFST frame-SPSWs is evaluated using the IDA method in this paper. Evaluating structural response modification factor systematically in a composite structural system of CFST frame-SPSWs will improve the seismic design and economy of engineering structures. The influence of story number, span number, and structural period on structural response modification factor R, ductility reduction factor Rμ, overstrength factor Rs, and displacement amplification factor Cd is analyzed. The reasonable values are presented for the CFST frame-SPSWs to provide a base value for the corresponding code.


## 2. CFST Frame-SPSWs Modeling

In order to evaluate the response modification factorR, ductility reduction factor Rμ, overstrength factor Rs, and displacement amplification factor Cd, CFST frame-SPSWs models were built using OpenSees.


### 2.1. Definition of Structural Response Modification FactorR

R is the ratio of the minimum strength to designed strength required to keep a structure fully elastic during a moderate earthquake. This coefficient is concerned with ductility and energy dissipation capacity, and it is an important coefficient for structural seismic design. Cd is the ratio between the maximum elastic-plastic deformation and displacement calculated by elastic analysis according to the reduced seismic effect at the same intensity level during a moderate earthquake. Using the displacement amplification factor, the largest inelastic displacement of the structure can be estimated by determining the elastic displacement generated by seismic action.The elastic-plastic deformation of a structure during an earthquake is shown in Figure1. The nonlinear curve is simplified using a bilinear elastic-plastic curve. The structural response modification factor R and displacement amplification factor Cd are calculated as follows:(1)R=VeVd=VeVyVyVd=RμRs,Cd=ΔmaxΔd.Figure 1
General structural response.In formula (1), Ve is the maximum base shear when the structure remains completely elastic under moderate earthquake; Vy is the base shear when the structure yields; Vd is the designed base shear; Δd is the top horizontal displacement related to the designed base shear; Δy is the top horizontal displacement when the structure yields; Δmax is the maximum top horizontal displacement of the structure during a moderate earthquake; Rμ is the structural ductility reduction factor; and Rs is structural overstrength factor.


### 2.2. Structural Response Modification Factor Modeling Process

The process for calculating the structural response modification factorR and displacement amplification factor Cd of the CFST frame-SPSWs using IDA is as follows:(1)
The structural analysis model was designed, and the corresponding design-based shearVd is solved according to the current domestic design code. The base shear method was used to analyze structures less than 40 m in height, and the mode decomposition method is used to analyze structures greater than 40 m in height.(2)
The CFST frame-SPSWs analysis model was built by using the finite software OpenSees based on the equivalent bars model of steel plate shear walls. Using the IDA method, the seismic response of real structures under the action of one artificial wave and multiple natural ground shocks was analyzed. The maximum base shear, top displacement, and interstory drift of the structure under different seismic levels were obtained by constantly adjusting the acceleration amplitude to analyze IDA. The curve of maximum base shear and top displacement under varying seismic was drawn and analyzed.(3)
Adjusting seismic peak acceleration of earthquake waves to the peak seismic acceleration under fortification seismic and conducting the time-history analysis of elastic structures, the maximum base shearVe of elastic structures under fortification seismic was calculated. Then, structural response modification factor R was calculated according to the ratio of maximum base shear Ve to designed base shear Vd.(4)
Adjusting seismic peak acceleration to seismic fortification peak acceleration can get the maximum top displacement of the structure. According to the ratio of Δmax to the design top displacement Δd of the elastic structure, the displacement amplification factor Cd could be calculated during various amounts of ground shaking. The average value of Cd is used as the analysis result.


## 2.1. Definition of Structural Response Modification FactorR

R is the ratio of the minimum strength to designed strength required to keep a structure fully elastic during a moderate earthquake. This coefficient is concerned with ductility and energy dissipation capacity, and it is an important coefficient for structural seismic design. Cd is the ratio between the maximum elastic-plastic deformation and displacement calculated by elastic analysis according to the reduced seismic effect at the same intensity level during a moderate earthquake. Using the displacement amplification factor, the largest inelastic displacement of the structure can be estimated by determining the elastic displacement generated by seismic action.The elastic-plastic deformation of a structure during an earthquake is shown in Figure1. The nonlinear curve is simplified using a bilinear elastic-plastic curve. The structural response modification factor R and displacement amplification factor Cd are calculated as follows:(1)R=VeVd=VeVyVyVd=RμRs,Cd=ΔmaxΔd.Figure 1
General structural response.In formula (1), Ve is the maximum base shear when the structure remains completely elastic under moderate earthquake; Vy is the base shear when the structure yields; Vd is the designed base shear; Δd is the top horizontal displacement related to the designed base shear; Δy is the top horizontal displacement when the structure yields; Δmax is the maximum top horizontal displacement of the structure during a moderate earthquake; Rμ is the structural ductility reduction factor; and Rs is structural overstrength factor.


## 2.2. Structural Response Modification Factor Modeling Process

The process for calculating the structural response modification factorR and displacement amplification factor Cd of the CFST frame-SPSWs using IDA is as follows:(1)
The structural analysis model was designed, and the corresponding design-based shearVd is solved according to the current domestic design code. The base shear method was used to analyze structures less than 40 m in height, and the mode decomposition method is used to analyze structures greater than 40 m in height.(2)
The CFST frame-SPSWs analysis model was built by using the finite software OpenSees based on the equivalent bars model of steel plate shear walls. Using the IDA method, the seismic response of real structures under the action of one artificial wave and multiple natural ground shocks was analyzed. The maximum base shear, top displacement, and interstory drift of the structure under different seismic levels were obtained by constantly adjusting the acceleration amplitude to analyze IDA. The curve of maximum base shear and top displacement under varying seismic was drawn and analyzed.(3)
Adjusting seismic peak acceleration of earthquake waves to the peak seismic acceleration under fortification seismic and conducting the time-history analysis of elastic structures, the maximum base shearVe of elastic structures under fortification seismic was calculated. Then, structural response modification factor R was calculated according to the ratio of maximum base shear Ve to designed base shear Vd.(4)
Adjusting seismic peak acceleration to seismic fortification peak acceleration can get the maximum top displacement of the structure. According to the ratio of Δmax to the design top displacement Δd of the elastic structure, the displacement amplification factor Cd could be calculated during various amounts of ground shaking. The average value of Cd is used as the analysis result.


## 3. Modeling and Validation of CFST Frame-SPSWs Using the Equivalent Bars Model

To simplify the CFST frame-SPSWs model, the steel plate shear walls can be considered as the equivalent bars model. Steel plate shear walls and equivalent bars provide the same shear force capacity and same horizontal stiffness. The SPSWs with two-side connections are regarded as bidirectional crossbar. The specifics of the methods can be found in [28]. The analytical model of the CFST frame-SPSWs composite structure with two-side connections was developed using the finite element software OpenSees. The core concrete [29, 30] was simulated using the Concrete02 model based on Kent–Scott–Park provided in OpenSees. The stress-strain relationship was confirmed using a concrete constitutive model under axial compression and bending. Steel tubes and beams were modeled using the Steel02 model based on Giuffre–Menegotto–Pinto in OpenSees [31]. The Bauschinger effect can also be considered using the Steel02 model. The softening rate from elastic to plastic phase in this model is R0 = 18, a1 = 0.925, and a2 = 0.15, respectively. Compressive and tensional yield stresses were considered equal to steel yield stress. The nonlinear beam-column element and fiber sections were used to simulate the CFST columns and steel beams. This element considers some characteristics like plastic, stress strengthening, large strain, and large deformation. Steel02 material with 2% strain-hardening is used for these fibers.The nonlinear beam-column element was used to simulate the CFST columns and steel beams. This element considers some characteristics like plastic, stress strengthening, large strain, and large deformation. The simplified bar model was adopted to simulate SPSWs with two-side connections, which allowed for the use of a shell element. The disadvantages of large amount of calculation and difficult in convergence can be avoided. This model uses two crossed steel bars to simulate the performance of SPSWs with two-side connections, and the two crossed steel bars have the same SPSWs hysteretic model under the tensile and compressive load. The two crossed steel bars were simulated using the Truss element in OpenSees, and thehysteretic uniaxial material is used to define the tension and compressive properties of simplified bars. The crossed steel bars hysteric model was determined using SPSWs hysteretic curves with characteristic points on corresponding skeleton curves and damage factors. The damage parameters “damage1” and “damage2” represent the damage of the material in every consecutive cycle in terms of ductility and energy, respectively. These parameters are considered as 0.005 and 0.01. The hysteretic uniaxial material also requires inputting the pinching parameters ‘pinchx’ and ‘pinchy,’ which was defined as follows [29]:(2)pinchy=0.07lnLH−0.11lnλ+0.8,pinchx=1.20λ1000.44−0.17λ100−0.98,where L is the length of SPSW, H is the height of SPSW, and λ is the height-to-thickness ratio of SPSW.The hysteretic performance tests of CFST frame-SPSW (specimens F2SW) and CFST frame (specimen CFST) conducted in Ref [26] were selected to validate the numerical model. The dimensions of specimens are shown in Table 1. The thickness and width, t and L1, of SPSW are 3 mm and 1100 mm, respectively. The measured yield strength and tensile strength of steel are 290 MPa and 421 MPa, respectively. By conducting the same loading as experiment as in the model, the calculated shear force at the F2SW and CFST base columns can be obtained. The comparison of hysteretic curves for F2SW and CFST obtained from the experiment by Guo et al. [26] and the simulations from this study are shown in Figure 2. The stiffness of loading and unloading in the hysteretic curve seems credible as the calculated curves and test curves are consistent. The measured peak load is slightly greater than the calculated peak load. In order to enhance the connection of steel beams and shear walls, each steel plate was attached to beams of the boundary frame through 6 mm thick fishplates. Length of each fishplate was the same as that of the infill plate. In the finite element model, the contribution of the fishtail plate is difficult to simulate. Hence, the load-carrying capacity in the experiment is slightly greater. To summarize, the finite element model can analyze the hysteretic performance under cyclic load of the CFST frame-SPSWs.Table 1
Dimension of specimens.
H (mm)L (mm) L1 (mm) t (mm)D×t (mm)Middle beam (mm)Top and bottom beam (mm)15002000 1100 3219  ×  4H194 × 150 × 6 × 9H300 × 150 × 6 × 9Note. The Chinese designation of H shapes corresponds to the United States designation of W shapes and reflects member depth, width, web thickness, and flange thickness (unit in mm), respectively. The columns were CFSTs, the steel tube with a diameter of D and depth of t (unit in mm).Figure 2
Comparison of experimental and calculated results: (a) specimen F2SW; (b) specimen CFST.
(a)(b)


## 4. Evaluating Structural Seismic Performance Using the IDA Method

In this study, the numerical model developed in Section2 was used to evaluate the structural seismic performance of CFST frame-SPSWs. Six planar structural models were designed with 10, 15, and 20 stories, respectively, and the influence of story number, span number, and structural period on the structural response modification factor R is studied. These buildings are located in 9 seismic precautionary intensity zone, and designed basis seismic acceleration is 0.4 g. In addition, using Chinese code [2], these buildings’ site classifications were selected as class 2, and their earthquake classification was selected as group one. Each model’s height and span are 3.6 m and 6m, with the span numbers of 3 and 5, respectively. In addition, SPSWs were designed with the span-to-depth ratio of 1.0 and were settled at the midspan of the frame. The steel of the SPSW is Q235, and the steel of the frame beams and CFSTs is Q345. Q235 and Q345 mean that the standard yield strength of steel is 235 MPa and 345 MPa, respectively, as per the Standard for design of steel structures (GB 50017-2017). The core concrete grade in the steel-tube columns is C50 (compressive strength design value of 23.1 MPa). The floors are east-in-place reinforced concrete with a thickness of 100 mm and concrete grade of C30 (compressive strength design value of 14.3 MPa). C50 and C30 mean that the standard cube compressive strength of concrete is 30 MPa and 50 MPa, respectively, as per the Code for design of concrete structures (GB50010-2010).The dead load of floor and roof is 4.2 kN/m2 and 4.6 kN/m2, respectively. The live load is 2 kN/m2. The dead load and live load are calculated according to load code for the design of building structures (GB50009-2012). The frames were designed according to the “Code for seismic design of buildings,” and the cross section dimensions are listed in Table 2.Table 2
Model dimensions.
Model numberFloor numberColumnD × t (mm)Beam (mm)Steel plate depth (mm)M-10-31–3450 × 10H500 × 300 × 11 × 158M-10-54–6400 × 9H600 × 300 × 12 × 20 (HBE)67–10350 × 86M-15-31–5500 × 12H500 × 300 × 11 × 1510M-15-55–10450 × 10H600 × 300 × 12 × 20 (HBE)811–15400 × 96M-20-31–5600 × 16H500 × 300 × 11 × 15126–10550 × 1510M-20-511–15500 × 12H600 × 300 × 12 × 20 (HBE)816–20450 × 106Note. Six planar structural models were designed with 10, 15, and 20 stories. The M-10-3 means the model has 10 stories and 3 spans. The HBE is horizontal boundary elements connected to shear walls. The beams were H-shaped steels and reflect member depth, width, web thickness, and flange thickness (unit in mm), respectively. The columns were CFSTs, and the steel tubes reflect diameter of D and depth of t (unit in mm).By comparing the acceleration response spectrum in seismic records with Chinese code, 8 seismic records including 7 ground motion records and 1 artificial seismic wave were selected from the 22 available long field ground motion records, which are recommended in FEMA P695. According to the spectrum characteristics, amplitude, and duration of seismic records, the selected seismic records are similar to the site design spectrum, and the 8 seismic records are selected. The 8 seismic records (as listed in Table3) were used in CFST frame-SPSWs seismic response evaluation using the IDA method. The peak accelerations of seismic records are amplified or reduced in proportion to ensure that the adjusted peak accelerations of seismic records satisfy the requirements of the highest value of acceleration time-history curves under the corresponding seismic levels in Chine code. Using this method, only the highest value in the seismic response spectrum is changed but the spectral characteristics remain the same.Table 3
Information from the selected earthquake records.
NumberLevelYearNameRecording stationGM16.51979Imperial ValleyDeltaGM26.51979Imperial ValleyEI Centro Array #11GM36.91989Loma PrietaCapitolaGM46.91989Loma PrietaGilroy Array #3GM57.41990Manjil, IranAbbarGM67.01992Cape MendocinoRio Dell OverpassGM76.61971San FernandoLA-Hollywood Stor Lot,090GM8Artificial waves


### 4.1. Capacity Curves of Model M-20-5

In the 8 selected seismic records, peak acceleration increased to 1.0 g, and the capacity curves of model M-20-5 were analyzed using the IDA method in OpenSees. The capacity curves of M-20-5 under different ground motions are shown in Figure3. The structural response increases gradually with increasing peak acceleration. Even when the acceleration is greater than the corresponding acceleration in the number 9 seismic fortification zone (the design basic acceleration is 0.4 g), the structure maintains good seismic performance.Figure 3
Capacity envelopes of structure: (a) maximum interstory drift; (b) maximum top displacement; (c) base shear-maximum interstory drift curves.
(a)(b)(c)Peak acceleration reaches 0.8 g under the artificial seismic curve and GM1, and story displacement angle increases rapidly, indicating the structure will collapse. Under other seismic curves, when the peak acceleration reaches approximately 1000gal, the structure maintains good seismic performance; hence, the anticollapse capacity of M-20-5 is 800gal.


### 4.2. Distribution of Interstory Drift

The envelope of interstory drift of M-20-5 under frequently occurring, moderate, and rare earthquakes is shown in Figure4. The change of structural maximum interstory drift under frequently occurring earthquakes for varying height of structure is small (maximum interstory drift is less than 4/1000). The average value in this situation is 0.26%, and the average value of maximum interstory drift during a moderate earthquake is 0.77%. The average value of maximum interstory drift during a rare earthquake is 1.3%. The model maximum interstory drift under frequently occurring and rare earthquakes can satisfy deformation requirement for elastic and elastic-plastic in the “Code for seismic design of buildings,” which is less than 1/300 and 1/50, respectively. It also satisfies the requirement for moderate earthquake fortification standards (0.004 h–0.008 h) (h is story height) in the “General rule.” Furthermore, the structural maximum interstory drift under frequently occurring and moderate earthquakes changes inconspicuously with height; however, these changes are significant in the bottom and middle-upper sections during rare earthquakes. The maximum interstory drift occurs at the 16th floor primarily because the structural members dimension as well as the stiffness is reduced at this floor. Under frequently occurring earthquakes, the structure is completely elastic, and under moderate earthquakes, the steel plates, acting as energy dissipation elements, yielded first and become plastic hinges to consume energy. In addition, the steel plates also absorb earthquake energy and prevent structural failure. Under rare earthquakes, numerous SPSWs and frame beams yielded to form plastic hinges; however, the structure does not collapse. After yielding, the maximum interstory drift decreased with increasing peak acceleration primarily because the location and order of structural plastic hinge change after the peak acceleration, resulting in internal force redistribution and changing the structure force transfer paths (Figure 4(a)). All of these research results show that CFST frame-SPSWs exhibit good seismic capacity.Figure 4
The maximum interstory drift with height of the structure under different seismic waves: (a) frequently occurring earthquake; (b) moderate earthquake; (c) rare earthquake.
(a)(b)(c)


### 4.3. Analysis of Structural Capacity Curve

The 8 capacity curves of maximum interstory drift-base shear for different models under ground motion are shown in Figure5. The structural seismic response on elastic phase under different ground motions is close to each other (Figure 5). Shear force increases with increasing peak acceleration until the structure yielded into the elastic-plastic phase. Then, the difference in structural response under different ground motions is larger, and the average values from the seismic records are adopted to reveal the structural performance. Although the seismic peak acceleration increased to 1.0 g, the structural maximum interstory drift is still less than 2% under the partial ground motions. Results show that CFST frame-SPSWs exhibit good seismic performance, and the structural seismic response is relatively large under the artificial seismic waves. When the peak acceleration increases to 0.8 g, interstory drift increases rapidly, and the structural anticollapse capacity reaches approximately 800 gal.Figure 5
Capacity envelopes of structures for a 9 seismic intensity: (a) Model M-10-3; (b) Model M-10-5; (c) Model M-15-3; (d) Model M-15-5; (e) Model M-20-3; (f) Model M-20-5.
(a)(b)(c)(d)(e)(f)


## 4.1. Capacity Curves of Model M-20-5

In the 8 selected seismic records, peak acceleration increased to 1.0 g, and the capacity curves of model M-20-5 were analyzed using the IDA method in OpenSees. The capacity curves of M-20-5 under different ground motions are shown in Figure3. The structural response increases gradually with increasing peak acceleration. Even when the acceleration is greater than the corresponding acceleration in the number 9 seismic fortification zone (the design basic acceleration is 0.4 g), the structure maintains good seismic performance.Figure 3
Capacity envelopes of structure: (a) maximum interstory drift; (b) maximum top displacement; (c) base shear-maximum interstory drift curves.
(a)(b)(c)Peak acceleration reaches 0.8 g under the artificial seismic curve and GM1, and story displacement angle increases rapidly, indicating the structure will collapse. Under other seismic curves, when the peak acceleration reaches approximately 1000gal, the structure maintains good seismic performance; hence, the anticollapse capacity of M-20-5 is 800gal.


## 4.2. Distribution of Interstory Drift

The envelope of interstory drift of M-20-5 under frequently occurring, moderate, and rare earthquakes is shown in Figure4. The change of structural maximum interstory drift under frequently occurring earthquakes for varying height of structure is small (maximum interstory drift is less than 4/1000). The average value in this situation is 0.26%, and the average value of maximum interstory drift during a moderate earthquake is 0.77%. The average value of maximum interstory drift during a rare earthquake is 1.3%. The model maximum interstory drift under frequently occurring and rare earthquakes can satisfy deformation requirement for elastic and elastic-plastic in the “Code for seismic design of buildings,” which is less than 1/300 and 1/50, respectively. It also satisfies the requirement for moderate earthquake fortification standards (0.004 h–0.008 h) (h is story height) in the “General rule.” Furthermore, the structural maximum interstory drift under frequently occurring and moderate earthquakes changes inconspicuously with height; however, these changes are significant in the bottom and middle-upper sections during rare earthquakes. The maximum interstory drift occurs at the 16th floor primarily because the structural members dimension as well as the stiffness is reduced at this floor. Under frequently occurring earthquakes, the structure is completely elastic, and under moderate earthquakes, the steel plates, acting as energy dissipation elements, yielded first and become plastic hinges to consume energy. In addition, the steel plates also absorb earthquake energy and prevent structural failure. Under rare earthquakes, numerous SPSWs and frame beams yielded to form plastic hinges; however, the structure does not collapse. After yielding, the maximum interstory drift decreased with increasing peak acceleration primarily because the location and order of structural plastic hinge change after the peak acceleration, resulting in internal force redistribution and changing the structure force transfer paths (Figure 4(a)). All of these research results show that CFST frame-SPSWs exhibit good seismic capacity.Figure 4
The maximum interstory drift with height of the structure under different seismic waves: (a) frequently occurring earthquake; (b) moderate earthquake; (c) rare earthquake.
(a)(b)(c)


## 4.3. Analysis of Structural Capacity Curve

The 8 capacity curves of maximum interstory drift-base shear for different models under ground motion are shown in Figure5. The structural seismic response on elastic phase under different ground motions is close to each other (Figure 5). Shear force increases with increasing peak acceleration until the structure yielded into the elastic-plastic phase. Then, the difference in structural response under different ground motions is larger, and the average values from the seismic records are adopted to reveal the structural performance. Although the seismic peak acceleration increased to 1.0 g, the structural maximum interstory drift is still less than 2% under the partial ground motions. Results show that CFST frame-SPSWs exhibit good seismic performance, and the structural seismic response is relatively large under the artificial seismic waves. When the peak acceleration increases to 0.8 g, interstory drift increases rapidly, and the structural anticollapse capacity reaches approximately 800 gal.Figure 5
Capacity envelopes of structures for a 9 seismic intensity: (a) Model M-10-3; (b) Model M-10-5; (c) Model M-15-3; (d) Model M-15-5; (e) Model M-20-3; (f) Model M-20-5.
(a)(b)(c)(d)(e)(f)


## 5. Analysis of Structural Performance Coefficient

For each model, the calculated resultsR, Rμ, Rs, and Cd are listed in Table 4. The comparison of structural performance coefficients and their corresponding calculated average values is shown in Figure 6.Table 4
Structural performance factors.
Model numberStructural basis periodStructural ductility reduction factorRμStructural overstrength factorRsStructural response modification factorRDisplacement amplification factorCdT/sM-10-31.061.2542.6603.3263.194M-10-51.251.3522.4023.2483.117M-15-31.571.1062.8813.1873.129M-15-51.791.1922.6693.1803.056M-20-31.991.0462.9383.0732.988M-20-52.191.0842.7943.0292.826Average1.1722.7243.1743.052Standard deviation0.1060.1760.0980.119Variation coefficient0.0900.0650.0310.039Figure 6
Structural performance factors: (a) structural ductility reduction factorRμ; (b) structural overstrength factor Rs; (c) structural response modification factor R; (d) displacement amplification factor Cd.
(a)(b)(c)(d)The structural performance coefficient changes with changing story number, span number, and structural period (Figure6). For the models in this contribution, the average values of R, Rμ, Rs, and Cd are 3.194, 1.172, 2.274, and 3.052, respectively. The Chinese “Code for seismic design of buildings” implies that the structural response modification factor is 2.81. The structural response modification factor and displacement amplification factor of CFST frame-SPSW are regulated the same as concrete frame in the “General rule,” and their values are 2.63 and 2.2, respectively. The CFST frames-SPSWs have a good seismic performance, and the structural performance coefficient currently used in Chinese code is conservative. This contribution can offer some reasonable suggestions regarding the design and research on some performance coefficients and structural response modification factors. If this result, R is 3.194, is adopted, the designed seismic action will decrease 12% compared with the “Code for seismic design of buildings.” Compared with the “General rule,” the designed action will decrease 17.7%.


### 5.1. Influence of Period

The influence of structural period on structural ductility reduction factorRμ, structural overstrength factor Rs, structural response modification factor R, and displacement amplification factor Cd is shown in Figure 6. As the number of spans and floors of the structure increases, the period of the structure keeps increasing, but for Rμ and Rs, this phenomenon is not significant (Table 4). In addition, R and Cd decrease slightly with increasing structural period.


### 5.2. Influence of Span Number

The influence of span number onRμ, Rs, R, and Cd is shown in Figure 7. Rμ increases with increasing span number, but the extent decreases gradually with increasing structural height. Rs decreases with increasing span number, but this trend still decreases with increasing structural height. Both R and Rs decrease with increasing span number, and the maximum variable magnitude is 5%, indicating that there is a minor influence between span number and structural performance coefficients within a given period.Figure 7
Influence of span number on structural performance factors: (a) structural ductility reduction factorRμ; (b) structural overstrength factor Rs; (c) structural response modification factor R; (d) displacement amplification factor Cd.
(a)(b)(c)(d)


### 5.3. Influence of Story Number

The influence of story number onRμ, Rs, R, and Cd is shown in Figure 8. Rμ, R, and Cd decrease with increasing story number, and Rs increases with increasing story number. This trend decreases gradually with increasing structural height for all 4 of these coefficients.Figure 8
Influence of story number on structural performance factors: (a) structural ductility reduction factorRμ; (b) structural overstrength factor Rs; (c) structural response modification factor R; (d) displacement amplification factor Cd.
(a)(b)(c)(d)


## 5.1. Influence of Period

The influence of structural period on structural ductility reduction factorRμ, structural overstrength factor Rs, structural response modification factor R, and displacement amplification factor Cd is shown in Figure 6. As the number of spans and floors of the structure increases, the period of the structure keeps increasing, but for Rμ and Rs, this phenomenon is not significant (Table 4). In addition, R and Cd decrease slightly with increasing structural period.


## 5.2. Influence of Span Number

The influence of span number onRμ, Rs, R, and Cd is shown in Figure 7. Rμ increases with increasing span number, but the extent decreases gradually with increasing structural height. Rs decreases with increasing span number, but this trend still decreases with increasing structural height. Both R and Rs decrease with increasing span number, and the maximum variable magnitude is 5%, indicating that there is a minor influence between span number and structural performance coefficients within a given period.Figure 7
Influence of span number on structural performance factors: (a) structural ductility reduction factorRμ; (b) structural overstrength factor Rs; (c) structural response modification factor R; (d) displacement amplification factor Cd.
(a)(b)(c)(d)


## 5.3. Influence of Story Number

The influence of story number onRμ, Rs, R, and Cd is shown in Figure 8. Rμ, R, and Cd decrease with increasing story number, and Rs increases with increasing story number. This trend decreases gradually with increasing structural height for all 4 of these coefficients.Figure 8
Influence of story number on structural performance factors: (a) structural ductility reduction factorRμ; (b) structural overstrength factor Rs; (c) structural response modification factor R; (d) displacement amplification factor Cd.
(a)(b)(c)(d)


## 6. Conclusions

The nonlinear finite element software OpenSees is adopted to develop the model for CFST frame-SPSWs connected with beams only. These models evaluate structural seismic performance using the IDA method and analyze governing factors, such asR and Cd. The following conclusions can be drawn:(1)
The SPSWs as energy dissipation elements yielded firstly to form plastic hinges under moderate earthquakes. In addition, most SPSWs and frame beams yielded under rare earthquakes, but the structure is not collapse.(2)
R and Cd decrease gradually with increasing story number, span number, and structural period. Rμ increases with increasing span number but decreases with increasing story number. Rs decreases with increasing span number but increases with increasing story number.(3)
The obtained overstrength factorRs and structural ductility reduction factor Rμ of CFST frame-SPSWs are 2.72 and 1.17, respectively.(4)
The recommended value of response modification factor and displacement amplification factor for CFST frame-SPSWs is 3.17 and 3.05, respectively. The recommendedR is greater than the value (2.8) in the “Chinese Code for seismic design of buildings” for composite structures, which indicates the code is conservative.



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*Source: 5850073-2021-08-14.xml*