Seismic vulnerability of prefabricated reinforced concrete frame structure based on local outsource steel tube bolted column

Abstract

In this paper, the seismic performance of a prefabricated frame structure with a local outsource steel tube bolted column–column connect is evaluated from the perspective of seismic vulnerability theory. Firstly, a simplified model of the prefabricated frame structure was constructed and validated by experiments. Then, a six-story prefabricated reinforced concrete frame structure (PRCS) and a cast-in-situ reinforced concrete frame structure (CRCS) were designed as examples to get the increment dynamic analysis (IDA) of the structure under 12 ground motions, and the two-parameter damage model was used as the structural requirement index. As a traditional structural requirement index-the maximum inter-storey drift angle cannot accurately describe the mechanism of structural damage. Therefore, two types of damage models are compared and analyzed. In addition, in order to evaluate the damage of frame structure effectively, a new damage index weighted combination method is proposed, and its feasibility is verified. Finally, the IDA curve and vulnerability curve with Kunnath two-parameter damage model and the maximum inter-story displacement angle as the requirement index are drawn. The results show that the two-parameter damage model is more accurate than the maximum inter-storey drift angle model in evaluating the seismic performance of the PRCS and CRCS. It shows that the maximum inter-story displacement angle model can overestimate the collapse resistance of the PRCS by 60.7% on average, and the collapse resistance of the CRCS by 75.67% on average. The seismic performance of the CRCS is better than that of the PRCS as the seismic intensity increases. Although the seismic performance of fabricated columns is similar to that of cast-in-place columns, there is still a certain gap in the seismic performance of frame structures.

Keywords

damage index weighted combination method damage model incremental dynamic analysis prefabricated frame simplified column–column joint model vulnerability

Highlights

We use the damage index D in the two parameter damage model as the structural requirement index instead of the maximum inter-storey drift angle.

The two-parameter damage model is more accurate than the maximum inter-storey drift angle model in evaluating the seismic performance of the frame structure.

We propose a simplified model to analyze prefabricated frame structure.

We propose a new damage index weighted combination method to evaluate the whole frame structure.

Introduction

In recent years, earthquakes have continued to occur in various countries around the world. To understand the damage mechanism of building structures under earthquakes, scholars from various countries have conducted a series of studies (Liu et al., 2016; Wei et al., 2017). Ang (1985) proposed a relationship between the two-parameter damage index (D) and the damage level of the structure. Later, Shinozuka et al. (2000) conducted research on the basis of the damage model to improve the seismic vulnerability analysis applied to CRCS. Beilic et al. (2017) studied different single-storey PRCS through the maximum inter-storey drift angle model, and examined the seismic performance of structures under different connection nodes. Casotto et al. (2015) studied more than 100 groups of PRCS through the maximum inter-storey drift angle model and established a set of corresponding vulnerability curves. Wu et al. (1993) and Clementi et al. (2016) studied the impact of different site conditions on a structure’s seismic performance, analyzed its soft storey, and the importance of the beam–column joint, and finally examined the entire structure’s vulnerability. Pasticier et al. (2008) built a frame structure on the basis of the SAP2000 plastic hinge model and used incremental dynamic analysis (IDA) to evaluate the structure’s seismic vulnerability and performance. Cruz (2010) studied a typical frame structure, input 12 ground motions for dynamic time history analysis, selected a number of different floors on the CRCS, and finally obtained vulnerability curves corresponding to different floors. Pavese et al. (2016) studied a kind of infilled CRCS with the maximum inter-storey drift angle model, examined the interaction of beam–column joints, and analyzed the damage mode of the joints through vulnerability. Magliulo et al. (2008) conducted a nonlinear dynamic analysis of the existing typical industrial plant on the basis of the maximum inter-storey drift angle model and obtained a set of vulnerability curves. Pan et al. (2018) studied the seismic vulnerability of an unbonded prestressed PRCS, and which shown that when the ground motion intensity is small, its seismic performance is essentially the same as that of CRCS, and when ground motion intensity is large, the gap becomes bigger.

In summary, most of the current analyses of seismic vulnerability focus on CRCS instead of PRCS, and use one structural requirement index which is still based on the maximum inter-storey drift angle model. However, this index cannot accurately predict the entire damage process, because whether the structure fails is usually determined by whether the elastic displacement or the plastic displacement exceeds to a critical value. The damage model that only considers single-parameter deformation does not consider the cumulative damage to the structure over time (Ye et al., 2018). However, the Kunnath-modified Park–Ang two-parameter damage model can account for both the deformation and the accumulation of energy in the seismic vulnerability analysis of the PRCS and CRCS, so the two parameter damage model is more accurate. This paper examines the seismic performance of a frame structure on the basis of a local outsource steel tube bolted to the assembly of a prefabricated column developed by the research group. The component has good ductility and energy consumption characteristics and achieved equivalent cast-in-situ reinforced concrete column performance (Wei, 2013). At present, it has been used in practical engineering projects (Figure 1), but the research on the whole seismic performance of PRCS is still lacking. Therefore, to further evaluate the seismic performance of the prefabricated frame structure, this paper uses IDA to analyze the seismic vulnerability of a six-story PRCS, with a two-parameter damage model as the structural demand parameter. Compared with the CRCS and combined with the the maximum inter-storey drift angle model as the requirement index, the feasibility of seismic performance evaluation based on the two-parameter damage index is explored, and the accuracy of a new weighted combination method of damage index proposed in this paper is verified.

Figure 1.

Project construction schematic.

Test introduction and damage model selection

Test specimen design parameters

Six reinforced concrete columns were designed for this test program: two long prefabricated outsource steel tube bolted columns, PRCC-L01 and PRCC-L02, and two short prefabricated outsource steel tube bolted columns, PRCC-L03 and PRCC-L04 (Figure 2), and two long cast-in-place reinforced concrete columns C-01 and C-02, and the design parameters are the same as PRCC-L01 and PRCC-L02. All concrete was C40-grade.The thickness of the steel tube of the long column was 8 mm, and for the short was 5 mm. The longitudinal reinforcement of the section was equipped with eight HRB400-grade steel bars with a diameter of 22 mm. The stirrups were high-strength stirrups with a yield strength of 1100 MPa and a diameter of 5 mm. The stirrup reinforcement zone had a distance of 30 mm and a cross-section size of 400 mm × 400 mm. The calculated length of the long column was 1800 mm and the actual length of the column was 2000 mm. The reinforcement of the short column section was reinforced with eight HRB400 steel bars with a diameter of 14 mm. The stirrup spacing at the joint was 60 mm. The remaining stirrup spacing was 30 mm, and the cross-section size of the short column was 250 mm × 250 mm, The calculated length of the long column was 1000 mm, In order to carry out the loading test, the loading beam was also placed on the top of the short column, but it will not affect the mechanical properties of the short column, so the loading beam does not need to be considered in the finite element model. The component reinforcement diagram is shown in Figure 3. The joint assembly diagram is shown in Figure 4. The mechanical properties of concrete materials are shown in Table 1. The steel materials index are shown in Table 2, and the component design parameters are shown in Table 3.

Figure 2.

Prefabricated column: (a) prefabricated long column and (b) prefabricated short column.

Figure 3.

Detailed design of prefabricated column joint: (a) prefabricated column node construction graphics and (b) schematic diagram of prefabricated column reinforcement.

Figure 4.

Schematic process of prefabricated column assembly.

Table 1.

Mechanical properties of concrete.

Material	Cube compressivestrength $f_{cu}$ /MPa	Axial compressivestrength $f_{c}$ /MPa	Modulus ofelasticity $E_{c}$ /MPa
Concrete	43.76	29.27	3.3 × 10⁴

Table 2.

Mechanical properties index of steel.

Diameter or thickness	Yield strength $f_{y}$ /MPa	Ultimate strength $f_{u}$ /MPa	Modulus of elasticity $E_{c}$ /MPa	Elongation rateafter fracture, %	Strength-yieldratio
5	1050	1170	2.05 × 10⁵	5.8	1.11
14	462.5	642.5	2.10 × 10⁵	19	1.39
22	437.5	615	2.00 × 10⁵	23.5	1.41
5	320	475	2.06 × 10⁵	21	1.48
8	290	405	2.06 × 10⁵	40	1.39

Table 3.

Specimen design parameter.

Specimen ID	Axialcompressionratio	Shearspanratio	Volume stirrupratio, %
PRCC-L01	0.2	4.5	0.79
PRCC-L02	0.6	4.5	0.79
PRCC-L03	0.04	2	1.18
PRCC-L04	0.1	1.5	1.18
C-01	0.2	4.5	0.79
C-02	0.6	4.5	0.79

Two-parameter damage model

The selection and combination of the damage model’s physical characteristics must not only reflect the failure mechanism of the structure under earthquake, but also facilitate the calculation and application of engineering personnel (Rajabi et al., 2013). The (D) describes the degree of damage to the structure or component, and its value range is [0,1]. If (D) = 0, then the structure or component is intact; If (D) = 1, then the structure or component is completely damaged; If 0 < (D)< 1, this indicates that the structure or component is in a certain state between no damage and damage (Ang, 1985). Ang (1985) proposed a two-parameter damage model on the basis of a linear combination of maximum deformation and cumulative hysteretic energy consumption, derived from the test results of a large number of reinforced concrete beam and column members. However, the physical meaning of the ratio of cumulative energy consumption to the product of yield strength and ultimate displacement is not clear. In this paper, Kunnath et al. (1992) modified Park–Ang damage model is used as follows:

D = \frac{δ_{m} - δ_{y}}{δ_{u} - δ_{y}} + β \frac{E_{h}}{P_{y} δ_{u}}

(1)

where D is the damage index, $δ_{m}$ is maximum deformation of components under earthquake, $δ_{u}$ is ultimate deformation of members under monotonic loading, $δ_{y}$ is deformation of components at yield, $P_{y}$ is loads of members at yields, $E_{h}$ is accumulated hysteretic energy consumption, $β$ is the cyclic load influence factor, the value range is changed from 0 to 0.85, and its average value is from 0.10 to 0.15. It is calculated according to the following formula:

β = (- 0.447 + 0.073 λ + 0.24 n_{0} + 0.314 ρ_{s}) \times 0 . 7^{ρ_{w}}

(2)

where $λ$ is shear span ratio ratio, If it is less than 1.7, take its value as 1.7, $n_{0}$ is axial pressure ratio, which takes 0.2 when less than 0.2, $ρ_{s}$ is longitudinal reinforcement ratio, $ρ_{w}$ is the stirrup reinforcement ratio.

However, the $E_{h}$ calculation usually comes from every beam and column. Obviously, the large amount of calculation for the analysis of the frame structure cannot be ignored, so this paper will provide a simplified calculation idea.

Simplified calculation method for Park–Angdamage model

The Park–Ang damage model, which is widely used by scholars, comprehensively considers the maximum deformation of the structure and the cumulative hysteretic energy consumption, However, the parameter calculation in this model is difficult, especially the hysteretic energy calculation of the whole frame structure, which limits the application of this method. In this paper, the relationship between the hysteretic energy consumption between the storeys and the maximum displacement of the structure from the energy perspective is examined (Ye and Otani, 2015). In addition, the relationship between the energy consumption of the floor plastic deformation and the maximum displacement of the structure is given, namely,

E_{h} = \frac{1}{2} F_{y} x_{y} + (1 + 4 ρ) F_{y} (x_{m} - x_{y})

(3)

where $E_{h}$ is plastic deformation energy consumption on a certain floor, $F_{y}$ is yield shear between storeys, $x_{y}$ is yield displacement between storeys, $ρ$ is the correction coefficient of the hysteretic model, which can be 0.33 for reinforced concrete structures (Ye and Otani, 2015), $x_{m}$ is maximum plastic displacement of structures under earthquake.

Finally, when combined with equation (1), the damage index can be calculated. However, this is only to calculate the damage index of a certain storey of the structure. In order to get the damage index of the whole structure, we need to calculate the damage index of each storey, and then we need to carry out a reasonable weighted combination of these damage indexes, and finally we can get the damage index of the whole structure. The following will introduce the weighted combination of several damage indexes, including a new weighted combination of damage indexes proposed in this paper.

Weighted combination of damage models

At present, there are two main methods for assessing damage to the whole structure. The first is to conduct a modal analysis of the structure, and evaluate its seismic performance through indicators the stiffness and frequency index of the structure. The second is the weighted combination method, in which members are weighted and combined based on the damage index of different floors or members. This paper adopts the second analysis method, combining the weighting methods (equations (4) and (5)) proposed by Ou and Niu (1993), Park and Ang (1985), etc. The Author improved the combination method of Park and Ang and proposed a new weighting method (equation (6)), which considers the influence of different floor positions on the structure and accounts for the fact that floors with greater energy consumption contribute more damage to the structure. The weighted combination of Park and Ang is named Park–Ang, the weighted combination of Ou is named Jinping Ou, and the weighted combination of this article is named Author.

η_{i} = \frac{E_{h}}{\sum_{i = 1}^{N} E_{h}}

(4)

η_{i} = \frac{(N - i + 1) D_{ci}}{\sum_{i = 1}^{N} (N - i + 1) D_{ci}}

(5)

η_{i} = \frac{(N - i + 1) E_{h}}{\sum_{i = 1}^{N} (N - i + 1) E_{h}}

(6)

where $η_{i}$ is weighting factor for the i-th floor, $D_{ci}$ is damage index of the i-th floor, and N is floor number.

Structural model and ground motion selection

Establishment of column–column model

Due to the use of solid elements to construct the outsourcing steel tube bolt model, there is a large amount of model calculation and it is difficult to converge. This paper proposes a simplified model to analyze this type of prefabricated frame structure. First, based on SAP2000 finite element software, this paper uses a multi-segment linear plastic connection unit to release the rotational stiffness of the prefabricated columns, In the R1 and R2 rotation directions of the nonlinear connection element, input the M-θ (equations (7) and (8)) of the prefabricated column joint in different stress stages to achieve its stiffness equivalence, the schematic diagram is shown in Figure 5, the characteristic points in the figure include crack point, yield point, peak point and ultimate point, and $K_{1}$ , $K_{2}$ , $K_{3}$ , $K_{4}$ are the stiffness of corresponding stage. The connection unit is composed of six decoupled springs, as shown in Figure 6. Three springs are located in the XOY plane: at the axial deformation, the shear deformation in the XOY plane, and the bending deformation in the XOY plane, where the point i is in the lower column, and point j is in the upper column, releasing the ij node to degrees of freedom and constraining its translational degrees of freedom. The columns adopt frame elements, the concrete constitutive model is calculated based on the Mander model, the reinforced constitutive model adopts the double-fold line strengthening model, and the hysteresis type selection Takeda. To verify the validity of the connection unit used in the modeling, four prefabricated column node tests were tested, and the aforementioned modeling method was used for modeling analysis. The test loading schematic diagram and the finite element loading schematic diagram are shown in Figure 7. The comparison between the calculation results and the test results is shown in Figure 8.

M = F \times L_{0}

(7)

θ = δ / L_{0}

(8)

where F is the shear force at the bottom of the column, $δ$ is the displacement at the top of the column, $L_{0}$ is the calculated height of the column.

Figure 5.

Stiffness values of prefabricated column joints in different failure stages.

Figure 6.

Schematic diagram of multi-segment linear plastic connecting element.

Figure 7.

Schematic view of the loading device: (a) schematic diagram of long column test loading, (b) schematic diagram of short column test loading, and (c) schematic diagram of finite element loading.

Figure 8.

Column–column node hysteresis curve verification: (a) PRCC-L01, (b) PRCC-L02, (c) PRCC-L03, (d) PRCC-L04,(e) C-01, and (f) C-02.

Establishment of the framework structure model

A six-story PRCS was designed according to Chinese building structure design codes (GB50010, 2010; GB50011, 2010). The structural earthquake was placed in the second group. The characteristic period of the site was 0.4 s. The site type was II, and the seismic fortification intensity degree was 8° (0.2 g). The plane and elevation dimensions are shown in Figure 9. The dimensions of the columns were 500 mm × 500 mm and 200 mm × 400 mm, the reinforcement grade was HRB400, and concrete was C40-grade. The boundary condition of the first floor column is fixed.

Figure 9.

Design drawing of PRCS and CRCS: (a) PRCS and CRCS plans and (b) PRCS and CRCS elevation.

Selection of ground motion

With reference to the principle of wave selection and amplitude modulation of Vamvatsikos and Cornell (2002), the research of Luco and Cornell (2000) showed that the selection of 10–20 ground motion records for high-rise building structures can provide sufficient accuracy to evaluate seismic performance. Among 12 ground motion records were selected from the strong earthquake database of the United States Pacific Earthquake Research Center. The target response spectrum and design response spectrum are shown in Figure 10. The selected 12 ground motion response spectra are essentially consistent with the design response spectra of China.

Figure 10.

Seismic response spectrum.

Seismic vulnerability analysis

Definition of structural limit state

In the past, the maximum inter-storey drift angle was often chosen as the structural demand index (DM). However, the maximum inter-storey drift angle index only considered the damage caused by structural deformation and could not take the cumulative damage effect on the structure during an earthquake into consideration (Ye et al., 2018). Therefore, to analyze the structure’s performance under earthquake, this paper determined the state of various performances of the structure on the IDA curve and selected the damage index (D). The maximum inter-storey drift angle (θ) as the structural demand parameters for comparison with damage index (D). The values for the structural behavior points are shown in Table 4 and are in accordance with the United States Federal Emergency Management Agency recommendations (FEMA 283, 1996). The $S_{a}$ ( $T_{1}$ ,5%) index of ground motion intensity was selected according to the recommendation of Vamvatsikos and Cornell (2002).

Table 4.

Damage index limits corresponding to each performance level.

Different performance levels	Basically intact	Slight damage	Moderate damage	Severe damage	Collapse
$D_{K}$	0–0.1	0.1–0.25	0.25–0.4	0.4–0.8	>0.8
$θ_{max}$	0%–0.2%	0.2%–1%	1%–2%	2%–10%	>10% or 0.2 $K_{e}$

Source: Where $D_{K}$ is the damage index value of the Kunnath model and $K_{e}$ is the slope of the initial elastic stage of the IDA curve.

IDA analysis

It can be seen from Figure 11 that the developmental trends of the IDA curves based on Jinping Ou, Park–Ang, and Author are essentially the same. Among the three weighting methods, Park–Ang had the largest damage value when the structure was subject to the same damage as the ground motion intensity. This is because Park–Ang does not consider the importance of floor position. The damage contribution value of the non-first floors of the frame structure is too high. It is assumed that when a certain amount of damage occurs to the structure above the first floor, it has the same effect as when the damage occurs to the first floor. However, the first floor of the frame structure is usually the softest storey of the structure, and its damage is generally the most serious one (Lin et al., 2009), so the damage to the first floor should be noted. Jinping Ou and Author both take the importance of the floor position of the frame structure into consideration. By considering the importance of the first floor, the accuracy of the degree of damage of the first floor versus the whole frame is improved. The results obtained by the two methods are relatively close, which shows that the weighting method in this paper has certain feasibility.

Figure 11.

IDA curve based on three weighting methods: (a) IDA curve of PRCS and (b) IDA curve of CRCS.

From Figures 11 and 12 it can be seen that the IDA curves using the two-parameter damage model and the maximum inter-storey drift angle model in the initial elastic stage are less discrete degree. As the damage degree continued to increase and the structure entered the plastic phase, the discrete degree of the IDA curve using the two-parameter damage model and the IDA curve using the maximum inter-storey drift angle model gradually increased, this is primarily due to the varying parameters of different ground motions. But the IDA curve discrete of the two-parameter damage model in the plastic stage was less than that of the IDA curve of the maximum inter-storey drift angle model. Moreover, the IDA curves using the two-parameter damage model were all softened types, however the IDA curves using the maximum inter-storey drift angle were either softened types or over-softened types. In summary, this shows that the IDA curve using the two-parameter damage model has better overall stability. To further verify the superiority of the two-parameter damage model as the structure’s demand parameter and the accuracy of the weighting method in this paper, the related seismic vulnerability was analyzed.

Figure 12.

IDA curve based on maximum interstory displacement angle: (a) IDA curve of PRCS and (b) IDA curve of CRCS.

Structural seismic probability demand model

Cornell et al. (2002) demonstrated that the structural demand parameter (DM) and the ground motion intensity parameter (IM) obey the following relationship:

\ln DM = \ln (a) + b \cdot \ln (IM) = A + B \cdot \ln (IM)

(9)

where A and B are unknowns and can be obtained by regression analysis.

By performing linear regression on Figures 11 and 12, an earthquake probability demand model based on three weighted combination modes of the PRCS and CRCS using a two-parameter damage model and an earthquake probability demand model based on the maximum inter-storey drift angle can be obtained. In Figures 13 to 15, A and B are the coefficients of equation (9), and R² is the degree of linear fitting.

Figure 13.

Seismic probability demand model based on maximum interstory displacement angle: (a) seismic probability demand model of PRCS and (b) seismic probability demand model of CRCS.

Figure 14.

Seismic probability demand model of PRCS: (a) based on Jinping Ou combination, (b) based on Park–Ang combination, and (c) based on Author combination.

Figure 15.

Probability demand model of CRCS: (a) based on Jinping Ou combination, (b) based on Park–Ang combination, and (c) based on Author combination.

Structural seismic vulnerability analysis

Assuming that the structural seismic demand parameter (DM) and the ground motion intensity parameter (IM) both obey the logarithmic normal distribution (Haluk et al., 1998), the formula for the probability of overtaking at a specific stage of the structure is (Ji et al., 2007).

P_{f} = Φ [\frac{\ln \bar{\hat{D}} \ln \hat{C}}{\sqrt{β_{c}^{2} + β_{d}^{2}}}]

(10)

where $P_{f}$ is the failure probability of the structural response to surpass a specific stage under the action of earthquake, $\hat{D}$ is the average of the structural demand parameters, $\hat{C}$ is the average of the structural capacity parameters, $β_{d}$ is the logarithmic standard deviation of $\hat{D}$ , $β_{c}$ is the logarithmic standard deviation of $\hat{C}$ , and $\sqrt{β_{c}^{2} + β_{d}^{2}}$ is recommended to be 0.4.

It can be seen from Figure 16 that based on a weighted damage model proposed in this paper, the development trend of vulnerability curves of PRCS and CRCS are basically the same. It can be seen that the damage weighted model proposed in this paper has certain credibility, which can provide a damage weighting method for damage index which mainly uses energy consumption.

Figure 16.

Seismic vulnerability curves of PRCS and CRCS: (a) slight damage, (b) moderate damage, (c) serious destruction, and (d) collapse failure.

It can be seen from Figure 16 that the PRCS and CRCS have the following characteristics: (1) At the slight failure stage, at the same probability of overtaking, the ground motion intensity corresponding to the vulnerability curve based on the maximum inter-storey drift angle model is smaller than that of the two-parameter damage model’s vulnerability curve. This is because the structure is still in the elastic phase at this time. The maximum inter-storey drift angle model holds that the structure does not have energy consumption in this stage, whereas the two-parameter damage model considers the energy consumption of the structure in this stage, so it can withstand a greater intensity of ground motion. (2) As the degree of structural damage deepens, the vulnerability curve based on the maximum inter-storey drift angle model shows a trend of shifting to the right, indicating that as the intensity of ground motion continues to increase, the model based on the maximum inter-storey drift angle model will makes the damage assessment of the structure is relatively small, that is, using the maximum inter-storey drift angle model will overestimate the structure’s collapse resistance. At the collapse failure stage, when the vulnerability curve based on the maximum inter-storey drift angle model reaches the probability of overtaking of 1.0, the ground motion intensity of the PRCS and CRCS are respectively $S_{a - PRCS}$ = 5.8 g, $S_{a - CRCS}$ = 11.35 g, which are greater than the ground motion intensity value based on the two parameter damage model, and 70% (Jingpin Ou), 56% (Park–Ang), 56% (Author) respectively for the PRCS, for the CRCS, it is 83% (Jingpin Ou), 77% (Park–Ang), and 67% (Author) larger respectively. It shows that the maximum inter story displacement angle model can overestimate the collapse resistance of the PRCS by 60.7% on average, and the collapse resistance of the CRCS by 75.67% on average.

It can be seen from Figure 16 that in the state of slight damage, the seismic strength of the PRCS and CRCS when the probability exceeds 1.0 is in the range of 0.85 to 1.0 g. At this stage, the seismic performance of the PRCS and CRCS is relatively similar. With the increase of ground motion intensity, the ground motion intensity of the PRCS and CRCS surpasses the probability of 1.0 under the conditions of moderate damage, severe damage, and collapse: $S_{a - PRCS}$ =1.6 g, $S_{a - CRCS}$ =2.05 g, $S_{a - PRCS}$ =1.6 g, $S_{a - CRCS}$ =2.55 g, $S_{a - PRCS}$ =2.55 g, and $S_{a - CRCS}$ = 4.55 g. The ground motion strengths of the PRCS and CRCS differed by 21.95%, 37.25%, and 41.38%, respectively, indicating that the seismic performance gap between the PRCS and CRCS will increase with an increase in seismic intensity. This is mainly due to the lack of stiffness in the PRCS of the outsource steel tube, and the possibility of local buckling, which aggravates the damage of the assembled structure.

Conclusion

In this paper, a simplified PRCS is established and how to use the two-parameter damage model in seismic vulnerability analysis is given. The following conclusions can be drawn accordingly:

(1) Through a comparative analysis of the Kunnath two-parameter damage model and the maximum inter-storey drift angle model, this paper finds that the inter-storey drift angle model not only underestimates the seismic performance of the structure in the elastic phase but also overestimates the structure’s plasticity Anti-collapse ability, for the PRCS overestimates 60.7%, and for the CRCS overestimates 75.67%. The two-parameter damage model fully considers the hysteretic energy consumption in the elastic phase and nonlinear deformation in the plastic phase, so the results are more accurate.

(2) This research, based on SAP2000’s multi-segment linear plastic connection unit, well simulates prefabricated column–column joints, and solves the problems of the traditional solid element model, which is difficult to converge and requires a lot of calculation. By analyzing the seismic performance of PRCS and CRCS, the research found that the seismic performance of PRCS can reach the equivalent of CRCS in the slight damage stage, but as the intensity of ground motion increases, the gap between the seismic performance of the PRCS and the CRCS also increases.

(3) According to the new damage index-weighted combination method proposed in this article, the development trend of the IDA curve and the vulnerability curve corresponding to Jinping Ou and Park–Ang is consistent and has good agreement, which shows that damage weighted model in this paper is feasible. The damage weighted model in this paper can provide a method for damage analysis considering energy consumption and deformation.

Footnotes

Authors’ note

We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us. We confirm that we have given due consideration to the protection of intellectual property associated with this work and that there are no impediments to publication, including the timing of publication, with respect to intellectual property. In so doing we confirm that we have followed the regulations of our institutions concerning intellectual property.

Declaration of conflicting interests

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

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Jiaolei Zhang

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Seismic vulnerability of prefabricated reinforced concrete frame structure based on local outsource steel tube bolted column–column connection

Abstract

Keywords

Highlights

Introduction

Test introduction and damage model selection

Test specimen design parameters

Two-parameter damage model

Simplified calculation method for Park–Angdamage model

Weighted combination of damage models

Structural model and ground motion selection

Establishment of column–column model

Establishment of the framework structure model

Selection of ground motion

Seismic vulnerability analysis

Definition of structural limit state

IDA analysis

Structural seismic probability demand model

Structural seismic vulnerability analysis

Conclusion

Footnotes

Authors’ note

Declaration of conflicting interests

Funding

ORCID iD

References