# Seismic Fragility of Chinese Light-Gauge Steel Keel Gypsum Board Partition Walls

Authors: Duozhi Wang; Xudong Zhi; Fangxu Zhu; Yixing Wang
Journal: Shock and Vibration
 (2021)

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## Abstract

A quasi-static experimental program of light-gauge steel keel gypsum board partition walls (LSKGBPW) was carried out to evaluate the seismic damage phenomena, failure mechanisms, and fragility. The 15 specimens in five groups were designed per current Chinese codes and engineering practice. Then, three damage states were defined based on the damage and repair measures, and the fragility data of each group were presented, providing basic data for the estimation of seismic damage and consequential loss of nonstructural components.


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## Body

## 1. Introduction

Structural damage (especially collapse) due to an earthquake often receives much attention. Accordingly, the mitigation of structural damage and human casualties has been regarded as the primary guiding principle in the seismic design codes of various countries and achieved remarkable results. However, the importance of nonstructural seismic safety has been largely ignored. In recent years, nonstructural seismic damages have led to enormous economic losses and impacted the resilience and postearthquake operations of buildings severely; hence, an increasing number of researchers have begun to pay attention to the seismic performance of nonstructural systems [1–5].Nonstructural systems consist of three parts: the nonstructural building components, the mechanical, electrical, and plumbing (MEP) systems, and the housed instruments and equipment. Even if the structure is still usable, severe nonstructural seismic damage will not only cause very high economic losses but also seriously affect the postearthquake operation and reduce the seismic resilience of the building. The light-gauge steel keel gypsum board partition wall (LSKGBPW) is a widely used nonstructural building component in modern high-rise buildings. It is mainly composed of light-gauge steel keels, gypsum boards, and connectors. The LSKGBPW is a common component for partitioning large spaces and is easy to install and remove. However, this type of wall often suffers severe damage in earthquakes [6, 7], and the damage usually occurs under low-intensity earthquakes, not only causing a very large amount of property loss but also hindering postearthquake repair work [8]. Therefore, research on the seismic behavior of LSKGBPWs can improve the seismic performance of the component itself and help to enhance the seismic resilience of the building.Research on the LSKGBPW has been conducted for a long time. Freeman and Rihal were among the earliest researchers, the performance of partition walls was studied experimentally [9, 10]. McMullin and Merrick conducted tests to analyze the fragility of the wood frame gypsum board partition [11]. Reynaud et al. conducted tests with 17 light-gauge steel keel partition components with both length and width of 8 feet [12]. Their study showed that a gypsum board partition wall has lower shear strength than a plywood wall, and gypsum boards arranged transversely have a higher stiffness than those arranged vertically. Lee et al. carried out hysteresis tests on four full-scale LSKGBPWs [13] and investigated the effects of opening doors and return wall sections on the seismic performance of the wall. Davies et al. constructed an I-shaped LSKGBPW model and used it to investigate the performance-based seismic design method for nonstructural components. They defined three damage states and the provided the interstory drift ratio corresponding to each damage state based on the test results. Davies et al. designed full-scale LSKGBPWs and conducted tests [14, 15]. A total of 55 full-scale components with a variety of construction types were tested using the methods of in-plane loading, out-of-plane loading, quasi-static testing, and dynamic testing. A parametric hysteresis model of LSKGBPWs was established and used to simulate the in-plane stress performance of the wall. At last, the time-history analysis of an actual case was carried out, showing that the lateral stiffness of the building was improved by considering the contribution of LSKGBPWs. Padilla-Llano et al. performed axial tensile tests on light-gauge steel keels with C sections [16], including 12 cyclic tests, 12 monotonic compression tests, and 2 monotonic tensile tests, and evaluated the hysteretic behavior, strength degradation, and energy dissipation characteristics of the light-gauge steel keels with C sections. Amer et al. conducted research on LSKGBPWs with dampers [17]. Quasi-static tests were performed with a varying number of dampers, showing that the ultimate bearing capacity of the wall with dampers was greatly increased. Rahmanishamsi et al. conducted monotonic loading tests and hysteretic tests to study the performance of LSKGBPWs [18–21], including 31 gypsum board steel stud connection specimens, 33 steel stud-track connection specimens, and 22 track-floor connection specimens. In addition, a series of nonlinear plasticity models of partition wall joints were developed in OpenSees for numerical analysis of the wall. Later, Jenkins et al. conducted a shaking table test on a two-story one-bay steel frame-LSKGBPW and evaluated the performance of the LSKGBPW [22].In this study, quasi-static tests on LSKGBPWs designed and installed based on Chinese codes and engineering practice are carried out, the damage phenomena and failure mechanisms are analyzed, three damage states are established based on damage phenomena and repair measures, the fragility data of each group are presented, and the effects of the partition wall-structure connection types on the performance and fragility of the partition wall are examined, providing basic data for the assessment of the seismic resilience of buildings considering nonstructural components.


## 2. Experimental Scheme and Results

### 2.1. Loading Apparatus

The tests were conducted in the structural laboratory of the Harbin Institute of Technology, with the aim to investigate seismic damage phenomena, failure mechanisms, and fragility of LSKGBPWs as well as the effects of the partition wall-structure connection type on the performance and fragility. The partition wall is a self-supporting component that only bears its own weight. Therefore, it is necessary to design a test apparatus that is easy to load and does not affect the actual performance of the partition wall. The test apparatus includes a single-story steel frame, lateral displacement-limiting device, roof/floor concrete slab, and high-precision electrohydraulic servo actuator. There is no joint connection between the beam and the column of the steel frame, but a rolling is installed on the top of the column to support the steel beam. The reinforced concrete roof slab is fixed under the steel beam through the embedded parts, and the roof slab can be replaced during the test. Displacement-limiting devices are installed on both sides of the roof slab to ensure that the roof slab only moves in the horizontal loading direction. As the steel beam moves horizontally, it drives the roof slab to move in the same direction to load the partition wall. The floor slab is fixed on the ground by anchor bolts. The top and bottom parts of the partition wall are fixed to the roof slab and the floor slab, respectively. During the test, the lateral load is provided by the high-precision electrohydraulic servo actuator. The horizontal force transfer path is actuator ⟶ steel beam ⟶ roof slab ⟶ partition wall [23]. Figures 1 and 2 show the I-shaped partition wall specimen tested.Figure 1
Loading apparatus.Figure 2
The specimen.


### 2.2. Test Specimens

In the tests, the lateral resistance performance of LSKGBPWs under horizontal low-cycle reciprocating load was investigated. Figure3 shows the view of the LSKGBPW design, and the construction details of the partition wall connection are shown in Figure 4. Table 1 lists the parameters of the specimens. All specimens met the code in the Light-gauge Steel Keel Gypsum Board Partition Wall and Suspended Ceiling standard [24]. The variables considered in the selection of the wall configurations include the following:(1)
The specimens were the independent I-shaped full-scale (1 : 1) partition walls with a height of 3 m and a span of 3 m, as the top and bottom tracks connect with roof slab and floor slab, respectively, as illustrated in Figure2.(2)
The detail of construction is illustrated in Figure3.(3)
The size of a single gypsum board is 3 m × 1.2 m × 12 mm according to Chinese code GB-T9775 (GB 2008).(4)
The U-shape track connects with the roof and floor slabs by shot pins, shot pin-backing plate, and expansion bolt, as illustrated in Figure4. The specimens were distinguished to five groups by the connection types as listed in Table 1.(5)
The size of U-shape track is 75 mm × 35 mm × 0.55 mm, as the size of C-shape steel stud is 73.5 mm × 45 mm × 0.55 mm as listed in Table1.(6)
The U-shape track connects with the C-shape steed stud by self-tapping screw spacing 600 mm. The gypsum board connects with steel stud and track by self-tapping screw spacing 200 mm.(7)
The gap was finished with caulking tapes and caulking plaster, as the external corner was protected with connerbead and caulking plaster.Figure 3
Section of the specimen design.Figure 4
Detail of construction (a) T joint. (b) The edge joint. (c) The top track joint. (d) The bottom track joint. (e) The bottom track joint with backing plate.
(a)(b)(c)(d)(e)Table 1
Information of partition wall specimens.
GroupNo.Connection type between track and floor slabConnection distance between shot pins (mm)C-shaped steel stud mm × mm × mmU-shaped track mm × mm × mmGypsum boardAA1Shot pin60073.5 × 45 × 0.5575 × 35 × 0.553 m × 1.2 m × 12 mmA2A3BB1Shot pin40073.5 × 45 × 0.5575 × 35 × 0.553 m × 1.2 m × 12 mmB2B2CC1Shot pin20073.5 × 45 × 0.5575 × 35 × 0.553 m × 1.2 m × 12 mmC2C3DD1Shot pin-backing plate20073.5 × 45 × 0.5575 × 35 × 0.553 m × 1.2 m × 12 mmD2D3EE1Expansion bolt20073.5 × 45 × 0.5575 × 35 × 0.553 m × 1.2 m × 12 mmE2E3


### 2.3. Loading Regime

The tests were conducted in the structural laboratory of the Harbin Institute of Technology. A high-precision electrohydraulic servo actuator was used to apply a horizontal low-cycle reciprocating load parallel to the wall.The loading regime was based on that proposed by Retamales et al, which was developed specifically to assess the fragility of nonstructural components that are sensitive to interstory drift [25]. In the method, the predicted interstory drift demand of nonstructural specimens is described by using a set of closed-form equations that should simultaneously satisfy the following conditions: (1) the ground response spectrum should be matched; (2) the target interstory drift ratio should be applied to the specimen; and (3) the number of story movement cycles applied to the specimen should be the same as that in actual seismic records. The displacement record generated based on this loading regime is shown in Figure 5. The LSKGBPW has a relatively low lateral stiffness, and its damage process is sensitive to the interstory drift ratio. This loading regime is characterized by many steps and small increments per step and can record in detail the variation processes of the interstory drift ratio and failure of the specimens, satisfying the needs of fragility research. The loading regime uses displacement control throughout the entire process with the minimum displacement increment of 0.5 mm. As loading progresses, the displacement increment per step increases gradually. In the tests, displacement sensors are placed in the middle of the reinforced concrete roof and floor to measure the displacement and calculate the interstory drift ratio.Figure 5
Loading regime.


### 2.4. Experimental Results

The damage characteristics of the LSKGBPW are described in detail in Table2 and Figure 6. The damage processes and characteristics of groups A, B, and C are similar, reflecting the influence of the shot pin distance, while those of groups C, D, and E reflect the effect of the connection type on the damage phenomena.Table 2
Failure patterns.
GroupNumber of specimensConnection typeConnection distance (mm)Damage phenomenaA3Shot pin600Cracks in the gypsum boards of the transverse walls on both sides, Figure6(a); cracks in the internal corner, Figure 6(b); loose, dislodged, sheared shot pins at the connection, Figure 6(c); tearing of the track, Figure 6(d); separation of the transverse and longitudinal wall, Figure 6(e).B3Shot pin400C3Shot pin200D3Shot pin-backing plate200Cracks in the gypsum boards of the transverse walls on both sides; cracks in the internal corner; loosening, dislodging, and shearing off of the shot pins at the connection; tearing of the track; separation of the transverse and longitudinal walls; cracking between the gypsum boards of the longitudinal wall, Figure6(f).E3Expansion bolt200Cracks appearing in the transverse walls on both sides, cracks in the internal corner, cracks between the gypsum boards of the longitudinal wall, loosening and dislodging of the self-tapping screws between the gypsum board and the keel, Figure6(g), local crushing of the gypsum boards, Figure 6(h), local separation of the gypsum board and keel, Figure 6(i), severe local buckling of the steel stud, Figure 6(j).Figure 6
. Damage phenomena. (a) Crack of the gypsum boards in the transverse wall. (b) Crack at the internal corner. (c) Loosening of a shot pin. (d) Tearing of the track at the shot pin connection. (e) Separation of the transverse wall from the longitudinal wall. (f) Crack at the connection of the gypsum boards of the longitudinal wall. (g) Pulling out self-tapping screw in the gypsum board. (h) Crushing of the gypsum board. (i) Separation of the gypsum board from the steel stud. (j) Severe buckling of the steel stud.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)Based on the damage characteristics of groups A, B, and C, it is found that, when the distance between shot pins was small, the damage on the partition wall-structure connection was delayed under the same load. Figures7(a)∼7(c) show the hysteresis loops observed for specimen in group A to C, respectively. Then, according to the damage characteristics of the specimens in group D, the backing plate strengthened the local track and could prevent it from tearing effectively. However, the damage to the partition wall-structure connection was dominated by shearing of the shot pins after adding the backing plates, while the partition wall-structure connection was affected by both the strength of the track and the strength of the shot pins. Therefore, the backing plate could not strengthen the partition wall-structure effectively, and the damage phenomena of the specimens in group D were similar to groups A, B, and C. Figure 7(d) shows the hysteresis loops observed for specimen in group D.Figure 7
Hysteresis behaviors of specimens. (a) Specimen in group A. (b) Specimen in group B. (c) Specimen in group C. (d) Specimen in group D. (e) Specimen in group E.
(a)(b)(c)(d)(e)In group E, first, the self-tapping screws at the edge of gypsum board were loosened. Then, the gypsum boards at the corner were crushed, and the self-tapping screws were loosened and pulled out severely. Crack occurred at the connection of two gypsum boards on the longitudinal wall. Finally, the steel stud buckled severely, or the gypsum boards were separated from each other on the longitudinal wall, and the specimen was failed. Compared to other specimens, the specimens of group E did not show any damage on the partition wall-structure connection, due to the strong expansion bolt, but the more self-tapping screws loosened or were pulled out, and the steel stud buckled. The damage phenomena of group E were different from other specimens, showing that strengthening the partition wall-structure connection could change the damage phenomena of the partition wall. Figure7(e) shows the hysteresis loops observed for specimen in group E.


## 2.1. Loading Apparatus

The tests were conducted in the structural laboratory of the Harbin Institute of Technology, with the aim to investigate seismic damage phenomena, failure mechanisms, and fragility of LSKGBPWs as well as the effects of the partition wall-structure connection type on the performance and fragility. The partition wall is a self-supporting component that only bears its own weight. Therefore, it is necessary to design a test apparatus that is easy to load and does not affect the actual performance of the partition wall. The test apparatus includes a single-story steel frame, lateral displacement-limiting device, roof/floor concrete slab, and high-precision electrohydraulic servo actuator. There is no joint connection between the beam and the column of the steel frame, but a rolling is installed on the top of the column to support the steel beam. The reinforced concrete roof slab is fixed under the steel beam through the embedded parts, and the roof slab can be replaced during the test. Displacement-limiting devices are installed on both sides of the roof slab to ensure that the roof slab only moves in the horizontal loading direction. As the steel beam moves horizontally, it drives the roof slab to move in the same direction to load the partition wall. The floor slab is fixed on the ground by anchor bolts. The top and bottom parts of the partition wall are fixed to the roof slab and the floor slab, respectively. During the test, the lateral load is provided by the high-precision electrohydraulic servo actuator. The horizontal force transfer path is actuator ⟶ steel beam ⟶ roof slab ⟶ partition wall [23]. Figures 1 and 2 show the I-shaped partition wall specimen tested.Figure 1
Loading apparatus.Figure 2
The specimen.


## 2.2. Test Specimens

In the tests, the lateral resistance performance of LSKGBPWs under horizontal low-cycle reciprocating load was investigated. Figure3 shows the view of the LSKGBPW design, and the construction details of the partition wall connection are shown in Figure 4. Table 1 lists the parameters of the specimens. All specimens met the code in the Light-gauge Steel Keel Gypsum Board Partition Wall and Suspended Ceiling standard [24]. The variables considered in the selection of the wall configurations include the following:(1)
The specimens were the independent I-shaped full-scale (1 : 1) partition walls with a height of 3 m and a span of 3 m, as the top and bottom tracks connect with roof slab and floor slab, respectively, as illustrated in Figure2.(2)
The detail of construction is illustrated in Figure3.(3)
The size of a single gypsum board is 3 m × 1.2 m × 12 mm according to Chinese code GB-T9775 (GB 2008).(4)
The U-shape track connects with the roof and floor slabs by shot pins, shot pin-backing plate, and expansion bolt, as illustrated in Figure4. The specimens were distinguished to five groups by the connection types as listed in Table 1.(5)
The size of U-shape track is 75 mm × 35 mm × 0.55 mm, as the size of C-shape steel stud is 73.5 mm × 45 mm × 0.55 mm as listed in Table1.(6)
The U-shape track connects with the C-shape steed stud by self-tapping screw spacing 600 mm. The gypsum board connects with steel stud and track by self-tapping screw spacing 200 mm.(7)
The gap was finished with caulking tapes and caulking plaster, as the external corner was protected with connerbead and caulking plaster.Figure 3
Section of the specimen design.Figure 4
Detail of construction (a) T joint. (b) The edge joint. (c) The top track joint. (d) The bottom track joint. (e) The bottom track joint with backing plate.
(a)(b)(c)(d)(e)Table 1
Information of partition wall specimens.
GroupNo.Connection type between track and floor slabConnection distance between shot pins (mm)C-shaped steel stud mm × mm × mmU-shaped track mm × mm × mmGypsum boardAA1Shot pin60073.5 × 45 × 0.5575 × 35 × 0.553 m × 1.2 m × 12 mmA2A3BB1Shot pin40073.5 × 45 × 0.5575 × 35 × 0.553 m × 1.2 m × 12 mmB2B2CC1Shot pin20073.5 × 45 × 0.5575 × 35 × 0.553 m × 1.2 m × 12 mmC2C3DD1Shot pin-backing plate20073.5 × 45 × 0.5575 × 35 × 0.553 m × 1.2 m × 12 mmD2D3EE1Expansion bolt20073.5 × 45 × 0.5575 × 35 × 0.553 m × 1.2 m × 12 mmE2E3


## 2.3. Loading Regime

The tests were conducted in the structural laboratory of the Harbin Institute of Technology. A high-precision electrohydraulic servo actuator was used to apply a horizontal low-cycle reciprocating load parallel to the wall.The loading regime was based on that proposed by Retamales et al, which was developed specifically to assess the fragility of nonstructural components that are sensitive to interstory drift [25]. In the method, the predicted interstory drift demand of nonstructural specimens is described by using a set of closed-form equations that should simultaneously satisfy the following conditions: (1) the ground response spectrum should be matched; (2) the target interstory drift ratio should be applied to the specimen; and (3) the number of story movement cycles applied to the specimen should be the same as that in actual seismic records. The displacement record generated based on this loading regime is shown in Figure 5. The LSKGBPW has a relatively low lateral stiffness, and its damage process is sensitive to the interstory drift ratio. This loading regime is characterized by many steps and small increments per step and can record in detail the variation processes of the interstory drift ratio and failure of the specimens, satisfying the needs of fragility research. The loading regime uses displacement control throughout the entire process with the minimum displacement increment of 0.5 mm. As loading progresses, the displacement increment per step increases gradually. In the tests, displacement sensors are placed in the middle of the reinforced concrete roof and floor to measure the displacement and calculate the interstory drift ratio.Figure 5
Loading regime.


## 2.4. Experimental Results

The damage characteristics of the LSKGBPW are described in detail in Table2 and Figure 6. The damage processes and characteristics of groups A, B, and C are similar, reflecting the influence of the shot pin distance, while those of groups C, D, and E reflect the effect of the connection type on the damage phenomena.Table 2
Failure patterns.
GroupNumber of specimensConnection typeConnection distance (mm)Damage phenomenaA3Shot pin600Cracks in the gypsum boards of the transverse walls on both sides, Figure6(a); cracks in the internal corner, Figure 6(b); loose, dislodged, sheared shot pins at the connection, Figure 6(c); tearing of the track, Figure 6(d); separation of the transverse and longitudinal wall, Figure 6(e).B3Shot pin400C3Shot pin200D3Shot pin-backing plate200Cracks in the gypsum boards of the transverse walls on both sides; cracks in the internal corner; loosening, dislodging, and shearing off of the shot pins at the connection; tearing of the track; separation of the transverse and longitudinal walls; cracking between the gypsum boards of the longitudinal wall, Figure6(f).E3Expansion bolt200Cracks appearing in the transverse walls on both sides, cracks in the internal corner, cracks between the gypsum boards of the longitudinal wall, loosening and dislodging of the self-tapping screws between the gypsum board and the keel, Figure6(g), local crushing of the gypsum boards, Figure 6(h), local separation of the gypsum board and keel, Figure 6(i), severe local buckling of the steel stud, Figure 6(j).Figure 6
. Damage phenomena. (a) Crack of the gypsum boards in the transverse wall. (b) Crack at the internal corner. (c) Loosening of a shot pin. (d) Tearing of the track at the shot pin connection. (e) Separation of the transverse wall from the longitudinal wall. (f) Crack at the connection of the gypsum boards of the longitudinal wall. (g) Pulling out self-tapping screw in the gypsum board. (h) Crushing of the gypsum board. (i) Separation of the gypsum board from the steel stud. (j) Severe buckling of the steel stud.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)Based on the damage characteristics of groups A, B, and C, it is found that, when the distance between shot pins was small, the damage on the partition wall-structure connection was delayed under the same load. Figures7(a)∼7(c) show the hysteresis loops observed for specimen in group A to C, respectively. Then, according to the damage characteristics of the specimens in group D, the backing plate strengthened the local track and could prevent it from tearing effectively. However, the damage to the partition wall-structure connection was dominated by shearing of the shot pins after adding the backing plates, while the partition wall-structure connection was affected by both the strength of the track and the strength of the shot pins. Therefore, the backing plate could not strengthen the partition wall-structure effectively, and the damage phenomena of the specimens in group D were similar to groups A, B, and C. Figure 7(d) shows the hysteresis loops observed for specimen in group D.Figure 7
Hysteresis behaviors of specimens. (a) Specimen in group A. (b) Specimen in group B. (c) Specimen in group C. (d) Specimen in group D. (e) Specimen in group E.
(a)(b)(c)(d)(e)In group E, first, the self-tapping screws at the edge of gypsum board were loosened. Then, the gypsum boards at the corner were crushed, and the self-tapping screws were loosened and pulled out severely. Crack occurred at the connection of two gypsum boards on the longitudinal wall. Finally, the steel stud buckled severely, or the gypsum boards were separated from each other on the longitudinal wall, and the specimen was failed. Compared to other specimens, the specimens of group E did not show any damage on the partition wall-structure connection, due to the strong expansion bolt, but the more self-tapping screws loosened or were pulled out, and the steel stud buckled. The damage phenomena of group E were different from other specimens, showing that strengthening the partition wall-structure connection could change the damage phenomena of the partition wall. Figure7(e) shows the hysteresis loops observed for specimen in group E.


## 3. Seismic Fragility Analysis

In accordance with the fragility test method in the ATC-58 Guidelines for the Seismic Performance Assessment of Buildings, the interstory drift ratio was used as the demand parameter for the fragility analysis of the nonstructural partition walls, quasi-static tests were conducted to obtain the data of the damage process of the LSKGBPWs, and the fragility curves of each group of specimens were calculated and comparatively analyzed.To perform the fragility analysis, the damage phenomena observed during the tests were classified into three damage states in Table3. The damage states of the partition wall were defined based on its damage characteristics and the corresponding repair measures. The damage state DS1 refers to damage to the decorative surface only, the damage state DS2 means that part of the LSKGBPW needs to be replaced, and damage state DS3 corresponds to the removal of the entire partition wall. Table 4 lists the measured interstory drift ratios corresponding to each damage state.Table 3
Division of damage states of LSKGBPWs.
Damage stateDescription of damageRepair measureDS1Cracks starting in the gypsum boards, slipping of the partition wall-structure connection, loosening of the self-tapping screws around the gypsum board. Cracks in the middle of the gypsum boards of the transverse wall.Replacement of the corner beads, caulking tapes, and loose self-tapping screws and surface plastering.DS2Cracks between the gypsum boards of the longitudinal wall, crushing of the gypsum boards at the wall corner, failure of the self-tapping screws around the gypsum board or loosening of the self-tapping screws in the middle of the gypsum boards.Replacement of the entire gypsum board and reinstallation of the self-tapping screws around the partition wall.DS3Failure of the partition wall-structure connection, separation of the gypsum board from the steel stud, local bending, and plastic hinge occurring in the steel stud.Removal of the damaged partition wall and installation of a new one.Table 4
Specimen damage state and interstory drift ratio (unit: %).
Damage stateDamage characteristicsA1A2A3B1B2B3C1C2C3D1D2D3E1E2E3DS1Cracks starting in the gypsum boards0.570.290.220.650.440.200.310.440.260.350.250.230.290.250.29Slipping of the partition wall-structure connection0.250.320.200.250.610.250.470.350.500.390.410.35———Loosening of the self-tapping screws around the gypsum board————————0.790.53——0.570.390.44Minimum drift level triggeringDS10.250.290.200.250.440.200.310.350.260.350.250.230.290.250.29DS2Cracks in the middle of the gypsum boards of the transverse wall0.740.960.831.021.090.900.900.840.791.721.261.36———Cracks between the gypsum boards of the longitudinal wall———1.021.861.591.721.591.360.901.021.021.360.871.17Crushing of the gypsum boards at the wall corner————————————0.840.741.09Failure of the self-tapping screws around the gypsum board or loosening of the self-tapping screws in the middle of the gypsum boards——————————1.72—1.261.591.72Minimum drift level triggeringDS20.740.960.831.021.090.900.900.840.790.901.021.020.840.741.09DS3Failure of the partition wall-structure connection0.901.720.901.262.340.842.011.261.090.901.471.17———Separation of the gypsum board from the steel stud————————————0.901.121.47Local bending and plastic hinge occurring in the steel stud————————————1.361.261.09Minimum drift level triggeringDS30.901.720.901.262.340.842.011.261.090.901.471.170.901.121.09Note: data in the table are interstory drift ratios (unit: %).The fragility functionFdm is defined as the probability that the LSKGBPW attains or exceeds the damage state dm given the interstory drift ratio edp. This function is expressed by a lognormal distribution as follows:(1)Fdmedp=Φlnedp/xmβ,where Φ is the cumulative standard normal (Gaussian) distribution function, xm is the mean of this distribution, and β is the logarithmic standard deviation of this distribution. Since the lognormal distribution model is very capable of fitting the failure data of various structural and nonstructural components, it has been widely and effectively used as a fragility function model in seismic fragility analysis [26]. Each damage state of each group of specimens with different construction configurations corresponds to a fragility function curve defined by xm and β, as shown in equations (2) to (5). The maximum likelihood estimation (MLE) method can be used to calculate the MLE values of xm and β according to the specimen data obtained experimentally. Table 5 gives the equations for calculating the MLE values of xm and β:(2)μ=1M∑i=1Mlnrij,(3)σ2=1M∑i=1Mlnrij−μ2,(4)β=σ2,(5)xmj=eμ+σ2,where j = 1, 2, and 3 denote the three damage states of a specimen, i represents the ith specimen in a group of specimens for fragility analysis, rij denotes the interstory drift ratio that triggers the jth damage state of the ith specimen, and M is the number of specimens in a group of specimens for fragility analysis, where M=3 in this study. The fragility curves are shown in Figures 8–12.Table 5
Summary of fragility curve parameters.
Damage stateABCDExmβxmβxmβxmβxmβDS10.2570.1920.2960.3320.3070.1220.2770.1810.2770.070DS20.8430.1071.0030.0790.8430.0530.9800.0590.8900.161DS31.1700.3051.4790.4211.4510.2611.1800.2001.1630.201Figure 8
Fragility curves for group A.Figure 9
Fragility curves for group B.Figure 10
Fragility curves for group C.Figure 11
Fragility curves for group D.Figure 12
Fragility curves for group E.The fragility curves of the 5 groups of specimens are comparatively analyzed. There are three types of partition wall-structure connections (the shot pin connections, the shot pin-backing plate connections, and the expansion bolt connections) in the tests, and the connection distance of shot pin was set to 200 mm, 400 mm, and 600 mm. Moreover, the damage of the specimen can be divided into two types by the location, partition wall-structure connection damage, and partition wall damage; and the two types of damage coexisted in the tests.When the partition wall-structure connection was strengthened, the energy was transferred to the partition wall by the connection effectively, which aggravated the damage of the partition wall. Conversely, when the partition wall-structure connection was weak, the damage to the partition wall-structure connection became more severe. As the energy was dissipated by the damaged connection, the energy transferred to the partition wall was reduced, which led to little damage to the partition wall.It was found that an appropriate reduction of shot pin distance could improve the performance of the partition wall-structure connection. However, the performance of the specimen did not increase monotonously with the reduction of shot pin distance. For example, as the shot pin distance decreased from 400 mm to 200 mm, although the damage to the partition wall-structure connection was reduced, the damage of the specimen was not improved effectively.The shot pin-backing plate connections were used in group D to investigate the influence of the backing plate on the performance of specimen. However, compared with the fragility data of group C, it shows that the backing plate did not strengthen the partition wall-structure connection effectively. The damage to the partition wall-structural connection resulted from both shot pin damage and track tearing. Although the backing plate could reduce the damage caused by the tearing of the track, it did not protect the shot pins effectively. Therefore, the backing plate could only change the damage phenomena of the partition wall-structure joint and improve bearing capacity of specimen effectively.Compared to other specimens, the specimens in group E were constructed with expansion bolt connections, leading to the highest strength of the partition wall-structure joint, hence no failure of the joints in the tests. However, the specimen did not show improved performance. When the partition wall-structure joint was strengthened, more energy was transferred to the partition wall. Therefore, the specimen in group E did not appear better performance than others.The fragility curvesDS2 and DS3 are crossing in groups A, B, and D. The fragility curve is calculated by cumulative standard normal (Gaussian) distribution function, as the values of edp range from 0 to 3. As long as xm and β satisfy certain conditions, the curve may cross. There may be a complete damage of DS3 following the slight damage of DS1 for construction of groups A, B, and D. It belongs to brittle failure. In addition, subsequent studies will increase the number of specimens and continue to examine the crossing of fragility curves.


## 4. Conclusion

The quasi-static tests were carried out on full-scale light-gauge steel keel gypsum board partition wall (LSKGBPW) specimens in the structural laboratory of the Harbin Institute of Technology. A total of 15 I-shaped partition wall specimens in five groups were designed. Among them, four groups of specimens were designed per the construction methods in the current Chinese codes, and one group of specimens was designed according to the strengthening method used in engineering commonly.The five groups of specimens differed in the partition wall-structure connection, for which the damage phenomenon of the specimens was different. The damage of the specimens with shot pin connection or shot pin-backing plate connection (groups A, B, C, and D) was different from group E with expansion bolt connection. More partition wall-structure joint damage occurred in groups A to D, as more partition wall damage occurred in the group E.Three damage states are defined according to the damage level and repair measures, and the fragility data for groups with different types of construction are provided, offering basic data for the assessment of the seismic performance and resilience of buildings considering nonstructural components. First, an appropriate decrease of shot pin distance could improve the strength of the partition wall-structure connection, thereby improving the seismic performance of the specimen. However, the performance of the specimen was not improved monotonously as the shot pin distance decreased. The specimen appeared the similar better performance when the shot pin distance of the specimens was reduced from 400 mm to 200 mm. Then, the backing plate could change the damage phenomenon of the partition wall-structure joint, but it could not improve the performance effectively. Moreover, expansion bolt connection can change the damage location but did not improve the performance of the specimen.



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*Source: 8875486-2021-06-01.xml*