Experimental Fragility Analysis of Suspension Ceiling Systems Siavash Soroushian,a) Esmaeel Rahmanishamsi,a) Ki P. Ryu,b) Manos Maragakis,a) and Andrei M. Reinhornb) The seismic response of suspended ceiling systems that were shaken at the University at Buffalo; University of Nevada, Reno; and E-Defense facilities is critically assessed in this paper After presenting a brief description of each experiment, the most repetitive damage observations in all experiments are discussed. Fragility curves are developed for ceiling perimeter connectors, supporting elements, and overall performance of ceiling systems by using 346 combinations of ceiling configurations and shake intensities. The key findings of these curves are the insufficient support of the 7/8-in. wall angles, unconservative code design capacity of connections for supporting elements, and early damage of ceiling systems because of ceiling-piping interaction. Acceleration amplification factors of ceiling systems with respect to suspending floor are computed. The amplification factors prescribed by the code were found to be unconservative due to the pounding of panels to the ceiling grids and deck vibration in a vertical direction. INTRODUCTION The seismic performance of critical facilities depends not only on the performance of the structural systems, but also on the functionality of their nonstructural systems (Soroushian et al., 2013). Additionally, damage to nonstructural systems represents a threat to life, may seriously impair a building’s function, and may result in major direct and indirect economic losses (Pentangelo, 2010). Suspended ceilings are one of the most widely used nonstructural systems in commercial and residential buildings. Their damage can prevent a building from remaining operational after an earthquake and in some cases, may endanger the life and safety of its occupants (Echevarria et al., 2012). Suspended ceiling systems are prone to several forms of earthquake damage such as: failure of supporting elements, damage near the ceiling perimeter, failure of ceiling grid a) Dept. of Civil and Environmental Engineering, University of Nevada, Reno, MS 0258, Reno, NV 895570258 b) Dept. of Civil, Structural and Environmental Engineering, State University of New York at Buffalo, 222 Ketter Hall, Buffalo, NY 14260 connections, falling of ceiling panels and buckling of ceiling grid members. Nearly all of these failure modes have been observed in past earthquakes such as the 1989 Loma Prieta Earthquake (Ding, 1990), the 1994 Northridge Earthquake (Los Angeles Times, 1994), the 2006 Hawaii Earthquake (RMS, 2006), the 2010 Chile Earthquake (Miranda et al., 2012), the 2010 Haiti Earthquake (FEMA E-74, 2011), and the 2011 Christchurch (New Zealand) earthquake (Gilani et al., 2013). In order to evaluate and understand the dynamic response of ceiling systems, experiments using earthquake simulators (shaking tables) have been conducted for more than two decades (ANCO, 1983; Rihal et al., 1984; Reinhorn, 2000; Yao, 2000; Badillo et al., 2006; Reinhorn et al., 2010; Soroushian et al., 2012; Ryu and Reinhorn, 2013; Gilani et al., 2013; Rahmanishamsi et al., 2014). However, researchers (Gilani et al., 2013; Ryu et al., 2012) believe that current design standards such as the IBC (ICC, 2006), ASTM E580/E580M11be1 (2011), ASCE/SEI 7-05 (2010), AC368 (ICC, 2012), ASTM C635 (2013), and ASTM C636 (2013) do not explicitly provide any guidelines for the seismic design of such suspended “structures” due to their heterogeneous and complex construction. This, in part, is due to experimental restrictions in areas such as experimental setup, geometry, input excitations, and ceiling configurations. Realizing shortcomings of each of the previous studies, this paper aims to perform a comprehensive study by blending the results obtained from three of the largest (previous) experimental studies. Three experimental setups at University at Buffalo (UB); University of Nevada, Reno (UNR); and E-Defense shake table facilities were developed and are presented herein. The damage observations and a brief explanation of the similar failure mechanisms between all the experiments are provided. A concise description of the instrumentation and data processing procedure is presented, followed by the fragility methodology used in this study. Finally, the ceiling amplification factors and the fragility curves for ceiling perimeters, supporting elements, and overall performance of ceiling systems are discussed in detail. SUSPENDED CEILING SYSTEM Suspended ceiling systems are a nonstructural component installed within buildings to serve as an aesthetic barrier between electrical, mechanical, and piping systems and the living space below. A typical U.S.-style suspended ceiling system with acoustic tiles is composed of grid members, boundary wall molding, hanger wires, and if braced, diagonal wire braces and compression posts. The grid system of a suspended ceiling system consists of inverted main 2 tee beams and inverted cross tee beams, made of light gauge steel, that interlock at locations of intersection and supported on light gauged L-shaped wall molding at its perimeter that is screwed to partition walls. A ceiling system in a low seismic zone (seismic design category C, ASCE 7-10 (2010)) has a minimum 3/8-in. clearance between grid and 7/8-in. wall molding on all boundaries. The perimeter conditions of a ceiling system in higher seismic zones (seismic design category D-E-F, ASCE 7-10 (2010)) are slightly different, with a minimum grid 2-in. wall molding clearance of 3/4in. on two adjacent boundaries and fixed connections to the wall along the other two boundaries. The size of these wall moldings can be reduced to 7/8in. in case perimeter seismic clips are used. Acoustic ceiling tiles are manufactured from a compressed, high-density mineral fiber material and are available in many shapes and sizes. The simplest tile geometry is a 2ft. x 2ft. square with a thickness ranging from 1/2in. to 3/4in. The acoustic tiles are placed within the tee beam grid system, simply resting on the flange of each tee beam. Hanger wires are placed at 4-ft. intervals around the ceiling perimeter at no more than 8 in. from the wall. The compression post and splay wire bracing is installed at 12-ft. intervals beginning 6ft from the wall. A compression post is used in a bracing assembly to react against the vertical component of the splay wire braces. The hanger wires and splay wires of braced systems are made of 12 gauge wire that is looped through holes in tee beams and connected to the supporting floor deck above the ceiling. SUB-SYSTEM CEILING TEST AT THE UNIVERSITY AT BUFFALO A series of experiments to investigate the seismic behavior of large area suspended ceiling systems were performed using a tandem of shake tables at the Structural Engineering and Earthquake Simulation Laboratory (SEESL) at the University at Buffalo (UB). These experiments attempted to comprehensively investigate the component-level performance of ceiling systems. Test Setup In these experiments, 15 assemblies having different test configurations were tested (Armstrong Prelude 15/16 in. exposed tee systems); ten assemblies were tested on the 20ft. by 50ft. and 10ft. high frame as shown in Fig. 1a and five assemblies were tested on the 20ft. by 20ft. and 10ft. high frame as shown in Fig 1b. 3 (a) 20ft. × 50ft. large test set up mounted on two shake tables (b) 20ft. × 20ft. small test set up mounted on single shake table Figure 1. Suspended Ceiling Shake Table Test Setup-UB The main objectives of this study were to: 1) identify failure mechanisms, which describe functionality (damage states) of a ceiling system, 2) investigate the influence of various conditions such as (i) uniaxial vs. multi-axial excitations, (ii) different panel weights, and (iii) different sizes of ceiling area, and 3) investigate the effects of bracing systems. The examples of some selected assemblies are presented in Table 1. Further details on the test configurations and the drawings can be found in Ryu et al. (2013). Table 1. Summary of Test Description at UB-SEESL Size Assembly Input (Nominal) # Direction* 2 (ft ) 1 ... 10 20×50 ... 20×50 3D ... 3D 11 ... 15 20×20 ... 12×12 3D ... 3D Panel Perimeter Plenum Weight Bracing Angle Height (psf) (in.) (in.) Performed on 20ft. × 50ft. test frame Heavy 1.05 Yes 2 29 ... ... ... ... ... Heavy 1.05 Yes 7/8+clip 65 Performed on 20ft. × 20ft. test frame Heavy 1.05 No 7/8+clip 29 ... ... ... ... ... Heavy 1.05 No 7/8+clip 29 Grid Duty Comments Early Failure ... Deep plenum vs. Assembly #7 ... vs. Assembly #7 *: The long side (50ft.) and the short side (20ft.) of the 20ft. × 50ft. frame are denoted as the longitudinal direction (x, east-west) and the transverse direction (y, north-south), respectively. The vertical direction is denoted as z. Excitation Protocol Each test configuration (i.e. each test series, denoted by Assembly # as shown in column 1 of Table 1) was subjected to incremental test motions. The peak vector sum of the horizontal shaking table acceleration varied from 0.16g to 2.56g, which resulted in maximum 3.40g frame horizontal accelerations at the center of the roof level (PFA). In the vertical direction, the maximum table acceleration was 0.68g, which resulted in 1.54g frame vertical accelerations in the mid-bay of the roof level. 4 SYSTEM CEILING TEST AT E-DEFENSE This experiment was part of a collaborative program on base-isolated buildings conducted under the Memorandum of Understanding between the National Institute of Earth Science and Disaster Prevention (NIED) of Japan and the National Science Foundation (NSF), George Brown Jr. Network for Earthquake Engineering Simulation (NEES) program of the U.S. As part of these full scale shake table tests performed at E-Defense, an integrated partition-ceiling-sprinkler piping system was installed on the fourth and fifth floors of a 5story steel moment frame building. These experiments attempted to comprehensively investigate the system-level performance of these nonstructural systems. Test Setup Nonstructural elements were installed in a five-story steel moment frame building (Fig. 2). This building is approximately 53 ft. tall, and asymmetric in plan with dimensions of 33 ft. by 40 ft. (2 bays by 2 bays). The building was tested under three different configurations: 1) base isolated with triple pendulum bearings (TPB), 2) base isolated with a combination of lead-rubber bearings and cross-linear bearings (LRB/CLB), and 3) base fixed. The fundamental periods of the base-fixed building were 0.65 sec. in North-South direction, and 0.68 sec. in the East-West direction. Further information about the building is provided in Dao and Ryan (2012). Hanger Wire Seismic Brace Light Representative 2ft Long Cross Tee Main Runner West 4 ft Long Cross Tee East South North Figure 3. Overall View of Ceiling System Layout Two ceiling assemblies, using USG Figure 2. 5-Story Steel Moment Frame Test Bed, E-Defense DONN 15/16-in. exposed tee system with different configurations were installed in the 5 two top floors of the building (Fig. 3). The main objectives of ceiling study were to: 1) identify failure mechanisms of a ceiling system, 2) investigate the effects of bracing systems, 3) study the effect of seismic isolation on the performance of ceiling systems, and 4) investigate the interaction with other nonstructural systems. The descriptions of all the test assemblies are summarized in Table 2. Further details on the test configurations and the drawings can be found in Soroushian et al. (2012). Table 2. Summary of Test Description at the E-Defense Size AssemblyInput (Nominal) Floor # Direction 2 (ft ) 33×40 3D-2D 1-4 33×40 3D-2D 2-5 Grid Duty Heavy Heavy Panel Weight (psf) 0.72 0.72 Bracing NO Yes Perimeter Plenum Angle Height (in.) (in.) 7/8+clip 36 7/8+clip 36 Comments No bracing Bracing Excitation Protocol The five-story building was subjected to several ground motions over six days of experiments in three base configurations of triple pendulum isolated, lead rubber isolated, and fixed-base. Out of 41 total shaking table excitations, 23 were triaxial (included a vertical component) and the aiming tests were performed using biaxial horizontal excitation. The achieved responses encompassed a wide range of intensities and frequencies, which allowed a comprehensive study of the vulnerabilities of the nonstructural systems. The peak vector sum of horizontal shaking table acceleration varied from 0.18g to 1.21g, which resulted in maximum 1.19g and 1.22g horizontal accelerations in the 4th and 5th floors, respectively. In the vertical direction, the maximum ground acceleration was 1.26g which resulted in 6.77g and 7.03g vertical accelerations in the mid-bays of the 4th and 5th floors, respectively. SYSTEM CEILING TEST AT THE UNIVERSITY OF NEVADA, RENO A series of system-level experiments were conducted at the UNR-NEES site using three shake tables. In this experiment, an integrated partition-ceiling-sprinkler piping system was installed on each floor of a two-story steelbraced frame building. These experiments attempted to investigate the system-level response and nonstructural systems including Figure 4. 2-Story Steel-Braced Frame Test Bedceiling, piping, and partitions. UNR 6 Test Setup As mentioned earlier, nonstructural elements were installed in a two-story braced frame building spanning over three biaxial shake tables (Fig. 4). This building is approximately 25 ft. tall and was planned with dimensions of 60 ft. by 12 ft. (2 bays by 1 bay). The proposed experimental program consisted of two phases. In the first phase (linear tests), the structure remained linearly elastic during all runs in order to investigate the responses of acceleration sensitive components, mainly ceiling systems. Yielding braces were implemented in the second phase (nonlinear tests) to achieve large drifts to evaluate the behavior of driftsensitive components. The fundamental period of structure was 0.23 sec. and 0.36 sec. for linear and nonlinear buildings, respectively. Further information about the building is provided in Soroushian et al. (2011). Twenty-two ceiling assemblies, using Armstrong Prelude 15/16-in. exposed tee systems, with fifteen different configurations were installed in two floors of the building (Fig. 5). The main objectives of this study were to: 1) identify failure mechanisms of a ceiling system, 2) investigate the influence of various conditions such as (i) different boundary conditions, (ii) different panel weights, (iii) different sizes of ceiling area, and (iv) the effects of bracing systems, and 3) study the interaction with other nonstructural systems. The details of some selected assemblies are presented in Table 3. Further details on the test configurations and the drawings can be found in Rahmanishamsi et al. (2013). Seismic Brace Hanger Wire Light Representative 4 ft Long Cross Tee 2ft Long Cross Tee Main Runner Figure 5. Example View of Ceiling System Layout, Configuration #2 Table 3. Summary of Test Description at the UNR Size AssemblyInput (Nominal) * Floor # Direction (ft2) 58×10 x 1-1 ... ... ... 58×10 x 22-2 Grid Duty Heavy ... Heavy Panel Weight (psf) 1.31 ... 1.31 Bracing NO ... Yes Perimeter Plenum Angle Height (in.) (in.) 2 36 ... ... 7/8+clip 36 *: The long side (58ft.) is denoted as the longitudinal direction (x, north-south). 7 Comments No bracing ... Nonlinear test Excitation Protocol A set of ramp-up table motions were generated using an analytical procedure in order to achieve the target motion on the shake tables for linear and nonlinear tests and on the second floor for the linear tests. The peak horizontal (unidirectional) shaking table acceleration varied from 0.12g to 2.00g, which resulted in maximum 1.59g and 2.47g horizontal accelerations in the first and second floors, respectively. EXPERIMENTAL OBSERVATIONS AND PHYSICAL DAMAGE In each of the above experiments, several ceiling panels Table 4. Damage Observations During Each Experiment Physical Damage of Ceiling System during large shake intensities (see Damage # 1 2 Fig. 6). Also during extreme 3 excitations, some of the grid 4 5 6 7 8 9 10 were dislodged or fell to the floor connections failed and part of the ceiling completely collapsed. In Table 4, a summary of physical Damage Definition UB E-Defense UNR Misaligned panel Fallen panel Damaged tile around sprinkler head Failed pop rivet Damaged seismic clip Buckled grid Damaged grid latches Failed grid connection Failed hangers/braces Complete failure Yes Yes Yes Yes Yes Yes NA Yes Yes Yes Yes No Yes Yes No Yes NA Yes No Yes Yes Yes Yes Yes Yes Yes Yes Yes No No damage observations during each experiment is given. Also, some of the highlighted failures will be discussed in the following text. Note that the failures occurred at different excitation levels depending on the different ceiling configuration and set up. UB E-Defense UNR Figure 6. Ceiling Condition after Large Excitation Simulations Ceiling Perimeter Damage: Pop Rivet The horizontal inertial force generated in the ceiling plane is a function of the ceiling dimension and the realized horizontal acceleration at the ceiling plane. Pop rivets are installed at the perimeter of ceiling systems to partially (in the case of braced ceilings) or completely (for unbraced ceilings) transfer this inertial force to the ceiling perimeter supports 8 (generally partitions). However, as pop rivets are installed regardless of ceiling size or the intensity of the motion, early failure of these members have been seen several times during UB and UB UNR (pop rivets were not part of the UNR E-Defense test program) experiments Figure 7. Pop Rivet Failure (see Fig. 7). Failure of pop rivets was seen for the first time at 1.18g and 0.80g peak floor horizontal acceleration at the UB and UNR experiments, respectively. Ceiling Perimeter Damage: Seismic Clip Figure 8 shows the damage observed at the unattached joints between grid members and wall molding during the three experiments. The mechanism is interpreted as follows: when the grid member moved away from the wall, the grid member lost contact with the wall UB E-Defense UNR Figure 8. Seismic Clip Failure molding (Fig. 9a). Since the middle slot Grid Move to the Right was large relative to the screw dimensions, Small Settlement of Grid Ceiling Grid the grid member settled slightly (Fig. 9b). (a) (b) As the settled grid member moved back toward the wall, it hit the wall molding to Middle Slot Screw Wall Molding Grid-Wall Molding Interaction cause the observed damage (Fig. 9c) (Soroushian et al., 2012). Failure of the (c) seismic clips was seen for the first time at 1.34g, 0.77g, and 0.40g peak floor ACM7 Seismic Clip Figure 9. Grid - Wall Molding Interaction Mechanism (Soroushian et al., 2012) horizontal acceleration at UB, E-Defense, and the UNR experiments, respectively. 9 Grid Connection Failure In all three experiments, failure of the grid connections was understood as the initiation of the partial or complete collapse of the ceiling system. Failure of the grid connections resulted in the failure of the ceiling panels that they directly held due to the missing vertical capacity and uneven inertia force distribution in the ceiling plane. In general, the ceiling system lost its integrity after the failure of just a few grid connections. Figure 10 shows the examples of this type of failure during three experiments. Failure of the grid connection was seen for the first time at 1.18g, 0.48g, and 0.84g peak floor horizontal acceleration at the UB, E-Defense, and UNR experiments, respectively. UB E-Defense UNR Figure 10. Ceiling Grid Connection Failure Damaged tile around sprinkler head Wherever rigid drop pipes were used, the ceiling panels sustained damage from pounding of the sprinkler heads regardless of whether the oversized gap configuration, which conformed to code requirements (ASTM, 2011), or the no gap configuration was used. During the E-defense and UNR experiments (rigid drop pipes were not part of the UB test program) with 1.13g and 1.06g, respectively, up to 8 in. of material was knocked out of the ceiling panel (Figs 11a and c). On the other hand, no damage was observed around the flexible hose fittings (Figs 11b and d). Rigid Drop Flexible Drop Rigid Drop (a) E-Defense (b) E-Defense (c) UNR Flexible Drop (d) UNR Figure 11. Comparison of Ceiling/Sprinkler Head Pounding Damage 10 EXPERIMENTAL RESULTS AND FRAGILITY STUDIES The table accelerations and the responses of structural (or test frame) and nonstructural components were monitored by nearly 132, 400, and 383 sensor channels during UB, EDefense, and UNR experiments, respectively. In the corresponding tests, the response of the nonstructural systems, including ceiling displacement, ceiling acceleration, and the axial force of the supporting ceiling elements were recorded using 77, 204, and 321 sensor channels. A 4-pole low-pass Butterworth filter with a cutoff frequency of 50 Hz was applied to all the recorded responses, while the sampling frequency was 256, 1000, and 256 Hz accordingly during the UB, E-Defense, and UNR experiments. Examples of each type of sensor are shown in Figure 12. a) UB b) E-Defense c) UNR Figure 12. Example of Instruments (a) Perimeter Displacement Transducer, (b) Accelerometer, and (c) Load Cell In the following sections, ceiling acceleration amplification relative to the supporting structures is discussed. Then, two fragility methodologies that are used in this study are briefly described. Finally, the fragility curves developed for the ceiling perimeter, its supporting members, and the overall ceiling performance are presented along with their corresponding discussions. Ceiling/Floor Amplification Factor A key aspect of the ceiling response is the acceleration amplification of the ceiling components (grid and panel) relative to the structural systems to which they are attached (column or deck). Based on the recorded sensor data previously described, Table 5 reports the vector sum acceleration amplification factor in the horizontal direction (peak ceiling grid acceleration normalized by maximum vector sum horizontal acceleration (PFA) at the 11 geometric center of each floor). Table 5 also reports peak ceiling members and deck acceleration normalized by peak column acceleration in the vertical direction. All of the ceiling configurations and excitation levels are considered for each experiment, named “Cases”, along with their statistics (max, min and median). In Table 5, “column” refers to column sensors (corner frame sensors in the UB experiment) while “deck” refers to slab sensors (center frame sensors in the UB experiment) on the given floor, valid only for vertical acceleration. Table 5. Maximum Ceiling to Column or Deck to Column Acceleration Amplification Case Number 1 2 3 4 5 ... Last Max= Min= Median Median Grid Floor XY 1.95 2.37 2.66 2.64 2.75 ... 2.30 9.27 1.76 3.21 Grid Column Z 3.52 3.29 3.21 3.56 3.77 ... 2.85 23.85 1.57 3.50 UB Deck Column Z 2.02 1.82 1.61 1.69 1.52 ... 1.00 2.37 0.94 1.37 Grid/Floor (XY) 3.16 UNR Panel Grid Grid Column Floor Floor Z XY XY 4.46 1.38 3.93 4.76 2.37 5.59 5.99 3.71 4.34 5.78 3.93 6.30 6.09 3.08 7.53 ... ... ... 6.25 2.33 3.07 25.04 7.31 14.92 1.87 0.99 1.19 4.11 2.89 4.16 All Data Grid/Column (Z) 3.83 E-Defense Grid Deck Column Column Z Z 7.48 5.19 8.49 5.23 2.52 2.08 4.39 2.43 5.52 2.74 ... ... 5.04 5.81 13.64 7.31 2.20 2.08 6.00 4.36 Panel Column Z 8.60 5.46 2.60 4.84 5.32 ... 1.55 20.78 1.55 5.39 Panel/Column (Z) 4.29 The component amplification factor ap in Eq. 13.3-1 of ASCE 7-10 (2010) accounts for the possible amplification of the component horizontal response relative to the attached structure due to the inherent component flexibility. The maximum recommended amplification is ap = 2.5 for components that are considered flexible; ap can be interpreted as a component amplification of 2.5 relative to the PFA. Table 5 indicates that the horizontal (XY) amplifications observed during the experiments were 3.21, 2.89, and 4.16 for the UB, UNR, and E-Defense experiments, respectively. Also, the median obtained from all data was 3.16 which is higher than the value suggested by the code; this could be due to the pounding of the ceiling panels against the grid members. In the vertical direction, the component amplification can be interpreted as: 1) the same value as for the horizontal direction (ap = 2.5) per ICC-AC156 (ICC, 2010) or 2) ap = 2.67, which is the ratio of the constant to short period spectral acceleration (0.8 CV SDS/0.3 CV SDS) (NEHRP, 2009). This component amplification can be interpreted as the vertical ground acceleration being transmitted directly to the nonstructural components and not accounting for amplification of the vertical acceleration as it travels from the ground through the 12 structure to the attachment point of the nonstructural component. In this study, the component amplification was evaluated by comparing the peak vertical acceleration of the nonstructural component to the peak acceleration recorded in the column (corner frame). Even this definition of component amplification is unconservative, since the vertical acceleration was sometimes amplified as it traveled from the shake table to the columns. The median amplification of ceiling vertical acceleration (sensors mounted on the ceiling grid members compared to sensors mounted on the columns) observed in the experiment was 3.5 and 6.0 for the UB and E-Defense ceilings, respectively. The large difference between the two amplification values observed from the two experiments is expected to be the function of deck vibration frequency. The stiffer deck at the UB experiment (20-22 Hz deck vertical vibration, Ryu and Reinhorn, 2013) resulted in 1.4 acceleration-amplification of deck versus column (see Table 5), while more flexible decks at the E-Defense experiment (ranges from 7.1-14 Hz, Ryan et al., 2013) generated 4.4 of similar amplification. This suggests that the majority of the vertical acceleration amplification was due to the vibration of the structural deck relative to the columns and not increased acceleration in the ceiling relative to the slab. The median value based on all data is 3.8, which is higher by 50% than the standard recommended ap. Furthermore, the median vertical amplification of the ceiling panel relative to the column sensors was 4.3 based on all available experimental data. The higher ceiling panel amplification factors can be a result of pounding of the panels on the ceiling grid and suggests that anchorage design forces of hanger wires may need to be increased to account for this pounding. Fragility Methodology Three hundred and forty-six combinations of ceiling configurations and shake intensities were considered in this study. Therefore, a fragility curve methodology was used to interpret and extend the test results to assess the seismic vulnerability of the ceiling systems. The experimental results were used to estimate the seismic demands, or engineering demand parameter (EDPs) (e.g. ceiling displacements, hanger forces), on ceiling systems. Seismic fragility curves are conditional probability statements about the vulnerability of a system under the seismic loading. Vulnerabilities are generally expressed in terms of damage states (DSs) that are physically meaningful in terms of repair (cost and/or time) and the system functionality (e.g. failure capacity of wire restrainers, percentage of fallen ceiling area), and the fragility statement shows the probability that the seismic demand exceeds a threshold 13 capacity associated with the damage state. The conditioning parameter of these probabilistic statements is often a single seismic intensity measure (IM) (e.g. PFA). Two different methodologies were used to assess the experimentally based fragility curves that can be summarized as follows: Method A: The relation between the demand and the IM can be approximately represented with the standard normal cumulative distribution function (Nielson and DesRoches, 2007): ln( S d / S c ) PEDP DS | IM d IM 2 C 2 (1) where Sd is the median seismic demand estimate as a function of IM, Sc is the median estimate of the damage state capacity, βd|IM is the logarithmic standard deviation of the demand estimate, βc is the dispersion of the damage state capacity, and Φ[·] is the standard normal cumulative distribution function. Note that βc was not considered in this study (βc=0), however this parameter could be easily added. The fragility study reported here highlights the relationship between seismic performance of ceiling systems using shake table facilities at the University at Buffalo (UB); University of Nevada, Reno (UNR); and E-Defense. To do so, the ceiling demands were conditioned on the experimentally observed (e.g. PFA) of the associated floor level. A regression analysis of this data was used to estimate the parameters Sd and βd|IM of the probabilistic seismic demand models according to (Cornell et. al., 2002): Sd aIM b ln( d N d|IM i 1 i ln( aIM b )) 2 N 2 (2) (3) where a and b are the unknown regression coefficients, di is the peak demand at the ith floor, and N is the number of data points. This method was used for generating the fragility curves for ceiling perimeters, ceiling hangers, and wire braces. Method B: According to the framework proposed by Porter et al. (2007), Fdm(edp) denotes the fragility function for damage state dm, deﬁned as the probability that the component or system reaches or exceeds damage state dm, given a particular EDP value (Eq. 4), and idealized by a lognormal distribution (Eq. 5): 14 ( ) (4) ( where ) ( ( ) ) (5) denotes the standard normal (Gaussian) cumulative distribution function, denotes the median value of the distribution, and denotes the logarithmic standard deviation. In this method, the individual damage states are characterized by representative values for the median, , and dispersion, β, for the component damage states distributions as follows: ∑ √ where ( ) ∑[ ( (6) )] (7) denotes the i-th measured PFA (or horizontal ceiling inertia force) corresponding to specific damage observation and is the number of ceiling cases that are considered for each level of damage observation. This method was used for generating the fragility curves for the overall system. Ceiling Perimeter Fragility Curves The maximum observed forward or reverse relative displacement between the ceiling and partition (or rigid boundary) was evaluated with respect to: 1) the maximum vector sum horizontal acceleration (PFA) at the geometric center of each floor or 2) the maximum generated inertia force in the ceiling plane. The inertia force in the ceiling plane was calculated based on the maximum vector sum horizontal acceleration in the ceiling panels among all sensors and the total mass of the ceiling system by considering grid weights and panels. The displacement versus PFA and inertia force trends for each experiment are shown in Figs. 13a and 13b, respectively, on a log-log scale along with regression lines. It can be understood from this figure that the discrepancy between the data points of each experiment is less in the plots based on ceiling inertia force (also see Table 6). The ceiling size (mass) was considered in the plots based on inertia forces (and not based on PFA), which can result in smaller dispersion values for each experiment. Both plots show that the displacement 15 responses from the UNR experiment had the highest trend, while E-defense had the lowest. In addition, similar procedures were applied for the ceiling systems considering different variables such as the effect of: 1) bracing system, 2) perimeter seismic clip, 3) perimeter boundary conditions (partitions or rigid boundary), 4) perimeter boundary supports (all free or two fixed sides), and 5) vertical excitation. The regression parameters of the previously mentioned ceiling conditions are summarized in Table 6. 1 10 1 0 10 0 UB Experiment Fitted line,UB Experiment UNR Experiment Fitted line,UNR Experiment E-Defense Experiment Fitted line,E-Defense Experiment Fitted line,All Experiments 10 -1 10 -1 10 -2 -2 10 10 -1-1 10 10 10 10 1 UB Experiment Fitted line,UB Experiment UNR Experiment Fitted line,UNR Experiment E-Defense Experiment Fitted line,E-Defense Experiment Fitted line,All Experiments 0 0 0 1010 10 Peak (PFA), g g PeakFloor FloorAcceleration Acceleration (PFA), 1 Maximum Ceiling Displacement, in. 10 Maximum Ceiling Displacement, in. Displacement, Ceiling MaximumCeiling in. in. Displacement, Maximum 10 10 10 10 10 1 1 0 -1 -2 -3 10 10-1 10 0 10 1 Inertia Force, kips -1 10 Figure 13. Ceiling-Partition (or Rigid Boundary) Relative Displacement Seismic Demand Based on: (a) PFA (b) Inertia Force Table 6. Demand Parameters and Median of Fragility Curves for 3/4in. Ceiling Displacement -2 10 Ceiling Condition (Cases) 10 UB Experiment UNR Experiment E-Defense Experiment All Data Two Fix Perimeter All Free Perimeter Unbraced Ceiling Braced Ceiling Horizontal Excitation 3D Excitation Partition Perimeter Rigid Perimeter With Seismic Clip Without Seismic Clip -1 0 Values Based on PFA, Units: 10 g and in. a b βd|IMAcceleration Median Fragility Peak Floor (PFA), g 0.340 0.832 0.810 2.590 0.539 1.175 0.608 1.324 0.269 1.220 0.523 2.319 0.382 1.149 0.744 1.800 0.370 1.157 0.735 1.842 0.877 0.763 0.088 0.814 0.403 1.096 0.863 1.764 0.358 1.245 0.573 1.812 0.500 1.389 0.641 1.339 0.286 0.999 0.761 2.628 0.480 1.404 0.654 1.374 0.403 0.756 0.760 2.276 0.335 1.157 0.761 2.005 0.475 0.956 0.650 1.613 1 Values Based 10 on Inertia Force, Units: kips and in. a b βd|IM Median Fragility 0.172 0.763 0.547 6.874 0.355 0.811 0.476 2.518 0.062 0.870 0.450 17.448 0.203 0.720 0.823 6.142 0.196 0.732 0.817 6.254 0.601 0.333 0.247 1.944 0.228 0.782 0.895 4.597 0.176 0.712 0.709 7.643 0.267 0.844 0.731 3.395 0.104 0.924 0.706 8.476 0.212 0.756 0.921 5.310 0.172 0.763 0.547 6.874 0.167 0.823 0.886 6.208 0.303 0.542 0.572 5.313 Figures 14a and 14b compare the trend lines of displacement demands from all the ceiling cases mentioned above. These figures demonstrate that, in most of the PFA and inertia force ranges, the ceiling system with free ends at all sides has the largest displacement demands, while ceiling systems subjected to 3D excitation and the E-Defense test data resulted in the lowest displacement demands. A similar trend is confirmed by the fragility curves presented in Figs. 14c and 14d. These fragility curves are generated by using equation 1, displacement regression parameters, and 3/4in displacement as the benchmark limit state. According to 16 ASTM E580/E580M-11ae1 (ASTM, 2011), for seismic design categories D, E, and F, grid members should be installed with the clear space of 3/4 in. from the partition walls on the floating side. Therefore 3/4in. displacement was used as the benchmark limit state, which corresponds to the pounding of grid members to the partition walls. The median values of each fragility curve from Figures 14c and 14d is tabulated in Table 6. Note the dispersion value of fragility curves are equal to βd|IM, as βc was set to zero in this study. The median fragility values of each pair of ceiling systems imply that ceiling systems with rigid boundary, bracing, seismic clip, and two fixed sides have lower failure probability. Surprisingly, the displacement demand of ceiling system under 3D excitation is less than those from horizontal only excitations. This effect could be because of: 1) uncertainty in the tested specimens (UNR ceilings (under horizontal excitation only) resulted in largest displacement demand), 2) reduction of ceiling horizontal mass due to uplift in ceiling panels, -1 -2 10 -1 10 (c) 0.8 1 Maximum Ceiling Displacement, in. 0 Probability 10 10 UB Experiment UNR Experiment E-Defense Experiment 0.4 All Experiments UB Experiment 0 -1 10 10 Two Fix Perimeter UNR Experiment 1 10 All Free Perimeter E-Defense Experiment 0.2 Unbraced Ceiling All Experiments 0 10 Braced Ceiling Two Fix Perimeter UB Experiment -2 Horizontal Excitation Only All Free Perimeter UNR Experiment 0 10 -1 0 1 0 0.5 1 1.5 2.5 3D Excitation 3 3.5 4 10 10 10 -12 Unbraced Ceiling E-Defense Experiment 10 Peak Floor Acceleration (PFA), g Perimeter Attachment Peak Floor Acceleration (PFA), g Partition Braced Ceiling All Experiments 0 Rigid Perimeter Attachment Horizontal Excitation Only UB Experiment 10 Two Fix Perimeter With Seismic Clip -1 3D Excitation UNR Experiment All Free Perimeter 10 Without Seismic Clip Partition Perimeter Attachment E-Defense Experiment Unbraced Ceiling Rigid Perimeter Attachment All Experiments Braced Ceiling 2 -2 Horizontal Excitation Only With Seismic Clip 10 Two Fix Perimeter 10 -1 1 0 Without Seismic Clip All Free Perimeter 3D Excitation 10 10 (b) 10-1 Unbraced Ceiling Peak Floor Acceleration (PFA), g Partition Perimeter Attachment 1 -2 Attachment 10 Braced Ceiling (d) Rigid Perimeter 0.8 10 -1 0 1 Horizontal Excitation Only With Seismic Clip 10 10 10 Peak Floor Acceleration (PFA), g Without Seismic Clip 03D Excitation 10 0.6 Partition Perimeter Attachment -2 Rigid Perimeter 10 Attachment -1 0 1 -1 With Seismic Clip 10 10 10 0.4 10 Without Seismic Clip Peak Floor Acceleration (PFA), g 10 10 1 -2 0.2 10 -3 10 -1 10 0.6 Probability 10 0 1 (a) Maximum Ceiling Displacement, in. 10 1 Maximum Ceiling Displacement, in. Maximum Ceiling Displacement, in. 10 1 Maximum Ceiling Displacement, in. Maximum Ceiling Displacement, in. 10 0 10 Peak Floor Acceleration (PFA), g 10 0 10 1 10 2 0 0 1 10 20 30 40 Inertia Force, kips Inertia Force, kips Figure 14. Seismic Displacement Demand Based on: (a) PFA (b) Inertia Force, Displacement Fragility Curves Based on: (c) PFA (d) Inertia Force 17 50 and 3) increase in perimeter shear resistance due to the pounding of panels and normal force amplification. Two types of 7/8-in. and 2-in. wall moldings are commonly used in the construction. According to ASTM E580/E580M-11ae1 (ASTM, 2011), three conditions exist for ceiling perimeters on the floating side: 1) Seismic design category D, E, F: using 2-in. wall molding with 3/4-in. gap between grids and partition walls, called the pounding gap hereafter. This pounding gap will leave 5/4-in. travel distance before the grid members unseat from the wall angle, called the unseating gap hereafter. 2) Seismic design category D, E, F: using 7/8-in. wall molding along with seismic clip. In this condition, the pounding and unseating gaps are 3/4in. and 1/8in., respectively. 3) Seismic design category C: using 7/8-in. wall molding with 3/8-in. and ½-in. pounding and unseating gaps, respectively. To identify the pounding and unseating failure of grid members from the partition walls, six different limit states were defined based on the values mentioned above, which are presented in Table 7. Also by using equation 1 and displacement demands from all the experiments, the displacement fragility curves on the floating side are generated (see Fig. 15). The median and dispersion values of these curves are presented in Table 7. 1 1 0.7 0.8 0.6 0.7 0.5 0.6 0.4 0.5 0.3 0.4 0.2 0.3 0.1 0.2 0 0.1 0 0 0 10 20 30 40 Probability of Exceedance 0.9 0.8 Exceedance of of Probability Exceedance Probability of Exceedance of Exceedance Probability Probability 1 0.9 Probability of Exceedance 1 1 0.9 1 0.9 0.9 0.8 0.8 0.9 0.7 0.8 0.7 0.8 0.6 0.6 0.7 0.5 0.7 0.5 0.6 0.4 0.4 0.6 0.5 0.3 0.3 0.5 0.2 0.4 0.2 0.4 0.1 0.1 0.3 Unseating,Design Category D-E-F,Seismic Clip + 7/8in. Wall Angle 0Pounding,Design Category C,7/8in. Wall Angle 0 0.3 Unseating,Design 0 10 Category 20D-E-F,Seismic 30 Clip + 7/8in. 40 Wall Angle 50 0 0.5 1Category 1.5 D-E-F,Seismic 2 2.5 Clip +3 7/8in.3.5 4 Unseating,Design Wall Angle 0.2 Inertia Force, kips Peak Floor Acceleration (PFA), g Unseating,Design Category C,7/8in. Wall Angle Pounding,Design Category C,7/8in. Wall Angle Pounding,Design Category C,7/8in. Wall Angle 0.2 Pounding,Design Clip + 7/8in. Wall Angle Unseating,Design Category Category D-E-F,Seismic C,7/8in. Wall Angle Unseating,Design Category C,7/8in. Wall Angle D-E-F,Seismic Clip + 7/8in. Wall Angle 0.1 Pounding,Design Category D-E-F,2in. WallClip Angle D-E-F,Seismic + 7/8in. Wall Angle Pounding,Design Category D-E-F,Seismic Clip + 7/8in. Wall Angle C,7/8in. Wall Angle 0.1 Pounding,Design Wall Angle Unseating,Design Category D-E-F,2in. D-E-F,2in. Wall Wall Angle Angle Unseating,Design Category Category D-E-F,2in. C,7/8in. Wall Angle Pounding,Design Category 0 Unseating,Design Category D-E-F,Seismic D-E-F,2in. WallClip Angle Pounding,Design Category + 7/8in. Wall Angle Unseating,Design Wall Angle 40 10 SideCategory 20 D-E-F,2in. 50 Figure 15. Ceiling Fragility on00the Floating Based on: (a)30PFA (b) Inertia Force Pounding,Design Category D-E-F,2in.30 Wall Angle Curves 10 20Perimeter 40 Inertia kips 0 50 10 20 Force, 30 40 50 Unseating,Design Category D-E-F,2in. Wall Angle Inertia Force, kips 50 Inertia Force, kips Table 7. Medians and Dispersion of Fragility Curves for 3 Different Ceiling Perimeters on the Floating Side Inertia Force, kips Ceiling Perimeter Seismic Clip + 7/8in. Wall Angle Design Category D-E-F 7/8in. Wall Angle Design Category C 2in. Wall Angle Design Category D-E-F Dispersion Unseating Pounding Unseating Pounding Unseating Pounding Values Based on PFA, Units :g and in. Limit State Median Fragility 0.125 0.378 0.750 1.800 0.500 1.265 0.375 0.985 0.750 1.800 1.250 2.808 0.744 18 Values Based on Inertia Force, Units : kips and in. Limit State Median Fragility 0.125 0.509 0.750 6.142 0.500 3.497 0.375 2.344 0.750 6.142 1.250 12.490 0.823 The median values of fragility data show that the unseating failure of ceiling systems with seismic clips is probable at very low shake intensities ( PFA=0.378g, inertia force = 0.509 kips). This probability of failure can be reduced by approximately 375%, if the seat length of wall angle is increased to 1.5in.. The same size of wall angle (1.5in.) can improve the unseating and pounding behavior of ceiling systems in design category C by 42% and 83%, respectively. By doing so, the median values of pounding and unseating failure in all ceiling configurations will be delayed until reaching PFA of 1.8g (inertia force of 6.142kips). It should be mentioned that the median values presented in Table 7 are based on all experimental data, which is mainly (334 out of 346) based on two fixed boundaries. However, all floating side perimeters can be used in ceiling systems designed based on design category C (ASTM, 2011). Therefore, in the ceiling systems with all floating sides, even by using 1.5-in. wall angles (see median values presented in Table 6), these ceiling might be considered weak at the perimeter (PFA = 0.814g, inertia force = 1.944). Further perimeter improvement can be reached by increasing the seat length of wall angles, while more installation consideration should be considered. Ceiling Hangers and Wire Restrainers Although only a few ceiling hangers failed during E-Defense experiment, recorded axial force in ceiling hangers and diagonal wires was larger than those defined by the code in some earthquake simulations. The robust behavior of these supporting elements was because of their stronger connection compared to the design values. However, in this section, a set of fragility curves were developed for these members based on design values determined by the code. To do so, the maximum axial force in hangers and diagonal wires was evaluated with respect to PFA and maximum generated inertia force in the ceiling plane. Note that there was no load cell and force measurement during the E-defense and some of the UNR and UB experiments. The axial force of hangers and diagonal wires versus PFA and inertia force trends for each experiment are shown in Fig. 16, on a log-log scale along with regression lines. These figures show, especially for hangers, that the incongruity between the data points of each experiment is less in the plots based on ceiling inertia force (also see Table 8). The demand estimations based on the UB experiment are higher than those from the UNR experiment, which is due to the absence of vertical excitation during the UNR experiments. However, the effect of vertical excitation is less pronounced in diagonal wires as the vertical force is 19 mainly resisted by compression posts. In addition, similar regression analyses were applied for the ceiling systems considering the effect of bracing system and vertical excitation. The regression parameters of the previously mentioned ceiling conditions (using equations 2 and 3) are summarized in Table 8. 10 10 0 Ceiling Hangers 10 Maximum Hanger Force, kips Maximum Hanger Force, kips 10 -1 -2 UB Experiment Fitted line,UB Experiment UNR Experiment Fitted line,UNR Experiment Fitted line,All Experiments -3 10 -1 10 10 0 10 10 0 Ceiling Hangers -1 -2 -3 10 10 -1 10 1 10 Peak Floor Acceleration (PFA), g 0 10 Diagonal Wires 10 10 Maximum Diagonal Wire Force, kips Maximum Diagonal Wire Force, kips 10 0 10 1 10 2 Inertia Force, kips -1 -2 1 Diagonal Wires 10 10 10 0 -1 -2 -3 -3 10 -1 10 10 0 10 1 10 -1 10 10 0 10 1 10 2 Inertia Force, kips Peak Floor Acceleration (PFA), g Figure 16. Force Demand on Hangers and Diagonal Wire Braces Based on PFA and Inertia Force Table 8. Demand Parameters and Median of Fragility Curves for Ceiling Hangers and Diagonal Wire Braces Ceiling Condition (Cases) UB Experiment UNR Experiment All Data Unbraced Ceiling Braced Ceiling Horizontal Excitation 3D Excitation UB Experiment UNR Experiment All Data Horizontal Excitation 3D Excitation Values Based on PFA, Units: g and kips a b βd|IM Median Fragility Ceiling Hangers 0.108 0.438 0.264 0.663 0.036 0.612 0.685 N/A 0.044 0.299 0.787 N/A 0.044 0.463 0.681 N/A 0.045 0.163 0.880 N/A 0.038 0.482 0.735 N/A 0.092 0.185 0.256 0.893 Ceiling Diagonal Wires 0.176 0.647 0.480 1.723 0.117 0.891 0.474 2.342 0.135 0.626 0.533 2.682 0.131 0.618 0.556 2.854 0.169 0.828 0.456 1.602 20 Values Based on Inertia Force, Units: kips and kips a b βd|IM Median Fragility 0.040 0.029 0.029 0.032 0.024 0.029 0.047 0.351 0.490 0.496 0.407 0.611 0.497 0.282 0.215 0.602 0.531 0.562 0.453 0.580 0.164 9.853 10.357 9.737 12.496 8.530 9.952 10.020 0.036 0.094 0.080 0.088 0.027 0.572 0.547 0.314 0.441 0.624 0.400 0.479 0.562 0.486 0.370 29.625 6.036 37.773 10.783 35.231 According to ASTM E580/E580M-11ae1 (ASTM, 2011), the connection of ceiling hangers and diagonal wire braces shall be capable of carrying not less than a 90lb and a 250lb allowable loads, respectively. These values were used for the failure limit state, the only considered limit state, of ceiling hangers (90lb) and diagonal wires (250lb). By knowing the limit states and demand regression parameters (Table 8), failure fragility curves of these supporting elements can be obtained from equation 1. Just as before, βc was set to zero for the generation of these fragility curves. The fragility curves for ceiling hangers and diagonal wires are presented in Fig. 17. These curves show that the ceiling hangers are vulnerable during the excitation with a vertical component. However, no consistent trends can be observed from the fragility curves for diagonal wire restrainers. The median values of fragility curves presented in Table 8 show that the failure of ceiling hangers and diagonal wire braces are probable at excitations with low amplitudes. However, this type of failure was not observed in the UNR and UB experiments. This conflict can be justified as: the connection of hangers and diagonal wire Ceiling Hangers 0.9 0.8 0.8 0.7 0.7 Probability Probability 0.9 1 0.6 0.5 0.4 0.5 0.4 0.3 0.2 0.2 0.1 0.1 0 0 0.5 1 1.5 2 2.5 3 3.5 0 0 4 0 Ceiling Hangers 0.6 0.3 Maximum Ceiling Displacement, in. 10 1 10 10 -1 -3 10 -1 10 10 Peak Floor Acceleration (PFA), g 0.9 0.8 0.8 0.7 0.7 0.6 0.5 0.4 0 10 0.5 0.4 0.3 0.2 0.2 0.1 0.1 0.5 1 1.5 2 2.5 3 3.5 Diagonal Wires 0.6 0.3 0 0 10 Peak Floor Acceleration (PFA), 30 40 50 g Inertia Force, kips 20 1 0.9 Diagonal Wires Probability Probability 1 UB Experiment UNR Experiment All Experiments Unbraced Ceiling Braced Ceiling Horizontal Excitation Only 3D Excitation -2 4 Peak Floor Acceleration (PFA), g 0 0 10 20 30 40 50 Inertia Force, kips Figure 17. Fragility Curves of Ceiling Hangers and Diagonal Wire Braces Based on PFA and Inertia Force 21 1 were able to carry larger forces compared to the design values. The maximum axial force in the hangers and diagonal wires obtained from the experiments above was 204lb and 320lb, respectively. These numbers can be used instead of code values to ensure adequate capacity within the connection of these elements. Ceiling Fragility Study The damage to ceiling system was assessed by inspecting all of the available video footage, pictures, and inspection sheets. Then, this assessment was qualitatively estimated by correlating the observed damage to the recorded peak demand parameters for every earthquake simulation. For the purpose of damage evaluation, three general damage states (Slight, Moderate, Extensive) were developed, each classified by several behaviors that occurred alone or in combination. The behaviors associated with the damage states are described in Table 9. Ceiling panel equivalent fallen areas were based on Gilani et al. (2013), wherein the total ceiling area suspended in the UB, UNR, and E-Defense experiments were 1000 sf (smaller areas: 400 sf, 256 sf and 144 sf), 532 sf (smaller area: 266 sf), and 900 sf, respectively. For the rest of the damage parameters (e.g. perimeter damage or ceilingsprinkler interaction), the author’s experience on repair effort was considered for defining each of the damage states. Partially dislodged ceiling panels were not considered part of the equivalent fallen area. Finally, note that the assigned damage states were generally determined by the most severe rating when the observed behaviors overlapped multiple states. Table 9. Definition of Ceiling Damage States in This Study Damage States No Damage Slight Moderate Extensive Description A few ceiling panels may be dislodged. Ceiling panels up to 5% equivalent ceiling area fall. Slight damage to ceiling panels at the sprinkler heads may be visible due to ceiling-sprinkler head pounding. The hole in the panel is enlarged by up to 1 inch in any direction. Slight damage to the perimeter connection (pop rivet failure) and unseated perimeter grid members or wall molding. Slight damage to grid connections. Ceiling panels between 5% and 20% of equivalent ceiling area fall. More significant damage to ceiling panels at the sprinkler heads may be visible due to ceiling-sprinkler head pounding. The hole in the panel is enlarged by up to 2 inches in any direction. Up to 10% grid connection failure. Up to 2% ceiling hanger may break. More damage to the perimeter connection (pop rivet or seismic clip) and unseated perimeter grid members or wall molding. Up to 10% grid buckling. Ceiling panels greater than 20% equivalent ceiling area fall. Large sections of the ceiling grid are compromised. For example, cross tees buckle, become misaligned, or the connections fail. More significant damage to ceiling panels at the sprinkler heads may be visible due to ceiling-sprinkler head pounding. The hole in the panel is enlarged by more than 2 inches in any direction. More than 10% grid connection failure. Damage to the perimeter seismic clips and wall molding is extensive. More than 2% of ceiling hangers may break. 22 The overall ceiling fragility curves were developed by assigning the PFA (or ceiling inertia force) values to one of the four bins of data, which were categorized based on damage states. The median ( ) and dispersion (β) PFA (or ceiling inertia force) value of each damage state were obtained by using equations 6 and 7. Then, fragility curves corresponding to each damage state were generated by using equation 5. The overall ceiling fragility curves of each experiment and all available data corresponding to each damage state based on PFA and ceiling inertia force are shown in Figs. 18a and 18b. These figures show that the most vulnerable ceiling systems were those installed in the E-defense experiment based on PFA and at UNR with respect to inertia force. The vulnerability within these two systems were found to be more than in the UB experiment due to: 1) extensive vertical excitation in some of the earthquake simulations during the EDefense experiment, 2) out-of-plane vibration of partition walls caused more damage in the ceiling perimeter during E-Defense and UNR experiments, 3) in many cases, ceiling-piping interaction was recognized as the dominant damage in ceiling systems, which was not included in the UB experiment. The median ( ) and dispersion (β) values of these fragility curves were presented in Table 10. Damage State: Slight Probability 1 Damage State: Moderate Damage State: Extensive 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.2 0.2 (a) 0.4 UB Experiment UNR Experiment E-Defense Experiment All Experiments 0.2 0 0 1 2 3 4 0 0 1 2 3 0 0 4 1 2 3 4 Peak Floor Acceleration (PFA), g Probability 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 0 0 (b) 2 4 6 8 10 0 0 2 4 6 8 10 0 0 2 4 6 Inertia Force, kips Figure 18. Overall Ceiling Fragility Curves Based on (a) PFA and (b) Inertia Force 23 8 10 Table 10. Fragility Parameters for Overall Ceiling Performance Values Based on PFA, Units: g and in. DS1 DS2 DS3 xm β xm β xm β 1.196 0.261 1.843 0.346 2.391 0.285 0.950 0.378 1.249 0.299 1.472 0.347 0.608 0.414 0.799 0.344 1.076 0.118 0.980 0.396 1.329 0.401 1.791 0.419 0.879 0.417 1.163 0.344 1.361 0.333 1.196 0.261 1.843 0.346 2.391 0.285 0.850 0.413 1.233 0.378 1.787 0.468 1.190 0.276 1.433 0.416 1.794 0.387 1.006 0.367 1.292 0.312 1.482 0.361 1.916 0.729 2.567 0.585 3.997 0.693 0.879 0.417 1.163 0.344 1.361 0.333 1.196 0.261 1.843 0.346 2.391 0.285 0.841 0.444 1.220 0.413 1.663 0.444 1.157 0.252 1.615 0.302 2.115 0.308 Ceiling Condition (Cases) UB Experiment UNR Experiment E-Defense Experiment All Data With Piping Interaction Without Piping Interaction Unbraced Ceiling Braced Ceiling Horizontal Excitation 3D Excitation Partition Perimeter Rigid Perimeter With Seismic Clip Without Seismic Clip Values Based on Inertia Force, Units: kips and in. DS1 DS2 DS3 xm β xm β xm β 5.928 0.400 5.276 0.729 8.010 1.010 1.552 0.631 2.324 0.483 3.500 0.486 2.359 0.407 4.157 0.153 4.495 0.577 2.608 0.819 3.149 0.657 5.410 0.873 1.669 0.615 2.549 0.495 3.726 0.507 5.928 0.400 5.276 0.729 8.010 1.010 1.932 0.688 2.836 0.541 4.795 0.821 3.931 0.814 3.495 0.750 5.938 0.918 0.928 0.455 1.399 0.532 2.144 0.397 4.963 0.596 4.565 0.628 7.211 0.943 1.669 0.615 2.549 0.495 3.726 0.507 5.928 0.400 5.276 0.729 8.010 1.010 1.839 0.736 2.814 0.515 4.163 0.659 3.815 0.738 4.061 0.863 9.751 1.028 In addition, similar fragility curves were generated for the ceiling systems considering different variables such as the effect of: 1) bracing systems, 2) perimeter seismic clips, 3) perimeter boundary conditions (partitions or rigid boundary), 4) interaction with piping systems, and 5) vertical excitation. The fragility curves of these ceiling conditions (see Fig. 19) show that in each pair, the ceiling systems with a partition perimeter attachment, with a seismic clip, and with piping interaction are more vulnerable. In this study, ceiling systems Damage State: Slight -2 10 -1 10 0 0 2 4 6 8 10 -2 10 -1 10 Figure 0 0 0 0 Damage State: Extensive 2 4 6 8 Inertia Force, kips 1 1 10 0 0 Probability Probability Maximum Ceiling Displacement, in. Maximum Ceiling Displacement, in. Maximum Ceiling Displacement, in. Maximum Ceiling Displacement, in. Probability -1 Probability 10 0 Maximum Ceiling Displacement, in. Maximum Ceiling Displacement, in. 10 1 Damage State: Moderate UB Experiment 1 UNR Experiment 1 1 0.8 0.8 10 0.8 E-Defense Experiment 10 All Experiments 0 10 0.6 0.6 Two Fix Perimeter UB Experiment UB0.6 Experiment All Free Perimeter 1 UNR Experiment UNR 1 10 0.4Experiment 0.4 Unbraced Ceiling 10 0.4Experiment E-Defense E-Defense Experiment Braced CeilingAll Experiments All Experiments 0 0 UBExperiment Experiment 0.2 0.2 10 0.2 UB Horizontal Excitation Two Fix PerimeterUB Experiment10 Two FixOnly Perimeter UNR Experiment UNR Experiment -1 3D Excitation All Free Perimeter All Free PerimeterUNR 1 10 Experiment 1E-Defense 1 0 0 0 Experiment E-Defense Experiment 10 0 Unbraced 0 1 2 Partition 3 Perimeter 4 Attachment 0 1 2 3 4 E-Defense Experiment Unbraced Ceiling 1 2 3 4 Ceiling AllAllExperiments Experiments Rigid Perimeter Peak All Floor Acceleration (PFA), g0Attachment Braced0 Ceiling Experiments Braced Ceiling 10 10 Two FixPiping Perimeter With Interaction With Seismic Clip 0.8 0.8 Horizontal Excitation Only UB Experiment Two Fix Perimeter Horizontal Excitation Only UB Experiment AllWithout Free Perimeter Piping Interaction Without Seismic Clip -1 3D Excitation UNR Experiment All Free Perimeter -1 3D Excitation UNR Experiment 10 10 Unbraced Ceiling Unbraced Ceiling Partition PerimeterUnbraced Attachment Ceiling Partition Perimeter Attachment E-DefenseE-Defense ExperimentExperiment 0.6 0.6 -2 Braced Ceiling Braced Ceiling Rigid Perimeter Attachment All Experiments Braced Rigid Perimeter Attachment 0 All Experiments 10 -1 Ceiling 0 Horizontal Excitation Only 1 10 10 10 Clip With Seismic Horizontal Excitation Only 10 Two Fix Perimeter Excitation Only With 1Seismic 1Two Fix Perimeter 1 Clip Horizontal -1 Acceleration 3D Excitation Peak Floor (PFA), g Without 0.4 0.4 All Free Perimeter -1 Seismic Clip 3D Excitation Without Seismic 3DClip Excitation All Free Perimeter 10 10 Partition Perimeter Attachment Partition Perimeter Attachment 0.8 0.8Unbraced Unbraced Ceiling Ceiling Partition Perimeter Attachment 0.8 Rigid Perimeter Attachment -2 -2 Braced Rigid Perimeter10Attachment Braced Ceiling Rigid Perimeter Attachment 10 -1Ceiling 0.2 1 0 10.2 With Seismic -1 0 Clip Excitation Only 0.6 With10 Seismic Clip10 0.6Horizontal Horizontal 0.6 10 10 Excitation Only 10 10 With Seismic Clip Without Seismic Clip -1 3D Excitation Peak Floor Acceleration (PFA), 3D Excitation Without Seismic Clip g Peak Floor Acceleration (PFA), g Without Seismic Clip 10 0.4Partition Perimeter 0.4 0.4 Partition Perimeter Attachment 0 0 Attachment -2 0 5 10 0 -2 10 Rigid Perimeter Attachment Rigid Perimeter Attachment -1 0 10 -1 0 1 10 10 Inertia Force, kips 0.2With Seismic 0.2 0.2 WithClip Seismic Clip 10 10 10 WithoutClip Seismic Clip Peak Floor Acceleration (PFA), g Peak Floor Acceleration (PFA), g Without Seismic 1 1 10 Maximum Ceiling Displacement, in. 1 under horizontal excitation were found to be more vulnerable after including UNR 10 2 4 6 8 10 10 10 10 10 19. Overall Ceiling Fragility Curves for Different Ceiling Conditions Based on (a) PFA and Peak Floor Acceleration Peak Floor Acceleration (PFA), g (PFA), g (b) Inertia Force 24 In (horizontal only) results. The early damage observation at the UNR experiment due to ceiling-piping interaction and ceiling perimeter damage might have biased the fragility parameters. However, according to each of the E-Defense (Soroushian et al., 2013) and UB (Ryu and Reinhorn, 2013) experiments, ceiling systems are more vulnerable under 3D excitations compared to the horizontal only excitations. The fragility parameters of the previously mentioned ceiling conditions are summarized in Table 10. SUMMARY AND CONCLUSIONS In this paper, a short summary is presented for the three experimental studies performed at the University at Buffalo (UB); University of Nevada, Reno (UNR); and E-Defense shake table facilities. The damage observations and a brief discussion of the similar failure mechanisms between all the experiments are provided. A concise description of instrumentation and data processing procedure is presented followed by the fragility methodology used in this study. Finally, the ceiling amplification factors and the fragility curves for ceiling perimeters, supporting elements, and the overall performance of ceiling systems is discussed in detail. The conclusions are listed below: The code component amplification factor, ap, found to be unconservative for ceiling systems, in both horizontal and vertical directions. The median fragility of each pair of ceiling systems show that ceiling systems with rigid boundary, with bracings, with seismic clips, and with two sides fixed have lower probability of failure at their perimeters. The fragility curves show that the unseating failure of ceiling system with 7/8-in-wall moldings is probable to occur at very low shake intensities. The fragility curves of ceiling hangers and diagonal wires show that the code connection capacity of these supporting elements should be increased. The overall ceiling fragility curves showed that in each pair, the ceiling system with partition perimeter attachment, with seismic clips, and with piping interaction are more vulnerable. Note that using the results of these experiments and a separate analytical development, Ryu and Reinhorn (2014) propose clipping the grid around the periphery and brace it using 25 vertical strut and diagonal ties at locations that can be determined through computations based on the structural resistance of grid components. ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation under Grant No. 0721399. This Grand Challenge (GC) project to study the seismic response of nonstructural systems is under the direction of M. Maragakis from the University of Nevada, Reno and Co-PIs: T. Hutchinson (UCSD), A. Filiatrault (UB), S. French (G. Tech), and B. Reitherman (CUREE). Any opinions, findings, conclusions or recommendations expressed in this document are those of the investigators and do not necessarily reflect the views of the sponsors. The input from Bob Bachman is gratefully acknowledged. The input provided by the Practice Committee of the NEES Nonstructural Project, composed of W. Holmes (Chair), D. Allen, D. Alvarez, and R. Fleming; by the Advisory Board, composed of R. Bachman (Chair), S. Eder, R. Kirchner, E. Miranda, W. Petak, S. Rose and C. Tokas, has been crucial for the completion of this research. REFERENCES ANCO, 1983. Seismic Hazard Assessment of Nonstructural Ceiling Components. NSF Rep. No. CEE8114155. Culver City, CA. ASCE, 2010. Minimum Design Loads for Buildings and Other Structures (ASCE/SEI 7-10), American Society of Civil Engineers, Reston, VA. ASTM-E580/E580M-11ae1, 2011. 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