Experimental Fragility Analysis of Suspension Ceiling Systems Siavash Soroushian, Esmaeel Rahmanishamsi,

Experimental Fragility Analysis of Suspension Ceiling Systems Siavash  Soroushian, Esmaeel  Rahmanishamsi,
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
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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
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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 )
PEDP  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.
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28
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