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J. Civil Eng. Architect. Res. Vol. 1, No. 2, 2014, pp. 110-128 Received: June 18, 2014; Published: August 25, 2014
Journal of Civil Engineering
and Architecture Research
Seismic Vulnerability Evaluation of Architectural Glass
in Curtain Walls
Ali M. Memari1,2, Ali Shirazi1, Paul A. Kremer1 and Richard A. Behr3
1. Department of Architectural Engineering, Penn State University, University Park, PA, USA
2. Department of Civil and Environmental Engineering, Penn State University, University Park, PA, USA
3. College of Engineering, Florida Gulf Coast University, Fort Myers, FL, USA
Corresponding author: Ali M. Memari ([email protected])
Abstract: A method for seismic vulnerability evaluation of architectural glass components within aluminum curtain wall systems is proposed. The methodology involves developing a relationship between the applied drift and the critical stresses generated in the glass and comparison with glass crack initiation stress obtained from test data. On the basis of this method, the existing curtain wall glass components or windows can be inspected, and based on the conditions of the curtain wall and the code specified maximum allowable drift, a score can be defined, which will represent cracking vulnerability of the glass panel at a given drift magnitude. The results of the vulnerability evaluation procedure can help improve decision making regarding prioritization of possible curtain wall seismic retrofit options. Key words: Architectural glass, curtain wall, seismic vulnerability evaluation, racking test.
1. Introduction
Seismic codes in the U.S. have now adopted the
provisions for the seismic design of architectural glass
components within curtain wall systems. The
provisions in ASCE 7-10 [1] require each glass panel
in a particular curtain wall to have in-plane drift
capacity, Δfallout, which is the drift that would cause
glass to fall out of the glass panel, to be at least 25%
greater than the maximum drift that the glass panel
would be subjected to during the design earthquake.
Δfallout is normally determined by mockup testing in
accordance with AAMA 501.6 [2]. The code also
permits the use of analytical approaches to predict the
glass drift capacity. Currently, such analytical
methods are not sufficiently developed to predict
Δfallout. Although additional research is needed, results
of a previous study [3] indicate the potential of using
finite element modeling as an aid in the design and
analysis of architectural glass curtain walls subject to
seismic loads. Besides the need for prediction of glass
capacity (i.e., Δfallout) for new designs, it is also
desirable to evaluate glazing systems on existing
buildings, e.g., as part of a seismic vulnerability study
with the intention of determining retrofit strategies. A
rating method to prioritize systems that are in need of
seismic retrofit would aid the evaluation process
significantly.
None of the available seismic rating methods for
existing buildings specifically address the seismic
vulnerability of glass curtain walls or windows. Fallen
glass fragments are potentially life threatening for
people close to the building perimeter during
earthquakes. The cost of repairing and replacing
cracked and damaged glass after the earthquake can be
significant. Disruption of normal building operations
due to damaged building enclosure systems can be
extremely expensive-often much more expensive than
Seismic Vulnerability Evaluation of Architectural Glass in Curtain Walls
111
the cost of the seismic repairs themselves. Mock-up
testing of new designs requires significant time and
expense, and mockup testing of existing curtain walls
or windows (for seismic performance evaluation) is
not practical.
The objective of this paper is to present the
development of a method that can lead to prediction of
curtain wall and window glass breakage in
earthquakes. A prediction system is a good alternative
to expensive and time consuming mock-up tests,
which are used to determine the magnitudes of
inter-story drifts that cause curtain wall glass damage,
or to verify that a given curtain wall glass will not
sustain damage under code-specified, maximum
permitted drifts. In this proposed rating method, the
existing curtain wall glass components or windows
can be inspected, and based on the conditions of the
curtain wall (e.g., the condition of glass, glazing frame,
and gaskets) and the code specified maximum
allowable drift, a score can be defined for the curtain
wall. The score will represent cracking vulnerability
of the glass panel at a given drift and can aid the
decision process regarding prioritization of possible
seismic retrofit options for existing curtain wall
systems.
2. Review of Seismic Vulnerability Evaluation Methods
In an effort to promote a program of mitigating the
seismic risk posed by existing hazardous buildings
during earthquake, the Federal Emergency
Management Agency (FEMA) sponsored preparation
of several documents under the National Earthquake
Hazards Reduction Program (NEHRP). The first
document, FEMA 154 [4] describes a “rapid visual
screening” method, which suggests a “sidewalk
survey” approach. Accordingly, an inspector identifies
features related to the seismic safety of the building
and assigns appropriate scores to each type of
structural lateral load resisting system observed to be
part of the building in question. The scoring system
assists the inspector in deciding whether the building
may pose a risk to life safety, is safe, or needs to be
evaluated more accurately using structural analysis.
The screening method of FEMA 154 [4], originally
developed by the Applied Technology Council and
published as ATC 21 [5], has been the subject of
various discussions in the past [6, 7].
Japanese researchers pioneered the development of
seismic screening and retrofit methods. A report by
Ohkubo [8] provides the details of the Japanese
developments in this field, which began in 1977.
Rating systems based on different kinds of scoring
schemes are commonly developed in various
disciplines when screening needs to be done of an
available infrastructure inventory. As an example of
other uses, this approach has been of great importance
in rating highway bridges [9-11]. The important
aspect of this approach is the appropriate assignment
of weights and scores (or indices) to various
performance attributes, which relies on an
application-specific knowledgebase. In the context of
curtain wall glazing systems, a weight and score
assignment scheme would require a good
understanding of the seismic performance of various
types of glazing systems.
For buildings that fail the screening process, a more
accurate seismic evaluation is needed, and this need is
addressed in a follow-up document by FEMA [12].
The procedure in this document, FEMA 178 [12],
involves seismic analysis of the structure to determine
demand forces and calculation of capacities to be
compared with demand forces to identify any
deficiencies. The procedure also requires qualitative
answers to some evaluation statements related to
various aspects of structural and nonstructural systems.
Each evaluation statement describes a certain building
characteristic that is essential to minimize the risk of
earthquake damage. The final evaluation would be a
statement about the condition of the building and what
needs to be done to avoid life-safety hazards. For
more accurate seismic assessment of glazing systems
Seismic Vulnerability Evaluation of Architectural Glass in Curtain Walls
112
(i.e., beyond the result of a rating process), mockup
testing is the practical approach for determining drift
capacity. Based on the available rating systems, an
approach suitable for glazing systems was developed
[13] as described below.
3. Proposed Vulnerability Evaluation Concept for Glazing Systems
Rating procedures rely on equations developed to
investigate the vulnerability of structures. The form of
the equations is highly dependent on the nature of the
problem, the level of accuracy demanded, and the
length of time available for investigation. A common
main step in most rating systems is a comparison of
the capacity of the structure with the demand. In some
rating systems, a limit state such as stress or
displacement is initially defined with respect to which
the capacity of the structure is then determined. Based
on the condition of the structure, the expected
performance (demand) of the structure in an assumed
hazard is then assessed. By comparing the demand
and the capacity, an index is defined. No detailed
rating system presently exists for architectural glass
components in curtain wall systems. However, some
recent development to evaluate damage index and
fragility of glazing systems include the work found in
references [14-17].
In this paper, equations are developed that rely on
experimental research studies on various glass panel
configurations within typical aluminum curtain wall
systems [18-20]. Crack initiation in glass is not only
dependent on the applied drift, but it is also a function
of the mullion-transom connection stiffness, dry
glazing gasket pressure, glass thickness, glass type,
and the environmental effects that glass may have
experienced in service. Fig. 1 is a sketch of a
dry-glazed aluminum curtain wall section
representative of common practice. Equations
developed in this study will compute an index that
represents the seismic glass vulnerability based on
curtain wall conditions and expected drift.
Kawneer 1600 Standard Glass-to-Frame Clearances:
Top: 14 mm Bottom: 10 mm
Left: 12 mm Right: 12 mm
Setting blocks
0.37 m 0.37 m
A
A
Side blocks
Glass Vision Panel1.83 m
Mullion
Horizontal
1.52 mKawneer 1600 shear blocks used to connect horizontals to mullions
TM
Glazing Pocket
Section A-A
1 m = 3.28 ft1 mm = 0.0394 in.
12 mm (Nom.)glass-to-aluminum clearance
6 mm AN monolithic glass panel
Thermal Break Gasket
Pressure Plate (attached to mullion by screws at 9 in. (229 mm) centers at a torque of 95 -100 in. ?lbs (10.7 - 11.3 N?m)
Perimeter Filler
14 mm 19 mm
Fixed Gasket
12 mm (Nom.) glass bite
Mullion
63.5 mm
95 mm
Glazing Lip
Fig. 1 Example curtain wall detail used in the experimental testing program.
Seismic Vulnerability Evaluation of Architectural Glass in Curtain Walls
113
Fig. 2 illustrates a flowchart for calculating what the
authors have named the Seismic Glass Vulnerability
Index, or SGVI. Initially, the information related to
the glass, frame, and gasket properties, along with
building properties such as seismic use and lateral
resistance system information are considered as input
data. The maximum inter-story drift can be obtained
from building structural analysis, or be determined
according to the building code maximum allowable
design drift [1] for a given structural system type and
building occupancy category.
Initial clearance between the glass panel perimeter
and the glazing frame pocket is overcome by the
relative movement between the glass panel and the
glazing frame due to interstory drift. Portions of glass
paneledges will contact the frame pocket resulting in
additional build-up of stress with further increase in
drift. If the contact stress at the glass edge reaches the
crack initiation stress (glass capacity), the glass starts
to crack. The generated stress corresponding to any
applied drift can be estimated if the relationship
between the stress in the glass panel and the applied
drift is developed. If stress in the glass panel exceeds
the ultimate crack initiation stress, then glass breakage
is expected. The Seismic Glass Vulnerability Index
(SGVI) can be defined as the ratio of applied stress to
the maximum crack initiation stress when subjected to
the maximum allowable drift. If this ratio is less than
one, the glass is in the safety margin and will not
likely crack. If the ratio is greater than one, the glass
has exceeded its ultimate crack initiation stress and
glass breakage is expected.
4. Development of Load-Drift Relationship
Relative story drift in buildings causes movement
between the glass panel and the glazing frame. Initial
clearance provided between the edge of a glass panel
and frame generally prevents glass-to-frame contact
under service level drifts. Before contact between the
glass and the frame, stresses in the glass in dry-glazed
glass framing systems are created by friction forces
along the front and back surface edges of the glass
panel perimeter and any gaskets and setting/side
blocks present in the system (Fig. 1). As drift
increases, the clearance is overcome, and the glass
begins to contact the frame, which leads to larger glass
stresses.
One of the main objectives of this study was to
predict the stress generated in the glass panel due to an
applied drift and to develop a relationship between
drift and the resulting surface stress generated in the
glass panel. Development of a drift-stress relationship
is based on the mechanism of contact between the
edge of the glass panel and the glazing pocket.
Bouwkamp [21] introduced Eq. 1 that shows the
relationship between the frame drift corresponding to
partial and full contact of the glass panel edge and the
frame pocket. In this equation, c is the initial clearance
between the glass edge and the glazing pocket, and h
and b are the height and the width of the curtain wall,
respectively. Fig. 3 shows that at a drift equal to two
times the initial clearance, partial contact is predicted.
b
hc 12 (1)
Eq. 1 ignores the effect of friction between the
gasket and glass panel perimeter. In dry-glazed curtain
wall systems, rubber gaskets attached to the aluminum
frame clamp the glass panel in place and restrict
out-of-plane movement along panel edges. The
gaskets distribute the confining pressure resulting
from pressure plate tightening on both faces of the
glass panel along its perimeter. When the glass panel
is subjected to an in-plane load, some resistance to
translation and rotation of the glass panel within the
aluminum frame pockets results from the frictional
force developed at the glass-to-gasket interface. This
frictional force, combined with the unglazed or “bare”
aluminum frame resistance, forms the overall shear
force resistance to in-plane racking displacement of
the mock-up before glass-to-frame contact. After
glass-to-frame contact, the slope of the load versus
Seismic Vulnerability Evaluation of Architectural Glass in Curtain Walls
114
applied drift curve (stiffness) increases significantly.
Fig. 4 represents the total measured load versus
applied drift in a typical dry glazed curtain wall panel
subjected to a static monotonic test. As will be
discussed subsequently, the static and dynamic cyclic
racking tests also show similar behavior to the static
monotonic test. This consistency is important since
the prediction model is intended to be applicable to
both monotonic and cyclic loading conditions. The
load-drift relationship shown in this figure can be
simplified (linearized) as shown in Fig. 5. Five
segments related to the contact mechanism can be
identified from Fig. 4. The critical drifts associated
with these segments are marked by circled numbers in
Fig. 4 and by letters (for simplification of the graph)
in Fig. 5. With reference to Fig. 5, the five segments
are as follows:
Fig. 2 Seismic glass vulnerability index calculation flowchart.
Start Input building properties Input glass, frame,
gasket properties
Calculate the maximum inter-story drift or use default value equal to maximum
inter-story drift permitted by building code
Generated stress (fc)
Maximum stress (Fc
Max) stress associated with crack initiation, causing wall failure
SGVI =
Maxc
c
F
f
SGVI < 1.0
The curtain wall does not need any retrofit
Y
Curtain wall will crack
N
Retrofit
Seismic Vulnerability Evaluation of Architectural Glass in Curtain Walls
115
Fig. 3 Schematic illustration of glazing frame deformation and glass panel movement due to lateral load.
Drift (mm)
0 20 40 60
Load
(N)
0
5000
10000
15000
20000
1
2
3
4
5
6
Start of uniform gasket-to-glass friction
Unglazed frame stiffness
Glass-to-framecontact at top left
corner
Small crack(lower right corner)
Glass-to-framecontact at bottom
right corner
Small crack(top left corner)
Large crack forms
Fig. 4 Example load-displacement diagram obtained from a static monotonic test.
Fig. 5 Simplified curtain wall glass general load-displacement curve obtained from a staticmonotonic test.
0
5
10
15
20
25
0 0.5 1 1.5 2 2.5 3 3.5
Displacement
Forc
e
B
A
C
D
E
Retroft
116
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Seismic Vulnerability Evaluation of Architectural Glass in Curtain Walls
117
Drift (mm)
-20 0 20
Load
(N)
-10000
-5000
0
5000
10000 Glass-Frame Separation
Glass-Frame Contact
Glass-FrameSeparation
Glass-FrameContact
Rubber FrictionForce
Fig. 7 Load-Displacement Diagram for 31.8 mm amplitude, 0.01 Hz cycle applied to curtain wall frame mock-up.
13
12
11
10
9
8
7
6
5
4
3
21
Dc
D2
D1
Load
Drift
14
Fig. 8 Simplified load-drift relations obtained by linearizing actual diagram resulting from cyclic loading at a specific racking step.
Fig. 9 Simplified qualitative load-drift relationship and also principal strain generated at glass corners under applied drift.
Seismic Vulnerability Evaluation of Architectural Glass in Curtain Walls
118
5. Definition of Effective Area for Stress
The general relationship between applied drift and
strain at glass corners forms the basis for the proposed
prediction model. With reference to Fig. 9, it can be
seen that the principal strain is constant for drift
values less than D1 (Point 2). Beyond D1, the glass
surface strain starts to increase. The slope of the
strain-drift relationship increases significantly after
glass-to-frame full diagonal contact at a drift equal to
D2 (Point 3). The glass panel starts to crack at a drift
equal to DC (Point 4).
A proportionality factor between the load-drift
diagram and strain-drift diagram in Fig. 9 can be
defined as the effective area on which stresses act and
is independent of the applied drift. In other words, this
proportionality factor defines a relationship between
the total load applied to a curtain wall (consisting of
glass panel, glazing frame, gaskets, and all
connections) and the generated strain at the corners
where the glass cracking typically initiates. Stress can
then be determined based on the glass panel diagonal
force and the effective glass-to-frame contact area.
Both load-drift and strain-drift relationships are linear
in each stage. Based on Fig. 9, the following equations
express the load (F) as a function of the applied drift
(D):
F = B, if D<D1 (2)
F= K1 (D-D1) + B, if D1<D <D2 (3)
F= K2 (D-D2) + K1 (D2-D1) + B, if D>D2 (4)
where F is the laterally applied load to a curtain
wall panel, K1 and K2 are the slopes of lines 2-3 and
3-4, respectively, in Fig. 9 and B is the total resisting
friction force in the glazed panel due to horizontal
racking displacements. Parameters K1, K2 and B can
be determined based on available laboratory test
results. D is the applied drift to a curtain wall panel.
To compute stresses at glass corners, the load
should conceptually be divided by an “assumed”
effective area. The equations for generated stress at
glass panel corner (f) due to an applied drift can be
expressed by Eqs. 2-4 with F divided by the effective
glass-to-frame contact area (Ae). This effective area
can be determined using the test results at cracking
conditions as discussed subsequently.
6. Seismic Glass Vulnerability Index and Associated Parameters
Glass in a curtain wall will start to crack at or close
to the corners where glass comes into contact with a
glazing pocket and where contact stresses are the
largest. Cracks propagate through the glass panel and
lead to fall out of pieces or shards of the glass panel.
The stress magnitude at glass crack initiation is
defined here as the crack initiation stress (Fc), which
depends on the type and condition of a given glass
panel and is based on test data. Seismic Glass
Vulnerability Index (SGVI) is defined as the ratio of
glass stress (f) to the crack initiation stress (Fc) as
follows:
SGVI = ec AF
B
)(, if D< D1 (5)
SGVI = ecec AF
B
AF
DDK
)()(
)( 11
, ifD1<D < D2(6)
2 2 1 2 1( ) ( )SGVI =
( ) ( ) ( )c e c e c e
K D D K D D B
F A F A F A
if D>D2 (7)
These equations represent the condition of the glass
at any drift applied to a curtain wall. At a specific drift,
if the computed SGVI is equal to or greater than one,
then glass is expected to crack.
Several parameters influence the vulnerability index.
A gasket compressed with larger torque magnitude
applied to the gasket pressure plate fasteners, or
shorter fastener spacing, increases the applied pressure
from the gasket to the glass edges, which increases the
gasket-to-glass friction. An increase in friction
generates higher in-plane stresses in the glass and
makes the glass more vulnerable to cracking when
Seismic Vulnerability Evaluation of Architectural Glass in Curtain Walls
119
glass-to-frame contact stresses are superimposed on
stresses in the glass due to gasket-to-glass friction. A
greater clearance between the glass panel edge and the
glazing pocket allows larger glass movement within
the frame before contact, and can also help a curtain
wall to withstand a greater applied drift before glass
cracking. The type of glass used (e.g., annealed,
heat-strengthened, or fully tempered) also has a direct
effect on the crack initiation stress. The effects of
parameters such as glass panel configuration (e.g.,
monolithic, laminated, or insulating glass unit), glass
panel dimensions, and glass panel thickness on the
SGVI are also important and should be considered.
Effects of some of these parameters on vulnerability
index can be determined from existing mock-up test
results. In these tests, curtain walls with various
configurations of glass and curtain wall framing were
subjected to cyclic applied drift in a
displacement-controlled loading protocol. As the
amplitude of the drift was increased, performance
metrics including the drift corresponding to cracking
were determined. A study of the load-drift
relationships resulting from existing test data helps to
identify the various stages shown in Fig. 8, where the
loads at Points 1 and 8 can be used to estimate
Parameter B (resisting friction force) used in SGVI
Eqs. 5-7. The slope of the line between points 2 and 3
and the slope of the line between Points 9 and 10
represent K1, while the slope of the line between
Points 3 and 4 and that of the line between Points 10
and 11 represent K2.
7. Probabilistic Form of SGVI Equations
Although the parameters needed for the SGVI
Eqs. 5-7 can be derived from the test results, it is clear
that no two tests will necessarily have identical
load-drift graphs. In order to develop a general graph
expressing the load-drift relationship for all tests,
consideration of the statistical distribution of each
control point in Fig. 8 is necessary. For example,
Point 4, which represents the load and drift
corresponding to crack initiation, varies in different
tests. Therefore, it is more appropriate to express the
load corresponding to crack occurrence as a statistical
distribution, which expresses the expected load range
that the curtain wall may experience at cracking.
Because the probability of occurrence for all load
magnitudes in this interval is not the same, the
probability of occurrence for each of these magnitudes
can be defined as well.
In order to present a general load-drift graph for
mockups of different curtain wall configurations, it is
necessary to show the average, the interval and the
probability of occurrence of control points on a
general load-drift graph for each configuration type.
The general load-drift graph can be represented using
the mean and statistical distribution of each point. Fig.
10 depicts a general load-drift graph with a schematic
form of the statistical distribution of different points
included.
The next step is to convert the deterministic
equation for SGVI (Eqs. 5-7) into a probabilistic form.
The probability of the SGVI can be computed based
on the probability of B, K1, K2, D1 and D2 as follows:
P (SGVI) = ec AF
BP
)(
)(, if D < D1 (8)
P (SGVI) = ecec AF
BP
AF
DPDKP
)(
)(
)(
))()(( 11
, if
D1 < D < D2 (9)
Statistical Distribution
Dc
D2
D1
Load
Displacement
Fig. 10 General simplified load-displacement relationship developed from test data and an indication of expected variation.
Seismic Vulnerability Evaluation of Architectural Glass in Curtain Walls
120
2 2 1 2 1( )( ( )) ( )( ( ) ( ))
( ) ( )
( )
( )
P (SGVI) = c e c e
c e
P K D P D P K P D P D
F A F A
P B
F A
if D>D2 (10)
where P(SGVI) represents the probability of SGVI
at an applied drift D. P(B), P(K1), P(K2), P(D1) and
P(D2) are the probabilities of B, K1, K2, D1 and D2,
respectively, when considering a series of repeated
tests.
8. Existing Test Results and Statistical Parameters
The load-drift test results used in this paper are
based on past research [18-20] by the authors.
Whereas previous publications have mainly reported
test observations and drifts corresponding to various
serviceability and ultimate damage states (e.g., glass
cracking and glass fallout), existing unreported data
from past tests are used here to develop load-drift
diagrams. In this section, the actual load-drift test data,
the parameters used in SGVI Eqs. 5-7, and the mean
and variance of these parameters are presented for the
following glass types: Annealed (AN) monolithic
glass with cut (i.e., scored and broken) edges, AN
monolithic glass with seamed (i.e., finished with a fine
belt sander) edges, Heat-strengthened (HS) glass, and
Fully-tempered (FT) glass. Both HS and FT glass
have seamed edges.
The deterministic value of SGVI for any given
drift can be computed using Eqs. 5-7. The existing
test results can be used to compute not only the
magnitude of the parameters in SGVI equations, but
also the statistical distribution of these parameters
using Eqs. 8-10. In previous studies, AAMA 501.6 [2]
was used as a guideline to test curtain walls with
architectural glass. Fig. 8 represents the general
shape of dry-glazed, monolithic glass load-drift
relationships under cyclic loading. The results of
mock-up tests for dry-glazed curtain walls with a
Kawneer 1600TM wall system were used to develop
the material discussed in this section. Glass panels
tested were AN monolithic glass panels 1,829 mm
high, 1,524 mm wide and 6 mm thick. Pressure
plates used to clamp the glass panel within the frame
were attached by screws at 300 mm center-to-center
at a torque equal to 10,700-11,300 N-mm. The
nominal initial gap between the glass panel and the
frame glazing lip was 11 mm.
Results of ten dynamic racking mock-up tests are
used to develop the statistical parameters. Fig. 11
depicts a typical drift-time history for one racking step
applied to a curtain wall mock-up under test. Load and
applied drift were acquired simultaneously and
continuously. For the particular loading step shown in
Fig. 11, drift was increased in four cycles to 38.1 mm,
repeated four cycles at 38.1 mm amplitude, and then
decayed in four cycles following the AAMA 501.6
profile [2]. The glass panel in this test started to crack
at +/- 38.1 mm drift amplitude. Fig. 12 shows the
load-drift relationship at various cycles for the entire
loading history for one of these tests, referred to as
Test Number 1. Fig. 13 shows the load-drift
relationship for drift cycles with 38.1 mm amplitude
when cracking occurred.
As discussed earlier, a multi-line graph provides a
reasonable estimate for the load-drift relationship in
curtain wall panels subjected to cyclic drifts. Fig. 8
shows the general multi-line diagram for the load-drift
relationship. The coordinates of different points
shown in Fig. 8 can be determined for the cyclic
load-drift relationship shown in Fig. 13. For example,
considering Test Number 1 results as shown in Fig. 13,
the coordinates of transition points as defined in Fig. 8
are listed in Table 1.
In order to use the load-drift relationship for SGVI
calculations, the points in the first quadrant (i.e., the
loading stage) as in Fig. 9 would be sufficient to
approximate the cracking load. Fig. 14 shows the
simplified tri-linear relationship between the load and
drift in Test Number 1 used in SGVI equations. The
Seismic Vulnerability Evaluation of Architectural Glass in Curtain Walls
121
coordinates of points in Fig. 14 were calculated using
the absolute average values in Table 1, and were
subsequently used to determine the following
parameters for SGVI Eqs. 5-7: K1 = 86.7 N/mm, K2 =
187.4 N/mm, D1 = 5.1 mm, D2 = 27.2 mm, Dc = 36.3
mm, and B = 8896 N.
Fig. 11 Typical acquired drift-time history for one dynamic racking step.
Drift (mm)
-40 -20 0 20 40
Load
(N)
-15000
-10000
-5000
0
5000
10000
15000
Fig. 12 Entire acquired cyclic load-drift relationship for an an monolithic glass panel identified as test No. 1.
Drift (mm)
-40 -20 0 20 40
Load
(N)
-15000
-10000
-5000
0
5000
10000
15000
Fig. 13 Acquired load-drift data for only 38 mm amplitude cycles for an monolithic glass panel test No. 1.
Seismic Vulnerability Evaluation of Architectural Glass in Curtain Walls
122
Drift (mm)
0 10 20 30 40
Load
(N)
0
2000
4000
6000
8000
10000
12000
Fig. 14 Simplified load-drift diagram computed for an monolithic glass panel test No. 1.
Table 1 Coordinates of the points shown on Fig. 8 for AN glass with cut edges for test number 1.
Point Load (N) Drift (mm)
1 8896 0
2 8896 6.6
3 10053 27.7
4 12099 36.6
5 0 30.0
6 -6806 25.1
7 -8896 10.7
8 -8896 0
9 -8896 -3.8
10 -11298 -27.2
11 -12633 -36.1
12 0 -27.4
13 6761 -18.0
14 8896 -8.9
Based on such information, crack initiation starts at
a drift equal to 27.2 mm in Test Number 1. Therefore,
the SGVI expressed by Eq. 7 at a drift equal to 1.43 in.
(D = 27.2 mm) is equal to 1.0. Substituting the above
parameter values in Eq. 7 yields the following:
SGVI = 2 2 1 2 1( ) ( )
( ) ( ) ( )c e c e c e
K D D K D D B
F A F A F A
Here,
187.4(36.3 27.2) 86.7(27.2 5.1) 8896
( ) ( ) ( )1.0 =
c e c e c eF A F A F A
The product (Fc)Ae can be computed from the above
relation, and with the availability of the value of Fc
(e.g., from manufacturer’s data), the effective area Ae
can be estimated.
If the same procedure that was explained for Test
Number 1 is used for the rest of the test results for AN
monolithic glass with cut edges, then from each test,
corresponding parameters involved in the SGVI
equations can be computed. Parameters resulting from
all tests can be used to compute the mean and variance
and, consequently, the assumed normal distribution
for each parameter. Table 2 lists the summary results
of the ten tests and shows the load-drift curve
transition point coordinates according to Fig. 8. If a
point shown in Fig. 8 could not be identified on the
load-drift curve resulting from a test, then NA is
shown instead of a coordinate in Table 2. The same
data are also plotted in Fig. 15. Using the same
procedure that was used for Test Number 1, the SGVI
equation parameters can be computed for all test
results. Table 3 shows these computed parameters for
AN monolithic glass with cut edges along with the
parameters for other glass types discussed
subsequently.
The same procedure was next used to find the SGVI
parameters for dry-glazed Kawneer 1600TM curtain
wall mock-ups with seamed-edge annealed monolithic
glass panels. Four mock-up test results were available
to calculate the SGVI parameters for this
configuration. First, load-drift curve transition point
Seismic Vulnerability Evaluation of Architectural Glass in Curtain Walls
123
coordinates as shown in Fig. 8 were extracted from the
load-drift diagrams for each test. Then, the SGVI
parameters corresponding to each test were computed
and are listed in Table 3 along with the average and
the variance of the SGVI parameters.
In a similar fashion, the SGVI parameters were
derived from the mock-up test results for dry-glazed
Kawneer 1600TM curtain wall panels with 6 mm thick
heat-strengthened (HS) monolithic glass plates with
seamed edges. The glass panels had the same
dimensions as in other tests, i.e., 1,829 mm height and
1,524 mm width. Pressure plates were used to clamp
the glass panel within the frame as previously
described to a torque of 10,700-11,300 N-mm. The
nominal initial gap between the glass panel and
glazing lip was also 11 mm for these tests. Six
available mock-up test results were used for
calculation of SGVI parameters. The same procedures
as described above were employed to determine the
SGVI summarized in Table 3 for these HS monolithic
glass panels.
Finally, the SGVI parameters were determined for
similarly glazed fully tempered (FT) monolithic glass
curtain walls following the aforementioned procedures.
The glass panels were FT monolithic with 6 mm
thickness and seamed edges. Five available mock-up
test results were used for calculation of the SGVI
parameters and their descriptive statistics presented in
Table 3.
Mean load-drift relationships for each of the four
sets of tests are also plotted in Fig. 16, which
illustrates the general pattern of individual tests (Fig.
14). The results show that the AN glass with seamed
edges had significantly higher cracking load and drift
capacity compared to that of AN glass with cut edges.
The capacity graphs show capacity of AN glass with
seamed edges to be close to those of FT glass with
seamed edges. For AN glass with cut edges and HS
glass with seamed edges, however, the load at
cracking is approximately the same, but HS glass
reaches cracking at a drift of 61.0 mm, as compared to
41.2 mm for AN glass. The former two types (AN
glass with seamed edges and FT glass with seamed
edges) exhibited about a 30% larger cracking load as
compared to the latter two types (AN glass with cut
edges and HS glass with seamed edges) for the panels
tested.
9. Modification of Model Parameters for Curtain Wall Configuration Variations
The statistical distributions of different parameters
that are involved in the SGVI equations were
computed from existing test results. Test results
presented are specific to a Kawneer 1600TM dry-glazed
curtain wall panel fitted with glass panels 1,829 mm
high, 1,524 mm wide and 6 mm thick, with a 11 mm
nominal clearance between the glass panel and the
glazing pocket, and pressure plates attached using
system-specific fasteners at 300 mm centers and a
torque of 10,700-11,300 N-mm. In order to use the
SGVI equations for curtain wall configurations, the
relationship between the SGVI parameters and the
curtain wall configuration variation should be
estimated, as explained below. In Table 4, SGVI
parameters, and their mean and variance for different
parameters corresponding to different glass
configurations considered (AN glass with cut edges,
AN glass with seamed edges, HS and FT glass with
seamed edges) were computed using laboratory test
results. As discussed above, the SGVI can be
expressed using a trilinear load versus drift curve.
Parameter B represents the force that is needed to
overcome the initial friction resistance between the
glass and pressure plates. The following equation can
be used to compute Parameter B for different screw
spacing:
( /11,000)
( / 300)o
TB B
S
(11)
where the value of Bo is the average measured B in
the mock-up tests when pressure plates were attached
by screws at 300 mm spacing and at a torque of
10,700-11,300 N-mm. T is the torque used to tighten
Seismic Vulnerability Evaluation of Architectural Glass in Curtain Walls
124
the screws (in.-lbs), and S expresses the spacing of the
screws (in.). Once Bo is determined from the test
results, B can be found for the torque applied and a
given spacing S.
Table 2 Coordinates of the points shown on Fig. 8 for AN glass with cut edges for all 10 tests.
Point Test 1 Test 2 Test 3 Test 4 Test 5
Load (N) Drift (mm)
Load (N)
Drift (mm)
Load (N)
Drift (mm)
Load (N)
Drift (mm)
Load (N)
Drift (mm)
1 8896 0.0 8434 0.0 9430 0.0 11112 0.0 7784 0.0
2 8896 6.6 8434 3.0 9430 6.6 11112 8.6 7784 7.6
3 10053 27.7 11196 27.4 11734 28.7 16200 23.4 8541 21.6
4 12099 36.6 16561 43.2 NA NA 13967 37.6 19274 43.9
5 0 30.0 0 35.8 0 26.7 0 33.0 0 31.2
6 -6806 25.1 -7464 27.7 -934 25.1 -6690 23.1 -7927 24.6
7 -8896 10.7 -10062 0.0 -11218 5.3 -9528 6.4 NA NA
8 -8896 0.0 -10062 0.0 -7784 0.0 -11218 0.0 -9528 0.0
9 -8896 -3.8 -10062 0.0 -11218 -4.8 -9528 -6.1 NA NA
10 -11298 -27.2 -11654 -31.5 -14679 -22.9 -11565 -18.0 NA NA
11 -12633 -36.1 NA NA -18984 -36.3 -18455 -36.1 NA NA
12 0 -27.4 0 -35.8 0 -30.2 0 -26.2 0 -26.4
13 6761 -18.0 7535 -26.9 6281 -20.1 6165 -19.1 NA NA
14 8896 -8.9 8754 0.0 11112 0.0 7784 -3.8 NA NA
Point Test 6 Test 7 Test 8 Test 9 Test 10
Load (N)
Drift (mm)
Load (N)
Drift (mm)
Load (N)
Drift (mm)
Load (N)
Drift (mm)
Load (N)
Drift (mm)
1 8896 0 10173 0 6939 0 6081 0 3474 0
2 8896 4.8 NA NA 6939 3.6 6081 1.3 3474 0
3 12575 24.9 NA NA 8251 27.9 7384 38.1 4341 31
4 NA NA NA NA 12597 50.8 9991 52.6 11294 43.4
5 0 28.7 0 19.1 0 45.7 0 46.7 0 38.9
6 -3336 22.1 NA NA -5645 26.9 -4341 33 -4341 26.9
7 NA NA -8896 4.6 -6081 3 -5231 3 -7384 5.8
8 -7340 0 -8896 0 -6081 0 -5231 0 -7384 0
9 -7340 -2.5 -8896 -2.5 -6081 0 -5231 0 -7384 -6.4
10 -10676 -25.1 -12086 -24.9 -8251 -36.1 -7384 -40.6 -9119 -27.9
11 13833 -43.2 16084 -37.1 9990 -51.6 10422 -53.6 12597 -43.4
12 0 -30.7 0 -24.4 0 -47 0 -43.7 0 -36.3
13 4066 -22.6 NA NA 3910 -34.3 4777 -29 2224 -28.4
14 8896 -1.3 NA NA 6939 -3.6 6081 -1.3 3474 -1.5
Table 3 SGVI parameters computed from different tests.
AN glass with cut edges Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Test 10
K1 (N/mm) 80.4 77.9 261.1 108.4 104.7 164.4 141.9 57.6 44.7 49.6
K2 (N/mm) 187.4 374.4 267.4 362.7 492.3 121.5 328.7 158.7 205.8 373.4
D1 (mm) 5.3 1.5 6.9 6.9 6.6 3.8 2.5 1.8 0.8 3.3
D2 (mm) 27.4 29.5 23.1 19.8 28.7 25.1 25.1 32.0 39.4 29.5
DC (mm) 36.3 43.2 36.3 36.8 43.9 43.2 37.1 51.3 53.1 43.4
B (N) 8,896 9,248 11,165 8,656 8,607 8,118 9,537 6,512 5,658 5,431
FCAe (N) 12,366 16,561 18,985 16,214 19,274 13,834 16,085 11,294 10,209 11,948
AN Glass with Seamed Edges Test 1 Test 2 Test 3 Test 4
K1 (N/mm) 69.9 101.3 97.4 75.6
K2 (N/mm) 247.3 200.5 103.9 NA
Seismic Vulnerability Evaluation of Architectural Glass in Curtain Walls
125
D1 (mm) 1.5 3.7 2.9 2.0
D2 (mm) 30.5 42.2 36.8 32.3
DC (mm) 55.6 62.4 62.7 NA
B (N) 11,321 11,672 14,043 11,917
FCAe (N) 19,563 19,617 20,039 NA
HS Glass with Seamed Edges Test 1 Test 2 Test 3 Test 4 Test 5 Test 6
K1 (N/mm) 22.1 12.4 7.2 12.8 238.0 200.0
K2 (N/mm) 80.9 111.0 150.1 65.8 601.9 587.7
D1 (mm) 1.3 1.8 3.8 3.0 3.8 7.9
D2 (mm) 39.9 47.5 34.0 36.3 32.3 35.8
DC (mm) 55.6 64.0 67.3 NA NA NA
B (N) 2,947 2,386 2,822 3,051 9,848 9,851
FCAe (N) 5,075 4,777 8,033 4,777 38,228 28,704
FT Glass with Seamed Edges Test 1 Test 2 Test 3 Test 4 Test 5
K1 (N/mm) 73.7 38.2 23.1 27.8 210.0
K2 (N/mm) 532.6 1196.8 142.6 341.8 938.9
D1 (mm) 5.6 3.3 2.8 4.3 7.1
D2 (mm) 58.7 51.8 38.6 43.4 53.8
DC (mm) 74.2 58.2 53.8 NA 67.1
B (N) 8,033 8,354 8,505 9,555 8,625
FCAe (N) 20,199 17,806 11,512 18,678 30,844
Table 4 Descriptive statistics for SGVI parameters.
SGVI parameter AN-cut edges AN-seamed edges HS-seamed edges FT-seamed edges
Mean (m) Variance (s2) Mean (m) Variance (s2) Mean (m) Variance (s2) Mean (m) Variance (s2)
K1 (N/mm) 109.1 4,379 89.5 293 82.1 11,422 74.6 6,123
K2 (N/mm) 287.2 13,935 183.9 5,349 266.2 65,635 630.5 186,685
D1 (mm) 5.3 5.5 2.5 1.2 3.6 5.5 4.6 2.9
D2 (mm) 28.4 28.8 35.6 34.2 37.6 30.0 49.3 65.0
DC (mm) 43.2 36.4 61.0 16.0 61.5 31.9 64.0 63.8
B (N) 8,182 3,281,926 12,344 2,196,161 5151 13,295,103 8,616 325,023
FCAe (N) 14,675 10,278,885 19,741 67,703 14928 216,646,228 19,808 49,004,950
Parameter D1 defined in Fig. 4 as the first
glass-to-frame contact (at one corner), can be
expressed as a function of the initial clearance
between the glass panel edge and glazing pocket. D1
can be computed using the following equation:
D1= (c1) (12)
Where c1 is the horizontal clearance between the
vertical glass edge and frame pocket (horizontal
clearances are assumed to be overcome before the
vertical clearances as shown in Fig. 3 and α is a
coefficient that relates the actual clearance (c1) to the
measured drift component at first contact D1.
Parameter D2 defined in Fig. 4 as the second
glass-to-frame contact can be computed based on the
following equation in ASCE 7-10 [1].
D2 =
1
21 12
cb
chc
p
p (13)
Where hp and bp are, respectively, the height and
width of the rectangular glass panel, and c2 is the
clearance between the horizontal glass edge and frame
pocket.
The average value of D1 in Table 4 is 5.3 mm.
Because the initial gap between the glass panel edge
and the glazing pocket was 11 mm, the value in
Eq. 12 can be taken as approximately equal to 0.5.
Seismic Vulnerability Evaluation of Architectural Glass in Curtain Walls
126
The average value of D2 resulting from the tests in
Table 5 is equal to 28.4 mm. The parameter D2 based
on Eq. 13 can be computed to be 48 mm. The average
value of D2 based on test results is approximately 60%
of the value of D2 computed from Eq. 13. This simply
indicates that if Eq. 13 is used to give the drift
corresponding to closing of glass-to-frame clearance
as in Fig. 3 (i.e., glass-to-frame contact at opposing
diagonal corners of the glass panel), the result may not
be conservative because realistic glass panel perimeter
boundary conditions (e.g., gaskets and pressure plates)
will cause the test values to be smaller than the
equation result. However, Eq. 13 can be modified to
give the same magnitude for D2 as the test results by
using a coefficient equal to 0.6. Therefore, after
modification, D1 and D2 can be obtained from Eqs.12
and 13, respectively, with α = 0.5 and with multiplier
1.2c1 substituting 2c1.
Drift (mm)
-60 -40 -20 0 20 40 60
Load
(N)
-30000
-20000
-10000
0
10000
20000
30000Test 1Test 2Test 3Test 4Test 5Test 6Test 7Test 8Test 9Test 10
Fig. 15 Plot of the coordinates of points listed in table 2 for all 10 tests of an glass with cut edges.
Drift (mm)
0 20 40 60
Load
(N)
0
5000
10000
15000
20000
ANAN SeamedHSFT
Fig. 16 Summary load-drift relationships from mock-up tests on 6 mm thickness 1,829 mm × 1,524 mm monolithic glass panels.
Seismic Vulnerability Evaluation of Architectural Glass in Curtain Walls
127
Next, the modified parameter for AN monolithic
glass with seamed edges is considered. The
parameters involved in the SGVI Eqs. 5-7 for
seamed-edge AN monolithic glass along with the
mean and variance are listed in Table 3. Using the
average value of B = 12,340 N from Table 4 for Bo,
Eq. 11 can be used to find B, D1 and D2 can be
determined from Eqs. 12 and 13, respectively, with α
= 0.23 and with multiplier 1.5c1 substituting 2c1.
Table 4 also shows the statistical distributions of
different parameters involved in the SGVI Eqs. 5-7 for
curtain walls with HS monolithic glass. The value of
B can be obtained from Eq. 11 by using the value of
5150 N for Bo from Table 4. Based on the same
procedure, D1 and D2 can be determined from Eqs. 12
and 13, respectively, by using α = 0.32 and a
multiplier of 1.56c1 instead of 2c1. Finally, based on
the summary results in Table 4 for curtain walls with
FT monolithic glass and using an average value 8,616
N for Bo, we can find the value of B for various screw
spacing and torque values from Eq. 11. The values of
D1 and D2 can similarly be found from Eqs. 12 and 13,
respectively, by using α = 0.42 and a multiplier of 2c1
for curtain walls with FT glass for any glass panel
dimensions and glass panel-glazing lip clearances.
SGVI values can then be determined accordingly
for glass curtain wall types discussed in this paper for
seismic vulnerability evaluation. Further discussion on
the topic, in particular the probabilistic aspects of the
method, and its application in development of a
seismic design methodology for glazing systems are
discussed in Shirazi [13].
10. Summary and Concluding Remarks
The Seismic Glass Vulnerability Index (SGVI) can
be used to evaluate whether a glass panel would
exhibit visible cracking under a given applied drift. If
the generated in-plane surface stress in the glass
exceeds the nominal crack initiation stress, then the
SGVI would be greater than 1.0, and it would indicate
the expectation of visible crack initiation in the glass
panel. The magnitudes of the parameters used in the
SGVI equations depend on parameters such as gasket
friction, stiffness resulting from glass panel-to-frame
compressive interaction, glass-to-frame contact area,
and glass crack initiation stress. Because of the
probabilistic nature of glass breakage, it is more
appropriate to express different SGVI parameters
statistically as a function of the probability of
occurrence for those parameter values. In other words,
once the probability distributions of parameters are
determined based on test results, SGVI probabilities
can be computed. This study supports the following
conclusions:
General seismic rating approaches now used for
other building systems are suitable for application to
aluminum curtain wall glazing systems.
Existing architectural glass racking test data can be
converted to a form useful for development of a
seismic rating approach for glazing systems.
(Additional data can be incorporated to enhance the
modeling.)
Cyclic racking test load-displacement hysteresis
data can be simplified to multi-linear curves for
development of a statistical-based prediction model.
A glass vulnerability index (“SGVI”) can be derived
as a function of load-displacement relation properties,
including gasket friction, glazing frame-glass
interaction stiffness, and glass-to-frame contact drifts.
The model can be modified to include variation of
parameters such as pressure plate screw torque and
spacing, and glass type.
Derived SGVI equations can be used to estimate the
probability of glass cracking for the type of specimens
discussed. Ultimately, this could serve as a method for
seismic vulnerability evaluation of curtain wall glass
components in existing buildings. The method
presented could also be used for new curtain wall
glazing designs. This preliminary study has presented
an approach requiring additional laboratory data and
further refinement to make it usable for general
practice.
Seismic Vulnerability Evaluation of Architectural Glass in Curtain Walls
128
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