Seismic Vulnerability Evaluation of Architectural Glass in ... · curtain wall and window glass...

19
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. Memari 1,2 , Ali Shirazi 1 , Paul A. Kremer 1 and Richard A. Behr 3 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, Δ fallout , 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. Δ fallout 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 Δ fallout . 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., Δ fallout ) 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

Transcript of Seismic Vulnerability Evaluation of Architectural Glass in ... · curtain wall and window glass...

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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

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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

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(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.

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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

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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

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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

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116

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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.

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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

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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.

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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

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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.

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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

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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

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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

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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.

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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.

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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.

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Seismic Vulnerability Evaluation of Architectural Glass in Curtain Walls

128

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