Structural Glass (Publ Hong Kong)

29Glass Structures

29.1 Introduction

Glass is a brittle material that is weak in tension because of its noncrystalline molecular structure. When

glass is stressed beyond its strength limit, breakage occurs immediately without warning, unlike steel and

aluminum where plastic mechanism can be formed. Stress or moment redistribution does not occur in

glass, and local and then consequential global failure is very common. Testing has shown that glass

strength is statistical in nature.

The main constituent of glass is silica sand. Zachariasen and Warren [1] suggested that glass is made

up of network formers and modifiers (Figure 29.1). Silicon and oxygen ions bonded together (formers)

to form the basic three-dimensional network structure in which ions of sodium, potassium, calcium, and

magnesium (modifiers) are bonded in the holes inside the siliconoxygen former network. Glass is one

of the most durable building materials. An extremely important property of glass is its resistance

to corrosion attack by water and acid.

There are three basic types of glass: float glass, plate glass, and sheet glass. Float glass is produced by

pouring continuously from a furnace onto a large shallow bath of molten tin. In the flow chamber the

atmosphere is controlled to prevent oxidation. The second type of glass is plate glass, which is produced

by grinding and polishing rough glass. The third type is sheet glass, which is produced by continuously

drawing molten glass from a bath through an annealing lehr. A simplified diagrammatic presentation of

the production process is illustrated in Figure 29.2. Nowadays, more than 90% of glass is produced by

the float process. The float glass is available in a number of modified forms: reflective coated glass, heat-

absorbing glass, tempered glass, insulating glass, acoustical glass, etc.

Glass as a building material has been widely used in curtain wall and glass wall systems, which

generally provide an esthetic appearance to the complete building. Large glass panels of size in

A. K. W. SoResearch Engineering Development

Facade and Fire Testing

Consultants Ltd.,

Yuen Long, Hong Kong

Andy LeeOve Arup & Partners

Hong Kong Ltd.,

Kowloon, Hong Kong

Siu-Lai ChanDepartment of Civil and Structural

Engineering,

Hong Kong Polytechnic University,

Kowloon, Hong Kong

29.1 Introduction ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29-1

29.2 Strength of Glass.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29-4Types of Glass

29.3 Design of Glass.. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29-8

29.4 Failure Criterion ... . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29-11

29.5 Stress Evaluation and Common Causes ofBreakages .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29-12Common Causes of Glass Breakage Impurities

29.6 Numerical Examples for Breakage Analysis of GlassStructure.. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29-13

29.7 Failure Test of In-Service Glass .. .. . . . . . . . . . . . . . . . . . . . . . . . 29-13

29.8 Curved Glass Panel. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29-15

29.9 Flexible Support for Full-Scale Mock-Up Test ... . . . . . 29-15

29.10 Conclusions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29-18

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29-18

0-8493-1569-7/05/$0.00+$1.50# 2005 by CRC Press 29-1

Copyright 2005 by CRC Press

excess of 1.5 m2 are commonly used in commercial buildings to date. In practice, they are

structurally glazed with structural sealants, on the four sides or on two sides with the other two

edges clamped mechanically along the transoms. For shop fronts and entrances of prestigious

buildings, an unobstructed view and architectural appearance can normally be provided by using a

glass wall system. Generally speaking, their esthetic appearance is more appealing than that of to

other finishes.

When compared to other building materials such as concrete, steel, or even timber, glass receives

relatively less attention from the researcher and the engineer. The probable reason for the lack of

research in glass may be the perceptively moderate tendency for collapse when compared with other

materials. However, as glass structures have no allowance for plastic deformation, overloading will

network formers

network modifiers

FIGURE 29.1 Simplified two-dimensional representation of a glass network.

Furnace Lehr

Cutting

FurnaceLehr

Twin grinding

Cutting

Furnace

(c)

(b)

(a) LehrCutting

Moltentin bath

FIGURE 29.2 Manufacturing processes of glass: (a) float glass, (b) plate glass, and (c) sheet glass.

29-2 Handbook of Structural Engineering


not be shed to other parts of a structure, and their breakage normally is without warning due to

their brittleness. The breakage will lead to casualties when debris falls onto the street from a high-

rise building. In the past two decades or so, it has been noted that glass structures are commonly

constructed in areas of high human exposure such as shopping arcades and city malls. The failure

of the structure may be catastrophic and cannot therefore be overlooked. Although the uses of

laminated and tempered glass can lower the chance of harmful damage, they may not be preferred

as they reduce the vision quality of glass.

The major reason for special care in the design of glass is that it has no ductility to allow moment or

force redistribution like steel and concrete frames. Further, the overdesign is costly. In Hong Kong, the

facade system normally takes a share from 15 to 20% of the total construction cost in a commercial

building. Obviously, the resources spent on research in glass are far less than for other materials like

concrete and steel. Although glass manufacturers provide design manuals for glass panels, many of these

are based on the linear theory [2], which is of inadequate accuracy under high wind pressure. The

American [3] and the Canadian [4] design codes of practice for glass require the consideration of

nonlinear effect when the glass plate deflection is large and of a magnitude more than three-fourths of its

thickness, which is very common in practice. In a general design of glass structures, the glass panel

exhibits considerable change in geometry, and an accurate analysis should allow for the geometrically

nonlinear effects in accordance with these design codes. Figure 29.3 shows the damage of buildings after

a typhoon attack.

Studies have shown that breakage of annealed glass is due to the tensile stress on the hairy cracks on the

surface of the panel, resulting in a serious stress concentration. Due to the difficulty in estimating the

density and the extent of these hairy cracks in all glass panels, the failure probability instead of direct

specification of failure load for a glass panel is usually used as a reference for safety of glass structures.

Generally speaking, the probability of failure (POF) of 8/1000 is acceptable for most purposes. In

congested areas, the POF should be further reduced.

In recent years, the extensive construction of high-rise buildings with curtain wall envelops in many

cities in China and Hong Kong has further highlighted the importance of conducting more research on

FIGURE 29.3 Damage of buildings after a typhoon attack.

Glass Structures 29-3


the safety of these structures. In fact, at the time of writing this chapter, use of glass curtain walling is

heavily criticized in China as a hanging bomb.

29.2 Strength of Glass

In most structural applications of glass it is necessary for the components to sustain mechanical

stress. When a material is stressed, it deforms, and strains are created. At a low level of stress, most

materials obey Hooks law, that is, strain is proportional to stress. While the stress level is high,

most materials deform plastically. Glass is a brittle material, which cannot accommodate this plastic

deformation but breaks without warning. The stressstrain curve in Figure 29.4 shows a perfect

linearity from zero strain to failure. The mechanical properties of glass as an engineering material

are tabulated in Table 29.1.

Generally speaking, it can be stated that the theoretical strength of a piece of glass is equal to about one

tenth of its modulus of elasticity [5]. Glass in compression is extremely strong. The compressive strength

can approach 10,000 MPa without breakage. However, glass in tension usually fails at stress levels less

than 100 MPa. It has been pointed out that the failure of glass [6] results from a tensile component of

stress. Nowadays, it is generally accepted that the failure of glass originates at surface flaws [7] at which

stresses are concentrated, as shown in Figure 29.5. Since basically no plastic flow is possible in glass, these

flaws lead to high stress concentrations when glass surface is in tension. Because of the random nature of

the flaws, a large variability in the strength of individual pieces of glass has been observed and reported [6].

Therefore, the failure strength of glass can only be expressed by means of a statistical analysis. Based on

these statistical results, we can only obtain a design value at which the risk of fracture of glass is

sufficiently low, but it provides no guarantee that the glass will survive under the design load level.

Stre

ss

Strain

Glass

SteelBrittle fracture

Plastic deformation

FIGURE 29.4 StressStrain diagram.

TABLE 29.1 Mechanical Properties of Glass

E Youngs modulus of elasticity 10.4 106 psi or 7.2 1010 N/m2G Modulus of rigidity 4.3 106 psi or 3.0 1010 N/m2m Poissons ratio 0.22a Coefficient of thermal expansion 88 107/Cr Density 157 lb/ft3 or 2.5 g/cm3



An important property of glass is that its strength depends on the duration of load [6] application and

on the environmental conditions. This concept is not familiar to engineers and architects. Basically, the

relationship between stress and time can be expressed as

snT constant 29:1

where s is the applied stress, while T is the duration of the stress, and n is a constant with a value between12 and 20. Figure 29.6 illustrates the strength of glass against time. Since the duration of loading is

Water vapor(a)

(b)

(c)

Glass

Water vapor uniformattack on the crack inthe absence of tensile stress

Preferential attack at the tipof the crack undertensile stress

FIGURE 29.5 Surface flaw: (a) two-dimensional model of flaw on glass surface, (b) attack of water vapor on the

crack, and (c) attack of water vapor on the crack under tensile stress.

Stre

ngth

, MPa

Time, s0.001 0.01 0.1 1 10 102 103 104 105 106

20

40

60

80

100

120

140

160

FIGURE 29.6 Glass strength and load duration.



important in determining the failure load for a given glass panel, it is necessary to define the loadings

in a time-dependent form.

29.2.1 Types of Glass

From a structural point of view, there are several types of glass used in buildings. Their basic properties

are discussed as follows.

29.2.1.1 Tempered (Toughened) and Heat-Strengthened Glass

The fracture of glass is initiated from surface flaws. Therefore, the practical strength of glass may be

increased by introducing a local high compressive stress near its surfaces. This can be achieved by means

of thermal toughening in which the glass plate is heated to approximately 650C, at which point it beginsto soften. Then, its outer surfaces deliberately are cooled rapidly by air blasts. The exterior layers are

quickly cooled and contracted. This creates a thin layer of high compressive stress at the surfaces, with a

region of tensile stress at the center of the glass. As illustrated in Figure 29.7, the stress distribution across

the thickness of a plate may be represented by a parabola. This parabolic stress distribution must also be

in self-equilibrium. However, the exact shape of this curve depends on the geometric shape of the glass

section and the physical properties of the particular glass composition used. The bending strength is

usually increased by a factor of 3 to 5 of the strength of annealed glass. Generally speaking, the nominal

breaking stress of the glass will be increased by an amount equal to the residual compressive stress

Compression

Neutral

Tension

Tension

Compression

Before bending After bending

Before bending

(a)

(b) After bending

App

lied

load

App

lied

load

FIGURE 29.7 Stress profiles: (a) annealed glass and (b) toughened glass.



developed at the surface. When the toughened glass is broken, it fractures into small, harmless dice,

which result from multiple crack branching due to the release of elastic energy.

29.2.1.2 Annealed Glass

This refers to those glass panels without heat treatment. The permissible stress is taken approximately as

15 N/mm2. Sometimes we cannot avoid using annealed glass because of manufacturing difficulties such

as the glass panels being too large for heat treatment. Due to its small strength, annealed glass is weak in

thermal resistance. Partial shading causes annealed glass to fail by thermal stress. Very often, glass fins are

annealed.

29.2.1.3 Tinted Glass

Tinted glass or heat-absorbing glass is made by adding colorant to normal clear glass. Light transmit-

tance varies from 14 to 85%, depending on color and thickness. Because of this, the tinted glass is hot,

and heat-strengthened glass is normally used in making tinted glass.

29.2.1.4 Coated Glass

Coated glass is manufactured by placing layers of coating onto the glass surfaces. There are two types, the

solar control (reflective) and the low-emissivity (low-e) types. They are more related to energy absorption

and light transmission and only indirectly affect the structural strength by changing the thermal stress.

Because of this, for colored glass to prevent excessive thermal stress, at least heat-strengthened glass

should be used.

29.2.1.5 Wired Glass

Wired glass is made by introducing a steel mesh into molten glass during the rolling process. It is weak in

resisting thermal stress and therefore has a high rate of breakage due to sunlight, etc. Polished wired glass

is generally used for fire rating since after its breakage, it is stuck to the wire mesh and prevents passage of

smoke. However, it is weak in resisting thermal stress. Figure 29.8 shows the damaged wired glass panels

under sunlight.

FIGURE 29.8 Broken glass panel due to thermal stress.



29.2.1.6 Laminated Glass

This is a very common form of glass formed by bonding two or more glass panes by interlayers like

polyvinyl butyral (PVB) or resin. The thickness of this interlayer is normally 0.38, 0.76, 1.52 mm, etc.

The major problem for laminated glass is the validity of composite action. Can we assume a composite

action, that is, an 8- 6-mm-thick laminated glass is equivalent to a 14-mm-thick glass? If not, does itbehave as two separated panes 8 mm and 6 mm thick?

The actual response for a laminated glass is somewhere between these two extremes. For short-

term load, the behavior is closer to composite assumption, while for long-term load, it behaves as

separated panes because of creeping effect in the interlayer. However, as the actual response is

dependent on the property of the interlayer, it may not be overgeneralized. One method is to use a

simple test to measure the deflection of the panel under a specific load and then compare this with

the deflection calculated by a finite element program. We can then adjust the equivalent thickness

in the program to give the same deflection so that we can determine the equivalent thickness of the

laminated glass pane and use it for economical and rational design. ASTM C1172 is a relevant

standard for further information and testing. Figure 29.9 shows the property of laminated glass

when broken.

29.3 Design of Glass

The linear deflection theory, which assumes that deflections are directly proportional to applied

load, is of sufficient accuracy for many engineering applications. However, for a thin glass plate

simply supported on four sides, the linear theory is invalidated when the deflection is larger than

three fourths of its thickness (Canadian code [4]). The typical load versus central deflection curve

for a glass panel is shown in Figure 29.10, and it can be seen that the linear theory is only valid in

a small loading range before deflection is significant. The use of the linear theory will result in a

deviation from the real solution as shown in Figure 29.10 for deflection and Figure 29.11 for stress.

In the linear theory, the location of maximum stress is predicted at the plate center. In fact, the

FIGURE 29.9 Laminated glass when it is broken.



location of maximum stress changes with the load level and the aspect ratio of glass plate. This

change is illustrated in Figure 29.11. From the figure, it can be seen that the maximum principal

stresses at the corner and the center are more or less the same for aspect ratio equal to 1 and load

level equal to 0.1 kPa in the glass plate under consideration. When the load level is increased to

0.76 kPa, the maximum principal stress at the corner increases more rapidly than the stress at the

center. Thus, the maximum stress location is at the corner of the plate. On the other hand, the rate

of increase of the maximum principal stress at the center is much faster than the rate of increase of

the maximum principal stress at the corner for aspect ratio equal to 5. In this case, the maximum

stress is located at the center of the plate. As mentioned above, the failure of glass depends on the

stress state and surface flaws. Thus, there is a need to develop a numerical procedure to find out

the stresses at various locations of the glass plate under different load levels in order to determine

its load capacity in terms of probability of failure.

00

1

2

3

4

5

Load

ing

pres

sure

, kP a

6

7

8

10 20 30Center lateral deflection, mm

40 50 60

Ultimate pressure by thelarge deflection theory = 7.4 kPa

Large deflection theory

Linear smalldeflection theory

Working pressure againstdeflection of span/60 = 2.7 kPa

Working pressure againstbreakage = Ultimate pressure 1.4 = 5.3 kPa

FIGURE 29.10 Load vs. center deflection of a 4-side simply supported glass pane of 2000 mm 1000 mm 5.6 mm.

Glass type Canadiana/U.S.b Australianc U.K.d Chinesee

Load duration (s) 60 3 3 60

Load factor 1.5 1.4

Annealed

(N/mm2)

2025 (edge/center,

following similar)

20 41 for t 6,34.5 for t 8,28 for t 10

28 for 5< t< 12

20 for 15< t< 19

Heat-strengthened

(N/mm2)

4050 32

Tempered (N/mm2) 80100 50 59 84 for 5< t< 12

59 for 15< t< 19

a Canadian General Standards Board (1989), Structural design of glass for buildings, CAN/CGSB-12.20-M89. The firstone refers to center stress and the second one to edge stress.b ASTM (1997), Standard practice for determining minimum thickness and type of glass required to resist a specifiedload, E130097.c Standards Australia (1994), Glass in buildings selection and installation.d Pilkington Glass (see IStructE, Structural Use of Glass in Buildings, 1999).e Technical code for glass curtain wall engineering, JGJ 102-96, 1996, Beijing, China.

Note: t thickness of glass plate.



The design load for glass is time-dependent. It is accepted worldwide that it should be based on the

1-min constant and uniform loads. However, for most applications of glass, load duration has little to no

effect on the long-term performance of glass. There are two common methods in the industry for

determining glass strength. The first is the empirical glass-to-destruction test method, and the second is

the analytical nondestructive computer method.

The empirical glass strength curves were developed from destructive test of glass plates to provide

factual data on glass strength. At least 25 glass panes each thickness and area were tested to produce

a statistical validity for the average breaking pressure under uniform load conditions. A typical design

chart produced from the results of testing glass-to-destruction is included in the appendix of the

ASTM Standard E300-84. The effect of aspect ratio of glass plate has not been indicated in this design

chart.

Nowadays, the advances in computer technology and the dramatic reductions in computer cost

make the computer method for determining glass strength more practical than previously. The finite

element method has made it possible to determine glass design data with various supporting systems

and loading cases effectively. The finite element method is adopted to calculate the magnitudes and

orientations of stress and deflections of the glass plate. The computer outputs are then used with

1 2 3 4 5

40

30

20

10

0

Stre

ss, M

Pa

Aspect ratio

Area = 5.88 m2

Thickness = 4.8 mmMax. principal stress atcorner

center

0.76 kPa

0.1 kPa

0.38kPa

FIGURE 29.11 Stress against aspect ratio at different load levels.



a statistical or failure prediction model [8] to find out the glass breakage probabilities under the

design condition. Glass breaks when the maximum principal tensile stress reaches the critical value

determined by the failure prediction model, which is discussed in the subsequent section. Finite element

computer analysis indicates that as the aspect ratio of the glass plate changes, the levels and locations of

maximum tension stress are also varied. Thus, the method is more realistic in representing the glass

strength.

29.4 Failure Criterion

For commercial glass widely used in curtain wall systems, failure and breakage are due to the

stress concentrated at the invisible hairy crack on its surfaces. The failure stress of a piece of glass

is more dependent on the density of these hairy cracks than the theoretical breakage stress, which can

be as high as 10,000 MPa. Thus, a rational design failure stress is expressed in terms of the duration of

load (Weibulls theory [9] for failure of brittle material). Treatment of glass to reduce surface tensile

stress and the area of the glass panel is being considered by glass manufacturers. As glass plates

are usually thin and undergo large displacements, the use of conventional thin plate linear

bending theory will yield erroneous results. Indeed, to accurately compute the maximum stress in

a panel for checking of stress against failure, the large deflection theory allowing for membrane

stress should be used. In the breakage analysis of glass panels, failure is assumed to occur

when the maximum tensile stress is equal to the breaking stress of the glass. For ductile material, the

yield strength can be accurately measured and, typically, varies over a narrow range. However, as

a brittle material, glass has no observable yield strength as other materials such as steel. Thus, the

failure of glass can only be represented by breakage stress, which is obtained from a statistical basis.

For tempered glass, the breakage stress is usually taken to be four times the failure stress for clear

float glass. For heat-strengthened glass, where the tempering process is lighter than for tempered

glass, the strength is twice that of annealed glass.

The Canadian Code has adopted the failure prediction model developed by Beason and Morgan [8].

The failure prediction model is based on the simplified formulation, which has been presented by Brown

[10] to model the glass strength with load duration. The resistance to failure of a surface flaw can be

expressed as follows:

Kf Z Tf

0

sTn dT 29:2

where T is the load duration and Kf is the resistance to failure of a surface flaw exposed to tensile stress

and water vapor. The nominal tensile stress, s(T), at the flaw is expressed as a function of time, and n is aconstant of which the value of the best fit, from experimental data, is found to be 16 (Dalgliesh and

Taylor [11]). The duration of the loading causing failure is expressed as Tf. The glass plate fails when Kfreaches some critical values which depend on the flaws characteristics and stress state at the flaw. With

Equation 29.2, we can adjust the strength of glass for different load durations. In a computer analysis,

we can compute constant pressure causing glass breakage and relate this to failure pressure with different

load durations as follows:

P60 Pf Tf60

1=n29:3



where P60 is the constant pressure causing failure of the panel in 60 s and Pf is the constant pressure

causing failure at a duration of Tf s.

The use of a design factor of 2.5 has been introduced to control the POF to 0.008. The POF can be

expressed in terms of Weibull distribution as follows:

POF 1 eB 29:4where B is a function that reflects the risk of failure and is given as

B AA0

Sm,p,r

S0

m29:5

where e is a natural number, A0 and S0 are the area and characteristic strength of the reference glass

panel, respectively and A and Sm,p,r are the area and characteristic strength of the glass panel, respectively.

Sm,p,r is a function of the Weibull parameter, m, pressure, p, and aspect ratio, r. Failure data for in-service

glass were collected (see Ref. [12]) and fitted to Equation 29.5. The fitted Weibull parameters m 7 andS0 32.1 MPa are adopted in Canadian Code, and the reference area, A0, is equal to 1 m2.

29.5 Stress Evaluation and Common Causes of Breakages

The failure of glass is assumed when the principal tensile stress is equal to or greater than the char-

acteristic strength calculated in Equation 29.5. The bending stress is assumed to vary linearly across the

thickness of the plate, and the membrane stress is constant across the thickness of the plate. The total

stress is obtained by superimposing the bending and membrane stresses. The stress components at each

of the three nodes of the element are then used to calculate the principal stresses within the element. The

nodal stresses are averaged at nodes that are attached to more than one element.

29.5.1 Common Causes of Glass Breakage

The causes of breakage for glass can be due to (not in order of importance)

Excessive stress from wind pressure or other loads. Thermal stress due to differential temperature on different parts of the pane (for 33C, the thermal

stress is 20.7 N/mm2). Buckling due to large compression (e.g., glass rod and glass fins). Surface or edge damage. Deep scratches or gouges. Severe weld splatter. Windborne missiles (i.e., debris impact). Direct contact with metal (e.g., window aluminum frame). Impurities like nickel sulfide (NiS). Excessive deflection bringing glass in contact with other hard objects.

29.5.2 Impurities

One big disadvantage in using tempered glass is the problem of spontaneous breakage due to impurities

like NiS. NiS is formed when nickel-rich contaminants like nichrome wire and stainless steel are

unavoidably introduced into the glass melting furnace, and when they are mixed with sulfur, NiS is

formed. They are harmless in annealed or heat-strengthened glass since the induced stress cannot break

the tensile failure stress of glass but causes instantaneous breakage when they are located at the tension

zone of tempered glass and expand with temperature and time. For surface stress less than 52 N/mm2,

NiS is not a problem since its expansion, together with the tensile prestress, cannot generate a breaking

stress higher than the failure tension stress of the glass. Therefore, using heat-strengthened glass is

a means of solving the problem of NiS. Heat-soaking test is a procedure to break the glass panels



containing NiS in the factory rather than after installation. The time and temperature are important in

heat-soaking, and their requirement varies from one country to another. Figure 29.12 shows a picture of

glass breakage due to NiS, which is signified by the origin as a pair of butterfly wings.

29.6 Numerical Examples for Breakage Analysis ofGlass Structure

Any numerical or analytical method must first be tested and validated before it can be actually used. The

limitations and scopes of the method must be clearly investigated and defined. This chapter presents a

verification study on the application of the developed finite element method for several nonlinear pro-

blems for glass structures. The accuracy of the developed method is then compared with the available

solution.

The first example is to compare the results of in-service glass obtained by the Institute for Research in

Construction (IRC) [12]. Totally, 47 pieces of in-service glasses obtained from the University of Ottawas

Thompson Residence tested to failure. The second example is the simulation of a curved glass panel

under positive and negative wind load. Curved glass panels are frequently used in the construction of

observation lift cladding or the exterior staircase of modern prestigious buildings. The third and fourth

examples are concerned with glass fin systems that are widely used in shop fronts and entrances of

buildings. Two examples of elastic supports are presented that visualize the effects of out-of-plane and

in-plane stiffnesses of sealants on the stress distribution within the loaded glass plate. Finally, the results

of the simulation of flexible support are compared with a full-scale mock-up test.

29.7 Failure Test of In-Service Glass

The strengths of new glass and in-service glass differ considerably. While the design of glass panels is

mostly based on new glass, the actual failure load of in-service glass is of greater interest when one

considers safety during the service life of a building.

FIGURE 29.12 Glass breakage due to nickel sulfide.



In this example, the testing results obtained by the IRC of the National Research Council of Canada for

47 in-service window glasses removed from the University of Ottawas Thompson Residence in 1986

were compared.

The breaking stress of glass is determined by Equations 29.4 and 29.5 with the characteristic

strength equal to 32.1 MPa, probability of failure equal to 0.008, reference area, A0, equal to 1 m2,

and the Weibull parameter, m, equal to 7 as recommended by the Canadian Code. It is generally

believed that in-service time reduces the breakage stress of a glass panel due to the increased density

TABLE 29.2 Test Results of In-Service Glass (Mean 2.51, Standard Deviation 0.62)No. P60 (kPa) Thickness (mm) X (mm) Y (mm) NAShell Ratio

1 2.84 4.10 1300 905 1.73 1.64

2 4.57 4.00 1300 905 1.73 2.64

3 2.26 4.10 1300 905 1.73 1.30

4 5.27 4.00 1300 905 1.73 3.04

5 4.47 4.05 1300 905 1.73 2.58

6 4.10 4.00 1300 905 1.73 2.37

7 5.62 4.07 1298 897 1.73 3.24

8 4.12 3.90 1300 930 1.73 2.38

9 5.29 4.00 1300 929 1.73 3.05

10 5.01 4.00 1300 930 1.73 2.89

11 4.47 3.93 1300 928 1.73 2.58

12 5.75 3.95 1300 925 1.73 3.32

13 3.66 3.84 1300 925 1.73 2.11

14 5.39 3.90 1300 924 1.73 3.11

15 4.79 3.95 1300 925 1.73 2.76

16 5.70 3.88 1300 930 1.73 3.29

17 5.73 4.04 1300 925 1.73 3.31

18 6.08 3.93 1300 900 1.73 3.51

19 4.58 3.90 1300 900 1.73 2.64

20 4.77 4.09 1300 900 1.73 2.75

21 5.16 4.01 1300 895 1.73 2.98

22 2.92 4.00 1300 900 1.73 1.68

23 3.38 3.97 1300 899 1.73 1.95

24 5.14 3.86 1300 930 1.73 2.97

25 5.54 4.00 1300 900 1.73 3.20

26 6.18 3.96 1300 975 1.70 3.65

27 5.04 4.00 1300 975 1.70 2.97

28 5.03 3.96 1300 975 1.70 2.97

29 4.04 3.96 1300 975 1.70 2.38

30 5.02 3.91 1300 975 1.70 2.96

31 2.19 3.83 1340 916 1.66 1.32

32 2.46 3.77 1340 916 1.66 1.48

33 2.54 3.69 1340 916 1.58 1.61

34 3.75 3.75 1342 916 1.66 2.26

35 2.73 4.00 1357 1300 1.43 1.91

36 3.11 4.05 1356 1300 1.43 2.17

37 3.11 3.93 1356 1300 1.36 2.29

38 4.64 4.01 1358 1300 1.43 3.24

39 4.83 4.81 1358 1300 1.81 2.67

40 2.66 3.80 1374 1342 1.21 2.21

41 1.86 3.83 1374 1342 1.21 1.54

42 3.01 4.05 1300 1062 1.81 1.66

43 3.27 3.94 1300 1062 1.66 1.97

44 4.27 4.04 1300 1065 1.73 2.46

45 4.51 3.86 1300 1065 1.66 2.72

46 3.98 3.87 1300 1065 1.66 2.40

47 3.08 3.74 1300 1065 1.58 1.95



of hairy cracks on glass surfaces in the course of resisting wind loads and also when subjected to

natural or man-made scratches.

The equivalent 60-s pressure of the testing results and output by NAShell [13] are tabulated in

Table 29.2. The average ratio of failure load to the predicted breaking load by NAShell is 2.51. This ratio

is considered to be in a reasonable range because the failure stress used in NAShell has included the

probability of failure of 8/1000. Not a single sample has a failure load lowered than the predicted load,

indicating the reliability of the suggested method in the design of in-service glass panels.

The standard deviation, however, for the failure loads is quite large and is equal to 0.62. This

demonstrates the variability of glass strength in practice and also that the nature and behavior of glass

strength can only be represented as a probability of failure.

29.8 Curved Glass Panel

In this example, a curved glass panel with base or projected dimension of 1500 mm 1500 mm,radius of 1500 mm, Youngs modulus of 70,000 MPa, Poissons ratio of 0.22 and thickness of 8 mm,

and under uniform lateral load is analyzed (see Figure 29.13). The longitudinal boundaries are

hinged and immovable, while the curved edges are restrained in the longitudinal direction. Due to

symmetry, only a quarter of the panel is analyzed with mesh size of 10 10. In Figure 29.14, wecan see the loaddeflection path at the plate center and the failure loads for annealed glass and

tempered glass under positive and negative pressure. Failure is assumed when the maximum

principal tensile stress reaches the characteristic strength of 14.25 MPa, which is calculated from

Equations 29.4 and 29.5. For tempered glass, the failure stress is assumed to be four times the value

for annealed glass [12].

From the figures, it can be seen that the failure pressure ratio for annealed and tempered glasses is the

same as the ratio of their stresses where the geometrical change is not significant. However, for com-

pressive load case, the failure pressure ratio for annealed to tempered glasses may not be equal to the

ratio of their failure stresses. This is due to the large change in geometry resulting in the nonlinearity

between the stress and the load.

29.9 Flexible Support for Full-Scale Mock-Up Test

In this example, the results obtained from a full-scale curtain wall test were compared with the

numerical results obtained from the computer program NAShell. In this analysis, the mullions and

R = 1500 mmL = 1500 mmE = 71,000 MPa = 0.22h = 8 mm

R

L

L

Negative pressure directionPositive pressure direction

Corner

Center

h

FIGURE 29.13 Layout and properties of curved glass panel.



transoms were modeled by beam element. The size of the glass panel is 1200 mm 1800 mm 10 mm(47.25 in. 70.9 in. 0.4 in.). The mullions and transoms are aluminum rectangular hollow sectionsof size 45 mm 100 mm 3 mm. The details of the section profile and layout are shown inFigure 29.15. The curtain wall is subjected to a lateral uniform pressure of 3.85 kPa (0.56 psi). Youngs

modulus of glass is taken as 71,700 MPa (10.4 106 psi) and Poissons ratio, as 0.22. Youngsmodulus of aluminum is 70,000 MPa.

This problem is aimed to investigate the influence of mullion and transom flexibility to the glass

strength. Structural members supporting glass panels are normally supported by brackets to concrete

slab or spandrel. Due to the high cost of aluminum and its small Youngs modulus of elasticity of about

one third that of steel, the members are generally flexible, so that deflection is commonly a design

criterion. In practice, a span of 1175

is the tolerance since it is believed that a large deflection in mullion or

transom will create a stress pattern on glass that is different from the assumed rigid support case.

This example is aimed to investigate the effect of flexible support due to flexibility in structural

members, which, to our knowledge, was not studied previously, though a limiting value of 1175

of span is

recommended in the Canadian Code of Practice [12].

Pres

sure

load

, kPa

0 0.4 0.8 1.2 1.6 2 2.4

200(a)

(b)

150

100

50

0

Failure load for annealed glass

Failure load for tempered glass

Deflection in loading direction, mm

0 10 20 30 40 50 60 70 80

80

70

60

50

40

30

20

10

0

Failure load for annealed glass

Failure load for tempered glass

Postbuckling path

Pres

sure

load

, kPa

Deflection in loading direction, mm

FIGURE 29.14 Loaddeflection path of the curved glass at the center: (a) positive pressure and (b) negative pressure.



From Table 29.3, we can see that we have underestimated the glass deflection of the glass plate if we

consider that the glass plate is fixed support (in rotation and translation) or even simply support

(restrained only in translation). The actual deflection of the glass is about double in the case of

fixed support and about 1.4 times in the case of simply support. On the other hand, we observe that

the deflections obtained by NAShell are close to those in the mock-up test, and the errors in the

prediction of deflections are acceptable in engineering practice. The underestimation of deflection would

FIGURE 29.15 Layout of the tested full-scale sample.

TABLE 29.3 Flexible Supports

Central deflection

of glass (mm)

Midpoint deflection

of mullion (mm)

Midpoint deflection

of transom (mm)

Full-scale mock-up test 12.84 7.45 1.43

NAShell 12.14 (94.55%) 7.36 (98.79%) 1.36 (95.10%)

Built-in fixed supporta 6.15 (47.90%) N/A N/A

Roller simply supportb 8.99 (70.02%) N/A N/A

a Lateral deflection and rotation are fixed.b Lateral deflection is fixed but free to rotate.

Note: Values in parentheses refer to the ratio of the deflections to the measured deflections in the test.



probably increase the chance of contact with hard objects such as a concrete wall behind the glass and

hence increase the failure rate. Deflection limit for serviceability requirement is normally taken as one-

sixtyth of shorter span.

29.10 Conclusions

The concept and method for design and analysis of glass panels is described in this chapter. The validity

of the finite element formulation has been demonstrated for flat and curved panels with in-plane edge

support flexibility. All these problems are related to the practical design of the glass system. Further,

a summary of possible causes of breakage for glass panels is presented. It can be seen that, with a proper

design and analysis method and methods of installation, glass structures can be designed to meet the

safety and serviceability requirements.

References

[1] Zachariasen, W.H. and Warren, B.E., The atomic arrangement in glass, J. Am. Chem. Soc., Vol. 54,

pp. 38413851, 1932.

[2] Libbey-Owens-Ford Co., Technical Information Strength of Glass under Wind Loads, ATS-109,

Toledo, OH, 1980.

[3] ASTM Standard E1300-89, Standard Practice for Determining the Minimum Thickness of Annealed

Glass Required to Resist a Specified Load, 1989.

[4] National Standard of Canada, Structural Design of Glass for Buildings, CAN/CGSB-12.20-M89,

Canadian General Standards Board, 1989.

[5] Scholze, H., Glass Nature, Structure, and Properties, Springer-Verlag, New York, 1990 (translated

by M.J. Lakin).

[6] Shand, E.B., Glass Engineering Handbook, McGraw-Hill, New York, 3rd edition, 1984.

[7] Griffith, A.A., The phenomena of rupture and flows in solids, Trans. R. Soc., Ser. A, Vol. 221,

pp. 163198, 1921.

[8] Beason, W.L. and Morgan, J.R., Glass failure prediction model, J. Struct. Eng., ASCE, Vol. 110, No. 2,

pp. 197212, 1984.

[9] Weibull, W., A Statistical Theory of the Strength of Materials, Royal Swedish Institute for Engi-

neering Research, Stockholm, Sweden, 1939.

[10] Brown, W.G., A practicable formulation for the strength of glass and its special application to large

plates, Publication No. NRC 14372, National Research Council of Canada, Ottawa, Ontario,

Canada, 1974.

[11] Dalgliesh, W.A. and Taylor, D.A., The strength and testing of window glass, Can. J. Civ. Eng., Vol. 17,

pp. 752762, 1990.

[12] National Standard of Canada, Structural Design of Glass for Buildings, CAN/CGSB-12.20-M89,

Canadian General Standards Board, 1989.

[13] So, A.K.W. and Chan, S.L., NASHELL, Computer program for geometrically nonlinear analysis of

glass panels, Users Manual, 1995.



SECTION V Special StructuresChapter 29 Glass Structures29.1 Introduction29.2 Strength of Glass29.2.1 Types of Glass29.2.1.1 Tempered (Toughened) and Heat-Strengthened Glass29.2.1.2 Annealed Glass29.2.1.3 Tinted Glass29.2.1.4 Coated Glass29.2.1.5 Wired Glass29.2.1.6 Laminated Glass

29.3 Design of Glass29.4 Failure Criterion29.5 Stress Evaluation and Common Causes of Breakages29.5.1 Common Causes of Glass Breakage29.5.2 Impurities

29.6 Numerical Examples for Breakage Analysis of Glass Structure29.7 Failure Test of In-Service Glass29.8 Curved Glass Panel29.9 Flexible Support for Full-Scale Mock-Up Test29.10 ConclusionsReferences

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