Structural Glass (Publ Hong Kong)

29 Glass Structures A. K. W. So Research Engineering Development Faç ade and Fire Testing Consultants Ltd., Yuen Long, Hong Kong

Andy Lee Ove Arup & Partners Hong Kong Ltd., Kowloon, Hong Kong

Siu-Lai Chan Department of Civil and Structural Engineering, Hong Kong Polytechnic University, Kowloon, Hong Kong

29. 9.11 Intr Introd oduc ucti tio on .... .... .... .... .... .... .... .... .... .... .... .... ... 29 29-1 -1 29. 9.22 St Stre reng ngth th of Gl Glas ass....... s....... .... .... .... .... .... .... .... .... .... ... 29 29-4 -4 Types of Glass

29.3 Design of of Gl Glass................ .......... .......... .......... .. 29-8 29. 9.44 Fai ailu lure re Cri rite teri rio on .... .... .... .... .... .... .... .... .... .... .... .. 2929-11 11 29.55 Str 29. Stress ess Evaluat Evaluation ion and Common Common Causes Causes of Breakages. .......... ......... .......... .......... .......... ..... 29-12 Common Causes of Glass Breakage  Impurities

29.6 Numerical Numerical Examples Examples for Breakage Breakage Analysis Analysis of of Glass Structure........................................................ 29-13 29.7 29 .7 Fa Fail ilur uree Test Test of In-Se In-Serv rvic icee Glass Glass .. ... ... .. ... ... ... ... ... .. 29-13 29-13 29. 9.88 Cur urve ved d Gla Glass ss Pan Panel el.... .... .... .... .... .... .... .... .... .... .... ... 29-1 29-15 5 29.99 Fle 29. Flexib xible le Support Support for for Full-Sca Full-Scale le Mock-Up Mock-Up Test Test .. .. .. .. 2929-15 15 29. 9.10 10 Con Concl clus usio ions... ns... .... ... .... .... .... .... .... .... .... .... .... .... .. 29-1 29-18 8 Ref efeeren encces .... ...... ..... ..... ..... ..... ..... ..... ..... ...... ..... .... 29-18

29.1 29.1 Intr Introd oduc ucti tion on 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 network formers and modifiers modifiers (Figure ( Figure 29.1). 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 magnesium (modifiers) (modifiers) are bonded bonded in the holes inside the silicon–ox silicon–oxygen ygen former network. Glass is one of the most most durabl durablee buildi building ng materia materials. ls. An extrem extremely ely import important ant proper property ty of glass glass is its resist resistance ance 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 production process process is illustrated 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, heatabsorbing 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 general generally ly provid providee an estheti estheticc appear appearance ance to the comple complete te buildi building. ng. Large Large glass glass panels panels of size size in 0-8493-1569-7/05/$0.00+$1.50 by CRC Press

# 2005

Copyright 2005 by CRC Press

29-1 29-1

29-2

Handbook of Structural Engineering

— network formers — network modifiers

FIGURE 29.1

Simplified two-dimensional representation of a glass network.

(a)

Furnace

Molten tin bath

Lehr Cutting

(b)

Furnace

Twin grinding

Lehr

Cutting

(c)

Furnace

Lehr Cutting

FIGURE 29.2

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

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


Glass Structures

29-3

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 highrise 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 dif ficulty 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.


29-4


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 Hook ’s 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 stress–strain 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 suf ficiently low, but it provides no guarantee that the glass will survive under the design load level.

Plastic deformation ss er t S

Steel

Brittle fracture

Glass

Strain FIGURE 29.4

Stress–Strain diagram.

TABLE 29.1

Mechanical Properties of Glass

E — Young’s modulus of elasticity G — Modulus of rigidity m — Poisson’s ratio a — Coef ficient of thermal expansion r — Density


10.4 Â 106 psi or 7.2 Â 1010 N/m2 4.3 Â 106 psi or 3.0 Â 1010 N/m2 0.22 88 Â 10À7/ C 157 lb/ft3 or 2.5 g/cm3

29-5

Glass Structures

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 n s T ¼

ð29:1Þ

constant

where s is the applied stress, while T is the duration of the stress, and n is a constant with a value between 12 and 20. Figure 29.6 illustrates the strength of glass against time. Since the duration of loading is (a)

Water vapor

Glass

(b)

Water vapor uniform attack on the crack in the absence of tensile stress (c) Preferential attack at the tip of the crack under tensile stress

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. FIGURE 29.5

160 140 120 a P

M 100 , th g ne

80 rt S

60 40 20 0.001 0.01

FIGURE 29.6

0.1

Glass strength and load duration.


1

10 102 Time, s

103

104

105

106

29-6


important in determining the failure load for a given glass panel, it is necessary to de fine 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 650  C, at which point it begins to 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

(a) Before bending

After bending

Tension da

Neutral ol d ei l p p A

Compression

(b) Before bending

After bending

Tension a

d lo d ei l

Compression

FIGURE 29.7


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

A

p

p

Glass Structures

29-7

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 dif ficulties 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 transmittance 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.


29-8

FIGURE 29.9


Laminated glass when it is broken.

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- þ 6-mm-thick laminated glass is equivalent to a 14-mm-thick glass? If not, does it behave as two separated panes 8 mm and 6 mm thick? The actual response for a laminated glass is somewhere between these two extremes. For shortterm 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 speci fic 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 de flection 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 suf ficient accuracy for many engineering applications. However, for a thin glass plate simply supported on four sides, the linear theory is invalidated when the de flection is larger than three fourths of its thickness (Canadian code [4]). The typical load versus central de flection 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 de flection and Figure 29.11 for stress. In the linear theory, the location of maximum stress is predicted at the plate center. In fact, the


29-9

Glass Structures

8 Large deflection theory

Ultimate pressure by the large deflection theory = 7.4 kPa

7

Linear small deflection theory

6 a P k

, 5 e r us s

er 4

Working pressure against breakage = Ultimate pressure 1.4 = 5.3 kPa

p g

Working pressure against d 3 deflection of span/60 = 2.7 kPa a ni o L

2 1 0 0

FIGURE 29.10

10

20 30 40 Center lateral deflection, mm

50

60

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

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. Canadiana/U.S.b

Australianc

U.K.d

Chinesee

Load duration (s) Load factor Annealed (N/mm2)

60 1.5 20–25 (edge/center, following similar)

3 — 20

60 1.4 28 for 5 < t < 12 20 for 15 < t < 19

Heat-strengthened (N/mm2) Tempered (N/mm2)

40–50

32

3 — 41 for t  6, 34.5 for t  8, 28 for t  10 —

80–100

50

59

84 for 5 < t < 12 59 for 15 < t < 19

Glass type

a

—

Canadian General Standards Board (1989), ‘‘Structural design of glass for buildings,’’ CAN/CGSB-12.20-M89. The first one 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 specified load,’’ E1300–97. 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 ¼ thickness of glass plate.


29-10


40 Area = 5.88 m2 Thickness = 4.8 mm Max. principal stress at corner center

30

0.76 kPa a P M ,s

20 s er t S

0.38kPa 10

0.1 kPa

0 1

2

3

4

5

Aspect ratio FIGURE 29.11

Stress against aspect ratio at different load levels.

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


29-11

Glass Structures

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 (Weibull’s 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 simpli fied 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: T f

K f ¼

Z

½sðT Þ n dT

ð29:2Þ

0

where T is the load duration and K f 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 a constant 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 T f. The glass plate fails when K f reaches some critical values which depend on the flaw ’s 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:

!

T f P 60 ¼ P f 60


1=n

ð29:3Þ

29-12


where P 60 is the constant pressure causing failure of the panel in 60 s and P f is the constant pressure causing failure at a duration of T f 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 ¼ 1 À eÀB

ð29:4Þ

where B is a function that reflects the risk of failure and is given as B ¼

S m, p,r S 0

   A A0

m

ð29:5Þ

where e is a natural number, A0 and S 0 are the area and characteristic strength of the reference glass panel, respectively and A and S ,p,r are the area and characteristic strength of the glass panel, respectively. S ,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 ¼ 7 and S 0 ¼ 32.1 MPa are adopted in Canadian Code, and the reference area, A0, is equal to 1 m2. m

m

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 characteristic 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 33  C, 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/mm 2, 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


Glass Structures

FIGURE 29.12

29-13

Glass breakage due to nickel sulfide.

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 signi fied by the origin as a pair of butter fl y wings.

29.6 Numerical Examples for Breakage Analysis of Glass 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 de fined. This chapter presents a verification study on the application of the developed finite element method for several nonlinear problems 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 Ottawa’s 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.


29-14


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 Ottawa ’s 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 1m2, 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 ¼ 2.51, Standard Deviation ¼ 0.62)

No.

P 60 (kPa)

Thickness (mm)

X (mm)

Y (mm)

NAShell

Ratio

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

2.84 4.57 2.26 5.27 4.47 4.10 5.62 4.12 5.29 5.01 4.47 5.75 3.66 5.39 4.79 5.70 5.73 6.08 4.58 4.77 5.16 2.92 3.38 5.14 5.54 6.18 5.04 5.03 4.04 5.02 2.19 2.46 2.54 3.75 2.73 3.11 3.11 4.64 4.83 2.66 1.86 3.01 3.27 4.27 4.51 3.98 3.08

4.10 4.00 4.10 4.00 4.05 4.00 4.07 3.90 4.00 4.00 3.93 3.95 3.84 3.90 3.95 3.88 4.04 3.93 3.90 4.09 4.01 4.00 3.97 3.86 4.00 3.96 4.00 3.96 3.96 3.91 3.83 3.77 3.69 3.75 4.00 4.05 3.93 4.01 4.81 3.80 3.83 4.05 3.94 4.04 3.86 3.87 3.74

1300 1300 1300 1300 1300 1300 1298 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1340 1340 1340 1342 1357 1356 1356 1358 1358 1374 1374 1300 1300 1300 1300 1300 1300

905 905 905 905 905 905 897 930 929 930 928 925 925 924 925 930 925 900 900 900 895 900 899 930 900 975 975 975 975 975 916 916 916 916 1300 1300 1300 1300 1300 1342 1342 1062 1062 1065 1065 1065 1065

1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.70 1.70 1.70 1.70 1.70 1.66 1.66 1.58 1.66 1.43 1.43 1.36 1.43 1.81 1.21 1.21 1.81 1.66 1.73 1.66 1.66 1.58

1.64 2.64 1.30 3.04 2.58 2.37 3.24 2.38 3.05 2.89 2.58 3.32 2.11 3.11 2.76 3.29 3.31 3.51 2.64 2.75 2.98 1.68 1.95 2.97 3.20 3.65 2.97 2.97 2.38 2.96 1.32 1.48 1.61 2.26 1.91 2.17 2.29 3.24 2.67 2.21 1.54 1.66 1.97 2.46 2.72 2.40 1.95


29-15

Glass Structures

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 Â 1500 mm, radius of 1500 mm, Young’s modulus of 70,000 MPa, Poisson’s 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 Â 10. In Figure 29.14, we can see the load–deflection 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 signi ficant. However, for compressive 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

Positive pressure direction

Negative pressure direction

Center L

Corner

h L

= 1500 mm L = 1500 mm E = 71,000 MPa  = 0.22 h = 8 mm R

R

FIGURE 29.13


Layout and properties of curved glass panel.

29-16


(a)

Failure load for tempered glass

200

a 150 P k , da ol

er 100 u ss er P

50

0

Failure load for annealed glass

0

0.4

0.8

1.2

1.6

2

2.4

Deflection in loading direction, mm (b)

80 70 Failure load for tempered glass 60 a P k

50 ,

Failure load for annealed glass

d a ol

40 er us s er P

30 20 10 0

Postbuckling path 0

10

20

30

40

50

60

70

80

Deflection in loading direction, mm FIGURE 29.14

Load–deflection path of the curved glass at the center: (a) positive pressure and (b) negative pressure.

transoms were modeled by beam element. The size of the glass panel is 1200 mm Â 1800 mm Â 10 mm (47.25 in. Â 70.9 in. Â 0.4 in.). The mullions and transoms are aluminum rectangular hollow sections of size 45 mm Â 100 mm Â 3 mm. The details of the section profile and layout are shown in Figure 29.15. The curtain wall is subjected to a lateral uniform pressure of 3.85 kPa (0.56 psi). Young ’s modulus of glass is taken as 71,700 MPa (10.4 Â 106 psi) and Poisson’s ratio, as 0.22. Young’s modulus of aluminum is 70,000 MPa. This problem is aimed to investigate the in fluence 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 Young ’s modulus of elasticity of about one third that of steel, the members are generally flexible, so that deflection is commonly a design 1 criterion. In practice, a span of 175 is the tolerance since it is believed that a large de flection 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 1 members, which, to our knowledge, was not studied previously, though a limiting value of 175 of span is recommended in the Canadian Code of Practice [12].


29-17

Glass Structures

FIGURE 29.15

TABLE 29.3

Layout of the tested full-scale sample.

Flexible Supports Central deflection of glass (mm)

Full-scale mock-up test NAShell Built-in fixed supporta Roller simply supportb a b

12.84 12.14 (94.55%) 6.15 (47.90%) 8.99 (70.02%)

Midpoint deflection of mullion (mm)

Midpoint deflection of transom (mm)

7.45 7.36 (98.79%) N/A N/A

1.43 1.36 (95.10%) N/A N/A

Lateral deflection and rotation are fixed. 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.

From Table 29.3, we can see that we have underestimated the glass de flection 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 de flection would


29-18


probably increase the chance of contact with hard objects such as a concrete wall behind the glass and hence increase the failure rate. De flection limit for serviceability requirement is normally taken as onesixtyth 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. 3841–3851, 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] Grif fith, A.A., The phenomena of rupture and flows in solids, Trans. R. Soc., Ser. A , Vol. 221, pp. 163–198, 1921. [8] Beason, W.L. and Morgan, J.R., Glass failure prediction model, J. Struct. Eng., ASCE , Vol. 110, No. 2, pp. 197–212, 1984. [9] Weibull, W., A Statistical Theory of the Strength of Materials , Royal Swedish Institute for Engineering 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. 752–762, 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 , User’s Manual, 1995.


Structural Glass (Publ Hong Kong)

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