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Mechanical properties and Robustness evaluation
of glass materials in building
Prof. Yiwang Bao
State Key Lab. Of Green Building Materials
China Building Materials Academy, 100024, Beijing
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Why glass?
• Admit daylight
• Provide external views
• Achieve feeling of spaciousness
• Functionality: self-cleaning, solar-energy
Photo-voltaic,…..
• Create durable weatherproof building
envelope
• New structural materials
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Structural glass application
All-glass building
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深圳三鑫公司所建的结构玻璃建筑
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Structural/functional
Combination
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BIPV glass components
• applications
德国柏林中央车站日本Sanyo太阳光电公司
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• Applications
Energy saving building in Qinghua Univ.Beijing South station
BIPV glass components
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Shanghai daily 2nd Aug. 2006:A glass curtain wall fall
down from 36th floor of Shanghai Jingjiang shopping center.
Debris and splinters covers 40 square meter. No body injured
Dangerous glass from high building
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Spontaneous breakage of glass curtain wall
Glass rain
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glass: typical brittle material
Brittle
breakage
Stress
Strain
Perfectly elastic
Brittle feature: no plastic deformation, low critical strain, high crack
growth speed, stress concentration strong
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Comparison of the deformation of metal and glass
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Three modes of failure of building glass
1. Spontaneous breakage (tempered glass)
2. Fracture due to strength degradation
3. Fall dawn of whole glass due to loosed
support or sealant.
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Annealed glass
• Breaks in to large
dagger like shards
• Sharp edges
• Dangerous to fall
through
• Danger if falls
This kind of glass is not safe
building material
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Toughened glass
• Thermally toughened glass
– Automotive glass
– Glass for construction
– Some domestic glass, e.g Pyrex dishes
• Chemically strengthened glass
– Chemical modification of the surface
– Used for laboratory glass, aeronautical glass,
etc
Safety glass: laminated glass; tempered glass
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Load bearing glass elementsweak tensile resistance but strong compressive
• Shells
– Curvature provided by bent glass or by
assembling the flat glass facets
– Use laminated annealed glass may provide
high residual strength for glass shells
– Double curved glass is feasible only for large
bending radii
• Walls
– Stability
Try to form compressive stress, rather than tensile stress in the glass
element for the sake of safety
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Glass beams/fins
• Pics of glass beam and fins
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Important requirement for building glass
---Robustness (鲁棒性)
Strength :the maximum tensile stress at fracture
Damage tolerance : capacity of bearing damage, or
energy dissipation ability
Durability: no degradation of strength with time
Post-breakage strength: residual strength after
breakage
Weathering resistance: property variation with weather
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Strength
depending on
surface crack
sizes
表面缺陷影响强度
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200nm
SEM photo of
glass surface
2007.10
玻璃表面微裂纹
的显微照片,
2007.10
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Size effect of strength
Long wire, lower strength
Short wire, high fracture strength Over 500 year ago, (达芬奇)
DaVinci found: strength
decreases with increasing
length of the steel wire.
Traditional Material mechanics : strength is the force in
unit area at fracture. It is related to only the section area,
regardless of the length.
contradiction to Galilei’s (伽利略) theory
Griffith’s experiment results: the larger the glass
thickness, the lower the strength will be.
Explanation : large specimen contains more defects
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suppose Material is consisted by many units, and
the strength depends on the weakest unit
(maximum crack), like a stressed chain.
Fracture initiates form the crack -----the origin of
the fracture mechanics
Weibull: probability of the defect (causing-failure crack)
depends on the sample size.
Statistic fracture mechanics
Weakest link theory
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Glass strength depend on crack sizes
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Strength data of glass
• Sensitive to surface crack size and impact load
• Great scatter (standard deviation: great)
• Low Weibull modulus
An approach to improve the deviation :
Two-step tempering (engineered stress glass)
1) Thermally tempered glass + 2) and then chemically (ion
exchange ) tempered
1) Chemically tempered + 2) chemically tempering
---- Low deviation , high Weibull modulus, but higher cost, Results of the two-step method
or
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Spontaneous breakage of tempered glass due to
silicon particle in the tensile zone
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The breakage from a indent, under uniform load.
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Impurity in the fracture section of the glass
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SEM Photo of the particle in the
fractured tempered glass
Hardness Hv=6.5GPa
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What is the component of particle? NiS ?
EDX line
scanning
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Silicon fraction along the line. No Ni and S was found,
the particle is monolithic silicon
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Component analysis in the particle
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Stress near the
boundaryP
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Stresses in and near the particle
for r≥a (a)3
1
r
aP
r
3
1
2 r
aP
t for r≥a (b)
]E/E)[(]/)[(
ET)(P
pmpm
mpm
2121
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Stress distribution around the particle and
between two particles
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Size effect of the particle
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Identify tempered glass and defects in
the glass by photo-elastic method
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Inspecting defect by Photo-elastic method
----stress concentration point
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-0.04MPa
0 MPa-0.02MPa
-0.06MPa
-0.08MPa
light spots in the vacuum glass under difference
vacuum degree
-0.1MPa
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Indentation diagram of soda-lime glass
before and after chemical strengthening
a)裂纹从压痕尖端扩展 b)压痕周围呈放射状光斑
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Different indentations for soda-lime
glass and strengthened glass
Common glass Tempered glass
最大载荷为100g 的压痕形貌
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after indentation load of 200g
no strengthening Strengthened glass
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钢化前 钢化后
Without tempered tempered glass
after indentation load of 300g
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钢化
前
钢化
后
2c≈101 m 2c≈48 m
2f ≈64 m
after indentation load of 500g
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卸载后钢化玻璃表面压痕参数随
时间变化(最大载荷为200g)
卸载后10s后情况
Indentation evolution after unloading (200g)
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卸载1min后情况
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6min after unloading of 200g
indentation load
卸载
6min后
压痕情况
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卸载13min后
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Indentation cracks in tempered glass under 1000g
load,
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10 sec after unloading
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After 20 sec
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After 30 sec
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Micro-cracks near the indent due to residual stress
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Conventional strength test for glass
---bending strength
Three-point bending test Four-point bending test
The strength is calculated by the Critical load at fracture
and the size of the sample and the span
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Questions
• Can we evaluate the strength of glass
nondestructively?
• How to know if the strength of a glass
element meet the need of expected value?
• How to measure the local strength in situ ?
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Evaluating the properties by using nondestructive test
—— diagnosing like traditional Chinese medicine
象中医号脉那样通过弹性接触无损测试材
料的性能---- 一个探索性的思路
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Spherical (Hertzian) indentation
The properties of the ball is known. The critical load for cracking reflects the strength. So it is possible to evaluate the local strength by Hertzian indentation.
Brittle Material
脆性材料
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m ax
20 .3 1
r
hE
R
R
aEP
r
3
43
Local strength evaluation by spherical indention
Hertz crack in glass
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Hertzian indentation
The maximum stress: at R=a
The maximum mean stress: at R>a
Process zone
对球压法:最大应力在接触区边缘,最大平均应力在接触区外面
Stress distribution along depth
Sample surface
For brittle material like glass, crack
initiation depends on the mean stress in the
surface layer, not depend on the maximum
stress _____Mean stress criterion
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Mean-stress criterion for contact stress
to determine local strength
iRdz
0
1
2arctan)1()(
)1(
2
31))(21(
2
1
2
3
2
u
a
a
u
ua
u
u
z
u
z
R
a
po
R
2/122
2222222
4)(2
1zaazRazRu
By Numerical integral
通过均强度准则
计算局部强度
iRNot simply use the criterion
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Distribution of surface stress and mean
stress(R>=a)
- 0 . 2
- 0 . 15
- 0 . 1
- 0 . 05
0
0. 05
0. 1
0 . 15
0. 2
0 . 25
0. 3
1 1. 1 1 . 2 1 . 3 1 . 4 1 . 5
R/ a
P0
s u r f a c e s t r e ss / po
/ p o , i n = 0 - - 0 . 0 4 mm
/ p o , i n = 0 - - 0 . 0 6 mm
Contact zone
表面应力和平均应力的分布
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Local strength of glass
The process zone, ~0.03 mm
2
2
023602862013730
c
c
ccloc
a
P.a.a.
31
2
32
2 1
4
3023602862013730
/
c
/
ccloc
r
P
k
E.a.a.
Where ac can be expressed by Pc , we get
The local strength can be evaluated using only Pc
对给定的压球,局部强度可以由临界压力确定
![Page 62: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/62.jpg)
Local strength as a function of the critical load for
given ball and glass
R=2. 5 mm WC spher e
0
50
100
150
200
250
300
350
400
0 200 400 600 800 1000 1200
Critical load(N)
Lo
cal
stre
ng
th (
MP
a)
局部强度随临界载荷的变化
![Page 63: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/63.jpg)
Variation of Stress
distribution with
increasing
indentation load
Stress analysis by Finite element method
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![Page 65: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/65.jpg)
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![Page 70: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/70.jpg)
![Page 71: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/71.jpg)
In situ measurement and observation
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In situ observation of the initiation and extension
of indentation crack in glassceramic ball (r=2.5 mm)
100 N
![Page 73: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/73.jpg)
Hertzian Crack initiation
crack initiation at 180 N
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Crack extension
200 N
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260 N
![Page 76: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/76.jpg)
300 N
![Page 77: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/77.jpg)
350 N
![Page 78: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/78.jpg)
400 N
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500 N
![Page 80: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/80.jpg)
Formation of a cone crack
600N
![Page 81: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/81.jpg)
Sphere size effects on tests
ceramic spheres
Over loaded
Crack under critical load
临界环形
裂纹
过载的裂
纹形貌
![Page 82: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/82.jpg)
Critical load Pc,
indentation stress Po,
ratio Pc/r
the local strength
varies with the sphere
radius
s o d a - l im e g la s s
s te e l s p h e re
0
500
1000
1500
2000
2500
2 4 6 8 10 12
Sp he r e r ad i u s , r / mm
Va
ria
ble
s
Pc ( N)
po ( MPa)
Pc / r
l oc a l s t r eng t h ( MPa)
s tre n g th e n e d s o d a - l im e g la s s
s te e l s p h e re
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
2 4 6 8 10 12
Sp he r e r ad i u s , r / mm
Va
ria
ble
s
Pc ( N)
po ( MPa)
Pc / r
l oc a l s t r engt h ( MPa)
Sphere indentation results varying with the sphere size for soda-lime glass
and tempered glass
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Measured local strength (at 10 points)
0 =232MPa for soda lime glass
普通玻璃
0′ =348 MPa for strengthened glass
钢化玻璃
![Page 84: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/84.jpg)
Comparison between the local strength and
conventional strength
0
50
100
150
200
250
300
拉伸强度 弯曲强度 局部强度
MP
a ..
.
Compressive 8000-1200MPa
理论强度高于10000MPa
![Page 85: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/85.jpg)
Residual stress in the surface
0′is the local strength of strengthened glass
0 is the strength of unstrengthened glass.
r is the residual stress on the surface ,
it was 348-232=116 MPa in previous example.
oor
玻璃表面残余应力的测定
![Page 86: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/86.jpg)
Proof test for glasses by spherical indentation
a) Given a strength requirement, o
b) Indentation loading until a known value (make
the maximum mean stress reaches to o
c) Check if or not a ring-crack occurs ( by AE)
d) If cracked, the strength is unqualified
e) If no ring crack, the tempered glass is qualified.
Procedure
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Schematic of Proof test by using Hertzian
indentation
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Determining the critical load by acoustic emission
声发射确定临界载荷示意图
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Required strength Fractured point Passed rate
200 MPa 0 100%
250 MPa 0 100%
300 MPa 0 100%
350 MPa 3 84%
370 MPa 7 63%
390 MPa 11 42%
400 MPa 13 32%
450 MPa 15 21%
500 MPa 19 0%
550 MPa 19 0%
Results of the strength proof tests by Hertzian indentation for different requirements to chemically strengthened glasses
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In situ testing by using auto-fix tester
Spherical indenter with AE alarm
Shows the critical load and the local strength of the test point
cupula
![Page 91: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/91.jpg)
Measured local strength on tin side of float glass
Mean strength
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Prediction of failure probability at a given stress
Failure
probability
Stress level
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Mean strength
Local strength measured on the tin side of strengthened glass
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Mean value
Local strength measured on air side of strengthened glass
A little higher than that of air face
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o── stress for failure probability 0.63
── applied stress
P ── failure probability
m ── Weibull modulus
m
o
P )(exp1
Weibull statistical fracture theory
621.02785.1s
m)/11(/0
m
for brittle materials
![Page 96: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/96.jpg)
Other requirement of glass design
• Impact resistance (冲击阻力)– Glass is brittle, so susceptible to impact breakage
– Standard test, e.g BS EN 12600
– Glass safety barrier
• Post-breakage strength (破裂后强度)– Robustness
– Failure of glass shall not cause proportional failure of the whole structures;
– Failure of glass shall not impose risk to the building user
– Mechanism of providing the post-brakages strength
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Design procedure for glass panels
① Select type of glass (玻璃种类)
② Establish design loads (设计载荷)
③ Rough sizing (尺寸和形状)
④ Structural analysis (结构分析)
⑤ Check safety and serviceability (检验安全和实用性)
⑥ Modify and recheck (修正并再检验)
⑦ Check post-breakage strength and impact resistance (usually by test)(后强度和冲击阻力)
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Design strength of glass (I)
不同类型的玻璃板的强度估计
Glass type Characteristic
strength (MPa)
Standards
Annealed glass 45 BS EN 572
Thermally toughened safety
glass;
Heat soaked thermally
toughened safety glass
120 BS EN12150
Heat strengthened glass 70 BS EN 1863
Chemically strengthened
glass
150 BS EN 12337
![Page 99: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/99.jpg)
Load bearing glass
elements
Design methods
– Permissible stress design
– Design according to
probability of fracture
– Limit state design
玻璃结构的三种设计思路
• 许用应力准则
• 最小破坏概率原则
• 极限状态准则
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1) Permissible stress design 许用应力
• A single safety factor is used
• May represent the reality inaccurately
• Relatively high safety factors are
necessary (k>3)
使用一个安全系数
可能在反映安全性方面不够准确 (因为玻璃强度的离散性)
需要用相对比较高的安全系数
![Page 101: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/101.jpg)
2) Limit state design (极限状态)
• The limit states are the states beyond
which the structure becomes unfit for its
intended use.
• Two limit states are considered:
– Ultimate limit state (ULS) (基于最终状态)
– Serviceability limit state (SLS) (服役状态)
准则:变形或载荷不能超过某一种极限状态
![Page 102: Mechanical properties and Robustness evaluation of glass materials · PDF fileMechanical properties and Robustness evaluation of glass materials in building Prof. Yiwang Bao State](https://reader031.vdocuments.net/reader031/viewer/2022030410/5a9a94257f8b9a8b5d8e41ff/html5/thumbnails/102.jpg)
3) Design according to probability of
fracture 破坏概率准则
• Based on fracture mechanics and
statistical theory
• Load duration, size effect
• More accurate than the permissible
stress design but complicated
准则: 发生破坏的概率不超过某一个微小值
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0
20
40
60
80
100
120
30 50 70 90 110
Applied stress (MPa)
Fai
lure
Pro
bab
ilit
y (
%)
m=29
m=10
m=20
m=15
m=6
Design based on Weibull statistical method
Characteristic strength
5% Failure probability
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Glass strength depends on surface defect size
----Approaches for Improving the strength: residual
compressive stress; less defects.
Robustness related to: strength, post-breakage
strength, damage tolerance, durability.
Spontaneous breakage of tempered stress is
due to various impurities and defects in the
glass.
Nondestructive test for strength and proof test
can be performed via spherical indentation
Safe design of glass structures involve three
design mode: Permissible stress design,
Failure probability, Limit state
Conclusions
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Thank you for your attention