advanced design of glass structures - upt · advanced design of glass structures application 4...

ADVANCED DESIGN OF GLASS STRUCTURES

Application 4

Design of insulated glass units Viorel Ungureanu

European Erasmus Mundus Master Course Sustainable Constructions

under Natural Hazards and Catastrophic Events 520121-1-2011-1-CZ-ERA MUNDUS-EMMC

2 2

Objectives

• Check of the insulating glass unit according to the prEN 13474

• Ultimate limit state

• Serviceability limit state

Application Vertical insulating glass unit 4mm toughened float glass / 12mm cavity / 6mm float glass, c1 1300mm wide x c2 900mm high, supported on all four edges, subjected to a wind load of c3 1.5kN/m2, glazed at an altitude of less than 400m.

Objectives

Aspect ratio

Coefficients and factors

Allowable stresses

Internal loads

Ultimate limit state

Serviceability limit state

3

h1 = 4 mm – toughened glass s = 12 mm h2 = 6 mm – float glass

a =

900m

m

b = 1300mm

1 2

Worked example Worked example Vertical insulating glass unit 4mm toughened float glass / 12mm cavity / 6mm float glass, 1300mm wide x 900mm high, supported on all four edges, subjected to a wind load of 1.5kN/m2, glazed at an altitude of less than 400m.

• aspect ration

• “a” shall be taken as the shorter dimensions

ba

Objectives

Aspect ratio


Allowable stresses

Internal loads



4 4

Worked example

• “four edge supported glass pane” (prEN 13474) • small deflection p* = 0 • linear interpolation between two values • from table B.2 coefficient k2 for calculation of the effective stress

p*

0 5 10 20 30 50 100 200 300 500 1,0 0,251 0,250 0,246 0,235 0,221 0,193 0,164 0,146 0,137 0,126 0,9 0,288 0,285 0,279 0,259 0,237 0,201 0,174 0,156 0,147 0,135 0,8 0,338 0,334 0,323 0,292 0,261 0,216 0,186 0,168 0,159 0,147 0,7 0,398 0,392 0,375 0,330 0,291 0,237 0,202 0,183 0,173 0,161 0,6 0,463 0,454 0,432 0,377 0,330 0,267 0,220 0,201 0,191 0,179 0,5 0,527 0,518 0,495 0,436 0,383 0,312 0,241 0,222 0,212 0,199 0,4 0,588 0,581 0,564 0,512 0,461 0,383 0,281 0,247 0,236 0,223 0,3 0,639 0,637 0,629 0,602 0,568 0,500 0,384 0,278 0,265 0,251 0,2 0,678 0,677 0,676 0,672 0,665 0,644 0,577 0,463 0,390 0,308 0,1 0,699 0,699 0,699 0,699 0,699 0,698 0,697 0,692 0,683 0,660 0,0 0,699 0,699 0,699 0,699 0,699 0,698 0,698 0,698 0,698 0,698

Table B2: Coefficient k2 for calculation of the effective stress

Objectives

Aspect ratio


Allowable stresses

Internal loads



5 5

Worked example

• from table B.3 coefficient k4 for calculation of maximum deflection p*

0 5 10 20 30 50 100 200 300 500 1,0 0,046 0,046 0,045 0,041 0,038 0,032 0,024 0,017 0,014 0,011 0,9 0,056 0,056 0,054 0,049 0,044 0,036 0,027 0,019 0,015 0,012 0,8 0,068 0,067 0,065 0,057 0,051 0,041 0,030 0,021 0,018 0,014 0,7 0,083 0,081 0,077 0,068 0,059 0,048 0,035 0,025 0,020 0,016 0,6 0,099 0,097 0,092 0,081 0,071 0,057 0,041 0,029 0,024 0,019 0,5 0,115 0,113 0,109 0,097 0,086 0,070 0,051 0,036 0,030 0,023 0,4 0,131 0,129 0,126 0,116 0,105 0,088 0,065 0,046 0,038 0,030 0,3 0,147 0,142 0,140 0,135 0,128 0,114 0,088 0,064 0,053 0,041 0,2 0,147 0,147 0,147 0,146 0,145 0,140 0,126 0,101 0,085 0,067 0,1 0,148 0,148 0,148 0,148 0,148 0,148 0,147 0,146 0,143 0,136 0,0 0,148 0,148 0,148 0,148 0,148 0,148 0,148 0,148 0,148 0,148

Objectives

Aspect ratio


Allowable stresses

Internal loads



6 6

Worked example

• from table B.4 coefficient k5 for calculation of the volume change p*

0 5 10 20 30 50 100 200 300 500 1,0 0,019 0,019 0,019 0,018 0,017 0,015 0,011 0,008 0,007 0,005 0,9 0,024 0,024 0,023 0,022 0,020 0,017 0,013 0,009 0,007 0,006 0,8 0,029 0,029 0,028 0,026 0,023 0,020 0,015 0,010 0,008 0,007 0,7 0,035 0,035 0,034 0,031 0,028 0,023 0,017 0,012 0,010 0,008 0,6 0,042 0,042 0,040 0,037 0,033 0,027 0,020 0,014 0,012 0,009 0,5 0,050 0,050 0,048 0,044 0,040 0,033 0,025 0,018 0,014 0,011 0,4 0,059 0,058 0,057 0,053 0,049 0,042 0,031 0,022 0,018 0,014 0,3 0,068 0,067 0,066 0,064 0,061 0,054 0,042 0,031 0,025 0,020 0,2 0,077 0,077 0,076 0,076 0,074 0,071 0,062 0,048 0,040 0,031 0,1 0,086 0,086 0,086 0,086 0,086 0,085 0,084 0,081 0,077 0,068 0,0 0,095 0,095 0,095 0,095 0,095 0,095 0,095 0,095 0,095 0,095

Objectives

Aspect ratio


Allowable stresses

Internal loads



7 7

Worked example • characteristic length of the unit a*

• partition of external and internal loads and effect of internal loads is determined by the insulating units factor

• partition of external load is determined by relative stiffness of the panes

250

532

31

32

31928

,

khhhhs,*a

4

1

1

*aa

32

31

31

1 hhh

32

31

32

2 hhh

stiffness of the pane 1 (outer pane) stiffness of the pane 2 (inner pane)

Objectives

Aspect ratio


Allowable stresses

Internal loads



8 8

Worked example

Glass product Uniformly distributed load duration

Glass type Processing

Short duration loads Wind loads

Medium duration loads Snow, climate loads

Permanent loads Self-weight, altitude

loads ULS SLS ULS SLS ULS SLS

Float glass and sheet

glass

annealed 17.0 30.7 8.5 15.3 6.4 11.5

heat strengthened

27.9 47.3 19.4 32.0 17.3 28.2

thermally toughened

49.6 80.7 41.1 65.3 39.0 61.5

chemically strengthened

62.7 100.7 54.2 85.3 52.0 81.5

Allowable stresses for panes up to 4.0m2 fg,d

For pane 1- toughened glass • wind load ULS fg,d = 49.6MPa = 49.6N/mm2

• wind load SLS fg,d = 80.7MPa

• climate load SLS fg,d = 65.3MPa • altitude load SLS fg,d = 61.5MPa

For pane 2- float glass • wind load ULS fg,d = 17.0MPa

• wind load SLS fg,d = 30.7MPa

• climate load SLS fg,d = 15.3MPa • altitude load SLS fg,d = 11.5MPa

Objectives

Aspect ratio


Allowable stresses

Internal loads



9 9

Worked example

Isochore pressure [kN/m2] Climatic action

pC,0 [kN/m2] Altitude action pH,0 [kN/m2]

For use up to 400 m altitude

For use up to 700 m altitude

summer +12,0 +3,6 +8,4 winter -15,0 -3,6 -8,4

Limiting conditions of internal loads, if the exact values for the internal loads can not be determined

Isochore pressure internal load Wind external load pH,0 = +3,6kN/m2 or -3,6kN/m2 w = 1,5 kN/m² Climatic action internal load pc,0 = +12,0kN/m2 or -15,0kN/m2

Objectives

Aspect ratio


Allowable stresses

Internal loads



10

Worked example

Internal actions • Serviceability limit state design loads shall be determined

External actions • Ultimate limit state design loads for one variable action on the outer

pane shall be determined

0022111211 9090190 ,C,Hkkj,j

Gjj

kkj,Gj,d p,pQ,GQ,GF

0022211122 9090901 ,C,Hkkj,j

Gjj

kkj,Gj,d p,pQ,GQ,GF

kj,j

Gjj

kkj,Gj,d GQ,GF 2111211 151

kj,j

Gjj

kkj,Gj,d GQ,GF 2211122 511

Objectives

Aspect ratio


Allowable stresses

Internal loads



11 11

Worked example

Design load on pane 1 (4mm toughened glass) SLS 1. Internal action (isochore pressure)

• Effective stress

• Deformation

00

22111211

90

90190

,C,H

kkj,j

Gjj

kkj,Gj,d

p,p

Q,GQ,GF

d,gdef fFhak 2

1

2

2

EF

hakw d

max 31

4

4

Objectives

Aspect ratio


Allowable stresses

Internal loads



11 12

Worked example



• Deformation

00

22111211

90

90190

,C,H

kkj,j

Gjj

kkj,Gj,d

p,p

Q,GQ,GF

pH,0 = ± 3,6 kN/m2

d,gdef fFhak 2

1

2

2

EF

hakw d

max 31

4

4

Objectives

Aspect ratio


Allowable stresses

Internal loads



11 13

Worked example



• Deformation

00

22111211

90

90190

,C,H

kkj,j

Gjj

kkj,Gj,d

p,p

Q,GQ,GF

pH,0 = ± 3,6 kN/m2

d,gdef fFhak 2

1

2

2

EF

hakw d

max 31

4

4

fg,d = 61,5 MPa for toughened glass, altitude loads

Objectives

Aspect ratio


Allowable stresses

Internal loads



12

Design load on pane 2 (6mm annealed glass) SLS 1. Internal action (isochore pressure)


• Deformation

00

22211122

90

90901

,C,H

kkj,j

Gjj

kkj,Gj,d

p,p

Q,GQ,GF

14

Worked example

d,gdef fFhak 2

2

2

2

EF

hakw d

max 32

4

4

Objectives

Aspect ratio


Allowable stresses

Internal loads



12



• Deformation

00

22211122

90

90901

,C,H

kkj,j

Gjj

kkj,Gj,d

p,p

Q,GQ,GF

15

Worked example

pH,0 = ± 3,6 kN/m2

d,gdef fFhak 2

2

2

2

EF

hakw d

max 32

4

4

Objectives

Aspect ratio


Allowable stresses

Internal loads



12



• Deformation

00

22211122

90

90901

,C,H

kkj,j

Gjj

kkj,Gj,d

p,p

Q,GQ,GF

16

Worked example

pH,0 = ± 3,6 kN/m2

d,gdef fFhak 2

2

2

2

EF

hakw d

max 32

4

4

fg,d = 11,5 MPa for annealed glass, altitude loads

Objectives

Aspect ratio


Allowable stresses

Internal loads



13 17

Worked example

Design load on pane 1 (4mm toughened glass) SLS 2. Internal action (isochore pressure + climatic action)


• Deformation

00

22111211

90

90190

,C,H

kkj,j

Gjj

kkj,Gj,d

p,p

Q,GQ,GF

d,gdef fFhak 2

1

2

2

EF

hakw d

max 31

4

4

Objectives

Aspect ratio


Allowable stresses

Internal loads



13 18

Worked example



• Deformation

00

22111211

90

90190

,C,H

kkj,j

Gjj

kkj,Gj,d

p,p

Q,GQ,GF

d,gdef fFhak 2

1

2

2

EF

hakw d

max 31

4

4

pH,0 = - 3,6 kN/m2

pc,0 = -15,0 kN/m2

Objectives

Aspect ratio


Allowable stresses

Internal loads



13 19

Worked example



• Deformation

00

22111211

90

90190

,C,H

kkj,j

Gjj

kkj,Gj,d

p,p

Q,GQ,GF

d,gdef fFhak 2

1

2

2

EF

hakw d

max 31

4

4

fg,d = 65,3MPa for toughened glass, altitude load + climatic action

Objectives

Aspect ratio


Allowable stresses

Internal loads



14

Design load on pane 2 (6mm annealed glass) SLS 2. Internal action (isochore pressure + climatic action)


• Deformation

00

22211122

90

90901

,C,H

kkj,j

Gjj

kkj,Gj,d

p,p

Q,GQ,GF

20

Worked example

d,gdef fFhak 2

2

2

2

EF

hakw d

max 32

4

4

Objectives

Aspect ratio


Allowable stresses

Internal loads



14



• Deformation

00

22211122

90

90901

,C,H

kkj,j

Gjj

kkj,Gj,d

p,p

Q,GQ,GF

21

Worked example

d,gdef fFhak 2

2

2

2

EF

hakw d

max 32

4

4

pH,0 = - 3,6 kN/m2

pc,0 = -15,0 kN/m2

Objectives

Aspect ratio


Allowable stresses

Internal loads



14



• Deformation

00

22211122

90

90901

,C,H

kkj,j

Gjj

kkj,Gj,d

p,p

Q,GQ,GF

22

Worked example

d,gdef fFhak 2

2

2

2

EF

hakw d

max 32

4

4

fg,d = 15,3 MPa for toughened glass, altitude load + climatic load

Objectives

Aspect ratio


Allowable stresses

Internal loads



15

Design load on pane 1 (4mm toughened glass) SLS 3. External action (wind load)

• Deformation

23

Worked example Design load on pane 1 (4mm toughened glass) ULS 3. External action (wind load)


d,gdef fFhak 2

1

2

2

EF

hakw d

max 31

4

4

kj,j

Gjj

kkj,Gj,d GQ,GF 2111211 151

kj,j

Gjj

kkj,Gj,d GQ,GF 2111211 101

Objectives

Aspect ratio


Allowable stresses

Internal loads



15


• Deformation

24



d,gdef fFhak 2

1

2

2

EF

hakw d

max 31

4

4

kj,j

Gjj

kkj,Gj,d GQ,GF 2111211 151

w = 1,5 kN/m2

kj,j

Gjj

kkj,Gj,d GQ,GF 2111211 101

Objectives

Aspect ratio


Allowable stresses

Internal loads



15


• Deformation

25



d,gdef fFhak 2

1

2

2

EF

hakw d

max 31

4

4

fg,d = 49,6 MPa for toughened glass, wind loads

kj,j

Gjj

kkj,Gj,d GQ,GF 2111211 151

kj,j

Gjj

kkj,Gj,d GQ,GF 2111211 101

Objectives

Aspect ratio


Allowable stresses

Internal loads



15


• Deformation

26



d,gdef fFhak 2

1

2

2

EF

hakw d

max 31

4

4


kj,j

Gjj

kkj,Gj,d GQ,GF 2111211 151

kj,j

Gjj

kkj,Gj,d GQ,GF 2111211 101

w = 1,5 kN/m2

Objectives

Aspect ratio


Allowable stresses

Internal loads



15


• Deformation

27



d,gdef fFhak 2

1

2

2

EF

hakw d

max 31

4

4


kj,j

Gjj

kkj,Gj,d GQ,GF 2111211 151

kj,j

Gjj

kkj,Gj,d GQ,GF 2111211 101

Objectives

Aspect ratio


Allowable stresses

Internal loads



16

Design load on pane 2 (6mm annealed glass) ULS 3. External action (wind load)


Design load on pane 2 (6mm annealed glass) SLS 3. External action (wind load)

• Deformation

kj,j

Gjj

kkj,Gj,d GQ,GF 2211122 511

28

Worked example

d,gdef fFhak 2

2

2

2

EF

hakw d

max 32

4

4

kj,j

Gjj

kkj,Gj,d GQ,GF 2211122 011

Objectives

Aspect ratio


Allowable stresses

Internal loads



16




• Deformation

kj,j

Gjj

kkj,Gj,d GQ,GF 2211122 511

29

Worked example

w = 1,5 kN/m2

d,gdef fFhak 2

2

2

2

EF

hakw d

max 32

4

4

kj,j

Gjj

kkj,Gj,d GQ,GF 2211122 011

Objectives

Aspect ratio


Allowable stresses

Internal loads



16




• Deformation

kj,j

Gjj

kkj,Gj,d GQ,GF 2211122 511

30

Worked example

d,gdef fFhak 2

2

2

2

EF

hakw d

max 32

4

4

fg,d = 17,0 MPa for annealed glass, wind load

kj,j

Gjj

kkj,Gj,d GQ,GF 2211122 011

Objectives

Aspect ratio


Allowable stresses

Internal loads



16




• Deformation

kj,j

Gjj

kkj,Gj,d GQ,GF 2211122 511

31

Worked example

d,gdef fFhak 2

2

2

2

EF

hakw d

max 32

4

4


kj,j

Gjj

kkj,Gj,d GQ,GF 2211122 011

w = 1,5 kN/m2

Objectives

Aspect ratio


Allowable stresses

Internal loads



16




• Deformation

kj,j

Gjj

kkj,Gj,d GQ,GF 2211122 511

32

Worked example

d,gdef fFhak 2

2

2

2

EF

hakw d

max 32

4

4


kj,j

Gjj

kkj,Gj,d GQ,GF 2211122 011

Objectives

Aspect ratio


Allowable stresses

Internal loads



17 33

Worked example

Design load on pane 1 (4mm toughened glass) SLS 4. Combination (isochore pressure + climatic action + wind load)


• Deformation

00

22111211

90

90190

,C,H

kkj,j

Gjj

kkj,Gj,d

p,p

Q,GQ,GF

d,gdef fFhak 2

1

2

2

EF

hakw d

max 31

4

4

Objectives

Aspect ratio


Allowable stresses

Internal loads



17 34

Worked example



• Deformation

00

22111211

90

90190

,C,H

kkj,j

Gjj

kkj,Gj,d

p,p

Q,GQ,GF

d,gdef fFhak 2

1

2

2

EF

hakw d

max 31

4

4

pH,0 = - 3,6 kN/m2

pc,0 = -15,0 kN/m2 w = 1,5 kN/m2

Objectives

Aspect ratio


Allowable stresses

Internal loads



17 35

Worked example



• Deformation

00

22111211

90

90190

,C,H

kkj,j

Gjj

kkj,Gj,d

p,p

Q,GQ,GF

d,gdef fFhak 2

1

2

2

EF

hakw d

max 31

4

4

fg,d = 80,7 MPa for toughened glass, altitude load + climatic action + wind action

Objectives

Aspect ratio


Allowable stresses

Internal loads



18

Design load on pane 2 (6mm annealed glass) SLS 2. Internal action (isochore pressure + climatic action+ wind load)


• Deformation

00

22211122

90

90901

,C,H

kkj,j

Gjj

kkj,Gj,d

p,p

Q,GQ,GF

36

Worked example

d,gdef fFhak 2

2

2

2

EF

hakw d

max 32

4

4

Objectives

Aspect ratio


Allowable stresses

Internal loads



18



• Deformation

00

22211122

90

90901

,C,H

kkj,j

Gjj

kkj,Gj,d

p,p

Q,GQ,GF

37

Worked example

d,gdef fFhak 2

2

2

2

EF

hakw d

max 32

4

4

pH,0 = + 3,6 kN/m2

pc,0 = +12,0 kN/m2 w = 1,5 kN/m2

Objectives

Aspect ratio


Allowable stresses

Internal loads



18



• Deformation

00

22211122

90

90901

,C,H

kkj,j

Gjj

kkj,Gj,d

p,p

Q,GQ,GF

38

Worked example

d,gdef fFhak 2

2

2

2

EF

hakw d

max 32

4

4

fg,d = 30,7 MPa for toughened glass, altitude load + climatic load + wind load

Objectives

Aspect ratio


Allowable stresses

Internal loads



19

Thank you for your kind attention

39

advanced design of glass structures - upt · advanced design of glass structures application 4...

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