glass structures

8/17/2019 Glass Structures

1/53

CTU in Prague

ADVANCED DESIGN OF GLASS

STRUCTURES Lecture L1_ME

Design of glass beams

Martina Eliášová

European Erasmus Mundus Master Course

Sustainable Constructions

under Natural Hazards and Catastrophic Events520121-1-2011-1-CZ-ERA MUNDUS-EMMC


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Objectives of the lectureObjectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods

• Introduction• Experimental research

• Elements subjected to bendings

• Lateral torsional buckling

• Design methods


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Museum of glass - Kingwindford, United Kingdom

• structure of extension: length 11,0 m

• distance 1,1 m

• height of column 3,5 m, depth 200 mm

• span of beam 5,7 m, depth 300 mm

• columns, beams – laminated

glass• snow load 0,75kN/m2

• roof, walls: insulated glass

units

Composition of insulated units:

• outer layer 10 mm float colourlesssolar-control glass

• cavity between the panels 10 mm

• inner layer: 2 x 6 mm of toughenedsafety glass with striped pattern of

baked-on ceramic ink

Practical examplesObjectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Connection between beam and

column

• three layered glass 3 x 10 mm

• bonded on site with casting resin – total thickness 32mm

Practical examples

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Eating room – family house in

London, UKBackdoor to the family

house - Germany

Practical examples

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Canopies – Nijmegen, Netherlands 1999

Cross section

1 – clamped steel column HEB300

2 – horizontal steel beam HEA300

3 – continuous glass beam – 3x10mm, float glass

4 – glass roof panels – 2x 10mm,

float glass

5 – vertical glass panel in gutter

Practical examples

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Glass canopy at the underground station – Tokyo, Japan

1996

• built-up beam

• size 10,6 x 4,8 m

• height 4,8 m

• length of cantilever 9 m• beam composed from

triangular fins

Practical examples

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Glass canopy at the underground station – Tokyo, Japan

1996

• panes with length 1,9 – 2,5 m

• toughened glass 2x 15 mm

• triangular fins (laminated glass 2x19 mm + acryl pane 40mm)

• acryl panes sufficient capacity incase of earthquake

• from 1 at top to 4 fins at supportwith respect to the bending

moment

• bolted connection

Practical examples

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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• span of main beams 14m indistance 2,7m; beams

composed of 13 fins withlength 4,5m – outer fins 2x

12mm, inner 10+19+10mm

• secondary beams in adistance 2,2m

primary

beams

secondarybeams

Glass roof of interior courtyard, commercial building in

Munich, Germany 2003

Practical examples

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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ELEMENTS SUBJETED TO BENDING

Glass roof of interior courtyard, commercial building in

Munich, Germany 2003

• secondary beams 2x 10mm, heatstrengthened glass

• bolted connection subjected by the

shear and bearing• roof – double insulated units (2,7 x

2,3m)

• high degree of precision – assembly

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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glass roof above interior

courtyard 24 x 30m

Glass roof for refectory at the TU Dresden, Germany 2006

Practical examples

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Glass roof for refectory at the TU Dresden, 2006

• span of the principal beams5,75m

• secondary beams indistance of 1,45m

• beams depth 350mm, 4x12mm fully tempered glass

installation of secondary beams

preparation for installing the roof

panels – placing the sealant strips

Practical examples

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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ELEMENTS SUBJECTED TO BENDING

Glass roof for refectory at the TU Dresden, 2006

TESTS 1:1• position of loads – joints,

eccentricity 120mm

• load-bearing capacity

• residual capacity of beams

• cyclic load, long term load

• deflection

Maximum breaking load 4,5

times higher than design load

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Glass roof for university of Glasgow, 2002

• triangular shape of glass roof

• maximum span 15,5m = 4x 3,9m,beams distance of 1,5m

• tempered glass 2x 19mm, friction grip

connection

Practical examples

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Glass roof for dry dock – Bristol, 2005

• historic passenger liner built from iron special dry dock to protect ship hull

• plates 2x 10mm heat-strengthened glass with size 4,35 x 1,5m – at waterline

• area 1000m2, 50mm of water weighing about 50 t – illusion of the dock

• the ship expand, contract and bend sideways in response to shifts in

temperature junction between the waterline plate and the ship had to

accommodate movements flexible collar

Practical examples

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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• beams: 3x 10mm heat-strengthened laminated glass, supportedon steel beams of trapezoidal cross-section, propped by struts

• accidental design case – dropping of a hammer from 15m, personfailing from deck, occasional foot traffic on the glass for cleaning

Practical examples

Glass roof for dry dock – Bristol, 2005


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Experimental research

LTB

Experiments

LTB of 3m laminated beam Belis, 2005 (UGent)

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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LTB

Experiments


Experimental researchObjectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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LTB

Experiments



Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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LTB

Experiments

LTB of 3m laminated beam

Belis, 2005 (UGent)


Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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LTB

Experiments

LTB of 3m laminated beam

Belis, 2005 (UGent)


Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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GLASS BEAMS

• horizontal elements• simply supported, cantilevering

• maximum length: float glass - 6,0 m

laminated glass - 4,5 m

tempered glass - 3,9 m

GLASS FINS • vertical or sloping beams used to support facades, wind load

• simple supported or fully cantilevering• longer than L 8m are usually top-hang shorter are bottom supported

DESIGN METHOD

• design according to the elastic stability

• finite elements methods

• tests 1:1

• how the overall structure will behave

• how the structure will behave after one or more glass elements

have failed

• safety of people at failure - injury by falling glass

Elements subjected to bendingObjectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Ultimate limit state

simplified check of lateral and torsional stability based on

M max maximum unfactored destabilising bending moment

E Young's modulus of elasticity

t thickness of the glass pane

υ Poisson's ratio

• it is possible to use for checking of buckling for glass fin with free

edges (without intermediate buckling restraint)

16

Et M M

3

max Ed

Elements subjected to bendingObjectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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LINEAR THEORY OF ELASTICITY

• perfect elastic beam without any imperfections with rectangular cross-section is subjected to an increasing load – bending moment M

• instability (combination of lateral deflection and twisting) occurs

suddenly when a critical load is reached M = MCR, where critical

torsional buckling moment is

• for rectangular cross-section including warping torsion

t y CR GI EI L

M

t 2

w 2

t y CR GI L

EI

1GI EI LM

Lateral torsional buckling

simplified formula without

warping torsion - conservative

simply supported beam loaded

by constant bending moment

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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t y CR GI EI L

M

t 2

w 2

t y CR GI L

EI

1GI EI LM


bending stiffness





Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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t y CR GI EI L

M

t 2

w 2

t y CR GI L

EI

1GI EI LM


torsional stiffness simplified formula withoutwarping torsion - conservative



Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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t y CR GI EI L

M

t 2

w 2

t y CR GI L

EI

1GI EI LM






critical length

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Critical torsional buckling moment depends on:

• different moment distribution over the beam

• boundary conditions

• distance between the centre of gravity and the point where the

load is applied


Influence of following aspects on behaviour of glass

beams must be taken into account:

• glass thickness

• initial deformation – float x tempered glass

• laminated glass: shear modulus of PVB foil temperature

• load duration• damage of glass surface

• tensile strength of glass

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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RESEARCH BASED ON EXPERIMENTAL TESTS

EPFL, Lausanne, Switzerland

• simple supported beam, concentrated load at mid-span

• stress distribution is nonlinear over the beam height

• lateral torsional buckling resistance is not limited by the critical

torsional buckling moment

• tensile strength of glass is determinant for the buckling resistance

• influence of elastic interlayer (PVB foil) on the buckling strength –

temperature, load duration, thickness of the glass as well as

thickness of the interlayer

Lateral torsional bucklingObjectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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A) Monolithic glass – Analytical model

Critical LTB

Moment


a

z

t

a z

CR z C

EI

LGI z C

L

EI C M 22

2

2

22

2

1

• C i , z a …take into account different boundary conditions, different bending

moment, distance between the centre of gravity and the load point

• LTB formulas for steel are valid, e.g. EC3

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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B) Laminated glass – Analytical model

• No homogene, isotropic material

• Shear deformation due to lateral

bending & torsion

Belis, 2005 (UGent)Critical LTB

Moment


a

eff z g

eff t

a

eff z g

CR z C I E

LGI z C

L

I E C M 22

2

2

22

2

1

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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• No homogene, isotropic material

• Shear deformation due to lateral

bending & torsion

Belis, 2005 (UGent)Critical LTB

Moment


a

eff z g

eff t

a

eff z g

CR z C I E

LGI z C

L

I E C M 22

2

2

22

2

1

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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• it is possible to use same formula for MCR

• lateral bending stiffness EIz and the torsional stiffness GIt are replaced by an

equivalent stiffness (EgIz)eff a (GIt)eff (determined by sandwich theory )

Effective bending stiffness (EgIz)eff



2

2

1

1 s g eff z g

I E I E ht t

t t t

t t I

g g

g g

int

g g

s

21

21

2

21

24

Luible

Wölfel

slower , z g eff z g B I E I E

2

2121

2

int g g

int g

int

g

g

s

t t Wt

L

t t

G

E

E B

α, β – same formulas as for compression member

Objectives

Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Effective torsional stiffness (GIt)eff

y

x

z

t1 t

2tPVB

h

PVB

Glas

Glas

MT B

tg1 tint tg2


Luible

Scarpino

compt glasst glasst eff t

GI GI GI GI 21

2

21h

htanh

GI GI scompt

21

21

g g int

g g int

t t t

t t

G

G

f GI GI t eff t

22

2223

6

3646

W G

Gt t t

t t t t W G

Gt t

f

g

int int g g

g int g int

g

int int g


Introduction

Experimental

research

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Interlayer shear stiffness - Gint


• Influence of the shear modulus GPVB on the critical lateral torsional bucklingload Mcr,LT

• The curves ratio Mcr,LT / Mcr,LT, without PVB

Objectives

Introduction

Experimentalresearch

Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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• calculation of structure with initial imperfections

• too complicated unsuitable for design of beams

C) Non-linear buckling analysis – second order calculation



• Stress problem is not solved analytically

Objectives

Introduction


Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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D) Laminated glass – Numerical model

Luible, 2004 (EPFL)

x

yz

Axis ofsymmetry

glass

u

vw

v 0

fork

support

φx

φy

φz

Bonding condition:

u=0, φy=φz=0

F/2


Introduction


Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Luible, 2004 (EPFL)

x

yz

Axis ofsymmetry

glass

u

vw

v 0

fork

support

φx

φy

φz

Bonding condition:

u=0, φy=φz=0

F/2

tPVB= 0

= 0t1

PVB (solid element)elastic or viscoelastic

Equal nodes glass(shell element)

with offset t/2


Introduction


Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Luible, 2004 (EPFL)

x

yz

Axis ofsymmetry

glass

u

vw

v 0

fork

support

φx

φy

φz

Bonding condition:

u=0, φy=φz=0

F/2

tPVB= 0

= 0t1

PVB (solid element)elastic or viscoelastic

Equal nodes glass(shell element)

with offset t/2

tPVB = 0

11

740

44My

5

9

coupling

PVB

glassBeam element


Introduction


Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Only existing code:

Australian Standard AS 1288: Glass in Buildings – selection andinstallation

Appendix C: Buckling of glass fins

Simple approach

Better design approaches:

• Non linear numerical model inlculding all imperfections

• Buckling curves

Design methods

71 ,

M M cr Ed

Objectives

Introduction


Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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determination of the lateral and torsional buckling

resistance

1) an appropriate FE model: tensile stress on glass surfaces can becompared to tensile strength - complicated

2) buckling curves

• slenderness ratio depends on tensile strength of the glass

where

σ p,t - tensile strength of glass,

σ CR - critical lateral torsional buckling stress,

M cr - elastic critical moment

hM

I 2

CR

y t , p

CR

t , p

Design methodsObjectives

Introduction


Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Design – buckling curve

• Slenderness

• Reduction factor LTB

• Bending strength taking into

account LTB

• Verification

D

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.5 1.0 1.5 2.0 2.5

D coefficient d’élancement

au déversement

,

,

p t D

cr D

,

y D

p t

slenderness

Design methods

h M

I

CR

yt , p

CR

t , p

LT

2

yt , p LT

y

t , p LT Rd W I

M 2

LT LT f

Ed Rd M M

LT

LT

LT

LT

Objectives

Introduction


Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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• Slenderness



account LTB

• Verification

D

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.5 1.0 1.5 2.0 2.5


au déversement

,

,

p t D

cr D

,

y D

p t

slenderness

Design methods

h M

I

CR

yt , p

CR

t , p

LT

2

yt , p LT

y

t , p LT Rd W I

M 2

LT LT f

Ed Rd M M

LT

LT

LT

LT

Objectives

Introduction


Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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• Slenderness



account LTB

• Verification

D

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.5 1.0 1.5 2.0 2.5


au déversement

,

,

p t D

cr D

,

y D

p t

slenderness

LTB buckling curves need to

be established for glass

Design methods

h M

I

CR

yt , p

CR

t , p

LT

2

yt , p LT

y

t , p LT Rd W I

M 2

LT LT f

Ed Rd M M

LT

LT

LT

LT

Objectives

Introduction


Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Design methods

slenderness LT

• for different types of loading, glass geometries, shear modulus of PVB

interlayer and initial deformations it is possible derived different buckling

curves reduction factor

• buckling curve (c) from Eurocode may be used as a conservative approach

Objectives

Introduction


Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Australian standard AS 1288 - 1994: apendix H

1. Beams with intermediate buckling restraints

where M CR critical elastic buckling moment

g 1 constant from table

Lay distance between effectively rigid buckling restraints

(EI)y effective rigidity for bending about the minor axis

GJ effective torsional rigidity

J torsional moment of inertia

for rectangular cross-section

d, b depth and breadth of the beam

501 , yay

CR GJ EI L g

M

d

b ,

db J 6301

3

3


Introduction


Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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intermediate buckling

restraintside view of beam

top view of beam

M

z

Lay

M

z

y

y

x

x

free restraint condition fixed restraint condition

1,0 3,1 6,3

0,5 4,1 8,20,0 5,5 11,1

-0,5 7,3 14,0

-1,0 8,0 14,0

Coefficient g1 Moment parameter

β = M1 / M2


Introduction


Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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2. Beams without intermediate buckling restraint


g 2 , g 3 constants from table

Lay distance between effectively rigid buckling restrains

(span of beam)



y h height above centroid of the point of load application

5 ,0 y ay h35 ,0 y ay

2 CR GJ EI L / y g 1GJ EI L

g M


Introduction


Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Type of loading Bending moment MCondition of endrestraint againstrotation about y-y

Coefficient

g2

g3

free

fixed

3,6

6,1

1,4

1,8

free

fixed

4,1

5,4

4,9

5,2

free

fixed

4,2

6,7

1,7

2,6

free

fixed

5,3

6,5

4,5

5,3

free

fixed

3,3

-

1,3

-

Lay 8

wL2 ay

Lay 12

wL2 ay

4

FLay

8

FLay

8

FLay

Lay

F

Lay

F

Lay

F/2 F/2


Introduction


Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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3. Continuously restrained beams on tension side


Lay distance between points of effective rigid rotational

restraints



d depth of beamy h location above the neutral axis of the loading point,

positive or negative values

y 0 distance of the restraints from neutral axis

h0

2 0

2

y

2 a

CR y y 2

GJ y 4

d EI L

M


Introduction


Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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Serviceability limit state

• deflection, vibration

• simple rule for natural frequency

where d midspan deflection of beam or tip deflection of cantilever [mm]f first natural frequency [Hz] - foot traffic and wind

Float glass – low tension stress levels usually deflection is not

problem

Laminated or tempered glass – higher stress levels important

check of deflection

Hz 5 d

16 f


Introduction


Elements

subjected to

bending

Lateral torsional

buckling

Design methods


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References

Educational pack of COSTActin TU0905 „Structural Glass - Novel design methods and next generation

products“

HALDIMANN, Matthias; LUIBLE, Andreas; OVEREND, Mauro.Structural Use of Glass. Structural Engineering Documents 10 , IABSE, Zürich:2008. ISBN 978-3-85748-

119-2

THE INSTITUTION OF STRUCTURAL ENGINEERS

Structural use of glass in buildings, London: The institution of Structural Engineers, 1999.

KASPER, Ruth.

Tragverhalten von Glasträgern, RWTH Aachen, Aachen: Shaker Verlag, 2005.

Australian Standard AS 1288.

Glass in Buildings – Selection and installation, Appendix C: Basis for determination of fin design to prevent

buckling, 2006.

AMADIO, Claudio; BEDON, Chiara.

Buckling of laminated glass elements in out-of-plane bending, Engineering Structures 32 (2010), 3780–

3788.

BELIS, Jan; MOCIBOB, Danijel; LUIBLE, Andreas; VANDEBROEK, Marc.

On the size and shape of initial out-of-plane curvatures in structural glass components, Construction and

Building Materials 25 (2011), 2700–2712.

LUIBLE, A.

Stabilität von Tragelementen aus Glas. Dissertation EPFL thèse 3014. Lausanne: 2004.

LINDNER, J.; HOLBERNDT, T.

Zum Nachweis von stabilitätsgefährdeten Glasträgern unter Biegebeanspruchung. Stahlbau 75(6) (2006),

488-498.


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Thank you

for your kind attention

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