Download - 2E5 Glass Structures L8 2014 VU
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ADVANCED DESIGN OF GLASS STRUCTURES
Lecture L13 Design of compressed members
Viorel Ungureanu / Martina Eliov
European Erasmus Mundus Master Course Sustainable Constructions
under Natural Hazards and Catastrophic Events 520121-1-2011-1-CZ-ERA MUNDUS-EMMC
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2 2
Objectives of the lecture Introduction Simple compression Fundamental stability phenomenas Influencing parameters Column buckling Design methods
Objectives Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Compressed members Glass pavilion for art exhibition, Arnhem, Netherlands, 1986
Columns: height 3650 mm depth 580 mm thickness 15 mm (toughened glass)
Glass columns bolted to the concrete foundation Steel truss span 6,2 m; depth 600 mm
Objectives Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Glass pavilion for art exhibition, Netherlands, 1986
10
slope
6000 6000 6000
ventilation
6000
ventilation ventilation
3
6
5
0
Longitudinal section
Cross section 6020
glass panel
glass column
Concrete foundation block
2x steel angle
1-1
3
6
5
0
steel truss
Section1-1
1
5
silicone joint
Compressed members Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Glass conservatory, Leiden Netherlands 2001 - 2002
area of conservatory 4,85 x 4,00 m height varies between 4,15 and 3,37 m basic structure = portal formed by glass post with a length of 3370mm and a
glass beam of 4000mm stiff corner where beam meets post UV-active glue was applied on site
glass column
glass beam
brick wall
roof insulated glass panel
4
,
1
5
m
3
,
3
7
m
single glass panel
Compressed members Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Glass conservatory, Leiden Netherlands 2001 - 2002 beam, post: three layers of float
glass with resin interlayer 3x 10mm
roof: insulated glass 10-12-2x 5,5 with PVB
facade: single toughened glass 12mm
cross section over glass roof beam
glued connection of insulated panel to glass beam
Compressed members
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8
glass beam: 3 x 10 mm float glass, resin layered
structural silicone joint 7,5 x 6 mm resin layered
33 6
2x PE backfill
insulated glass: 10 12 2x 5,5 PVB
Objectives Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Height of column is 3,20m (10 + 15 + 10 mm float glass) Maximum loading according to the calculation 69 kN One-to-one tests maximum force at failure 430 kN In the case of collapse of one or even all glass columns, a
structural steel system in the roof would hold the construction, partly by means of a tension ring around the patio
Town hall of Saint-Germain-en-Laye, France, 1994
Compressed members Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Span of the truss 5,20m Top member 120 x 80 x 5 mm Compressive glass bar d = 30 mm Tensile steel bars d = 10 mm Two problems: Broken glass member Connection between glass bar and steel cable
Restaurant Amstelveen, Netherlands, 1994 - 1996
Compressed members Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Compression members in a truss
glass rod
double glass
cross-section
cable, rod
Compressed members Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Glass in contact to different materials Size of glass pane: 120 x 120 mm 150 x 150 mm 180 x 180 mm Thickness of glass pane: 10, 12, 15 mm Edge finishing: fine ground edge polished edge Material of inserts: steel aluminium polyamide epoxy resin Length of inserts: 60, 90, 180 mm
F F Lpu
Lpb
t
p
b
t
p
u
L
g
tg
Lc
inserts
Geometry of the test set-up for the glass in contact under pressure
Simple compression Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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test set-up transparent box for
protection
Simple compression Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
The experiments served for determination of resistance for glass in contact with different material. Glass panel were placed between two inserts and loaded by a force to the collapse. Two test machines with load capacity 400 and 1000 kN were used. We carried out 4 set of test with Al, Pa, Fe, and Ep inserts. Size and thickness of glass panels, edge finishing, length and material of inserts were changed. Transparent box allowed to determinate first crack appearance as well as the shape of the failure.
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Material of inserts
Youngs Modulus [MPa]
Poissons ratio Tensile strength [MPa]
Aluminium 69 000 0,34 265
Polyamide 3 500 0,39 76
Epoxy resin 5 700 - 52
Steel 210 000 0,32 400
Standard coupon tests EN 1288-3: Glass in building Determination of the bending strength of glass. EN 10002-1: Metals : Tensile test. EN ISO 527: Plastics - Determination of tensile properties.
Material properties of inserts
Simple compression Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Measurements of test specimen and of inserts
Glass pane: size, thickness
Inserts: length, thickness before and after testing
10 mm
Strength of glass in contact
45
a = 1,5 mm
before testing
after testing
Plastic deformation of insert
Objectives Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Initial failure modes
Strength of glass in contact Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Failure modes at collapse
Strength of glass in contact Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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identical size, thickness and edge finishing of glass panels identical length of inserts
0 100 200 300 400 500 600 700
0 1 2 3 4 5 6 Number of the test
F
e
x
p
[
k
N
]
Steel Aluminium
Epoxy resin Polyamide
Different material of inserts
Strength of glass in contact Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Reduction of the resistance
Fred = j fc,u Ai
j material coefficient, Ai contact area of the glass, fc,u strength of glass in compression (500 MPa)
0
0,2
0,4
0,6
0,8
0 1 2 3 4 5 Material of insert
F
e
x
p
/
F
t
h
e
o
r
Aluminium Polyamide Steel Epoxy resin
Material Aluminium Steel Polyamide Epoxy resin
Coefficient j 0,50 0,55 0,25 0,25
Strength of glass in contact Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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critical (Euler's) load 1744
critical stress
geometrical slenderness is defined as
2
2
LIENcr
pi=
ANcrcr =
crE pi =
pipi === iLiLIEALE 2222
Stability of the perfect compressed member
N < Ncr (stable)
N > Ncr (instable)
N = Ncr N = Ncr (indifferent)
---- impulse impulse
Ncr
N
Fundamental stability phenomenas Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Critical load of compressed columns Basic stability conditions pin-ended column with end point loads cantilever with concentrated end axial point load cantilever with uniformly distributed axial load
Ncr/N = 2EI/(NL2) 2EI/(4NL2) 7,84EI/(pL3)
L
N
N N
p
p
p
Fundamental stability phenomenas Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Fundamental stability phenomenas Ideal versus real column
N
w
z
y
L0
x
w
cr
Ideal beam buckling by bifurcation
Linear buckling Nonlinear buckling
N
w0
z
y
L0
x
Real beam buckling by divergence
w
cr failure
w0
initial imperfection
Objectives Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Buckling tests at EPFL Lausanne 2003
Column buckling - tests
Fundamental stability phenomenas
failure
experiment analytical model
Objectives Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Influencing parameters Geometry
Thickness Length of compressed member
Material parameters Elastic modulus glass Interlayer stiffness in laminated glass
Residual stresses Initial curvature Eccentricities Boundary conditions
Deviation from nominal values IMPERFECTIONS
Objectives Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Initial curvature
depending on glass type annealed glass is assumed FLAT!
Product standards define tolerances on (local and global) bow
Influencing parameters Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Initial curvature (measured values) Characteristic value of initial geometrical imperfection = u0/L = 0.0025 mm/mm Global bow = u0 = L/400 Good shape approximation = half SINUS wave (alternative: parabola) = first eigenmode! => GLOBAL bow is relevant for stability!
0
1
2
3
4
5
6
7
8
0 500 1000 1500 2000 2500 3000z [mm]
u
0
(
z
)
[
m
m
]
Influencing parameters Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Eccentricities Load application with eccentricities, depending on : Deflection of the glazing and therefore rotation of the edge Oblique (no 90) edge Lamination process Pane offset
Influencing parameters Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Influences on the behaviour of compression glass
production tolerances glass thickness
initial deformation (float x tempered glass) visco-elastic PVB interlayer used for laminated safety glass
shear modulus GPVB = 0,01 10 MPa
ultimate breaking stress in glass, depends on:
embedded compressive surface stress due to tempering process
degree of damage of the glass surface
load duration
Influencing parameters - summary Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Influencing parameters - summary Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
The glass thickness and the initial deformation of glass panels were measured for more than 200 test specimen from two different glass manufacturers. The thickness of annealed flat glass panels differs from the nominal value because glass manufacturers try to save material. The real glass thickness is often less than the nominal value, therefore reducing the moment of inertia of the cross section and, thus the buckling strength. The measurements confirmed that the values follow a normal distribution.
The initial geometric deformation w0 of flat glass is mainly caused by the tempering process. The results confirmed that non-tempered annealed flat glass has a very low initial deformation (< 1/2500) while heat-strengthened and fully toughened glass can have a sinusoidal initial deformation up to 1/300 of the length L. However maximum initial deformations depend strongly on the quality of the furnace and can therefore vary between different glass manufacturers.
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load carrying behaviour of single layered glass can be describe using second order differential equation
N axial compression L length of bar w0 initial sinusoidal deformation e eccentricity
Critical buckling load Ncr
Geometrical slenderness
1) Monolithic (single layered) glass analytical model
perfect bar
imperfect bar with initial deformation w0
w0 w
N
Ncr,K
N
N
w0 w
e
LK
Column buckling
( ) ( ) 0xweLx
sinwNxwEI 0''
=
+++pi
2
2cr L
EIN pi=
crK,crK
EN
EA
pipi ==
Objectives Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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1) Monolithic (single layered) glass analytical model
Column buckling Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Solution of second order differential equation
Maximum deformation is given by:
Maximum surface stress can be determined as:
( ) K,cr0
K,crK NN1w
NN2/Lcose
w
+=
( )
+=K,cr
0
K NN1w
EIN2/Lcose
WN
AN
1) Monolithic (single layered) glass analytical model Column buckling
A area W section modulus I moment of inertia E Young modulus
( )ewwWN
AN
WM
AN
max ++== 0
Objectives Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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EF1
N1 N2 N3
EF2 EF3
1 w0
w0
N
w
N
w0
Ncr,K
1. Modelling
2. Eigenvalue/-form analysis smallest eigenvalue corresponds to critical
buckling load Ncr,K
3. Application of imperfections the imperfection w0 is applied as a scaled
shape of the first eigenform
4. Non linear analysis of the imperfect system
5. Evaluation of stress and deflection
+
2) Monolithic glass non linear FEM analysis
Column buckling Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Approach Critical
buckling load
Stress Non-linear interlayer behaviour
Design concept
Luible (2004) X X (with teff)
Kutterer (2005) X X X
Blaauwendraad (2007) X X X
Amadio (2011) X X X
example: Kutterer 2005
3) Laminated glass analytical models
Column buckling Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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glass
glass
PVB
gravity axis
t1
t2
tPVB z1
z2 PVB
glass
glass
glass t1
t1
t2
tPVB
tPVB z1
z1
Elastic theory for sandwich structures critical buckling load of a two layer elastic sandwich with a width b and the geometrical slenderness are given as
pipi
2
2
11
+
++=
AI
L
s
sandwich,k( )22
22
11
K
sK,cr L
EIN pipipi
+
++=
3) Laminated glass analytical models
Column buckling Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Coefficients for laminated glass Double layered glass Triple layered glass
2k
s2
1PVB
PVB
LEI
bzGt
=
211s zEbt2EI =
s
21I
II2 +=
( )PVB21 tttbA ++=( )222211s ztztEbEI +=
12bt
I3i
i =
s
21I
II +=
( ) 2ks
221PVB
PVBLEI
zzbGt
+=
12bt
I3i
i =
( )PVB21 ttt2bA ++=
3) Laminated glass analytical models
Column buckling
example: Luible 2004
Objectives Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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( )313231 12 sw,ef Ihhh ++=
Effective thickness according to the prEN 13 474-1 effective thickness of double layered glass pane for calculation of deflection
effective thickness of double layered glass pane for calculation of stress
3) Laminated glass analytical models
Column buckling
shear transfer coefficient for the interlayer of laminated glass
21
3
1 2,s
w,ef,ef, hh
hh +
=
12
3
2 2,s
w,ef,ef, hh
hh +
=
effective thickness for the first ply and second ply
( ) vs hhh,h ++= 215021
11 hh
hhh s,s +
=
thickness of the interlayer
212
221 ,s,ss hhhhI +=
21
22 hh
hhh s,s +
=
Objectives Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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for wind = 1,0
other actions = 0,0
Type of glass Shear transfer coefficient
Short duration actions, e.g. wind Other actions Laminated glass 0 0 Laminated safety glass 1 0
==i
iw,ef,ef hhh
33=
iiw,ef hh
j
ii
j,,ef h
hh
=
3
Effective thickness according to the prEN 13 474-2 3) Laminated glass analytical models
Column buckling Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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prEN 13474: Glass in building Determination of the strength of glass panes by calculation and testing Effective thickness shear transfer coefficient depends on the interlayer stiffness family
Load case family 0 family 1 family 2 family 3 Wind load (Mediterranean areas) 0,0 0,0 0,1 0,6 Wind load (other areas) 0,0 0,1 0,3 0,7 Personal load - normal duty 0,0 0,0 0,1 0,5 Personal load - crowds 0,0 0,0 0,0 0,3 Snow load - external canopies 0,0 0,0 0,1 0,3 Snow load - roof 0,0 0,0 0,0 0,1 Permanent load 0,0 0,0 0,0 0,0
Snow load external canopies 3 weeks -20C < T < 0C Snow load roof of heated buildings 5 days -20C < T < 20C
Column buckling Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Analysis is similar to monolithic glass.
4) Laminated glass non linear FEM analysis
Column buckling
bonding
a) without restriction of displacement
b) with partial restriction of displacement
deformed undeformed
Objectives Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Strength of compressed structural glass members generally limited by tensile strength of the material
Influence of residual stress due to tempering and inherent strength
5) Load carrying behaviour
Column buckling Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Buckling curves Slenderness ratio Reduction factor Buckling strength
Buckling strength analysis Appropriate analytical or numerical
model (including all imperfections) Buckling strength check
To be established
Safety concept
(example buckling curves: Langosch, 2010)
5) Design
Column buckling Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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initial fracture occurred always on the tensile surface weakest point is the point of the highest tensile stress load carrying behaviour is independent of the embedded compressive surface stresses, toughened glass showed higher deformations and stresses at breakage
influences: glass thickness initial deformation w0 load eccentricity e tensile strength of glass p,t shear modulus of PVB foil GPVB
The buckling strength of glass is limited by the maximum tensile strength of glass p,t
Design methods Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Column buckling curves
STEEL to simplify the design of compressive members buckling curves were developed, curves are based on slenderness ration design of members with different steel grade
GLASS same approach = buckling curves 1) slenderness ratio for glass must be based on the maximum tensile strength p,t, compressive strength is not limiting its buckling strength
IMPRACTICAL = large variations for different tensile strength of glass
k
t,p
K
E
KK
E pi
==
Design methods Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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2) Buckling curves can be determined using geometric slenderness
family of curves for different tensile strength
CHECK OF THE COMPRESSIVE ELEMENT
where k is maximum compressive strength of glass element from diagram
additional lateral loads and end moments can be taken into account by means of interaction formulas similar to the design of compressive steel members
crK,crK
ENEA
pipi ==
K
KRd,Ked
ANN
=
Design methods Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Euler 20 MPa 40 MPa 80 MPa
test results for heat-strengthened glass
K
[
M
P
a
]
K
400 350 150 100 250 300 200 50 0
30
10
20
40
50
p,t
w0 = LK/300
Example of the buckling curves which are based on the geometrical slenderness
Design methods Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Elastic second order equation
direct calculation of the maximum tensile stress by means elastic second order equation
in contrast to steel construction this is relatively simple to carry out because of the ideal elastic behaviour of glass
take into account glass thickness and initial deformation
Check of the compressed members
( )
+=K,cr
0
K NN1w
EIN2/Lcose
WN
AN
K
t,pRdEd
=
Design methods
The calculated maximum tensile stress has to be smaller than tensile surface strength of the glass.
Objectives Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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Laminated safety glass
effect of the interlayer on the load carrying capacity due to the different temperature and loading speed
low temperature and very short loading almost monolithic section
long-term loading and temperature higher than 25C composite effect is marginal
simplification: same methods for single glass can be applied to laminated glass elements sandwich cross-section can be replaced by an effective monolithic cross-section with the effective thickness
Design methods Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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47
Critical structural issues how the structure will behave how the structure will behave after one or more glass elements have
failed safety implications of failure of a glass piece, people can be injured by
falling glass
Two ways for column glass 1) use glass only for uppermost part
of column (protection from likely impact + elements supported by the glass fall only a short distance)
2) Use of additional glass layers to protect an inner = load bearing
X
load path in a roof after a column failure
Design of compressed members Objectives
Introduction
Simple compression
Fundamental stability
phenomenas
Influencing parameters
Column buckling
Design methods
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48
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, Zrich: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. LUIBLE, A. Stabilitt von Tragelementen aus Glas. Dissertation EPFL thse 3014. Lausanne: 2004. .
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This lecture was prepared for the 1st Edition of SUSCOS (2012/14) by Prof. Martina Eliasova (CTU).
Adaptations brought by Prof. Viorel Ungureanu (UPT) for 2nd Edition of SUSCOS
-
http://steel.fsv.cvut.cz/suscos
Thank you for your attention