2e5 glass structures l8 2014 vu

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

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

3

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


Simple compression


phenomenas


Column buckling

Design methods

4

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


phenomenas


Column buckling

Design methods

5

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


Introduction

Simple compression


phenomenas


Column buckling

Design methods

6

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

34

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


Simple compression


phenomenas


Column buckling

Design methods

7

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


Introduction

Simple compression


phenomenas


Column buckling

Design methods

8

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


Introduction

Simple compression


phenomenas


Column buckling

Design methods

9

Compression members in a truss

glass rod

double glass

cross-section

cable, rod


Introduction

Simple compression


phenomenas


Column buckling

Design methods

10

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


phenomenas


Column buckling

Design methods

11

test set-up transparent box for

protection


Introduction

Simple compression


phenomenas


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.

12

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


Introduction

Simple compression


phenomenas


Column buckling

Design methods

13

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


Simple compression


phenomenas


Column buckling

Design methods

14

Initial failure modes

Strength of glass in contact Objectives

Introduction

Simple compression


phenomenas


Column buckling

Design methods

15

Failure modes at collapse


Introduction

Simple compression


phenomenas


Column buckling

Design methods

16

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


Introduction

Simple compression


phenomenas


Column buckling

Design methods

17

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


Introduction

Simple compression


phenomenas


Column buckling

Design methods

18

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


phenomenas


Column buckling

Design methods

19

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


phenomenas


Column buckling

Design methods

20

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


Simple compression


phenomenas


Column buckling

Design methods

21

Buckling tests at EPFL Lausanne 2003

Column buckling - tests

Fundamental stability phenomenas

failure

experiment analytical model


Simple compression


phenomenas


Column buckling

Design methods

22

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


Simple compression


phenomenas


Column buckling

Design methods

23

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


phenomenas


Column buckling

Design methods

24

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

]


Introduction

Simple compression


phenomenas


Column buckling

Design methods

25

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


Introduction

Simple compression


phenomenas


Column buckling

Design methods

26

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


phenomenas


Column buckling

Design methods

27

Influencing parameters - summary Objectives

Introduction

Simple compression


phenomenas


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.

28

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 ==


Simple compression


phenomenas


Column buckling

Design methods

29

1) Monolithic (single layered) glass analytical model

Column buckling Objectives

Introduction

Simple compression


phenomenas


Column buckling

Design methods

30

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


Simple compression


phenomenas


Column buckling

Design methods

31

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


Introduction

Simple compression


phenomenas


Column buckling

Design methods

32

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


Introduction

Simple compression


phenomenas


Column buckling

Design methods

33

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

+

++=



Introduction

Simple compression


phenomenas


Column buckling

Design methods

34

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 ++=


Column buckling

example: Luible 2004


Simple compression


phenomenas


Column buckling

Design methods

35

( )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


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 +

=


Simple compression


phenomenas


Column buckling

Design methods

36

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


Introduction

Simple compression


phenomenas


Column buckling

Design methods

37

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


Introduction

Simple compression


phenomenas


Column buckling

Design methods

38

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


Simple compression


phenomenas


Column buckling

Design methods

39

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


Introduction

Simple compression


phenomenas


Column buckling

Design methods

40

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


Introduction

Simple compression


phenomenas


Column buckling

Design methods

41

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


phenomenas


Column buckling

Design methods

42

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

==


Introduction

Simple compression


phenomenas


Column buckling

Design methods

43

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

=


Introduction

Simple compression


phenomenas


Column buckling

Design methods

44

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


Introduction

Simple compression


phenomenas


Column buckling

Design methods

45

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.


Simple compression


phenomenas


Column buckling

Design methods

46

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


Introduction

Simple compression


phenomenas


Column buckling

Design methods

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


phenomenas


Column buckling

Design methods

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. .

49

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

[email protected]

http://steel.fsv.cvut.cz/suscos

Thank you for your attention

2e5 glass structures l8 2014 vu

Documents

glass post

glass conservatory

toughened glass glass

layers of float glass

single toughened glass

parameters column

float glass maximum

broken glass member