Thierry Mainil Exploratory investigation on the cold bending of thin glass Academic year 2014-2015 Faculty of Engineering and Architecture Chairman: Prof. Dr. Ir. Luc Taerwe Department of Structural Engineering Master of Science in de ingenieurswetenschappen: architectuur Master's dissertation submitted in order to obtain the academic degree of Supervisors: Prof. Dr. Ir.-Arch. Jan Belis, Univ-Prof. Dr. Ing. Geralt Siebert (UniBW) Counselor: Captain Dipl.-Ing. Gordon Nehring
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Thierry Mainil
Exploratory investigation on the cold bending of thin glass
Academic year 2014-2015Faculty of Engineering and ArchitectureChairman: Prof. Dr. Ir. Luc TaerweDepartment of Structural Engineering
Master of Science in de ingenieurswetenschappen: architectuurMaster's dissertation submitted in order to obtain the academic degree of
Supervisors: Prof. Dr. Ir.-Arch. Jan Belis, Univ-Prof. Dr. Ing. Geralt Siebert (UniBW)Counselor: Captain Dipl.-Ing. Gordon Nehring
Confidentiality
This master dissertation contains confidential information and/or confidential research results proprietary to Ghent University or third parties. It is strictly forbidden to publish, cite or make public in any way this master dissertation or any part thereof without the express written permission of Ghent University. Under no circumstance this master dissertation may be communicated to or put at the disposal of third parties. Photocopying or duplicating it in any way other is strictly prohibited. Disregarding the confidential nature of this master dissertation may cause irremediable damage to Ghent University. The stipulations above are in force until the embargo date.
Confidential up to and including 01/01/2017 Important
Thierry Mainil
Exploratory investigation on the cold bending of thin glass
Academic year 2014-2015Faculty of Engineering and ArchitectureChairman: Prof. Dr. Ir. Luc TaerweDepartment of Structural Engineering
Master of Science in de ingenieurswetenschappen: architectuurMaster's dissertation submitted in order to obtain the academic degree of
Supervisors: Prof. Dr. Ir.-Arch. Jan Belis, Univ-Prof. Dr. Ing. Geralt Siebert (UniBW)Counselor: Captain Dipl.-Ing. Gordon Nehring
Foreword and acknowledgements
Glass is a fascinating material full of contradictions. It is very tough and durable, but a small scratch can make it brake. It separates and protects us from the outdoor conditions, but it is transparent, and has been defining the way our buildings’ outlook for multiple decennia. This ambiguity makes the process of designing with glass very interesting and never without surprises. Even though glass has not been the broad subject during the studies of architectural engineering, the material and its specific properties have drawn the attention of both, the architect and the engineer in me. This master thesis has given me the opportunity to research the material extensively with both, an experimental, and a theoretical approach. I would like to thank Prof. Dr. Ir.-Arch. J. Belis and Univ.-Prof. Dr. Ing. G. Siebert, for making it possible for me to do this research abroad and for guiding me in the right direction during this time. This experience has allowed me not only to develop my knowledge about glass, but also to get to know myself better. I would like to thank Gordon for the counseling and motivation until the very end. I would also like to thank Daniel and Robert, as well as the workers in the laboratory, for their advice and help with the experimental study. It would not have been the same without any one of them. I wish to thank my friends from the Oskar von Miller Forum for creating a pleasant working environment. In particular Mariano, Jan, Jaco, Christine and Phillipp for their support during the last weeks. I thank LiSEC for the generous contributions of time, knowhow and products, and also the Universität der Bundeswehr München for providing the space and financial means to perform the experiments. I am very grateful to my parents and brothers for believing in me and being there when I needed them. And last, but not least, I am very grateful for the unconditional and loving support of my girlfriend, who supports my dreams even if it means being apart for so long.
“The author gives permission to make this master dissertation available for consultation and to copy parts of this master dissertation for personal use. In the case of any other use, the copyright terms have to be respected, in particular with regard to the obligation to state expressly the source when quoting results from this master dissertation.”
January 19, 2015
Thierry Mainil
Abstract
In the underlying exploratory investigation, the most important factors for the cold bending of thin glass (t < 3 mm), have been mapped in an attempt to create an affordable and easy alternative for the production of doubly curved anticlastic shapes. In the first chapter, some properties and generalities of the material glass have been presented as well as the production of thin glass. Afterwards the focus shifts to the usage of glass in architecture. The second chapter is about the current bending techniques for glass. The advantages and disadvantages of warm, cold and lamination bending have been explained and two case studies of cold bending were discussed. In the third chapter, numerical analyses have been performed on quadratic (1 m x 1 m) and rectangular (1.1 m x 0.36 m) monolithic thin glass panes with ANSYS Workbench 15.0. This to have a basis to compare the experiments with and to investigate specific factors, which are not perceivable in reality, e.g. the internal stresses. Here, as well as during the experimental research, the shaping of the doubly curved form was integrated in the boundary conditions, being four point supported and two edge linear supported, and achieved by lifting one corner. The experiments were then described in chapter four. For that, the quadratic and rectangular thin glass panes were deformed while measuring the midpoint displacement and the edge displacement with displacement transducers, and the maximum normal stresses with strain gauges. This was done until a corner displacement of 105 mm and that for both the bearing principles and in a vertical and horizontal direction. In that way, the influence of the own weight could be perceived and the horizontal setup allowed loading the pane to observe the form-activation. Before starting the conclusions, a small example design was made to present the possibilities of thin glass. In the interpretation from the numerical analyses and the experimental tests, it was noticed that the most influential factors were the boundary conditions and the width-to-length ratio of the glass pane. It could be concluded that a two edge linear supported pane allows greater corner displacements as a four point supported pane. In addition, a decreasing width-to-length ratio results in an increasing peak midpoint displacement. Next to that, it was also seen that a stiffening effect takes place when twisting the pane. Keywords: Cold bending, thin glass, anticlastic double curvature, numerical analysis, experimental research
Exploratory investigation on the cold bending of thin glass
Thierry Mainil
Supervisors: Prof. Dr. Ir.-Arch. Jan Belis, Univ.-Prof. Dr.-Ing. Geralt Siebert, Captain Dipl.-Ing. Gordon Nehring
Abstract – This article describes the most important factors for
the cold bending of thin glass (t < 3 mm). By mapping the influential factors it is attempted to develop an affordable and simple alternative for the production of doubly curved anticlastic shapes.
The development of computer aided design technologies in the past twenty years has led to an increased freedom of forms in contemporary architecture. It makes the use of curved glass in building applications more than ever favored. Additionally, it facilitates the creation of unique free-form facades that are characterized by a combination of aesthetic appeal, transparency and use of natural light within buildings.
Cold bending is an energy efficient method to construct curved glass panes. It is based on the elastic deformation of glass combined with applications of out of pane loads to construct the required shape. The deformations still remain limited though. Nevertheless, the limitations can be diminished by applying thin glass (t < 3 mm). Since internal stresses created by cold bending depend on the pane thickness, thin glass can enable larger deformations. The result is more freedom in architecture [1].
The internal stress is not the only factor that needs to be considered. Staaks has already reported on instability as well as on deformation modes in terms of forcing one corner out of the plane to create a hypar surface. In the first mode, a curved shape characterizes the diagonals and the edges preserve its initial shape. However, if the out of plane displacement of the corner is larger than 16.8 times the pane thickness, the plate buckles. It causes instability at the point where one diagonal straightens and the edges will become curved [2].
In this study, the influential factors of cold twisting thin glass have been investigated for multiple pane sizes and multiple boundary conditions. Experiments were conducted in order to create an affordable and simple alternative for the production of doubly curved shapes.
II. NUMERICAL INVESTIGATION
A geometric non-linear finite element analysis was performed with the ANSYS Workbench 15.0 software. The results for cold twisting normal glass (t > 3 mm) found in literature are compared to the behaviour of thin glass. A parameter study has been executed to evaluate the comparison.
T. Mainil is a student with the Faculty of Engineering and Architecture at
Ghent University (UGent), Gent, Belgium. E-mail: [email protected]. .
Next to that, the behaviour of cold bending thin glass has been investigated for multiple boundary conditions. This kind of investigation was necessary to monitor the factors that cannot be perceived during the tests (e.g. the internal stresses). In addition, the investigation is proficient to validate the experimental research.
A. Parameter study
A four point supported, quadratic shell model was constructed, as it can be seen in Figure 1. A downward imperfection load was added to the model in order to influence the buckling direction and to create consistent data.
Figure 1 Four point supported, quadratic basis model in ANSYS Workbench.
After that, the model was modified to examine the influence of thickness, size and width-to-length ratio of the glass pane and the boundary conditions that support the pane.
B. Thin glass analysis
Since not everything can be observed in the experimental study, a deeper analysis about the behaviour of thin glass during buckling was conducted. For that, the movement of the free edges, the middle axis and the diagonals were observed as well as the changes in the membrane stresses.
C. Results
From the numerical analyses it can be concluded that the critical corner displacement has many influence factors. It cannot be simply summarized in a thickness depending factor of 16.8. Many other factors have to be taken into account.
The boundary conditions as well as the pane’s width-to-length ratio are two factors that are essential. Both have an impact on the behaviour of the pane and they affect the critical corner displacement. Furthermore, it can be noticed that a two edge linear supported pane allows greater corner displacements as a four point supported pane. Additionally, a decreasing
width-to-length ratio results in an increasing peak midpoint displacement.
Subsequently, it was observed that a pure hyperbolical paraboloid could not be made, since it is an unwindable shape. Therefore, the free edges display a slight S-shaped curvature, even for the slightest corner displacement. In the case of its prevention by the linear support, it results in higher stresses in the pane.
Looking at the effects of the buckling on the shape and the internal stresses, it was noticed that in the supported diagonal BD a plain arose after buckling. The plain can also be perceived in the principal stresses that indicate an increasing compressive zone in the middle of the pane. Next to that, the membrane stresses undergo a shift from a double symmetric distribution around the middle axes to a more diagonally oriented distribution.
III. EXPERIMENTAL STUDY
The stability of cold bent thin glass was also a subject within the experiment. Two test setups were built for that, being a four point supported and a two edge linear supported setup, as it can be seen in figure 2. Both designs allowed the lifting of one corner to create the desired doubly curved anticlastic shape for multiple pane sizes. In addition, they were equipped with displacement transducers to measure the midpoint displacement and displacement of the middle of the supported edge AD.
Figure 2 Boundary conditions of the test setups, four point supported (left) and two edge linear supported (right).
All performed tests concerning the research were executed in the laboratory of the Universität der Bundeswehr München in a controlled environment with a constant temperature of 20.5°C.
A. Monolithic experiments
In these experiments, two pane sizes were tested: a quadratic 1 m x 1 m and rectangular 1.1 m x 0.36 m (w x l) shape, both with a nominal thickness of 2 mm. This was carried out to monitor the effect of the width-to-length ratio.
After the physical and laser-optical measurement of the entire test specimens, strain gauges were applied on one of each kind to examine the normal stresses generated by the cold bending.
At that point, the testing sequence can be started for both setups and both pane sizes. This meaning the lifting of one corner for a total of 105 mm, divided in steps of 5 mm. After each step, the measured data was noted to be compared with the numerical analysis. The tests were conducted in a vertical and a horizontal direction not only to be capable of examining the influence of the own weight but also to apply a known load onto the structure. Based on the deflections it can then be defined if the cold bending had an effect on the pane stiffness or not.
B. Laminated experiments
After defining all pane properties, the identic tests have been performed for the laminated thin glass panes as for the
monolithic panes. It includes also the quadratic and the rectangular panes. Two differences have to be mentioned though. First, no strain gauges were applied on the panes. Because of that, the normal stresses could not be measured during the sequence. Second, two different PVB thicknesses (0.76 mm and 1.52 mm) were available for the rectangular laminates. It enabled a brief analysis of the interlayer thickness during cold bending and more interesting during the loading when bent.
C. Results
For the experiments, the same conclusions can be made as for the numerical study, which validates both. Firstly, linearly supported edges instead of solely point fixed corners allowed a greater corner displacement before buckling. Secondly, the influence of the width-to-length ratio can be seen. The rectangular panes permit greater corner displacements than the quadratic ones. In addition, it can be noticed that the maximum normal stresses are lower for the four point supported panes as for the two edge linear supported. Further on, the horizontal two edge linear supported tests presented that a form-activation was achieved and the deflections for known loads decreased for increasing corner displacements, although the shape was never a perfect hypar surface. The same results may be expected for the vertical setups as long as the buckling point is not reached, even though it was not explicitly tested. From this point on, the pane was not stable anymore and hence it was not capable of carrying loads. Simply focusing on the shape, the tests with laminated thin glass demonstrated the best results. In terms of the vertical position and linearly supported at two edges, a shape that was as close as possible to a hypar surface, was formed for both the quadratic and the rectangular panes.
IV. CONCLUSIONS
The application of cold twisted thin glass is able to form an attractive alternative for warm bending in the field of doubly curved architecture. The experimental and numerical research resulted in a valid model to predict the pattern of deformation, which can be used for design purposes. The key influence factors that were detected in both the studies were the boundary conditions and the width-to-length ratio of the glass pane.
The most promising result for shape forming was achieved with the laminated panes. There, the primary deformation created an almost perfect hypar surface. If these panes are loaded with a constant load in a horizontal setup decreasing deflections were perceived for increasing corner displacements. This proves the form-activation of the shape.
ACKNOWLEDGEMENTS
The author would like to acknowledge the suggestions of Prof. Dr. Ing.-Arch. J. Belis, Univ.-Prof. Dr.-Ing. G. Siebert and Captain Dipl.-Ing. G. Nehring during the research project. A lot of gratitude is also shown to the company LiSEC for providing the test specimens.
REFERENCES [1] Arend, S., Untersuchung zum Tragverhalten von Schalen aus Dünnglas,
Master thesis, Universität der Bundeswehr München, 2014. [2] Staaks, Koud torderen van glaspanelen in blobs, Master thesis,
Technische Universiteit Eindhoven, 2003.
Table of content
1. Glass as a building material ...................................................................................... 1
A ]Overview ............................................................................................................ 1
B ]Composition and structure ................................................................................ 3
C ]Production of flat glass ...................................................................................... 4
D ]Structural application of glass ........................................................................... 6
E ]Free-form design ............................................................................................... 7
2. Bending of glass ....................................................................................................... 9
A ]Overview ............................................................................................................ 9
B ]Current technics................................................................................................. 9
In contrast to other solid materials that solidify in a perfectly structured arrangement of
molecules, glass cooled down from the fluid state does not change to a crystalline phase,
as it can be seen in Figure 1.3. The molecules of glass, called SiO4-tetrahedra, remain
loose elements that share an oxygen atom. Due to the Si-O-Si bridges only a three-
dimensional network structure is formed instead of a logical molecule grid. The achieved
amorphous state, which is then reached, is characteristic for liquids. It is responsible for
the transparency, but also makes it very vulnerable. Flaws are easily formed on the glass
surface, which reduces the theoretically strong tensile strength of the material.
C ] Production of flat glass
People have been fascinated by glass already for centuries. The application of this brittle
transparent material in architecture generated a search for transparency, which was
powered by technical progress, but even more by technical limitations. The limitations
related to the production (e.g. limited pane sizes) still determine the development in the
glass sector.
When glass was first discovered many centuries ago, it had always been linked to a
certain status. Because of its unknown combination of transparency and hardness it was
a very sought-after material, which was most commonly used for jewelry in the beginning.
For the first application in architecture we have to go back to the Roman times, where
Vitruvius wrote that this material possessed the three necessary qualities for good
architecture. Small glass windows combined the properties of functionality (utilitas),
durability (firmitas) and beauty (venustas), although they were still of bad quality. As the
2 Wurm, J., Glas als Tragwerk: Entwurf und Konstruktion selbsttragender Hüllen, Basel, Birkhäuser Verlag, 2007, p. 36.
Glass as a building material 5
workability improved, the optical quality of glass also improved and when eventually
ovens were used for the production, the transparency became better and better.
The development of glass blowing led to the creation of new technics that resulted in the
production of larger glass plates. What started from blowing spheres, that were twisted
into circular glass panes, went onto blown cylinders that were cut and rolled open to
create larger flat panes so that bigger windows could be made. This had a significant
effect on architecture at that time, which was less and less defined by mass. But it led,
combined with the increase of knowledge in other sectors, to a more transparent
architecture where the openings now defined the buildings’ outlook. This transparency
created a new contact to the outside world and enabled a lot more daylight to come in.
Of course, today flat glass is not produced like this anymore. The float glass production,
also known as the Pilkington process was invented around the 1950s and is now still the
current standard for glass production. In this process, multiple phases are connected
within a production line that can reach a length of over 500 meter (see Figure 1.4).
Figure 1.4: Principal steps in the manufacture of float glass.3
Generally, continuously operating ovens melt the raw materials to glass. Afterwards, the
viscous mass flows over a bath of molten tin, which gives the glass a perfectly flat
surface. The ribbon comes out of the bath with a natural flow thickness of around
6.8 mm. Pulling or pushing the borders allows it to adjust the thickness to the required
size. Subsequently, it is cut to the desired size up to a maximum of 6.0 m x 3.2 m (l x w),
which are the so called jumbo panes.
This is not the way thin glass is produced though. Although thicknesses as low as
2 mm can be produced with the float glass procedure, the glass that will be used in the
3 Schittch, C., Staib, G., Balkow, D., Schuler, M., Sobek, W., Detail: Glass Construction Manual, Basel, Birkhäuser Verlag AG, 2007, p. 61.
Glass as a building material 6
master thesis is produced in a different way, called the down draw process. In this
process, the molten glass is pulled down vertically as it can be seen in Figure 1.5. The
key advantages are thickness control, that is by norm the same as float glass (± 0.2 mm
for thicknesses up to 4 mm, but in reality it is only ± 0.15 mm), and the fact that the glass
has two equal surfaces. This is not the case for float glass, where a tin side and an airside
surface are distinguishable. Within this process, (thin) glass panes with a maximum width
of 1.4 m and a length of 10 m can be produced [15].
Figure 1.5: Principle of the down draw process.4
D ] Structural application of glass
Since the 1950s glass has been used as a structural material itself. The invention of safety
concepts, that assure the stability after fracture, enabled the development of innovative
load-bearing glass structures. By thermal hardening of glass panes the tensile strength
improved and the glass shards got smaller and less sharp, compared to the fractured
conventional glass.
Another safety concept consisted of the connecting of multiple panes, together with an
adhesive synthetic foil. This process of lamination allows the construction to be stable
after fracture and avoids the falling down of splinters. After that, glass beams and
columns were no concept anymore. Nevertheless, they formed the structure as for
example for the New York Apple Store on Fifth Avenue, where full transparency was
achieved (see Figure 1.6).
4 Schott AG, http://www.schott.com/xensation/english/products/look/Production.html, (accessed Oktober 2014).
Glass as a building material 7
Although glass has evolved into a universal building material by its transparency, this is
not always desired. How can a total transparent building be architecture? How does
glass architecture relate to more traditional construction methods? These are questions
that are inseparable from designing with glass, a material that can add an interesting
contribution to architecture just by its limitations and contradictions.
An example for this interaction with the transparency of glass could be the glass house
by P. van der Erve in Leerdam. Here the entire house was made out of glass panes. This
creates a surprising effect because of its combination of transparent elements for
separating components (see Figure 1.7). While moving, the glass walls change from
translucent to almost see-through and vice versa. It also creates an interesting shadow
play during the day.
Figure 1.6: Fifth Avenue Apple Store, Bohlin Cywinski Jackson, New York.5
Figure 1.7: Glass house,
P. van der Erve, Leerdam.6
56
E ] Free-form design
When looking at the current practice of the application of glass it can be seen that most
of the structures are made out of connected flat glass panes. For a free-form design,
triangulation is the most common construction method. It shows that the material still has
certain limitations. Mainly high production costs, technical limitations from the production
and a lack of appropriate safety concepts are responsible for that. Many examples can
5 Apple, https://www.apple.com/retail/fifthavenue/, (accessed July 2014). 6 Schleifer, R., Architecture materials: glass, Köln, Evergreen, 2008, pp. 156-167.
Glass as a building material 8
be found for this, but the roof of the British Museum designed by N. Foster, as can be
seen in Figure 1.8, might be a well-known one.
Figure 1.8: British museum, Foster + Partners, London.7
It can be clearly seen that a curved form is constructed with glass triangles. What is very
remarkable is that although the bearing structure is designed rather light, the main image
is still determined by it.
Compared to other materials, glass is still a bit left behind if talking about double curved
surfaces. There are already some examples, but it has not yet reached the level of timber
or concrete. Purely from a geometric point of view, the constructions, known from Oscar
Niemeyer for example, are far ahead on what is capable with glass nowadays (see Figure
1.9).
Figure 1.9: National congress building, Oscar Niemeyer, Brasilia.8
There are some exceptions though; it exists more than a handful of structures that are
reaching the limits of glass and define complex, curved geometries, as will be
demonstrated in the case studies in the following chapter.
7 Foster & Partners, http://www.fosterandpartners.com/projects/great-court-at-the-british-museum/, (accessed July 2014). 8 BBC, http://www.bbc.com/news/in-pictures-20266899, (accessed Oktober 2014).
9
2.
Bending of glass
A ] Overview
Bending glass is not a novelty anymore. It can be noticed, that the industry produces
curved glass and establishes standards for it. By giving flat plates a specific (well thought
over) curvature, geometries with greater stiffness and aesthetic qualities are formed.
Additionally, in the context of free-form architecture, curved glass has an ever more
increasing value.
The production of the curved forms can be executed in multiple ways that have their
specific advantages and restraints. For instance the bending radii will always reach
limitations. In this chapter the different production methods, together with their
advantages and disadvantages are scrutinized and explained.
B ] Current technics [16]
A brief focus on the existing production methods is made in the following. The described
processes are those that are common and the most used by now. Later on, the
advantages and disadvantages of cold bending will be explained more deeply by case
studies of existing buildings.
B.1 ] Warm bending
This process enables the biggest geometrical freedom. Warm bending can be described
as the way of shaping glass by heating. Flat panes are placed on a mold of steel or a
ceramic material that will be placed in an oven and heated. The temperatures for the
process vary between 600 – 650 °C. Within this range, glass loses its brittle character
and turns in a rubbery state, where deformations can easily be applied to the panes.
When the glass is cooled down it returns to its amorphous solid state and keeps its now
permanent deformation.
Bending of glass 10
The deformation is typically done through gravity, i.e. the own weight is responsible for
the curving around the mould. This technique makes it possible to receive good results
for smaller deformations on a big scale. For bigger deformations it is not always sufficient
though. For a single cylindrical deformation, for example, minimal bending radii of 2 m
are attainable.
The application of weight on top as well as a vacuum under the glass can be used to
help creating smaller radii. Another technique is the mechanical forcing of the pane into
the mould. It enables larger deformations that are only depending on the thickness of the
glass pane.
However, the big formability has some economical drawbacks. The energy needed for
the heating and the production of the mould makes the process more expensive than
other production ways. Furthermore, the transportation of the panes is rather inefficient,
because the panes are not flat anymore and hence shipping requires a lot more effort.
Next to that, extra costs for producing replacement panes after breakage arise easily.
A single cylindrical curvature is already currently applied. The moulds are easy to
produce and can be reused, which decreases the costs, when repetitive elements are
being produced. For more complex geometries CNC-machines are used to create
custom made moulds out of heat resistant material. The additional costs for this are
disadvantageous for the economic feasibility and make the process very expensive and
time-consuming.
There are already experimental applications where reusable moulds are designed. The
shape-forming surface here is made from parallel bars that can be adjusted in height at
the ends (see Figure 2.1).
Bending of glass 11
Figure 2.1: Bending and tempering line at a pivoting roller bending plant without forms.9
B.2 ] Cold bending
As the name already suggests, this process is based on cold bending panes. Straight
panes are temporarily deformed and are fixed to a bearing structure, so it remains in the
predefined shape. Because the pane is forced into a shape, this deformation is coupled
with permanent internal stresses.
While glass has a brittle character and is quasi linear-elastically deformable with limited
maximal tensile strength, it is impossible to deform standard annealed glass panes with
large deformations without fracture. Tempering is necessary, to be capable of deforming
flat glass to a useful extent. This can be achieved in two ways: thermally or chemically,
and allows bigger deformations due to the higher resistance to tensile stresses. The
biggest deformations can be obtained with thermally tempered glass. Here the glass is
heated first to around 600°C and is then quenched with cool air (see Figure 2.2). The
outcome is that the outside cools down faster than the inside, which has as a final result
that compressive stresses are created in the outer layer (and tensile stresses in the
center).
Figure 2.2: Manufacturing steps for tempering flat glass.10
9 Wurm, J., Glas als Tragwerk: Entwurf und Konstruktion selbsttragender Hüllen, Basel, Birkhäuser Verlag, 2007, p. 36. 10 Wurm, J., Glas als Tragwerk: Entwurf und Konstruktion selbsttragender Hüllen, Basel, Birkhäuser Verlag, 2007, p. 54.
Bending of glass 12
This quenching can be done at different speeds to get a different level of tempering.
Typically, only two specific speeds are used to produce the so called heat strengthened
and fully tempered glass (respectively HSG and FTG) (see Figure 2.3). If then the panes
are bend, the created compressive stresses will be compensated by the introduced
tensile stresses.
Figure 2.3: Typical stress diagrams for different tempering processes, from left to right: FTG, HSG and CSG.10
Another method consists of inserting the glass pane into a hot salt bath. This is called
chemically strengthened glass (CSG). There, the pressure zones are significantly smaller,
because the process relies on the exchange of the sodium ions of the glass surface with
larger potassium ions from the salt bath. This leads to compressive stresses at the
surface. The glass demonstrates a high resistance to mechanical and thermal loads [19].
Because during cold bending the panes are often already deformed in such a way that
60 percent of the allowed bearing strength is reached, the overall capacity of these panes
is by definition lower than warm bent glass, but because of shape advantages this does
not have to be true for the absolute capacity.
The permanent nature of this way of deforming requires the usage of tempered glass of
high quality and long durability. Furthermore, it is also necessary to have a stronger
carrying structure to keep the glass under tension and thereby in shape. Most typically,
the installation takes place in multiple stages. First of all, the deformation is mechanically
applied. This can be achieved in the factory or on site. The panes are then mounted on
the bearing structure and after that they are permanently connected to the specific
substructure.
Bending of glass 13
A big advantage of this technique is that the glass panes can be delivered flat to the site.
It is even more interesting that it is not necessary to create moulds and that there is no
need for high temperatures. However, there is a need for a stronger bearing structure to
fix the glass on.
In general, the applied deformation is almost always a single curvature, whereby the
maximum radius of the deformation is linked to the thickness of the glass and the amount
of tempering. But also the type of interlayer plays a big role in the bending radius, as are
the pane dimensions and the bearing conditions. Single curvature is however, not the
only possibility. There exist already some cases with a double curvature, e.g. the railway
station in Strasbourg, designed by J.-M. Duthilleul (see Figure 2.4 and 2.5).
In this section, the properties of the glass panes that will be used for testing, are
measured and described as the test setups that have been built. Next to that, the first
tests as well as the necessary modifications to the setups will be mentioned here.
C.1 ] Pane properties
For this part, two pane sizes, 1000 mm x 1000 mm and 360 mm x 1100 mm (w x l) of
heat strength thin glass with a nominal thickness of 2 mm were available for testing. Out
of them, five of each were selected that came out of the same batch.
The first step, before testing them, was to define the exact properties of the available
panes. For that, the length, width and exact thickness was measured for each pane. In
addition, the breaking pattern of one of the panes was analyzed according to DIN EN
12150 (01/2005) to check which kind of glass it could be.
15 Galuppi, L., Massimiani, S., Royer-Carfagni, G., ‘Large deformations and snap-through instability of cold-bent glass’, Challenging Glass 4 & COST Action TU0905 Final Conference,London, Taylor & Francis Group, 2014, pp. 681-690.
Experimental study 44
Figure 4.6: HSG fracture pattern of one of the test panes.16
Based on the fracture pattern it can be concluded that the glass had to be heat
strengthened glass (HSG), although the standard norm (DIN EN 12150) does not
describe 2 mm thin glass yet [13]. This can also be seen in Figure 4.6. The pane did not
break into small pieces (dice), but instead into larger fragments, which is typical for heat
strengthened glass. It was informed though that the breaking pattern of the fully tempered
thin glass looks really similar, what is normally not the fact. This is because the tempering
process is still in the developing phase. The machine (produced by LiSEC), used to
temper the thin glass, does not let the glass roll on from the oven to the quencher.
Instead, it has the glass panes floating on so called air pillows that enables it to develop
tempered glass without the usual roller waves and therefore a clearer view [11]. It is still
in a developing phase, with the result that they are still not capable of creating the
standard breaking pattern for the fully tempered glass (small dice), although the internal
stresses are stated to be correct. Because of that, the panes were also investigated by
laser-optical measurements so that the exact amount of pre-stressing can be known,
(this is done with a SCAttered Light Polarimeter SCALP-05 and the accompanied
software GlasStress 5.7.0.8.)
Physical measurements
As it can be seen in the following tables and figures, all the panes were carefully
measured. For the physical measurements the widths and lengths were measured at the
two edges and in the middle, and the thicknesses at the four corners (see Figure 7).
Afterwards, the average was taken of all these measurements and it was used for the
numerical model (see Table 4.1 and 4.2).
16 Nehring, G., Beitrag zur Bemessung von kaltverformten Strukturen aus Dünnglas, ongoing PhD research (internal), Universität der Bundeswehr München, 2015.
Rectangle LAvg. [mm] WAvg [mm] tAvg [mm] TVG RE 1 1100 360 2,08 TVG RE 2 1100 360 2,09 TVG RE 3 1100 360 2,08 TVG RE 4 1101 360 2,07 TVG RE 5 1100 360 2,08
Laser-optical measurements
After the physical measurements, the pre-tensioning of the panes was determined. For
that, multiple points (S#) were investigated as it can be seen in Figure 4.7. At each point,
both directions were measured. Since the values can vary slightly, three measurements
were done at each position in both directions.
Figure 4.7: SCALP measurement points.
In table 4.3 and 4.4, an overview of the most important data concerning both sets of
panes is provided. As it can be seen by the amount of pre-stressing, the glass is indeed
HSG and not FTG. This is also not necessary for the research, because the stresses
caused by cold bending (, which the panes will undergo,) are not so high due to the small
thickness.
Experimental study 46
Table 4.3: Square laser-optical measurements.
Square U [MPa] M [MPa] L [MPa] Avg. X Y
-70.8 -73.3
33.2 32.5
-70.5 -72.8
Std. Dev. X Y
3.03 2.29
1.39 1.71
3.25 2.40
Var. X Y
9.16 5.25
1.94 2.93
10.53 5.77
95% C.I. X Y
-69.94 -72.59
32.83 32.00
-69.52 -72.11
Table 4.4: Rectangle Laser-optical measurements.
Rectangle U [MPa] M [MPa] L [MPa] Avg. X Y
-69.6 -74.5
32.9 32.8
-69.4 -74.2
Std. Dev. X Y
4.23 7.55
2.32 2.74
4.03 7.94
Var. X Y
17.91 57.01
5.40 7.51
16.25 62.99
95% C.I. X Y
-68.13 -71.77
32.08 31.86
-67.91 -71.37
Avg. = Average; Std. Dev. = Standard Deviation; Var. = Variance; C.I. = Confidence Interval U = Upper Surface; M = Middle; L = Lower Surface.
In Table 4.4 it can be noticed that the variance for the rectangular pane is very high. This
is because the measurements at the corner and in the middle show large differences
(see Attachment B). At the corner, the stresses in the Y-direction seem to be higher (5 –
15 MPa). This is not unusual since at the corners, not only the upper and lower surface
have to be taken into account during the quenching, but also the edges. This can create
local differences (,another influential factor can be the flow direction during the tempering
process, but since this could not be traced back, no remarks were given).
Edges, corners and surface [13]
As can be seen in Figure 4.8 and 4.9, the edges of the panes are grounded. At the
corners, this is not the way as expected. It seems like the pane, which rolls through the
grinding machine, moves a bit at the start and towards the end. Because of that the
process does not produce a perfect symmetrical corner. The short length of the panes
can explain this. Probably the panes are not entirely supported and tilt a bit towards the
end and the beginning. Next to that, some pane specifications are etched in the corner.
These things would be taken into account if a pane breaks, since it could locally reduce
the strength.
Experimental study 47
Figure 4.8: Corner detail.17
Figure 4.9: Etched details in the glass.17
17
Strain gauges
To be capable of comparing the numerical calculations with experimental tests, strain
gauges have been applied on the glass panes. The positioning of the strain gauges has
been specified on the base of the analysis executed in the last chapter.
One square pane has been taken over from the test performed by Arend [1], which was
measured as TVG SQ 1. The positioning of the strain gauges on the pane can be seen
in Figure 4.10. A second square pane has been necessary, since during the four point
supported test, the first pane was broken. For that, the pane TVG SQ 2 was also used.
To save some expenses, only six strain gauges have been installed on the same
positions as the first pane, but a few were passed upon. For the rectangular pane, the
pane marked as TVG RE 1 was used.
Figure 4.10: Strain gauge positions on TVG SQ 1 and TVG RE 1.
17 Nehring, G., Beitrag zur Bemessung von kaltverformten Strukturen aus Dünnglas, ongoing PhD research (internal), Universität der Bundeswehr München, 2015.
Experimental study 48
C.2 ] Test setup properties
Two simple, but effective, test setups were designed and built. The focus was on the
supporting ways and the capability of testing both the square and the rectangular panes
that were available for testing. The first bearing method is the four point support, which
means that the four corners are fixed, as it has been described by Van Laar [18] and
others. Still, this seemed relevant, because the bending behaviour of rectangular thin
glass has not yet been described for a four point support and it will enable to make a
better comparison between the different bearing types. The second method is a two edge
linear support. It is a bearing type that can be seen more often in real practices and has
not yet been described. This will limit the movement of two edges and should by doing
so postpone the buckling effect.
As it was already said, for the creation of the desired double curved anticlastic shape
with these bearing types multiple methods were considered. However, only one corner
was lifted. This allowed to make an easier setup and provided more control over the
corner displacement. Next to that, the numerical modeling showed that the differences
between the various models were negligible.
Four point support
The basis for the setup was the design of Arend [1]. The metal frame, the point fixings
and the movable corner were all part of his design. It was adjusted to be capable to fit a
rectangular pane, too. To reduce effort, the length of the metal framework (1 m x 1 m)
was not adjusted. This means that the rectangular pane slightly popped out of the point
fixings and therefore not the corners but a part of the edge close to it was supported as
it can be seen on the middle drawing in Figure 4.11.
Experimental study 49
Figure 4.11: Drawings of the four point support test setup.
Further on, in the drawing the original setup can be seen at the left and at the right the
elevation, which shows the displaceable corner C. A detailed picture of that is displayed
in Figure 4.13. Here, the threaded bar, which can be freely rotated to lift the corner, is
visible as is the point fixing of Corner C. For the point fixings, a facade element of Pauli &
Sohn was used, which has an articulated raised head (, product information can be found
in Attachment C). This allows rotation in all directions, which was also possible in the
numerical model.
Furthermore, the points where the displacements are going to be measured (Midpoint
and Middle AD) are also marked on the drawings. There, the (HBM) inductive standard
displacement transducers will be attached, which will be explained later.
Figure 4.12: Four point support test setup.
Figure 4.13: Detail image of the adjustable corner C.
Experimental study 50
Two edge linear support
The basic concept for this setup is similar to that of the four point support. It makes it
possible to gradually move up one corner. The most difficult part was again being
capable of using one setup for both the square and the rectangular panes.
For the setup two timber beams were mounted with metal brackets on a large wooden
plate. One was fixed rotationally that it can rotate around corner D if lifted in corner C, as
can be seen in the drawings in Figure 4.14. For the second one, small holes were
prepared in the base plate so the brackets could be fixed with small bolts and unscrewed
again that the edge AB can be moved for the different pane widths.
As it can be seen in Figure 4.16, the base plate is only locally supported to leave space
for the displacement transducers. They were mounted in the middle of the pane and the
middle of the edge AD as marked in Figure 4.14. For that multiple holes where prepared
in the pane that they can be used for the square and the rectangular panes. Since the
metal four point supported setup was mounted on the wooden base plate to use these
transducers, the plate bended slightly under the weight. This was not tolerable since the
panes needed to be loaded afterwards. This would make the base plate bend even more.
No measurements were done in this (bended) situation and a wooden frame was added
to the construction to stiffen the base plate.
Figure 4.14: Drawing of the two edge linear support test setup.
Experimental study 51
Aluminum press-fit clamping bars were used, to keep the glass in place. The rubber
down part was pasted to the timber beams and the upper part can be screwed on the
beam to fixate the glass panes as required (see Figure 4.15). After that, the whole edge
CD, was able to be moved by the threaded bar in corner C. While the beam is more than
stiff enough, there was no worry about the edge not staying straight.
Figure 4.15: Detailed elevation drawing of corner D of the two edge linear support.
Figure 4.16: Side view of the two edge linear support test setup, before addition of the frame.
Figure 4.17: Overview of the setup.
Figure 4.18: Detailed view of edge BC in lifted position.
Experimental study 52
C.3 ] Test setup adjustments
After some preliminary tests, the setups showed that they were doing what they were
designed for, but nonetheless, some improvements were made. Here, the adjustments
and its influences are mentioned for both the setups.
Four point support
Two small adjustments had to be made before the real tests were performed. Both are
concerning the fixating of the pane. Since the panes are not filling up the whole area of
the point fixings, a rubber with the same thickness had to be placed on the free area that
they can be clamped correctly (see Figure 4.19 and 4.20).
The other point of attention was the metal screw-head in the middle of the support. It had
to be covered with a small piece of PVC tube, as it can be seen in Figure 4.20. The glass
corners could not accidentally get pushed against it when tightening the other clamps,
as happened with the square pane TVG SQ 1. This is normally included in the packaging
of the point fixing, but since these clamps were remainders of earlier tests, not all the
parts were there. And gently tightening the clamps was not precautious enough.
Figure 4.19: Point fixing detail, square.
Figure 4.20: Point fixing detail, rectangle.
Two edge linear support
The most important improvement was the edge clamping. For greater displacements, it
was noticed that the standard press-fit clamping bar created an unwanted curve in the
upper edge of the pane (see Figure 4.21). This creates secondary and undesired tensile
stresses in the glass that should be avoided. To do so, a hard rubber tube with a diameter
of 5 mm was fixed on to the beam and pressed into the fitting (for the normal rubber) of
Experimental study 53
the clamp so that the glass edges have a minimal amount of restrictions during the
bending (see Figure 4.22). The adjustment was inspired by the conclusions of Callewaert
[5].
On the other side of the clamp a wooden batten has been used to compensate the height
of the rubber tube and clamp the glass evenly, as it is also visible in Figure 4.22.
Figure 4.21: Detail flat clamping edge.
Figure 4.22: Detail round clamping edge.
This was not the only adjustment though. Originally, the displacement measuring of the
midpoint and the edge AD was planned to be done with inductive standard displacement
transducers, as it can be seen in Figure 4.23. But since the internal springs were slightly
pushing the panes up and thereby creating an extra supporting point, they were replaced
by displacement transducers with a magnetic head and a plunger. Those had such a
minimal weight (39.2 g) that there was no need to be scared of unwanted influences (see
Figure 4.24 and Attachment D).
Figure 4.23: Inductive displacement transducer.
Figure 4.24: Transducer with magnetic head.
Experimental study 54
A final small change was made: the corner lifting principle with the threaded bar, which
can be screwed up gradually had to be changed because it allowed too much movement
of the edge CD when loading the panes. For that, little wooden blocks were cut for every
5 mm displacement. Afterwards the beam was fixed using a clamp that the edge would
not be capable of moving anymore.
D ] Square experiments
Here, the experiments and the associated data is presented. First of all, the experiments
are divided by pane shape, starting with the square panes. Secondly, by bearing type,
being the four point support and the two edge linear support and thirdly, by the direction
in which the pane is put, horizontal or vertical. The idea behind the different directions
was to get a feeling about the influence of the own weight, but also to have the possibility
to load the panes and watch its response. This to look if the form activation takes place
and if the structure becomes stiffer after the corner displacements.
Next to that, also a comparison is made with the ANSYS model to find out if both are in
accordance with each other.
D.1 ] Four point support
Horizontal
As previously said, the first test was the four point supported square pane (TVG SQ 2).
After having leveled the supports that corner C was at the same height, the pane was
mounted upon the setup, taking into account the corner detailing and connecting the
displacement transducers (see Figure 4.25). Important was always to be sure in which
way to put the pane that the strain gauges were measuring the required values and to
make sure that they were all well connected to the computer.
Afterwards, a ritual was started, which has been performed on every single test. First of
all the values were set to zero (also the displacement transducers), although the pane
was already bent under its own weight and that downward movement would have been
interesting to capture. This was done while the displacement transducers were often
moved (for measurements of the rectangular panes) and sometimes the whole structure
Experimental study 55
was flipped into a vertical position and back. This made it impossible to have it set
perfectly to be capable of measuring the movement from the origin.
Secondly, the camera was put in position to capture the movement. Thirdly, when
horizontally tested, the pane was loaded with a known weight (a 3925 g steel sphere) in
the middle and in the middle of the edge AD (Midpoint and Edge AD in the graphs)
(see Figure 4.27 and 4.28). Then corner C was lifted up 5 mm, the values of the strain
gauges and the displacement transducers were noted and everything was repeated until
the corner was moved 105 mm (see Figure 4.26). After that, the test had to be stopped.
This was not because the glass pane would break otherwise, but since it was noticed
that the rubbers that hold the pane, were slightly getting torn out of the bearing together
with the pane.
Figure 4.25: Horizontal square four point support test,
0 mm corner displacement.
Figure 4.27: Horizontal square four point support test, 0 mm corner displacement, loaded midpoint.
Figure 4.26: Horizontal square four point support test,
105 mm corner displacement.
Figure 4.28: Horizontal square four point support test,
0 mm corner displacement, loaded edge AD.
After all was done, the selected data, which results from the tests, was put into a graph
and compared to the FE-analysis, as it can be seen in Figure 4.29. All the graphs
throughout this section are built up in the same way and present the same measuring
points to be easily compared. First of all, the experimental data are represented by a dot
for each measurement. To keep the graph readable, not everything is presented, but the
most important parts are. First, the midpoint displacement (Midpoint) and the
displacement of the middle of edge AD (Edge AD) are presented for all the corner
Experimental study 56
displacements. Second, the differences of the displacements with that ones in the loaded
situation are added (Δz midpoint and Δz Edge AD). Third, the maximum normal stress is
compared to the corner displacement on a second Y-axis. This is not always in the same
location, but it is shown in the drawing at the top left of each graph (DMS).
All dots were connected with trend lines to have a better view on the course of the data
(full line for displacements, dotted line for the normal stresses). They were compared to
the midpoint displacement and the maximum normal stress, which was calculated with
the FE-model. These lines were then also full for displacements and dotted for normal
stresses, but instead of being a trend line of measurement points, they were just lines
since they were calculated more continuously.
To be capable of comparing the FE-data more easily with the experimental data, it was
choosen to shift the initial displacements and stresses to the origin for the horizontal test,
as it has been done at the start of the experiments.
Figure 4.64: Data from the vertical square and rectangle experiments of TVG SQ 1, TVG SQ 2 and TVG RE 1. 4P = four point support; 2L = two edge linear support.
Looking at the graph, the same conclusions can be made as was done for the numerical
study of the boundary conditions (in chapter three). Linearly supporting the edges
instead of only point fixing the corners allows a greater corner displacement before
0
7
14
21
28
35
42
49
-10
-5
0
5
10
15
20
25
0 15 30 45 60 75 90 105
No
rma
l str
ess
[MP
a]
Dis
plac
emen
t [m
m]
Corner displacement [mm]
Midpoint 4P SQ Midpoint 2L SQ Midpoint 4P RE
Midpoint 2L RE Max. Normal Stress 4P SQ Max. Normal Stress 2L SQ
Max. Normal Stress 4P RE Max. Normal Stress 2L RE
Experimental study 79
buckling. Next to that, the influence of the width-to-length ratio can be seen. The
rectangular panes allow greater corner displacements than the quadratic and it can be
noticed that the maximum normal stresses are lower for the four point supported panes
as for the two edge linear supported.
Further on, the horizontal two edge linear supported tests showed that a form-activation
was achieved and the deflections for known loads got smaller for increasing corner
displacements, although the shape was never a perfect HP. The same can be expected
for the vertical setups and as long as the buckling point is not reached, even though they
were not explicitly tested. From there on, the pane is not stable anymore and is not
capable of carrying loads.
Looking at the shape again, the tests with the laminated thin glass displayed the best
results. In the vertical position and linearly supported at two edges, a shape, which was
as close as possible to a HP, was formed for both the quadratic as for the rectangular
pane.
80
5.
Application of thin glass
A ] Overview
Having studied the behaviour of thin glass during cold bending, it also seemed relevant
to create a small design to show the possibilities of it outside of the laboratory. In this
design, the material and its shape should be the main subject, but of course, designing
something without a context is not so evident.
An indoor element that is not accessible, was decided upon, because the panes were
not loaded with real wind or snow loads during the tests. Since pre-tensioned thin glass
is still a new and unknown product, a promotional element was chosen as a subject.
B ] Concept
With the upcoming Bau 2015 (world’s leading trade fair for architecture, materials and
systems) [2], an element for an exhibition booth was put forward. It cannot be anything,
which is just presented though. It needs to be something functional. Since exhibitions are
typically very short term, the structure should be light and the assembly should be as
simple as possible.
With the performed tests in mind, the most suitable panes seem the quadratic 1 m x 1 m
laminated panes in a setup where the edges are supported. It is known though, that 1 m
x 2 m (w x l) laminated thin glasses are also produced, since two of them came in the
same delivery as the panes used before. Although no tests were performed on these,
since the setups did not allow tests on such large panes, an estimation of an allowable
deformation was made based on the previous experiments.
Knowing that the square (1 m x 1 m) laminated pane enabled a corner displacement of
100 mm without breaking, nor buckling. A good assumption could be that a 1 m x 2 m
Application of thin glass 81
rectangular pane would allow a corner displacement of 150 mm, which is less than
combining two square panes.
This assumption is based on the result from the numerical research made in chapter 3
and the experiments in chapter 4. First, it is known that a two edge linear supported
quadratic pane does not buckle for a corner displacement of 100 mm in the vertical
position. Second, it is noted that the width-to-length ratio has a positive influence on the
critical corner displacement. Third, the larger the pane gets the smaller the internal
stresses get for a constant ratio.
C ] Design
If taking all elements into account now, a possible application could be a see-through,
cold bent, glass dividing wall for an exposition booth. This allows the exposition of the
cold bent glass, but it can also function as a practical element on an exhibition by splitting
up the site in multiple parts, although simultaneously staying visibly connected.
For the design, a square ground floor of 10 m x 10 m is assumed that is divided in four
equal parts. This seems like an average exposition site and allows to keep the design
simple. A walkway with a width of 1 m is left free that an easy passage from one zone to
another is possible, as it can be seen in Figure 5.1.
Figure 5.1: Elevation and floorplan of the setup,
left: concept drawing; right: twisted design with cold bent glass.
Application of thin glass 82
Since the cold bent glass ought to be the main subject of the wall, the use of different
materials is reduced to two, being timber and glass. This also makes the structure, which
is built up from four identical timber frame walls around a central pole, light enough to be
carried by two people and put together without big machinery (see Figure 5.2). The thin
glass allows this, since a laminated pane of two times 1 m x 2 m x 2 mm (w x l x t) only
weighs about 20 kg.
Figure 5.2: Partial section.
The different walls would be made up from timber beams that are designed to fit together
with a carpentry connection so that they can easily be positioned correctly and are
afterwards screwed together to create sufficiently stiff connections (for the stability) (see
Figure 5.4). Small slots would have to be made into the beams to enable sliding in the
glass panes. This connection of glass and timber should not create any problems since
timber only has a Mohs’ hardness of 2 - 3 compared to 5.5 for glass.
Figure 5.3: Connection detail of the frame.
Figure 5.4: Connection frame and substructure.
Application of thin glass 83
To ensure the stability of the whole structure, a connection to the underground is
necessary. Often a temporal floor is put up on an exposition site, which could make this
possible. For that, tapped slots could be prepared in the lower beam with which the walls
could be connected to a base structure made out of a timber frame. In that frame thread
inserts would have to be prepared to bolt the wall to it and guarantee a secure
construction (see Figure 5.4). Afterwards, some OSB plates and a typical exposition
carpet could finish the flooring for the booth.
When everything comes together then, a possible perspective of the booth could be seen
in Figure 5.4.
Figure 5.4: Rendered perspective.
84
6.
Conclusions and recommendations
A ] Conclusions
In the underlying exploratory investigation, the most important factors for the cold
bending of thin glass (t < 3 mm) have been mapped in an attempt to create an affordable
and easy alternative for the production of doubly curved anticlastic shapes. For that,
numerical analyses and experimental tests have been performed on quadratic and
rectangular shaped thin glass panes. Creating the double curved shape was integrated
in the boundary conditions and achieved by lifting one corner. This was done for the
numerical as well as the experimental research.
Based on the numerical analyses it can be concluded that many factors influence the
critical corner displacement where the pane buckles. The key factors were the boundary
conditions and the width-to-length ratio. The two edge linear supported setup allowed a
greater corner displacement (before buckling) than the four point supported setup.
Additionally, a similar result can be seen for decreasing w/l-ratios: the smaller the ratio,
the higher the critical displacement.
Next to that, a relation between the glass thickness and the buckling point was found.
For the four point supported vertical setup this resulted in: ΔZBuckling = 16.0 · t, for
thicknesses smaller than or equal to 3 mm. It was noticed that for increasing thicknesses,
the internal tensile stresses also increased during the cold bending. A similar effect was
visible for decreasing pane sizes, with a constant width-to-length ratio. The smaller the
pane got, the higher the internal stresses rose, although the critical buckling
displacement remained constant.
The experimental results were consistent with the former numerical analyses. For the
vertical tests the same conclusions could be made as for the numerical analysis. The
boundary conditions as well as the width-to-length ratio appeared again to be an
influential factor on the critical corner displacement.
Conclusions and recommendations 85
The primary deformation of the setups created a close fit to a perfect hyperbolical
paraboloid. This cannot be stated about the horizontal test. Here, the initial deflection
caused by the own weight prohibited the desired deformation and produced a similar
shape as was formed when the pane buckled in the vertical setup, the "double cylindrical"
deformed shape (although the lack of stability was not visible there). This can also be
seen in the numerical data. Furthermore, in the horizontal experiments it was noted that
a form-activation took place. This was proven by the decreasing deflections for a
constant load and increasing corner deflections. Additionally, it can run up to about 40%
less deflection for a corner displacement of 105 mm for the two edge linear supported
square pane.
To take everything into account, some final tests have been performed on laminated thin
glass, too. They were truly promising for the practical application since the buckling point
was only reached after larger corner displacements. Therefore, they can enable a reliable
usage in doubly curved architecture.
B ] Recommendations
Now, knowing more about the behaviour of thin glass during cold bending, two directions
could be challenging and interesting for a follow-up research. Bending laminated thin
glass has already shortly been touched in this thesis and yielded promising results for
the creation of double curved glass architecture. A further study could concentrate on
the internal stresses created by cold bending of laminated thin glass and the behaviour
of multiple interlayers during the bending process. The main focus would be the correct
modelling of the interlayers in a numerical environment.
Another direction, which could form a fascinating subject for a further investigation, would
be the boundary conditions. Clamping the panes with point fixings and linear press-fit
bars has proven to be very effective. But such devices are also always visible on both
sides of the glass. The current technics of adhesively bonded connections are very
promising and could allow a fully glazed doubly curved outlook of buildings and
structures. Interesting would be the stress diagram and distribution in the connections
during the shaping process. For that, a correct numerical modelling will again be the
center of attention.
86
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