Glass Vaults

Introducing an Adjustable Mould for Casting Glass Voussoirs for Transparent Shell Structures

Felix van der Weijst

Glass Vaults

Introducing an Adjustable Mould for Casting Glass Voussoirs for Transparent Shell Structures

by Felix van der Weijst

In partial fulfilment of the requirements to attain the degree of Master of Science

In Building Technology

At the Delft University of Technology

July 2, 2019

Graduation committee

1st supervisor Ir. F. Oikonomopoulou

2nd supervisor Dr. Ing. M. Bilow

Delegate of the Board of Examiners Dr. E. Louw

Abstract Glass is a material that has a high compressive strength and a low tensile strength. While being mostly produced as flat sheets of float glass, it can also be casted into components that have a thicker geometry and thus a higher buckling resistance. These properties make cast glass components suitable for the construction of shell structures that are mainly subjected to compressive stresses. Shell structures often have the shape of surfaces with varying Gaussian curvature. When constructing such a shell structure out of cast glass components, components of varying geometries are needed.

During this research, an adjustable mould was developed that can be used for the casting of glass voussoirs of varying geometries. The possible voussoirs geometries that can be cast in the adjustable mould are limited to voussoirs with planar, convex polygonal intrados and extrados. These voussoirs can be used to construct fully transparent shell structures. The voussoirs are dry-assembled with an interlayer in between that compensates for any production tolerances and avoids glass to glass contact. Furthermore, by using dry-assembly instead of an adhesive as a bonding method, the structure allows for disassembly and full recyclability. Tongue and groove shaped interfaces ensure an interlocking connection. The interlocking connection prevents any lateral movement and will guide the voussoir into the right position during assembly.

By tessellating a shell structure, the shell structure is divided into a discrete number of voussoirs that can be cast in the adjustable mould. Several aspects have to be taken into account when optimizing the tessellation pattern including planarity, alignment to the flow of forces, face size, interior angle size and if the pattern is staggered or not. A comparison was made between three different regular tessellation patterns (triangular, quadrangular and hexagonal) with these aspects kept in mind.

A shell structure was designed to cover a courtyard of the Armamentarium in Delft. This shell structure served as a case study used to demonstrate the design and production process developed for this thesis. The shape of the shell was generated through a form finding process and its structural performance was validated with a FEM analysis. The shell was tessellated into a triangular tessellation. An algorithm used for assigning either tongues or grooves to the interfaces of each voussoir was developed. A list was generated containing the following information for each voussoir: voussoir index number, interface types, edge lengths, voussoir joining angles and the adjacent voussoir index numbers. The data in this list serves as input data for the set-up of the adjustable mould. Furthermore, the connection between the shell structure and the existing structure was designed and an assembly method was developed.

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Acknowledgements Last November, I had the idea of using adjustable moulds for the production of cast glass voussoirs of varying geometry for transparent shell structures. I had no clue how this mould should work nor how a shell structure should be subdivided into smaller components that could be casted in that mould. Maybe this idea had some potential or maybe I would find out after a month that it would not work out at all. Looking back at the last seven months, I am very satisfied to see that this idea has developed into a prototype of an adjustable mould, lead to the casting of three glass voussoirs and resulted in a design for a glass shell structure. However, this would not have been possible without the contribution of some people for which I want to express my gratitude.

First of all, I would like to thank Faidra Oikonomopoulou, my first mentor. Thanks to the structural design elective course that she was teaching in the second semester of the master’s programme, I got introduced to glass as a structural material. Her enthusiasm about structural glass inspired me to pursue this as a topic for my graduate thesis. The knowledge on the topic of cast glass that she shared with me was absolutely essential for doing the research presented in this thesis.

Also, I am very grateful to Marcel Bilow, my second mentor who showed great enthusiasm for the research topic since the moment I approached him to ask if he want to be my mentor for the graduation trajectory. His wide knowledge on manufacturing and construction in general made him give the right advice to push me in the right direction.

Other people I would like to thank are Fred Veer for supervising the compression test experiments, Telesilla Bristogianni for helping me with the casting of the glass voussoirs, Hans Hoogenboom for helping me with an attempt at performing a DEM analysis and James O’Callaghan for two inspiring consults at the very beginning and end of the seven months that I worked on this thesis.

Furthermore, I would like to thank my parents, Frans and Jeanne, for supporting me throughout my studies and life in general. Finally, I want to thank Eefje for her endless support and for her patience during the last busy months.

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Contents I Introduction ...... 1 1 Research framework ...... 2 Problem statement ...... 2 Research objective ...... 2 Research questions ...... 2 Methodology ...... 3 Relevance ...... 3

II Literature review ...... 4 2 Glass technology ...... 5 Chemical composition ...... 5 2.1.1 Soda-lime glass ...... 7 2.1.2 Borosilicate glass ...... 8 2.1.3 Lead glass ...... 8 2.1.4 Aluminosilicate glass ...... 8 2.1.5 High silicate glass ...... 9 Production methods ...... 9 2.2.1 Float process ...... 9 2.2.2 Casting process ...... 12 2.2.3 Extrusion process ...... 16 Structural glass ...... 17 2.3.1 Float glass ...... 17 2.3.2 Cast glass ...... 20 2.3.3 Extruded glass ...... 26 Safety ...... 27 Recycling ...... 28 3 Shell structures ...... 30 Structural performance of shells ...... 30 Form finding ...... 32 3.2.1 Physical hanging models ...... 32 3.2.2 Computational form finding...... 35 Construction methods ...... 36 3.3.1 Monolithic casting ...... 37 3.3.2 Discrete construction ...... 38

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4 Design criteria ...... 46 Construction method ...... 46 Production method ...... 46 Bonding method ...... 46 Shell shape ...... 47 Mould and tessellation pattern ...... 47 Type of glass ...... 47

III Production and design ...... 48 5 Interfaces ...... 49 Interface testing ...... 50 6 Adjustable mould ...... 54 Intrados and extrados geometry variables ...... 54 Interface geometry variables ...... 56 Vertex modules ...... 57 Dimensions ...... 59 Prototype ...... 62 Improved design ...... 64 Mould manufacturing ...... 67 Casting process ...... 67 7 Tessellation pattern ...... 70 Node valency ...... 71 Intrados/extrados mould variables ...... 71 Planarity ...... 71 Spheres at the nodes ...... 72 Risk of sliding at shell openings ...... 73 Staggered bond ...... 74 8 Node components ...... 76 Dimensions ...... 76 Mould design ...... 77 9 Interlayers ...... 79 Interlayer in between the interfaces ...... 79 Interlayer in between the voussoirs and the node components ...... 79

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IV Case study...... 81 10 Armamentarium Delft ...... 82 Form finding ...... 83 Structural validation ...... 84 Tessellation ...... 87 Voussoir generation ...... 88 Adjustable mould design...... 91 Supports ...... 93 Assembly ...... 98

V Conclusions, limitations and recommendations ...... 102 11 Conclusions ...... 103 12 Limitations and recommendations ...... 105

References ...... 106 Literature ...... 106 Figures ...... 110 Appendix A: Interface experiment results ...... 113 Test 1 ...... 113 Test 2 ...... 116 Appendix B: Mould manufacturing ...... 118 Tongue edge module ...... 118 Groove edge module ...... 119 Tongue vertex module ...... 120 Groove vertex module ...... 122 Tongue cylinder ...... 123 Tongue insert ...... 125 Appendix C: FEM analysis results ...... 128 Loadcase 1 ...... 128 Loadcase 2 ...... 129 Loadcase 3 ...... 131 Loadcase 4 ...... 133 Loadcase 5 ...... 134 Appendix D: Adjustable mould input data ...... 137

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I Introduction

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1 Research framework Problem statement Glass is a material with a high compressive strength and a low tensile strength. As a structural material it is therefore best applied in a structure that is mainly subjected to compressive stresses. These types of structures are shell structures including domes, vaults and arches.

After a golden age of shell construction in the mid-20th century, shell structures lost their popularity. One of the reasons for the decline of concrete and masonry shells is because these shells are dark and form enclosed spaces (Tang, 2015). Concrete and masonry are opaque and do not permit light to enter the space. A shell structure made of glass would solve this problem.

So far, two examples of structural glass domes exist. These are made of planes of float glass and have a span up to 8.5 meters (Veer et al., 2003; Blandini & Sobek, 2014) . Larger spans are unlikely to be possible when using the similar flat planes of glass due to an increased risk of buckling failure as the span increases. Cast glass elements, that have a three-dimensional geometry as opposed to the two- dimensional geometry of float glass, could be used for the construction of a shell structure with a large span without the risk of buckling failure. Research by Bristogianni et al. (2016) explored the possibility of a dome out of cast glass components. This research was however limited to the design of a spherical shape instead of a complex shape which is often the case for shell structures.

Due to the complex shape of shell structures, they cannot be constructed with elements of just one single geometry. Cast glass elements of different geometries are needed to construct a shell structure which means that a large number of different moulds are needed for the production process. This renders the production process economically inefficient. An adaptive mould could be used to produce cast glass components of different geometries while keeping the costs for the moulds to a minimum. Research objective The objective of this research is to find a way to build transparent shell structures out of cast glass components. When the objective is reached, this knowledge should be applied to a case study. The research objective can be divided into multiple sub-objectives.

- Designing a shell structure that is mainly subjected to compressive stresses - Explore a method of subdividing the shape of a shell structure into castable components - Finding an efficient way to cast the components - Developing a method to support and assemble the shell Research questions Based on the previously mentioned research objectives, the following research question is formulated:

How can a transparent shell structure out of cast glass components be engineered to be fabricated in an efficient way?

This research questions can be broken down to the following sub-research questions:

- What is the optimal shape of a shell structure in order to be mainly subjected to compressive stresses? - How can a shell structure be divided into components that can be casted? - How can the components be casted in an efficient way? - How can a shell structure out cast glass elements be supported and assembled? 2

Methodology The research is structured into several phases. The first phase consists of a literature study focussed on glass technology and shell structures. The goal of the literature study is to obtain insight in the mentioned topics and to be aware of the possibilities that the current state-of-art technology has to offer. Based on the conclusions drawn from the literature research, several design criteria are stated for the design of shell structures out of cast glass components.

The second phase is the development phase in which a design and production process is developed to divide a shell structure into multiple castable components and to cast all these components in an efficient way.

The third phase covers the application of the design and production process developed in the second phase. A case study is introduced to serve as a context to demonstrate the design and production process. Furthermore, a structural analysis is done, the details of how the shell structure is supported are designed and a way to assemble the shell structure is described.

Finally, the fourth phase involves evaluating the whole research and drawing conclusions. Recommendations for further research regarding the design of shell structures out of cast glass components will be given. Relevance The potential of cast glass components is not yet fully developed and only a limited number of projects that involve the use of cast glass components have been built. By doing further research on this topic, the potential might develop further and can eventually be used by architects to incorporate into their designs. Since glass waste is currently the third largest packaging waste material in the EU (Eurostat, 2018) and glass is, given the right circumstances, recyclable, further research on building materials made of recycled glass could contribute to a sustainable way of building.

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II Literature review

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2 Glass technology Glass made its first appearance into the built environment being used for glazing in villas in Pompeii and Herculaneum (Schittich et al., 1999). The Romans used small, translucent glass elements to let daylight enter their buildings while being protected from rain and wind but also to display their wealth. Over the years the quality of the glass has improved by altering its chemical composition and better production methods up to a point that glass can be used for structural purposes.

The properties of a glass product are determined by its material properties but also by its geometrical properties. The properties of a glass product are dependent on the chemical composition of the used glass, on the production method and the post-production processes. Therefore, glass can be categorised based on its chemical composition and on the used production method and post- production processes.

This chapter discusses the most occurring chemical compositions and the resulting properties. This chapter also discusses different production and post-production processing methods, how glass is used for structural purposes, how safety of these structures can be guaranteed and how glass can be recycled. Chemical composition Despite that glass has the appearance of a solid state of matter, it is a liquid which is cooled down to a rigid state (Wigginton, 1996). Viscous molten glass consists of a network of randomly ordered SiO4 tetrahedra. When the molten glass is rapidly cooled down to a rigid state in a controlled manner there is no time for the atoms to arrange themselves in a crystalline network. This means that the random network will be ‘frozen’ in a rigid state. Due to this random ordered network, glass owes its transparency. Figure 2.1 shows the randomly ordered network of glass.

Figure 2.1: Molecular structure of glass

As mentioned, glass consists of a randomly ordered network of SiO4 tetrahedra. The SiO4 tetrahedra are formed when silicate (SiO2), the main component of sand, is heated to its melting point of 1726°C (Wigginton, 1996). Several additives can be added to the silicate in order to lower the melting point or to alter the properties of the final product. Besides silicate, sand can also contain other materials that are considered impurities. These impurities also have an impact on the properties of the final 5 product. For instance, the green tint that is commonly found in float glass is due to 0.1% of iron oxide (FeO), in the sand mixture.

By adding other chemicals to the silica mixture, the chemical composition of the glass and its properties will change. The properties that are the most affected are the thermal properties, the mechanical properties and the production costs.

Among the thermal properties are four values for temperature corresponding to specific values for viscosity. These are the softening point, the flow point, the annealing point and the strain point. The softening point is the temperature at which glass has a viscosity of 106.5 to 107 Pa·s, low enough for glass to deform under its own weight (Shand, 1958). At this point, glass becomes suitable to undergo primary shaping processes. For easier processing, glass is often heated beyond the softening point to further decrease its viscosity to 103 Pa·s. This point is known as the flow point and the range between the softening point and the flow point is known as the working range (Lillie, 1953).

The annealing point is the temperature that corresponds with a viscosity of 1012 Pa·s (Shand, 1958). At this viscosity, the atoms are able to move freely while the shape of the glass object remains intact. This allows for the relieving of any internal stresses built up during the shaping process. When glass reaches a viscosity of 1013.5 Pa·s, the internal stresses cannot be relieved anymore. This viscosity corresponds with a temperate value known as the strain point. The range between the strain point and the annealing point (i.e. the range where internal stresses can be relieved), is known as the annealing range. Figure 2.2 shows a graph in which the viscosity of the glass is plotted against the key temperatures.

Figure 2.2: Typical graph of temperature points corresponding to specific viscosities

In general, a chemical composition with a low thermal expansion coefficient, high thermal shock and chemical resistance will also have a higher softening point and is more expensive to produce. The most common chemical compositions of glass are soda-lime glass, borosilicate glasses, lead glasses, aluminosilicate glasses and high silicate glasses. Table 2.1 and Table 2.2 gives an overview of the thermal and mechanical properties of these glass types. Instead of a single value for each property, the values are given as a range. This is because slight alterations in the recipe of each glass type lead to different values for the thermal and mechanical properties.

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Table 2.1: Thermal properties of different types of glass (based on Shand (1958))

Glass type Strain point [°C] Annealing point Softening point [°C] Flow point [°C] (η=1013.5 Pa·s) [°C] (η=106.5 – 107 Pa·s) (η=103 Pa·s) (η=1012 Pa·s) Soda-lime 465 – 510 505 – 553 696 - 735 880 – 920 Borosilicate 435 – 520 480 – 565 703 – 820 900 – 1075 Lead 390 – 425 430 – 465 580 – 648 720 – 850 Aluminosilicate 670 – 675 715 – 720 915 1090 High silicate 820 – 1070 910 – 1140 1500 – 1667 -

Table 2.2: Mechanical properties of different types of glass (based on Granta Design Limited (2018))

Glass type E [GPa] Fc [MPa] Ft [MPa] Fyield [MPa] Soda-lime 68 - 72 302 - 342 30.2 – 34.2 30.2 – 34.2 Borosilicate 48 - 70 220 - 351 22.0 – 37.7 22.0 – 37.7 Lead 53 - 64 232 – 1.37e3 23.2 - 137 23.2 – 137 Aluminosilicate 84 - 89 376 - 439 37.6 – 43.9 37.6 – 43.9 High silicate 66 - 75 1.05e3 – 1.68e3 45.7 - 168 45.7 - 168

The mechanical properties are similar for most types of glass except for high silicate glasses which are significantly stronger. The tensile strength is around 10% of the compressive strength. Since the yield strength is equal to the tensile strength, glass is not capable of deforming plastically. As a result, glass will break when tensile stresses occur that exceed the yield strength. The low tensile strength can be attributed to the occurrence of microcracks in the surface of all glass specimens (Stanworth, 1950). These cracks act as stress multipliers. When tensile stress occurs at the surface of a glass specimen, stress concentrations will accumulate around the tip of the crack resulting in further propagation of the crack leading to failure of the glass.

The different glass types will be briefly discussed.

2.1.1 Soda-lime glass At 90% of the total glass production, soda-lime glass is the most common type of glass (Amstock,

1997). The main component of the mixture is silicate but also sodium oxide (Na2O) and calcium oxide (CaO) are added. The sodium oxide acts as a flux, a material that significantly lowers the melting temperature. By adding sodium oxide to the mixture, the melting point of the mixture is lowered from 1726°C to 800-900°C. However, the sodium oxide makes the glass water soluble. To increase the chemical durability, calcium oxide is added to the mixture. In some cases, magnesium oxide (MgO) and aluminium oxide (Al2O3) are added to further increase the durability. Table 2.3 gives an overview of the chemical composition of soda-lime glass.

Due to the low softening temperature of soda lime glass, less energy is needed to produce soda lime glass compared to other glasses. This makes soda lime glass the cheapest type of glass. The thermal shock resistance is relatively low (47-53 K) and the thermal expansion coefficient is relatively high (8.9- 9.5 10-6K-1). Due to these thermal properties, soda lime glass is used for applications where it is not subjected to rapid temperature fluctuations like windows and containers.

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Table 2.3: Chemical composition of soda-lime glass (based on Wigginton (1996), Amstock (1997) and Schittich et al. (1999))

SiO2 69 - 74 % Na2O 13 - 17 % CaO 5 - 12 % MgO 0 – 4 % Al2O3 0 - 3 %

2.1.2 Borosilicate glass

To produce borosilicate glass, boric oxide (B2O3) is added to the silica mixture to act as a flux. Sodium oxide, aluminium oxide and potassium oxide (K2O) are added in small percentages. Table 2.4 gives an overview of the chemical composition of borosilicate glass. Compared with the use of sodium oxide as the main flux, the use of boric oxide leads to a glass with a lower thermal expansion coefficient (3.1- 5.3 10-6K-1) and a higher thermal shock resistance (83-159 K). Due to its higher softening temperature, borosilicate glass is harder to process and is more expensive than soda-lime glass.

Borosilicate glass is typically used to produce heat resistant applications like kitchenware, laboratory ware and enclosures for hot lamps.

Table 2.4: Chemical composition of borosilicate glass (based on Wigginton (1996), Amstock (1997) and Schittich et al. (1999))

SiO2 60 – 87 % B2O3 7 – 25 % Na2O 0 – 8 % Al2O3 1 – 8 % K2O 0 – 8 %

2.1.3 Lead glass Lead glass contains at least 20% of lead oxide (PbO). High lead glasses can contain up to 80% of lead oxide. The lead oxide drastically lowers softening temperature to 626 °C and makes the glass relatively soft. Due to the high atomic mass of the lead atom, the density of lead glass is high compared with other types of glasses. Besides lead oxide, lead glass usually contains sodium oxide and potassium oxide in quantities smaller than 10%. Table 2.5 gives an overview of the chemical composition of lead glass.

Table 2.5: Chemical composition of lead glass (based on Wigginton (1996) and Amstock (1997))

SiO2 3 – 70 % PbO 18 – 80 % Na2O 4 – 20 % K2O 5 – 20 %

Lead glass is the cheapest type of glass after soda-lime glass. The low price, low softening point and easy workability makes lead glass the preferred glass for artists. When the content of lead oxide is high, lead glass is also used for application where x-rays need to be absorbed. 2.1.4 Aluminosilicate glass Aluminosilicate glass is comparable with borosilicate glass but has a higher content of aluminium oxide than boric oxide. Also, calcium oxide is added, and potassium oxide can be added. As a result, aluminosilicate has a higher softening point than borosilicate and therefore requires a higher 8 temperature to process (Amstock, 1997). Table 2.6 gives an overview of the chemical composition of aluminosilicate glass.

Table 2.6: Chemical composition of aluminosilicate glass (based on Wigginton (1996) and Amstock (1997))

SiO2 50 – 62 % Al2O3 9 – 40 % CaO 5 – 50 % B2O3 0 – 10 % K2O 0 – 16 %

Aluminosilicate glass is typically used for high temperature applications similar to borosilicate applications, fiberglass and mobile phone screens. 2.1.5 High silicate glass The high silicate glasses consist of 96% to more than 99.5% silicate. This gives high silicate glasses a very low thermal expansion coefficient and an excellent resistance against thermal shock and chemical corrosion. However, its high softening point makes high silicate glass the most expensive type of glass and the hardest to process. Table 2.7 gives an overview of the chemical composition of high silicate glass. High silicate glass is only used for high-tech applications where its exposed to high temperatures such as furnace windows, or where deformations due to thermal expansion are critical such as astronomical telescope mirrors.

Table 2.7: Chemical composition of high silicate glass (based on Wigginton (1996) and Amstock (1997))

SiO2 96 – 99.5 % B2O3 0 – 3 %

Production methods The production of glass can be separated into three different steps. The first step is the processing of the raw materials into a molten glass mixture. During the second step, the shaping process, the molten glass is shaped into a certain geometry. The third step includes several post-production processes. The possible post-production processes are dependent on the used shaping process.

Glass can be shaped in various ways for various purposes. For structural purposes, there are three types of shaping processes that are the most common. These are the float glass process, casting and extruding. There are several other techniques, but these are either outdated (e.g. crown glass spinning) or not used for the construction industry (e.g. blow moulding). Therefore, only the three mentioned production processes are further described.

2.2.1 Float process The float process was developed in the 1950’s by Sir Alastair Pilkington (Pilkington, 1969). This fully automated method is suitable for producing large flat sheets of glass of high optical quality and is currently the most common method to produce flat glass. Typical applications for float glass are its use for windows in buildings but it can also be used for structural applications. Figure 2.3 shows a drawing of a float glass production line. Raw materials are melted at approximately 1500°C. The molten glass is then poured over a bath of molten tin. The glass will flow out over the tin bath and will form a flat sheet with uniform thickness. The glass sheet will then enter the annealing lehr where it is gradually cooled down.

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Figure 2.3: Float glass process

During the annealing phase, the glass is slowly cooled to make sure that the rate of cooling is similar at the surface of the sheet as in the core of the sheet. When the rate of cooling is similar the shrinkage is also similar. Without the annealing phase, the glass sheet would cool down faster at the surface than at the core (Stanworth, 1950). This would cause the glass at surface to shrink and solidify first while the glass at the core shrinks and solidifies later. This would induce compressive stress at the surface and tensile stress at the core of the sheet. When these stresses exceed the yield strength, the glass will crack during the cooling. The duration of the annealing process depends on the thickness of the glass. Thicker sheets of glass need a longer time to anneal than thinner sheets of glass. The annealing time increases exponentially as the thickness of the glass increases linearly. Therefore, the production of float glass becomes economically inefficient when the thickness is exceeding 25 mm.

When the glass is annealed, the sheets pass an automated quality inspection where possible flaws are cut out. After the quality inspection the glass is cut to the desired size.

The benefit of the float glass process is that large sheets of glass can be produced. The standard size of float glass sheets are 3.2 by 6 meters but larger sizes are possible. Theoretically, there is no limit in the length of a sheet of float glass since the float process is a continuous production process. However, the length is limited to approximately 20 meters due to logistical constraints. The typical thickness of float glass ranges from 2 to 12 mm but a thickness up to 25 mm is possible.

Note that the price of float glass exponentially increases as the thickness increases. Another method to achieve float glass with a higher thickness is by laminating multiple glass sheets together with a PVB interlayer. However, the strength of a laminated glass plane is lower than the strength of a monolithic glass plane of the same thickness. Also, due to the interlayer the recyclability of laminated glass is compromised.

After primary production, float glass can be subjected to several post-production processes. These include mechanical working, bending, heat treatments, laminating, and several surface treatments. The post-production processes will be briefly discussed.

Mechanical working of the glass includes all methods to cut the glass to certain sizes and shapes and the drilling of holes. This can be done by waterjet-cutting or using diamond abrasive tools. Also, the sharp edges can be grinded and polished in several profiles.

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Another possible post-production process is the possibility to bend the float glass into single or double curved surfaces. This can be done either by cold bending or hot bending. The cold bending method can be applied for relatively low curvature. The glass is elastically deformed into the desired shape against a frame and is hold into place by connectors. When cold bent there will be a permanent stress in the glass which has an influence on its further structural performance.

For the hot bending method, a glass plane is heated up to its softening point. (Schittich et al., 1999; Wigginton, 1996) At this point the viscosity of the glass is low enough to allow for plastic deformation. The glass is either pressed or sagged by gravity into the desired shape and is cooled down. This method allows for higher curvature than the cold bending method and no residual stresses due to the bending are occurring in the glass.

Float glass can be subjected to a heat treatment to induce a surface compressive stress (O’Regan, 2014). During the heat treatment the float glass is reheated to its annealing point. Then the glass is quenched by jets of cooled air. This will quickly cool and solidify the surface while the core is still hot. When the core cools and shrinks, stresses will occur in the glass plane. As a result, the surface will be under compression and the core will be under tension. Figure 2.4 shows the stress distribution within the thickness of the glass plane.

Figure 2.4: Stress distribution in a glass plane after heat treatment

There are two different heat treatments: heat strengthening and fully tempering. The major difference is that the quenching for heat strengthened glass is done less intense then for fully tempered glass. As a result, the induced compressive strength in the surface is 24 to 52 MPa for heat strengthened glass and 80 to 150 for fully tempered glass. This induced compressive stress makes the glass stronger when subjected to bending stresses. For failure, the tensile stresses need to exceed the sum of tensile strength of the glass and the induced compressive stress. Note that all mechanical working of the glass like cutting and drilling needs to be done before the heat treatment since penetration of the compressive stress layer will lead to breakage.

A side effect of the thermal treatment is the change in fracture pattern. Figure 2.5 shows the fracture patterns of annealed glass, heat strengthened glass and fully tempered glass. Annealed and heat strengthened glass fracture in large and sharp shards that can still have some residual strength. Failure of fully tempered glass results in a fast crack propagation that fully shatters the glass in small blunt shards without any residual strength left.

Figure 2.5: Fracture patterns of a) annealed glass, b) heat strengthened glass and c) fully tempered glass 11

As mentioned, the maximum thickness of float glass is limited due to the time required for annealing. In order to produce thicker pieces of glass, several sheets can be bonded by means of a viscoelastic interlayer. This process is called lamination (O’Regan, 2014). Figure 2.6 shows the edge of a laminated glass plane that consists of two planes of glass with a PVB interlayer. The most common type of interlayer is PVB and usually comes in a thickness of a multiple of 0.38 mm. The process starts with stacking the glass sheets and interlayers and pass it through rollers to squeeze out any air. Then the stack enters an autoclave where a bond between the glass and the interlayer occurs while being heated under pressure in a vacuum bag. The size of the panels that can be laminated is limited to the size of the available autoclave (O’Callaghan, 2010).

Figure 2.6: Laminated glass plane

Further post-production processing consists of surface treatments. These include treatments that roughen the surface like acid etching and sandblasting. These treatments produce a matt translucent surface. Other surface treatments are based on adding a coating to the glass surface. These techniques include enamelling and printing which involve applying a coloured layer of ceramic or plastic respectively. Other coatings that can be applied are metallic coatings to modify the light and heat transmitting properties of the glass.

2.2.2 Casting process Among all shaping processes for glass, glass casting is the oldest and was the most prevalent technique for glass shaping until the invention of glassblowing (Cummings, 2001). With the casting process, three dimensional, non-prismatic, solid objects can be made. Typical everyday cast glass objects include kitchen bowls and glass art-objects, but the same technique is also used to make high-precision telescope mirrors with a diameter of over 8 meters. Recently, cast glass has made its appearance in architectural applications.

The casting process involves pouring molten glass into a mould with the desired shape. There are two methods for glass casting: hot-forming and kiln-casting. Hot forming involves producing a glass melt from raw ingredients prior to pouring it into the mould. After the glass is poured, the mould including the glass melt is placed in a kiln for annealing. It is also possible to let the glass cool down below its softening point outside of the kiln, remove the mould and then place the glass in the kiln for annealing. In this case all the sides of the components are directly exposed to the hot air in the kiln which results in a faster annealing process compared to annealing within the mould. Figure 2.7a shows the hot- forming process. Kiln-casting involves placing a container filled with pieces of glass (either new or

12 recycled) on top of a mould. The container and the mould are then heated in a kiln. When the temperature reaches the softening point of the glass, the glass will flow through a hole in the bottom of the container and flows into the mould. Figure 2.7b shows the kiln-casting process.

Figure 2.7:a) hot-forming process and b) kiln-casting process

There are four prevalent types of moulds used to produce cast glass objects (Oikonomopoulou et al., 2018a). These are the disposable mould, the open metal mould, the press metal mould and the adjustable mould (Figure 2.8). Moulds can also be categorised by material they are made of. Table 2.8 gives an overview of the different types of moulds categorised by the material they are made of and their properties.

Figure 2.8a) disposable mould, b) open mould, c) press mould, d) adjustable mould

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Table 2.8: Characteristics of prevailing mould types for glass casting (Oikonomopoulou et al., 2018a)

Material Silica Plaster Alumina-silica (Stainless) steel Graphite Reusability Disposable Disposable Permanent Permanent Variation - - Adjustable/Fixed/Pressed Adjustable/Fixed Production Investment Milling Milling/cutting and Milling or grinding method casting welding Manufacturing Low High Moderate to High High costs Top temperature 900 – 1000 °C 1650 °C 1200 – 1260 °C Unknown Glass annealing Mould not Mould not Mould usually removed Mould removed method removed removed but can remain for higher accuracy Release method Immerse in water Water pressure Release coating Release coating necessary necessary Level of precision Low/moderate High Moderate to high / high / Moderate to high/ very high high Finishing surface Translucent Translucent Transparent Transparent Applicability Low volume Low volume High volume production High volume production production production

The selection for a mould is based on the required level of accuracy and batch size of the final product and driven by cost and time. Cast glass objects in low batch sizes are usually casted in disposable moulds since disposable moulds are generally cheaper than permanent moulds. Therefore, disposable moulds are used by artists who make unique one-off objects or are used to produce prototypes. Two types of disposable moulds can be distinguished: the silica plaster mould and the alumina silica fiber mould. The silica plaster mould is relatively cheap but can only operate at temperatures up to 1000 °C which doesn’t make it suitable for every type of glass composition. The alumina silica fiber mould is more expensive but can operate at temperatures up to 1650 °C and achieves a higher level of accuracy. The use of both disposable moulds leads to objects with a rough surface quality that require polishing for a transparent result.

For high batch sizes, permanent moulds are usually preferred. These can be either made of steel or when a smoother surface is required, out of the more expensive graphite. The moulds need to be coated with a release agent in order to release the glass object from the mould after casting. Furthermore, the mould should be pre-heated prior to the casting to prevent that the hot glass melt comes in contact with the cold mould surface which will lead to surface chills. Complex features in the final object, like holes or notches, are possible but may require expensive multi-part moulds.

Variations of the permanent mould include the open mould, the press mould and the adjustable mould. The open mould has an open top surface that is exposed to the environment. The face of the glass object corresponding with the open face of the mould might have a lower optical quality than the faces corresponding with the closed faces of the mould. A press mould eliminates the open face and thus leads to objects with a higher level of precision. Adjustable moulds for casting glass have only been used for one single project: Ice Falls by James Carpenter Design Associates Inc. For this project an open adjustable graphite mould was used that was able to create prismatic components with a variable length (Figure 2.9).

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Figure 2.9: Adjustable graphite moulds for the Ice Falls project

Due to their three-dimensional geometries, cast glass components need a longer time to anneal than two-dimensional float glass. According to the research done during the development of glass bricks for the Crystal House by Oikonomopoulou et al. (2017), the annealing time exponentially increases as the volume of the cast glass components increase. Soda-lime glass bricks with 65 mm × 105 mm × 210 mm dimensions required 8 hours of annealing compared with 36-38 hours of annealing for glass bricks with 65 mm × 210 mm × 210 mm dimensions. Since more energy is needed for a longer annealing time, shapes with a very long annealing time can become economically unfeasible. Therefore, the annealing time and its subsequent costs need to be considered when designing a cast glass component.

During the annealing process, the hot glass cools down from the annealing point to the strain point. The surface of the glass object that is in direct contact with the air of the kiln will cool down faster than the core. This also means that the glass at the surface will shrink faster than the glass at the core. When the temperature at the surface drops below the strain point, the glass becomes too viscous to allow for the SiO4 network to restructure and to relieve any existing stresses (Shand, 1958). At this point the glass at the core still shrinks further as it cools down and pulls the viscous glass at the surface inwards. This will cause internal tensile stresses since the glass at the surface is not able to deform anymore. When this is done in a controlled way, (like during the heat treatment of float glass described in 2.2.1), the internal stresses will not exceed the yield strength and no problem occurs. However, when this is done in a non-controlled way, the internal stresses can exceed the yield strength and will cause the glass to crack. In order to avoid this from happening, the temperature difference between the surface and the core needs to be limited to a maximum of 4°C (Cummings, 2001). This means that large objects with a large distance from the surface to the core need a longer time to anneal than small objects with a small distance from the surface to the core. Also, geometry with large variations in cross sections take longer to anneal than compact geometries like spheres.

Special design measures can be taken to reduce the volume of cast glass objects and thus reduce the annealing time (Jacobs et al., 1984). A good example of this is the design of the Palomar telescope mirror (Figure 2.10). Instead of a solid mirror, a mirror with a honeycomb pattern is designed in order to reduce the total glass volume and thus reducing the annealing time to 10 months. Note that an

15 annealing time of 10 months is acceptable for high-tech observatory applications but not for applications in the building industry.

Figure 2.10: Glass mirror of the Mt. Palomar telescope

After the production of a cast glass component, the component can be subjected to several post- production processes. Cast glass can be polished to achieve a flatter and more transparent surface. Also, cast glass components can be cut by waterjet cutting or using diamond abrasive tools. However, it is more economically efficient to avoid post-production cutting by using moulds that directly lead to the desired geometry.

2.2.3 Extrusion process Glass extrusion is used to produce linear elements with a fixed cross-sectional profile. Figure 2.11 shows the glass extrusion process. During this process a glass melt billet is placed in a cylinder. A ram presses the billet trough a shaped die. A large amount of different cross sections are possible that can either be solid rods or hollow tubes. Figure 2.12 shows several extruded glass profiles.

Figure 2.11: Extrusion process

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Figure 2.12: Extruded glass profiles

Compared with float glass and cast glass production, glass has a higher viscosity when extruded (Roeder, 1971). Since the viscosity of the glass is dependent of the temperature it means that glass extrusion can be done at lower temperatures and that less energy is needed when compared to floating or casting. Structural glass When glass is applied in the building industry, it usually serves as glazing in the façade to allow for daylight entering the building while maintaining a barrier that divides the interior from the exterior. However, due to its mechanical properties, glass is also a suitable material for structural applications. This paragraph gives an overview of structural applications of float glass, cast glass and extruded glass. 2.3.1 Float glass Due to their geometry, two-dimensional planar elements have a low stiffness. This results in low resistance to bending or even failure when subjected to out of plane loads and makes them prone to bucking when subjected to in plane loads. Since planes of float glass are two-dimensional planar elements, they need to be stiffened when used for structural applications. This is usually done by connecting several strips of float glass, so called ‘fins’, along the entire float glass plane.

A good example of this principle can be found in the glass cube of the Fifth Avenue Apple Store in New York. It was designed by Bohlin Cywinski Jackson and engineered by Eckersley O’Callaghan. As shown in Figure 2.13, the cube consists of four vertical surfaces acting as facades and one horizontal surface acting as a roof. The surfaces are reinforced by glass fins that prevent failure due to out of plane loads and failure due to buckling (O’Callaghan, 2010). The resulting cube is fully transparent since no opaque substructure is present.

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Figure 2.13: Apple Store, Fifth Avenue

A crucial part when engineering glass structures is the design of the connections. A connection should be designed in such a way that stress concentrations, which can lead to failure, are avoided. Possible connections are clamp connections, bolted connections, embedded connections and adhesive connections (O’Regan, 2014).

Clamp connections consist of elements that clamps a glass plane on one end and are either fixed on a support structure or are clamped to another glass plane. Figure 2.14 shows a clamp connection. It is important that direct contact between the clamp and the glass is prevented by layer of rubber. No holes need to be drilled in the glass to make a clamp connection.

Figure 2.14: Clamp connection

Bolted connections require holes to be drilled in the glass. To avoid high stress concentrations around the holes, bushings made of a soft material need to be placed between the bolt and the hole. Compared to clamp connections, bolted connections (Figure 2.15a) are usually smaller and therefore

18 improve the overall transparency of the structure. This is especially the case when countersunk (Figure 2.15b) or undercut (Figure 2.15c) connections are applied.

Figure 2.15:a) bolted connection, b) countersunk bolted connection and c) undercut bolted connection

Adhesive connections have the benefit over mechanical connections that the load transfer is more evenly spread. When a transparent adhesive is used it also leads to a better overall transparency of the structure than when mechanical connections are used. Figure 2.16 shows the subtility of an adhesive connection. A downside of adhesive connections is that their permanence makes them unsuitable for disassembly and recycling.

Figure 2.16: Adhesive connection

Besides adding glass fins to reinforce a float glass panel, float glass can be hot-bended into corrugated panels that have a higher stiffness than flat panels (Nijsse & Wenting, 2014). The MAS in Antwerp, designed by Neutelings Riedijk and engineered by ABT, includes corrugated panels up to 11 meters in height in the façade. Figure 2.17 shows the corrugated panels. The corrugated panels are supported by hinged supports at the top and bottom and an additional horizontal support in the middle. The panels carry their own dead weight and are able to withstand lateral wind forces.

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Figure 2.17: Corrugated panels in the MAS

Research by Hobbelman et al. (2002) showed that due to the high compressive strength of glass, the ideal structure for glass would be a dome where the glass would be loaded in compression only. Veer et al. (2003) built a 5.5 meter spanning dome out of 8 mm thick float glass. The dome consisted of 64 flat trapezium shaped panels in four different sizes connected with clamped connections. The dome is shown in Figure 2.18a. The glass dome by Blandini and Sobek (2014) has a span of 8.5 meter. This dome was built out of 44 double curved laminated glass panels with a thickness of 10 mm that were bonded with adhesive connections. This dome is shown in Figure 2.18b. When constructing similar domes with larger spans the risk of buckling failure will increase (Bristogianni et al., 2016). To prevent this, either stiffening elements that reduce transparency need to be applied or the thickness of the glass need to be increased to a thickness that could clash with production standards of float glass.

Figure 2.18: Glass domes by a) Veer et al. (2003) and b) Blandini and Sobek (2014)

2.3.2 Cast glass In contrast to float glass, only a limited number of projects are realised where cast glass elements are part of the load bearing structure. These are the Optical Glass House in Hiroshima, the Atocha memorial in Madrid and the Crystal House in Amsterdam. Besides these realised projects, research is done on novel interlocking glass systems and arches and domes out of cast glass. These projects can be categorised by the way the cast glass components are bonded.

Mechanical bonding

The Optical Glass House in Hiroshima was designed by Hiroshi Nakamura and completed in 2012. Part of the Optical Glass House is an 8.6m by 8.6 m surface in the façade that consists of 6000 solid cast

20 borosilicate blocks (Oshima, 2012). Figure 2.19a shows one of these blocks and Figure 2.19b shows how the blocks are configured into the façade. The blocks are stacked on top of each other and are strung together by steel rods that pass through holes in the blocks. The glass caries its own weight while any lateral forces are diverted through steel rods to the main structure. Two steel fins are added to the back of the surface to withstand any wind loads. Since the glass blocks are only carrying its own dead load, the structure is relatively slender. The use of steel rods to string the blocks together results in a mortar free structure that can easily be disassembled but also decreases the overall transparency of the façade.

Figure 2.19:a) cast glass component for the Optical Glass House and b) facade of the Optical Glass House

Adhesive bonding

The Atocha memorial in Madrid designed by FAM consists of an aboveground structure on top of an underground mediation room. Figure 2.20 shows the above ground structure. The aboveground structure is an 11 meter high wall in an elliptical shape and consists out of 15.600 cast glass blocks. (Paech & Göppert, 2008). The blocks are joined with an UV curing adhesive. Due to the elliptical shape, the wall becomes a rigid structure that can withstand lateral loads. This eliminates the use of steel elements for lateral load bearing capacity that would disturb the transparency. Five float glass beams that carry the roof are spanning from one side of the ellipsoid to the other and thus further stiffen the shape.

Figure 2.20: The Atocha Memorial

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The local climate can subject the glass blocks to high temperature fluctuations when cold rain falls on the blocks after being heated in the sun. Therefore, borosilicate glass is used due to its low thermal expansion coefficient compared with soda-lime glass. The 8.4 kg blocks of 300 mm × 200 × 70 mm in dimensions were casted in a press mould and needed 20 hours of annealing. The geometry of the block includes two opposed concave and convex sides (Figure 2.21). This geometry allows for irregular curved walls to made with one single unit while maintaining full contact between adjacent units.

Figure 2.21: Cast glass component for the Atocha Memorial

The blocks are bonded with a UV-hardening acrylic adhesive. Adhesives perform optimally when applied in thin layers of roughly 0.33 mm. However, due to tolerances in the glass brick, the thickness of the adhesive layer can be up to 2.5 mm. Special templates were developed to control the position and the amount of glue to make sure that enough glue was applied to ensure a proper connection while minimising overflow and the occurrence of air bubbles. Before the adhesive was applied, the surfaces of the bricks that were going to be glued together were cleaned with isopropanol. After the position of each new brick, the glue was cured by exposition to UV radiation for 4 minutes. To protect the adhesive joints against moisture, all seams between the blocks were sealed on the outside with a transparent silicone.

For the Crystal House in Amsterdam designed by MVRDV, a new façade has been designed and engineered to replace a traditional nineteenth century brickwork façade with a transparent façade while maintaining the traditional brick pattern. (Oikonomopoulou et al., 2017). The new façade consists of 6500 cast glass bricks of three different sizes that are bonded with an UV curing adhesive. The compressive strength of the glass bricks is high enough for the façade to carry its dead load. Four buttresses, constructed out of the same glass bricks, guarantee the lateral stability. This results in a fully transparent, load bearing façade that does not require a substructure. Figure 2.22 shows the façade of the Crystal House.

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Figure 2.22: Facade of the Crystal House

The adhesive used for the bonding of the glass bricks has an optimal bonding when having a thickness of 0.2 to 0.3 mm. In contrast to the Atocha Memorial where the adhesive layer has a thickness of up to 2.5 mm, the adhesive layer thickness in the Crystal House bricks had to meet the optimal thickness. Therefore, every glass brick needed to have a flat top and bottom surfaces within a 0.25 mm tolerance for guaranteeing an adhesive layer of the highest strength. When using borosilicate, which has a low thermal expansion coefficient, in combination with high precision press moulds, the achieved tolerance is ±1.0 mm. To achieve an accuracy of 0.25 mm, post-production polishing is inevitable, even when the borosilicate and high precision press moulds are used. Therefore, soda-lime glass and open moulds were used followed by post-production polishing to lower the production costs.

The construction process of the Crystal House was characterised by a level of accuracy uncommon at constructions sites. This started with the levelling of 12 meter long steel plate to an accuracy of 0.25 mm on top of which the first layer of bricks were placed. Before the bonding of every new brick, the seam was measured to check if it fits within the 0.25 mm tolerance. Then the bonding surfaces were cleaned and the adhesive was applied. The adhesive was later cured by exposing it to UV radiation for 60 to 120 seconds. After building every two meters of elevation, the level recorded with high accuracy instruments. Possible deviations in the height were compensated by adding a layer of glass bricks with a 0.5 to 1.0 mm reduction in height. The meticulous construction method of gluing glass bricks stands in sharp contrast with traditional bricklaying where a mason uses mortar for binding the bricks but also to accommodate tolerances in the size of the bricks.

Bristogianni et al. (2016) researched the possibility for a dome out of adhesively bonded cast glass components. This research mainly focussed on the subdivision of the dome into components that could be casted and the casting process of the individual components. To limit the number of different components, the design of the dome was based on Buckminster Fuller’s Geodesic dome. This is a spherical dome which can be constructed with components of just two different geometries: a 23 pentagon and a hexagon. Most part of the research focused on the production of the prototypes in disposable moulds and the analysis of residual stresses in the prototypes. The research lacked any exploration on the construction method. Given that the construction of the cast glass façade of the Crystal House, a relatively simple wall, was a very meticulous process, it is likely that the construction of a cast glass geodesic dome, a relatively complex double curved surface, will be an even more difficult process.

Dry-assembly

A third way to build with cast glass components without the need for a substructure or for an adhesive bond is to use cast glass components that are designed in such a way that they are interlocking. Interlocking systems out of cast glass components have not been applied in realised structures but are currently researched in the academic world (Oikonomopoulou et al., 2018b).

The stability of a system built of interlocking components is guaranteed due to a combination of weight and friction. Due to the weight of each component, a dead load is exerted on the component below and thus an overall compressive stress is present within the structure. Any lateral movement of the components is prevented by interlocking feature and the friction between the components that occurs due to the compressive stress.

In between the interlocking components, a dry, transparent interlayer acts as a medium to prevent glass-to-glass contact and to spread out the load transfer to avoid peak stresses (Oikonomopoulou et al., 2018b). The most important properties of the material used for the interlayer are hardness, tear resistance and creep resistance (Oikonomopoulou et al., 2019). The material used for the interlayer should be flexible enough to deform under compression in order to adapt to the glass surface and thus accommodates for any inevitable tolerance in the glass surface. However, the material has to be stiff enough to avoid penetration resulting in glass-to-glass contact. Since the interlayer compromises the overall stiffness of the dry-assembled cast glass structure, the interlayer should be as thin as possible. The most suitable material to use as an interlayer is currently being researched. Polyurethane (PU) rubber is considered to be the most promising (Aurik et al., 2018; Oikonomopoulou et al., 2018b). Of the different PU rubbers that have been tested by Oikonomopoulou et al (2019), PMC770 and Task 16 have the best performance.

Several types of interlocking components have been developed by Oikonomopoulou et al. (2018b). Multiple design criteria relating to the interlocking properties and relating to the casting process have been taken into account during this development. The interlocking system should confine movement in both longitudinal and transverse direction. Shear capacity should be optimised, the interlocking system should lead to easy self-alignment of the components and the interlocking system should allow for multiple configurations to be made. Regarding the casting process, the components should have a limited volume and not exceed a mass of 10 kg to avoid a long and costly annealing process. Rounded shapes are preferred to shapes with sharp, pointed edges to prevent internal stresses due to inhomogeneous shrinking. Finally, the number of different components needed for the interlocking system should be kept to a minimum for easier construction and to reduce overall production costs.

The most promising developed component that meets the previously mentioned design criteria are the osteomorphic blocks. Figure 2.23 shows several of these blocks stacked into a wall configuration. The osteomorphic block was developed by Dyskin et al. (2003). The top and bottom surface of the blocks are wave-like convex-concave surfaces that perfectly fits into one another. A benefit of those blocks is that walls with corners can be easily made with just a single type of block. Custom made bricks with one flat surface need to be placed at the periphery to ensure a proper transition between

24 the cast glass wall and the building element adjacent to it. An increased amplitude of the wave like surface increases the shear capacity but increases the complexity of the casting process.

Figure 2.23: Osteomorphic interlocking cast glass components

Other notable research done on interlocking cast glass components include the design of an arched bridge (Snijder et al., 2016; Aurik, 2017; Bristogianni et al., 2017) and the design of a dome (Janssens, 2018). Both designs were based on the principle that the excellent compressive strength of glass would be put to its full use when applied in compressive based structures like an arch or dome.

Aurik (2017) designed an arched bridge made of interlocking cast glass components as shown in Figure 2.24. Note that all components except the ones at the support all have the same geometry. The top and bottom surface of the components have an interlocking geometry that are not running parallel but are slightly wedged. When these components are stacked, the resulting shape is a circular arc. In order to make a non-circular arc like a catenary arc, different components with different wedge angles should be used.

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Figure 2.24: Cast glass arch bridge prototype

As opposed to an arc, a dome is curved in two directions. Therefore, the component designed by Janssens (2018) to construct a dome does not only have an interlocking geometry on the top and bottom but also on the sides. The component consists of two spheres joined with a smaller sphere in the middle. The two outer spheres have slightly different radii, so the component is slightly wedged. With this component, both the vertical and horizontal circular arc shapes of the dome can be constructed. Figure 2.25 shows a perspective of the component (a), how the component interlocks vertically (b) and how the component interlocks horizontally (c). Note that with this component only a spherical dome can be made. For non-spherical domes like catenary domes, different components with different wedge angles should be used.

Figure 2.25: Component for a cast glass dome, a) perspective, b) vertical configuration and c) horizontal configuration

2.3.3 Extruded glass Unlike float glass and cast glass that are usually also functioning as a façade when applied as a structure, extruded glass cannot be applied as a façade due to the nature of its geometry. Therefore, extruded glass is usually applied as a linear structural member.

An example of extruded glass applied in structures can be found in the façade of the Tower Place in London. The building is designed by Foster + Partners and the engineering of the façade was done by ARUP. 4 meter long extruded glass tubes support the curtain wall and divert the compressive lateral forces on the façade to the substructure (Carpenter Lowings, n.d.). A 10 mm thick post-tensioned steel rod runs through the glass tube and provides resistance against tension due to suction of the wind (Figure 2.26).

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Figure 2.26: Extruded glass in the Tower Place façade

Extruded glass can also be bundled to create structural members with larger cross-sections. A benefit of bundling multiple extruded glass rods that in case one rod cracks, the other rods are still intact and the decrease in structural performance is limited. An example of a structure that involved bundled extruded glass rods is a truss bridge by Snijder et al. (2018). For this project the diagonals of the truss are made of bundled extruded glass rods. Figure 2.27a shows one of the bundled diagonals and Figure 2.27b shows how the diagonals are part of the truss. The bundles were made of a six glass rods with a diameter of 6 mm glued to a glass starshaped hollow tube. By pre-tensioning a steel rod inside the tube, a pre-compression is introduced in the glass rods. This makes sure that any tension in the diagonals of the truss does not lead to tensile stresses in the glass.

Figure 2.27: a) bundled glass rods b) as diagonals in a truss

Safety Since glass is a brittle material it does not show excessive bending before failure. This can cause dangerous situations as a glass structure can suddenly collapse without showing any prior indication through large deformations. When designing glass structures, it is of utmost importance to take special safety measures into account.

An obvious safety measure for float glass structures is to use heat strengthened or fully tempered glass instead of regular annealed glass since they have a higher resistance to bending. Heat treated glasses also have a higher impact resistance which makes them harder to destroy by vandals.

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The use of laminated glass not only increases the thickness and thus the stiffness of a plane but also creates the possibility to introduce a sacrificial layer (Kaiser et al., 2000). The sacrificial layer is a thin sheet of glass that is on the exposed side of the laminated panel. The added stiffness of the sacrificial layer is not taken into account for the structural calculation. When subjected to a high impact, the sacrificial layer will break but the other sheets in the laminated panel will remain intact and keeps its structural capacity.

Lamination also makes sure that when the sheet breaks, the shards will remain bonded to the interlayer (O’Regan, 2014). This reduces the risk of injuries caused by the sharp shards. Also, when the shards are sufficiently large, their still might be some structural capacity left after breaking.

Cast glass structures consist of multiple small components while float glass structures consist of large planes. The benefit of cast glass structures regarding safety is that a crack does not propagate beyond the small component while a crack in float glass can propagate over several meters.

Interlocking components have proven to be safe during seismic loading (Estrin et al., 2011). Small movements of the components are possible and are thus able to dissipate vibration energy by resettling. Also, when the interlocking pattern is sufficiently staggered, the failure of several components does not lead to failure of the total structure since the other components are kept in place by the kinematic constraints from adjacent components. A wall of osteomorphic blocks for example still does not collapse when nearly 25% of the blocks have failed (Dyskin et al. 2003). Recycling Theoretically, glass can be endlessly recycled without loss in quality. Discarded glass can simply be re- melted and processed into new objects. Provided that the energy needed for the recycling is collected from renewable recourses, glass has the potential to be a very sustainable material. However, the recycling process becomes increasingly complicated when waste glass does not meet the industries high quality standard. This can be due to different softening temperatures of the chemical composition of the glass or due to contaminations by coating, interlayers or adhesives.

Only for soda-lime container glass, an infrastructure for collecting, sorting and processing is established (Dyer, 2014). Glass containers are collected separated from other municipal waste. An automated process removes foreign materials like paper labels, metal lids or corks. The glass is then sorted according to colour, crushed, remolten and processed into new containers. It is important, especially for clear glass, that contaminations are kept to a very low concentration.

Besides soda-lime containers, other types of glass waste include household waste, building waste, electronic waste and industrial waste. The recycling percentages of the types of glass waste is very low. These types are usually down-cycled to products like aggregates for concrete or glass wool insulation, or end up in landfill (Dyer, 2014).

Bristogianni et al. (2018) researched the possibilities of recycling discarded glass waste and process them into cast glass components for construction purposes. Successful experiments were done by kiln casting various types of glass waste like CRT panels, tableware and float glass. Borosilicate laboratory glassware proved to be suitable for casting very clear components but required a relatively high working temperature of around 1200 °C. Aluminosilicate glass was considered as unsuitable for recycling into cast glass components since it kept at high viscosity even at 1500°C. Figure 2.28 shows the successful castings of the experiment. Also, the components shown in Figure 2.23 are made of recycled glass. Glasses contaminated with coatings laminates or adhesives were excluded from the research. Future research has still to be done to validate the structural performance of the recycled components. 28

Figure 2.28: Recycled cast glass components of (from left to right) float glass, bottle, laboratory tube, CRT panels, lens, and mouth blown glass

A recent development regarding the sustainable use of glass in the building industry is the Re3 Glass strategy. (TU Delft, Glass & Transparency Research Group, n.d.). This strategy is based on three principles: recyclability, reducibility and reusability. Figure 2.29 shows a diagram of the Re3 Glass strategy. The first step in the engineering of a cast glass building system in accordance with the Re3 Glass strategy is to only use recycled discarded waste glass that contains impurities or has a different chemical composition than soda-lime glass. Secondly, the component should be designed in such a way that it includes cavities or notches were possible. This reduces the amount of material used for the building system and reduces the time needed for the component to anneal. Finally, the components should feature an interlocking geometry that allows for dry-assembly. This ensures that the building system can be easily disassembled and reused. The reusability is further improved if the geometry of the component allows for multiple configurations.

Figure 2.29: Re3 Glass strategy

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3 Shell structures Shell structures have been used for thousands of years to make structures of large span from relatively small and manageable stones or bricks in times before the introduction of steel and reinforced concrete in the building industry (Addis, 2007). Williams (2014) defines shells as curved surfaces that are thin in the direction perpendicular to the surface and are made of a relatively rigid material. Shells can be either curved in a single direction like a barrel vault, or it can be curved in two directions like a dome.

According to Adriaenssens et al. (2014) three different types of shells can be categorised based on how they are generated. These include freeform shells, mathematical or geometrical shells and funicular shells. Freeform shells are designed by prioritising the sculptural expressions over the structural performance. A good example of such a shell is the Eastman Kodak Pavilion by Kahn and Jacobs Architects in New York (Figure 3.1a). Mathematical or geometrical shells are generated by mathematical equations and result in shapes like hyperboloids and ellipsoids. Felix Candela is well known for the design of such shells like the Oceanographic in Valencia (Figure 3.1b). Funicular shells are generated by a structurally informed design process. These processes results in shapes with optimal structural performance. A good example of a funicular shell is the Deitingen Service Station by Heinz Isler in Deitingen. (Figure 3.1c)

Figure 3.1:a) Eastman Kodak Pavilion, b) the Oceanographic, c) Deitingen Service Station

The freeform shells and mathematical shells are usually designed by architect. After the design they are analysed and dimensioned by an engineer. A proper structural performance is guaranteed by an increased thickness of the shell or by including reinforcement to withstand any tensile stresses. Since funicular shells are designed for optimal structural performance, they are only loaded in compressions and can be very thin. This puts the amount of used material to a minimum and is therefore a sustainable solution for creating large spans.

This chapter will focus on funicular shells. The structural performance of funicular shells will be explained. Also, several form finding methods and construction processes will be discussed. Structural performance of shells In order to understand how a curved shell works, the structural performance of a straight beam need to be understood first (Williams, 2014). A straight beam can be loaded in two different ways, by axial forces and by perpendicular forces. Forces diagonal to the beam can be split into an axial and a perpendicular force. Figure 3.2a shows a simple supported beam loaded by an axial force. The deadload of the beam is neglected. Figure 3.2b and c show the normal force and moment diagrams. Only a normal force is present which result in an axial stress which is equal across the entire cross section of the beam. The axial stress causes a (neglectable) negative stretch of the beam.

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Figure 3.2:a) beam loaded by an axial force, b) its normal force diagram and c) its moment diagram

Perpendicular forces result bending moments. Figure 3.3a shows a simple supported beam loaded by a perpendicular force. The deadload of the beam is neglected. Figure 3.3b and c show the normal force and moment diagrams. Only a bending moment is present which result in axial stresses which are different across the cross section of the beam. Tensile stresses are occurring on the bottom half of the cross section while compressive stresses are occurring on the top half of the cross section. These stresses result in the bending of the beam.

Figure 3.3:a) beam loaded by a perpendicular force, b) its normal force diagram and c) its moment diagram

The bending of the beam caused by a bending moment due to a perpendicular force is relatively large when compared to the stretching of the beam caused by axial stress due to an axial force. By designing the beam in a way that bending moments are avoided and only axial stresses occur, bending of the beam can be avoided.

Figure 3.4a shows a supported kinked beam loaded by a perpendicular force. The deadload of the beam is neglected. Notice the horizontal reaction forces. These are called thrust forces. Figure 3.4b and c show the normal force and moment diagrams. The only stresses that occur in the beam are compressive normal stresses. No bending moment occurs in the beam even though the beam is loaded by a perpendicular force. Thus, by optimising the shape of the beam, bending moments and their resulting tensile stresses can be avoided.

Figure 3.4:a) kinked beam loaded by a perpendicular force, b) its normal force diagram and c) its moment diagram

For the previous example, the deadload is neglected. In reality, beams are also loaded by their deadload which is considered as a distributed load. The optimised shape for a beam only subjected to its deadload to avoid bending moments and tensile stresses in an arched shape. More specifically the shape of a catenary. This will be further explained in §3.2.1. Figure 3.5 shows a catenary arch loaded by its deadload. Figure 3.5b and c show the normal force and moment diagrams. As can be seen in the diagrams, the only stress that occur in the arch are compressive stresses due to the normal force in the arch.

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Figure 3.5:a) catenary arch loaded by its deadload, b) its normal force diagram and c) its moment diagram

The same theory can be applied to two dimensional surfaces (Williams, 2014). Just like beams, plates can be loaded in two different ways. Instead of axial and perpendicular loading, the terms in-plane and out-of-plane loading are used. In plane loading causes four types of membrane stresses. These are normal stress in x-direction, normal stress in y-direction, shear stress in the x-direction and shear stress in the y-direction. Out-of-plane loads causes bending moments that lead to tensile stresses and plate bending. Just like beams, plates can be curved (either single curved or double curved) to avoid bending moments due to out-of-plane loads. These curved plates are called shells structures. Form finding In order to design a funicular shell, a form finding process is employed. Rippmann (2016) defines the goals of the form finding as ‘to define a geometry that only develops membrane stresses for the assumed, dominant load case while also meeting desired architectural, programmatic and aesthetic criteria’ (p. 46). Several methods for form finding have been developed. These include the use of physical hanging models and computational methods.

3.2.1 Physical hanging models In order to find the optimal shape for a funicular shell structures, designers have used form-finding techniques applied to small-scale physical models (Addis, 2014). These techniques are useful when the available calculation methods are too complex, time-consuming or when normal structural analysis methods do not adequately model the desired structure.

When applying tension to a chain, the chain will form to a straight line. When this straight line formed and the tension is still applied, the chain does not stretch. When relieving the tension and applying just a minimum amount of compression, the chain will show buckling-like behaviour. It can be said that a chain has no compressive strength while having a high tensile strength. When a chain is hung between two points, the chain is loaded by its own weight. Gravity will pull the chain down resulting in the chain to form a hyperbolic cosine function (Figure 3.6a). The shape of this curve is also known as the catenary. Since a chain has no compressive strength, the only stresses that occur in the chain are tensile stresses. When an arch is built in the shape of an inverted catenary, the same gravitational forces will act on the arch as to a hanging chain (Figure 3.6b). Since the arch is an inverted catenary the stresses in the arch are the same as the inverted stresses in the catenary. Therefore, the only stresses that occur in an arch shaped as an inverted catenary subjected to gravitational forces, are compressive stresses (Heyman, 1995). This principle was discovered by Robert Hooke in 1676.

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Figure 3.6:a) hanging chain in tension and a b) standing catenary arch in compression

One of the earliest applications of this principle can be found in the St Paul’s Cathedral in London designed by Christopher Wren (Addis, 2007). The shape of the masonry cone that carries the lantern corresponds to the shape of an inverted hanging chain with an extra weight attached to it (Figure 3.7). The attached weight corresponds with the weight of the lantern and results in a catenary that is slightly pointed.

Figure 3.7: Catenary arch in the St. Paul's Cathedral

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Antoni Gaudi took form finding with hanging models to the next level by creating complex three- dimensional networks of strings and weights (Collins, 1963). Figure 3.8a shows the hanging model for the Colonia Güell. By changing the length of the strings and by redistributing the weights, Gaudi was able to steer the shape according to his design intent. When a satisfying form was found Gaudi used to directly sketch on inverted photographs of the hanging model (Figure 3.8b).

Figure 3.8:a) hanging model of the Colonia Güell and b) a sketch on top of the inverted photograph

A limitation of the form finding process with hanging chains is that it only results in the structural optimisation of one-dimensional elements like ribs and arches instead of the structural optimisation of two-dimensional elements like shells (Tomlow, 2011). The white pieces of fabric in the hanging between the strings in the models of Gaudi are often mistaken for representations of structural shells. However, these pieces of fabric were only added to improve the visual appearance of the hanging model in order to make it appear more like a building instead of just a bunch of strings and weights.

Heinz Isler found a way for the form finding of two-dimensional shells. He did this by using a sheet of cloth instead of chain. Mechanically speaking, a cloth can be seen as a two-dimensional chain. When applying tension to the cloth, the cloth will deform to a stable state but when only a little compression is applied, the cloth will wrinkle together. Like a chain, a cloth has no compressive strength while having a high tensile strength. By hanging pieces of cloth from a couple of supported points, Isler created geometries where the only occurring stresses are tensile stresses (Chilton, 2012). The inverted geometries resemble a shell structures loaded in compression only. Later, Isler started to use high quality latex rubber membranes instead of cloth because he realised that the anisotropy caused by the orientation of the weaving pattern of the cloth influenced the form-finding process. By using hanging models Isler found a way to improve the bucking stiffness of a shell. By making the cloth or rubber slightly larger than the area between the supports, a stiff rib with negative Gaussian curvature would appear at the edges when hanged (Figure 3.9).

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Figure 3.9: Hanging models by Isler with stiff double curved edges

There are several disadvantages of the use of physical hanging models (Block, 2009). Making physical models is tedious and time-consuming work. Also, the steering of the shape could be difficult since a local change in the length of a string can result in major changes of the shape of the global network resulting in the requirement of the weights to be redistributed. Furthermore, physical hanging models are suitable for obtaining insight in the optimal geometries for funicular shells but do not give any insight in the quantities of the compressive stresses that occur in the shells. 3.2.2 Computational form finding Since the introduction of the computer, several computational form finding methods have been developed to overcome the disadvantages of form finding by using physical hanging models. Computational form finding methods are based on numerical algorithms. The computational form finding method that will be further discussed is the particle-spring system.

The particle-spring system is a method that has been extensively used in the field of computer graphics for realistic cloth animation simulations but can also be used for the form finding of funicular structures (Kilian & Ochsendorf, 2005). The particle-spring system contains of a network of particles with a certain mass that are connected by linear elastic springs that are assigned a rest length and a spring stiffness and have no mass. By constraining the allowable movement of certain particles, supports can be defined. By applying forces to the particles (e.g. forces due to gravitational acceleration), the equilibrium of the system will be destabilized. This causes a displacement of the particles and an elongation of the attached springs. The stretching of the spring will cause the spring to exert a reaction force on the particle that is linearly proportional to its elongation. A solver is used to calculate the movement of the particle-spring system over time. Due to the damping of the springs, the system will converge towards an equilibrium. When the movement in the system has reached a value below a set threshold, the simulation is stopped. Figure 3.10 shows the first few time steps of a particle-spring system simulation used for the form finding of a shell structure by Kilian and Ochsendorf (2005). Figure 3.11 shows the form found shape in equilibrium at the end of the simulation.

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Figure 3.10: Particle-spring system simulation in the first few time steps

Figure 3.11: Particle-spring system in equilibrium

Just like Isler used excess cloth in his hanging model to create structural ribs (as described in §3.2.1), the final shape of the particle-spring network in equilibrium can be steered by changing the stiffness or rest length for certain springs in the network. For example, structural ribs can be created by increasing the stiffness of springs that are placed along the same line in the system.

Several solvers have been developed to simulate particle-spring networks. It is also featured in the Kangaroo physics engine developed by Piker (2013). The benefit of Kangaroo is that it is that it is a plug-in for Grasshopper and is thus a fully parametric tool that allows for the integration with other Grasshopper tools and plug-ins Construction methods Due to their curved geometry, shells are challenging to construct. This is especially the case for funicular shells that have a geometry with a varying gaussian curvature and thus cannot be subdivided to components of one single geometry (Rippmann, 2016). Usually, for the construction of a shell structure, a formwork is needed which is expensive and time-consuming to construct. 36

Shells structures can be categorised by their construction method. Three different constructions methods can be distinguished. These are monolithic casting, discrete assembly with mortar and discrete dry assembly. 3.3.1 Monolithic casting Monolithic shells are made by casting wet concrete on a formwork. One of the earliest examples of a monolithic shell is the Pantheon in Rome which was built in second century. A formwork was made of coffers that were supported by wooden scaffolding. Roman concrete, consisting of cement and various types of aggregate, was laid on the formwork in horizontal layers (Addis, 2007). By using different types of aggregate with different densities, the dome is lighter at the top than at the base. The self-loading was further reduced by making the thickness of the concrete layers thinner at the top and thicker at the base.

Modern monolithic shells include reinforcement. This permits tensile stresses in the structure and thus allows for the construction of freeform or mathematical shells without a drastic over dimensioning of the shell thickness to ensure the structural integrity. The possibility to include reinforcement is a major benefit that is not possible for discrete shells (Faber, 1963).

The curved formwork and scaffolding needed to cast a monolithic shell are labour-intensive to construct. This is especially the case for thin, funicular shells that are sensitive to small changes in geometry. The construction of formwork for these structures requires highly skilled labour since tolerances for the formwork are tight (Meyer & Sheer, 2005). Formwork for monolithic casting also requires a lot of material. When used for one-off projects these materials can of only be used once (Tang, 2015). The high quantities of labour and materials required for the construction of the formwork and scaffolding result in the high costs that are involved in the construction of monolithic shells. These high costs are one of the reasons for the decline of concrete shells after an increased popularity in the mid-20th century (Meyer & Sheer, 2005; Tang, 2015).

To decrease the cost of the formwork and scaffolding, several techniques have been developed. The geometry of the shells designed by Felix Candela were usually ruled surfaces like hyperbolic paraboloids and conoids. These double curved geometries could be casted on formwork made of straight timber planks (Faber, 1963; Tang, 2015). Figure 3.12 shows construction workers building a formwork using straight timber planks for the Bolsa de Valores de México by Candela.

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Figure 3.12: Formwork for a double curved shell constructed with straight timber planks

To further reduce the material and labour needed for the construction of the formwork for a shell structure, different types of pneumatic formwork systems have been used. These systems rely on a membrane fixed to ground that is inflated with compressed air. After inflation, reinforcement and concrete can be applied on the membrane. Instead of regular concrete, sprayed shortcrete is often used. The main drawback of pneumatic formwork is that the formwork often does not accurately represents the shape of the designed shell (Kromoser & Huber, 2016). While this may not be problematic for reinforced concrete shells, it can be disastrous for unreinforced funicular shells.

3.3.2 Discrete construction Rippmann (2016) defines discrete structures as structures that consist of individual components forming a bond without mechanical connections. Two different types of discrete shell structures can be distinguished: wet-assembled and dry-assembled discrete shells.

Wet-assembled discrete shells consist multiple relatively small components bonded with mortar. These components are usually a standardized component like bricks and tiles that are not specifically made for constructing surfaces with a certain curvature. The standard component can either be directly used or be roughly cut to size in order to fit. The inevitable gaps that occur when constructing a double curved shell with components without the proper wedge, are filled with mortar (Rankine, 1889). Besides accommodating for the curvature, the mortar makes sure that the stress is equally distributed from the surface of one component to the surface of another component.

A method for the construction wet-assembled discrete shells that limits the use of scaffolding and formwork is the timbrel vaulting technique. Timbrel vaults are also known as Guastavino vaults or Catalan vaults. Timbrel vaults are made by laminating multiple layers of thin tiles (Addis, 2007). Only the main ribs need scaffolding to be built. The gaps in between the ribs are filled in with a layer of tiles that are bonded with a fast setting mortar. Since the tiles are very thin and thus relatively light, a bond with the fast setting mortar on two edges is enough to keep the tile in place (Figure 3.13). After a span of one layer of tiles is constructed, two additional layers of tiles are bonded to the first layer with regular mortar. This results in a shell of laminated tiles that is thick enough to resist any inevitable live loads. Note that timbrel vaults can only built without scaffolding for a limited amount of shapes. More 38 complex funicular shapes require scaffolding when constructed with the timbrel vaulting technique (López López et al., 2014).

Figure 3.13: Construction of a timbrel vault without formwork

Another method to construct discrete shells with mortar is the Nubian vault or dome technique. With this construction method, catenary vaults or domes can be constructed without the need of formwork or scaffolding. (Minke, 2012). These structures are usually made of flat adobe bricks and use mud as a mortar. Nubian vaults can be constructed by constructing series of arches that are inclined at a 65° to 70° angle. The inclination and the stickiness of the mud prevent the adobe bricks from falling down. When an arch is completed, the bricks are permanently locked in place by compressive stress due to the deadload of the bricks. Figure 3.14 shows the construction of a Nubian vault.

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Figure 3.14: Construction of a Nubian vault without formwork

Dry-assembled discrete shells consist of multiple components that are not bonded by mechanical connections nor by mortar. These components are relatively large compared with the components used for wet-assembled discrete shells. Dry-assembled discrete shells rely solely on compression to keep the components together (Rippmann, 2016). Since no mortar is used between the components for equal stress distribution, the components need to be shaped in such a way that the surfaces of adjacent components are making proper contact. To construct double curved surfaces like shells, the components need be wedge-shaped. Such a wedge-shaped component is called a voussoir (Figure 3.15). The art of cutting voussoirs out of stone blocks is called stereotomy. The outward facing surface of a voussoir is called the extrados and the inward facing surface is called the intrados. The contact surfaces of the voussoir that are adjacent to the other voussoirs are called interfaces. Ideally, the interfaces are perpendicular to the line of thrust to avoid possible sliding between voussoirs when considering no friction between the voussoirs (Heyman, 1995).

Figure 3.15: Terminology of a voussoir

Early examples of dry-assembled discrete structures are the arches built by the Romans like the arch of Drusus in Rome (Figure 3.16a). A contemporary type of dry-assembled discrete construction is the 40

Arch-Lock system (Figure 3.16b). Both the arch of Drusus and the arch made with the Arch-Lock system are semi-circular arches that feature only one type of voussoir geometry.

Figure 3.16: a) Arch of Drusus and b) Arch-Lock system

In order to construct double curved surfaces, voussoirs with varying wedge angles between the interfaces need to be used. One of the most sophisticated examples of stereotomy used for a double curved surface can be found in the vault of the Hôtel de Ville in Arles (Fallacara et al., 2011). This vault spans over 16 meter and is constructed out of hundreds of dry-assembled voussoirs, each with a unique geometry (Figure 3.17)

Figure 3.17: Vault of the Hôtel de Ville

Ideally, the interfaces of the voussoirs in an arch or shell structure, are perpendicular to the flow of forces. This avoids possible sliding failure when considering no friction between the voussoirs (Rankine, 1889). This is less relevant for shell structures that are fully supported along their boundaries like the dome shown in Figure 3.18a. In this structure each voussoir is kept in place by its neighbouring voussoirs or supports. However, for structures that have unsupported open edges, failure due to the sliding of voussoirs might occur (Rippmann & Block, 2018). 41

Figure 3.18: a) fully supported shell, b) risk of sliding at the unsupported edges, c) tessellation pattern alligned with the force flow

Figure 3.18b shows a hexagonal-dominant tessellated barrel vault. The interfaces of the voussoirs at the edges are orientated at a 60° angle relative to the flow of forces. Due to this angle, these voussoirs might slide outwards resulting in the collapse of the structure. By flattening the hexagonal-dominant tessellation, the angle between the interfaces and the flow of forces is increased and the risk of sliding is reduced (Figure 3.18c). The minimum angle between the interface of a voussoir and the flow of forces to prevent sliding is called the friction angle. The friction angle can be defined with equation 3.1 wherein θ is the angle between the surface normal of the interface and the local force direction and μs is the static coefficient of friction.

−1 휃 = tan 휇푠 (3.1) While it is it is relatively simple for a barrel vault to design a tessellation pattern wherein the interfaces are perpendicular to flow of forces, it becomes more complex when designing and constructing complex shell structures. Designing a shell structure with the interfaces of the voussoirs perpendicular to the line of thrust often results in sophisticated tessellation patterns. An example of this is the way how skew vaults are tessellated into individual voussoirs. A skew vault is a barrel vault that is distorted in the horizontal plane resulting in a parallelogram shaped plan view. Figure 3.19a shows a skew vault and its flow of forces. Figure 3.19b shows the tessellation pattern of a skew vault with voussoirs positioned as in a regular barrel vault, also known as a false skew vault. Since the interfaces of the voussoirs are not perpendicular to the flow of forces, the false skew vault has a reduced stability compared to a regular barrel vault due to an increased risk of sliding between the voussoirs.

Figure 3.19: Isometric and plan view of a skew vault: a) the flow of forces, b) false skew vault tessellation pattern, c) optimal tessellation pattern and d) intermediate voussoir courses in the optimal tessellation pattern.

The optimal tessellation pattern for a skew vault can be generated by drawing lines on the shell geometry that are perpendicular to the flow of forces (Rankine, 1889). The interfaces of each horizontal course of voussoirs should be aligned to those curves. Figure 3.19c shows the tessellation pattern of a skew vault with the voussoirs positioned according to this tessellation pattern. Note that the voussoirs in a horizontal course are larger one on side of the vault and smaller on the other side 42 of the vault. The larger voussoirs might be difficult to fabricate or handle. To avoid larger voussoirs, intermediate courses of voussoirs can be introduced as shown in Figure 3.19d.

The geometry of a skew vault and its corresponding optimal tessellation pattern are more complex than the geometry and optimal tessellation pattern of a barrel vault but are relatively simple compared to the geometry and optimal tessellation pattern of a funicular shell structure. The generating of an optimal tessellation patterns of a funicular shell structure becomes often too difficult or time consuming to do by manual geometric constructing approaches. Therefore, computational methods have been developed to generate these tessellation patterns by Oval et al. (2017) and Rippmann and Block (2018). These methods are focussed on hexagonal tessellations and take multiple constraints into account. The main constraint is related to the flow of forces and results in the interfaces of the voussoirs being perpendicular to the flow of forces and that the voussoirs are configured in a staggered bond. Other constraints are related to fabrication and construction. These constraints result in the faces of the tessellations pattern being convex geometries (i.e. no interior angles larger than 180°) and thus making the voussoirs easier to fabricate. Also, the constraints ensure that vertices in the tessellation pattern with a high valency (a high number of edges connected to a vertex) are eliminated. This avoids that a high number of voussoirs are joining at a single point which would be difficult to assemble or not even possible due to production tolerances.

Other research has focussed on developing computational methods for the aligning quadrangular tessellations with the principal stresses and curvature directions (Greco, 2018; Pellis & Pottmann, 2018). These methods have initially been developed for the optimisation of gridshells but could also be applied for the optimisation of discrete funicular shell structures. A benefit of these methods is that the resulting quadrangles are close to being planar.

The stability of the generated tessellation patterns can be verified with physical scale models or computational numerical analysis. Since the stresses in a shell structure are limited to a small percentage of the yield strength of the material, the structural integrity of the shell is a matter of stability of the geometry and not of strength of the material. The stability of a geometry is independent of scale and thus scale models can be used to verify the stability of a shell structure (Heyman, 1995). Previous research has shown that scaled models made of 3D printed voussoirs can be used to verify the stability and give insight in the collapse mechanisms of hemispherical domes (Zessin et al., 2010) and funicular shell structures (Block et al., 2010). A limitation of using physical models for verifying the stability of a discrete shell structure is that the material used for the voussoirs of the scale models might not be the same as the material used for the voussoirs of the actual structure. This could result in a different coefficient of friction in de the scale model than in the actual structure. Also, the tolerances of the voussoirs of the scale model might not be proportionate to the tolerances of the voussoirs of the actual structure.

To overcome these limitations and to eliminate the costs of 3D printing a model, computational numerical analyses can be done. These analyses use Discrete Element Method (DEM) software which is commonly used for geotechnical analysis of rock formations. DEM software has the capacity of treating voussoirs as separate units that can interact with each other. Van Mele et al. (2012) compared the physical scale model analysis with the DEM analysis of the stability of a discrete shell structure. The results of the tow analyses are comparable although the DEM analysis generally results in a better stability than the physical scale model analysis. This difference in results is attributed to the difference in tolerances. Some inevitable imperfections are present in the voussoirs of the physical scale model while the DEM model can be considered as ‘perfect’.

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An alternative to DEM software is Rigid Body Dynamics (RBD) that is often featured in physics engines used in the video game industry. DEM provides similar results as RBD (Kao et al., 2017). DEM is slightly more accurate since it takes the deformations of the voussoirs due to stresses into account while the calculation time of RBD is approximately 10 times as fast.

An example of a contemporary dry-assembled discrete shell structure that has been developed with the use of computational form finding and computational tessellation is the Armadillo Vault. The Armadillo Vault was developed by the Block Research Group for the 2016 Venice Biennale of Architecture (Rippmann et al., 2016). It has the shape of a funicular shell that was generated through a form finding process in RhinoVAULT. The Armadillo Vault has a triangle like shape floor plan with two openings in the middle. The structure is supported by three linear supports and one support in the middle. Figure 3.20 shows the Armadillo Vault.

Figure 3.20: The Armadillo Vault

The tessellation pattern is aligned to the force flow to avoid sliding between the voussoirs. The shell is tessellated in to 399 voussoirs that are predominantly shaped as irregular hexagons although quadrangle shaped voussoirs are present at the boundary of the shell. Due to the staggered tessellation pattern, the interlocking of the voussoirs is ensured. Figure 3.21 shows the tessellation pattern of the Armadillo Vault.

Figure 3.21: Tessellation pattern of the Armadillo Vault in a) 3d and b) plan view

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The voussoirs are cut out of limestone blocks with a CNC (Figure 3.22a). The cutting process resulted in tolerances between 0.4 and 0.8 mm. Male and female notches were milled in the block for easy alignment during the assembling process. The notches are not of sufficient size to create an interlocking feature. During the assembling process, the voussoirs are stacked on a customised formwork (Figure 3.22b). The last voussoirs to be put in place are the keystones. These are fabricated after all the other voussoirs are assembled and their correct shape is measured. Due to this method, the accumulation of tolerances can be compensated. The Armadillo Vault perfectly illustrates the complexity of the fabrication and assembly of a dry-assembled discrete funicular shell structure.

Figure 3.22: a) fabrication of a voussoir and b) assembly of the voussoirs

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4 Design criteria When designing a transparent vault, the knowledge gained from the literature review on the topics of glass and shell structures need to be combined to formulate multiple design criteria. Eight design criteria are formulated in a sequacious order. In most cases, the design criteria are influenced by previously stated criteria. Figure 4.1 shows the scheme of how the design criteria are established. The design criteria will be further explained.

Figure 4.1: Scheme of the design criteria Construction method The use of glass as the material of the shell limits the options for the construction method. Monolithic casting is not an option since the annealing time required for the cooling of a cast glass element the size of a shell structure would be extremely long. This would also require the on-site construction of a kiln large enough for the shell to fit which is economically unfeasible. This means that the shell has to be constructed by the discrete construction process which means that the shell should be made of multiple glass components. Production method A production method to produce the glass components need to be selected. With the float glass process, only flat planar components of a limited thickness can be produced which may not be suitable since the limited thickness leads can lead to buckling failure when the span of the shell is too large. This could be solved by thicker components of laminated float glass, but this results in components that cannot be recycled due to the PVB interlayer. Extruded components can also not be used since they are linear elements unsuitable to construct surfaces like a double curved shell structure. Glass casting has the most potential as a production process since this process allows for the production of three-dimensional glass voussoirs with a sufficient thickness to prevent buckling failure. Bonding method A more elaborate criteria for the construction method can be established by determining how the cast glass voussoirs are bonded. The three bonding methods are mechanical bonding, adhesive bonding and dry-assembly. Mechanical bonding requires the use of opaque construction elements which lead to an overall decreased transparency of the shell. It is therefore a non-preferred bonding method. The construction process of the Crystal House illustrated the complexity of building with adhesively bonded cast glass bricks. Considering that a double curved shell structure is has a more complex geometry than the planar façade of the Crystal House, it is expected that a shell structure out of adhesively bonded cast glass components will be even more difficult to construct. Also adhesively bonded cast glass components require very low tolerances that cannot be achieved by the casting process and thus need post-production polishing which leads to increased production costs. Furthermore, the adhesive makes the structure difficult to disassemble and recycle. Adhesive bonding is thus not suitable as a bonding method.

The most promising bonding method is dry-assembly with a transparent interlayer. This bonding methods results in a shell that is fully transparent and relatively easy to construct. The interlayer 46 compensates for tolerances in the components and therefore makes the components easier to produce. The dry-assembly bonding allows for quick de- and re-assembling and does not obstruct recyclability. An interlocking feature should be integrated into the voussoirs to assure self-alignment during assembly and improve the resistance against sliding between the voussoirs. Shell shape The type of shell (freeform, mathematical or funicular) that can be constructed with cast glass is limited by the maximum thickness of cast glass components. Freeform and mathematical shells rely on increased thickness or reinforcement to guarantee proper structural performance. Increasing the thickness is not an option when constructing the shell out of cast glass components since their size is limited due to an increase in annealing time for increased thicknesses. Reinforcement is also not possible for discrete structure. Therefore, a shell should have a funicular shape when made of cast glass components. Mould and tessellation pattern Since funicular shells have a surface of varying curvature, they cannot be tessellated into voussoirs of equal geometry. This means that multiple cast glass voussoirs with unique geometries need to be produced in order to build a funicular shell structure. Fixed and pressed permanent moulds have high production costs and can only be used to make components of a single geometry and are thus not suitable. Using disposable silica plaster moulds is suitable to make one-off-a-kind components but when keeping in mind the large amount of voussoirs needed to build an entire shells structure, will result in a time-consuming and expensive process.

An adjustable mould that can be adjusted to the geometry of every single voussoir could be a solution. An adjustable mould would keep the costs and time to produce the moulds to a minimum. However, the design process of such a mould will be very complex. The tessellation of the shell has an influence on the geometries that the adjustable mould is required to produce and vice versa. Also, the inclusion of an interlocking feature of the voussoirs will add an increased complexity in the adjustable mould. Type of glass Finally, the type of glass used to for the voussoirs need to be selected. Ideally, recycled waste glass is used that would otherwise be downcycled or end up in landfill (so no soda-lime waste glass). With this type of glass, it is not possible to make a very clear transparent shell structure except if recycled borosilicate glass is used. However, by using coloured, slightly translucent voussoirs, an aesthetically interesting pattern can be designed. It must be noted that this is only a possibility if future research proves that recycled glass components have adequate structural properties. If this is not the case, soda-lime glass or borosilicate glass will be used.

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III Production and design

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5 Interfaces The adaptive mould used for the production of the cast glass voussoirs should be able to adapt to each voussoir geometry present in the shell structure. The voussoir geometry is dependent of the geometry of the interfaces and of the geometry of the intrados and extrados. As discussed in §4.3, the geometry of the interfaces should contain an interlocking feature. Figure 5.1 shows three types of interface geometries for voussoirs joining at three different angles. Figure 5.1a shows a planar interface which is the conventional type of interface in traditional discrete shell structures, Figure 5.1b shows a tongue and groove interface and Figure 5.1c shows a convex-concave interface.

Figure 5.1: Joining of two voussoirs with a) planar interfaces, b) tongue and groove interfaces and c) convex-concave interfaces

The tongue and groove and the convex-concave interfaces are interlocking interfaces and provide additional resistance against out of plane loads. Also, the convex-concave interface has a larger contact area and thus an increased amount of friction between the voussoirs, ensuring a better connection.

The main benefit of the convex-concave interface is that the voussoirs can be joined at different angles while for the other interfaces only allow for the joining of voussoirs at one specific angle. When casting the voussoirs with a planar or tongue and groove interface in an adjustable mould, the adjustable mould should be able to adjust to each joining angle. This is not the case for an adjustable mould used for casting voussoirs with a convex-concave interface since each different joining angle can be made with the same interface geometry. As a result, the number of variables of an adjustable mould used for the casting of voussoirs with a convex-concave interface geometry is lower than the number of variables of an adjustable mould used for the casting of voussoirs with an interface geometry dependent on the angle between the voussoirs. This reduces the complexity of the mould and makes it easier to design such a mould.

A disadvantage of the convex-concave interface is that the joint between voussoirs can act as a hinge. Figure 5.2 shows a catenary arch consisting out of voussoirs with convex-concave interfaces. The hinge lines are indicated with the dotted lines. The structure is in unstable equilibrium. When not taking friction between the voussoirs into account, the slightest external load will destabilize the structure and cause it to collapse.

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Figure 5.2: Catenary arch consisting out of voussoirs with convex-concave interfaces. a) hinge lines b) collapse mechanism

The same principle does not directly translate to discrete shell structures since these are three dimensional structures. For the arch in Figure 5.2, all hinge lines are parallel which makes the arch unstable. For a three-dimensional shell structure consisting out of voussoirs with convex-concave interfaces, the hinge lines are orientated in multiple directions which makes the shell a stable structure. Interface testing In order to get a better insight in the stability of a discrete shell structure with convex-concave interfaces compared with the stability of discrete shell structure with planar interfaces, an experiment is conducted. A simple shell structure consisting of 17 triangular voussoirs was designed in Grasshopper with the Kangaroo2 plug-in. Figure 5.3 shows the design process of the shell. First the geometry of the shell was generated. Each voussoir was given a thickness of 12 mm and convex or concave interfaces were added. By trimming the voussoirs at the nodes, the intersection of voussoirs was eliminated. Spheres were placed at the nodes to fill the gaps caused by the trimming of the voussoirs.

Figure 5.3: Design process of the shell structure used for the interface comparison test

Each voussoir was manufactured out of two laser cut pieces of 6 mm thick MDF. Two holes in each voussoir allowed for the insertion of two bolts to ensure proper alignment when glued together. The convex and concave interfaces were shaped with a router. The router was also used to shape the nodes into a concave profile with a radius of 12.5 mm in order to allow for the placing of wooden beads with a 25 mm diameter. A baseplate was manufactured with a raised edge around the shell that functions as a tension ring. With the aid of a simple formwork, the structure could easily be assembled. After assembly, the formwork was removed through a hole in the baseplate. A second model with the same shell geometry was made with planar interfaces. Figure 5.4 shows the two models.

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Figure 5.4: MDF models with a) convex-concave interfaces and b) planar interfaces

An observation was made during the assembly of the two models. The convex-concave interface model was easier to assemble than the planar interface model. When assembling the convex-concave interface model, the convex-concave geometry guides the voussoirs in the right position while the planar interface model required for small adjustments after the initial assembly.

Both models were subjected to two types of tests. For test 1, a point load was applied to nodes A, B, C, D and E (Figure 5.5a). For test 2, a distributed load was applied on the extrados of three voussoirs (Figure 5.5b). The test was done using a Zwick Z010 materials testing machine. The machine was set to perform a continuous displacement of 5 mm per minute. The load that the testing machine exerted on the model during the performance was recorded. Detailed results of the test recordings can be found in appendix A.

Figure 5.5: Load locations for a) test 1 and b) test 2

During test 1 for both models, a load built up on one of the nodes until a critical load was reached. After this point, the load decreased while the deformation increased until the structure fully collapsed. Figure 5.6 shows both models during test 1A. The collapse was caused by disturbance of the stability, not by exceeding the yield strength of the MDF voussoirs. Table 5.1 shows the maximum load applied at the models at the critical point.

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Figure 5.6: Test 1A. a) convex-concave interface model, b) planar interface model

Table 5.1: Results for test 1

Test Convex-concave Planar 1A 18.19 N 35.69 N 1B 25.41 N 252.6 N 1C 30.52 N 69.99 N 1D 23.52 N 82.34 N 1E 185.6 N 558.3 N Average 56.66 N 199.8 N As shown in Table 5.1, the load at the critical point is significantly lower for the convex-concave interface model than for the planar interface model. On average the critical load for the planar interface model is 3.5 times higher than the critical load for the convex-concave interface model. It can be concluded that the planar interface model has a better structural performance than the convex-concave interface model when subjected to point load on the nodes.

During test 2 for the convex-concave interface model a distributed load was steadily built up on the voussoirs until the concave interface of one of the voussoirs broke. This failure resulted in the interface losing its interlocking capability (Figure 5.7). After this point, the load decreased while the deformation increased until the structure fully collapsed. Figure 5.8a shows the convex-concave interface model during test 2. The collapse was caused by exceeding the yield strength of the MDF voussoir and not by disturbance of the stability.

Figure 5.7: Broken convex-concave interface voussoir

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Figure 5.8:Test 2. a) convex-concave interface model, b) planar interface model

During test 2 for the planar interface model, a collapse mechanism was observed that was similar to the collapse mechanism observed during test 1. A distributed load built up on the voussoirs until a critical load was reached. After this point, the load decreased while the deformation increased until the structure fully collapsed. Figure 5.8b shows the convex-concave interface model during test 2. The collapse was caused by disturbance of the stability, not by exceeding the yield strength of the MDF voussoirs. Table 5.2 shows the maximum applied load at the critical point.

Table 5.2: Results for test 2

Test Convex-concave Planar 2 1011 N 88.00 N

As shown in Table 5.2, the load at the critical point is 11.5 times higher for the convex-concave interface model than for the planar interface model. It can be concluded that the convex-concave interface model has a better structural performance than the planar interface model when subjected to distributed loads on the voussoirs.

The different interfaces both have their strength and weaknesses. Convex-concave interfaces prevent sliding between the voussoirs when subjected to distributed loads but also create a hinging mechanism leading to an early collapse when subjected to point loads at the nodes. Planar interfaces do not have this hinging mechanism but do not offer any resistance against sliding between the voussoirs.

Ideally, the interfaces should have geometry that has an interlocking geometry to prevent sliding between the voussoirs without creating a hinging mechanism. An example of this is the tongue-and- groove interface previously shown in Figure 5.1b. As mentioned before, these type of interface geometries are dependent on the joining angle between the voussoirs and thus an adjustable mould used for the production of these voussoirs need to be able to adjust to the different joining angles.

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6 Adjustable mould The adjustable mould should be suitable for the production of each voussoir geometry that is present in the shell structure. The geometry of a voussoir has the following variables:

- Intrados and extrados geometry variables - Edge count - Integer - Edge lengths - Float - Interior angles (angles between the edges) - Float - Planarity (whether the intrados or extrados surface is planar or not) - Boolean - Interface geometry variables - Joining angle (the angle at which an adjacent voussoir joins) - Float - Tongue/groove connection (whether the interface has a tongue or groove profile) - Boolean

An adjustable mould was designed with adjustable features corresponding to the variables of the voussoir geometry. The process of designing the mould will be described at the basis of the stated variables. Intrados and extrados geometry variables Figure 6.1 shows three adjustable moulds by Bamboo Tools (n.d.) used for pottery to make quadrangular, hexagonal or octagonal bowls. The edge lengths can be adjusted to allow for a large variety of shapes to be made with a single mould. The mould is placed on a planar surface that acts as the base of the mould. A similar system to the adjustable pottery moulds is the adjustable routing template by Festool (2019).

Figure 6.1: Moulds with adjustable edge lengths for a) quadrangular, b) hexagonal and c) octagonal shapes

The adjustability of these moulds is limited to adjustability of the edge length. By placing hinges at the vertices, the interior angle becomes variable as well. Figure 6.2 shows three moulds with adjustable edge lengths and interior angles for triangular, quadrangular and hexagonal shapes. A vertex module with a bracket that hooks on an edge module, can slide along an edge module and can be fixed at the desired edge length. Another edge module can be connected to the vertex module at a variable angle. With this modular system, multiple edge modules can be connected to make moulds for prismatic polygons of variable edge count, edge lengths and interior angles. T-slots on top of the edge modules allow for the clamping of the vertex modules on the edge modules at any desired edge length with the use of a bolt and T-slot nut.

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Figure 6.2: Moulds with adjustable edge lengths and interior angles for a) triangular, b) quadrangular and c) hexagonal shapes

With three different edge lengths given as input variables, only one possible triangle can be constructed. For polygons other than triangles, additional variables besides the edge lengths need to be given as input variables for the set-up of the mould. The additional variables can either be angles or diagonal lengths. A quadrangle for example, can be defined by five variables. Different combinations variables can be given like four edge lengths and one angle, three edge lengths and two angles or four edge lengths and one diagonal length. Since an error in the set-up up of an angle is magnified over distance (Abbe error), it is more accurate to set-up the adjustable mould for non- triangular polygons by setting up the diagonals than by setting up the angles. Therefore, diagonal modules are added to the mould when set-up for non-triangular polygons (Figure 6.3). One side of the diagonal module is connected with a loosely tightened bolt to one of the vertex modules. The other side of the diagonal module is clamped to another vertex module at a variable distance with a properly tightened bolt. For the connection of the diagonal modules to the vertex modules, screw thread has to be tapped at the hinge points in the vertex modules.

Figure 6.3: Diagonal modules added to the adjustable moulds for a) quadrangular and b) hexagonal shapes

The mould should be placed on a planar base. This base will shape the extrados of the casted voussoir. This mould is thus only suitable for voussoirs with planar extrados. For non-planar extrados, the base should be adjustable as well. Adjustable moulds for double curved surfaces been developed such as the Stampo Deformabile by Piano (1969) and the Kine-Mould by Schippers et al. (2015) as shown in Figure 6.4. These moulds consist of a flexible surface placed on a grid of pistons. By moving the pistons, the surface can be formed into the desired shape. These moulds are suitable for casting concrete or the lay-up of FRP’s. Adjustable moulds that can operate at temperatures up to 660 °C to produce double curved glass panels have also been developed (Adapa, n.d.). These are used for the hot- bending of float glass (as described in §2.2.1) which is a production process unrelated to glass casting and is done at far lower temperatures. Besides the problems related to temperature, an adjustable mould that can adjust to any polygon while also being able to be placed on an adjustable, double curved base, will be extremely complex.

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Figure 6.4: a) Stampo Deformabile, b) Kine-Mould

A different approach to the problem of designing an adjustable mould for the production of voussoirs with a double curved intrados and extrados, is to avoid the presence of such voussoirs in the shell structure in the first place. This can be done by tessellating the shell structure in a way that it consists entirely out of planar polygons. Since this is a far less complex approach, it is decided to tackle the problem of double curved intrados and extrados by avoiding it instead of solving it with the design of an extremely complex adjustable mould. Interface geometry variables The adjustable moulds shown in Figure 6.2 is suitable for the casting of voussoirs with planar interfaces that have voussoir joining angles of 0° and thus do not form a curved surface when joined together. To allow for the adjustability of the voussoir joining angles and to add an interlocking feature to the interface , two edge modules are introduced that can replace the edge modules of the moulds shown in Figure 6.2. Figure 6.5 shows the two edge modules.

Figure 6.5: a) groove edge module, b) tongue edge module with adjustable voussoir joining angle

The groove edge module consists of one single part with a protrusion along its length that will form a groove in the casted object. The tongue edge module consists of four parts: a rotating cylinder, a stationary part and two parts that function as a protractor. The notch along the cylinder length will form a tongue in the casted object. By rotating the cylinder, the tongue can be tilted to the right joining angle. The protractor consists of two parts that are bolted on the cylinder and the stationary part. The slot in the protractor allows for the fixation of the cylinder at the right joining angle with a nut and

56 bolt. Figure 6.6 shows a section of the tongue edge module with the voussoir joining angle set to three different values. Figure 6.7 shows the joining of two voussoir casted in the adjustable mould for three different joining angles. Note that the groove is in a fixed position relative to the voussoir while the position of the tongue is adjusted to the right joining angle.

Figure 6.6: Section of the tongue edge module with the voussoir joining angle set to a) 0°, b) 15° and c) 30°

Figure 6.7: Joining of two voussoirs at a voussoir joining angle of a) 0°, b) 15° and c) 30° Vertex modules Due to the cylindrical vertex modules, the voussoirs will contain cylindrical cavities at the points where two interfaces intersect. A shell structure made of these voussoirs will contain holes at the vertices resulting in a structure that is not watertight. The holes at the vertices will have the shape of a solid union of multiple cylinders with different rotational orientations. The rotational orientation of each cylinder is determined by the surface normal of intrados/extrados of the adjacent voussoirs. Figure 6.8a shows the assembly of four quadrangular voussoirs with a hole at the node. Figure 6.8b shows the shape of this hole. Since the orientation of the cylinders will be different for every node in the shell structure, each hole will have a unique geometry.

Figure 6.8: a) assembly of voussoirs cast in a mould with cylindrical vertex model and b) the shape of the hole at the node

By replacing the cylindrical vertex modules with spherical vertex modules, the voussoirs will contain spherical cavities at the points where two interfaces intersect (Figure 6.8a). The resulting holes at the 57 vertices of the shell structure will have the shape of a sphere (Figure 6.8b). In this case, the geometry of the holes at the vertices are all equal since for spheres, the rotational orientation does not affect the way it is occupying space. As a result, all the holes in the shell structure can be filled with glass spheres of equal geometry. The glass spheres used to fill the holes will be further discussed in §8

Figure 6.9: assembly of voussoirs cast in a mould with spherical vertex model and b) the shape of the hole at the node

Two spherical vertex modules are needed: one that fits to the tongue edge module and one that fits to the groove edge module. These modules will be further referred to as tongue vertex module and groove vertex module respectively. Figure 6.10 shows both vertex modules.

Figure 6.10: Spherical vertex modules that fit on a) the groove edge module and b) the tongue edge module

The tongue vertex module consists of two parts. The main part is the spherical hinge that can slide over the tongue edge module. A smaller part named the tongue insert (Figure 6.11), is placed in the notch of the cylinder of the tongue edge module to seal the gap between the cylinder and the tongue vertex module. When the cylinder is rotated to be set at the desired voussoir joining angle, the tongue

58 insert can move along with this rotation while maintaining a flush connection with the sphere of the tongue vertex module (Figure 6.12).

Figure 6.11: Tongue insert part

Figure 6.12: Connection of the tongue vertex module and the tongue edge module with the voussoir joining angle set to a) 0°, b) 15° and c) 30° Dimensions The dimensions of the mould modules are dependent on the voussoir. This is obvious for the height of the edge modules. The height is directly influenced by the thickness of the voussoirs which is determined by structural requirements of the shell structure. Less obvious is that the radius of the spheres of the node of the vertex modules is also influenced by the thickness of the voussoirs.

Figure 6.13 shows the connection of a tongue edge module to another tongue edge module at a 90° and 45° interior angle. For the 90° connection no problems occur but for the 45° connection the edge modules are intersecting. This problem can be solved by increasing the radius of the sphere of the vertex module. The minimum radius can be calculated with equation 6.1 wherein rv is the radius of the sphere of the vertex module, tv is the voussoir thickness and αi, min is the minimum occurring interior angle. Figure 6.15 shows the interior angle plotted against the minimum radius according to equation 6.1

Figure 6.13: Connection of a tongue edge module to another tongue edge module at a) a 90° interior angle and b) a 45° interior angle

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푡 푟 > 푣 (6.1) 푣 1 2 sin ( 훼 ) 2 푖,푚푖푛 Note that this problem of edge module intersection at small angles only occurs for tongue edge module to tongue edge module connection. Instead of solving this problem by increasing the sphere radius of the vertex module, it can also be solved by making sure that for small angles only tongue to groove edge module, groove to groove edge module or tongue to groove edge module connections are needed.

A similar problem occurs for large angles. Figure 6.14 shows the connection of groove edge module to a tongue edge module at 90° and 135° interior angle. For the 90° connection no problems occur but for the 135° connection the edge modules are intersecting (left of the vertex module in Figure 6.14b). This intersection also occurs when connecting a tongue edge module to another tongue edge module at a 135 angle. This problem can be solved by increasing the radius of the sphere of the vertex module.

The minimum radius can be calculated with equation 6.2 wherein rv is the radius of the sphere of the vertex module, tv is the voussoir thickness and αi, max is the maximum occurring interior angle. Figure 6.15 shows the interior angle plotted against the minimum radius according to equation 6.2

Figure 6.14: Connection of a groove edge module to a tongue edge module at a) a 90° interior angle and b) a 135° interior angle

푡 푟 > 푣 (6.2) 푣 1 2 cos ( 훼 ) 2 푖,푚푎푥 Note that this problem of edge module intersection at large angles only occurs for groove edge module to tongue edge module connections. As with the problem for small angles, the problem can be solved by increasing the sphere radius of the vertex module but also avoiding certain connections at large angles. For large angles, tongue to tongue edge module, groove to groove edge module or tongue to groove edge module connections are preferred.

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2.5t

2.0t

1.5t

[mm] Tongue to tongue edge v r 1.0t connection Groove to tongue edge 0.5t connection

0.0t 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

αi [°]

Figure 6.15: The interior angle plotted against the sphere radius of the vertex module for tongue to tongue edge connections and groove to tongue edge connections

A shell structure consists of multiple voussoir that all contain intrados and extrados with different interior angles. For each interior angle that is either formed by a tongue to tongue interface or a groove to tongue interface present in the shell structure, a different value for the minimum radius for the sphere of the vertex module can be calculated. Out of all these values for the radius for the sphere of the vertex module that are calculated, the highest value will determine the radius for the final mould design. This means that either the smallest interior angle that occurs in the tessellation pattern at which a tongue edge module is connected to another tongue edge module, or the largest interior angle that occurs in the tessellation pattern at which a groove edge module is connected to a tongue edge module determines the value for the radius for the sphere of the vertex module.

The tongue interfaces contain pointy edges where the interface meets the intrados and extrados. These pointy edges intersect with the adjacent voussoir when joined at a joining angle other than 180° (Figure 6.16a). By chamfering the pointy edges, this intersection is avoided (Figure 6.16b). Besides avoiding an intersection, the elimination of the pointy edges also results in a shape with reduced stress concentrations that is easier to anneal. The minimum chamfer distance can be calculated with equation 6.3 wherein dc is the chamfer distance, tv is the voussoir thickness and αvj, max is the maximum occurring voussoir joining angle. The width of the tongue edge module has to be increased with the minimum chamfer distance.

Figure 6.16: Voussoir joining at a 30° angle a) with intersecting edges and b) with chamfered edges 1 푑 > 푡 sin(푎 ) (6.3) 푐 2 푣 푣푗,푚푎푥 Another dimension related voussoir joining angle is the width of the tongue and the groove. Figure 6.17 shows two tongue edge modules with different tongue thicknesses set to a voussoir joining angles of 45°. Note that the width of the tongue includes the fillet dimensions between tongue and the

61 cylinder. When a tongue edge module with a large tongue thickness is set to a large voussoir joining angle, the tongue of the casted voussoir will only be partially connected to the voussoir (Figure 6.17a). To avoid this problem, the thickness of the tongue should be limited to a certain value (Figure 6.17b). The maximum thickness of the tongue (and thus also the thickness of the groove can be calculated with equation 6.4 wherein wtg is the width of the tongue and the groove, tv is the voussoir thickness, avj,max is the maximum occurring voussoir joining angle and dc is the chamfer distance.

Figure 6.17: Tongue edge module set to a voussoir joining angle of 45° with a) a large tongue thickness and b) a small tongue thickness

−1 2푑푐 푡푡푔 < 푡푣 cos (푎푣푗,푚푎푥 + sin ( )) (6.4) 푡푣 Prototype In order to verify if the design of the mould is working properly, a small-scale prototype was made of 3D printed PLA. The design was slightly modified in order to make it a suitable geometry for 3D printing. These modifications included the removing of the T-slots, simplification of the protractors and the splitting of edge modules in two parts. The two parts of the edge modules were later connected with two screws. M6 screw thread was tapped into the hinge point of the vertex modules to allow for the fixation of the edge modules to the vertex modules at a set length and angle. MDF rulers and protractors were lasercut and glued to the mould to assist with precise setup of the mould. A sheet of shuttering plywood was used as a base plate for the mould. Figure 6.18 shows the prototype in three different configurations.

Figure 6.18: Prototype of the adjustable mould in three different configurations

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The dimensions of the prototype are given in Table 6.1. These dimensions determine certain minimum and maximum values for the set-up of the adjustable mould. These minimum and maximum settings are given in Table 6.2.

Table 6.1: Dimensions of the adjustable mould prototype

Edge length 235 mm Edge height 40 mm Sphere radius 40 mm Chamfer distance 7.5 mm Tongue and groove width 20.5 mm

Table 6.2: Minimum and maximum values for the set-up of the adjustable mould prototype

Minimum/maximum edge length 100 / 185 mm Minimum tongue to tongue edge module connection angle 60° Maximum groove to tongue edge module connection angle 120 ° Minimum/maximum voussoir joining angle - 37.1° / 37.1°

Since PLA does not withstand the high temperatures at which glass casting is done, modelling wax was used as a substitute for glass to do a casting test. Before the casting, a coating of petroleum jelly acting as a mould release agent was applied to the mould and the baseplate. The petroleum jelly also smoothened the rough surface of the mould caused by the 3D printing process. When the mould was adjusted to the right settings, it was clamped to the baseplate (Figure 6.19a) and the hot liquid wax was poured (Figure 6.19b). After four hours, the wax was hardened, and the mould was removed (Figure 6.19c). Four castings were done with different mould settings. The resulting casts are shown in Figure 6.20.

Figure 6.19: a) Set up of the adjustable mould, b) casting of the wax, c) demoulding

Figure 6.20: Casted wax voussoirs of different geometry

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The removal of the mould was possible without damaging the mould or the hardened wax but was difficult and required a lot of force. The large amount of force for demoulding can be attributed to the geometry of tongue and groove that has a draft angle (the angle between the casted object geometry and the direction of the mould during demoulding) of 0°. This results in a large amount of friction during the demoulding. Due to the coarse tolerances of the 3D printing process, the demoulding was further impeded by small amounts of wax that flowed into the seams between the modules. This, however, will not be a problem for the final mould made of CNC-milled steel since CNC-milling can achieve far tighter tolerances than 3D printing.

Three of the wax casts where used in the lost-wax casting process to produce disposable silica plaster moulds. The disposable moulds were used for glass kiln-casting. Shards of discarded soda-lime window glass was used for the casting. Since silica plaster moulds were used for the casting process, the resulting cast glass voussoirs had a rough surface finished. The voussoirs were polished in order to mimic the surface quality that would be achieved when the casting would be done in an adjustable steel mould. Figure 6.21 shows the cast glass voussoirs after polishing.

Figure 6.21: Cast glass voussoirs of different geometry Improved design Based on the findings of the prototype the design of the mould is improved in several ways. The first improvement is a redesign of the tongue and groove feature on the edge modules to include a draft angle to ensure easy demoulding. Furthermore, it should be taken into account that the glass voussoir will be assembled with a 3mm thick interlayer in between. The thickness of the interlayer is based on the research by Aurik et al. (2018). To accommodate for the thickness of the interlayer, the surfaces of the edge modules that are in contacted with the glass melt during the casting, are offset by half the thickness of the interlayer (1.5 mm). Figure 6.22 shows sections of the redesigned edge modules.

Figure 6.22: Sections of the a )improved groove edge module and b) improved tongue edge module

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Figure 6.23 shows the redesigned vertex modules. By removing the brackets to hook the vertex modules onto the edge modules, the mould becomes easier to disassemble during the demoulding process. The removal of the brackets also results in simplified manufacturing since an undercut feature of the vertex module geometry is eliminated.

Figure 6.23: a) improved groove vertex module, b) improved tongue vertex module

The tongue vertex module is further improved by including a slot in the main part (Figure 6.24a) and adding a protrusion to the tongue insert (Figure 6.24b). This prevents the movement of the tongue insert along the notch in the tongue edge module cylinder while allowing for the movement of the tongue insert during the rotation of the cylinder when setting up the voussoir joining angle. Furthermore, the redesigned tongue insert contains a planar surface which allows for simplified manufacturing.

Figure 6.24:a) improved tongue insert containing a protrusion and planar surface, b) improved tongue vertex module containing a notch

Figure 6.25, Figure 6.26 and Figure 6.27 show the improved design of the mould in a configuration with 3, 4 and 6 edges respectively.

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Figure 6.25: Improved design of the adjustable mould, 3 edge configuration

Figure 6.26: Improved design of the adjustable mould, 4 edge configuration

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Figure 6.27: Improved design of the adjustable mould, 6 edge configuration Mould manufacturing Since the mould is produced in a low batch size and requires tight tolerances, all mould parts should be made by CNC machining. The edge modules require a 5-axis CNC mill to be manufactured. Due to the complex geometry of the edge modules, the workpieces need to be fully accessible for machining on five sides. By using a magnetic workhold and a spoilboard (a sacrificial part between the workpiece and the workhold), maximum accessibility is guaranteed. After the shaping process, rulers need to be engraved on the edge modules. This should be done with a laser engraving machine. The tongue cylinder, vertex modules and tongue insert require a CNC combination lathe mill. Appendix B gives an overview of the different machining operations required for the manufacturing of the mentioned mould parts.

The protractors and diagonals have a relatively simple geometry compared to the other mould parts. These parts can be made with a 3-axis CNC mill. As with the edge modules, the protractors and diagonals need to be engraved with a laser engraving machine after the shaping process. Casting process The casting process of the glass voussoirs consists of several steps. These steps are showed in Table 6.3.

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Table 6.3: Casting process

1. Set up the variables of the mould by tightening the bolts of the T-slots, protractors and diagonal. Coat the contact surfaces with a release agent and preheat the mould to avoid surface chills.

2. Pour the hot glass melt in the mould.

3. Let the glass cool down to a temperature between its annealing point and its softening point.

4. Remove the bolts and hinge pins and carefully take the mould apart.

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5. Place the glass with the baseplate in the annealing kiln.

6. Gradually cool down the glass to its strain point.

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7 Tessellation pattern By tessellating a shell structure, the shell structure is divided into a discrete number of voussoirs. In order to be able to produce all these voussoirs with the adjustable mould described in §6, The tessellation pattern should meet the following criteria:

- The tessellation should consist of polygons (i.e. only straight lines) - The polygons have to be convex (i.e. no interior angles larger than 180°) - The polygons have to be planar - Each edge should be longer than twice the sphere radius of the vertex module

Other criteria include:

- The area of the polygons should be limited to avoid components with a large mass to ensure proper handleability during assembly and to limit the annealing time. - For aesthetical reasons, the area of the polygons should be as uniform as possible - The tessellation pattern should be aligned to the principal stress directions

There are three regular tessellation patterns: triangular, quadrangular and hexagonal (Figure 7.1). Table 7.1 gives an overview of the properties of the different tessellation patterns.

Figure 7.1: Regular tessellations patterns. a) triangular b) quadrangular c) hexagonal

Table 7.1: Properties of the three regular tessellation patterns

Triangular Quadrangular Hexagonal Node valency 6 4 3 Intrados/extrados 3 5 9 mould variables Planarity Yes Not guaranteed Not guaranteed Spherical segment at Large Small Large node Risk of sliding at shell Yes No Yes openings Staggered bond No No Yes

Since all types of tessellation patterns have their advantages and disadvantages, there is not a single preferred tessellation pattern that should be used for every shell shape. The preferred tessellation pattern is dependent on the properties of the shell. These properties include the Gaussian curvature, the presence of unsupported boundaries and the maximum allowable mass of the voussoirs. Also, for some shells complex algorithms might need to be developed for planarization and alignment to the force flow depending on the tessellation pattern that is selected. A well-considered choice should be made when selecting a tessellation pattern with both the properties of the shell geometry and the 70 properties of the tessellation patterns kept in mind. Also, the appearance off the shell structure is significantly influenced by the tessellation patterns. Therefore, the aesthetic qualities should also be considered when designing a tessellation pattern. The properties of the different tessellation patterns will be further described. Node valency The node valency of regular triangular, quadrangular and hexagonal tessellation patterns has a value of 6, 4 and 3 respectively. These numbers will vary when the tessellation patterns are applied to double curved surfaces instead of planar surfaces. For common tessellated structures, a low node valency is preferred since less complex nodes will be easier to assemble. In this case however, the spherical segments at the nodes preclude that multiple voussoirs are joining at a single point and thus makes the node valency not a relevant property of the tessellation patterns. Intrados/extrados mould variables As discussed in §6.1, a triangular intrados or extrados requires three variables to define; three values for the edge lengths. Quadrangular and hexagonal voussoirs also require diagonal lengths to define their intrados or extrados and thus require a total of 5 or 9 variables to set respectively. Therefore, the time to set up the adjustable mould will be the highest for a hexagonal voussoir and the lowest for a triangular voussoir. Planarity The main benefit of a triangular tessellation is that each face is guaranteed to be planar and thus suitable as the intrados or extrados of a voussoir to be made with the adjustable mould. Quadrangular and hexagonal tessellations do not necessarily have planar faces.

Hexagonal tessellations are more complicated to planarize than quadrangular tessellations. Also, hexagonally tessellated surfaces that contain regions of negative Gaussian curvature can only be planarized with the incorporation of concave faces (Wang & Liu, 2009). This is illustrated by the torus shown in Figure 7.2 that is composed of planar hexagons. The hexagons are convex at regions where the Gaussian curvature is positive while the hexagons are concave at regions where the Gaussian curvature is negative. Since the adjustable mould is not suitable for the casting of voussoirs with concave intrados or extrados, a hexagonal tessellation can only be applied to shell structures that do not contain any regions of negative Gaussian curvature.

Figure 7.2: Planar hexagonal tessellation of a torus

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The planarization of quadrangular and hexagonal tessellations is a topic of research in the field of computer graphic science. Due to the complexity of this topic, the planarization of tessellated shell structures is beyond the scope of this research. Spheres at the nodes The size of the spheres of the node components, is dependent on the interior angles of the voussoir intrados and extrados. As discussed in §6.4, the radius of the sphere of the hinge module is determined by either the smallest interior angle that occurs in the tessellation pattern at which a tongue edge module is connected to another tongue edge module, or by the largest interior angle that occurs in the tessellation pattern at which a groove edge module is connected to a tongue edge module. Whichever of these angles has the largest deviation from 90° determines the radius of the sphere of the node components.

A quadrangular tessellation consists of faces with an average interior angle of 90°. When the tessellation is properly generated, the maximum deviation from the average interior angle will not be large and thus the spherical segments at the nodes of a quadrangular tessellated shell structures can be relatively small. Triangular and hexagonal tessellations consist of faces with interior angles that on average have 30° deviation from 90°. As a result, the spherical segments at the nodes of triangular and hexagonal tessellated shell structures are relatively large.

Figure 7.3 shows the three regular tessellation patterns. As discussed, the spherical segments at the nodes are relatively large for the triangular and hexagonal tessellation pattern compared to the quadrangular tessellation pattern. The faces of each pattern are of similar size and thus of similar volume and mass when given the same thickness.

Figure 7.3: Regular tessellation patterns including the spheres at the nodes. a) triangular b) quadrangular, c) hexagonal

When comparing the tessellation, it is quite clear that the spheres are a more dominant feature in the hexagonal tessellation pattern than in the other tessellations. While this is not a problem for the regular tessellation pattern shown in Figure 7.3, it might cause problems for non-equilateral tessellation patterns that are necessary to tessellate double curved surfaces. Non-equilateral tessellation patterns have edges of varying length. When there are edges present in the tessellation that are shorter than twice the radius of the sphere, a problem occurs. Figure 7.4a shows a non- equilateral hexagonal tessellation pattern. Figure 7.4b shows that at the edges shorter than twice the radius of the sphere, spheres are intersecting. This problem could be solved by scaling up the tessellation pattern. Since the radius of the spheres is dependent on the thickness of the shell structure and on the minimum and maximum occurring angles of the tessellation pattern and not on the size of the edges of the tessellation pattern, the size of the spheres remains unchanged when scaling up the tessellation pattern. However, by scaling up the tessellation pattern, other problems relating might occur. A larger tessellation pattern results in larger voussoirs with a higher mass that could jeopardize the handleability of the voussoirs and an increased annealing time.

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Figure 7.4:a) Flattened hexagonal tessellation pattern, b) intersecting spheres at the nodes Risk of sliding at shell openings As discussed in §3.3.2, voussoirs are at risk of sliding when the angle between the surface normal of the interfaces and the local force direction is larger than the friction angle. Ideally, the surface normal of the interfaces are parallel to the local force direction. Figure 7.5 shows three barrel vaults with three different tessellation patterns (triangular, quadrangular and hexagonal). For the triangularly and hexagonally tessellated vaults, some of the voussoirs at the unsupported boundaries are at risk of sliding.

Figure 7.5: Barrel vault with a) a triangular tessellation pattern with a risk of sliding, b) a quadrangular tessellation pattern and c) a hexagonal tessellation pattern with a risk of sliding

By one-dimensional scaling of the tessellation pattern, the angle between the surface normal of the interfaces and the local force direction becomes smaller than the friction angle and thus the risk of sliding is prevented (Figure 7.6). Note that for the triangular tessellated vault, the one-dimensional scaling of the tessellation pattern results in triangles with a high aspect ratio with one very sharp interior angle. Hexagonal tessellations patterns on the other hand, will feature faces with some very large interior angles after one-dimensional scaling. As discussed in §6.4, very small or very large interior angles will result in large spheres at the nodes. This will in turn lead to voussoirs with a high mass as discussed in §7.4.

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Figure 7.6: Barrel vault with a) a flattened triangular tessellation pattern without risk of sliding and b) a flattened hexagonal tessellation pattern without risk of sliding

The benefit of a quadrangularly tessellated shell structures is that the interface normals can potentially be aligned with one of the two principal stress directions. This results in quadrangles of similar interior angles close to 90°. This will lead to small spheres at the nodes and voussoirs of a low mass. As mentioned in §3.3.2, computational methods for aligning a quadrangle tessellation pattern to the principal stress directions have been researched by Greco (2018) and Pellis and Pottmann (2018). However, these methods are very complex to apply and are therefore beyond the scope of this research. Staggered bond A staggered bond in dry-assembled structures makes sure that each component is supported by at least two other components. In turn, the two components on which the first component is resting are supported by at least four other components. This network of load distribution ties the structure together (Rankine, 1889). Furthermore, since every component is supported by at least two other components, the component will still be supported if one of its supporting components fails.

For regular tessellation patterns, only a hexagonal tessellation pattern contains a staggered bond. However, by introducing the spheres at the nodes, the triangular and quadrangular tessellation become staggered as well. Figure 7.7a shows voussoirs configured in a quadrangular tessellation with one voussoir highlighted. The highlighted voussoir is pulled down by a gravitational force but is kept in place by an equal reaction force exerted by the voussoir below. When the voussoir below fails, the equilibrium of forces is disturbed and the highlighted voussoir will slide downwards (Figure 7.7b).

Figure 7.7: a) voussoir kept in place by the voussoir below, c) voussoir sliding down due to failure of the voussoir below

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Figure 7.8a shows voussoir configured in a quadrangular tessellation with spheres positioned at the nodes. The highlighted voussoir is kept in place by a reaction force exerted by the voussoir below and two minor reaction forces exerted by the spheres below. When the voussoir below fails, the reaction forces exerted by the spheres below will increase and the equilibrium of forces will be maintained (Figure 7.8b).

Figure 7.8: a) voussoir kept in place by the voussoir and spheres below, b) voussoir kept in place by the spheres after failure of the voussoir below

While the spheres add some form of staggering, a staggered bond due to a hexagonal tessellation is still preferred. This is due to the connection of the spheres with the voussoir which is a hinging connection. As discussed in §5.1, a hinging connection is not performing well when the shell is subjected to point loads compared to the tongue and groove connection between two voussoirs.

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8 Node components As discussed in §6.3, the spherical vertex modules will cause spherical cavities in the voussoirs. When a shell of these voussoirs is constructed, the spherical cavities will form spherical holes at the nodes of the structure. The holes can be filled with glass spheres to make the structure watertight and to ensure a staggered bond in combination with the voussoirs. Figure 8.1a shows a simple shell structure consisting of triangular voussoirs and spheres at the nodes. The radius of the sphere is quite large compared to the thickness of the voussoirs, which results in the spheres being a dominant factor in the aesthetic appearance of the shell. Figure 8.1b shows the same shell but with spherical segments at the nodes instead of spheres. This results in a smoother appearance of the shell while it remains watertight and still contains a staggered bond. Furthermore, the volume of the node components is reduced which results in lighter components that have a better handleability and shorter annealing time.

Figure 8.1: Shell structure with a) spheres at the nodes and b) with spherical segments at the nodes Dimensions A spherical segment can be defined as the part of a sphere between a pair of parallel planes. The three variables to describe a spherical segment are the radius of the sphere, the distance between the center of the sphere and the first plane and the distance between the center of the sphere and the second plane (Figure 8.2).

Figure 8.2: Dimensions of a spherical segment

The radius of the spherical segment is equal to the radius of the sphere of the vertex modules minus the thickness of the interlayer. The distances between the center of the sphere and the planes should be large enough to make sure that the node components do not form cavities in the surface of the shell structure where water can accumulate (Figure 8.4). The minimum distance to prevent the occurrence of cavities is different for each node component. This is because the minimum distance is dependent on the angle between the vertex normal of the specific node and the face normals of the

76 adjacent intrados/extrados which is different for each node. This would result in a different spherical segment geometry for each node and thus requires different moulds for each spherical segment. To avoid the high costs involved with the customisation of each spherical segment, it is opted to determine the dimensions of the largest spherical segment present in the structure and use this geometry for each node.

Figure 8.3: Cavities due to node components with small distances between the center of the sphere and the planes

The distances between the center of the sphere and the planes, d1 and d2, can be calculated with equation 8.1 and equation 8.2 wherein rv is the radius of the sphere of the vertex modules, ti is the thickness of the interlayer, tv is the thickness of the voussoirs and αvf, max is the maximum occurring angle between the vertex normal and its adjacent face normal in the entire structure.

−1 푡푣 푑1 = 푟푣 cos (cos ( ) + 훼푣푓, 푚푎푥) (8.1) 2푟푣

−1 푡푣 푑2 = 푟푣 cos (cos ( ) − 훼푣푓, 푚푎푥) (8.2) 2푟푣

The radius of the spherical segment, rn can be calculated with equation 8.3 wherein rv is the radius of the sphere of the vertex modules and ti the thickness of the interlayer.

푟푛 = 푟푣 − 푡푖 (8.3) Mould design Since the node components have two surfaces that are not in contact with other components and thus require no high precision, the node components can be cast in an open steel mould. The mould consists of three parts: two parts that enclose the component and one baseplate. The parts that enclose the component are connected through a pin and slot connection that properly aligns the parts and keeps the appearance of the seam to a minimum. Figure 8.4 shows the mould used for the casting of the node components.

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Figure 8.4: Mould used for the casting of the node components

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9 Interlayers As discussed in §2.3.2, a transparent interlayer should be placed between the cast glass components to prevent peak stresses and to accommodate for production tolerances of the casting process. This topic is currently being research and no definitive conclusions have been made about the material that should be used or what the thickness of the interlayer should be. Since the subject of thesis is not focussed on the properties and structural performance of the interlayer, an assumption will be made regarding its thickness. Based on the research by Aurik et al. (2018), it is assumed that the interlayer should have a thickness of 3 mm. No decision will be made regarding the material of the interlayer since this will not have an influence on geometry of the voussoirs and thus will not have an influence on the adjustable mould and the tessellation pattern.

Two different interlayer geometries are required: one for in between the interfaces of two voussoirs and another one for in between the voussoirs and the node components. Interlayer in between the interfaces Figure 9.1 shows a cross-section of two voussoirs at three different joining angles with an interlayer between the interfaces. Since the contact area between the interfaces of two voussoirs is different for every voussoir joining angle, the interlayer includes extended flaps along both sides of the interlayer. These flaps can accommodate for the variation in voussoir joining angles and ensures a maximum contact area with the interfaces. After assembly, the part of the flaps that is not in contact with both interfaces can be removed by simple cut with a utility knife. However, since the interlayer smoothly fits around the groove edge, it is also an option to leave the flaps in place.

Figure 9.1: Interlayer in between the interfaces of the voussoir with a voussoir joining angle of a) 0°, b) 10°, and c) 20°

Since the interlayer has a constant cross-sectional profile, it is a suitable geometry to shape by extrusion. However, the material used for the interlayer should be suitable for this production process. Interlayer in between the voussoirs and the node components Figure 9.2 shows the interlayer between the voussoirs and the node components. The interlayer contains a cut which allows the interlayer to be wrapped around the spherical zone of the node component. Note that not the entire part of the interlayer is in contact with both the voussoir and the node component. As with the previously interlayer in between the interfaces of the voussoirs, these parts can be either removed with a utility knife or kept in place depending on the preference of the architect.

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Figure 9.2: Interlayer in between the voussoirs and the node component. a) axonometric view, b) cross section

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IV Case study

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10 Armamentarium Delft While monolithic and discrete shells are rarely being constructed anymore, gridshells are still commonly built. A typical application of gridshells is to cover courtyards of historic buildings to increase the total interior space. The Great Court covering of the British Museum in London by Foster + Partners (Figure 10.1a) and the glass roof of the Dutch Maritime Museum in Amsterdam by Ney & Partners (Figure 10.1b) are good examples of such gridshells.

Figure 10.1: Courtyards of a) the Great Court of the British Museum and b) the Dutch Maritime Museum

As a case-study that will serve as a context to demonstrate the design and production process described in part III, a similar courtyard covering is designed. The covering will be designed for the southern courtyard of the Armamentarium in Delft. Figure 10.2 shows an aerial view of the Armamentarium in which the courtyard is visible. Figure 10.3 shows a rough sketch of the concept. The courtyard has a dimension of approximately 16.5 by 10.3 meters. Figure 10.4 shows a schematic floor plan of the courtyard in which the dimensions are given.

Figure 10.2: Aerial view of the Armamentarium in Delft

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Figure 10.3: Section of the Armamentarium showing the courtyard and the proposed covering

Figure 10.4: Schematic plan of the courtyard

The design process for the courtyard covering consists of the following steps:

- Form finding - Structural validation - Tessellation - Generating the voussoirs and input variables for the adjustable mould - Mould design

Furthermore, the connections between the shell and the existing building have to be detailed. Also, assembly method has to be developed. Form finding The first step of the form finding process was to fillet the corners of the plan in order to avoid stress concentrations at sharp corners. The form finding was done with the particle-spring system method using the solver of the Kangaroo2 plug-in for Grasshopper. Figure 10.5 shows the particle-spring network in its original state and Figure 10.6 shows the particle-spring network after form finding. The 83 form found shape has a maximum height of approximately 2.4 meters which is visible in the elevation shown in Figure 10.7.

Figure 10.5: The particle-spring network before the form finding process

Figure 10.6: The particle-spring network after the form finding process

Figure 10.7: Elevation of the particle-spring network after the form finding process Structural validation In order to verify if the shell meets the structural requirements, two types of structural analysis are done. The first type is a finite element method (FEM) analysis to check if the maximum allowable stresses and deformations of the structure are not exceeded. The second analysis is a discrete element method (DEM) analysis to analyse the stability of the structure. Doing a DEM analysis requires the skill 84 to work with complex software (3DEC) which is not possessed by the author. Therefore, a DEM analysis is beyond the scope of this research and the structural validation will be limited to a FEM analysis.

The FEM analysis was done using Karamba, a parametric structural analysis plug-in for the Grasshopper environment (Preisinger, 2013). Table 10.1 shows the geometrical and material properties of the shell that were used for the FEM analysis. Hinged supports were assigned along the boundary of the mesh. The shell was subjected to different loads that are shown in Table 10.2. The variable loads are based on general variable load values used for the structural calculations of duo- pitch roofs with a roof angle of 30° (Wagemans et al., 2014).

Table 10.1: Geometrical and material properties used for the FEM analysis

Thickness 100 mm Density 2500 kg/m3 Young’s modulus 70 GPa Shear modulus 28 GPa Yield strength 30 MPa

Table 10.2: Loads used for the FEM analysis

Category Load Safety factor Loadcases Dead load 2.5 kN/m2 1.2 1, 2, 3, 4, 5 Live load, distributed 0.0 kN/m2 1.5 - Live load, concentrated 1.5 kN 1.5 2, 5 Wind load (asymmetric) 0.0 – 0.48 kN/m2 1.5 3, 5 Snow load 1.1 kN/m2 1.5 4

The wind load is asymmetrically distributed over the shell. The different values for the windload, qv, are calculated with equation 11.1 wherein cscd is the structural factor, cf is the force coefficient for the part of the roof and qp(ze) is the peak velocity pressure at height ze (Wagemans et al., 2014). The structural factor for low-rise buildings has a value of 1. The peak velocity pressure is dependent on the geographical location and the height. For the city of Delft at a height of 10 meter, the peak velocity pressure has a value of 0.68 kN/m2. The values for the force coefficients are shown in Figure 10.8a. Figure 10.8b shows the calculated wind loads for the different parts of the shell.

푞푤 = 푐푠푐푑푐푓푞푝(푧푒) (11.1)

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Figure 10.8: a) force coefficients for a duo pitched roof, b) wind loads acting on the shell structure

Table 10.3 shows the maximum displacements and minimum and maximum principal stresses occurring in the shell structuring for each loadcase. Detailed results of the FEM analysis can be found in appendix C.

Table 10.3: Results of the FEM analysis

Loadcase Displacement Principal stress 1 [MPa] Principal stress 2 [MPa] [mm] min max min max 1 0.02 -0.13 -0.00 -0.26 -0.02 2 0.03 -0.31 0.04 -0.38 0.00 3 0.02 -0.13 0.01 -0.31 -0.02 4 0.03 -0.20 -0.00 -0.41 -0.03 5 0.02 -0.30 0.04 -0.38 -0.02

In general, the maximum allowable displacement for a span is the length of the span divided by 500. Since the shell has a span of approximately 10.3 meters, the maximum allowable displacement is 20.6 mm. The maximum displacement that occurs is 0.03 mm. This is far below the maximum allowable displacement and can be attributed to the minimum amount of bending moments that occur in the shell. However, the actual maximum displacement will be higher than 0.03 mm since the deformation of the elastic interlayer has not been taken into account.

The shell structure acts in pure compression when subjected to loadcase 1, and 4. Very small amounts of tension are present in one of the corners in the first principal direction when subjected to load 3. The largest tensile stresses occur when subjected to loadcase 2 and 5. At the point where the concentrated load is exerted on the shell, tensile stress concentrations occur at the bottom layer of the shell. The maximum tensile stresses are small compared to the compressive stresses and are far below the yield strength of the glass. The maximum occurring tensile stress has a value of 0.04 MPa which is only 0.1% of the yield strength. Also, the tensile stresses only occur at the bottom and not throughout the entire thickness of the shell which would indicate the separation between the voussoirs. However, the tensile stresses at the bottom in combination with a compressive stress at the top results in small bending moments. Since the voussoirs are joined by interfaces with an

86 interlocking feature that prevent any rotation, these bending moments will not likely lead to failure of the structure. However, to be sure that there is no movement between the voussoirs, a DEM analysis should be done. Tessellation Since the shell structure is fully supported along its boundary, there is no risk of sliding of the voussoirs when the tessellation is not properly aligned with the principal stress directions. Therefore, all types of tessellations (triangular, quadrangular and hexagonal) can be used. By using a triangular tessellation, the complex process of planarizing the tessellation can be circumvented. The constraints for the tessellation are as following:

- Maximize the smallest occurring edge length to avoid the intersection of the node components (§7.4) - Maximize the smallest occurring interior angles to reduce the radius of the node components (see §6.4) - Minimize the area of each mesh face to reduce the mass of the voussoirs

These are conflicting constraints since an increase in edge lengths and interior angles will lead to increased face areas and thus to voussoirs with a higher mass. Theoretically, the radius of the spheres can be reduced by decreasing the thickness of the voussoirs, but this will conflict with the structural requirements. Since non-intersecting node components and sufficient voussoir thickness are essential constraints to make this structural system function properly, these constraints are prioritized over the minimalization of the mass of the voussoirs. This will come at the cost of an increased annealing time and a reduced handleability of the voussoirs.

The tessellation was generated using T.MAP, a mesh parameterization tool for Rhino developed by EvoluteTools. The generated tessellation was further post-processed by hand to increase the minimum occurring edge length and to increase the minimum occurring interior angle. Figure 10.9 shows the tessellation pattern. The tessellation consists of 676 vertices and 1250 faces. Table 10.4 gives an overview of different properties of the tessellation.

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Figure 10.9: Tessellation pattern of the shell structure

Table 10.4: Properties of the tessellation pattern

Minimum Maximum Average Standard deviation Interior angle [°] 34.2 97.3 60.0 7.00 Edge length [mm] 330 782 538 57.7 Face area [m2] 0.051 0.186 0.125 0.018 Voussoir joining angle [°] -6.9 20.2 2.1 2.9

Voussoir generation The main objective of the voussoir generation is to assign the type of interface (tongue or groove) to each face edge. This should be done in such a way that the assignment of two tongue interfaces at face edges joining at the smallest occurring interior angles is avoided since this would cause a large radius of the node components (see §6.4). An algorithm was written in Grasshopper to assign the type of interface to each face edge that with a constraint that prioritized the avoidance of the assignment of two tongue interfaces to the face edges joining at the smallest occurring interior angles wherever possible. Figure 10.10 shows a flowchart of the algorithm.

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Figure 10.10: Flowchart of the interface type assigning algorithm

After the algorithm assigned the type of interfaces to each face edge, the smallest angle at which two face edges to which both tongue interfaces were assigned, was measured. This angle has a value of

44.8°. With equation 6.1, the minimum radius of the vertex edge module, rv, was calculated to be

131.2 mm. This value was rounded up to 132 mm. The maximum voussoir joining angle, αvj, was measured to be 20.2°. The minimum chamfer distance, dc, was calculated with equation 6.3 and has a value of 17.3 mm. This value was rounded up to 18 mm. Finally, with equation 6.4 the maximum tongue width was calculated to be 75.1 mm. This value was rounded down to 75 mm.

At this point, all the different values to determine the geometry of each voussoirs are known. Based on these values, a list was generated that contains the following information for each voussoir:

- Voussoir index number - For each edge: - Type of interface (tongue or groove) - Edge length - Voussoir joining angle when the edge has a tongue interface - Adjacent voussoir index numbers

The list can be found in appendix D. The data in this list serves as input data for the set-up of the adjustable mould. When setting up the mould, the data should be applied to the three edges in clockwise direction. As a result, the extrados of each voussoir is the face that is in contact with the baseplate when casted. The voussoir index number and adjacent voussoir index numbers should be

89 subtly marked on the voussoir after casting. The index markings are used to keep the voussoirs apart from each other and assist during the assembly.

Also, a digital model of each voussoir was generated. These models were used to calculate the volume and the subsequent mass of each voussoir. Table 10.5 gives an overview of the masses of the voussoirs. Figure 10.11 shows the components with index 1237, 957 and 999, which are displayed to scale. These are the voussoirs with the smallest, median and largest mass respectively.

Table 10.5: Mass of the voussoirs

Minimum Maximum Average Standard deviation Mass [kg] 5.41 38.5 24.6 4.70

Figure 10.11: a) voussoir 1237, b) voussoir 957, c) voussoir 999

The maximum occurring angle between the vertex normals and its adjacent face normal, αvf, max, was measured to be 20.2°. With this value and the values for the radius of the vertex edge module (132 mm) and the thickness of the interlayer (3 mm), the dimensions of the node components can be calculated using equation 8.1, equation 8.2 and equation 8.3. The dimensions of the node components are shown in Table 10.6. Figure 10.12 shows one of the node components.

Table 10.6: Dimensions of the node components rn 129 mm d1 54 mm d2 73 mm

Figure 10.12: Node component

With all the dimensions of the voussoirs and the node components known, a model of the entire shell structure was generated. Figure 10.13 and Figure 10.14 show how all the voussoirs and node components make up the entire shell structure.

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Figure 10.13: Rendered axonometric view of the shell structure

Figure 10.14: Rendered elevation of the shell structure Adjustable mould design Based on the dimensions of the voussoirs, the adjustable moulds can be dimensioned. Table 10.7 gives an overview of the key dimensions of the adjustable moulds that are calculated with equation 6.1, equation 6.3 and equation 6.4. Figure 10.15, Figure 10.16, and Figure 10.17 show the adjustable mould set up to the variables of the voussoirs with index 1237, 957 and 999 respectively.

Table 10.7: Key dimensions of the adjustable mould rv 132 mm dc 18 mm ttg 75 mm

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Figure 10.15: Adjustable mould with the variables set up to the input data of voussoir 1237

Figure 10.16: Adjustable mould with the variables set up to the input data of voussoir 957

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Figure 10.17:Adjustable mould with the variables set up to the input data of voussoir 999 Supports The shell structure has to be fully supported along its boundary. As shown in Figure 10.9, the boundary of the shell consist of four linear boundaries and four curved boundaries at the corners. However, as shown in Figure 10.13, the linear boundaries are not continuous since the linear edges of the voussoirs are interrupted by the curved geometry of the node components. This makes it difficult to design a proper connection between the shell and the existing structure. Therefore, a new type of node component is introduced called the boundary node component. Figure 10.18 shows a boundary node component. The geometry of the node component consists of two halves: one halve similar to a regular node component and one halve that is cylindrical. The radius of the cylinder is the same as the radius of the groove edges of the voussoirs.

Figure 10.18: Boundary node component

By replacing all the regular node components at the boundary with boundary node components, the linear boundaries of the shell become continuous (Figure 10.19) and can be supported by a steel profile with a fixed cross-section. Such a profile can be manufactured out by extrusion. The curved boundaries at the corners form an exception and require a more complex support that can be manufactured by welding small lengths of extrusion profiles together at different angles.

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Figure 10.19: Shell structure with boundary node components

Figure 10.20 shows the rain gutter on top of the courtyard walls. The shell structure should be supported along the top of the walls. Figure 10.21 shows a detailed section of how the roof and rain gutter are connected to the walls. The masonry walls have a thickness of approximately 600 mm. It is assumed that these walls are strong enough to withstand the vertical load and horizontal thrust exerted by the shell structure. The rain gutter on top of the walls is made of lead sheets. Also, note the fencing mounted on the walls with anchor plates.

Figure 10.20: Rain gutter on top of the walls, a) side view, b) front view

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Figure 10.21: Detail drawing of the connection between the walls and the roof (scale 1:10)

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Figure 10.22: Detail drawing of a voussoir held in place by the support profile (scale 1:5)

Figure 10.22 and Figure 10.23 show detail drawings of how the shell structure is connected to the existing structure. Both the tongue edges of the voussoirs and the boundary node components are supported by the same extruded steel profiles. Before installing the support profiles, the fencing has to be removed and the rain gutter has to be shortened and folded towards the roof to make space for the support profiles. Since the rain gutter is made of lead, it can be easily cut to the right size. The support profiles are placed on multiple shims that compensate for the tolerances in the masonry and allow for the support profiles to be levelled. The support profiles are fixed to the walls with anchor bolts. Once the support profiles are installed, the lead sheets have to be folded back over the support profiles to form a new rain gutter. After this is done, the glass components can be placed. Interlayers between the support profiles and the glass voussoirs and boundary node components accommodate 96 for tolerances in the glass and prevent direct contact between the steel and the glass which would otherwise lead to peak stresses in the glass. Figure 10.24 shows a visual impression of how the shell structure is situated in the courtyard of the Armamentarium.

Figure 10.23: Detail drawing of a boundary node component held in place by the support profile (scale 1:5)

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Figure 10.24: Visual impression of the shell structure Assembly The assembly method for the shell structure consists of several steps. These steps are described in Table 10.8. The assembly method is partly based on the assembly method of the Armadillo Vault by Rippmann et al. (2016) (see §3.3.2).

Table 10.8: Steps of the assembly method

1. Construct a scaffolding in the courtyard up to the height of the walls.

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2. Install the supports as described in §10.6.

3. Expand the scaffolding to a shape that roughly resembles the geometry of the shell structure.

4. Construct a waffle structure out of plywood that serves as a formwork for the shell structure.

5. Assemble the voussoirs and node components on the waffle structure. The interlocking geometry will guide the voussoirs in the correct position. Use shims to compensate for any tolerances in the formwork. Seal all seams with transparent silicone.

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6. Remove the formwork and scaffolding.

During step 5, each voussoir is placed by sliding it in position against the adjacent voussoirs that have already been placed. The sliding movement is a movement parallel to the intrados and extrados of the voussoir. This movement allows for the tongues to slide into the grooves. This would not be possible if the voussoir would be placed with a movement perpendicular to its intrados and extrados. A problem occurs when placing the last voussoir, the keystone (voussoir 652). When placing the keystone, all the adjacent voussoirs are already placed and thus leave no space for placing the keystone with a sliding movement parallel to its intrados and extrados.

To solve this problem, the keystone is split in two parts: a bottom part that contains the intrados and a top part that contains the extrados (Figure 10.25). This way the bottom keystone can be placed with a movement perpendicular to the intrados from below and the top keystone can be placed with a movement perpendicular to the extrados from above. After placing, the two parts of the keystone are bonded by a transparent UV-curing adhesive. Table 10.9 shows the how the keystone is placed in three steps. In order to ensure a proper bond, the surfaces to which the adhesive is applied should be flat within a 0.25 mm tolerance (Oikonomopoulou et al., 2017). Note that due to the adhesive, the recyclability of the keystone is compromised.

Figure 10.25: a) bottom keystone and b) top keystone

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Table 10.9: Placing the keystone

1. Place the bottom keystone on the formwork.

2. Place the voussoirs that are adjacent to the keystone on the formwork.

3. Apply the adhesive to the bonding surface of the bottom keystone and place the top keystone on the bonding surface. Cure the adhesive by exposing it to UV-radiation coming from a UV- light.

The interfaces of the keystone are assigned to be grooves since the splitting a keystone with tongue interfaces would result in result in a geometry with fragile features when made of cast glass. The assignment of groove interfaces to the keystone overrules the types of interfaces that have been assigned to the keystone by the algorithm described in §10.4.

The top keystone is cast in the adjustable mould set-up according to the input data for voussoir 652 found in appendix D. By pouring the mould only half full with glass melt only the top keystone is casted. For casting the bottom keystone, the mould is set-up according the same input data but applied in counter-clockwise order. As with the casting of the top keystone, the mould is only poured half full with glass melt to cast the bottom keystone. After casting the top and bottom keystones, the bonding surfaces should be polished to achieve a flat surface within a 0.25 mm tolerance.

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V Conclusions, limitations and recommendations

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11 Conclusions This thesis has explored the objective to engineer transparent shell structures that can be produced in an efficient way. Based on the literature study, several conclusions can be made to provide a basis for this objective. First, cast glass has a good potential to be used for the construction of shell structures. The material has a high compressive strength that is stronger than concrete while having a low tensile strength. This matches perfectly with the structural performance of shell structures since shell structures are predominantly subjected to compression and no or little tension. While float glass comes in two-dimensional orientated geometries and extruded glass comes in one-dimensional orientated geometries, cast glass comes in three-dimensional oriented geometries which provides the thickness that is necessary to allow for the construction of large spanning shell structures and gives the shell resistance to buckling.

The most suitable method for the joining of cast glass components to build a structure is dry-assembly. This is a bonding method analogous to the construction of dry-assembled discrete shell structures. Dry-assembled connections perform excellent when pressed together but offer no resistance when pulled apart. Therefore, the ideal shape of a dry-assembled discrete shell is a funicular shape. A funicular shell shape can be generated through a form-finding process.

The main challenge of engineering dry-assembled discrete shells is the design of a tessellation pattern that subdivides the shell into a discrete number of voussoirs. A comparison was made of three tessellation patterns: triangular, quadrangular and hexagonal. The choice for the tessellation pattern is different for every shell geometry. These properties of the shell that have to be taken into account when tessellating the shell include Gaussian curvature and whether the shell contains unsupported boundaries. Also, the maximum allowable mass of the voussoirs and aesthetic qualities influence the selecting of a tessellation pattern. Furthermore, complex algorithms might need to be developed for planarization and alignment to the force flow depending on the tessellation pattern that is selected and the shape of the shell.

The voussoirs needed to construct a shell will all have a unique geometry. When casted in traditional open moulds, a unique mould would be required for each voussoir. In order to considerably reduce the costs of the casting process, an adjustable mould was developed that can be used for the casting of voussoirs for varying geometry. In order to simplify the design of the adjustable mould, the structural performance of a convex-concave interface was explored. With a convex-concave interface, voussoirs can be joining at a varying angle which means that the voussoir joining angle should not be included as a parameter in the variable mould. However, due to the interfaces forming a hinge, the convex-concave interface proved to impair the structural performance of a shell when subjected to point loads at the nodes compared to the structural performance of conventional planar interfaces. The shell with the convex-concave interfaces performed better when subjected to distributed loads due to the interlocking feature of the interface which increased the resistance to out of plane shear forces. A special part of the mould was developed that allows for the casting of voussoirs with tongue and groove interfaces with a tongue that can be adjusted to the desired voussoir joining angle. The tongue and groove interfaces omit the hinging feature of the convex-concave interfaces while maintaining the resistance to out of plane shear forces due to its interlocking feature.

The final design of the adjustable mould can be used for the casting of voussoirs with tongue and groove interfaces and planar, convex intrados and extrados. The voussoirs of the shell structure of any shape can be made if the shape can be tessellated into planar and convex faces.

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As a result of using the adjustable mould to cast the voussoirs of a certain shell structure, spherical holes are present at the nodes of the shell. A node component was developed in the shape of a spherical segment that can be used to be placed in those holes. Also, the interlayers required to accumulate for tolerances in the cast glass voussoirs and to avoid peak stresses were developed.

A case study was introduced to serve as a context to which the gained knowledge from this thesis could be applied. For the case study, a cast glass shell structure that served as a courtyard covering for the Armamentarium in Delft was designed. The shell structure was developed in several steps. The first step a form finding processes in which a funicular shape was generated. The structural performance of this shape was validated with a FEM analysis. For a 100 mm thickness, the shell maintains its structural integrity when loaded by its dead load, a concentrated live load, wind load, snow load and combinations of these loads.

A triangular tessellation pattern was deemed the most suitable for subdividing the shell into multiple voussoirs. An algorithm was developed to assign either a tongue or groove interface to the edges of each voussoir. This was done in such a way that as a result, the radius of the spherical holes at the nodes was minimised. A list was generated that contained the following information for each voussoir: voussoir index number, interface types, edge lengths, voussoir joining angles and the adjacent voussoir index numbers. The data in this list serves as input data for the set-up of the adjustable mould.

In order to simplify the connection between the shell and the existing structure, a boundary node component was introduced to replace the regular node components at the boundary. This resulted in a boundary of the shell that can be placed in a support profile with a fixed cross-section that can be easily manufactured by extrusion. Finally, an assembly method was developed that requires a temporary formwork to be installed. The keystone voussoir required to be split in a top and bottom part to be placed. After placing, the parts are joined with a UV-curing adhesive. The resulting shell structure is fully transparent and fully recyclable with the exception of the keystone.

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12 Limitations and recommendations The tongue and groove joint can withstand a bending moment and thus prevents rotation between voussoirs. However, when the bending moment exceeds a certain value, the tongue will break off of and the joint will become a hinge. The bending moment at the point of failure should be quantified in order to be able to use this data for a structural analysis of the shell structure. This can be done with a FEM analyses of a detailed model at the joint level and should be verified with data gained from physical experiments.

An important part of the design and production process of a cast glass shell structure that starts with the form finding of the shell and ends with casting of the voussoirs using the adjustable mould, is the design of the tessellation pattern. Different criteria that have to be taken into account when designing the tessellation pattern have been stated in §7. An algorithm should be developed that generates a tessellation pattern while taking into account the stated criteria. When different criteria are conflicting, the algorithm should find a balance between the criteria or prioritize some criteria over other criteria.

For the structural analysis that is described in §10.2, a simplified model is used. The shell is modelled as a 100 mm thick monolithic glass shell and does not take into account that the shell is actually composed of a discrete number of glass voussoirs with elastic interlayers in between. This leads to results that do not represent the structural behaviour of the shell accurately. DEM analyses are used to accurately model the behaviour of dry-assembled blocky material. However, since DEM analyses are suitable for the evaluation of materials consisting of multiple, discrete particles, it is unlikely that this method is also suitable to accurately model the elastic behaviour of the interlayer. Current research is being done on the behaviour of the interlayer within a dry-assembled cast glass structural system. This research has the potential to provide the knowledge necessary for the accurate analysis of the structural behaviour of a discrete shell structures out of cast glass voussoir with an interlayer in between.

Some of the voussoirs of the case study have a very high mass and require a long annealing time. The high mass is due to the large thickness required for structural performance and due to the large face area of some voussoirs. This high mass can be reduced by improving the tessellation pattern to contain faces of a more uniform size. Another way to reduce the mass is by introducing an adjustable mould with a base plate that contains a protrusion. This would result in voussoirs with a cavity in the middle of the intrados or extrados. These voussoirs have a reduced mass while the moment of inertia is only slightly lowered. This would be a similar approach as the ‘reduce step’ of the Re3 Glass strategy described in §2.5 by the TU Delft Glass & Transparency Research Group (n.d.). Consequently, this approach would lead to a different distribution in mass along the shell that might have implications for the structural performance. However, the reduction of mass of the voussoirs by using a baseplate with a protrusion is an idea worth investigating if the mass cannot be reduced by improving the tessellation pattern.

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References Literature Adapa. (n.d.) Adaptive moulds for affordable, sustainable, and smarter production of curved surfaces. Aalborg, Denmark: Adapa.

Addis, B. (2007). Building: 3000 Years of Design Engineering and Construction. New York, NY: Phaidon Press.

Addis, B. (2014). Physical Modelling and Form Finding. In S. Adriaenssens, P. Block, D. Veenendaal, C. Williams (Eds.), Shell Structures for Architecture: Form Finding and Optimization (pp. 33-43). London, England: Routledge.

Adriaenssens, S., Block, P., Veenendaal. D., Williams, C. (2014). Introduction. In S. Adriaenssens, P. Block, D. Veenendaal, C. Williams (Eds.), Shell Structures for Architecture: Form Finding and Optimization (pp. 1-4). London, England: Routledge.

Amstock, J.S. (1997). Handbook of Glass in Construction. New York, NY: McGraw-Hill.

Aurik, M. (2017). Structural Aspects of an Arched Glass Masonry Bridge (Master’s thesis). Delft University of Technology, Delft, The Netherlands.

Aurik, M., Snijder, A., Noteboom, C., Nijsse, R., Louter, C. (2018). Experimental analysis on the glass- interlayer system in glass masonry arches. Glass Structures & Engineering, 3(2), 335-353. https://doi.org/10.1007/s40940-018-0068-7

Bamboo Tools. (n.d.) Adjustable Rectangular Slump Moulds. Retrieved 2019, April 2, from http://www.bambootools.com/moulds/SS001_detail.htm

Blandini, L., Sobek, W. (2014). 10 Jahre Stuttgarter Glasschale ‐ eine Zwischenbilanz. Stahlbau, 83, 77-86. doi:10.1002/stab.201490076

Block, P. (2009). Thrust Network Analysis (Doctoral dissertation). Massachusetts Institute of Technology, Cambridge, MA.

Block, P., Lachauer, L., Rippmann, M. (2010). Validating Thrust Network Analysis using 3D-printed, structural models. In Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2010, Shanghai (pp. 1086-1095).

Bristogianni, T., Nijsse, R., Oikonomopoulou, F., Veer, F.A. (2016). Design & Production of a Structural Cast Glass Element for a Transparent Dome. In A. Zingoni (Ed.), Insights and Innovations in Structural Engineering, Mechanics and Computation (pp. 1662-1667). doi:10.1201/9781315641645- 274

Bristogianni, T., Oikonomopoulou, F., Justino de Lima, C., Veer, F.A., Nijsse, R. (2018). Structural cast glass components manufactured from waste glass: Diverting everyday discarded glass from the landfill to the building industry. Heron, 63(1/2), 57-102.

Bristogianni, T., Oikonomopoulou, F., Veer, F.A., Snijder, A., Nijsse, R. (2017). Production and Testing of Kiln-cast Glass Components for an Interlocking, Dry-assembled Transparent Bridge. In Glass Performance Days 2017 Conference Proceedings (pp. 101-106). Tampere, Finland: Glass Performance Days, Glaston Finland Oy.

106

Carpenter Lowings. (n.d.). Glass Tube field. Retrieved 2019, January 6, from https://carpenterlowings.com/portfolio_page/glass-tube-field/

Chilton, J. (2012). Form-finding and fabric forming in the work of Heinz Isler. In J. Orr, M. Evernden, A. Darby, T. Ibell, (Eds.), Proceedings of the Second International Conference on Flexible Formwork, ICFF 2012 (pp. 84-91). Bath, England: BRE CICM.

Collins, G.R. (1963). Antonio Gaudi: Structure and Form. Perspecta, 8, 63-90. doi:10.2307/1566905

Cummings, K. (2001). Techniques of Kiln-Formed Glass (2nd ed.). Philadelphia, PA: University of Pennsylvania Press.

Dyer, T.A. (2014). Glass Recycling. In E. Worrell, M.A. Reuter (Eds.), Handbook of Recycling (pp. 191- 209). https://doi.org/10.1016/B978-0-12-396459-5.00014-3

Dyskin, A.V., Estrin, Y., Pasternak., E., Khor, H.C., Kanel-Belov, A.J. (2003). Fracture Resistant Structures Based on Topological Interlocking with Non-Planer Contacts. Advanced Engineering Materials, 5(3), 116-119. https://doi.org/10.1002/adem.200390016

Estrin, Y., Dyskin, A.V., Pasternak, E. (2011). Topological Interlocking as a Material Design Concept. Materials Science and Engineering, C31(6), 1189-1198. doi:10.1016/j.msec.2010.11.011

Eurostat. (2018). Packaging Waste Statistics. Retrieved 2019, January 7 from https://ec.europa.eu/eurostat/statistics- explained/index.php/Packaging_waste_statistics#Time_series_of_packaging_waste_generation_and _treatment

Faber, C. (1963). Candela: The Shell Builder. New York, NY: Reinhold

Fallacara, G., Resta, F., Spalluci, N., Tamboréro, L. (2011). The Vault of the Hôtel de Ville in Arles. Nexus Network Journal, 13(3), 599-629. https://doi.org/10.1007/s00004-011-0091-3

Festool. (2019). Catalogue 2019. Wendlingen, Germany: Festool GmbH

Granta Design Limited. (2018). CES EduPack software. Cambridge, England: Granta Design Limited

Greco, L. (2018). Optimized Quad Gridshell from Stress Field and Curvature Field. In C. Mueller, S. Adriaenssens (Eds.), Proceedings of the IASS symposium 2018, Creativity in Structural Design (pp. 1- 8).

Heyman, J. (1995). The Stone Skeleton. Cambridge, England: Cambridge University Press.

Hobbelman, G. J., Timm, B., Veer, F. A., van Swieten, P. M. J. (2002). The design of a full glass dome using a new glass/polymer composite material. In J.B. Obrebski (Ed.), Proceedings of the International IASS Symposium on lightweight structures in civil engineering (pp. 828-831). Warsaw, Poland: Micro-publisher Jan B. Obrebski.

Jacobs, S.F., Shough, D., Connors, C. (1984). Thermal Expansion Uniformity of Materials for Large Telescope Mirrors. Applied Optics, 23(23), 4237-4244. https://doi.org/10.1364/AO.23.004237

Janssens, E. (2018). The Glass Dome (Master’s thesis). Delft University of Technology, Delft, The Netherlands.

107

Kaiser, N.D., Behr, R.A., Minor, J.E., Dharani, L.R., Ji, F., Kremer, P.A. (2000). Impact Resistance of Laminated Glass Using “Sacrificial Ply” Design Concept. Journal of Architectural Engineering, 6(1), 24- 34. https://doi.org/10.1061/(ASCE)1076-0431(2000)6:1(24)

Kao, G.T.C., Körner, A., Sonntag, D., Nguyen, L., Menges, A., Knippers, J. (2017). Assembly-aware design of masonry structures: a computational approach. In A. Bögle, M. Grohmann (Eds.), Proceedings of the IASS Annual Symposium 2017. (pp. 1- 10).

Kilian, A., Ochsendorf, J. (2005). Particle-Spring Systems for Structural Form Finding. Journal of the International Association for Shell and Spatial Structures, 46(148), 77-84.

Kromoser, B. Huber, P. (2016). Pneumatic Formwork Systems in Structural Engineering. Advances in Materials Science and Engineering, 2016(6), 1-13. https://doi.org/10.1155/2016/4724036

Lillie, H.R. (1952). A Method for Measuring the Flow Point of Glass. Journal of the American Ceramic Society, 35(6), 149-155. doi:10.1111/j.1151-2916.1952.tb13089.x

López López, D., Domènech Rodríguez, M., Palumbo Fernández, M. (2014). “Brick-topia”, the thin- tile pavilion. Case Studies in Structural Engineering, 2, 33-40. https://doi.org/10.1016/j.csse.2014.09.001

Meyer, C., Sheer, M.H. (2005). Do Concrete Shells Deserve Another Look? Concrete International, 27(10), 43-50.

Minke, G. (2012). Building with Earth: Design and Technology of a Sustainable Architecture. Basel, Switzerland: Birkhäuser.

Nijsse, R., Wenting, R. (2014). Designing and Constructing Corrugated Glass Facades. Journal of Facade Design and Engineering, 2, 123–131. doi:10.3233/FDE-140014

O’Callaghan, J. (2010). Thinking Big with Structural Glass. In U. Knaack, T. Klein (Ed.), The Future Envelope 3: Facades, the Making of (pp. 15-24). doi:10.3233/978-1-60750-672-0-15

Oikonomopoulou, F., Bristogianni, T., Barou, L., Veer, F.A., Nijsse, R. (2018a). The potential of cast glass in structural applications. Journal of Building Engineering, 20, 213-234. https://doi.org/10.1016/j.jobe.2018.07.014

Oikonomopoulou, F., Bristogianni, T., Barou, L., Jacobs, E., Frigo, G., Veer, F.A., Nijsse., R. (2018b). Interlocking cast glass components, Exploring a Demountable Dry-Assembly Structural Glass System. Heron, 63(1/2), 103-138.

Oikonomopoulou, F., Bristogianni, T., Veer, F.A., Nijsse, R. (2017). The Construction of the Crystal House Façade: Challenges and Innovations. Glass Structures & Engineering, 1-22. https://doi.org/10.1007/s40940-017-0039-4

Oikonomopoulou, F., Veer, F., Bristogianni, T., Barou, L. (2019). Dry interlayers out of cast polyurethane rubber for interlocking cast glass structures: experimental exploration and validation. Manuscript in preparation.

O’Regan, C. (2014). Structural Use of Glass in buildings (2nd ed.). London, England: The Institution of Structural Engineers.

Oshima, K.T. (2012, December). Optical Glass House. Architectural Review, 232(1390) 40-45

108

Oval, R., Rippmann, M., Van Mele, T., Baverel, O., Block, P. (2017). Patterns for Masonry Vault Design. In A. Bögle, M. Grohmann (Eds.), Proceedings of the IASS Annual Symposia, IASS 2017 Hamburg Symposium: Computational Design. (pp. 1-10).

Paech, C., Göppert, K. (2008). Innovative Glass Joints – The 11 March Memorial in Madrid. In C. Louter, F. Bos, F.A. Veer (Eds.), Proceedings of Challenging Glass: Conference on Architectural and Structural Applications of Glass. (pp. 111-118). Delft, The Netherlands, IOS Press.

Pellis, D., Pottmann, H. (2018). Aligning prinicipal stresses and curvature directions. In L. Hesselgren, A. Kilian, S. Malek, K.G. Olsson, O. Sorkine-Hornung, C. Williams (Eds.), Advances in Architectural Geometry 2018. (pp. 34-53). Vienna, Austria: Klein

Piano, R. (1969, April). Progettazione sperimentale per strutture a guscio - Experimental project of shell structures. Casabella, 335, 38–49.

Piker, D. (2013). Kangaroo: Form Finding with Computational Physics. Architectural Design, 83(2), 136-137. doi:10.1002/ad.1569

Pilkington, L.A.B. (1969). The Float Glass Process. Proceedings of the Royal Society of London, 314(1516), 1-25. https://doi.org/10.1098/rspa.1969.0212

Preisinger, C. (2013). Linking Structure and Parametric Geometry. Architectural Design, 83(2), 110- 113. doi:10.1002/ad.1564

Rankine, W.J.M. (1889). A Manual of Civil Engineering (17th ed.). London, England: Charles Griffin and Company.

Rippmann, M. (2016). Funicular Shell Design: Geometric approaches to form finding and fabrication of discrete funicular structures (Doctoral dissertation). ETH Zurich, Zurich, Switzerland.

Rippmann, M., Block, P. (2018). Computational Tessellation of Freeform, Cut-Stone Vaults. Nexus Network Journal, 20(3), 545-566. doi:10.1007/s00004-018-0383-y

Rippmann, M. Van Mele, T., Popescu, M., Augustynowicz, E., Echenagucia, T., Barentin, C., Frick, U., Block, P. (2016). The Armadillo Vault, Computational Design and Digital Fabrication of a Freeform Stone Shell. In S. Adriaenssens, F. Gramazio, M. Kohler, A. Menges, M. Pauly (Eds.), Advances in Architectural Geometry (pp. 344-363). Zürich, Switzerland: vdf Hochschulverlag.

Roeder, E. (1971). Extrusion of Glass. Journal of Non-Crystalline Solids, 5, 377-388.

Schipper, H. R., Eigenraam, P., Grünewald, S., Soru, M., Nap, P., Van Overveld, B., Vermeulen, J. (2015). Kine-Mould: Manufacturing technology for curved architectural elements in concrete. In J. Coenders, A. Borgart, A. Pronk (Eds.), Proceedings of the International Society of Flexible Formwork (ISOFF) Symposium. Amsterdam, The Netherlands. KIVI.

Schittich, C., Staib, G., Balkow, D., Schuler, M., Sobek, W. (Eds.). (1999). Glass Construction Manual. Basel, Switzerland: Birkhäuser.

Shand, E.B. (1958). Glass Engineering Handbook (2nd ed.). New York, NY: McGraw-Hill.

Snijder, A., Nijsse, R., Louter, C. (2018). Building and Testing Lenticular Truss Bridge with Glass- Bundle Diagonals and Cast Glass Connections. In C. Louter, F. Bos, J. Belis, F. Veer, R. Nijsse (Eds.), Proceedings of the Challenging Glass Conference 6 (CGC 6): International Conference on Architectural and Structural Applications of Glass (pp. 647-660). doi:10.7480/cgc.6.2185

109

Snijder, A., Smits, J., Bristogianni, T., Nijsse, R. (2016). Design and Engineering of a Dry Assembled Glass Block Pedestrian Bridge. In J. Belis, F. Bos, C. Louter (Eds.), Proceedings of the Challenging Glass Conference 5 (CGC 5): International Conference on Architectural and Structural Applications of Glass (pp. 547-556). https://doi.org/10.7480/cgc.5.2281

Stanworth, J.E. (1950). Physical Properties of Glass. London, England: Oxford University Press.

Tang, G. (2015). An Overview of Historical and Contemporary Concrete Shells, their Construction and Factors in their general disappearance. International Journal of Space Structures, 30(1), 1-12.

Tomlow, J. (2011). Gaudi’s reluctant attitude towards the inverted catenary. Engineering History and Heritage, 164(4), 219-233. http://dx.doi.org/10.1680/ehah.2011.164.4.219

TU Delft, Glass & Transparency Research Group. (n.d.). Re3 Glass. Retrieved 2019, February 11 from https://www.tudelft.nl/bk/over-faculteit/afdelingen/architectural-engineering-and- technology/organisatie/leerstoelen/structural-design/glass-transparency-research-group/research- topics/re3-glass/

Van Mele, T., McInerney, J., DeJong, M.J., Block, P. (2012). Physical and Computational Discrete Modelling of Masonry Vault Collapse. In. J Jasieńko (Ed.), Proceedings of the 8th International Conference on Structural Analysis of Historical Constructions (pp. 2552-2560). Wroclaw, Poland: DWE.

Veer, F.A., Wurm, J., Hobbelman, G.J. (2003). The Design, Construction and Validation of a Structural Glass Dome. In J. Vitkala (Ed.), Proceedings of the Glass Processing Days 2003. (pp. 156-158). Tampere, Finland: Tamglass.

Wagemans, L.A.G., Soons, F.A.M., Van Raaij, B.P.M. (2014). Quick Reference (Rev. ed.). Delft, The Netherlands: TU Delft

Wang, W., Liu, Y. (2009). A Note on Planar Hexagonal Meshes. In I.Z. Emiris, F. Sottile, T. Theobald (Eds.), Nonlinear Computational Geometry. The IMA Volumes in Mathematics and its Applications, 151 (pp. 221-233). doi: 10.1007/978-1-4419-0999-2_9

Wigginton, M. (1996). Glass in Architecture. London, England: Phaidon Press.

Williams, C. (2014). What is a shell? In S. Adriaenssens, P. Block, D. Veenendaal, C. Williams (Eds.), Shell Structures for Architecture: Form Finding and Optimization (pp. 21-31). London, England: Routledge.

Zessin, J., Lau, W., Ochsendorf, J. (2010). Equilibrium of cracked masonry domes for the analysis of masonry structures. Proceedings of the Institution of Civil Engineers - Engineering and Computational Mechanics, 163(3), 135–145. doi:10.1680/eacm.2010.163.3.135 Figures Figures not referenced in this list are property of the author

Figure 2.3 Tom Belger, Liverpool Echo, https://www.liverpoolecho.co.uk/incoming/gallery/pilkington-st-helens-look-inside- 10509794 Figure 2.6 Colorminium, https://colorminium.com/news/posts/laminated-architectural-glass/ Figure 2.7 Oikonomopoulou et al. (2018a) Figure 2.8 Oikonomopoulou et al. (2018a) Figure 2.9 Oikonomopoulou et al. (2018a) 110

Figure 2.10 Corning Museum of Glass, https://www.cmog.org/article/reflections-glass- telescope-mirrors Figure 2.11 TechMiny, https://techminy.com/extrusion/ Figure 2.12 Tectonica-online, http://www.tectonica-online.com/products/schott/conturax- borosilicate-glass-tubing/2879/ Figure 2.13 ROAS, https://roas.com.tr/kurumsal-kimlik-ve-ic-mekan/bcj153_n524-1440x960/ Figure 2.14 Origin Architectural https://originarchitectural.co.uk/glass-clamps-and-adapters/ Figure 2.15 Weller, http://ebookcentral.proquest.com/lib/delft/detail.action?docID=1075600 Figure 2.16 Eckersley O’Callaghan, https://www.eocengineers.com/en/projects/vidre-slide-274 Figure 2.17 Sarah Blee, http://sarahblee.com/sarah_blee_portfolio.html Figure 2.18a Veer et al. (2003) Figure 2.18b Blandini and Sobek (2014) Figure 2.19 Hiroshi Nakamura & NAP Co., Ltd http://www.nakam.info/en/ Figure 2.20 Usuario Barcex, https://es.m.wikipedia.org/wiki/Archivo:Madrid_- _Puerta_de_Atocha_-_Monumento_11-M_-_20070324a.jpg Figure 2.21 Oikonomopoulou et al. (2018a) Figure 2.22 Bart van Vlijmen, https://bartvanvlijmen.nl/crystal-house-amsterdam/ Figure 2.23 Aart van Bezooijen, https://www.core77.com/posts/81377/Dutch-Design-Week- Highlights-New-Material-Award Figure 2.24 Aurik (2017) Figure 2.25 Janssens (2018) Figure 2.26 Waagner Biro, https://www.waagner-biro.com/en/divisions/steel-glass- structures/references/reference/tower-place Figure 2.27 Snijder et al. (2018) Figure 2.28 Bristogianni et al. (2018) Figure 2.29 TU Delft, Glass & Transparency Research Group (n.d.) Figure 3.1a Bill Cotter, https://savingplaces.org/stories/photos-lost-relics-1964-65-worlds- fair#.XNQw8o4zaUk Figure 3.1b Ciudad FCC http://www.ciudadfcc.com/en/-/museo-de-las-artes-y-las-ciencias-y- oceanografico-valencia- Figure 3.1c Yoshito Isono, https://structurae.net/photos/96731-deitingen-service-station Figure 3.7 Addis (2007) Figure 3.8 Collins (1963) Figure 3.9 Build LLC, http://blog.buildllc.com/2009/04/heinz-isler-a-few-important-things/ Figure 3.10 Kilian & Ochsendorf (2005) Figure 3.11 Kilian & Ochsendorf (2005) Figure 3.12 Hidden Architecture http://hiddenarchitecture.net/bolsa-de-valores-de-mexico/ Figure 3.13 Garcia Fritz, https://doarchvaultingspace2015.wordpress.com/2015/10/08/catalan- vault-_-how-to-build-the-vault/ Figure 3.14 Dezeen, https://www.dezeen.com/2016/12/01/video-interview-thomas-granier- nubian-vault-transform-housing-future-africa-movie/ Figure 3.16a Nick, https://commons.wikimedia.org/wiki/File:Appia_antica_2-7-05_003.jpg Figure 3.16b Lock-Block Ltd, http://www.lockblock.com/arches.php Figure 3.17 のほほーんとのほほーん, https://www.tripadvisor.nl/Attraction_Review-g187211- d8815025-Reviews-Hotel_de_Ville- Arles_Bouches_du_Rhone_Provence_Alpes_Cote_d_Azur.html#photos;aggregationI d=101&albumid=101&filter=7&ff=247168862 Figure 3.18 Rippmann & Block (2018) Figure 3.19 Author, based on Rankine (1889) Figure 3.20 Rippman et al. (2016) Figure 3.21a Rippman et al. (2016), edited by the author

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Figure 3.21b Rippman et al. (2016) Figure 3.22 Rippman et al. (2016) Figure 6.1 BambooTools (n.d.) Figure 6.4a Piano (1969) Figure 6.4b Schippers et al. (2015) Figure 7.2 Wang & Liu (2009) Figure 10.1a Foster + Partners https://www.fosterandpartners.com/projects/great-court-at-the- british-museum/ Figure 10.1b Ney & Partners https://www.ney.partners/nl/project/glass-roof-dutch-maritime- museum.html Figure 10.2 cepezed projects b.v. http://www.arsenaaldelft.nl/arsenaaldelft-anterieure- overeenkomst-ondertekend/

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Appendix A: Interface experiment results Test 1 1A convex-concave interfaces 20

15

10

5

Standardforce [N] 0 -5 0 5 10 15 20 25 30 -5 Deformation [mm]

1A planar interfaces 40 35 30 25 20 15 10

Standardforce [N] 5 0 -5 -5 0 5 10 15 20 25 Deformation [mm]

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1B concave-convex interfaces 30 25 20 15 10

Standardforce [N] 5 0 -5 0 5 10 15 20 25 30 35 40 Deformation [mm]

1B planar interfaces 300 250 200 150 100

50 Standardforce [N] 0 0 5 10 15 20 -50 Deformation [mm]

1C convex-concave interfaces 35 30 25 20 15 10

5 Standardforce [N] 0 -5 -5 0 5 10 15 20 25 30 35 40 Deformation [mm]

114

1C planar interfaces 80 70 60 50 40 30 20 Standardforce [N] 10 0 -2 0 2 4 6 8 10 12 14 16 Deformation [mm]

1D convex-concave interfaces 25

20

15

10

5 Standardforce [N] 0 -5 0 5 10 15 20 25 30 35 40 -5 Deformation [mm]

1D planar interfaces 100

80

60

40

20 Standardforce [N] 0 -2 0 2 4 6 8 10 12 14 16 -20 Deformation [mm]

115

1E convex-concave interfaces 200

150

100

50 Standardforce [N]

0 -5 0 5 10 15 20 25 30 Deformation [mm]

1E planar interfaces 600 500 400 300 200

Standardforce [N] 100 0 0 2 4 6 8 10 12 Deformation [mm]

Test 2 2 convex-concave interfaces 1200 1000 800 600 400

Standardforce [N] 200 0 -2 0 2 4 6 8 10 12 Deformation [mm]

116

2 planar interfaces 100

80

60

40

Standardforce [N] 20

0 -1 0 1 2 3 4 5 6 7 8 Deformation [mm]

117

Appendix B: Mould manufacturing Tongue edge module 0. placing the blank on a magnetic workhold with a spoilboard in between

1. drilling + tapping Tools: drill + spiral flute tap (only the holes where the protractor will be attached have to be tapped)

2. milling Tool: end mill

3. milling Tool: ball nose end mill

118

4. milling Tool: T-slot cutter

Groove edge module 0. placing the blank on a magnetic workhold with a spoilboard in between

1. Operation: drilling Tool: drill

2. milling Tool: end mill

119

3. milling Tool: ball nose end mill

4. milling Tool: T-slot cutter

Tongue vertex module 0. Place the blank in the jaw chuck

1. turning Tool: single-point cutting tool

120

2. drilling + tapping Tools: drill + spiral flute tap (tapping is only required if a diagonal has to be fixed to the node component)

3: milling Tool: end mill

4. milling Tool: ball nose end mill

5. parting Tool: parting tool

121

Groove vertex module 0. Place the blank in the jaw chuck

1. turning Tool: single-point cutting tool

2. drilling + tapping Tools: drill + spiral flute tap (tapping is only required if a diagonal has to be fixed to the node component)

3: milling Tool: end mill

122

4. milling Tool: ball nose end mill

5. parting Tool: parting tool

Tongue cylinder 0. Place the blank in the jaw chuck

1. Drilling + tapping Tools: drill + spiral flute tap

123

2. Clamp other end of the workpiece

3. turning Tool: single-point cutting tool

4. turning (facing) Tool: single-point cutting tool

5: milling Tool: end mill

124

6: milling Tool: ball nose end mill

7: milling Tool: end mill (only required when voussoirs with large interior angles need be casted)

8. parting Tool: parting tool

Tongue insert 0. Place the blank in the jaw chuck

125

1. turning Tool: single-point cutting tool

2. turning (facing) Tool: single-point cutting tool

3: milling Tool: end mill

4: milling Tool: ball nose end mill

126

5. parting Tool: parting tool

127

Appendix C: FEM analysis results Loadcase 1

Displacement

Principal stress 1, bottom layer

Principal stress 1, top layer

128

Principal stress 2, bottom layer

Principal stress 2, top layer Loadcase 2

Displacement

129

Principal stress 1, bottom layer

Principal stress 1, top layer

Principal stress 2, bottom layer

130

Principal stress 2, top layer Loadcase 3

Displacement

Principal stress 1, bottom layer

131

Principal stress 1, top layer

Principal stress 2, bottom layer

Principal stress 2, top layer

132

Loadcase 4

Displacement

Principal stress 1, bottom layer

Principal stress 1, top layer

133

Principal stress 2, bottom layer

Principal stress 2, top layer Loadcase 5

Displacement

134

Principal stress 1, bottom layer

Principal stress 1, top layer

Principal stress 2, bottom layer

135

Principal stress 2, top layer

136

Appendix D: Adjustable mould input data Edge 1 Edge 2 Edge 3 i Type l αvj iav Type l αvj iav Type l αvj iav [mm] [°] [mm] [°] [mm] [°] 0 G 361.5 - 1 T 562.7 1.8 87 G 387.7 - - 1 G 390.6 - - G 417.2 - 88 T 361.5 9.7 0 2 G 548.5 - 87 T 619.2 4.6 89 G 396.5 - - 3 G 451.6 - - T 437.1 -2.6 90 G 451.5 - 88 4 G 599 - 89 T 556.3 7.5 98 G 380.5 - - 5 G 460.2 - - T 456.6 -2 93 G 480.4 - 90 6 G 463.3 - - T 468.7 -1.3 100 G 494.3 - 93 7 G 486.9 - - G 479.8 - 107 G 498.8 - 100 8 G 494.2 - - T 492.6 -0.8 110 T 498.2 1 107 9 G 502.6 - - T 501.5 -1 120 G 503.1 - 110 10 G 509.7 - - G 512.9 - 131 G 512 - 120 11 T 454.4 4.4 118 G 442.8 - 138 G 419.4 - - 12 G 514.3 - - G 526.1 - 140 T 521 0.6 131 13 G 515.1 - - G 540.3 - 149 T 529.5 0.6 140 14 G 512.3 - - G 554.5 - 160 T 537 0.2 149 15 T 484.4 2.7 138 G 462 - 165 G 426.6 - - 16 G 506.3 - - G 567.6 - 173 T 543.1 0.3 160 17 G 497.8 - - G 578.4 - 186 T 547.2 0.1 173 18 T 504.1 2 165 T 480.9 -1.5 196 G 446.3 - - 19 G 487.4 - - G 585 - 195 T 548.2 0 186 20 G 476.1 - - G 584.7 - 210 T 543.1 -0.3 195 21 G 464.6 - - G 576.7 - 223 T 531 -0.4 210 22 G 508.4 - 196 T 499.9 -1.2 234 G 473.1 - - 23 G 445 - - G 582.5 - 236 T 541.6 -0.4 223 24 G 391.2 - - G 588.2 - 251 T 577.4 -0.4 236 25 G 514.2 - 234 T 513.3 -1 278 G 484 - - 26 G 523 - 278 G 523 - 323 G 494.9 - - 27 T 531.7 0.8 323 G 531.5 - 369 G 498.7 - - 28 G 360.3 - - T 517.4 0 383 G 514.7 - 351 29 T 540 0.7 369 G 539.8 - 410 G 497.8 - - 30 G 472.3 - - G 565 - 422 G 581.2 - 383 31 T 547.6 0.5 410 G 547.6 - 34 G 495.3 - - 32 G 495.9 - - G 600.6 - 457 T 601.1 0.3 422 33 T 554.1 0.4 34 G 554.2 - 36 G 493 - - 34 T 494.1 3.2 453 G 554.1 - 33 T 547.6 -0.4 31 35 G 505.9 - - G 604.3 - 500 T 599.7 0.4 457 36 T 492.2 3.1 492 G 559.8 - 37 T 554.2 -0.3 33 37 T 559.8 0.3 36 G 559.9 - 530 G 491.2 - - 38 G 518.6 - - G 596.5 - 544 T 592.1 0.3 500 39 T 564.6 0.2 530 G 564.6 - 574 G 489.7 - -

137

40 G 527.7 - - G 588.7 - 586 T 585.7 0.2 544 41 T 568.5 0.1 574 G 568.3 - 617 G 488.2 - - 42 G 533.8 - - G 583 - 630 T 581.4 0.1 586 43 T 571.4 0.1 617 G 571 - 653 G 486.8 - - 44 G 537 - - G 578.5 - 673 T 578.1 0.1 630 45 T 573.4 0 653 G 572.7 - 685 G 485.2 - - 46 G 537.6 - - G 574.5 - 715 T 575.2 0 673 47 T 574.3 -0.1 685 G 573.3 - 729 G 483.5 - - 48 G 535.4 - - T 569.8 0.1 759 G 571.6 - 715 49 T 574.1 -0.1 729 G 572.9 - 773 G 481.8 - - 50 G 530.5 - - T 563.8 0.2 803 G 566.8 - 759 51 T 572.6 -0.2 773 G 571.3 - 809 G 480.1 - - 52 G 522.8 - - T 555.1 0.3 847 G 559.1 - 803 53 T 569.7 -0.3 809 G 568.4 - 849 G 478.6 - - 54 T 565.2 -0.4 849 G 564 - 891 G 477.4 - - 55 G 511.1 - - T 541.6 0.3 895 G 546.1 - 847 56 T 559 -0.4 891 G 558.1 - 929 G 476.4 - - 57 G 497.7 - - T 521.4 0.3 935 G 523.9 - 895 58 T 551.2 -0.6 929 G 550.8 - 972 G 475.1 - - 59 G 480.8 - - T 495.6 0.3 978 G 493.8 - 935 60 T 541.9 -0.6 972 T 542.3 0.8 1016 G 471.6 - - 61 G 531.2 - 1016 T 533.5 1 1056 G 464.2 - - 62 G 516.9 - 1056 T 525.9 1.2 1094 G 453.8 - - 63 T 589.8 6.2 1079 G 417.7 - - G 527.4 - 1108 64 G 499.4 - 1094 G 521.7 - 1137 G 432.3 - - 65 T 482.8 -1.3 1137 G 514.7 - 1167 G 375.8 - - 66 G 428.6 - 1133 G 330.1 - - T 483.7 0.2 1138 67 G 503 - 1138 G 384.6 - - T 550.3 0.2 1143 68 G 590 - 1143 G 405.4 - - T 617.2 -1 1150 69 G 630.3 - 1150 G 425.9 - - T 658 -0.1 1155 70 T 449.6 -0.3 1167 G 463.6 - 1195 G 331.4 - - 71 G 654.4 - 1155 G 424.4 - - T 663.7 -0.1 1173 72 G 661.4 - 1173 G 430.3 - - T 648.4 -0.4 1172 73 G 632.6 - 1172 G 442.1 - - T 599.8 -0.6 1182 74 T 402.7 -0.9 1195 G 394.4 - 1212 G 338.6 - - 75 G 622.5 - 1182 G 499.1 - - T 579.8 0.3 1191 76 G 603.7 - 1191 G 509.7 - - T 563.6 0.2 1200 77 G 584.9 - 1200 G 513.6 - - G 553.4 - 1207 78 T 570.8 0 1207 G 510.5 - - G 542 - 1214 79 T 557.3 -0.8 1214 G 504.3 - - G 532.5 - 1219 80 G 549.1 - 1219 G 494.3 - - T 525.3 1.2 1222 81 G 552.3 - 1222 G 480.7 - - T 523.2 1 1225 82 G 556.6 - 1225 G 461.9 - - T 534.6 1.9 1226 83 G 587.3 - 1226 G 440.7 - - T 566.6 2.9 1227

138

84 G 629.2 - 1227 G 432.6 - - T 599.7 4.6 1228 85 G 685.4 - 1228 G 444.3 - - T 623.9 9.2 1229 86 G 711.2 - 1229 G 488.2 - - T 537.4 20.2 1230 87 G 562.7 - 0 G 375.6 - 92 T 548.5 10.2 2 88 T 451.5 4.4 3 G 466.5 - 91 T 417.2 -1.1 1 89 G 619.2 - 2 T 359.1 5.7 96 T 599 6.9 4 90 T 480.4 3.1 5 G 463.3 - 94 G 437.1 - 3 91 T 466.5 5.5 88 T 424.1 -2.4 95 G 469.1 - 92 92 T 469.1 6.5 91 G 510 - 97 T 375.6 3.3 87 93 T 494.3 1.9 6 G 465.8 - 101 G 456.6 - 5 94 T 463.3 5.7 90 T 459.1 -2.1 102 G 508.8 - 95 95 T 508.8 4.2 94 G 479.5 - 105 G 424.1 - 91 96 T 515.4 7.4 97 G 503.6 - 103 G 359.1 - 89 97 T 510 7.6 92 T 414.5 -2.4 106 G 515.4 - 96 98 G 556.3 - 4 T 391 2.7 104 T 528.9 2.3 99 99 G 528.9 - 98 T 369.1 10.2 117 G 380.8 - - 100 T 498.8 1.6 7 G 466.5 - 108 G 468.7 - 6 101 T 465.8 5.6 93 G 488.5 - 109 G 532.7 - 102 102 T 532.7 3.3 101 G 471.7 - 111 G 459.1 - 94 103 T 503.6 7.3 96 T 415.5 -2.6 116 G 514.6 - 104 104 T 514.6 7.7 103 G 463.3 - 119 G 391 - 98 105 T 479.5 7.9 95 T 450.8 -3.4 112 G 504.8 - 106 106 T 504.8 6.5 105 G 484.9 - 115 G 414.5 - 97 107 G 498.2 - 8 T 478.8 4.2 113 T 479.8 -1.2 7 108 T 466.5 4.7 100 G 508.1 - 114 T 541.2 3.2 109 109 G 541.2 - 108 T 466.7 6 121 T 488.5 -2.4 101 110 T 503.1 1 9 G 492.9 - 123 G 492.6 - 8 111 T 471.7 6.5 102 T 477.7 -2.7 122 G 515.1 - 112 112 T 515.1 5.7 111 G 480.6 - 125 G 450.8 - 105 113 G 478.8 - 107 G 516.3 - 124 T 547.1 2.4 114 114 G 547.1 - 113 T 467.9 5.3 129 T 508.1 -2 108 115 T 484.9 7.6 106 T 443.8 -3.5 126 G 493 - 116 116 T 493 7.6 115 G 486.5 - 128 G 415.5 - 103 117 G 369.1 - 99 T 421.1 -4 118 G 336 - - 118 T 449.7 6.4 119 G 454.4 - 11 G 421.1 - 117 119 T 463.3 5.6 104 G 420.5 - 127 G 449.7 - 118 120 T 512 1.1 10 G 503 - 132 G 501.5 - 9 121 G 466.7 - 109 T 502.3 -2.8 130 G 523.3 - 122 122 T 523.3 3.8 121 G 477 - 134 G 477.7 - 111 123 T 492.9 3.6 110 G 517.8 - 133 T 536.5 1.8 124 124 G 536.5 - 123 T 471.6 5 136 T 516.3 -1.5 113 125 T 480.6 7.5 112 T 468.1 -3.1 135 G 496.9 - 126 126 T 496.9 6.6 125 G 490.1 - 141 G 443.8 - 115 127 T 467 7 128 G 490.8 - 139 T 420.5 -2.3 119

139

128 T 486.5 6.3 116 G 440.9 - 142 G 467 - 127 129 G 467.9 - 114 T 524.7 -1.8 137 G 540.5 - 130 130 T 540.5 4 129 G 477.9 - 147 G 502.3 - 121 131 G 521 - 12 T 508.4 3.5 143 T 512.9 -0.7 10 132 T 503 3.4 120 G 521.8 - 144 T 534.2 1.3 133 133 G 534.2 - 132 T 486.2 4.6 145 T 517.8 -1.3 123 134 T 477 7 122 T 493.2 -3.3 148 G 504.8 - 135 135 T 504.8 6.2 134 G 486.1 - 152 G 468.1 - 125 136 G 471.6 - 124 G 542 - 146 T 549.7 2.7 137 137 G 549.7 - 136 T 473.5 5.8 158 G 524.7 - 129 138 T 436.2 6.3 139 G 484.4 - 15 T 442.8 -2.6 11 139 T 490.8 4.4 127 G 442.1 - 154 G 436.2 - 138 140 G 529.5 - 13 T 509.3 3.5 150 T 526.1 -0.7 12 141 T 490.1 6.9 126 G 465 - 153 G 472.6 - 142 142 T 472.6 7.1 141 G 496.5 - 155 T 440.9 -3.1 128 143 G 508.4 - 131 G 530.4 - 151 T 537 1 144 144 G 537 - 143 T 498.1 4 156 T 521.8 -0.6 132 145 G 486.2 - 133 G 542.8 - 157 T 551.2 2.3 146 146 G 551.2 - 145 T 470.1 4.9 167 T 542 -1.9 136 147 T 477.9 6.3 130 T 514.2 -2.3 159 G 518.3 - 148 148 T 518.3 4.4 147 G 487.9 - 163 G 493.2 - 134 149 G 537 - 14 G 506.7 - 161 T 540.3 -0.2 13 150 G 509.3 - 140 T 541.6 -0.4 162 T 542.9 0.7 151 151 G 542.9 - 150 T 502.8 4 169 T 530.4 -0.8 143 152 T 486.1 6.6 135 G 483.6 - 164 G 482 - 153 153 T 482 6.8 152 G 501.3 - 171 T 465 -3.4 141 154 T 451.6 6.2 155 G 511.9 - 166 T 442.1 -2.5 139 155 T 496.5 5.1 142 G 459.6 - 172 G 451.6 - 154 156 G 498.1 - 144 G 541.9 - 170 T 551.2 2 157 157 G 551.2 - 156 T 482.9 4.7 176 T 542.8 -1.4 145 158 G 473.5 - 137 T 537.3 -2.9 168 G 528 - 159 159 T 528 4.7 158 T 481.6 5.9 178 G 514.2 - 147 160 G 543.1 - 16 G 501.4 - 174 T 554.5 -0.3 14 161 T 506.7 3.3 149 T 553.7 -0.3 175 G 550 - 162 162 T 550 0.7 161 G 502.7 - 180 G 541.6 - 150 163 T 487.9 6.7 148 T 504.9 -3.1 179 G 493.9 - 164 164 T 493.9 6 163 G 498.4 - 182 T 483.6 -3.1 152 165 T 437.6 5.5 166 G 504.1 - 18 T 462 -1.9 15 166 T 511.9 3.5 154 G 460 - 184 G 437.6 - 165 167 G 470.1 - 146 T 556 -1.8 177 G 540.4 - 168 168 T 540.4 3.7 167 T 482.5 5.9 191 G 537.3 - 158 169 G 502.8 - 151 G 547.6 - 181 T 556.3 1.1 170 170 G 556.3 - 169 T 494.7 4.4 187 T 541.9 -0.9 156 171 T 501.3 5.7 153 G 479.4 - 183 G 463.5 - 172

140

172 T 463.5 6.4 171 G 513.7 - 185 T 459.6 -2.7 155 173 G 547.2 - 17 G 494 - 189 T 567.6 -0.2 16 174 T 501.4 3.4 160 T 565.9 -0.1 190 G 556.9 - 175 175 T 556.9 0.2 174 G 499.3 - 193 G 553.7 - 161 176 G 482.9 - 157 G 555.8 - 188 G 548.2 - 177 177 T 548.2 2.6 176 T 477.2 5.6 202 G 556 - 167 178 G 481.6 - 159 T 524.5 -2.7 192 G 508.8 - 179 179 T 508.8 5.2 178 G 497.5 - 198 G 504.9 - 163 180 T 502.7 3.7 162 T 556.7 -0.1 194 T 563.7 1 181 181 G 563.7 - 180 T 498.8 4.2 200 T 547.6 -0.7 169 182 T 498.4 6.1 164 G 498.9 - 199 G 474.4 - 183 183 T 474.4 6.4 182 G 510.7 - 207 T 479.4 -2.8 171 184 G 447.2 - 185 T 526.6 2.9 197 T 460 -2.1 166 185 T 513.7 4.1 172 G 477.7 - 206 T 447.2 5.5 184 186 G 548.2 - 19 G 485.1 - 204 T 578.4 0 17 187 G 494.7 - 170 G 556.6 - 201 T 561.6 2.3 188 188 G 561.6 - 187 G 486.6 - 211 T 555.8 -1.4 176 189 T 494 3.5 173 T 577.2 0.5 205 G 563.5 - 190 190 T 563.5 0.2 189 T 493.9 3.7 208 G 565.9 - 174 191 G 482.5 - 168 T 543.4 -2.1 203 G 521.3 - 192 192 T 521.3 4.6 191 T 494.9 5.7 213 G 524.5 - 178 193 T 499.3 3.9 175 T 566.7 -0.4 209 G 571.7 - 194 194 T 571.7 0.5 193 G 498.8 - 215 G 556.7 - 180 195 G 543.1 - 20 G 475.2 - 217 T 585 0.4 19 196 G 443.4 - 197 T 508.4 1.5 22 G 480.9 - 18 197 G 526.6 - 184 T 479.4 -1.7 219 T 443.4 4.8 196 198 T 497.5 6 179 G 514.7 - 214 T 489.2 6 199 199 G 489.2 - 198 G 512.9 - 221 T 498.9 -3.1 182 200 G 498.8 - 181 T 562.1 -0.2 216 T 572.4 1.4 201 201 G 572.4 - 200 T 494.6 5.1 226 T 556.6 -1.1 187 202 G 477.2 - 177 T 564.2 -2.1 212 G 532.5 - 203 203 T 532.5 4.1 202 T 489.5 5.5 228 G 543.4 - 191 204 T 485.1 3.9 186 T 588.1 0.3 218 G 568.9 - 205 205 T 568.9 -0.3 204 T 486.7 3.8 224 G 577.2 - 189 206 T 456.7 5.7 207 G 527 - 220 T 477.7 -2.1 185 207 T 510.7 4.8 183 G 491 - 222 G 456.7 - 206 208 G 493.9 - 190 T 577.5 0.7 225 G 581.1 - 209 209 T 581.1 0.5 208 G 497 - 232 G 566.7 - 193 210 G 531 - 21 G 465 - 230 T 584.7 0.5 20 211 T 486.6 5.2 188 G 565.8 - 227 T 552.3 3 212 212 G 552.3 - 211 T 486 5.3 245 G 564.2 - 202 213 G 494.9 - 192 T 532.5 -2.3 229 G 498.3 - 214 214 T 498.3 5.3 213 G 508 - 237 T 514.7 -2.8 198 215 T 498.8 4.1 194 T 568.9 0 233 G 581.9 - 216

141

216 T 581.9 1.1 215 G 498.7 - 243 G 562.1 - 200 217 T 475.2 3.8 195 T 600.4 0.8 231 G 574.1 - 218 218 T 574.1 0.1 217 T 478.1 4.3 239 G 588.1 - 204 219 G 438.4 - 220 T 531.1 2.2 235 G 479.4 - 197 220 T 527 3.4 206 G 492.8 - 241 T 438.4 5.1 219 221 T 512.9 5.4 199 G 508.5 - 238 G 468.9 - 222 222 T 468.9 5.7 221 G 524.1 - 242 T 491 -2.5 207 223 G 541.6 - 23 G 457.3 - 247 T 576.7 0.5 21 224 G 486.7 - 205 T 589.4 1 240 G 593.6 - 225 225 T 593.6 0 224 G 494.6 - 249 G 577.5 - 208 226 G 494.6 - 201 T 567.6 -0.8 244 T 569.5 2.3 227 227 G 569.5 - 226 T 492.4 5.1 256 T 565.8 -1.4 211 228 G 489.5 - 203 T 552.7 -2.3 246 G 513.9 - 229 229 T 513.9 4.8 228 G 503.5 - 254 G 532.5 - 213 230 T 465 4 210 T 617 1.9 248 G 583.3 - 231 231 T 583.3 -0.5 230 T 468.7 5.3 252 G 600.4 - 217 232 T 497 4.5 209 T 576.3 0.8 250 G 592.8 - 233 233 T 592.8 0.1 232 G 501.4 - 260 G 568.9 - 215 234 G 470.6 - 235 T 514.2 1.2 25 G 499.9 - 22 235 G 531.1 - 219 T 498.5 -1.4 258 T 470.6 4.4 234 236 G 577.4 - 24 G 455 - 262 T 582.5 0.5 23 237 T 508 5.6 214 G 529.2 - 255 T 479.5 5.7 238 238 G 479.5 - 237 G 518.6 - 264 T 508.5 -2.6 221 239 G 478.1 - 218 T 604.7 2.1 253 G 612.4 - 240 240 T 612.4 -0.9 239 G 492.4 - 266 G 589.4 - 224 241 T 448.8 5.2 242 G 534.5 - 259 T 492.8 -2 220 242 T 524.1 3.9 222 G 510 - 265 G 448.8 - 241 243 T 498.7 4.7 216 T 570.5 -0.2 261 G 581.1 - 244 244 T 581.1 1.8 243 G 499.3 - 270 G 567.6 - 226 245 G 486 - 212 T 565.9 -1.8 257 G 525.1 - 246 246 T 525.1 4.3 245 T 496.5 5.7 272 G 552.7 - 228 247 T 457.3 5.1 223 T 623.1 3.5 263 G 615 - 248 248 T 615 -2.1 247 G 466.7 - 268 G 617 - 230 249 T 494.6 4.5 225 T 583.9 1.3 267 G 608.1 - 250 250 T 608.1 0.4 249 G 504.4 - 276 G 576.3 - 232 251 G 535.7 - 1245 G 370.5 - 275 T 588.2 2.8 24 252 G 468.7 - 231 T 624.6 3.1 269 G 643.3 - 253 253 T 643.3 -1.2 252 G 492.2 - 284 G 604.7 - 239 254 T 503.5 5.4 229 G 542.6 - 273 T 489.8 5.4 255 255 G 489.8 - 254 G 514.8 - 280 T 529.2 -2.5 237 256 G 492.4 - 227 T 569.3 -0.9 271 G 549.4 - 257 257 T 549.4 3.1 256 T 497 5.7 286 G 565.9 - 245 258 G 463.4 - 259 T 529 1.6 279 G 498.5 - 235 259 T 534.5 2.9 241 T 506.6 -1.7 282 T 463.4 4.6 258

142

260 T 501.4 4.6 233 T 573.3 0.5 277 G 592.6 - 261 261 T 592.6 1.3 260 G 506 - 288 G 570.5 - 243 262 T 455 7.6 236 T 608.9 5.1 274 G 636.5 - 263 263 T 636.5 -3.8 262 G 478.1 - 290 G 623.1 - 247 264 T 518.6 4.3 238 G 524.5 - 281 G 462 - 265 265 T 462 5.3 264 G 534.3 - 283 T 510 -2.3 242 266 T 492.4 4.9 240 T 592.1 2.1 285 G 630.1 - 267 267 T 630.1 -0.4 266 G 509.2 - 292 G 583.9 - 249 268 T 466.7 6.2 248 T 642 4.8 291 G 693.9 - 269 269 T 693.9 -2 268 G 500.1 - 302 G 624.6 - 252 270 T 499.3 5 244 T 569.9 -0.3 289 G 566 - 271 271 T 566 2.3 270 T 503.3 4.9 298 G 569.3 - 256 272 G 496.5 - 246 T 562.4 -1.9 287 G 504.9 - 273 273 T 504.9 4.5 272 G 512.9 - 294 T 542.6 -1.9 254 274 T 560.9 -1.2 275 T 479.8 8.1 306 G 608.9 - 262 275 T 370.5 8.9 251 T 554.3 2.7 321 G 560.9 - 274 276 T 504.4 4.4 250 T 575.4 1.4 293 G 606.7 - 277 277 T 606.7 0.3 276 G 513.1 - 304 G 573.3 - 260 278 G 488.6 - 279 T 523 1 26 G 513.3 - 25 279 G 529 - 258 T 511.5 -1.2 296 T 488.6 4 278 280 T 514.8 4.6 255 G 541.2 - 295 T 471.8 5.5 281 281 G 471.8 - 280 G 528 - 300 T 524.5 -2.3 264 282 G 460.6 - 283 T 536.9 2.1 297 G 506.6 - 259 283 T 534.3 3.4 265 G 517.9 - 301 T 460.6 4.8 282 284 T 492.2 5 253 T 601.1 3.7 303 G 663.1 - 285 285 T 663.1 -1.1 284 G 518.5 - 310 G 592.1 - 266 286 G 497 - 257 T 566.5 -1.9 299 G 522.2 - 287 287 T 522.2 4.2 286 G 509.1 - 308 G 562.4 - 272 288 T 506 4.9 261 T 569.6 0.2 305 G 579.4 - 289 289 T 579.4 1.9 288 T 511.4 4.6 315 G 569.9 - 270 290 T 478.1 7.2 263 T 660.5 7 307 G 742.9 - 291 291 T 742.9 -3.9 290 G 514.2 - 330 G 642 - 268 292 T 509.2 4.5 267 T 575.3 2.2 311 G 624.7 - 293 293 T 624.7 0.2 292 G 522 - 332 G 575.4 - 276 294 T 512.9 4.8 273 G 549.6 - 309 T 485.2 5.2 295 295 G 485.2 - 294 G 526.3 - 325 T 541.2 -1.8 280 296 G 485.1 - 297 T 533.8 1.5 324 G 511.5 - 279 297 G 536.9 - 282 T 516.4 -1.3 328 T 485.1 4.2 296 298 G 503.3 - 271 T 566.9 -0.8 316 G 541.3 - 299 299 T 541.3 3.8 298 T 512.9 4.4 334 G 566.5 - 286 300 T 528 3.8 281 G 531.3 - 326 G 466.2 - 301 301 T 466.2 4.9 300 G 540.9 - 329 T 517.9 -1.9 283 302 T 500.1 5.7 269 T 610.5 5.9 331 G 713.8 - 303 303 T 713.8 -2.1 302 G 538.9 - 338 G 601.1 - 284

143

304 T 513.1 4.7 277 T 567.9 1 333 G 592.6 - 305 305 T 592.6 1.5 304 G 520.3 - 336 G 569.6 - 288 306 G 479.8 - 274 T 683.2 8.6 322 G 707.2 - 307 307 T 707.2 -4.9 306 G 509.8 - 348 G 660.5 - 290 308 T 509.1 4.3 287 G 558.2 - 335 T 493.8 4.9 309 309 G 493.8 - 308 G 527.6 - 340 T 549.6 -2.2 294 310 T 518.5 4.7 285 T 570.7 3.4 339 G 646.5 - 311 311 T 646.5 -0.5 310 G 534.6 - 346 G 575.3 - 292 312 G 411.8 - - G 426.6 - 313 T 459.6 8.5 1233 313 G 443.4 - 314 T 367.5 6.4 319 T 426.6 11.7 312 314 G 593.8 - - T 405.2 7.6 351 T 443.4 10.2 313 315 G 511.4 - 289 T 565.8 -0.1 337 G 557.6 - 316 316 T 557.6 2.7 315 T 519.5 4.6 352 G 566.9 - 298 317 G 395.2 - 1233 T 490.5 14.4 318 G 462.6 - 1232 318 T 562.8 4.8 319 G 419 - 327 G 490.5 - 317 319 G 367.5 - 313 T 527.3 6.6 350 G 562.8 - 318 320 G 539.4 - 321 T 631.1 10 327 G 558.9 - 322 321 T 506.9 0.6 1232 T 539.4 12.3 320 G 554.3 - 275 322 T 558.9 -4.5 320 T 556.4 7 362 G 683.2 - 306 323 G 497.1 - 324 G 531.7 - 27 T 523 -0.8 26 324 G 533.8 - 296 G 523 - 342 T 497.1 3.7 323 325 T 526.3 3.9 295 G 539.8 - 341 T 474.2 5.4 326 326 G 474.2 - 325 G 542.1 - 344 T 531.3 -1.5 300 327 T 419 2.6 318 T 569.4 4.9 356 G 631.1 - 320 328 G 483.1 - 329 T 542.3 1.8 343 G 516.4 - 297 329 T 540.9 2.7 301 T 522.3 -1.1 345 T 483.1 4.3 328 330 T 514.2 6.9 291 T 573.9 7.3 349 G 704.5 - 331 331 T 704.5 -3.5 330 G 529.1 - 360 G 610.5 - 302 332 T 522 4.4 293 T 563.9 1.8 347 G 605.8 - 333 333 T 605.8 0.7 332 G 530.4 - 354 G 567.9 - 304 334 G 512.9 - 299 T 561.4 -0.5 353 G 515 - 335 335 T 515 3.9 334 G 527 - 358 T 558.2 -1.7 308 336 T 520.3 4.3 305 T 563.3 0.7 355 G 571.7 - 337 337 T 571.7 2.1 336 T 527.7 4.2 364 G 565.8 - 315 338 T 538.9 4.7 303 T 555.7 4.8 361 G 668.3 - 339 339 T 668.3 -0.8 338 T 552.2 3.7 373 G 570.7 - 310 340 T 527.6 4.1 309 G 548.9 - 359 T 484.4 4.9 341 341 G 484.4 - 340 G 541 - 366 T 539.8 -1.8 325 342 T 494.6 3.9 343 G 540.9 - 370 T 523 -0.9 324 343 G 542.3 - 328 T 525.7 -0.9 372 G 494.6 - 342 344 T 542.1 2.9 326 G 532.7 - 367 T 479.7 4.7 345 345 G 479.7 - 344 T 547.8 1.9 371 G 522.3 - 329 346 T 534.6 4.2 311 T 555.8 2.7 374 G 617.7 - 347 347 T 617.7 0.6 346 G 542.4 - 375 G 563.9 - 332

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348 T 509.8 7.5 307 T 637.3 8.3 363 G 751.8 - 349 349 T 751.8 -3.2 348 G 603 - 389 G 573.9 - 330 350 T 444 8.6 351 T 467.8 -0.7 357 G 527.3 - 319 351 G 405.2 - 314 T 514.7 -0.5 28 G 444 - 350 352 G 519.5 - 316 T 561.8 -0.5 365 G 534.2 - 353 353 T 534.2 3.5 352 G 530.3 - 377 G 561.4 - 334 354 T 530.4 4.1 333 T 559.2 1.3 376 G 583.5 - 355 355 T 583.5 1.8 354 G 537 - 379 G 563.3 - 336 356 T 532.9 8 357 T 547.5 -3.1 368 G 569.4 - 327 357 G 467.8 - 350 T 594.9 2.6 384 G 532.9 - 356 358 T 527 4.5 335 G 555.1 - 378 T 498.3 4.4 359 359 G 498.3 - 358 G 540.3 - 381 T 548.9 -1.2 340 360 T 529.1 4 331 T 571.3 5.3 390 G 670.2 - 361 361 T 670.2 -0.2 360 G 569.5 - 391 G 555.7 - 338 362 G 556.4 - 322 T 566.6 7.2 368 G 606.1 - 363 363 T 606.1 -2.3 362 T 664.6 5.7 405 G 637.3 - 348 364 G 527.7 - 337 T 560.7 0.3 380 G 550 - 365 365 T 550 3 364 G 536 - 393 G 561.8 - 352 366 T 541 3.2 341 G 542.6 - 382 G 483.6 - 367 367 T 483.6 5.1 366 G 549.7 - 385 T 532.7 -1.3 344 368 G 547.5 - 356 T 626.3 4.5 397 G 566.6 - 362 369 T 498.3 3.4 370 G 540 - 29 T 531.5 -0.7 27 370 T 540.9 1 342 G 532.5 - 388 G 498.3 - 369 371 G 547.8 - 345 T 531.8 -0.9 386 T 490.5 4.3 372 372 G 490.5 - 371 T 548.1 1.3 387 G 525.7 - 343 373 G 552.2 - 339 G 542.2 - 392 T 622.4 0.2 374 374 G 622.4 - 373 T 555.5 3.3 395 G 555.8 - 346 375 T 542.4 3.6 347 T 552.9 2.3 396 G 591.5 - 376 376 T 591.5 1.3 375 G 547.3 - 401 G 559.2 - 354 377 T 530.3 4 353 G 558 - 394 T 515.7 4.4 378 378 G 515.7 - 377 G 541.3 - 399 T 555.1 -1 358 379 T 537 3.9 355 T 558.1 1 402 G 562.2 - 380 380 T 562.2 2.5 379 T 543.3 3.5 411 G 560.7 - 364 381 T 540.3 3.3 359 G 549.9 - 400 T 492.4 4.8 382 382 G 492.4 - 381 G 550 - 403 T 542.6 -0.9 366 383 G 517.4 - 28 T 581.2 0.1 30 G 441 - 384 384 T 441 6.6 383 T 580.2 -2.4 398 G 594.9 - 357 385 T 549.7 2.2 367 G 539.6 - 404 T 488.7 4.4 386 386 G 488.7 - 385 T 552.8 1.5 407 G 531.8 - 371 387 G 548.1 - 372 G 535.9 - 408 G 495.6 - 388 388 T 495.6 3.7 387 G 547.4 - 409 T 532.5 -0.7 370 389 T 603 2.5 349 T 543.4 8.2 413 G 676.1 - 390 390 T 676.1 -1.3 389 G 560 - 415 G 571.3 - 360 391 T 569.5 3.2 361 T 526.2 5.1 416 G 610.5 - 392

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392 T 610.5 0.3 391 G 566.7 - 417 T 542.2 4 373 393 T 536 3.9 365 G 558.8 - 412 T 531.3 3.6 394 394 G 531.3 - 393 G 544.7 - 419 T 558 -0.6 377 395 G 555.5 - 374 G 545.4 - 418 T 593.3 1.1 396 396 G 593.3 - 395 T 557.6 3 423 G 552.9 - 375 397 G 464.7 - 398 T 661 -2.3 406 G 626.3 - 368 398 G 580.2 - 384 G 633 - 421 T 464.7 6.4 397 399 T 541.3 3.1 378 G 554.8 - 420 T 504.8 4.5 400 400 G 504.8 - 399 G 550.6 - 425 T 549.9 -1.2 381 401 T 547.3 3.6 376 T 554.7 1.7 424 G 570.6 - 402 402 T 570.6 2.1 401 G 551.6 - 429 G 558.1 - 379 403 T 550 2.5 382 G 547 - 426 G 491.6 - 404 404 T 491.6 4.8 403 G 555.4 - 427 T 539.6 -0.7 385 405 G 479.5 - 406 T 741.7 -3.3 414 G 664.6 - 363 406 G 661 - 397 T 653.1 3.9 437 T 479.5 6.5 405 407 G 552.8 - 386 G 540.9 - 428 G 493.1 - 408 408 T 493.1 4.1 407 G 553.5 - 431 T 535.9 -0.7 387 409 T 547.4 0.8 388 G 541.1 - 432 G 496.4 - 410 410 T 496.4 3.3 409 G 547.6 - 31 T 539.8 -0.5 29 411 G 543.3 - 380 T 558.4 0.7 430 G 544.2 - 412 412 T 544.2 3.4 411 G 549.8 - 433 T 558.8 -0.1 393 413 G 692.1 - 414 T 642.8 0.4 436 G 543.4 - 389 414 G 741.7 - 405 G 504.6 - 451 T 692.1 2.1 413 415 T 560 3.4 390 T 523.7 5.3 435 G 583.3 - 416 416 T 583.3 0.8 415 G 573.9 - 439 G 526.2 - 391 417 T 566.7 2.5 392 T 540 4 440 G 587.3 - 418 418 T 587.3 1.3 417 G 567.1 - 443 T 545.4 3.2 395 419 T 544.7 3.2 394 G 557.4 - 434 T 518.1 4.2 420 420 G 518.1 - 419 G 552.6 - 441 T 554.8 -0.5 399 421 G 465.9 - 422 G 625 - 438 T 633 2.4 398 422 T 565 -0.3 30 G 601.1 - 32 T 465.9 4.9 421 423 G 557.6 - 396 G 551.5 - 444 T 574.4 2 424 424 G 574.4 - 423 T 559.9 2.6 447 G 554.7 - 401 425 T 550.6 2.5 400 G 552.7 - 442 G 499.2 - 426 426 T 499.2 4.7 425 G 557.1 - 445 T 547 -1.1 403 427 T 555.4 1.5 404 G 546.5 - 446 G 493.2 - 428 428 T 493.2 4.5 427 G 557.8 - 449 T 540.9 -0.7 407 429 T 551.6 3.2 402 T 557.3 1.1 448 G 553.9 - 430 430 T 553.9 2.9 429 G 556 - 454 G 558.4 - 411 431 T 553.5 0.9 408 G 544.3 - 450 G 494.6 - 432 432 T 494.6 3.6 431 G 553.6 - 453 T 541.1 -0.5 409 433 T 549.8 3 412 G 558.7 - 455 T 530.3 3.8 434 434 G 530.3 - 433 G 555.9 - 458 T 557.4 -0.3 419 435 G 617.5 - 436 T 602.7 0.1 460 G 523.7 - 415

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436 G 642.8 - 413 G 519.9 - 462 T 617.5 2.2 435 437 G 460.2 - 438 T 718.3 -3.4 452 G 653.1 - 406 438 T 625 -1.1 421 G 629 - 456 T 460.2 5.7 437 439 T 573.9 1.3 416 T 540.6 4 461 G 580.4 - 440 440 T 580.4 1.6 439 G 575.8 - 464 G 540 - 417 441 T 552.6 2.5 420 G 556.4 - 459 G 509.2 - 442 442 T 509.2 4.5 441 G 558.9 - 466 T 552.7 -0.5 425 443 T 567.1 2.3 418 T 550.2 3 465 G 574.4 - 444 444 T 574.4 2 443 G 567.6 - 468 T 551.5 2.4 423 445 T 557.1 2 426 G 551.8 - 467 G 496.8 - 446 446 T 496.8 4.4 445 G 560.8 - 470 T 546.5 -0.6 427 447 G 559.9 - 424 G 556.5 - 469 G 560.3 - 448 448 T 560.3 2.8 447 G 562.4 - 474 G 557.3 - 429 449 T 557.8 1.1 428 G 548.5 - 471 G 493.9 - 450 450 T 493.9 3.9 449 G 558.6 - 472 T 544.3 -0.5 431 451 T 589.9 4.1 452 G 689.1 - 463 T 504.6 6.1 414 452 G 718.3 - 437 T 548.1 3.9 476 G 589.9 - 451 453 T 553.6 0.7 432 G 549.2 - 473 G 494.1 - 34 454 T 556 2.6 430 G 559.2 - 475 T 540.6 3.7 455 455 G 540.6 - 454 G 560.4 - 478 T 558.7 0.3 433 456 T 494.7 4.4 457 G 661.8 - 477 T 629 1.3 438 457 T 600.6 -0.4 32 G 599.7 - 35 G 494.7 - 456 458 T 555.9 2.6 434 G 558.8 - 479 G 519.7 - 459 459 T 519.7 4.2 458 G 561.3 - 480 T 556.4 -0.3 441 460 G 602.7 - 435 T 541.6 3.9 482 T 590.5 2.3 461 461 G 590.5 - 460 T 588.6 0.4 484 G 540.6 - 439 462 T 601.1 3.2 463 G 631.9 - 483 T 519.9 4.8 436 463 T 689.1 -1.4 451 G 542.6 - 495 G 601.1 - 462 464 T 575.8 1.4 440 G 551.7 - 485 G 574.2 - 465 465 T 574.2 2.4 464 G 574.9 - 488 G 550.2 - 443 466 T 558.9 2.1 442 G 556 - 481 G 503.4 - 467 467 T 503.4 4.6 466 G 563.2 - 486 T 551.8 -0.4 445 468 T 567.6 2 444 G 556.8 - 489 G 564.1 - 469 469 T 564.1 2.6 468 G 568.6 - 493 T 556.5 1.8 447 470 T 560.8 1.4 446 G 552.6 - 487 G 495.5 - 471 471 T 495.5 4.2 470 G 562.5 - 490 T 548.5 -0.4 449 472 T 558.6 0.8 450 G 551.6 - 491 G 493.4 - 473 473 T 493.4 3.5 472 G 559.4 - 492 T 549.2 -0.4 453 474 T 562.4 2.3 448 G 559.8 - 494 G 548.6 - 475 475 T 548.6 3.2 474 G 565.2 - 497 T 559.2 0.8 454 476 G 528.5 - 477 T 641.4 -1 496 G 548.1 - 452 477 T 661.8 -1.5 456 G 585.2 - 499 T 528.5 3.5 476 478 T 560.4 2.3 455 G 560.5 - 498 G 529.7 - 479 479 T 529.7 4 478 G 564.5 - 501 T 558.8 0 458

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480 T 561.3 2 459 G 559 - 502 G 511.8 - 481 481 T 511.8 4.6 480 G 565.5 - 503 T 556 -0.4 466 482 T 590.9 3 483 G 603 - 506 G 541.6 - 460 483 T 631.9 -0.8 462 G 544.9 - 513 G 590.9 - 482 484 G 588.6 - 461 T 553.5 3.2 505 T 578.5 2.7 485 485 G 578.5 - 484 T 582.3 0.8 509 T 551.7 3 464 486 T 563.2 1.5 467 G 556.3 - 504 G 499.5 - 487 487 T 499.5 4.4 486 G 565.7 - 507 T 552.6 -0.4 470 488 T 574.9 1.3 465 G 558.4 - 510 G 567.3 - 489 489 T 567.3 2.8 488 G 574.2 - 515 T 556.8 2.3 468 490 T 562.5 0.8 471 G 554.6 - 508 G 494.1 - 491 491 T 494.1 3.9 490 G 563.5 - 511 T 551.6 -0.3 472 492 T 559.4 0.5 473 G 555.9 - 512 G 492.2 - 36 493 T 568.6 1.9 469 G 560.8 - 516 G 554.9 - 494 494 T 554.9 3.2 493 G 570 - 517 T 559.8 1.3 474 495 T 544.4 3.8 496 G 630 - 514 T 542.6 3.6 463 496 G 641.4 - 476 T 565.1 1.7 519 G 544.4 - 495 497 T 565.2 2.2 475 G 561.7 - 518 G 538.5 - 498 498 T 538.5 3.9 497 G 568.1 - 521 T 560.5 0.6 478 499 T 512.9 3.4 500 G 612.9 - 520 T 585.2 1.6 477 500 T 604.3 -0.3 35 G 592.1 - 38 G 512.9 - 499 501 T 564.5 1.9 479 G 561.1 - 522 G 520.7 - 502 502 T 520.7 4.3 501 G 568.1 - 523 T 559 -0.1 480 503 T 565.5 1.6 481 G 559.3 - 524 G 505.6 - 504 504 T 505.6 4.5 503 G 568.4 - 525 T 556.3 -0.3 486 505 T 580.4 3 506 G 590 - 531 G 553.5 - 484 506 T 603 -0.2 482 G 554.1 - 533 G 580.4 - 505 507 T 565.7 1 487 G 557.6 - 526 G 496.6 - 508 508 T 496.6 4.1 507 G 567 - 527 T 554.6 -0.2 490 509 G 582.3 - 485 T 560 2.5 532 G 571.1 - 510 510 T 571.1 3 509 G 579.2 - 535 T 558.4 2.5 488 511 T 563.5 0.6 491 G 557.8 - 528 G 492.2 - 512 512 T 492.2 3.4 511 G 564.2 - 529 T 555.9 -0.2 492 513 T 565.9 3.4 514 G 609.9 - 534 T 544.9 3.1 483 514 T 630 -1.2 495 T 556.8 2 539 G 565.9 - 513 515 T 574.2 1.4 489 G 562.2 - 536 G 560.2 - 516 516 T 560.2 3.3 515 G 574.3 - 537 T 560.8 1.7 493 517 T 570 1.7 494 G 562.9 - 538 G 546.2 - 518 518 T 546.2 3.6 517 G 571.8 - 541 T 561.7 0.9 497 519 G 526.9 - 520 T 612.7 -0.7 540 G 565.1 - 496 520 T 612.9 -0.7 499 G 578.5 - 543 T 526.9 3.3 519 521 T 568.1 1.7 498 G 562.7 - 542 G 529.5 - 522 522 T 529.5 4.3 521 G 571 - 545 T 561.1 0.3 501 523 T 568.1 1.6 502 G 561.5 - 546 G 513.1 - 524

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524 T 513.1 4.6 523 G 571 - 547 T 559.3 -0.1 503 525 T 568.4 1.1 504 G 560.1 - 548 G 500.9 - 526 526 T 500.9 4.3 525 G 570.1 - 549 T 557.6 -0.2 507 527 T 567 0.7 508 G 559.7 - 550 G 493.7 - 528 528 T 493.7 3.9 527 G 568.1 - 551 T 557.8 -0.3 511 529 T 564.2 0.3 512 G 561.1 - 552 G 490.6 - 530 530 T 490.6 3 529 G 564.6 - 39 T 559.9 -0.2 37 531 T 590 0.2 505 G 560.7 - 553 G 573.6 - 532 532 T 573.6 3.4 531 G 583.9 - 555 G 560 - 509 533 T 571.7 3.3 534 G 595.7 - 554 T 554.1 2.7 506 534 T 609.9 -0.6 513 T 557.6 1.9 557 G 571.7 - 533 535 T 579.2 0.9 510 G 563.6 - 556 G 564.9 - 536 536 T 564.9 3.3 535 G 578.1 - 559 T 562.2 1.9 515 537 T 574.3 1.4 516 G 564.2 - 560 G 553 - 538 538 T 553 3.6 537 G 575.2 - 561 T 562.9 1.3 517 539 G 543.6 - 540 T 606.3 -0.6 558 G 556.8 - 514 540 G 612.7 - 519 T 568.6 1 563 T 543.6 3.4 539 541 T 571.8 1.6 518 G 564 - 562 G 537.9 - 542 542 T 537.9 4.1 541 G 574 - 565 T 562.7 0.7 521 543 T 525 3 544 G 598.9 - 564 T 578.5 0.8 520 544 T 596.5 -0.2 38 G 585.7 - 40 G 525 - 543 545 T 571 1.5 522 G 563.2 - 566 G 521.4 - 546 546 T 521.4 4.5 545 G 573.5 - 567 T 561.5 0.2 523 547 T 571 1.3 524 G 562.1 - 568 G 506.7 - 548 548 T 506.7 4.4 547 G 572.7 - 569 T 560.1 0 525 549 T 570.1 0.8 526 G 561.6 - 570 G 496.8 - 550 550 T 496.8 4 549 G 571.2 - 571 T 559.7 -0.1 527 551 T 568.1 0.4 528 G 562.5 - 572 G 491.1 - 552 552 T 491.1 3.4 551 G 568.3 - 573 T 561.1 -0.2 529 553 T 571.3 3.4 554 G 587.7 - 575 T 560.7 2.2 531 554 T 595.7 -0.2 533 T 561.7 1.8 577 G 571.3 - 553 555 T 583.9 0.4 532 G 564.4 - 576 G 568.5 - 556 556 T 568.5 3.4 555 G 581.3 - 579 T 563.6 2 535 557 G 556.9 - 558 T 596.9 -0.3 578 G 557.6 - 534 558 G 606.3 - 539 T 564.4 1.1 583 T 556.9 3.3 557 559 T 578.1 1 536 G 565.3 - 580 G 559 - 560 560 T 559 3.6 559 G 578.2 - 581 T 564.2 1.5 537 561 T 575.2 1.3 538 G 565 - 582 G 545.6 - 562 562 T 545.6 3.9 561 G 576.8 - 587 T 564 1 541 563 G 534.6 - 564 T 597.7 -0.3 584 G 568.6 - 540 564 T 598.9 -0.4 543 G 576.7 - 585 T 534.6 3.1 563 565 T 574 1.4 542 G 564.3 - 588 G 529.7 - 566 566 T 529.7 4.4 565 G 576.1 - 589 T 563.2 0.5 545 567 T 573.5 1.3 546 G 563.5 - 590 G 513.9 - 568

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568 T 513.9 4.5 567 G 575.3 - 591 T 562.1 0.2 547 569 T 572.7 0.8 548 G 563.1 - 592 G 501.4 - 570 570 T 501.4 4.3 569 G 573.9 - 593 T 561.6 0 549 571 T 571.2 0.5 550 G 563.6 - 594 G 492.9 - 572 572 T 492.9 3.8 571 G 571.7 - 595 T 562.5 -0.1 551 573 T 568.3 0.3 552 G 565.2 - 596 G 489.2 - 574 574 T 489.2 3 573 G 568.5 - 41 T 564.6 -0.1 39 575 T 587.7 0.2 553 T 564.9 1.6 597 G 569.4 - 576 576 T 569.4 3.7 575 G 583.8 - 599 T 564.4 1.9 555 577 G 563.6 - 578 T 589.4 0 598 G 561.7 - 554 578 G 596.9 - 557 T 564.6 1.1 601 T 563.6 3.4 577 579 T 581.3 0.7 556 G 566.1 - 600 G 563.9 - 580 580 T 563.9 3.7 579 G 580.7 - 603 T 565.3 1.6 559 581 T 578.2 1 560 G 565.8 - 604 G 552.8 - 582 582 T 552.8 3.9 581 G 579.3 - 607 T 565 1.2 561 583 G 545.2 - 584 T 593.4 -0.2 602 G 564.4 - 558 584 G 597.7 - 563 T 571.3 0.6 605 T 545.2 3.2 583 585 T 532.4 2.8 586 G 589.5 - 606 T 576.7 0.4 564 586 T 588.7 -0.1 40 G 581.4 - 42 G 532.4 - 585 587 T 576.8 1.3 562 G 565.1 - 608 G 538 - 588 588 T 538 4.3 587 G 578.5 - 609 T 564.3 0.8 565 589 T 576.1 1.3 566 G 564.4 - 610 G 521.8 - 590 590 T 521.8 4.6 589 G 577.8 - 611 T 563.5 0.4 567 591 T 575.3 0.8 568 G 564.1 - 612 G 507.5 - 592 592 T 507.5 4.4 591 G 576.5 - 613 T 563.1 0.1 569 593 T 573.9 0.5 570 G 564.5 - 614 G 496.2 - 594 594 T 496.2 4 593 G 574.6 - 615 T 563.6 0 571 595 T 571.7 0.3 572 G 565.9 - 616 G 489.9 - 596 596 T 489.9 3.4 595 G 571.7 - 618 T 565.2 -0.1 573 597 G 566.4 - 598 T 584.9 0.3 619 G 564.9 - 575 598 G 589.4 - 577 T 566.2 1.1 621 T 566.4 3.6 597 599 T 583.8 0.5 576 G 566.6 - 620 G 567 - 600 600 T 567 3.7 599 G 582.4 - 623 T 566.1 1.7 579 601 G 554.2 - 602 T 588.2 0 622 G 564.6 - 578 602 G 593.4 - 583 T 568.7 0.6 625 T 554.2 3.3 601 603 T 580.7 0.9 580 G 566.4 - 624 G 559.1 - 604 604 T 559.1 3.8 603 G 581.3 - 627 T 565.8 1.4 581 605 G 539 - 606 T 588.1 -0.1 626 G 571.3 - 584 606 T 589.5 -0.2 585 G 575.9 - 629 T 539 2.9 605 607 T 579.3 1.1 582 G 565.6 - 628 G 546 - 608 608 T 546 4.1 607 G 580.8 - 631 T 565.1 1 587 609 T 578.5 1.2 588 G 564.8 - 632 G 530.1 - 610 610 T 530.1 4.5 609 G 580.1 - 633 T 564.4 0.6 589 611 T 577.8 0.8 590 G 564.6 - 634 G 514.4 - 612

150

612 T 514.4 4.6 611 G 578.9 - 635 T 564.1 0.4 591 613 T 576.5 0.6 592 G 565.1 - 636 G 501.1 - 614 614 T 501.1 4.2 613 G 577.3 - 638 T 564.5 0.1 593 615 T 574.6 0.3 594 G 566.3 - 637 G 492 - 616 616 T 492 3.8 615 G 574.6 - 640 T 565.9 0 595 617 T 487.8 3 618 G 571.4 - 43 T 568.3 -0.1 41 618 T 571.7 0.1 596 G 568.3 - 639 G 487.8 - 617 619 G 584.9 - 597 T 567.3 1 642 T 567.3 3.9 620 620 G 567.3 - 619 T 583 0.5 643 T 566.6 1.4 599 621 G 560.5 - 622 T 584.2 0.3 641 G 566.2 - 598 622 G 588.2 - 601 T 568.4 0.7 645 T 560.5 3.4 621 623 T 582.4 0.7 600 G 566.7 - 644 G 564 - 624 624 T 564 3.9 623 G 582.7 - 647 T 566.4 1.4 603 625 G 546.5 - 626 T 585 0 646 G 568.7 - 602 626 G 588.1 - 605 T 572.5 0.3 649 T 546.5 3.1 625 627 T 581.3 1 604 G 565.8 - 648 G 553.5 - 628 628 T 553.5 4.1 627 T 582.8 0.9 652 T 565.6 1.2 607 629 T 536.8 2.7 630 G 582.9 - 650 T 575.9 0.2 606 630 T 583 -0.1 42 G 578.1 - 44 G 536.8 - 629 631 T 580.8 1.1 608 G 564.9 - 651 G 538.6 - 632 632 T 538.6 4.4 631 G 582.4 - 656 T 564.8 0.9 609 633 T 580.1 0.8 610 G 564.7 - 655 G 522.2 - 634 634 T 522.2 4.6 633 G 581.4 - 660 T 564.6 0.6 611 635 T 578.9 0.5 612 G 565.2 - 659 G 507.2 - 636 636 T 507.2 4.4 635 G 579.7 - 662 T 565.1 0.3 613 637 T 495.4 4 638 G 577.3 - 658 T 566.3 0.1 615 638 T 577.3 0.3 614 G 566.4 - 661 G 495.4 - 637 639 T 488.6 3.3 640 G 574.2 - 654 T 568.3 0 618 640 T 574.6 0.2 616 G 568.3 - 657 G 488.6 - 639 641 G 584.2 - 621 T 568.7 0.7 670 T 564.8 3.6 642 642 G 564.8 - 641 T 582.2 0.5 675 G 567.3 - 619 643 G 583 - 620 T 567.3 1 676 G 567.1 - 644 644 T 567.1 3.9 643 G 583.2 - 679 T 566.7 1.2 623 645 G 553.6 - 646 T 581.9 0.3 669 G 568.4 - 622 646 G 585 - 625 T 571 0.4 672 T 553.6 3.2 645 647 T 582.7 0.8 624 G 565.9 - 680 G 560.2 - 648 648 T 560.2 4 647 G 584.2 - 684 T 565.8 1.2 627 649 G 541.3 - 650 T 581 0.1 671 G 572.5 - 626 650 T 582.9 0 629 T 574.8 0.1 674 T 541.3 2.8 649 651 T 547 4.3 652 G 584.5 - 682 T 564.9 1.1 631 652 G 582.8 - 628 G 564.7 - 683 G 547 - 651 653 T 486.3 3 654 G 573.4 - 45 T 571 0 43 654 T 574.2 0.1 639 G 570.5 - 663 G 486.3 - 653 655 T 530.6 4.5 656 G 583.7 - 678 T 564.7 0.8 633

151

656 T 582.4 0.8 632 G 564.3 - 681 G 530.6 - 655 657 T 490.8 3.8 658 G 576.8 - 664 T 568.3 0.1 640 658 T 577.3 0.2 637 G 568.1 - 665 G 490.8 - 657 659 T 514.4 4.6 660 G 582.1 - 668 T 565.2 0.6 635 660 T 581.4 0.6 634 G 565 - 677 G 514.4 - 659 661 T 500.2 4.2 662 G 579.8 - 666 T 566.4 0.3 638 662 T 579.7 0.4 636 G 566.1 - 667 G 500.2 - 661 663 T 487.1 3.3 664 G 575.7 - 686 T 570.5 0.1 654 664 T 576.8 0.1 657 G 569.8 - 687 G 487.1 - 663 665 T 494.2 4.1 666 G 579.2 - 688 T 568.1 0.2 658 666 T 579.8 0.1 661 G 567.4 - 689 G 494.2 - 665 667 T 506.4 4.5 668 G 582.3 - 690 T 566.1 0.5 662 668 T 582.1 0.4 659 G 565.4 - 691 G 506.4 - 667 669 G 581.9 - 645 T 570.5 0.4 698 T 560.1 3.4 670 670 G 560.1 - 669 T 579.9 0.5 699 G 568.7 - 641 671 G 581 - 649 T 572.8 0.1 694 T 547.2 3 672 672 G 547.2 - 671 T 578.6 0.2 697 G 571 - 646 673 T 578.5 0 44 G 575.2 - 46 G 538.5 - 674 674 T 538.5 2.6 673 T 577.5 0.1 693 G 574.8 - 650 675 G 582.2 - 642 T 568.3 0.7 700 G 567.8 - 676 676 T 567.8 3.9 675 G 582.3 - 703 G 567.3 - 643 677 T 522.4 4.6 678 G 584.6 - 692 T 565 0.8 660 678 T 583.7 0.6 655 G 564.2 - 695 G 522.4 - 677 679 T 583.2 0.8 644 G 566.1 - 704 G 565.6 - 680 680 T 565.6 3.9 679 G 584.9 - 706 T 565.9 1.1 647 681 T 539.4 4.4 682 G 586 - 696 T 564.3 1 656 682 T 584.5 0.8 651 G 563.6 - 701 G 539.4 - 681 683 T 555 4.1 684 G 586.2 - 702 T 564.7 1.2 652 684 T 584.2 0.9 648 G 564.4 - 705 G 555 - 683 685 T 484.7 3 686 G 574.3 - 47 T 572.7 0.1 45 686 T 575.7 0 663 G 571.6 - 707 G 484.7 - 685 687 T 489.2 3.8 688 G 577.9 - 708 T 569.8 0.2 664 688 T 579.2 0.1 665 G 569 - 709 G 489.2 - 687 689 T 498.9 4.3 690 G 581.6 - 710 T 567.4 0.5 666 690 T 582.3 0.1 667 G 566.3 - 711 G 498.9 - 689 691 T 513.7 4.6 692 G 584.8 - 712 T 565.4 0.8 668 692 T 584.6 0.4 677 G 564.3 - 713 G 513.7 - 691 693 G 577.5 - 674 T 573.1 0 716 T 541.8 2.8 694 694 G 541.8 - 693 T 575.2 0.2 717 G 572.8 - 671 695 T 531.2 4.5 696 G 587.1 - 714 T 564.2 1 678 696 T 586 0.6 681 G 563 - 719 G 531.2 - 695 697 G 578.6 - 672 T 572 0.1 718 T 554 3.3 698 698 G 554 - 697 T 576.5 0.5 721 G 570.5 - 669 699 G 579.9 - 670 T 569.9 0.3 722 T 565.9 3.6 700

152

700 G 565.9 - 699 T 579.9 0.8 725 G 568.3 - 675 701 T 548.4 4.3 702 G 588.2 - 720 T 563.6 1.2 682 702 T 586.2 0.8 683 G 562.8 - 723 G 548.4 - 701 703 T 582.3 0.7 676 G 566.9 - 726 G 569.4 - 704 704 T 569.4 3.9 703 G 584.4 - 728 T 566.1 0.9 679 705 T 562.5 4 706 G 587.4 - 724 T 564.4 1.1 684 706 T 584.9 0.9 680 G 564.2 - 727 G 562.5 - 705 707 T 485.3 3.4 708 G 576.2 - 730 T 571.6 0.1 686 708 T 577.9 -0.1 687 G 570.5 - 731 G 485.3 - 707 709 T 492.5 4.1 710 G 580.1 - 732 T 569 0.4 688 710 T 581.6 0 689 G 567.8 - 733 G 492.5 - 709 711 T 504.9 4.5 712 G 584.1 - 734 T 566.3 0.7 690 712 T 584.8 0.1 691 G 564.8 - 735 G 504.9 - 711 713 T 522 4.6 714 G 587.4 - 736 T 564.3 1 692 714 T 587.1 0.4 695 G 562.7 - 737 G 522 - 713 715 T 574.5 0.1 46 T 571.6 -0.1 48 G 537.7 - 716 716 T 537.7 2.6 715 T 572.2 0.2 739 G 573.1 - 693 717 G 575.2 - 694 T 572.2 0 740 T 547 3 718 718 G 547 - 717 T 572.7 0.5 741 G 572 - 697 719 T 540.6 4.3 720 G 589.7 - 738 T 563 1.2 696 720 T 588.2 0.8 701 G 561.5 - 743 G 540.6 - 719 721 G 576.5 - 698 T 571.5 0.1 742 T 561.7 3.4 722 722 G 561.7 - 721 T 576.1 0.9 745 G 569.9 - 699 723 T 557.5 4 724 G 590.1 - 744 T 562.8 1.2 702 724 T 587.4 0.9 705 G 561.9 - 747 G 557.5 - 723 725 G 579.9 - 700 G 568.4 - 746 G 571.1 - 726 726 T 571.1 3.8 725 G 582.2 - 749 T 566.9 0.8 703 727 T 569.1 3.8 728 G 587.7 - 748 T 564.2 1 706 728 T 584.4 1 704 G 564.4 - 750 G 569.1 - 727 729 T 482.9 3.1 730 G 574.1 - 49 T 573.3 0.1 47 730 T 576.2 -0.1 707 G 571.9 - 751 G 482.9 - 729 731 T 487.2 3.8 732 G 578 - 752 T 570.5 0.4 708 732 T 580.1 -0.1 709 G 569.1 - 753 G 487.2 - 731 733 T 497 4.3 734 G 582.4 - 754 T 567.8 0.6 710 734 T 584.1 0 711 G 566 - 755 G 497 - 733 735 T 512.2 4.6 736 G 586.9 - 756 T 564.8 1 712 736 T 587.4 0.1 713 G 562.9 - 757 G 512.2 - 735 737 T 531.3 4.5 738 G 590.3 - 758 T 562.7 1.3 714 738 T 589.7 0.5 719 G 560.8 - 761 G 531.3 - 737 739 G 572.2 - 716 T 570.4 -0.1 760 G 540 - 740 740 T 540 2.9 739 T 569.2 0.4 763 G 572.2 - 717 741 G 572.7 - 718 T 572.1 -0.1 764 G 554.6 - 742 742 T 554.6 3.2 741 T 571.2 0.9 765 G 571.5 - 721 743 T 550.5 4.1 744 G 592.3 - 762 T 561.5 1.4 720

153

744 T 590.1 0.9 723 G 560 - 767 G 550.5 - 743 745 G 576.1 - 722 T 570.4 0.1 766 G 570.1 - 746 746 T 570.1 3.5 745 G 578.2 - 769 T 568.4 0.4 725 747 T 566.4 3.8 748 G 591.4 - 768 T 561.9 1.2 724 748 T 587.7 1.1 727 G 561.5 - 771 G 566.4 - 747 749 T 582.2 1.1 726 G 565.5 - 770 G 574.6 - 750 750 T 574.6 3.8 749 G 586.6 - 772 T 564.4 0.9 728 751 T 483.4 3.5 752 G 575.4 - 774 T 571.9 0.3 730 752 T 578 -0.1 731 G 570.3 - 775 G 483.4 - 751 753 T 490.1 4.2 754 G 579.9 - 776 T 569.1 0.5 732 754 T 582.4 -0.1 733 G 567.4 - 777 G 490.1 - 753 755 T 502.7 4.6 756 G 585.1 - 778 T 566 0.9 734 756 T 586.9 0 735 G 563.7 - 779 G 502.7 - 755 757 T 520.9 4.6 758 G 589.9 - 780 T 562.9 1.3 736 758 T 590.3 0.2 737 G 560.6 - 781 G 520.9 - 757 759 G 569.8 - 48 T 566.8 -0.1 50 G 534.3 - 760 760 T 534.3 2.7 759 T 566.5 0.3 783 G 570.4 - 739 761 T 541.6 4.2 762 G 593.4 - 782 T 560.8 1.5 738 762 T 592.3 0.7 743 G 558.8 - 785 G 541.6 - 761 763 G 569.2 - 740 T 570.3 -0.2 784 G 545.3 - 764 764 T 545.3 3.1 763 T 566.3 0.8 787 G 572.1 - 741 765 G 571.2 - 742 T 572.1 -0.1 788 T 565.1 3.4 766 766 G 565.1 - 765 T 572.2 1.4 791 G 570.4 - 745 767 T 561 3.8 768 G 594.6 - 786 T 560 1.4 744 768 T 591.4 1.2 747 G 558.8 - 789 G 561 - 767 769 T 578.2 1.3 746 T 567.8 0.3 792 G 578.1 - 770 770 T 578.1 3.6 769 G 583.4 - 794 T 565.5 0.6 749 771 T 575.1 3.7 772 G 591.9 - 790 T 561.5 1.1 748 772 T 586.6 1.3 750 G 561.8 - 793 G 575.1 - 771 773 T 481.1 3.1 774 G 572.6 - 51 T 572.9 0.2 49 774 T 575.4 -0.2 751 G 571.2 - 795 G 481.1 - 773 775 T 484.7 3.8 776 G 576.6 - 796 T 570.3 0.5 752 776 T 579.9 -0.1 753 G 568.6 - 797 G 484.7 - 775 777 T 494.2 4.4 778 G 582.2 - 798 T 567.4 0.8 754 778 T 585.1 -0.2 755 G 565.2 - 799 G 494.2 - 777 779 T 510 4.6 780 G 588.2 - 800 T 563.7 1.3 756 780 T 589.9 0 757 G 560.9 - 801 G 510 - 779 781 T 530.9 4.3 782 G 593.3 - 802 T 560.6 1.6 758 782 T 593.4 0.4 761 G 558 - 805 G 530.9 - 781 783 G 566.5 - 760 T 565.6 -0.3 804 G 535.6 - 784 784 T 535.6 2.9 783 T 562.6 0.7 807 G 570.3 - 763 785 T 552.9 4 786 G 596.7 - 806 T 558.8 1.6 762 786 T 594.6 0.9 767 G 556.8 - 811 G 552.9 - 785 787 G 566.3 - 764 T 571.6 -0.4 808 G 555.1 - 788

154

788 T 555.1 3.3 787 T 565 1.4 813 G 572.1 - 765 789 T 572.1 3.6 790 G 596.8 - 812 T 558.8 1.3 768 790 T 591.9 1.5 771 G 558.1 - 817 G 572.1 - 789 791 G 572.2 - 766 T 571 -0.1 814 G 578.4 - 792 792 T 578.4 3.4 791 G 577.7 - 819 G 567.8 - 769 793 T 583.6 3.4 794 G 591.1 - 818 T 561.8 1.1 772 794 T 583.4 1.7 770 T 563.2 0.5 820 G 583.6 - 793 795 T 481.2 3.5 796 G 573.1 - 810 T 571.2 0.4 774 796 T 576.6 -0.2 775 G 569.5 - 815 G 481.2 - 795 797 T 486.9 4.3 798 G 578.2 - 816 T 568.6 0.7 776 798 T 582.2 -0.2 777 G 566.5 - 821 G 486.9 - 797 799 T 499.7 4.6 800 G 585.1 - 822 T 565.2 1.2 778 800 T 588.2 -0.2 779 G 562.2 - 823 G 499.7 - 799 801 T 519.1 4.6 802 G 591.9 - 824 T 560.9 1.6 780 802 T 593.3 0.1 781 G 557.8 - 825 G 519.1 - 801 803 G 563.8 - 50 T 559.1 -0.2 52 G 527.9 - 804 804 T 527.9 2.8 803 T 559.5 0.5 827 G 565.6 - 783 805 T 542.3 4 806 G 597 - 826 T 558 1.8 782 806 T 596.7 0.8 785 G 555.5 - 831 G 542.3 - 805 807 G 562.6 - 784 T 566.4 -0.4 828 G 540.9 - 808 808 T 540.9 3.3 807 T 558.7 1.3 833 G 571.6 - 787 809 T 479.4 3.2 810 G 569.7 - 53 T 571.3 0.3 51 810 T 573.1 -0.3 795 G 569.5 - 829 G 479.4 - 809 811 T 565.3 3.3 812 G 600 - 832 T 556.8 1.8 786 812 T 596.8 1.4 789 G 555.4 - 837 G 565.3 - 811 813 G 565 - 788 T 573.6 -0.4 834 G 572 - 814 814 T 572 3.5 813 G 568.4 - 839 G 571 - 791 815 T 481.8 3.9 816 G 573.7 - 830 T 569.5 0.6 796 816 T 578.2 -0.3 797 G 567.6 - 835 G 481.8 - 815 817 T 584.3 3.2 818 G 598.8 - 838 T 558.1 1.5 790 818 T 591.1 1.9 793 G 558.2 - 843 G 584.3 - 817 819 T 577.7 1.9 792 T 567.1 0.2 840 G 591.4 - 820 820 T 591.4 3.3 819 G 588.1 - 844 G 563.2 - 794 821 T 490.2 4.6 822 G 580.5 - 836 T 566.5 1 798 822 T 585.1 -0.4 799 G 563.6 - 841 G 490.2 - 821 823 T 507 4.6 824 G 588.8 - 842 T 562.2 1.5 800 824 T 591.9 -0.2 801 G 558.4 - 845 G 507 - 823 825 T 530 4.2 826 G 595.7 - 846 T 557.8 2 802 826 T 597 0.3 805 G 554.7 - 851 G 530 - 825 827 G 559.5 - 804 T 556.7 -0.3 848 G 526.9 - 828 828 T 526.9 3.1 827 T 554.8 1.1 855 G 566.4 - 807 829 T 478.9 3.6 830 G 569 - 850 T 569.5 0.5 810 830 T 573.7 -0.4 815 G 568 - 853 G 478.9 - 829 831 T 555.3 3.7 832 G 600.9 - 852 T 555.5 2.1 806

155

832 T 600 1.1 811 G 553.5 - 859 G 555.3 - 831 833 G 558.7 - 808 T 570.5 -0.5 856 G 554.9 - 834 834 T 554.9 3.4 833 T 556.8 2.3 861 G 573.6 - 813 835 T 482.9 4.3 836 G 574.7 - 854 T 567.6 0.9 816 836 T 580.5 -0.4 821 G 565.2 - 857 G 482.9 - 835 837 T 579.3 3.1 838 G 603.6 - 860 T 555.4 2 812 838 T 598.8 2 817 G 554.5 - 863 G 579.3 - 837 839 T 568.4 2.1 814 T 573.7 -0.1 862 G 595.7 - 840 840 T 595.7 3.2 839 G 581 - 867 G 567.1 - 819 841 T 495.3 4.6 842 G 583.9 - 858 T 563.6 1.5 822 842 T 588.8 -0.3 823 G 559.8 - 865 G 495.3 - 841 843 T 598.6 2.9 844 G 600.6 - 864 T 558.2 1 818 844 T 588.1 2.4 820 T 560.2 0.9 868 G 598.6 - 843 845 T 516.7 4.4 846 G 593 - 866 T 558.4 2.2 824 846 T 595.7 0.1 825 G 554.4 - 869 G 516.7 - 845 847 G 555.1 - 52 T 546.1 -0.3 55 T 517.6 3 848 848 G 517.6 - 847 T 551.1 0.8 873 G 556.7 - 827 849 G 477.9 - 850 G 565.2 - 54 T 568.4 0.4 53 850 T 569 -0.4 829 G 566.7 - 871 T 477.9 3.3 849 851 T 543 3.5 852 G 599.8 - 870 T 554.7 2.6 826 852 T 600.9 0.9 831 G 552.1 - 877 G 543 - 851 853 T 478.3 4 854 G 568.7 - 872 T 568 0.8 830 854 T 574.7 -0.5 835 G 566.1 - 875 G 478.3 - 853 855 G 554.8 - 828 T 557.6 -0.6 874 G 530.5 - 856 856 T 530.5 3.4 855 T 548.4 2 879 G 570.5 - 833 857 T 485.2 4.6 858 G 577.3 - 876 T 565.2 1.4 836 858 T 583.9 -0.4 841 G 561.4 - 881 G 485.2 - 857 859 T 569.6 2.9 860 G 604.9 - 878 T 553.5 2.4 832 860 T 603.6 1.6 837 G 552.6 - 883 G 569.6 - 859 861 G 556.8 - 834 T 578.7 -0.7 880 G 586.4 - 862 862 T 586.4 3.3 861 G 565.2 - 885 G 573.7 - 839 863 T 595.6 2.5 864 G 608.6 - 884 T 554.5 1.7 838 864 T 600.6 2.7 843 G 554.7 - 889 G 595.6 - 863 865 T 503.2 4.5 866 G 588.4 - 882 T 559.8 2.3 842 866 T 593 -0.1 845 G 554.9 - 887 G 503.2 - 865 867 T 581 3 840 T 566.7 0.6 886 G 616.6 - 868 868 T 616.6 2.7 867 G 602.2 - 890 G 560.2 - 844 869 T 529.2 4 870 G 597.2 - 888 T 554.4 2.7 846 870 T 599.8 0.3 851 G 550.5 - 897 G 529.2 - 869 871 G 476.5 - 872 G 562.8 - 892 T 566.7 0.6 850 872 T 568.7 -0.5 853 G 565.6 - 893 T 476.5 3.7 871 873 G 551.1 - 848 G 538.1 - 896 T 510.2 3.4 874 874 G 510.2 - 873 T 546.4 1.5 901 G 557.6 - 855 875 T 477.7 4.5 876 T 569.5 -0.8 894 T 566.1 1.2 854

156

876 T 577.3 -0.7 857 G 563 - 899 G 477.7 - 875 877 T 557.7 3.2 878 G 603.6 - 898 T 552.1 2.8 852 878 T 604.9 1.4 859 G 550.9 - 905 G 557.7 - 877 879 G 548.4 - 856 T 567 -1 902 G 549.9 - 880 880 T 549.9 3.8 879 T 542.8 3.5 907 G 578.7 - 861 881 T 489.7 4.8 882 G 581.7 - 900 T 561.4 2 858 882 T 588.4 -0.6 865 G 555.8 - 903 G 489.7 - 881 883 T 585.2 2.4 884 G 609.2 - 906 T 552.6 2.3 860 884 T 608.6 2.4 863 G 553.4 - 911 G 585.2 - 883 885 T 565.2 3.5 862 T 583.9 -0.3 908 G 638.5 - 886 886 T 638.5 2.7 885 G 601.2 - 918 G 566.7 - 867 887 T 514.5 4.4 888 G 593.3 - 904 T 554.9 2.6 866 888 T 597.2 -0.1 869 G 549.7 - 913 G 514.5 - 887 889 T 618.2 2.1 890 G 618.1 - 912 T 554.7 1.7 864 890 T 602.2 3.6 868 T 556.4 1.5 917 G 618.2 - 889 891 G 476.6 - 892 G 559 - 56 T 564 0.4 54 892 T 562.8 -0.5 871 G 563 - 909 T 476.6 3.4 891 893 G 473.8 - 894 G 561.5 - 910 T 565.6 1 872 894 G 569.5 - 875 T 563.9 1.4 915 T 473.8 4.2 893 895 G 541.6 - 55 T 523.9 -0.3 57 T 502.6 3.4 896 896 G 502.6 - 895 G 540.4 - 919 T 538.1 -0.7 873 897 T 544.3 3.4 898 G 601 - 914 T 550.5 2.9 870 898 T 603.6 0.5 877 G 548.1 - 923 G 544.3 - 897 899 T 478.2 4.8 900 G 572.7 - 916 T 563 1.7 876 900 T 581.7 -0.9 881 G 557.7 - 921 G 478.2 - 899 901 G 546.4 - 874 T 538.7 -1.2 920 G 507.3 - 902 902 T 507.3 3.9 901 T 535.2 2.8 925 G 567 - 879 903 T 498.4 4.6 904 G 587.4 - 922 T 555.8 2.6 882 904 T 593.3 -0.6 887 G 548.7 - 927 G 498.4 - 903 905 T 573.2 2.4 906 G 606.2 - 924 T 550.9 2.7 878 906 T 609.2 1.9 883 G 552.3 - 933 G 573.2 - 905 907 G 542.8 - 880 T 597.5 -1.5 926 G 623.4 - 908 908 T 623.4 3.3 907 G 565.9 - 943 G 583.9 - 885 909 G 473.7 - 910 G 554.7 - 930 T 563 0.8 892 910 T 561.5 -0.7 893 T 562.5 1.2 931 T 473.7 3.9 909 911 T 601.7 1.8 912 G 614.4 - 934 T 553.4 2.3 884 912 T 618.1 3.2 889 G 557.7 - 939 G 601.7 - 911 913 T 529.7 3.7 914 G 597.6 - 928 T 549.7 3.2 888 914 T 601 0.3 897 G 545.1 - 945 G 529.7 - 913 915 T 470.7 4.8 916 T 562.7 -0.9 932 G 563.9 - 894 916 T 572.7 -1.1 899 G 560 - 937 G 470.7 - 915 917 T 665.7 1.8 918 G 650.3 - 940 G 556.4 - 890 918 T 601.2 4.4 886 T 561.5 1.6 944 G 665.7 - 917 919 T 540.4 0.9 896 G 507.7 - 936 G 484.3 - 920

157

920 T 484.3 4 919 T 533.8 1.8 941 G 538.7 - 901 921 T 482.3 5 922 G 578.9 - 938 T 557.7 2.4 900 922 T 587.4 -1.1 903 G 549.5 - 947 G 482.3 - 921 923 T 561.1 2.5 924 T 602.9 0.6 946 T 548.1 3.4 898 924 T 606.2 1.4 905 G 548.4 - 951 G 561.1 - 923 925 G 535.2 - 902 T 550.3 -2.1 942 G 521.8 - 926 926 T 521.8 4.7 925 T 509.6 4.2 959 G 597.5 - 907 927 T 512.4 4.4 928 G 593.3 - 948 T 548.7 3.3 904 928 T 597.6 -0.5 913 G 541.3 - 957 G 512.4 - 927 929 G 475.2 - 930 G 551.2 - 58 T 558.1 0.6 56 930 T 554.7 -0.6 909 T 558.2 0.9 949 T 475.2 3.6 929 931 T 468.1 4.3 932 T 552.3 -0.9 950 G 562.5 - 910 932 G 562.7 - 915 T 561 1.8 953 G 468.1 - 931 933 T 588.3 1.7 934 G 606.3 - 952 T 552.3 2.8 906 934 T 614.4 2.7 911 G 559.2 - 961 G 588.3 - 933 935 G 521.4 - 57 T 493.8 -0.3 59 T 485.6 3.9 936 936 G 485.6 - 935 G 526.5 - 955 T 507.7 -0.8 919 937 T 469 5 938 G 567.4 - 954 T 560 2.2 916 938 T 578.9 -1.3 921 G 552.3 - 963 G 469 - 937 939 T 614 1.1 940 G 616.5 - 962 T 557.7 2.2 912 940 T 650.3 4.2 917 G 574.9 - 967 G 614 - 939 941 G 533.8 - 920 T 506.9 -1.2 956 G 466.9 - 942 942 T 466.9 4.8 941 T 511.7 3.8 965 G 550.3 - 925 943 T 565.9 6 908 T 640.5 -2 960 G 736.8 - 944 944 T 736.8 1.1 943 G 648.9 - 968 G 561.5 - 918 945 G 548.2 - 946 G 600 - 958 T 545.1 3.5 914 946 G 602.9 - 923 T 542.5 3.8 969 T 548.2 3.2 945 947 T 493.3 4.6 948 G 587.1 - 964 T 549.5 3.2 922 948 T 593.3 -1.1 927 G 539.1 - 975 G 493.3 - 947 949 T 469.7 4.2 950 T 544.7 -0.8 971 G 558.2 - 930 950 G 552.3 - 931 T 558.6 1.5 973 G 469.7 - 949 951 G 579 - 952 T 601.4 1.2 970 T 548.4 3.4 924 952 T 606.3 2.1 933 G 552.7 - 983 T 579 1.8 951 953 T 461.6 5 954 T 554.7 -1.3 974 G 561 - 932 954 T 567.4 -1.2 937 G 555.5 - 979 G 461.6 - 953 955 T 526.5 1.4 936 G 464.8 - 977 G 448.2 - 956 956 T 448.2 4.3 955 T 514.7 2.8 981 G 506.9 - 941 957 T 532 3.5 958 G 597.7 - 976 T 541.3 3.7 928 958 T 600 -0.1 945 G 535.1 - 985 G 532 - 957 959 G 509.6 - 926 G 545.9 - 966 G 530 - 960 960 T 530 5.6 959 T 546.9 7.4 998 G 640.5 - 943 961 T 602.1 0.8 962 G 599.2 - 984 T 559.2 3.1 934 962 T 616.5 3.8 939 G 577.5 - 989 G 602.1 - 961 963 T 473.7 5.1 964 G 577 - 980 T 552.3 3.1 938

158

964 T 587.1 -1.4 947 G 539.6 - 987 G 473.7 - 963 965 G 511.7 - 942 T 518.5 -2.2 982 T 497.7 5.1 966 966 G 497.7 - 965 G 486.8 - 1007 T 545.9 -2.2 959 967 T 596.8 0.9 968 G 584.4 - 990 T 574.9 2.1 940 968 T 648.9 5.5 944 G 602.1 - 999 G 596.8 - 967 969 G 568.8 - 970 T 599.5 0.4 986 G 542.5 - 946 970 G 601.4 - 951 T 542.1 4 1001 T 568.8 2 969 971 G 544.7 - 949 T 552.8 1.1 992 T 472.5 3.8 972 972 G 472.5 - 971 G 541.9 - 60 T 550.8 0.6 58 973 T 460 4.6 974 T 542.4 -1.2 991 G 558.6 - 950 974 G 554.7 - 953 G 556.2 - 993 G 460 - 973 975 T 512.6 4.2 976 G 594.6 - 988 T 539.1 4 948 976 T 597.7 -0.7 957 G 528.6 - 1005 G 512.6 - 975 977 G 443.6 - 978 T 505.6 1 995 T 464.8 -1.2 955 978 G 495.6 - 59 T 447.3 -0.3 997 T 443.6 4.7 977 979 T 458.2 5.3 980 G 562.9 - 994 T 555.5 2.7 954 980 T 577 -1.7 963 G 543.5 - 1003 G 458.2 - 979 981 G 514.7 - 956 T 475.2 -2.8 996 T 473.9 5.7 982 982 G 473.9 - 981 T 484.7 6 1009 G 518.5 - 965 983 G 599.2 - 984 T 595.6 1.8 1002 T 552.7 3.7 952 984 T 599.2 2.9 961 G 559.4 - 1011 T 599.2 0.9 983 985 G 555.6 - 986 T 599.1 -0.4 1006 T 535.1 4.2 958 986 G 599.5 - 969 T 531 4.5 1022 T 555.6 2.7 985 987 T 489.9 4.8 988 G 588.9 - 1004 T 539.6 3.9 964 988 T 594.6 -1.5 975 G 524.6 - 1020 G 489.9 - 987 989 G 627.2 - 990 T 583 3.6 1012 T 577.5 3.2 962 990 T 584.4 5 967 G 602.5 - 1024 T 627.2 -0.2 989 991 G 542.4 - 973 T 554 2 1013 G 461.8 - 992 992 T 461.8 4.4 991 T 533.2 -1 1015 G 552.8 - 971 993 T 450.5 5.3 994 G 548.7 - 1014 T 556.2 2.4 974 994 T 562.9 -1.7 979 G 547.4 - 1018 G 450.5 - 993 995 G 505.6 - 977 T 420.2 -1.2 1017 T 440.2 6 996 996 G 440.2 - 995 T 480.2 4.8 1026 G 475.2 - 981 997 G 374.2 - - T 436.3 0.2 1244 G 447.3 - 978 998 G 546.9 - 960 G 660.8 - 1008 T 692.4 4.9 1000 999 G 782.3 - 1000 T 629.9 5.4 1025 T 602.1 4.9 968 1000 G 692.4 - 998 G 514.9 - 1049 T 782.3 -4 999 1001 G 592 - 1002 T 596.4 1.1 1023 G 542.1 - 970 1002 G 595.6 - 983 G 541.6 - 1028 T 592 1.3 1001 1003 T 467.2 5.3 1004 G 577.6 - 1019 T 543.5 3.9 980 1004 T 588.9 -1.8 987 G 525.3 - 1030 G 467.2 - 1003 1005 G 539.2 - 1006 T 599.1 -1.2 1021 T 528.6 4.4 976 1006 G 599.1 - 985 T 521.1 5 1038 T 539.2 3.4 1005 1007 T 486.8 6.8 966 G 551.9 - 1010 T 597.5 6.5 1008

159

1008 G 597.5 - 1007 G 471.8 - 1048 T 660.8 -3.4 998 1009 G 484.7 - 982 G 503.1 - 1027 T 547.9 6.4 1010 1010 G 547.9 - 1009 T 447.9 8.6 1051 T 551.9 -3.3 1007 1011 G 628.5 - 1012 T 589.8 2.4 1029 T 559.4 3.7 984 1012 G 583 - 989 G 556.6 - 1040 T 628.5 -0.1 1011 1013 T 444.7 4.9 1014 T 534.3 -1.5 1032 G 554 - 991 1014 T 548.7 -1.7 993 G 547.8 - 1036 G 444.7 - 1013 1015 G 533.2 - 992 T 548.1 1.5 1033 G 465.8 - 1016 1016 T 465.8 4.1 1015 T 531.2 -0.8 61 G 542.3 - 60 1017 G 399.1 - 1244 T 444.4 0.6 1035 G 420.2 - 995 1018 T 452.2 5.6 1019 G 564.8 - 1037 T 547.4 3.6 994 1019 T 577.6 -2.2 1003 G 527.6 - 1042 G 452.2 - 1018 1020 G 518.6 - 1021 G 598 - 1031 T 524.6 4.7 988 1021 G 599.1 - 1005 T 512.6 5.5 1044 T 518.6 4 1020 1022 G 580.5 - 1023 T 597.8 0.2 1039 G 531 - 986 1023 G 596.4 - 1001 T 527.7 4.4 1046 T 580.5 1.4 1022 1024 G 701.5 - 1025 T 586 4.2 1041 T 602.5 4 990 1025 G 629.9 - 999 G 466 - 1057 T 701.5 -1 1024 1026 G 480.2 - 996 G 445 - 1034 T 511.3 7.4 1027 1027 G 511.3 - 1026 T 456.6 10.1 1059 T 503.1 -4.1 1009 1028 G 617.9 - 1029 T 594.2 1.5 1047 T 541.6 4.1 1002 1029 G 589.8 - 1011 G 535 - 1065 T 617.9 0.2 1028 1030 T 493.7 4.9 1031 G 591.8 - 1043 T 525.3 4.8 1004 1031 T 598 -1.8 1020 G 507.1 - 1063 G 493.7 - 1030 1032 G 534.3 - 1013 G 550.2 - 1054 G 444.9 - 1033 1033 T 444.9 4.7 1032 T 520.8 -1.3 1055 G 548.1 - 1015 1034 G 528.3 - 1035 T 511.3 13.1 1067 T 445 -3.8 1026 1035 G 444.4 - 1017 G 354.6 - 1248 T 528.3 10.1 1034 1036 T 437.4 5.7 1037 G 550 - 1053 T 547.8 3.2 1014 1037 T 564.8 -2.4 1018 G 532.3 - 1061 G 437.4 - 1036 1038 G 566.8 - 1039 T 599 -0.6 1045 G 521.1 - 1006 1039 G 597.8 - 1022 T 516.5 4.8 1069 T 566.8 2.3 1038 1040 G 666.4 - 1041 T 594.5 2.9 1066 T 556.6 4.3 1012 1041 G 586 - 1024 G 531.1 - 1077 T 666.4 -1.1 1040 1042 T 473.3 5.6 1043 G 575.5 - 1062 T 527.6 4.6 1019 1043 T 591.8 -2.6 1030 G 508.9 - 1075 G 473.3 - 1042 1044 G 550.6 - 1045 T 600.1 -1.7 1064 G 512.6 - 1021 1045 G 599 - 1038 T 506.8 5 1083 T 550.6 3 1044 1046 G 604.4 - 1047 T 596.5 0.8 1070 G 527.7 - 1023 1047 G 594.2 - 1028 G 521.7 - 1081 T 604.4 0.9 1046 1048 G 606.6 - 1052 T 635.4 3.9 1050 T 471.8 7.6 1008 1049 G 636.1 - 1050 T 643.7 4.4 1058 T 514.9 6.9 1000 1050 G 635.4 - 1048 T 440.8 8.9 1104 T 636.1 -2.9 1049 1051 G 447.9 - 1010 G 543.5 - 1060 T 630.9 4.9 1052

160

1052 G 630.9 - 1051 T 430.3 10.4 1100 T 606.6 -2.6 1048 1053 T 550 -2.2 1036 G 539.2 - 1071 T 423.7 5.3 1054 1054 G 423.7 - 1053 G 530.2 - 1073 T 550.2 2.6 1032 1055 G 520.8 - 1033 T 547.9 1.9 1074 G 451.4 - 1056 1056 T 451.4 4.5 1055 T 516.9 -0.9 62 G 533.5 - 61 1057 G 675.3 - 1058 T 652.4 3.3 1078 T 466 5.8 1025 1058 G 643.7 - 1049 G 455 - 1106 T 675.3 -3.2 1057 1059 G 456.6 - 1027 G 470.4 - 1068 T 575.4 5 1060 1060 G 575.4 - 1059 T 416.1 11.7 1099 T 543.5 -2.9 1051 1061 T 453 5.8 1062 G 553.8 - 1072 T 532.3 4.5 1037 1062 T 575.5 -2.6 1042 G 516.4 - 1085 G 453 - 1061 1063 G 529 - 1064 T 598 -2.4 1076 T 507.1 5.5 1031 1064 G 600.1 - 1044 T 498.1 5.5 1089 T 529 4.2 1063 1065 G 642.8 - 1066 T 597.6 1.8 1082 T 535 4.6 1029 1066 G 594.5 - 1040 G 519.6 - 1091 T 642.8 -0.7 1065 1067 G 511.3 - 1034 G 375.8 - 1079 T 577.6 3.5 1068 1068 G 577.6 - 1067 T 489.5 11.7 1102 T 470.4 -1.3 1059 1069 G 590.6 - 1070 T 597.4 -0.2 1084 G 516.5 - 1039 1070 G 596.5 - 1046 G 512.5 - 1095 T 590.6 0.9 1069 1071 T 436.6 6.3 1072 G 536.7 - 1088 T 539.2 3.8 1053 1072 T 553.8 -2.8 1061 G 523.2 - 1097 G 436.6 - 1071 1073 T 530.2 -2 1054 G 546.8 - 1087 G 413.4 - 1074 1074 T 413.4 5.2 1073 T 507.4 -1.6 1093 G 547.9 - 1055 1075 G 501.9 - 1076 G 581.4 - 1086 T 508.9 5.7 1043 1076 G 598 - 1063 T 494.6 6 1109 T 501.9 4.9 1075 1077 G 677.4 - 1078 T 606.7 2.7 1092 T 531.1 5 1041 1078 G 652.4 - 1057 G 449.8 - 1111 T 677.4 -1.1 1077 1079 T 589.6 11.4 1080 G 589.8 - 63 T 375.8 11.5 1067 1080 T 544.7 9.2 1248 G 389 - - G 589.6 - 1079 1081 G 623.5 - 1082 T 598.3 1 1096 T 521.7 4.8 1047 1082 G 597.6 - 1065 G 511.4 - 1115 T 623.5 -0.1 1081 1083 G 577.2 - 1084 G 597.5 - 1090 G 506.8 - 1045 1084 G 597.4 - 1069 T 505.7 5.1 1119 T 577.2 2.1 1083 1085 T 481.9 5.7 1086 G 561.4 - 1098 T 516.4 5.6 1062 1086 T 581.4 -2.6 1075 G 499.7 - 1121 G 481.9 - 1085 1087 G 416.7 - 1088 G 519.7 - 1113 T 546.8 3.1 1073 1088 T 536.7 -2.8 1071 G 525.8 - 1117 T 416.7 6 1087 1089 T 562.3 2.6 1090 G 598.7 - 1110 G 498.1 - 1064 1090 T 597.5 -1 1083 G 498.9 - 1125 G 562.3 - 1089 1091 G 654.5 - 1092 T 605.7 1.5 1116 T 519.6 4.6 1066 1092 G 606.7 - 1077 T 504.2 4.8 1127 T 654.5 -0.8 1091 1093 G 507.4 - 1074 G 552.6 - 1114 T 427.2 5 1094 1094 G 427.2 - 1093 T 499.4 -1.2 64 G 525.9 - 62 1095 G 607 - 1096 T 596.7 0.1 1120 T 512.5 4.9 1070

161

1096 G 598.3 - 1081 G 506.4 - 1131 T 607 0.8 1095 1097 T 464.3 6.1 1098 G 541.1 - 1118 T 523.2 5.3 1072 1098 T 561.4 -3.1 1085 G 502.8 - 1123 G 464.3 - 1097 1099 G 416.1 - 1060 G 494.6 - 1103 T 582.3 3 1101 1100 G 562.2 - 1101 T 659.9 1.5 1105 G 430.3 - 1052 1101 G 582.3 - 1099 T 374.7 7.9 1138 T 562.2 -1.5 1100 1102 G 489.5 - 1068 T 395.3 6.6 1108 T 483.5 4.4 1103 1103 G 483.5 - 1102 G 367 - 1133 T 494.6 -2.2 1099 1104 G 618.8 - 1105 T 670.8 1 1107 G 440.8 - 1050 1105 G 659.9 - 1100 T 426.7 6.8 1143 T 618.8 -1.4 1104 1106 G 660 - 1107 T 652.1 1.8 1112 T 455 6.6 1058 1107 G 670.8 - 1104 T 419.7 6.1 1150 T 660 -0.9 1106 1108 T 527.4 9 63 T 508.2 4.2 1134 G 395.3 - 1102 1109 T 538.2 3.8 1110 T 594.6 -2.7 1122 G 494.6 - 1076 1110 T 598.7 -1.6 1089 G 490 - 1141 G 538.2 - 1109 1111 T 653.8 -1.7 1112 G 641.5 - 1128 T 449.8 5.5 1078 1112 G 652.1 - 1106 G 454.6 - 1155 G 653.8 - 1111 1113 T 519.7 -2.3 1087 G 529.3 - 1129 T 394.4 5.6 1114 1114 G 394.4 - 1113 G 493.4 - 1136 T 552.6 2.4 1093 1115 G 633.3 - 1116 T 604.2 0.9 1132 T 511.4 4.3 1082 1116 G 605.7 - 1091 G 498.1 - 1144 T 633.3 -0.4 1115 1117 T 443.6 6.8 1118 G 519.7 - 1130 T 525.8 4.8 1088 1118 T 541.1 -3.2 1097 G 512.2 - 1139 G 443.6 - 1117 1119 G 591.2 - 1120 T 593.7 -0.3 1126 G 505.7 - 1084 1120 G 596.7 - 1095 T 503.1 4.5 1146 T 591.2 0.6 1119 1121 G 515.7 - 1122 T 577.9 -3 1124 T 499.7 5.9 1086 1122 G 594.6 - 1109 T 480.7 6.4 1151 T 515.7 5.2 1121 1123 G 490.5 - 1124 G 549.5 - 1140 T 502.8 6.1 1098 1124 G 577.9 - 1121 T 486.7 7.1 1160 T 490.5 5.6 1123 1125 G 575.7 - 1126 T 590.6 -1.3 1142 T 498.9 5.6 1090 1126 G 593.7 - 1119 T 500.2 4.4 1156 T 575.7 1.6 1125 1127 T 668 -0.8 1128 T 608.9 1.3 1145 G 504.2 - 1092 1128 T 641.5 1.6 1111 T 457.2 4.2 1173 G 668 - 1127 1129 G 427.6 - 1130 G 498.6 - 1148 T 529.3 3.6 1113 1130 T 519.7 -3.3 1117 G 516 - 1153 T 427.6 7.1 1129 1131 G 613.2 - 1132 T 599.9 0.5 1147 T 506.4 4.2 1096 1132 G 604.2 - 1115 G 496.9 - 1158 T 613.2 0.1 1131 1133 G 451.7 - 1135 T 428.6 0.8 66 T 367 9.6 1103 1134 G 508.2 - 1108 G 347.5 - - T 361.7 7.5 1135 1135 G 361.7 - 1134 G 335 - - T 451.7 -0.3 1133 1136 T 493.4 -2.1 1114 G 541 - 1149 T 388.2 5.6 1137 1137 G 388.2 - 1136 G 482.8 - 65 T 521.7 1.4 64 1138 G 483.7 - 66 T 503 -0.2 67 G 374.7 - 1101 1139 T 470.2 6.4 1140 G 527.3 - 1154 T 512.2 6 1118

162

1140 T 549.5 -3.3 1123 G 492.4 - 1164 G 470.2 - 1139 1141 G 558.3 - 1142 T 594.7 -1.7 1152 T 490 5.7 1110 1142 G 590.6 - 1125 T 494.2 4.6 1168 T 558.3 2.7 1141 1143 G 550.3 - 67 T 590 -0.2 68 G 426.7 - 1105 1144 G 637.1 - 1145 T 616.3 0.8 1159 T 498.1 4.5 1116 1145 G 608.9 - 1127 G 459.3 - 1172 T 637.1 -0.5 1144 1146 G 594.5 - 1147 T 593.2 -0.4 1157 G 503.1 - 1120 1147 G 599.9 - 1131 T 499.1 4 1170 T 594.5 0.4 1146 1148 T 498.6 -3.4 1129 G 515.5 - 1162 T 403.8 7 1149 1149 G 403.8 - 1148 G 458.5 - 1166 T 541 2 1136 1150 G 617.2 - 68 T 630.3 0.6 69 G 419.7 - 1107 1151 G 546.7 - 1152 T 595 -2.3 1161 G 480.7 - 1122 1152 G 594.7 - 1141 T 482.7 5.4 1178 T 546.7 3.3 1151 1153 T 445.7 7.3 1154 G 500.4 - 1163 T 516 5.6 1130 1154 T 527.3 -3.6 1139 G 499.8 - 1174 G 445.7 - 1153 1155 G 658 - 69 T 654.4 -0.1 71 T 454.6 5.3 1112 1156 G 578.4 - 1157 T 586.5 -0.9 1169 G 500.2 - 1126 1157 G 593.2 - 1146 T 501 4.1 1180 T 578.4 0.8 1156 1158 G 611.2 - 1159 T 608 0.2 1171 T 496.9 4.4 1132 1159 G 616.3 - 1144 T 484.9 3.7 1182 T 611.2 -0.2 1158 1160 G 523.6 - 1161 T 577.2 -4.1 1165 G 486.7 - 1124 1161 G 595 - 1151 T 469.1 5.6 1185 T 523.6 4.6 1160 1162 G 415.9 - 1163 G 471.6 - 1176 T 515.5 5 1148 1163 T 500.4 -3.7 1153 G 505.3 - 1183 T 415.9 7.7 1162 1164 G 500.6 - 1165 G 548.2 - 1175 T 492.4 6.6 1140 1165 G 577.2 - 1160 T 472.9 6.9 1189 T 500.6 6.3 1164 1166 T 458.5 -2.2 1149 G 524.1 - 1177 T 378.4 6.7 1167 1167 G 378.4 - 1166 G 449.6 - 70 T 514.7 0.4 65 1168 T 565.3 1.4 1169 G 583.5 - 1179 G 494.2 - 1142 1169 G 586.5 - 1156 T 500.1 4.3 1187 G 565.3 - 1168 1170 G 590.6 - 1171 T 596.8 -0.3 1181 G 499.1 - 1147 1171 G 608 - 1158 T 495.7 3.3 1191 T 590.6 0.5 1170 1172 G 648.4 - 72 T 632.6 0.9 73 T 459.3 3.7 1145 1173 G 663.7 - 71 T 661.4 0.6 72 G 457.2 - 1128 1174 T 474.4 6.5 1175 G 520.2 - 1184 T 499.8 6.8 1154 1175 T 548.2 -3.6 1164 G 483.7 - 1196 G 474.4 - 1174 1176 T 471.6 -2.7 1162 G 509.3 - 1192 T 390.6 7.7 1177 1177 G 390.6 - 1176 G 419.7 - 1194 T 524.1 4.1 1166 1178 T 558.1 1.9 1179 G 584.9 - 1186 G 482.7 - 1152 1179 T 583.5 -0.7 1168 G 494.9 - 1198 G 558.1 - 1178 1180 G 574.1 - 1181 T 584.9 -0.5 1188 G 501 - 1157 1181 G 596.8 - 1170 T 503 3.7 1200 T 574.1 0.4 1180 1182 G 599.8 - 73 T 622.5 -0.3 75 G 484.9 - 1159 1183 T 442.7 8 1184 G 486.7 - 1193 T 505.3 6.2 1163

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1184 T 520.2 -4.1 1174 G 493.9 - 1203 G 442.7 - 1183 1185 T 554.6 3.2 1186 G 592.8 - 1190 G 469.1 - 1161 1186 T 584.9 -1.8 1178 G 484.6 - 1205 G 554.6 - 1185 1187 T 561.3 0.6 1188 G 574.4 - 1199 G 500.1 - 1169 1188 G 584.9 - 1180 T 505.9 3.7 1207 G 561.3 - 1187 1189 T 534.9 3.3 1190 T 568.4 -2.6 1197 G 472.9 - 1165 1190 T 592.8 -2.5 1185 G 466.7 - 1210 G 534.9 - 1189 1191 G 579.8 - 75 T 603.7 0.1 76 G 495.7 - 1171 1192 G 409.6 - 1193 G 442.4 - 1202 T 509.3 4 1176 1193 T 486.7 -4 1183 G 507.7 - 1208 T 409.6 9.5 1192 1194 T 419.7 -2.4 1177 G 502.7 - 1201 T 369.2 9 1195 1195 G 369.2 - 1194 G 402.7 - 74 T 463.6 0.9 70 1196 G 518 - 1197 T 545.3 -4.4 1204 T 483.7 7.8 1175 1197 G 568.4 - 1189 T 463.7 6 1215 T 518 5.4 1196 1198 T 553.5 1 1199 G 566.5 - 1206 T 494.9 4.6 1179 1199 T 574.4 -0.2 1187 G 505.3 - 1214 G 553.5 - 1198 1200 G 563.6 - 76 T 584.9 -0.4 77 G 503 - 1181 1201 G 427.6 - 1202 G 360.7 - 1238 T 502.7 3.4 1194 1202 T 442.4 -2.1 1192 G 540 - 1243 T 427.6 8 1201 1203 G 488.5 - 1204 G 524.1 - 1209 T 493.9 7.6 1184 1204 G 545.3 - 1196 T 471 7.5 1217 T 488.5 7.1 1203 1205 T 550.8 1.4 1206 G 565.3 - 1211 T 484.6 5 1186 1206 T 566.5 -1.1 1198 T 500.8 4.1 1219 G 550.8 - 1205 1207 T 553.4 0.3 77 G 570.8 - 78 G 505.9 - 1188 1208 T 447.3 9.1 1209 G 492.5 - 1213 T 507.7 6.8 1193 1209 T 524.1 -4.6 1203 G 487.2 - 1220 G 447.3 - 1208 1210 G 548.3 - 1211 T 584.3 -2.2 1216 T 466.7 5.6 1190 1211 T 565.3 -1.3 1205 T 488.5 4.3 1222 T 548.3 2.6 1210 1212 G 341.8 - 1238 G 359.8 - 1237 T 394.4 6 74 1213 T 492.5 -4.1 1208 G 535 - 1224 T 434 11.8 1243 1214 T 542 0.4 78 G 557.3 - 79 T 505.3 3.9 1199 1215 G 570.7 - 1216 T 586.9 -2.9 1218 G 463.7 - 1197 1216 G 584.3 - 1210 T 470 5.6 1225 T 570.7 2.9 1215 1217 G 547.9 - 1218 T 569 -3.1 1221 G 471 - 1204 1218 G 586.9 - 1215 T 450.9 6.4 1226 T 547.9 4.3 1217 1219 T 532.5 0.7 79 T 549.1 -1 80 G 500.8 - 1206 1220 G 513.1 - 1221 T 556.9 -5.3 1223 T 487.2 9 1209 1221 G 569 - 1217 T 457.8 7.8 1227 T 513.1 6.3 1220 1222 G 525.3 - 80 T 552.3 -0.6 81 G 488.5 - 1211 1223 G 556.9 - 1220 T 477.8 10.3 1228 T 482.6 10.4 1224 1224 G 482.6 - 1223 G 543.5 - 1241 T 535 8.4 1213 1225 G 523.2 - 81 T 556.6 -1.6 82 G 470 - 1216 1226 G 534.6 - 82 T 587.3 -1.6 83 G 450.9 - 1218 1227 G 566.6 - 83 T 629.2 -3.4 84 G 457.8 - 1221

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1228 G 599.7 - 84 T 685.4 -4 85 G 477.8 - 1223 1229 G 623.9 - 85 T 711.2 -3.7 86 T 506.1 13.4 1241 1230 G 537.4 - 86 G 451.2 - - G 516.3 - 1235 1231 T 525.4 3.2 1235 G 370.5 - - G 433.4 - 1234 1232 T 418.5 6.9 1246 T 462.6 6.9 317 G 506.9 - 321 1233 G 459.6 - 312 T 395.2 2.6 317 T 440.6 8.9 1249 1234 G 342.6 - 1239 T 433.4 11.5 1231 G 472.8 - 1236 1235 T 421.1 9.4 1240 T 516.3 5.1 1230 G 525.4 - 1231 1236 T 472.8 -6.9 1234 G 334 - - G 338.7 - 1237 1237 T 359.8 -4.7 1212 T 338.7 16.6 1236 G 330.9 - - 1238 T 360.7 1.1 1201 G 383 - 1239 T 341.8 7 1212 1239 G 414.5 - 1242 T 342.6 6.7 1234 T 383 3.2 1238 1240 G 448.8 - 1241 G 421.1 - 1235 T 483.9 6.7 1242 1241 T 543.5 -4.4 1224 G 506.1 - 1229 T 448.8 13.3 1240 1242 T 421.8 -0.2 1243 G 483.9 - 1240 T 414.5 8.3 1239 1243 G 434 - 1213 G 421.8 - 1242 T 540 3.7 1202 1244 G 436.3 - 997 T 435.4 3.2 1247 T 399.1 5.5 1017 1245 G 363 - - G 549.9 - 1246 T 535.7 -2.3 251 1246 G 430.3 - 1249 G 418.5 - 1232 T 549.9 4.4 1245 1247 G 533.6 - - G 462.3 - 1248 G 435.4 - 1244 1248 T 462.3 2.7 1247 G 544.7 - 1080 T 354.6 6.8 1035 1249 G 515.3 - - G 440.6 - 1233 T 430.3 4.3 1246

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