Author: Eline Ouwerkerk. Graduation committee: Prof.ir. R. Nijsse TU Delft. Dr.ir. M.A.N. Hendriks TU Delft. Dr.ir. F.A.

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1 Glass columns A fundamental study to slender glass columns assembled from rectangular monolithic flat glass plates under compression as a basis to design a structural glass column for a pavilion Eline Ouwerkerk 24 June 2011

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3 Author: Eline Ouwerkerk Graduation committee: Prof.ir. R. Nijsse TU Delft Dr.ir. M.A.N. Hendriks TU Delft Dr.ir. F.A. Veer TU Delft Ir. S. Pasterkamp TU Delft Ir. L.I. Vákár Movares Publication date: 24 June 2011 Delft University of Technology Faculty of Civil Engineering and Geosciences 3

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5 Preface This research project is carried out within the framework of the final course of the Master of Science program of Civil Engineering at the Delft University of Technology. The project took place under supervision of the section of Building Engineering, part of the faculty of Civil Engineering and Geosciences. It is also done in cooperation with the engineering consultant Movares, department Lichte Constructies. The topic of this research enabled me to be busy for one college year with my interests in Civil Engineering. Building projects consisting of an elegant solution for an essential structural problem. It is not necessary for a structural component to be overwhelming and dirty-looking. Also, the variety in scientific and engineering activities resulted in a nice research that kept fascinating me during the whole project. Furthermore, as the glass column is still in its early phases of design, this specific project was a nice opportunity for me to take up this challenge to contribute to the development of the structural glass column. Many people contributed their time, effort and ideas to the development of this research. First of all, the members of my examination committee are gratefully acknowledged. It has been an honour to receive their expertise comments on my research. I wish to express my gratitude to Prof. Rob Nijsse and Fred Veer for initiating this research and providing advice and expertise. Also, I would like to thank László Vákár, who invited me to do my research project in Utrecht at Movares and who was always ready to discuss the progression of the research with me. Furthermore, I owe a debt of gratitude to Max Hendriks and Sander Pasterkamp to discuss my thoughts about special topics in this research relating to numerical modelling and structural engineering. Additionally, within the company of Movares, I would like to thank the department of Lichte Constructies for spending several lunch breaks on listening to my progress presentations and providing me from some criticism. My sincere thanks goes out to the staff in the Stevin Laboratory of the Faculty of Civil Engineering and Geosciences in Delft. In particular, I owe my gratitude to Kees Baardolf for his guidance throughout the experimental phases by tackling all the technical issues. Moreover, I would like to thank Liesbeth Eekhout, Albert Bosman and Fred Schilperoort for operating the test bench during my experiments. The support of Barendsen Special Products, especially Ton Romein, is highly appreciated. This company has offered all the materials needed for this research. Additionally, Ton Romein offered me the opportunity to visit the Semcoglas factory in Nordhorn, Germany. Obviously, I am very grateful to my parents giving me advice whenever needed and to get the most out of my study days. Finally, I would like to thank my dear friend and housemate Robin for his patience and care. Eline Ouwerkerk Delft, June

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7 Summary In the world of structural engineering glass is an innovative material. Compared to other conventional structural materials like concrete, steel and timber, it is especially the transparency property that makes it a valued material. Due to the increasing demand for transparency or translucency in contemporary architecture, much more structural components as beams, plates, portals and columns are developed in glass. Besides the transparency property, the brittleness of glass makes it essentially an unsafe structural material as the residual capacity is limited. Therefore, the structural glass column is still in its early phases of development. As architects and clients, in general, do not like columns, they are said to block the view and stand in the way. Engineers need to add columns to buildings to provide support. These conflicting desires can be solved by developing a more attractive column, a glass column. The aim of this research project was to focus on further knowledge and understanding of the structural design aspects specifically related to structural glass columns and, on the basis of these findings, to design a glass column as a structural element in a pavilion. The considered slender columns were assembled from rectangular monolithic flat glass plates into different configurations. An exploratory study to the design aspects of glass columns was performed by doing experiments. One-metre-high glass columns were assembled from glass plates 8 millimetres thick, 100 millimetres wide and 1000 millimetres long and glued with a two-component adhesive based on epoxy resin (Araldite 2000 PLUS 2013) into five different configurations. These columns were compressed by a test bench with felt as the interlayer material to distribute the stresses uniformly over the crosssectional area. A thorough analysis of the columns and their structural behaviour resulted in three design aspects that should be considered in the design process of a structural glass column: - a difference in the vertical position between the assembled glass plates; - susceptibility to peak stresses at the edges of the glass column; - the stiffness properties of the glue; - imperfections like holes and scratches. As it was not observed that the latter causes initial fracture in the prototypes, it is assumed that this design aspect has minor influence. The other three aspects were investigated in more detail by both numerical and experimental investigations. A two-dimensional numerical model was developed to study two of the considered design aspects. The effect of a difference in the vertical position between the assembled glass plates (which results in protruding edges) and the stiffness properties of the glue on the stress development in the glass were studied. It was demonstrated that due to a difference in the vertical position between the glass plates, tensile stresses in the structural glazing occur. For a difference in the vertical position between the glass plates of 2.0 millimetres at an applied vertical displacement of 20 millimetres, almost the characteristic tensile strength of glass (8 MPa) was reached. From the stiffness analysis it was found that the adhesive with reduced stiffness resulted in lower stresses. This counted especially for the tensile stress, which is the most critical one in the structural design of a glass column. Furthermore, the adhesive with low stiffness resulted in a more even distribution of the stresses over the column, which significantly reduced the tensile (peak) stresses in 7

8 the column. Due to the lower Young s modulus value of the adhesive, the distance to transfer the forces from the protruding edge into the web was increased. The FE model showed good correspondence with the related experimental results: - the location of the tensile peak stresses in the numerical model due to a difference in the vertical position between glass plates coincided with the origin of the initial crack in the tested H profile column. Due to the protruding edge, the glass column was loaded uneven. As a result, shear stresses develop between the protruding flange and the web and tensile stresses arise at the bottom edge of the web. - the compressive stresses were in the same order of magnitude. The tested H profile column failed at an applied displacement of about 20 millimetres with a compressive stress of about 50 N/mm 2. In the numerical analysis a column with a difference in vertical position of 1.0 millimetres of one of the flanges compared to the other glass plates resulted in a similar stress value as the tested column at the same applied displacement of 20 millimetres. - the development of the stresses over the glass column for the different adhesives in the numerical model coincides with the observed failure modes: local failure of the adhesive with high Young s modulus and global failure for the adhesive with low Young s modulus. Another series of experiments was performed to study the effect of several design options on the load bearing capacity of the column. The tests were almost similar to the previously performed tests. The only difference was that this time the test bench was not able to rotate along the longitudinal axis, more attention was given to levelling of the column and all the columns consisted of H profile configurations. It was chosen to focus on the glue stiffness and the load introduction between the metal and the glass. For the first aspect two adhesives with totally different stiffness values were applied to the prototypes and for the second aspect several load introduction systems were tested: different interlayer materials (lead and aluminium), the column cast in polyurethane rubber and steel connectors glued to the surfaces of the glass, which results in loading of the column by means of shear forces. The experiments revealed that avoiding the chance of uneven loading due to a difference in the vertical position between the glass plates by introducing the forces by means of shear forces in the column resulted in a higher structural capacity of the glass columns. Also, it was concluded that an adhesive with low stiffness was able to distribute the stresses more uniformly over the glass column than an adhesive with high stiffness. In addition, levelling the column and preventing the support from rotating along the longitudinal axis showed that there was increased structural capacity and so that it should be considered as well in the design of a glass column. Finally, the findings of the experimental and numerical investigations were integrated into the structural design of a glass column for a pavilion. The preliminary design of a pavilion, which consists of ten columns, served as a context for the structural glass columns (each four metres high). Two main aspects were distinguished in the design process of the column: the boundary connection system and the related cross-section. The boundary connection system was studied in detail by considering the transition between the glass and the metal, the type of support and the transitions between these aspects. A special support system was developed to create an optimal situation for structural glass columns. For the cross-section of the column the configuration and the dimensions were determined. On the basis of several criteria the H profile configuration was selected, which consists of three glass plates. Each of these plates was 28 millimetres thick, 350 millimetres wide and 4000 millimetres long. Finally, a safety concept was developed for the monolithic glass column by, among others, applying an outer layer of safety glazing around the structural glass column. 8

9 To conclude, from this research it is found that different design aspects play an important role in the bearing capacity of slender glass columns assembled from rectangular monolithic flat glass plates. On the basis of the experimental and numerical results the most relevant aspects related to designing a structural glass column are listed: - load introduction by means of shear forces into the whole cross-sectional area; - the facility to deal with production tolerances or a difference in vertical position between the glass plates due to the assembling procedure; - the H profile configuration; - a low stiffness of the adhesive for bonding the glass plates together in the correct configuration; - the design strength of the glass, which is, based on the results and including some extra safety, assumed to be 27 MPa; - the support system which allows rotation along the width of the column and is fixed for rotation along the longitudinal axis of the column; - the ability to level the column on site by a base plate consisting of adjustment nuts; - the concept of safety to prevent the column from impact by an outer layer of safety glass. 9

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11 Table of contents Preface... 5 Summary... 7 List of symbols Chapter 1 - Introduction Problem definition Glass as a structural material Structural glass columns Scope of research project and methodology Objective Outline PART I Literature overview Chapter 2 - Literature Material glass Glass production Glass types Mechanical properties Safety concepts Design guidelines Column design Failure mechanisms Section properties End connections PART II Experimental and numerical investigations Chapter 3 Experiment I Introduction Prototypes

12 3.2.1 Specimen material properties Specimen dimensions Specimen bonding Test setup End connections Expectations Machinery Testing procedure and measurements Experimental results Configuration Configuration Configuration Configuration Configuration Other considerations Summary and conclusions Chapter 4 Finite element analysis Introduction FEM model Geometrical model Material properties Loads and boundary conditions Analysis Parameter I: difference in vertical position between glass plates Parameter II: stiffness of the glue Summary and conclusions Difference in vertical position between glass plates Stiffness of the glue The experimental versus the numerical results Chapter 5 Experiment II Introduction Prototypes

13 5.2.1 General specimen properties Experiment II A Experiment II B Test setup Machinery and testing procedure Expectations Experimental results Experiment II A Experiment II B Overview experimental results Other considerations Summary and conclusions Glue stiffness Polished edge treatment Introduction of forces PART III Case-study pavilion Chapter 6 Design structural glass column Introduction Pavilion Design concept Preliminary design Requirements structural glass column Column boundary connections Boundary connection requirements Boundary connection concept Column section Single glass Laminated glass Selection column section Dimensions of the glass column Safety concept Final column design

14 6.7 Evaluation PART IV Retrospect and prospect Chapter 7 Conclusions Introduction Conclusions drawn from the experimental investigations Conclusions drawn from the numerical investigations Conclusions drawn from the design process of a structural glass column Chapter 8 Recommendations Introduction Experimental analysis Numerical model Final glass column design Others Bibliography Appendices Appendix A Internal stresses Appendix B Principal directions Appendix C Measurements test specimens experiment I Appendix D Expectation experiment I Appendix E Felt stiffness Appendix F Model files and command files DIANA Appendix G Distribution of stresses in the numerical analysis Appendix H Measurements test specimens experiment II Appendix I Expectation experiment II Appendix J Preliminary design pavilion Appendix K Capabilities different cross-section configurations Appendix L Dimensions glass column

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17 List of symbols A cross-sectional area C degrees Celsius E Young s modulus EI bending stiffness F θ,e Euler torsional buckling strength FEM Finite Element Model G shear modulus I moment of inertia I w warping stiffness MPa mega Pascal N Newton N buc Euler buckling strength N θ Euler torsional buckling strength NEN-EN European norm NEN Dutch norm PVB polyvinylbutyral SGP SentryGlassPlus b e h k n k s kn l buc m mm q t w x y z width eccentricity height stiffness in normal direction stiffness in tangential direction kilo Newton buckling length metre millimetre uniform distributed load thickness horizontal displacement x-direction y-direction z-direction є ν σ σ t strain Poisson s ratio stress tensile strength 17

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19 Chapter 1 - Introduction This chapter provides an introduction to the research. The research topic and the aspects that will be considered are briefly introduced. Additionally, an outline of the research is presented. 19

20 1.1 Problem definition Glass as a structural material Normally we base our architectural designs on available materials and products. In the field of structural glass, we only applied fins in facades. The glass column appeals to me because of its capacity to create special effects with light and the ability to create a floor that seems to float. A marginal comment: attention should be paid to prevent people walking against it. If possible, I would like to keep informed about the development of the glass column. [R. de Jong, architect and partner DP6] Glass is an innovative material in the world of structural engineering. It is especially the transparency property of this material that makes it a valued material when compared to other structural materials like concrete, steel and timber. In contemporary architecture transparency or translucency is very often desired. As is mentioned by R. De Jong, architects are fond of the way glass plays with light and shadow and creates special effects. Therefore nowadays glass elements are not only used in the building envelope, to create a transparent border between the inner and outer climate, but also load-bearing components made out of glass are becoming more common. Besides its transparency, other useful material properties of glass are its strength and the fact that water cannot go through. It is very important to be aware of these properties in order to use glass structurally. Although glass is a very strong material, it is highly prone to imperfections on the surface. Scratches cause a certain loss of strength, which means that fixed values for its strength are difficult to use. Moreover, the compressive and tensile strength of glass differs enormously. Due to advanced production techniques glass can handle high compressive stresses. The weakness of the material lies in its inability to handle large tensile stresses. The brittleness of glass is the main reason why it is not yet widely accepted and used as a common building material for structural elements. Once a fracture occurs, the element will lose nearly all its strength and stiffness. This may give rise to unsafe situations. However, scientists are currently putting a great deal of effort into constructing even more things out of glass. Beams, plates and portals have already been realized. The glass stair in the Arnhem City Hall, see Figure 1, is an example of where glass has been used as a floor plate. The glass steps project from the natural stone wall. Another example where glass is used as a structural element is in the Apple Store in New York, see Figure 2. The ceiling and walls as well as the portals (the distance between two portals is 1.65m) are made of glass. Actually, only the connections are manufactured in another material. This entrance building shows that most structural elements lie within the bounds of what is possible with glass. 20 Figure 1 Glass stairs in Arnhem city hall [Nijsse, 2003] Figure 2 Apple Store New York [Kleinman, 2008]

21 1.1.2 Structural glass columns The glass column is still in its early phases of design compared to the other structural elements. In the world of structural engineering the column is a frequently discussed topic. Architects and clients do not like it. They are said to block the view and stand in the way. But, engineers need to add columns to buildings to provide support and transfer the forces to the foundation. These conflicting desires can be solved by developing a more attractive column, a glass column. In Figure 3 the elegance of a glass column is shown: it is possible to look through the column and the shadow is only slightly observable. In the façade of the Apple Store in New York vertically loaded elements are used. These are called fins. A fin is part of the façade and therefore has other structural requirements than the column that will be considered in this research project. Such a structure is part of the primary structural system of a building, has to take a higher load capacity compared to the fin. When developing a glass column the fin is a first step. In France glass columns were already realized in 1994 to carry the roof of the city hall in Saint-Germain-en-Laye. In case of failure of one or even all of the columns, a structural steel frame in the roof will bear the load of this building. Over the past decades the glass column has fulfilled more requirements and has become stronger, thus resulting in more and more new uses. Ultimately, the challenge is to construct a whole building of several floors out of glass. Figure 3 Danfoss entrance with cruciform glass columns [Bagger, A. 2010; Denmark] Recently, in Denmark, a new glass reception building was constructed for the office of Danfoss, see Figure 3 and Figure 4. Glass portals are supported by glass columns to reduce the span and keep the depth of the construction low. Initially circular glass columns were considered, but eventually the choice fell with cruciform glass columns. The production aspects and aesthetics were the main factors considered when determining the right shape for the column section. This follows from the next phrases written by A. Bagger, structural designer of the reception building. My first idea was a circular tube, because I liked the concept of no protruding parts (so there is no part that is easily damaged), and the natural extra stiffness by the curved shape. However, no producer (at that time) could produce that (6 meters tall columns, taking up 400kN each). ( ) So, the next idea was for a cross shaped section. [Bagger, A.; 2010] Figure 4 Danfoss Column boundary connection [Bagger, A. 2010; Denmark] 21

22 Preceding research at the TU Delft explored the potential of slender glass columns assembled from rectangular monolithic flat glass plates assembled by an adhesive. Since 1995 the Zappi research project has run at the Faculty of Architecture of the Delft University of Technology. The goal of this research programme is: to develop novel scientific principles for architectural components that combine transparency with the ability to carry loads safely. [Pastunink, 1999] One of the projects of the Zappi research programme is illustrated in Figure 5. F.A. Veer and two of his graduate students, E.J. van Nieuwenhuijzen (2005) and J.R. Pastunink (2009) have been performing research on the development of a transparent tubular column that can be used as a structural member in a construction. They invented a process to manufacture laminated tubular glass columns. The curing process had to be controlled carefully to laminate the two stiff glass tubes with a clear temperature-dependent resin. This was a very time-consuming process. Nevertheless, the strength and failure behaviour, which is also very dependent on the way the column is supported, proved to be similar to steel or aluminium columns. [Nieuwenhuijzen, 2005; Pastunink, 1999] Because of the time-consuming and thus expensive process of producing laminated tubular glass columns, a new experiment into glass columns was performed in The experiment involved glass columns made out of flat glass, see Figure 6. The tested column is shown in Figure 6. The prototype was made out of glass sheets that were 800mm long, 80mm wide and 8mm thick. The adhesive used was Delo Glass Bond, a water resistant UV curing adhesive. The result was promising and thereby a new research topic arose. [Veer, 2005] The current research project therefore focuses on further knowledge and understanding of the structural design aspects of glass columns assembled from rectangular monolithic flat glass plates. An exploratory study to the design aspects of glass columns is experimentally investigated. Furthermore, both numerical and experimental investigations are performed to gain more understanding about the considered design aspects. Finally, the findings of the investigation have been applied to the structural design of a glass column for a pavilion. Figure 5 Zappi glass column [Veer, F.A. 2005; Delft] Figure 6 Cross section glass column [Veer, F.A. 2005; Delft] 22

23 1.2 Scope of research project and methodology In this research both experimental and numerical investigations are performed. Since there is a lot unknown about the structural response of slender glass columns, an experimental study is the best way to acquire innovative knowledge. The experiments focussed on determining the design aspects of structural glass columns. By both experimental and numerical investigations the design aspects are investigated more thoroughly. Several assumptions as well as limitations and simplifications have been made to narrow down the scope of this research project. For the final design of the column, a case-study is developed, to create a bit of a framework. A two-floors-high pavilion of 22.5m wide and 45m long, is the context for ten similar structural glass columns. The lower floor is enclosed by a glass façade and concrete roof, which results in an inner climate. The first floor, the roof, is more like a terrace and can be reached by an external staircase. The final goal is to develop a structural glass column for this pavilion. Other assumptions are listed in the following. - The column section will comprise of rectangular monolithic glass panes. Since a single glass plate is the most commonly used glass type compared to solids and open tubes, it is selected for this research. Moreover, as there is still a lot unknown about the structural behaviour of single glass plates, the research focuses on monolithic glass panes. Variations on a column in laminated glass are proposed by R. Nijsse [Nijsse, 2003]. - The glass panes used in the experiments consist of float glass (also known as flat glass) and are cut by the waterjet cutting technique. - Furthermore, as it is found in 2005 that a column assembled by just annealed glass results in a promising structural capacity, the glass panes are not pre-stressed by an extra treatment. - The Master project has to be done within a year. Thereby only the short-term behaviour of slender glass columns is tested in the experiments. Important topics that will be addressed are: - aspects that need to be considered by designing a structural glass column - the design strength and the failure modes of the considered glass columns - the geometry of the column, which involves the section, build-up and end-connections of the column - safety concepts for both the single glass column and the pavilion as a whole - the development of a numerical model - the preliminary design of a pavilion, the case-study The Master project is the final course of the Master of Science program of Civil Engineering at the Delft University of Technology. The topic discussed above, however, has some structural and architectural aspects. Although these two kind of engineering fields became closer to each other in the last decade, the emphasis in this research will lie on the structural point of views. 23

24 1.3 Objective The objective of this graduation is: To design a glass column as a structural element in a pavilion based on a fundamental study to slender glass columns assembled from rectangular monolithic flat glass plates under compression. 1.4 Outline Figure 7 presents the outline of this research. The report is subdivided in four different parts, each with its specific focus. Firstly, part I provides a literature overview of relevant topics for this research, see Chapter 2. Some background theory is given on the material glass: the material properties, manufacturing, structural glass products and safety concepts. Subsequently, aspects considering the design of a glass column are explained, which include: failure mechanisms, section properties and end connections. Part II deals with experimental and numerical investigations into the design aspects of structural glass columns. Chapter 3 presents an exploratory investigation into the design aspects related to structural glass columns. Goal of this test series is to get more insight into the structural behaviour of glass columns and get acquainted with fabricating glass columns out of monolithic float glass. Imperfections in the edges of glass plates, differences in vertical position between glass plates and the quality of the glue line are evaluated in detail, which should result in understanding the main parameters that influence the structural response of a glass column. The effects of the obtained design aspects on the structural response of a glass column are studied more accurately by a numerical analysis, see Chapter 4. As experiments are laborious and costly, the development of this numerical model is advantageous to study the influence of essential parameters. For the development of the model the finite element analysis program DIANA is used. Subsequently, the design aspects obtained in Chapter 3 are more thoroughly investigated by means of new series of tests, see Chapter 5. In this experiment the influence of the considered design aspects on the structural response of the columns is studied in a more exploratory way. Different designs are tested to discover the best solutions for a structural glass column assembled from rectangular single glass plates. In part III a case-study is performed to integrate the findings of part II in a realistic situation, see Chapter 6. Final goal is to design a structural glass column assembled from rectangular single glass plates. The preliminary design of a pavilion is made to create a context for the structural glass columns and to understand the forces that need to be transferred by the glass columns. The pavilion consists of ten structural glass columns. For the design of the structural glass columns two main aspects are distinguished: the boundary connection system and the related cross-section. For each of them the design concept is based on the experimental results. The boundary connection system is studied in detail by considering the transition between the glass and the metal, the type of support and the transitions between these aspects. For the cross-section of the column the configuration and the dimensions are determined. During the whole design process the assembling of the column is kept in mind. Furthermore, a safety concept is developed for the pavilion as a whole and for the structural glass columns in this part of the research. Finally, part IV encloses this research by providing the conclusions from the research, see Chapter 7, and by providing recommendations for future studies, see Chapter 8. 24

25 Figure 7 Outline of the research 25

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27 PART I Literature overview 27

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29 Chapter 2 - Literature This chapter involves background information and basic knowledge on varying topics that are of interest within the framework of this graduation project. The main topics are therefore the production of glass, different types of glass, the mechanical properties of this material, safety concepts, design guidelines, failure mechanisms of glass columns, section properties and end connections. 29

30 2.1 Material glass Raw materials Glass production For the production of glass the necessary raw materials are silica (SiO 2 ), lime (CaO) and sodium oxide (Na 2 O). Silica, also known as quartz, is the main component of different sands and rocks. It has a melting temperature around 1723 C. Most sands have large amounts of colouring oxides. This is very important to be aware of, while only sand with few impurities is suitable for the production of glass. Thus very often in the beginning of the production process it is necessary to purify the sand. The second raw material, lime, is obtained from limestone (CaCO 3 ) crushed in a very fine size. It gives the glass a certain hardness. The last raw material, sodium oxide, is obtained from soda ash (Na 2 CO 3 ). It reduces the melting temperature of glass. To enhance certain properties some other materials like dolomite will be added to the standard raw materials mentioned in the previous. The proportion between the raw materials which is generally used in soda lime silica glass is shown in the chart in Figure 8. [Pilkington, 2010] However, to reduce the melting temperature sometimes higher percentages of soda are used than shown in the chart. The consequence is a decrease in strength of the glass. The European standard (EN 572-1:2004) gives guidelines for the production of soda lime silica glass to keep the proportions between the ingredients between certain limits. After carefully weighing and mixing the raw materials, they will be melted. Very often also a certain amount of waste glass will be added to the glass batch. This cullet has been already melted and makes the melting of the other raw materials easier. [Lehman, 1995] sand (72.6%) limestone (13.0%) soda (8.4 %) other (6.0%) Figure 8 Raw materials of glass and their proportions in general Figure 9 Molecule structure quartz and soda lime glass [Schittich, 1999] Molecule structure During the melting process a chemical reaction occurs. The sand, soda and limestone molecules change in SiO 4 and carbon dioxide molecules, as well as sodium and calcium atoms. The carbon dioxide disappears as a gas through the chimney and the SiO 4 becomes the main molecule of glass. The negative outside of the SiO 4 -molecule is responsible for the little gaps in the material allowing light to pass as well as for the quick cracking of glass. Sand Soda Chalk heat SiO4 Carbon dioxide Sodium Calcium Figure 10 Glass production chemical reaction 30

31 When cooling down the melted substance below the melt point no crystallization occurs and no crystalline structure evolves. In other words, the molecules do not form a regular pattern. This is caused by the high viscosity of molten glass. This irregularity of the glass structure makes glass an amorphous material and results in the transparency and brittleness properties. Production techniques Figure 11 Blowing glass in the National Glass Museum in Leerdam Natural glass has existed since the beginnings of history. Nobody knows exactly when glass was first made. Probably, it has been fused from sand and sodium carbonate in high-temperature volcanic areas. Through the ages it is manufactured in different ways. A major breakthrough in glassmaking was the discovery of the glassblowing pipe around 200 B.C. By blowing air through a hollow iron pipe in a molten gob of glass it was possible to form hollow glass objects. The new discovery allowed glassmakers more freedom in forming their products into any desired shape, size and thickness than before. Later on it was invented that by blowing glass in a wooden mould it was feasible to produce standardized or duplicated products. [Lehman, 1995] Due to further developments in glass technology, the applicability of glass has extended to architectural purposes, especially for windows. Clear glass was discovered by the Romans around AD 100 and in the 14 th century it became possible to blow not only a sphere but also a cylinder. By cutting open this cylinder under heat, flat planes of glass were obtained. In around 1750 this technique resulted in sizes of 1000 x 800 square millimetres. [Nijsse, 2003] At the beginning of the 20 th century experiments took place with pulling a heat-resistant bar vertically out of a batch of viscous molten glass. Due to the viscosity of the molten glass a plate formed under the bar. While being pulled up, the glass plate started to cool down. This mechanical way of producing glass was discovered by Emile Fourcault. In 1914 the first factory opened using this technique to produce flat glass plates. One year later the Libbey Owens system was also being used. During this process the glass is pulled up vertically, bent over a cooled steel roller and led horizontally over rollers to a cooling furnace. This resulted in much thinner glass panes, varying from 0.4 to 20 mm. In 1921 the glass thickness was enhanced by pulling glass through a system of top rollers, located right above the melt, to get more even planes of glass. The thickness could be adjusted by changing the distance between the rollers, but also by varying the pulling velocity. This way of glass production was called the Pittsburgh system. [Renckens, 1996] Fourcault system Libbey Owens System Pittsburgh system Figure 12 Three glass production systems: Fourcault system, Libbey Owens system and Pittsburgh system [Leung, 2010] 31

32 One of the latest improvements in the production techniques of glass was made in 1952 by the British company Pilkington Brothers Ltd. Liquid glass is poured on a bath of molten tin. Because of the difference in specific gravity, the glass will float over the tin. Molten metals have the property to have a perfectly flat surface, which results in a nice flat pane of glass on the lower side. The upper surface is flattened by gravity. Glass thickness is controlled by the rate at which the molten glass is poured onto the tin. After the tin bath the glass is cooled down and solidifies. Finally, the strip of glass is cut in pieces. The end product is named after the production technique: float glass. Because of this continuous process of making glass panels large quantities can be produced. The sizes are restricted to a maximum of 3.21 metres wide and 6.1 metres long in Europe. In the U.S.A. and Canada, on the other hand, the maximum is 3.76 metres wide and 6.1 metres long. These restrictions are caused by transport limitations. Occasionally, bigger sizes can be produced. The thickness generally varies between 0.4 and 25 mm. The Pilkington float process is widely used. The advantage of the Pilkington float process compared to drawing processes is the lack of distortion caused by pulling the molten glass. Figure 13 Float process [Loughran, 2003] 1. raw materials 6. cooling 2. mixing 7. cutting 3. melting 8. breaking 4. refining 9. storage 5. molten tin float bath The actual produced thickness varies sometimes from the desired thickness. Limitations for these tolerances are worked out in the NEN-EN and are listed in Table 1. nominal thickness [mm] tolerances on thickness [mm] 3 ± ± ± ± ± ± ± ± ± ± 1.0 Table 1 Production tolerances 1 According to NEN-EN the tolerances on nominal dimensions for the length and the width are about 5 millimetres. 1 NEN-EN

33 Edges The standard production process of glass includes only the cutting of the glass plates in the right sizes. As a result, the glass has some sharp edges and small imperfections at the edges. An edge treatment reduces these imperfections. There are different cutting methods on the market. At the moment water jet cutting is a very innovative technique for glass cutting. It is based on injecting water under high pressure through the glass. The advantage of this technique is the low temperature in which the glass can be cut. In this way the cutting process does not change the material properties of the glass. [Usinouvelle, 2011] The finishing process, in general, could be distinguished in two main edge treatments. The first one only polishes the sharp edges and the second one polishes both the sharp edges and the flat side of the edges. Figure 14 Waterjet cutting machine [Usinouvelle, 2011] According to [Veer & Zuidema, 2003] the edge quality, which is determined by both the cutting and finishing processes, is dominant in determining the strength of glass. During their research the specimens with polished edges showed a reduction in standard deviation compared to just cut glass. However, increased edge quality not always resulted in increased engineering strength Glass types The earlier described production techniques are mostly used for producing flat glass. Also solids or hollow sections are possible to produce nowadays. However, this research will focus on the more common flat glass products. In this range the main glass types are float glass, wired glass, drawn sheet glass, patterned glass, wired patterned glass and polished wired glass. Float glass and drawn sheet glass are transparent flat glass types. Patterned glass is more an architectonical type of glass. The pattern does not have a structural meaning. Wired glass seems to be stronger than ordinary annealed glass, because of the steel mesh. In practice the wires do not act as reinforcement but as crack inducers. As a consequence they weaken the glass. It is assumed that wired glass is half as strong as ordinary annealed glass of the same thickness. [Alsop, 1999] For the glass column float glass or drawn sheet glass will be considered. Laminated glass The different glass types can be used as single sheets or laminated. Laminating is a process in which two or more pieces of glass are bonded by an interlayer. There are two main advantages of laminating. The first one is the possibility to protect one layer by another. If the outer layer fails, the inner layer could be still unbroken and transfer the forces. The second one is the ability of the interlayer to bond pieces of glass in case one of the panes is broken. This prevents pieces to fall down and protects individuals against the risk of injury. Other, non-structural, properties of laminated glass are the ability of sound absorption, solar control and putting foils with prints in between the glass sheets in a durable way. 33

34 The manufacturing of laminated glass is a special process. After the plates of glass are produced and cut into the right size, they will be bonded by an interlayer to become ready for the next mechanical process in an autoclave, see Figure 15. This reactor heats the plates and takes out any air (vacuum) to bond the plates together. The result is laminated glass. In the Netherlands there are autoclaves with the dimensions of 4 metres in length and 2 metres in diameter. Polyvinyl butyral (pvb) is the most common sheet interlayer material. It is prepared from polyvinyl alcohol. Another example of an interlayer is Sentry Glass Plus (SGP) produced by DuPont. This interlayer is supplied in the form of cut sheets as well, but has the mechanical properties that can be compared with a resin. Most used resins are acrylic and polyester. A resin is carefully poured between two glass sheets to get an even result without any air in between the sheets. Curing occurs by chemical reaction or UV light. In accordance with a research that has been conducted by Belis it shows that the shear stiffness (G) of SGP equals the shear stiffness of pvb for short-term loading, but the shear stiffness of SGP is about 38 times stronger than the shear stiffness of pvb for long-term loading. [Nijsse, 2007] The properties of these two interlayer materials are shown in Table 2. property PVB SGP unit Density kg/m 3 Young s modulus N/mm 2 Thermal conductivity 468 x x 10-6 K -1 Tensile strength > N/mm 2 Table 2 Material properties of polyvinylbutyral and Sentry Glass Plus [Nijsse, 2007] The structural behaviour of laminated glass is determined by the glass type and the properties of the interlayer. The buckling force, for example, is highly dependent on the shear stiffness of the foil which connects the two layers. The buckling force of laminated glass is therefore bounded by the lower limit when no foil is present (two separate planes of glass) and the upper limit when the foil is infinitely stiff (the glass layers are ideally coupled). Professor Blaauwendraad has coupled the buckling formulas of Sattler, Zenker and Allen to a new one to provide insight into this boundary principle. [Blaauwendraad, 2007] s Figure 15 Autoclave for laminated glass in the Semco Glass factory in Nordhorn The formula shows the importance of the shear stiffness of the foil. Due to the visco-elastic property of the interlayer the load carrying behaviour depends also on the temperature and the load duration. [Luible, 2004] 34

35 The level of collaboration for the glass plates differs per load type. For short-term loading, both sheet laminating and resin laminating will have maximum cohesion between the layers. For long-term loading, a sheet laminated glass panel will lose its maximum contact after already one minute and a resin laminated glass panel will lose its maximum contact after one hour. If the temperature is above 50 C, then there will not be a connection at all. [Nijsse, 1997] In general, a glazing denoted as 66.2 has two panes of glass measuring 6 mm separated by two PVB films each 0.38 mm thick. Sometimes it is described by its total thickness, namely in the case of Mechanical properties Glass is an amorphous material which behaves perfectly elastic until the moment it fractures. This elasticity can be explained by its molecular structure. Fracture behaviour is usually determined by environmental factors, like the surface treatment, the environment and the loading, and not by the inherent strength of the bonds. The lack of a crystal lattice prevents the atoms from dislocating if the covalent bonding between atoms is broken. This enables the possibility of plasticity. Any local stresses around a defect that exceed the chemical bond strength will thus cause bond failure and increase the local stresses. As a conclusion, the material glass only deforms elastically or fractures. [Veer, 2007] Figure 16 curve 2 shows the stress-strain relation of glass, which is linear elastic behaviour, compared to other structural materials. Figure 16 Material behaviour of glass (2) compared to steel (1) and timber (3) [Loughran, 2003] Other mechanical properties that are inherent to the material glass are known. According to NEN-EN Table 3 shows the general mechanical properties of normal annealed glass without any further tempering. This process will be discussed later on in this section. characteristic symbol numerical value density (at 18 C) ρ 2500 kg/m 3 Young s modulus E 7 x Pa thermal expansion coefficient α T 9 x 10-6 /K thermal conductivity λ 1 W/(m x K) characteristic bending strength F g,k 45 x 10 6 Pa hardness 6 units (Mohs scale) Poisson s ratio ν 0.2 Table 3 Properties of annealed float glass [NEN-EN 572-1] Main differences from other structural materials It can be concluded that glass has some essential differences from other commonly used structural materials such as steel, timber and concrete. Compared to these materials glass has the following characteristics. - it has a transparent and/or translucent appearance, depending on the chosen type of glass - it has an ideally elastic behaviour until fracture occurs 35

36 - it has no plastic behaviour to prevent fracture, which results in brittle behaviour - it has a very good compressive strength compared to its tensile strength - it is dimensionally stable at high and low temperatures - it is scratch-resistant - it is not water-permeable As a consequence of these characteristics common design rules of for example steel are not directly of use for glass. [Luible, 2004] Strength of glass As the properties of glass in Table 3 are well known, its strength is very unpredictable. In theory, it should be extremely strong. The theoretical tensile strength of perfect glass based on molecular forces has a range between 6000 N/mm 2 and N/mm 2 and the theoretical compression strength is much higher. [Haldimann, 2006] But, because of surface flaws and defects the strength of glass decreases dramatically. Glass cannot plastically deform and redistribute applied loads, which makes its strength dependent upon damages. These scratches, which are not always visible by eye, can develop in small cracks on the glass surface or at the edge and due to cyclic loading these cracks could grow to their critical length and failure of the glass will occur. [Shelby, 2005] As the strength of glass is uncertain full-scale tests have been conducted to gain valuable data about the strength of glass of a specific design before applying the structural glazing to a building. In compression glass is a very good structural material. According to [Luible, 2004] the design strength of float glass is found to be between N/mm 2. However, as concluded in [Veer, 2007] the way the glass is processed influences the strength capacity of each data set. The dimensions, edge treatment and production process determine the strength of each glass specimen. Therefore, glass does not have one specific strength value compared to the structural materials steel or concrete. In compression, small cracks will be closed. In tension, on the other hand, each flaw becomes easily a serious crack. Therefore, glass never fails from compression but rather from tensile stresses or bending. Although the theoretical tensile strength of glass (based on molecular forces) is extremely high, the practical design strength should be much lower. During the process of solidification, after the glass leaves the oven, small cracks come into existence of the material. These are called Griffith flaws and cause a serious decrease in strength of the material. Some guidelines for the tensile strength of normal float glass are given in Table 4. This shows the enormous influence of the Griffith flaws on the tensile strength. characteristic tensile strength (N/mm 2 ) theoretical Griffith flaws 80 after 30 years 8 Table 4 Characteristic tensile strength [Derkink, 2002] After a longer period of time the glass surface is exposed to different types of loading and several weather circumstances. The Griffith flaws and other small cracks increase, which results in even more reduction of the tensile strength. Especially the presence of water and fluctuations in temperature are the main factors that influence the tensile strength of glass by increasing the size of the cracks. A crack results into a certain stress concentration. This is shown in Figure 17. The lines of stress are interrupted and curved, which results in a stress concentration on the glass surface. An estimation of this stress concentration can be calculated by the following formula: 36

37 Figure 17 At the crack point the stress lines are interrupted and curved, which results in local stress concentration. [Simonis, 1997] It can thus be concluded that the strength of glass is not a constant value but mainly depends on the governing stress distribution and the surface quality. [Veer, 2007] Strengthening of glass One of the major disadvantages of glass is its tendency to break because of external forces, falling or quickly changing temperatures. The sharp fragments of broken glass can cause injury. Special treatment can make the glass less susceptible to breaking and reduces the chance of injury. An improvement of the strength properties will be the result. Annealing Annealing is the basic process that is used to produce float glass. It is a process of gradual and even cooling of the glass, which allows the inside of the glass to cool at the same rate as the outside and thus prevents the formation of uneven stresses that would make the glass easy to break. [Lehman, 1995] After this process it is still possible to cut the glass. Annealed glass is also vulnerable for thermal shock. This causes cracking due to internal stresses resulting from temperature differences between different parts of the same sheet of glass. Critical temperature difference has been found to be 33 o C. [Lehman, 1995] If thermal shock is found to be a problem then the glass needs to be implemented as heat strengthened or toughened, which will be described in the following. Tempering The tempering process is also known as the toughening process. After manufacturing the float glass (annealing), this process will further develop the glass plates to meet the specific requirements. The secondary process involves heating the plates until it becomes flexible again and immediately afterwards it is cooled down evenly and rapidly. As a result, the internal glass mass cools more slowly than the external surface. In a while the external surface is already solidified while the internal glass is still contracting. This makes the external surface subjected to compression and the inside subjected to tension. In other words, the glass panels are pre-stressed, see Figure 18. Any flaws at the surface are being closed. The glass supplier Pilkington has predicted that toughened glass is five times stronger than annealed glass of the same thickness. The pre-stressing of glass is also possible by chemicals. Only the outer surface is modified to get compressive stresses in this top-layer. The method of chemical pre-stressing is based on ion exchange. [Pfänder, 1983] 37

38 Figure 18 Pre-stressed glass panel with the external surface subjected to compression and the inside subjected to tension [Luible, 2004] Figure 19 Internal stresses of a pre-stressed glass panel [Simonis, 1997] glass type level of residual surface other frequently used terms compression annealed glass almost nothing float glass heat strengthened glass average partly toughened glass, partly tempered glass (fully) tempered glass high safety glass, toughened glass Table 5 Different glass types, their residual strength of glass and other frequently used terms for these types [Lehman, 1995] ultimate flexural strength (N/mm 2 ) long term mid term short term annealed glass heat strengthened glass toughened glass Table 6 Ultimate flexural strength 2 characteristic compressive strength (N/mm 2 ) over 1000 N/mm 2 Table 7 Characteristic compressive strength [Alsop, 1999] 2 NEN

39 The compression layer of pre-stressed glass (not chemical pre-stressing) has a thickness of about 2/9 of the glass thickness. The compressive stress goes to 150 MPa at the glass surface for the glass section in Figure 19. In the centre of the glass plate the tensile stress goes to about 60 MPa. These values vary for different glass types. Any cracks that are present in the compression layer will be closed until the external tensile stresses exceed the internal compressive stress. [Simonis, 1997] Since the strength of the glass is improved, heat-strengthened and tempered glass have residual surface compressions, which suppress the occurrence of tensile stresses. The remaining stress depends on the toughening treatment. In general: annealed glass would have the least residual strength, heat strengthened glass would have increased residual strength and tempered glass the highest level of residual strength. [Loughran, 2003] The heat-treatment results in different types of flat glass products. In Table 5 the main glass types are compared by their residual strength. Also other frequently used terms for these products are written down. Heat-treated products In most engineering materials the failure stress for a large test series shows an average and a standard deviation. However, the results of glass testing do not show such a nice distribution. [Veer, 2007] Hence, the values that are shown in Table 6 and Table 7 can be used as guidelines. As already explained in the previous, for the characteristic compressive strength there is no exact value (Table 7). When the glass is subjected to compression, the defects in the glass surface will be closed. Therefore the capacity of glass is much higher for this type of loading than when it is subjected to tension. Due to imperfections in the glass or boundary system (i.e. out of straightness, flaw, eccentrically loading) glass, although subjected to compressive forces, fails by tension. The size of the manufacturer s furnace determines the largest pane that can be toughened. Generally, sizes up to about 4.0 metres x 2.5 metres can be made. [Alsop, 1999] In the East probably larger furnaces are available up to a maximum of 6 metres long. For toughened glass all thickness are possible. Although, 25 mm thick glass is difficult to toughen adequately. Break pattern As a consequence of the different heat-treatments each glass type has a specific break pattern. In case of fracture, there will be an increased release of energy, resulting the fully tempered glass to break in the smallest pieces with the fewest sharp edges compared to the others. It is said that it reduces the chance to injury, but a large amount of small pieces can still cause harm. Figure 20 shows the different break patterns. Figure 20 Break patterns for annealed (left), heat strengthened (middle) and fully tempered glass (right) [Loughran, 2003] 39

40 It is not only impact that causes brittle fracture of annealed glass. Bending stresses, thermal stresses and imposed strains also cause elastic deformation and may cause fracture. Whether or not fracture will occur depends on the flaws in the glass, the stress level, the stressed surface area and the duration of the load. The flaws in the glass may be inherent or may result from the cutting and from the environment to which the glass has been subjected. Humidity encourages crack growth. [Alsop, 1999] Long term behaviour Due to scratches, glass will not have the same strength permanently. These scratches can develop in small cracks on the surface or at the edge. Due to cyclic loading or the action of water, the cracks could grow to their critical length and failure of the glass will occur. Under the influence of permanent stresses some materials tend to creep. For glass this is not an issue, because of its absence of plastic behaviour. At the Delft University of Technology J. Luttmer demonstrated this in his thesis in By using Newton s theory on viscosity he explained that window glass of 10 mm thickness needed more than years to deform mm, loaded by its self-weight at room temperature. The long term behaviour of laminated glass is slightly different. The visco-elastic behaviour of the interlayer is dependent on the load duration and the temperature. This means that for long term load duration or high temperature exposure relaxation of the interlayer occurs. As a consequence the laminated glass can be assumed to be separate plates of glass, which reduces the buckling force to the lower limit as described in Section Safety concepts Concerning its properties, glass is considered to be an unsafe structural material. Especially the ability of sudden failure, which is caused by the non-crystalline structure, is not required in structures. Surface flaws or inaccurate detailing or execution result in stress concentrations. Stress redistribution does not occur in glass. Consequently, sudden failure is very common. The high Young s modulus makes that for small distortions already high stresses occur. A structural design should be safe enough. In literature there is no consensus about the way to design a safe structure. Also, the building codes leave this information for everyone s own opinion and give no guidelines for experimental verification. [Derkink, 2002] Nijsse makes a distinction between a safe and an unsafe structural element by reflecting on the failure behaviour. If a structure is capable of giving a person fair warning, it is considered as safe. Bos did a PhD in safety concepts for structural glass members. He discovered that the Dutch and European building codes focus primarily on the probability of the risk of failure. The Eurocode, nowadays, provides more guidance in a consequence-based approach, but only at the level of the complete structure. Since structural glass is sensitive to numerous failure causes, Bos proposes requirements for a consequence-based approach for each structural glass element. It makes the design of structural glass members more standardized. [Bos, 2007] For the total structure the requirements of safety need to be fulfilled as well. If a glass column fails, an alternative load path could be a solution to keep up the building. This requires enough residual strength of the total structure. 40

41 2.1.5 Design guidelines Almost no design standards for glass exist yet. Some European Norms are under development at the moment, but these design guidelines are still limited (NEN-EN 572 and NEN 2608). Results of testing deliver the most valuable information, since the load carrying behaviour of glass is not that obvious. However, three different approaches for the column buckling design of glass elements can be distinguished [Haldimann, 2008]: - Buckling curves; For steel it is common practice to use buckling curves by designing a column (NEN 6770, 2001). These curves are based on a slenderness ratio and enables the design of members with different steel grades using the same curve. However, in contrast to steel, the slenderness ratio for glass must be based on the maximum tensile strength as the compressive strength does not limit the buckling strength. The application of buckling curves to glass columns is studied by Luible. [Luible, 2004] - Analytical models based on second order theory; the maximum tensile stress in a structural glass member can be determined by means of the second order theory. This approach is, however, limited to elementary structural systems and boundary conditions. - Nonlinear numerical model; When the column buckling design is approached by a finite element model, initial imperfections and specific boundary conditions can be taken into account. According to safety some test and classification standards have been published. NEN-EN gives an impact test method for flat glass. Some other standards are related to security glazing. 2.2 Column design Failure mechanisms According to the properties of glass, this material fails in tension or by buckling. A glass column under increasing axial load deforms elastically until sudden failure is initiated, either by elastic instability or by a lateral load, which causes bending at the surface that magnifies the tensile stress. Protection from lateral impacts can be provided by outer layers. The load bearing element is then sandwiched between a degree of redundancy. Two types of failures related to structures can be distinguished namely material failure and form or configuration failure. Material failure occurs when the stresses exceed the permissible values. In glass, this may result in cracks and can be described as a loss of stability by tensile stress. In form or configuration failure the stresses are within the permissible range, but the structure is unable to maintain its original configuration. This can be caused by external disturbances. Configuration failure can be described as a loss of stability by compressive forces, which is often referred to as buckling. [Gambhir, 2004] Stability The definition of stability lies in the relation between load and deformation. A stability problem is considered to exist if at a certain load situation no unambiguous state of equilibrium can be defined. [Luible, 2004] In the stability theory three states of equilibrium can be distinguished namely the stable, unstable and indifferent equilibrium. [Pflűger, 1964] This is often explained by analogy to the behaviour of a rigid ball of some weight placed in position at different points on a surface shown in Figure 21. The ball is assumed to be in equilibrium at zero slopes. However, in response to a slight 41

42 disturbance the ball will not anymore be in equilibrium in cases (a) and (c). In case (a) the ball will return to its original position after the disturbance is removed, which is called the stable state. The next one (b) shows a situation where the ball will move and only stops when the disturbance is removed, which is called the indifferent state of equilibrium. The ball does not come back by itself to its original location. The last state of equilibrium is the unstable one (c). Even after a slight disturbance the ball is not able to come back to its original location. Figure 21 Ball analogy for the different states of equilibrium: stable state (a), indifferent state (b) and unstable state (c). [Roebroek, 2009] It should be noted that the state of indifferent equilibrium is very rare. In reality there are always imperfections like initial inaccuracies in the dimensions of an element, residual stresses or lack of homogeneity and eccentrically applied loads. These imperfections make the system not reach the critical state of equilibrium. [Luible, 2004] For a structure a stable state of equilibrium is desired. In [Gambhir, 2004] the stable state of equilibrium is defined as the ability of the structure to remain in position and support the given load, even if it is forced slightly out of its position by a disturbance. If the load increases until it exceeds the critical value, then the structure is in a state of unstable equilibrium. This means that each slight disturbance results in buckling. The state of indifferent equilibrium is characterized by the fact that besides the straight position of the structure there is a random deformed position for which equilibrium exists as well. [Roebroek, 2009] A stability analysis, often referred to as the buckling analysis, consists in the determination of buckling loads at which a certain structure becomes unstable and the corresponding deformed shape of the structure. Often the lateral deformation cannot be neglected in determining the equilibrium. Therefore a second order analysis should be performed. In general, the solution of stability problems can be determined either analytically or numerically. Buckling The high slenderness and high compressive strength of glass columns make that glass columns tend to fail because of instability: column buckling. [Luible, 2004] In general, the buckling strength of a column is calculated by the formula in Figure 22. The buckling length is also considered in NEN Figure 22 shows the buckling length for different boundary conditions. The buckling strength of glass is limited by the maximum tensile strength of the glass surface. Therefore Luible claims that the initial breakage of a glass element under compression always occurs on the surface under tensile stress. Because of imperfections and the eccentricity e of the applied load the critical load N cr,k will never be obtained. This is shown in Figure 23. The maximum load N K is the point where the maximum stresses in the material are reached. The glass thickness t, the initial deformation w 0, the load eccentricity e and the degree of damage to the surface of the glass (including edges and drilled holes) have the most important influence on this maximum load. Since some of these variables are very unambiguous, it is hard to predict the maximum load. 42

43 2 2 Figure 22 Buckling length (l buc or l k ) for different boundary conditions [Nipius, 2011] Figure 23 Eccentrically loaded bar with initial deformation w 0 [Luible, 2004] For laminated glass the interlayer, which behaves like a shear connection, has to be taken into account. The critical buckling load of a two layer laminate with a width b can be calculated by using the following formulas [Luible, 2004]:, (1) (2) (3) Figure 24 Laminated glass with two layers (4) 43

44 Torsional buckling Torsional buckling is another type of instability for a vertical structural element. If the torsional rigidity of a cross-section under compressive forces is lower than its bending stiffness, torsional buckling could be the failure mode of a column. Torsion, on the other hand, is a phenomenon that occurs without the influence of compressive forces. It occurs when there is a moment available which tends to twist the column. In literature the distinction between torsional buckling and torsion is not very unambiguous. NEN 6770 and the book Construeren A describe them as two different types of instability. [Schipholt, 2001] The formulas, however, are found to be similar. Timoshenko and Hartsuijker, on the other hand, explain that buckling and torsional buckling are the two types of instability for a compressed column. Their definition of torsional buckling is the one that makes a distinction between the torsional rigidity and the bending stiffness of a cross-section. The strut axis remains straight, but the sections rotate. [Hartsuijker, 2004; Timoshenko, 1961] Figure 25 Torsional buckling of a cruciform section [ESDEP, 1998] A cross-section with maximum torsional rigidity is a circle. Moreover, closed cross-sections tend to be more stiff to torsion compared to open sections. Also, if the number of the sides of a cross-section increases it will be more resistant to torsion. The centre of twist normally coincides with the centroid. In symmetric sections the centre of twist lies at the intersection between the axes of symmetry. [Rees, 2009] Figure 25 shows a cruciform section, which shape is sensitive to torsion, that fails by torsional buckling due to compressive forces. The formula to calculate the torsional buckling strength is given in Figure 26., 2 2 (1) I I I (2) 2 1 I 1 3 ht open sections (3) (4) I 4 O s t closed sections (5) Figure 26 Closed cross-section with parameters to calculate the warping stiffness (I w ) of a closed section. Protruding edges are not taken into account. [Jong, 1985] (6) 44

45 Thermal stresses Thermal stresses are a kind of material failure. It is an internal force created by a temperature difference between two locations. If the thermal stress has exceeded the critical stress, the glass will crack. There are two situations in which thermal stresses can become a serious problem. The first situation it is caused by a difference in temperature on the glass surface and the second situation is caused by a difference in temperature between the inner and outer surface of the glass. Both situations will be discussed in this section. The thermal stress caused by a difference in temperature between the centre and the edge of a piece of glass is commonly caused by partial shading. [Alsop, 1999] Hence, the difference in temperature causes the problem and not the absolute temperature. To assess the thermal risk of a structural element the following factors should be taken into account: external - location of the building - orientation - other buildings, trees or louvers internal - type of glass - edge quality - framing material, including thermal breaks and gaps in mullion and transom - window size - internal heating system The thermal stress caused by a difference in temperature between the inner and outer surface of glass can become an issue for closed column sections. The air temperature is related to the air pressure by the law of Boyle and Gay-Lussac. Subsequently, big differences in air pressure will result in internal stresses in the glass, which may crack the glass. In Appendix A the internal stresses caused by a difference in air pressure between the inside of a hermetically sealed column and the outside is calculated. The column has a square cross section, is one metre high and 0.1 metre wide in both directions. It showed that for a difference of about 25 C between the two surfaces the internal stresses for this column can be neglected. Due to the differences in production process between toughened glass and annealed glass, toughened glass has a higher level of resistance against thermal stresses. Toughened glass can resist differences in temperature of approximately 200 C, while in annealed glass breakage can occur under temperature differences of approximately 30 C. These values can vary considerably on, for example, the quality of the edge processing. [Glass, 2010] Fire Fire resistance is the ability of an element of construction to perform its design function during its exposure to fire. Glass breaks by exceeding the critical value of tensile stress. This value is determined by the difference in temperature on the glass surface and the modulus of elasticity and expansion coefficient of the glass. When the difference in temperature during a fire does not lead to glass failure in the first ten minutes as a consequence of thermal stresses, the glass can be loaded until temperatures of about 520 degrees Celsius. [Kruys, 1997] This is the transformation temperature of glass. From this temperature on, it cannot be loaded anymore. However, if the glass is heated a bit to quickly it already fails in an earlier stage. 45

46 Normal float glass breaks after being exposed to fire for just a few minutes. The difference in temperature between the glass surface and the glass edges results in thermal stresses. A difference of 40 degrees Celsius gives already glass failure in about 1 minute. [Nijsse, 2007] Toughened glass is considerably more resistant, as it has higher strength than normal float glass. But if the duration of the fire is too long, the pre-stress level of the tempered glass will fall. [Veer, 2001] Other glass treatments that can be found in literature are: an intumescent coating, an organic interlayer and a foaming interlayer. The intumescent coating should be able to increase the fire resistance of glass without affecting the unique transparency of the glass. It reduces the heat buildup and thus slows down the development of thermal strain in the glass. The organic interlayer and the foaming interlayer can be used in laminated glass only. If the outer glass pane breaks, the interlayers protect the other panes by isolating. This reduces the amount of heat radiation and the temperature to the inner glass panes. The fire resistance of these different glass treatments are listed in Table 8. It can be concluded that laminated tempered glass with a foaming interlayer will be the best resistance against fire. type of glass minutes until the critical temperature of 520 degrees Celsius will be reached normal float glass 15 coated glass 40 organic interlayer (not foaming) 30 foaming interlayer >60 Table 8 Fire resistance in minutes until the critical temperature is reached for different glass treatments In het Bouwbesluit (2003), a collection of regulatory requirements for everything that will be constructed in the Netherlands, the criterion for fire resistance of an element of construction is 30 minutes. All the people inside a building need to be able to go outside before it becomes really dangerous. A pavilion is considered to be a building which is not that high. For these buildings the criteria are less strict (NEN 6702). Since there is still a lot uncertain about the fire resistance of glass and het Bouwbesluit gives almost no requirements for a building with a height of only 4 metres, fire resistance of glass will not be considered during the rest of this study. Moment of inertia Section properties These are the general formulas to calculate the moment of inertia of a section. This magnitude has a strong relation with the failure mode buckling and is therefore very valuable. The higher the second moment of area, the more resistant the structural element is against buckling. This counts for both the y-direction and the z-direction. In some cases the original coordinate system does coincide with the principal directions. This is the case for reflection symmetrical sections: the axes of symmetry correspond to the principal directions. 46

47 If the section consists of a rotation or point symmetry, then the principal directions need to be determined by the formulas in Appendix B. However, there is one exception. If a section has rotation symmetry over 45 degrees, then the I yz is equal to zero and it follows that the principal directions are equal to the original axes. This makes that the I yy and the I zz are the minimum and maximum values of the second moment of area. Closed or open profile Besides the resistance of the section to torsion, a closed section also has its disadvantages. A closed profile sometimes has some very little gaps where insects or other vermin are able to go through. Since a structural glass element is transparent, this will be visual from the outside. Cleaning of the inside is not an option, while there is no opening to accomplish this. To keep away these organism from the inside of the column, the section should be hermetically sealed. This means that there is definitely no way to get in and that the junctions are really stiff. In case of high differences in temperature, the glass should still be able to take up these local peak stresses. These temperature stresses in the glass can arise when too much solar radiation is absorbed or unevenly absorbed by the glass. The latter can happen when the glass is printed or shaded by other components. This is already explained in the previous section End connections A connection needs to transfer the forces from one element to the other. For load-bearing structures the demands for strength, stiffness and reliability are high compared to for non-load-bearing structures. The material glass behaves elastic. Therefore it is not able to redistribute stresses. A connection in glass causes stress concentrations, which makes that they need to be designed with great care to prevent failure. Currently techniques and products exist for connecting either glass-to-glass or glass to other materials. Generally, a distinction is to be made between three types of connections namely mechanical connections (i.e. linear support glazing, local edge supports and local point supports), glued connections and physical connections. This section is only to provide a very brief overview of the different types with corresponding qualities and shortcomings. Mechanical connections Linear supports are mainly applied to glazing which is loaded perpendicular to its plane. Two or more edges are restricted. The local edge support is developed to have less visual impact compared to the linear support system. Local point supports are essentially bolted connections. If members are joined by a bolted connection, high bearing stresses occur around the bolt holes. In the case of members that are made of brittle material such as glass, the material is unable to redistribute any local stress concentrations. Any flaws caused by the drilling of the hole may in fact cause even higher local stresses. Glued connections In glued connections compression forces are transferred by way of friction. In other words, the axial force is transmitted to the glass by means of shear force. The strength of a glued connection does not only depend on the intrinsic strength of the bond material, but is based on both the adhesive and cohesive qualities of the connection. The strength of the glued connection depends on the bond material (i.e. adhesive and cohesive properties), the design of the joint (e.g. geometry of the bond, governing forces to be transferred) and several aspects relating to workmanship and curing. [Nijsse, 2007] These aspects include: 47

48 - the preliminary treatment of the joint surfaces, like cleansing, degreasing or polishing - the mixture of components and the possible presence of enclosed air bubbles - the method of application and curing - the ambient temperature and humidity Because of the great diversity in adhesives it is important to choose the most appropriate one for the system. Specifications like curing, bonding, resistance to water, resistance to UV, resistance to differences in temperature and, of course, a suitable shear strength. Also, the surface hardness of the adhesive needs to be smaller than the surface hardness of glass to prevent the glass surface from flaws. [Weller, 2010] The molecular structure influences the thermo-mechanical properties. An important indicator for the (thermo)mechanical behaviour of an adhesive is the glass transition temperature. Generally, an adhesive with a low glass transition temperature is flexible at normal temperatures, i.e. temperatures significantly lower than the glass transition temperature. On the contrary, adhesives with a high glass transition temperature, like epoxy, are rigid and stiff at normal temperatures. In Construeren met glas - stand der techniek the general properties of different types of adhesives are discussed. [Nijsse, 2007] Physical connections Artists and glass blowers use the welding technique very often to join glass objects together. If the cooling rate is too fast, the glass will crack. Therefore the realization of large joints requires extreme temperature control, which is almost impossible. In a connection usually other materials are used with glass. By choosing this material the intrinsic properties, such as the thermal expansion, and the coatings used with materials can cause incompatibilities. [Alsop, 1999] Contact between metal and glass in the connections must be omitted. In façades setting blocks are used to fix the position of the glass panes within their frames and to transfer the loads, including self-weight, smoothly to another structural element. A certain minimum size of this stress transfer zone is essential to avoid excessive stress peaks. The resistance of the blocks to long-term compressive load as well as their compatibility with the other materials used must be verified. [Schittich, 1999] The selection on the connection system depends mainly on the forces that need to be transferred. Glued connections may offer a solution for the two main disadvantages of mechanical connections: the undesired visual impact of the mechanical fixings and the stress concentrations that occur due to the introduction of loads at discrete locations. The physical connection system is not ready for structural applications. In this way, the glued connection system is denoted as the best joining technique for glass. 48

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51 PART II Experimental and numerical investigations 51

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53 Chapter 3 Experiment I Five prototypes have been tested for this set of experiments. Each prototype was one meter high and composed of three or four glass plates in different configurations. The goal was to explore the material behaviour of glass under compression. Furthermore, stress-deformation relations have been derived to obtain data about the occurring stresses in the glass. This chapter describes the preparation of the prototypes, the test setup and the testing procedure. Finally, the results of the experiments are presented. 53

54 3.1 Introduction The goal of this part of the research is to get more insight into the behaviour of glass under compression. Since the strength of glass is not a pure material property but instead a variable dependent on the degree of damage to the surface of the glass, experiments will be the best way to get more acquainted with the material. The tested glass columns are built up from a few plates of glass into different configurations. In this way, this first set of experiments has been done to get not only more acquainted with the material behaviour of glass under compressive forces for several configurations, but also to enhance the skills of bonding the plates together. Furthermore, this set of experiments generates data about the occurring stresses in glass and gives insight into the failure behaviour of glass columns. This chapter starts with a description of the prototypes (Section 3.2). The prototypes involve five glass columns with different cross-sections. They are built up by bonding glass plates together with a glue. The properties of the glass and the glue and the fabrication procedure is explained. Then an expectation of the failure load and failure mode is worked out. Both inspection and structural mechanics analysis have been taken place. The inspection of the prototypes has given insight into the imperfections of the columns, which could lead to failure of a glass column under compression. The analysis based on structural mechanics has comprised the compressive strength, the buckling strength and the torsional buckling strength. The obtained strength values are pure theoretical values, since they do not contain any imperfections or out-of-straightness. The last part of the test setup (Section 3.3) contains the machinery and the testing procedure. To gain an as even as possible distribution of forces into the glass column an interlayer is placed between the test bench and the glass column. The experimental results (Section 3.4) start with some general information about the obtained data. Then, the experiment will be explained in detail for each configuration separately. This contains the location of the first crack, the observed steps during failure, the failure load and other considerations. Since the glass plates are numbered during the inspection, references to these numbers are used to point out different locations. This section ends with a consideration of what has been observed during the five tests in general. It illustrates the structural behaviour of a glass column under compression. Explanations for the observed structural behaviour are included to get more acquainted with the parameters that influence the strength of a glass column. These findings and others are listed in the conclusions (Section 3.5). 3.2 Prototypes Specimen material properties The applied glass type is annealed float glass. The material properties of annealed float glass are described in Table 3. The specimens were cut by waterjet. This technique is explained in Section To polish the edges a bit more, abrasive paper is used Specimen dimensions Each glass plate is 1000 mm long, 100 mm wide and 8 mm thick. In total 20 glass plates were ordered, but one failed during transport and did not arrive in Delft. As a consequence of the production, deviations in the nominal sizes of the plates are possible. Hence, the specimens have 54

55 been measured before composing the columns. These measurements showed that the tolerances were within the range of acceptation according to NEN-EN (Table 1). The results of the measurements are listed in Appendix C. During these measurements it was found that the waterjet cutting technique resulted in a difference in width of the glass plate over the thickness of 8 mm. The waterjet cutting process projects water with high speed through a glass plate. At the time it has passed through, it reflects back. This results in edges that are placed under an angle. On average the lower sides were 0.35 mm smaller than the upper sides of the glass plates. This is visualized in Figure 27. Figure 27 Average deviation of 0.35mm (2 x 0.175mm) in width of the glass specimen based on measurements carried out on 19 glass plates Specimen bonding By bonding, five different columns are composed out of the 19 specimens. Four out of which were composed of four glass plates and the fifth column was composed of only three glass plates. The configurations of the columns with their dimensions are shown in Figure 28. Configuration 1 Configuration 2 Configuration 3 Configuration 4 Configuration 5 Figure 28 Five prototypes with different configurations which have been tested in experiment I Since there were slight differences in dimensions of the glass plates (3.2.2 Specimen dimensions), for each column the most similar ones have been used. For example, configuration 2 consists of two bodies. To get a perfect cross-section with straight angles, it is important to have two glass plates for the bodies with similar width. This has been taken into account during the selection procedure of the plates for the different configurations. Before the specimens could be bonded together, the glass surface had to be degreased by using propanol to get optimal adhesion between the glass plates. The glue material is Araldite 2000 PLUS 2013, which is a very strong two-component glue based on epoxy resin. This material is suitable for vertical applications and is more often used for glass structures. The glue is metal coloured, which does not give a nice appearance by combining it with transparent glass. But, it makes the inspection of the glued lines easier than for a transparent glue. In total, the bonding procedure took about six working days. One of which consisted of inspecting and measuring the specimens. Another one was necessary to make timber setting blocks with scratched corners (Figure 29 b). These blocks keep the glass plates in position during bonding. And the last four days were occupied with gluing and curing. All the steps that took place during the bonding procedure are shown in Figure 29 on the next page. 55

56 a) measurement tools and the 19 glass plates b) timber setting blocks with scratched corners c) glue gun, phial with propanol and ventilation system d) step by step fixing the specimens together with fasteners to keep the glass in place during curing e) fixation of the last glass plates to these sections f) the prototypes during the last period of curing Figure 29 a-f The bonding procedure of the five different prototypes 56

57 3.3 Test setup End connections Between the machinery and the glass column prototype compressive forces are transferred. To realize an even distribution of forces an intermediate layer is preferred. This layer needs to smooth the imperfections at the edge of the column. Any difference in vertical position, out-of-straightness or imperfection in the glass, which could influence the strength of the column, should be avoided as much as possible. Therefore a layer of felt is placed between the test bench and the glass column at both ends. The non-linear material behaviour of the felt is explained in Section Expectations For each prototype it is checked whether the glass plates were in the same vertical position at the edges, the connections were totally filled with glue and the glass contains imperfections. This inspection for each column is shown in a 3D Revit model in Figure 31 and Figure 32. The green arrows are related to a difference in vertical position at the edge, the blue lines correspond to imperfections in the glued junctions and the small red dots show the locations of imperfections in the glass plates. The figures also show numbers. Before the bonding procedure started, the glass plates have been numbered from 1 to 19 randomly. In this way each plate has its own number and references to specific plates are possible. The numbers (1-19) are added in the model. In reality the glass prototypes have been marked as well. This is shown in Figure 30. The results of the inspection are summarized in Table 11. The column difference in vertical position gives the number of the glass plates that protrude at the edge. If one or more plates are glued slightly higher or lower than the other plates, then it is expected that these are more sensitive to higher stresses. The last two columns describe the numbers that correspond to certain glass plates, which are subjected to imperfections in the glass or in the glue line. These flaws increase the possibility of an early collapse of the glass column. a) imperfection in the glass plates b) imperfection in the glue line Figure 30 a-b Imperfections in the prototypes are marked up in red 57

58 Figure 31 Revit model (3D) of the five configurations which shows the observed imperfections. The green arrows correspond to a difference in vertical position, the blue lines to an imperfection in the glue line and the small red figures to holes in the glass. Figure 32 Top view of the Revit model with the corresponding numbers of the glass plates 58

59 configuration difference in vertical position imperfections in glass plates 1. Square 11 or 19 6 and 11 have one broken edge imperfections in glue line 5-6 bottom; bottom 2. Double Web 2 or lot of small ones edges not totally filled 3. H Profile 18 each plate some top not totally filled 4. Star 7 and 8 or 1 and one big one; others small ones 1-7 edges not totally filled 5. Cross 13 3, 9 and 16 small ones 13 over whole height Table 9 Overview of the imperfections in the glass columns (the numbers correlate to a specific glass plate) Besides accidental types of failure due to imperfections in the glass column, there are in general two structural failure modes for columns under compression due to instability: Euler buckling and torsional buckling. If the column is not sensitive to instability, the column can fail by exceeding its compressive strength. The formulas applied to calculate the strength values for these failure modes are described in Section Failure mechanisms. Compared to the inspection of the column, these formulas result in theoretical strength values. No imperfection factor or material factor is added to the calculated strength. The Euler buckling and torsional buckling strength are based on the boundary conditions of the structural system. For a glass column it is preferred to have hinges at each side to reduce the tensile stresses as much as possible. In the test setup the glass column is placed in the machine with a layer of felt at both the bottom edge and the top edge. Since the edges of the glass column are not fastened to the test bench, they are not able to transfer moments. The edge connections are modelled as hinges and the buckling length is assumed to be 1000 mm. The bottom part of the machine, however, is able to rotate along the longitudinal axis of the column. As the experiment involves only compression tests, this torsional rotation will only occur for cross-sections with low torsional stiffness at the moment it starts to collapse. Before this type of instability under compressive loading, it is not of importance whether the bottom part of the machine is able to rotate or not for the strength of the column. Therefore, the torsional buckling length also equals 1000 mm. The compressive strength of a column is calculated by using the allowable compressive stress. According to a course of CUR Bouw & Infra/Kenniscentrum Glas, this value is assumed to be 900 N/mm 2. [Nijsse, 2007] Again, no imperfections, material factor or out-of-straightness is taken into account. The strength is a pure theoretical value. The calculation of the Euler buckling, torsional buckling and compression strength are defined in Appendix D. The general properties of the configurations are listed in Table 10. The expected failure mode and failure load are shown in Table 11. configuration number of glass plates area [mm 2 ] second moment of area (I yy ) [mm 4 ] 1. Square Double Web H Profile Star Cross Table 10 General properties of the configurations second moment of area (I zz ) [mm 4 ] 59

60 configuration buckling [kn] torsional buckling [kn] compression [kn] expected failure load (kn) expected failure mode 1. Square compression 2. Double Web buckling 3. H Profile buckling 4. Star buckling 5. Cross torsional buckling Table 11 Expected failure load en failure mode of the different prototypes As a result, buckling is found to be the most common failure mode. The square cross-section is expected to be the strongest configuration considering the structural failure modes and will not fail due to instability but as a result of compression. The cross is expected to be the weakest configuration and has a low resistance against torsional buckling. In reality the columns are not as perfect as in theory. Hence, these failure load expectations are upper values Machinery The test installation (Figure 33) that has been used for the experiments is located in the Stevin Laboratory of the Faculty of Civil Engineering and Geosciences in Delft. In pre-set steps this machine was able to press the prototypes by moving up the bottom part of the test installation. This bottom part of the machinery is able to rotate, which makes it possible to notice torsional buckling if this occurs. The machine had a capacity of +/- 600 kn. According to the experience of one of my tutors, this was expected to be sufficient Testing procedure and measurements Before starting the test installation, a felt (12 mm thick) has been placed between the machinery and the glass prototype to gain an as even as possible distribution of forces into the column and prevent the glass from peak stresses at the edges. Also, the glass prototype has been placed in a vertical position by measurement tools. Figure 33 Test installation in Stevin Laboratory The procedure of testing was displacement controlled. Compared to load controlled, this method prevents the machine from crushing the prototype. For the first prototype the displacement speed was mm/sec. The other prototypes were tested at a higher rate, namely 0.16 mm/sec, since the first test resulted in a feeling for the strength of the glass columns. In this way a reduction in time to carry out the experiments was arranged. The displacement of the machine (mm) and the resistance of the glass column against this displacement (N) 3 were recorded by a computer. This data is visualised in stress-displacement graphs in Section Actually, the obtained forces are determined by both the resistance of the glass and the resistance of the interlayer material (in this case felt). Therefore, the derived stress values can be assumed as upper-limits. 60

61 3.4 Experimental results The stress-displacement graphs in this section give insight into the failure mode and failure strength of the different configurations. For each configuration there is a description. Since one of the configurations consists of three glass plates instead of four, the graphs show the occurring compressive stresses at a certain displacement instead of the occurring forces against the displacement. This results in a better comparison between the different configurations. After the descriptions of the different configurations, the failure modes are described in a more general way to find out which parameters have an influence on the compression strength of glass columns. Figure 34 shows the stress-displacement graphs of the five tested configurations. From zero to about ten millimetres displacement the graphs show almost similar exponential behaviour, which could be explained by the material behaviour of the felt. Progressively, the stress in the glass increases. Then a reduction in strength occurs; the graphs become less steep or even get a negative slope. The load values and the stress values at the starting point of the stress reduction are shown in Table Stres [N/mm 2 ] Square 2. Double Web 3. H Profile 4. Star 5. Cross Displacement [mm] Figure 34 Stress-displacement diagram of the five configurations configuration load area cross-section compressive stress [kn] [mm 2 ] [N/mm 2 ] 1. Square Double Web H Profile Star Cross Table 12 The load and stress at the moment of strength reduction for each configuration From the above values it can be concluded that these five configurations were able to carry at least a compressive stress of 22.1 N/mm 2 before non-linear behaviour occurred. An explanation of the non-linear behaviour of the different configurations will be given in the next subsections. Each configuration will be discussed separately. Finally, subsection Other considerations gives an overview of the different tests and points out which parameters had an influence on the compression strength of the glass columns. 61

62 3.4.1 Configuration 1 The prototype of experiment 1 consisted of a square cross-section. The load-displacement diagram is shown in Figure 35 and the process of failure is illustrated in Figure 36. After a displacement of about 9 millimetres, cracking noises have been noticed. Although these sounds suggested failure of the glass column, the column was still able to resist more vertical displacement. Progressively the stress in the column increased. Suddenly, at the top edge of plate 19 initial failure started. Gradually, the crack moved downwards over twothird of the height of the plate until local buckling occurred in the connected plate number 11. During the crack growth, the column was still able to handle higher stresses under increasing vertical shortening of the column. The initial cracks in plate 19 were not caused by large imperfections in the plate. Actually, during the inspection no visible imperfections have been observed in this plate at all. Possibly, the tensile stresses reached the critical value due to a small difference in vertical position between plate 19 and 11 (Figure 32, Table 9). The connection between these plates was not very even. Noticeable is the maximum displacement of this configuration. Compared to the other configurations failure occurred very early. The displacement was just 12 millimetres. 62

63 Stres [N/mm 2 ] Square Displacement [mm] Figure 35 Stress-displacement diagram of prototype 1 Failure load: kn Figure 36 Gradual crack growth of configuration 1. From left to right: column at the beginning of the test, crack growth from the top in plate 19, still crack growth in plate 19 and collapse in the top of the column. 63

64 3.4.2 Configuration 2 The prototype of experiment 2 consisted of an II-shaped cross-section, which is called in this research the Double Web configuration. Compared to configuration 1, the graph in Figure 37 shows non-linear behaviour in the stress-displacement diagram. Although a decrease in stress occurs twice, the vertical shortening of the column still increases. Finally the column fails at a stress value of 45 N/mm 2 very abruptly. In more detail, at the ultimate load value of 45 N/mm 2, plate 2 has failed due to local buckling. Slightly before this failure, some small cracks have been noticed in one of the webs. This process of failure is illustrated in Figure 38. At the time these cracks occurred, the non-linear phase in the diagram almost ended. According to this, it can be concluded that the glass column did not warn in reality, but on the monitor already some non-linear behaviour has been observed. An explanation for the failure of plate 2, one of the flanges, could be a difference in vertical position again. In the inspection it was noticed that there was a slight difference between flange 2 and the two webs (Figure 32, Table 9). While this was also the case for flange 12, it is not clear why especially this flange has been broken. Moreover, in glass plate 12 7 imperfections have been observed. Some holes or damages were a bit bigger than others. This experiment showed that these imperfections did not influence the type of failure since plate 2 was the first one that collapsed. Failure occurred at a displacement of more than 20 millimetres. Compared to configuration 1, this column was able to resist a much higher vertical displacement. 64

65 Stres [N/mm 2 ] Displacement [mm] Figure 37 Stress-displacement diagram of prototype 2 2. Double Web Failure load: kn Figure 38 Rapid failure process of configuration 2. From left to right: column at the beginning of the test, small cracks start in the bottom of the web (side view), in the meantime the flange breaks as well (side view) and the column has been failed. 65

66 3.4.3 Configuration 3 The prototype of experiment 3 consisted of an I-shaped cross-section (three glass plates). According to the graph in Figure 40 initial weakening of the prototype occurred at a compressive stress of 22.1 N/mm 2. Since the first cracks became visual at a stress of about 50 N/mm 2, the latter is considered to be the failure load. Compared to the previous prototypes, the behaviour of this column shows similarities with configuration 2. Non-linear behaviour occurs, which means that under increasing vertical shortening the stresses in the column altered in positive and in negative directions in the graph. Also, the process of failure occurred very suddenly. The column did not warn before it started to collapse. The process of failure is illustrated in Figure 41. During the process of failure an initial crack started at the top edge of the web in the section, glass plate 15. Suddenly, another crack appeared in the web. This one was directed towards the flange, plate 18. This resulted in immediate failure at the top of the column. The bottom 50 centimetres of the prototype did not show any damage. Since there was a small difference in vertical position between glass plate 15 and 18 (Figure 32, Table 9), this could have been again the cause of the initial failure in these plates. At the moment of failure the glass column had experienced a vertical displacement of about 20 millimetres. This value is similar to the displacement of configuration 2, but much more than the final displacement of the first prototype (12 mm). After the glass column had failed, the pieces of broken glass are checked. It was found that the glued connection between the web and the flange was still there. The column had not failed in the glued junction, but a few millimetres adjacent to the junction in the glass plates (Figure 39). This indicates that the glue was very well attached to the glass and that the junction was very strong and stiff. Figure 39 The glued junction between the web and the flange of the broken glass column is still intact 66

67 60 Stres [N/mm 2 ] H Profile Displacement [mm] Failure load: kn Figure 40 Stress-displacement diagram of prototype 3 Figure 41 Sudden failure process of configuration 3. From left to right: column at the beginning of the test, initial crack in the web, a second crack in the web that grows towards the flange and very rapidly final collapse. 67

68 3.4.4 Configuration 4 The prototype of experiment 4 consisted of a star-shaped cross-section. Failure of this prototype occurred in a similar way as prototypes 2 and 3 had failed. In the stress-displacement diagram (Figure 42) the graph starts with exponential growth, which is followed by non-linear behaviour. This process can be considered as initial warning on the monitor. But on the column itself nothing was visible. Only some cracking noises have been noticed. For a real structural element it should be preferred to notice this process of weakening on the column itself. After 20 millimetres of increased shortening of the column local buckling occurred in both plates 1 and 17. The column was broken suddenly and rapidly. In Figure 43 the failure process of configuration 4 is illustrated. The instability in both plates took place about 25 centimetres from the bottom of the column. At a high speed the glass plates moved out-of-plane, which resulted in total failure of the two glass plates and immediately it was followed by global failure of the glass column. During the inspection it was observed that there was a small difference in vertical position between plates 1 and 17 compared to plates 7 and 8 (Figure 32, Table 9). Also, the glued junction between plates 1 and 7 was found to be not perfect (Figure 31, Table 9). Furthermore, no imperfections in the glass plates were noticed at the location of local buckling (Figure 31). Since the two glass plates failed simultaneously by local buckling at a location where no holes in the glass have been observed, it is assumed that again the initial failure is caused by a difference in vertical position. Compared to the moment of failure of the previous prototypes, this configuration has failed at similar displacement as configurations 2 and 3. 68

69 Stres [N/mm 2 ] Displacement [mm] 4. Star Figure 42 Stress-displacement diagram of prototype 4 Failure load: kn Figure 43 Sudden process of failure of configuration 4. From left to right: column at the beginning of the test, local buckling in plates 1 and 17 without any warning, the buckled plates turn downwards again with high speed and immediate collapse of the whole column. 69

70 3.4.5 Configuration 5 The prototype of experiment 5 consisted of a cross-shaped cross-section. After 80 seconds of increased vertical shortening, the resistance of the column equalled 83.2 kn and the stress 25.9 N/mm 2 (Figure 44). At this moment the first cracks became visual. This failure process is illustrated in Figure 45. The cracks start in the centre of the cross-section at the bottom edge of plate 13 and shortly after also in plate 3 and 9. Along the surface they gradually move up to the side edges at a height of about 40 centimetres in plate 13 and at a height of 20 centimetres in plate 3. A few seconds later, these cracks lead to torsional buckling at the bottom part of the prototype. This started with a slight rotation of the column along its longitudinal axis before an even bigger rotation took place. Finally, the upper 45 centimetres of the prototype were still intact. The stress-displacement diagram shows a global and a local maximum. The first time the stresses decrease is related to the development of the first cracks. The second time coincides with the first part of the torsional buckling. Each time the glass column was capable of carrying higher stresses after a reduction. But, the second part of the torsional buckling resulted in failure of the column. It was not able to bear more vertical displacement. During the analysis of Section it was observed that the glued connection of plate 13 was not very good. Glue was missing at some places along the junction. Also, the vertical position of plate 13 showed some difference with the other three plates. As noticed in the experiment plate 13 experienced the initial failure. Since this failure started at the edge of the glass plate in the middle, it seems that it was not caused by the imperfections in the glued junction. Hence, it is assumed that the difference in vertical position was again the cause for the initial failure in plate 13. At the moment of failure the glass column had experienced a vertical shortening of about 16 millimetres, which is less than the final displacements of configurations 2, 3 and 4 and more than the displacement of configuration 1. 70

71 30 Stres [N/mm 2 ] Cross Displacement [mm] Figure 44 Stress-displacement diagram of prototype 5 Failure load: 83.2 kn Figure 45 Failure process of configuration 5. From left to right: column at the beginning of the test, gradual crack growth from the bottom of the prototype, torsion of the bottom part of the column and even more torsion of the lower part of the column. 71

72 3.4.6 Other considerations In this subsection two considerations will be described. The first deals with configurations 2, 3 and 4 and their non-elastic behaviour. The second one discusses the possible cause of failure for configurations 1 and 5. Configurations 2, 3 and 4: the non-elastic behaviour From literature it is known that glass has linear-elastic material behaviour. The graphs of prototypes 2, 3 and 4 in Figure 46 show non-elastic behaviour. Moreover, these configurations have not shown any signs of warning in reality besides some cracking noises. Also, in the previous subsections it was found that for at least these configurations the highest stresses (initial failure) occurred in the glass plates that showed a difference in vertical position. A slight difference in vertical position between the plates in a column results in partially loaded glass plates. At a certain moment, the glass plates want to shift a bit up or down to distribute the stresses more uniformly over the different plates. Material properties of the glue determine to what extent the plates are able to slide along each other. The higher the stiffness of the glue, the more the glass plates are restrained to move. The lower the stiffness of the glue, the more the glass plates are able to slide along each other. The non-linear behaviour in the diagram indicates a redistribution of stresses in the column. Each time the stresses decrease, the stresses are more uniformly distributed over the cross-section of the column. An explanation for the redistribution could be that the glue enabled the glass plates to slide along each other. But also, marginal cracks in the glue line can result in slight movements. Cracking noises, that refer to the second argument, have been noticed during the non-linear phase of the stress-displacement diagram. The assumption that the non-elastic behaviour is caused by a difference in vertical position in combination with the stiffness of the glue will be explained in the following by considering configuration 2 the Double Web. During the inspection (Figure 47, left) it became clear that glass plate 12 protrudes slightly at the bottom of the column and glass plate 2 at the top. After increased shortening of the column, the vertical structural element was subjected to cracks. Figure 47 (right) shows the break pattern of the column. The glass plate at the left side is glass plate number 12. It is assumed that this plate wanted to shift up, which resulted in a crack pattern in the bottom of the flange. Not the glue line, but the glass was broken. The glass plate at the left is glass plate number 2. It is assumed that this glass plate wanted to shift down slightly, which resulted in local peak stresses in the middle of the column. It seems that the glass plates were not able to distribute the stresses more uniformly over the column by shifting glass plates 2 and 12. Since the glue lines were still intact, a possible reason for this failure behaviour could be that the epoxy glue was too stiff to enable these small movements. More research into the material behaviour of the glue in relation to the problem of a difference in vertical position would be recommended to get more insight into the structural behaviour of a glass column. 72

73 60 Stres [N/mm 2 ] Double Web 3. H Profile 4. Star Displacement [mm] Figure 46 Non-linear behaviour of configurations 2, 3 and 4 Figure 47 The Double Web configuration with its imperfections visualized in Revit 3D before testing (left) and the broken column after the experiment took place (right) 73

74 Configurations 1 and 5: the cause of failure Another consideration discusses the failure mode of configurations 1 and 5. The stress-displacement diagram of these configurations is shown in Figure 48. During loading a gradual crack growth was observed. The initial crack started in the top edge of configuration 1 and in the bottom edge of configuration 5. This suggests that the edges are subjected to local peak stresses, tensile stresses, which result into a crack. An explanation for this could be very fine imperfections in the edges that cause stress concentrations on the glass surface, which tend to break the glass Stres [N/mm 2 ] Square 5. Cross Displacement [mm] Figure 48 Stress-displacement diagram of configuration 1 and 5 with increasing crack growth until failure In Figure 17 a formula for this phenomenon is given. In the situation of the formula, the glass plate is under tensile stresses and each imperfection causes a serious increase in local stress in the crack point. This makes the glass very vulnerable to early failure. In configurations 1 and 5 the sections are a square and a cross respectively. The way the glass plates are assembled makes that each plate is able to expand in one direction. If the glass plates were not able to expand because of fixation, tensile stresses would have been the result. For these configurations it is not directly clear why tensile stresses occur at the edges. But probably there is a relation between the very fine imperfections at the edges of the glass plates and the initial failure mode. 74

75 3.5 Summary and conclusions To get more insight into the types of failure that occurred for the different test specimens an overview of the most remarkable failure aspects is made in Table 13. The table shows the ultimate load, the ultimate load compared to the expected failure load from Table 11, the number of the glass plate that showed initial failure, the failure mode and whether there was initial weakening visible in the stress-displacement diagram or not. configuration number of plates ultimate load [kn] ultimate load/ expected failure load initial fracture in plate(s) failure mode 1. Square crack no initial weakening in diagram 2. Double Web crack and buckling yes 3. H Profile and 18 buckling yes 4. Star and 17 buckling yes 5. Cross crack and torsional buckling no Table 13 Overview of the most remarkable aspects at the moment of failure for the different configurations In general it is found that for columns assembled from four plates of float glass (8x100x1000 mm 3 ) the average ultimate load value is kn, which equals a compressive stress of 36.6 N/mm 2, and for three plates this value equals kn (based on one prototype). These values indicate that the test specimens have a much lower compressive stress value at the moment of failure than glass is expected to have according to theory (2.1.3 Mechanical properties). In other words, the tensile strength is exceeded long before the critical compressive stresses are reached. Also, the columns fail far below the expected failure load. Other conclusions that followed from experiment I: - All the columns did not fail below a compressive stress of 26 N/mm 2 and were able to carry at least a compressive stress of 22.1 N/mm 2 before non-linear behaviour occurred. This can be concluded from Table 14. It also shows that the different stress values of the columns composed of four glass plates at the moment of strength reduction have a lower distribution compared to the ultimate stress values. 75

76 stress at the moment of ultimate stress value strength reduction [N/mm 2 ] [N/mm 2 ] 1. Square Double web H Profile Star Cross average stress value of the columns with 4 plates standard deviation Table 14 Overview of the occurring stress values at the moment of strength reduction and at the moment of failure - The experiment was displacement controlled. Around a displacement of 10 millimetres each configuration started to decrease in strength. This could be explained by the thickness of the felt, which was 12 millimetres. - The prototypes with configurations 1 and 5 already failed at a displacement of 12 and 16 millimetres respectively. Failure started with a crack in the top or bottom edge. The other three configurations, 2, 3 and 4, failed more or less at a displacement of 20 millimetres. These prototypes were subjected to local buckling. From the above it can be deduced that especially crack growth from the top or bottom edge should be avoided by designing a glass column. - The plate or plates that were subjected to initial failure were mostly (4 out of 5 experiments) the ones that showed a small difference in vertical position at the edges. In Section these were denoted as the plates where the highest stress was expected. This indicates that slight differences in vertical position are of big influence on the ultimate load values of the columns. - For 3 out of 5 experiments the initial failure started with a crack. For configuration 1 and 5 the gradual crack growth was clearly visible. The crack developed in almost the same direction as the applied load. This seems to indicate that the tensile stresses in the surface of the glass plates at the edges, perpendicular to the direction of the applied load, overstressed the maximum tensile stress of the float glass. A possible explanation for this failure behaviour will be very fine edge imperfections. - Configurations 1 and 5 showed some kind of initial warning before failure occurred. Initial warning is something that would be preferred in a structural element. The other configurations failed suddenly, but on the monitor they showed already a decrease in strength and cracking noises were noticeable. - The load-displacement diagrams of experiments 2, 3 and 4 showed some kind of non-linear behaviour. Probably this is caused by a redistribution of stresses over the column due to a difference in vertical position in combination with the material properties of the glue. In the beginning just one or two glass plates are loaded and after a few seconds the displacement of the test installation has increased to a value that the other glass plates are activated as well. At this moment the prototype is able to strengthen again. Sometimes this behaviour 4 76

77 was noticed by cracking noises in the glue, but most of the time it was only visible on the monitoring screen. - The glued connection lines did not show any failure in the glue or in the interface between the glue and the glass. This indicates that the glue lines were very strong and able to keep the cohesion between the glass plates. Sometimes cracking noises have been noticed. These were probably caused by the glued joints. Since the glue, based on epoxy, was very stiff, this possibly has been a reason for local peak stresses in the glass along the glued connections. Plates of glass with a difference in vertical position were not able to shift slightly up or down and redistribute the stresses more uniformly over the different plates. - During the experiments it has not been noticed that imperfections in the glass plates, like holes in the edges or corners, were crack inducers during loading. Even in glass plate number 12 of configuration 2 with quite a lot of imperfections, these holes did not influence the initial fracture in the prototype. - The failure modes were gradual crack growth, local buckling and torsional buckling. However, failure occurred at a much lower stress value than calculated by mechanical formulas for these failure modes. The ratio ultimate load/expected failure load varies between 0.04 and Although it is hard to say which cross-section is the most suitable one on the basis of one experiment per configuration, the experiments give an indication of the behaviour of each configuration. The load bearing capacity was in the same order of magnitude for the five different prototypes. As a result, there were a few parameters that seemed to have an influence on the initial fracture and therefore the loading capacity of the glass columns. These parameters were: - difference in vertical position between the glass plates - quality of the edges of the glass - properties of the glued joints - imperfections in the glass, like holes in the edges or corners (minor influence) Since the theoretically expected loads for the configurations were much higher than has been found during the experiments, it is interesting to study the parameters that have demonstrated to be of high influence in more detail. This would lead to more fundamental knowledge of glass under compressive forces and thereby to a more realistic prediction of the load bearing capacity. 77

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81 Chapter 4 Finite element analysis This chapter deals with key aspects of a numerical model, which includes the representation of the geometry and the material properties, the boundary conditions and applied loads, and the analysis itself including the selected analysis procedure. Goal of the numerical analysis is to study the influence of some essential parameters on the load bearing capacity of the glass column. 81

82 4.1 Introduction Experiments, such as performed during this research, are laborious and costly. In this respect, the development of a numerical model would be advantageous to study the influence of essential parameters that determine the structural capacity of a vertical loaded glass column. As found in the previous experiment the structural behaviour of a glass column and, more important, the material behaviour of glass is not very obvious. Some essential parameters for the structural behaviour of a glass column have been derived (Section 3.5). Developing a numerical model gives the opportunity to study the influence of certain parameters: - the difference in vertical position between the assembled glass plates; Four out of five prototypes in the previous chapter showed initial failure in a protruding glass plate. The deviation in vertical position of these columns varied between 0.5 and 1.5 millimetres. A numerical analysis is suited to evaluate the influence of this type of imperfection on the structural capacity. The occurring stress values and the locations of the peak stresses have been analysed in this chapter by varying the size of the imperfection. - the material properties of the glue; For all the prototypes of experiment I the same adhesive has been used. In this respect, the influence of the glue on the load bearing behaviour cannot be taken for granted. A numerical model offers the possibility of changing the stiffness of the adhesive easily. As a result, a relation between the stiffness of the glue and the structural capacity of the glass column can be derived. Also, the stiffness of the glue in combination with a difference in vertical position will be considered in this chapter. - the quality of the edges of glass. The third aspect deals with very fine imperfections at the edges of glass plates. Without having carried out measurements on the edge qualities, it has been explained to be an essential parameter in Section Since a lot is unknown about these kind of imperfections (i.e. location, size, shape) the development of an accurate model would be time-consuming and it will be difficult to obtain valuable results. Therefore, this aspect will not be studied in more depth in this research. Summarizing, the focus of the analysis in this chapter is to gain more insight into the influence of a difference in vertical position between the different glass plates of a column and into the influence of the stiffness of the adhesive in combination with a difference in vertical position between the glass plates on the structural behaviour of a glass column. Both models are validated by comparing their numerical results to the experimental results of the H-profile glass column which has been described in Chapter 3. Section 4.2 illustrates the glass column as it has been modelled in the finite element analysis program, which includes the geometry, material properties, boundary conditions and applied loads. Together, this is the basis for the analysis that will be performed in Section 4.3. After an explanation of the solution procedure that has been used for this numerical analysis, the influence of the two parameters is explained separately. 82

83 4.2 FEM model The finite element analysis program used for this research is DIANA. It has been developed by TNO for civil engineering applications and is often used, for example, by the department of Structural Mechanics from the faculty of Civil Engineering at the Delft University of Technology. To implement the model into DIANA the interface FX + has been used. The intention of the numerical model is to get more insight in the influence of the parameters considered in Section 4.1, which includes a difference in vertical position between glass plates and the stiffness of the glue. Thereby, it has been chosen in this stage to limit the numerical model to a two-dimensional problem. This simplification implies no out-of-plane deformations. Also, no differences in stresses in the third direction can be observed. The considered cross-section in this analysis is the H profile, see Figure 49. The equivalent twodimensional model is illustrated in Figure 50. Figure 49 Dimensions of the considered H profile cross section Figure 50 Dimensions of the two-dimensional model 83

84 4.2.1 Geometrical model The geometry of the finite element model is based on the experiment performed in the previous chapter. The materials that can be distinguished include glass, glue and felt. Also, the steel from the test bench has been modelled. Figure 52 shows the model with the dimensions, different materials and axes. By using the interface FX + the x,y-plane of the test setup has been modelled. The generated mesh consisted of two types of 2D-elements. The glass planes are presented by Q8MEM elements (Figure 51a). These are four-node quadrilateral plane stress elements, also referred to as membrane elements. Each node has two variable translations: u η and u ξ. The thickness of the element is uniform. [TNO DIANA, 2008] The adhesive bonded joint and the interlayer of felt are represented by interface elements. Interface elements serve to transfer normal and shear forces across discontinuities in the model. For the purpose of this two-dimensional model line interface elements are used: L8IF (Figure 51b). This element consists of an interface element between two lines with nodes at the ends. The four nodes have two variable translations: u x and u y [TNO DIANA, 2008]. The thickness of the glue line in x- direction is set to 0.4 millimetres. topology displacement a) Q8MEM plane stress element b) L8IF linear interface element Figure 51 Element types applied for the numerical calculation in DIANA [TNO DIANA, 2008]. The 2-dimensional modelling in the finite element analysis program of the glass column is illustrated in Figure 53. The plane stress elements are visualized by rectangles and the interface elements by parallel lines. The colours relate to specific materials. The term compressed will be explained in Section

85 Figure 52 Schematic representation of the glued glass column with an interlayer of felt in longitudinal direction. The considered cross-section is an H profile. 85

86 86 Figure 53 The 2D-modelling of the H-profile cross-section in the finite element analysis program DIANA including all the materials, the axis and the applied mesh

87 4.2.2 Material properties The materials that have been applied to the numerical model are glass, steel, glue and felt. In succession, the input of the different materials will be explained. Glass For the material glass only the linear part of the stress-strain relation has been adopted (Figure 54), while it is not intended to imitate the crack pattern of a glass column, but only the maximum occurring stresses and their locations. Another reason for the simplification of the material behaviour of glass to a linear stress-strain relation is that the Young s modulus is a generally accepted characteristic of glass that can be used in calculations [NEN-EN 572-1: 2004]. Also, the brittle behaviour of glass results in a steep negative slope, which causes difficulties for the numerical program to solve the problem. The material properties of annealed glass that have been applied to the model are listed in Table 15. σ f t N/mm 2 Figure 54 The adopted linear stress-strain relation for annealed glass ε Steel The modelled steel implies the steel from the test bench. These elements have been modelled very stiff, as they only need to transfer the applied displacement in the structural glass column. The material properties of the steel that have been adopted in the model are listed in Table 15. annealed glass steel Young s modulus E N/mm Poisson s ratio ν mass density ρ kg/m Table 15 Material properties of annealed glass and steel adopted for the numerical model Glue The adhesive that has been applied in Experiment I was a two-component epoxy called Araldite 2000 plus 2013 (Section 3.2.3). The applied properties of this glue are listed in Table 16. It is assumed to have linear material behaviour. 5 Although the actual Young s modulus of steel equals N/mm 2, it is modelled as an extra stiff material to make sure the loads are applied equally and the test bench does not influence the behaviour of the glass column. 87

88 glue Araldite 2000 plus 2013 Young s modulus E N/mm stiffness normal direction 6 k n N/mm stiffness shear direction 7 k s N/mm Table 16 Material properties of Araldite 2000 plus 2013 glue adopted for the numerical model Felt Felt, on the other hand, is determined to have non-linear material behaviour. Based on the outcomes of Experiment I (Section 3.4), it has been found that the non-linear behaviour of felt affects the structural behaviour of a glass column. The non-linear material behaviour of felt is derived from the results of Experiment I. Since the material properties of the applied felt were unknown, it is assumed that the initial values of the stress-displacement graphs of Experiment I are related to the material behaviour of the felt. The average values of the stresses from zero to 10 millimetres displacement have been considered. In Appendix E the values of the five tested specimens in Experiment I are gathered together to get the average stiffness value of the felt. Moreover, the experimental results of Experiment I are related to both the felt and the glass. To derive the stiffness of the felt, the formula for an equivalent spring constant of a system in series has been used, see Appendix E. The glass stiffness, applied in the formula, is derived by the Young s modulus of glass, which is equal to N/mm 2 (Table 3). As a result, the non-linear behaviour of felt is visualized in Figure 55. Due to the solution procedure of the numerical program, the stress value is extrapolated to a displacement of minus 20 millimetres and plus 10 millimetres. All together, these values are implemented in the numerical model in DIANA to describe the non-linear material behaviour of the felt. 6 ; with t is the thickness of the material in shortening direction. 7 ; with ν is assumed to be

89 sigma [N/mm 2 ] displacement [mm] sigma [N/mm 2 ] displacement [mm] Figure 55 Stress-displacement diagram of the felt based on measurements done in Experiment I. This material behaviour of felt is adopted to the numerical model in DIANA. In the lower diagram (-10 to 0 mm displacement) the development of the curve is shown in more detail Loads and boundary conditions The boundary conditions of the column are assumed to be perfectly pin-ended (Figure 52). As the bottom boundary was exposed to certain loading during the experiments, this edge is not fixed in the vertical direction (i.e. the y-axis). Loading took place by increased displacement of the test machine with a maximum displacement of 20 millimetres, which is based on the displacement values of Experiment I (Section 3.4). At a displacement of 20 millimetres four out of the five specimens had no residual strength anymore. 89

90 4.3 Analysis In this section two essential parameters will be studied: the difference in vertical position and the stiffness of the glue. The numerical analysis for each of the parameters is based on a physical nonlinear analysis. The solution procedure is the commonly used Full Newton Raphson method, which updates the stiffness every iteration. The applied maximum displacement of 20 millimetres is introduced in 20 steps. Two specific model files and command files that have been used in this research are provided in Appendix F Parameter I: difference in vertical position between glass plates The first parameter describes an imperfection. The glass plates from which the column is assembled are not always exactly in the same vertical position or have a slight difference in length, which results in uneven edges. According to Figure 31 the flanges of the H-profile of Experiment I protrude at both the top and the bottom edge. The idea of the uneven edges is visualized in Figure 57. The imperfection is modelled by adapting the stiffness of the felt. Assuming that the column is placed in a right angle, the felt above (or below) a protruding edge is already compressed. In this way, it has a higher stiffness compared to the felt that is not located next to a protruding edge. As a result, the locations with compressed felt are exposed to the highest stresses. In Figure 53 the elements with compressed felt material properties have been illustrated. The non-linear material properties of the compressed felt have been deduced from the experimental results. Figure 55 shows the material behaviour of the felt without initial compression. In Appendix E the non-linear material behaviour of felt has been derived for the compressed situation. Differences in vertical position of 0, 0.5, 1.0, 1.5 and 2.0 millimetres have been considered. Figure 56 illustrates the obtained stress-displacement relations of the compressed felt. sigma [N/mm 2 ] displacement [mm] Figure 56 Stress-displacement diagram of the material felt based on the results of Experiment I (orange line). The other graphs are translated over 0.5, 1.0, 1.5 and 2.0 millimetres to model a compressed material with higher stiffness caused by a difference in vertical position between the glass plates. 90

91 Figure 57 Geometrical model of the glass H profile column with the flange on the right slightly displaced in vertical direction, which results into felt exposed to compression already before the test starts. 91

92 The analysis has been performed to study the stresses in both the x-direction and the y-direction. For each direction the five different values for the imperfection have been considered. The data extracted from the models is originated from the element with the highest stress, while these values, on the basis of maximum allowable stresses, determine the strength of the column. As the x- direction is situated perpendicular to the loading direction, in this direction the critical tensile stresses have been observed. The y-direction corresponds to the maximum compressive stresses. The stresses extracted from these elements are gathered in Figure 58 for the x-direction and in Figure 59 for the y-direction. Stresses in x-direction From the stress-displacement diagram in Figure 58 it is found that only zero imperfection results in tensile stresses almost equal to zero. From a difference in vertical position of 0.5 millimetres, tensile stresses have been observed. As the applied displacement increases, the stress values show exponential growth. The maximum tensile stress measured is related to the situation with the biggest imperfection and was equal to 7.0 N/mm 2, which is almost equal to the characteristic tensile strength of 8 N/mm 2 (Table 4). In Appendix G the development of the stresses in the x,y-plane for an applied displacement of 20 millimetres has been illustrated for 0, 0.5, 1.0, 1.5 and 2.0 mm imperfection. From this it is found that the peak stresses in x-direction occur in the web of the glass column at the bottom edge. Due to the protruding edge, the glass column is loaded unevenly. As a result, shear stresses develop between the protruding flange and the web, which results in tensile stresses at the bottom edge of the web. In Experiment I failure of the H profile column occurred at an applied displacement of about 20 millimetres. The initial crack started at the edge of the web next to the protruding glass flange (Figure 41). This coincides with the location with the highest stresses in the numerical model. Also, in the numerical model the stresses at this location almost reach the critical strength value at 20 millimetres applied displacement and with 2 millimetres difference in vertical position. The origin of the crack could have been caused by the considered tensile stresses. Stresses in y-direction The stress-displacement diagram in Figure 59 shows exponential growth of the compressive stresses for increased applied displacement. The exponential growth could be explained by the rising stiffness of the felt for increased applied displacement. From the graph it is also found that the compressive stresses increase as the difference in vertical position becomes bigger, which is in line with what should be expected. The compressive stresses reach to a maximum value of 63.7 N/mm 2. The situation with zero imperfection has a maximum compressive stress of 37.4 N/mm 2. Compared to Experiment I, these stresses are only a bit higher. The tested H profile column failed at an applied displacement of about 20 millimetres with a stress value of about 50 N/mm 2. This difference could be explained by a difference in strain. Possibly, in the experiment the felt has taken up a bigger part of the applied displacement. The applied displacement in the glass was lower than in the numerical model, which results in a lower strain and thus lower stresses in the glass. 92

93 tensile stress [N/mm 2 ] 10,0 9,0 8,0 7,0 6,0 5,0 4,0 3,0 2,0 1,0 0,0 x-direction applied displacement [mm] difference in vertical position between glass plates [mm]: Figure 58 Stress-displacement diagram in x-direction (the horizontal axis) for columns subjected to different imperfections in vertical position between glass plates compressive stress [N/mm 2 ] y-direction difference in vertical position between glass plates [mm]: applied displacement [mm] Figure 59 Stress-displacement diagram in y-direction (the longitudinal axis) for columns subjected to different imperfections in vertical position between glass plates 93

94 Moreover, considering a glass column with infinitely stiff material properties of the felt, all the 20 millimetres of applied displacement need to be taken up by the glass column. In this case the compressive stresses in the column would be equal to 1400 N/mm 2 8. An average compressive stress of 50.3 N/mm 2 (Figure 59) equals an applied displacement of millimetres in the glass. The other millimetres of applied displacement have been taken up by the felt, which is feasible. The location of the peak stresses in the numerical model is found to be in the web at the top edge and at the bottom of the protruding flange, see Appendix G. The compressive forces have been transferred in diagonal direction between the two protruding edges Parameter II: stiffness of the glue The second parameter involves the stiffness (i.e. the Young s modulus) of the applied adhesive. In Experiment I only the epoxy paste Araldite has been used. To study the influence of a glue with a lower stiffness value than Araldite, the stiffness has been reduced to 1.6 N/mm 2 in the numerical model. This value is deduced from a polymer based adhesive. In Table 17 the adopted properties of the low stiffness adhesive and the Araldite adhesive are listed. low stiffness glue glue Araldite Young s modulus E N/mm stiffness normal direction 10 k n N/mm stiffness tangential direction 11 k s N/mm Table 17 The adopted properties of the adhesive with low stiffness compared to the properties of Araldite. The thickness of the glue line is assumed to be 0.4 millimetres for each type of adhesive. On the basis of this value the stiffness in normal direction and the stiffness in tangential direction are derived. During the inspection of the columns of Experiment I, it has been noticed that most of the columns had a slight difference in vertical position between the glass plates. Therefore, in this analysis not only the stiffness of the glue will be considered, but also the stiffness in combination with a prescribed imperfection as performed in the previous analysis (Section 4.3.1). The obtained stress-displacement diagrams for the x-direction and the y-direction are shown in Figure 61 and Figure 62 respectively. First the occurring stresses due to the adhesive with lower stiffness than Araldite will be discussed for both directions. Then, a comparison between the obtained stresses for both adhesives is made. The data has been extracted from the same elements as done in the previous analyses to obtain a good comparison between the structural performance of the glass column glued by Araldite and the structural performance of the glass column glued by an adhesive with much lower stiffness properties. The development of the stresses for both the x-direction and the y-direction has been illustrated in Appendix G. 8 Hooke s law: / 9 Hooke s law: ; with t is the thickness of the material in shortening direction. 11 ; with

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96 Stresses in x-direction From the stress-displacement diagram in Figure 61 it is found that the tensile stresses in a glass column assembled with a low stiffness adhesive reach a maximum tensile stress value, for an imperfection of 2.0 millimetres and an applied displacement of 20 millimetres, of 0.4 N/mm 2. This value is below the characteristic tensile strength of glass (Table 4). Due to the low stress values, the graphs showed almost similar stress values. Also, intersection between the lines occurs. In the column without a difference in vertical position between the glass plates the tensile stresses were about 0 N/mm 2. Stresses in y-direction In Figure 62 the stress-displacement diagram for a glass column glued by an adhesive with low stiffness is illustrated. The compressive stresses reach to a maximum of 57.8 N/mm 2. For the glass column without imperfection the compressive stress at an applied displacement of 20 millimetres is 37.4 N/mm 2. Due to increased applied displacement the compressive stress grows exponentially, which is caused by the felt stiffness. Araldite versus an adhesive with much lower stiffness Figure 60 shows the stress-displacement diagrams of a glass column bonded by the two considered adhesives with a difference of 2 millimetres in vertical position for both the x-direction and the y- direction. In general, the stresses in the glass column are lower by using the glue with only 1.6 N/mm 2 Young s modulus. For the compressive stress, the difference in stresses is only a fine distinction. But, for the tensile stress, usually the most critical one for structural glazing, the adhesive with the lowest Young s modulus reduces the tensile stresses considerably. Moreover, if the tensile stresses can be reduced in this way, according to this numerical model the capacity of the column to carry loads could be increased. low stffness adhesive epoxy Araldite tensile stress [N/mm 2 ] applied displacement [mm] applied displacement [mm] a) x-direction b) y-direction compressive stress [N/mm 2 ] Figure 60 The stress-displacement diagrams of the columns with 2 millimetres vertical displacement between the glass plates with the two types of adhesive in both the x-direction and the y-direction. 96

97 tensile stress [N/mm 2 ] 2,0 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 x-direction applied displacement [mm] difference in vertical position between glass plates [mm]: Figure 61 Stress-displacement diagram in x-direction (the horizontal axis) for columns assembled by a glue with very low stiffness and subjected to different imperfections in vertical position between glass plates. compressive stress [N/mm 2 ] y-direction applied displacement [mm] difference in vertical position between glass plates [mm]: Figure 62 Stress-displacement diagram in y-direction (the longitudinal axis) for columns assembled by a glue with very low stiffness and subjected to different imperfections in vertical position between glass plates. 97

98 The influence of a difference in stiffness properties of the adhesive on the development of the stresses in the glass columns has been considered as well. In Figure 63 the distribution of stresses over the column at an applied displacement of 20 millimetres for both the x-direction and the y- direction has been illustrated. From the comparison of the development of stresses in the numerical model the following aspects have been observed. Bonding the glass plates by an adhesive with a Young s modulus of 2550 N/mm 2 results in: - higher peak stresses for both the x-direction and the y-direction, which are very locally distributed over the column. - a glue line which is able to transfer the forces from the protruding flange edge at the bottom side at a small distance into the web. Bonding the glass plates by an adhesive with a Young s modulus of 1.6 N/mm 2, on the other hand, results in: - more evenly distributed stresses over the column for both the x-direction and the y- direction. As a consequence this column is subjected to a smaller amount of peak stresses. - a glue line which is able to transfer the forces from the protruding flange edge at the bottom side at a bigger distance into the web. In conclusion, bonding the glass plates by an adhesive with lower stiffness results in more evenly distributed stresses over the column and thus lower peak stresses. However, due to the lower shear modulus value of the adhesive the distance to transfer the forces from the protruding edge into the web has been increased before getting a homogenous stress distribution over the cross-section of the column. In this situation the lower stiffness was sufficient. 98

99 x-direction y-direction E adhesive = 2550 N/mm 2 E adhesive = 1.6 N/mm 2 E adhesive = 2550 N/mm 2 E adhesive = 1.6 N/mm 2 Figure 63 Stress development in both the x-direction and the y-direction for two types of adhesive at an applied displacement of 20 millimetres 99

100 4.4 Summary and conclusions A numerical model to describe the structural response of glass columns is developed in this chapter to demonstrate the potential of a numerical model to optimize the structural response of a glass column and to study two essential parameters for the load bearing capacity of glued glass plates under compression. The parameters that have been studied are the vertical displacement between glass plates and the stiffness of the glue. The first parameter is modelled by changing the material properties of the felt next to the protruding glass plate(s). Increased stiffness of the felt simulates that the protruding glass plates are already higher loaded than the non-protruding glass plates. The second parameter is studied by comparing an adhesive with very high Young s modulus (i.e N/mm 2 ) and an adhesive with very low Young s modulus (i.e. 1.6 N/mm 2 ). In general, it is found that the non-linear material behaviour of the felt is clearly recognized in the results from the numerical analysis. The graphs show exponential growth for increased applied displacement. The two parameters will be considered separately in the following subsections. Finally, in Section 4.4.3, the experimental results have been compared with the numerical results Difference in vertical position between glass plates It is found in the imperfection analysis that only zero imperfection results in tensile stresses almost equal to zero. Due to a difference in vertical position between glass plates, tensile stresses in the structural glazing develop. For a difference in vertical position between glass plates of 2.0 millimetres at an applied displacement of 20 millimetres, almost the characteristic tensile strength of glass (8 MPa) has been reached. Moreover, the location of the tensile peak stresses in the numerical model due to a difference in vertical position between glass plates coincides with the origin of the initial crack in the tested H profile column in Experiment I. Due to the protruding edge, the glass column is loaded unevenly. As a result, shear stresses develop between the protruding flange and the web, which results in tensile stresses at the bottom edge of the web. In addition, the stresses at an applied displacement of 20 millimetres are almost similar to the observed stresses in Experiment I. From these columns three out of five failed at an applied displacement of about 20 millimetres with almost similar stress values Stiffness of the glue From the stiffness analysis it is concluded that the adhesive with reduced stiffness results in lower stresses. This counts especially for the tensile stress, which is the most critical one for the load bearing capacity of a glass column. Unless other failure modes occur, like poor adhesion, this seems to indicate that the capacity to carry loads can be increased by using an adhesive with lower stiffness. Furthermore, it can be concluded that the adhesive with low stiffness has resulted in a more even distribution of the stresses over the column, which reduces the tensile (peak) stresses in the column considerably. However, due to the lower Young s modulus value of the adhesive the distance to transfer the forces from the protruding edge into the web has been increased. 100

101 4.4.3 The experimental versus the numerical results The results from the numerical two-dimensional analysis show similarities with the experimental results in Chapter 3: - The compressive stresses are in the same order of magnitude. The tested H profile column failed at an applied displacement of about 20 millimetres with a compressive stress of about 50 N/mm 2. In the numerical analysis a column with a difference in vertical position of 1.0 millimetres of one of the flanges compared to the other glass plates resulted in the same stress value as the tested column at the same applied displacement of 20 millimetres. - The location of the tensile peak stresses coincides with the location of the initial crack in the H profile in Experiment I. The initial crack in the glass column started in the web next to the protruding edge of a flange, which is the same location of the tensile peak stresses in the numerical model. - The development of the stresses over the glass column for the different adhesives in the numerical model coincides with the observed failure modes: local failure of the adhesive with high Young s modulus and global failure for the adhesive with low Young s modulus. 101

102 102

103 Chapter 5 Experiment II This chapter involves the procedure and results of the second experiment. It shows the similarities and differences compared to experiment I. Goal of this test program is to get more insight into the influence of some design aspects on the total strength of the column. As a result, this information will be used for the design of the structural glass column in Chapter

104 5.1 Introduction In general, the goal of the second experiment is to find out which adaptations in the column design enhance the structural strength of a glass column compared to the observed strength capacity in Experiment I. It was found, in the previous experiment, that the glass columns failed by a lower strength compared to the theory. In literature it is expected that the compressive design strength of glass equals 600 N/mm 2 (Section 2.1.3), whereas the average ultimate stress value of the columns with four glass plates in Experiment I was 36.6 N/mm 2 (Section 3.5). It is assumed that the columns failed before reaching their compressive design strength due to local instability or other imperfections (Appendix D). The observed failure load compared to the theoretical strength by buckling (i.e. torsional buckling and Euler buckling) or pure compression is illustrated in Figure 64. reality Strength instability: torsion, buckling compression Time Figure 64 The reality graph represents the observed strength of the columns in Experiment I, which is far below the theoretical strength of the column by failure due to for example buckling and pure compression. The dotted line illustrates the desired optimized strength of the column. Based on the findings of the first experiment (Chapter 3) this Chapter focuses on obtaining enhanced understanding of the structural behaviour and the influence of three aspects: - the deviation in vertical position between glass plates - very small imperfections in the edges of the glass - the glued joints. The program of experiment II is divided into two test groups. Experiment II A focuses on the glass column itself. This part includes a study to the influence of the glue and to the influence of polished edges. Experiment II B, on the other hand, deals with the introduction of the forces into the column. It entails loading by pure compression with different interlayer materials, transfer of forces by shear from the connection into the glass column and vice versa, and a combination of both. More specific, the tests that will be performed in Experiment II are: Part A the glass column - a variation in glue stiffness - polished edges versus unpolished edges 104

105 Part B transition from glass to metal - lead and aluminium as the interlayer material - connection fastened to the glass surface - column cast in polyurethane rubber The prototypes are based on the same glass plates as the prototypes of experiment I (Section 3.2). The column height is in this way similar. Each test only has a slight difference, by a variation of: the load introduction, the interlayer material and the stiffness of the glue. The next section (5.2) gives a detailed description of each test. The test setup is explained in Section 5.3. An overview of the experimental results is given in Section 5.4. Finally, Section 5.5 contains the conclusions. 5.2 Prototypes General specimen properties As explained in the introduction, in general, all the prototypes are built up from the same materials as the prototypes in experiment I (Section 3.2). In this way the different tests can be compared more easily. The dimensions of the glass plates are 1000 mm high, 100 mm wide and 8 mm thick. The annealed float glass has been cut by waterjet technique and the material properties are similar to the values in Table 3. If not mentioned explicitly, Araldite 2000 Plus 2013 is used as the bonding material and felt is used as the interlayer material. During the preparation the glass specimens have been measured to check whether the deviations in glass thickness and width are within the tolerances considered in NEN-EN (Table 1). The results are listed in Appendix H. It was found that the measured deviations are in accordance with the tolerances. Since an extra number of glass plates has been ordered, the plates with the least number of visible imperfections and the smallest imperfections have been selected for the tests. For the assembled columns, the plates with similar dimensions have been gathered together Experiment II A The first series of tests, experiment II A, focuses on the glass column itself. Some slight adaptations in the glass column will be studied, among which a more flexible glue (A.1) and polished edges (A.2). These two tests will be explained separately in the following. 105

106 Experiment II A.1 the glue In the first experiment a two component epoxy paste has been used (Section 3.2.3), which was rather stiff, to assemble the glass plates. Since the influence of the stiffness of the glue on the structural behaviour of the column is not very clear yet, this test is meant to give more insight. One of the previous configurations will be tested, the H Profile (Section 3.4.3), see Figure 65. But, this time another type of glue is chosen. There are several types of glue on the market. In [Vrenken, 2006] a classification of some different adhesives has been made based on the Young s modulus (Table 18). A high Young s modulus was assumed to be above a couple of hundreds of MPa. A low Young s modulus, on the other hand, was assumed to be below this value. The adhesive that has been selected for this test is Hercuseal Sealer 302, which is a one component waterproof packing and adhesive based on polymer, based on the criteria of low Young s modulus (i.e. lower than the Young s modulus of Araldite 2000 Plus 2013 of 2550 MPa) and almost equal thickness of the glue line. Other requirements are limited shrinkage, to prevent local stresses, and moisture resistance. Experiment II A.1 consists of three tests: two columns bonded by Araldite 2000 Plus 2013 (which is already done once in experiment I, Section 3.4.3) and two columns bonded by Hercuseal Sealer 302. Due to the enormous difference in stiffness (i.e. the Young s modulus), it is intended to gain insight into the influence of the glue on the structural behaviour of the glass column. The geometrical properties and the mechanical behaviour differ for the 1 component polymer and the 2 component epoxy. The thickness of the epoxy is about 0.3 millimetres, where the glued junction with Hercuseal has a thickness of about 0.7 millimetres. Polymers are more sensitive to external influences such as temperature, loading time, loading rate, environment (humidity, oxygen, etc.) and UV-radiation. Moreover, polymers exhibit tough behaviour for slow loading rates. For a more extensive description of polymers and their mechanical behaviour is referred to [Louter, 2011]. 106

107 glues with low Young s modulus glues with high Young s modulus 1 component polyurethane 1 component epoxy 1 component polymer 2 component epoxy 1 component acrylate 2 component polyurethane silicone 2 component (meth)acrylate two sided tape Table 18 Classification of different glues in two categories based on the Young s modulus [Vrenken, 2006] Figure 65 Dimensions of the H profile 107

108 Experiment II A.2 polished edges The second test examines the influence of an edge treatment. The upper and lower side of the glass, where the forces are transferred into the column, have been polished, both the sharp side and the flat side of the edge. Since the goal of this test is to obtain more insight into the influence of a polished edge, only single glass plates will be tested. The dimensions of the test specimens are visualized in Figure 66. Half of the test specimens will have the normal waterjet cut edges and the other half will have polished edges. To avoid the contact between glass and steel, an interlayer of felt is placed between each specimen and the test bench both at the bottom and at the top Experiment II B The second series of tests, experiment II B, deals with the introduction of the forces into the glass column, the boundaries. In the first experiment the forces were applied just by compression. Felt was placed between the machinery and the glass column to distribute the forces more uniformly in the glass plates. In this test program not only felt, but also other ways of load introduction will be studied. Lead at both edges of the glass column, aluminium at both edges of the glass column, a steel connection glued to the edges of the glass and the column cast in polyurethane rubber will be considered. Goal of this experiment is to obtain enhanced understanding of the influence of different types of load introduction on the structural behaviour of the glass column. As applied in Experiment II A.1, the H Profile(Figure 65) is also the considered prototype for these tests. Experiment II B.1 lead and aluminium as the interlayer material This compression test is almost similar to the test setup of Experiment I (Section 3.3). The only difference is the interlayer material. The felt is replaced by another interlayer material than felt. Lead and aluminium (99%) have been selected due to their hardness and homogeneous material properties. Aluminium and lead have a hardness of 2.75 and units on Mohs scale respectively, which is lower than the glass hardness of 6 units on Mohs scale (Table 3). Felt does not have the same material qualities uniformly, because of its threads. Lead and aluminium, on the other hand, have uniform material properties, which may reduce the height of the peak stresses in the edges of the glass column. The test setup is visualized in Figure

109 Figure 66 Dimensions of the glass plates with polished (upper and lower side) and unpolished edges for Experiment II A.2 Figure 67 Lead or aluminium as interlayer material for Experiment II B.1 109

110 Experiment II B.2 connection fastened to the glass surface The second test of experiment II B arose from the idea that the edges of glass plates are susceptible to very fine imperfections (Figure 17), which may result in early failure of the glass column. In the design of the connection considered in this experiment any contact with the bottom or top edge is therefore avoided. The connection is fastened to the surfaces of the glass plates. The design is illustrated in Figure 68 and visualized in Figure 69. Since the steel connection system is glued to the glass, the compression forces are transferred to the glass by means of shear forces. The strength of this glued connection depends not only on the intrinsic strength of the bond material, but is based on both the adhesive and cohesive qualities of the connection. The used bonding material is the two-component epoxy Araldite 2000 Plus 2013, which is also the adhesive used in experiment I (Section 3.2.3). According to technical data this glue should have good adhesion properties with glass as well as with steel. [Huntsman cooperation, 2010] An epoxy, in general, has high cohesive qualities compared to other glues. In addition to the advantage of the design to avoid any contact between the edges and the steel plate, the connection system also omits the problem of differences in vertical position between glass plates (Section 3.4). If a plate protrudes less than the height of the air gap between the glass and the steel, there will be no contact between these materials. The steel connection system is shown in Figure 68. The weight of these elements is 5.54 kg each. The bolts are placed in oval holes, which enable the vertical steel plates to move and fit in with the glass column. Hereby the design accounts for the assembling procedure. As should be mentioned, the steel connection system is only connected to the flanges of the glass column. Therefore the transfer of forces from the steel to the glass and vice versa only occurs via the flanges. a) side view b) top view Figure 68 Steel connection system for experiment II B.2 before assembling 110

111 cross section AA top view side view Figure 69 Connection detailing that transfers the axial forces in the glass column by shear. The bottom and top edge are not in contact with the metal frame. Only the surfaces of the glass are in contact with the metal by a glued connection. 111

112 Experiment II B.3 column cast in polyurethane rubber The last experiment of this series of tests studies a connection system where the glass column is cast. In this way, the forces are transferred by a combination of compression and shear between the connection system and the glass column. The design of this connection system is illustrated in Figure 70 and visualized in Figure 71. The casting material is Vytaflex 30, which is a polyurethane rubber. The characteristics of this material were consistent with the requirements: bonding both glass and metal, amount of creep almost negligible, sufficient stiffness and moisture proof. It is based on two parts of liquid. After mixing these together and a night of curing, the rubber becomes a solid. The polyurethane rubber is cast in a steel shoe (Figure 70). The shape of the shoe corresponds to the shape of the H profile. Only the dimensions are increased to prevent the glass column from contact with the steel. A layer of about five millimetres of polyurethane rubber is left around the glass column. The weight of one steel connection element equals 3.73 kg. a) side view b) top view Figure 70 Steel shoe experiment II B.3 During the assembling procedure first a layer of polyurethane rubber with a thickness of ten millimetres has been cast in the steel shoe. This layer prevents the glass column from contact between the bottom or top edge with the steel. After curing, the glass column is placed in position and the rest of the rubber is cast in the shoe. Due to manual work, the height of the shear connection (i.e. glass in connection with the rubber) differs slightly among the edges. These values are given in Table 19. column edge minimum height connection glass with rubber [mm] 30, 20, 32 top bottom , 19, 24 top 96.2 bottom 94.3 Table 19 In each steel shoe the polyurethane rubber is in contact with the glass. Due to manual work some slight differences in contact length between the glass and the rubber have been measured. For each shoe the height of this shear connection is given. The numbers in the first column correspond to the glass specimens from which the column is assembled. 112

113 cross section AA top view side view Figure 71 Connection detailing of the steel shoe. The glass column is cast in a polyurethane rubber. 113

114 5.3 Test setup The test setup encloses the last preparations before the real tests take place and the results can be gathered together (Section 5.4). The used test bench, the related testing procedure and the expectations will be explained in this section Machinery and testing procedure The machinery that has been used for the second experiment is similar to the one that has been used for the first experiment (Section 3.3.3). It was expected that enough compression capacity was left when some of the prototypes would have been stronger than the prototypes of the first experiment. Only the bottom boundary of the test bench is now restrained from rotation. The testing procedure was the same as in Experiment I (Section 3.3.4). The machine for the compression tests was displacement controlled. The displacement speed for the different tests has been 0.08 mm/s. Between the glass column and the machine different interlayer materials have been used to realize an even distribution of forces into the glass column. If no interlayer material was mentioned in the experiment, felt has been used. A small adaptation in the test setup has been arranged for the tests with the single glass plates. Single glass plates tend to be more sensitive to eccentric loading, while the slenderness is much higher than for the assembled columns (1:125 compared to 1:10). A special substructure (Figure 72) has been developed to level the glass plates and make sure the plates are placed in a vertical position for axial loading. By turning the four steel bars the column has been levelled in two directions. To prevent the plate from peak stresses next to the steel bars, a strip of Teflon is placed in between. a) single glass plate that starts to buckle b) substructure to level the glass plate Figure 72 Test setup single glass plates for experiment II A.2 114

115 5.3.2 Expectations In this section the different prototypes have been split up in two categories: the H Profiles and the single plates. For each category an overview of the observed imperfections is given. Finally this section will be concluded with a discussion about the expected failure load and failure mode for the single glass plates. H Profiles In total, nine glass columns have been assembled for experiment II. The imperfections in these prototypes that have been observed are listed in Table 20. experiment configuration [plate numbers] A.1 H Profile (17, 1, 21) A.1 H Profile (23, 3, 32) A.1 H Profile (2, 4, 10) B.1 H Profile (12, 6, 15) B.1 H Profile (13, 7, 28) B.2 H Profile (27, 8, 31) B.2 H Profile (16, 14, 22) B.3 H Profile (24, 19, 29) imperfections in columns [plate numbers] difference in imperfections in vertical position glass plate , 21 none 23, none imperfections in glue line not totally filled 12 or 15 6, edges not totally filled 13 or 28 13, plastic foil in glue 27 27, 31 none 16 or none 24 or top not totally filled B.3 H Profile (30, 20, 33) none Table 20 Overview of the imperfections in the glass columns (all the numbers correlate to a specific glass plate) Compared to the previous experiment (Section 3.3.2), less imperfections in the glass plates and in the glue lines have been observed. Only, scratches have been found on the surface of specimen 2 and 17 (Figure 73). Since no scratches have been noticed during the inspection of the specimens from the first experiment, the influence of this type of imperfection on the failure behaviour of the glass column is not known yet. 12 scratches have been observed 13 scratches have been observed Figure 73 Scratch on the surface of a glass plate between the red lines 115

116 Prototype 3 of Experiment I consisted of an H Profile configuration as well. This column failed at a load of kn by local buckling (Section 3.4.3). Although, it was expected that the column would fail at a load of 924 kn (Table 11). The ratio between the ultimate load and the expected failure load resulted therefore in 0.13, where the average was (based on five tests) (Section 3.5). It is assumed in Chapter 3 that one of the reasons of the early collapse of this column is a difference in vertical position of the plates. The H Profiles of experiment II are assembled by different glues, will be compressed with another interlayer material than felt or have special end-connections. If these adaptations increase the strength of the column to a value above kn, or not, will be investigated by performing this experiment. The results are gathered together in Section 5.4. Single plates Another part of the experiment makes use of single glass plates. Some of them have polished edges and others the normal waterjet cut edges. An overview of the imperfections in the glass plates is listed in Table 21. experiment configuration [plate number] imperfections in glass plates damaged corner scratch A.2 rectangle (18) A.2 rectangle 1-1 (34) A.2 rectangle (9) A.2 rectangle (5) A.2 polished rectangle (A) A.2 polished rectangle (B) A.2 polished rectangle (C) A.2 polished rectangle (D) A.2 polished rectangle (E) Table 21 Overview of the imperfections in the glass plates The failure behaviour of a glass plate will differ from an assembled column. Not only the crosssectional area has been reduced, but also the slenderness of the column has increased. Therefore, the column is very vulnerable for Euler buckling. In Appendix I the expected failure load has been calculated for three failure modes: Euler buckling, torsional buckling and pure compression. Some of the specimens have polished edges. Since it is assumed that this treatment reduces the amount of very fine imperfections at the edges, it is expected that the glass plates with polished edges will be slightly stronger than the normal waterjet cut plates. hole 116

117 5.4 Experimental results The results of the tests performed for Experiment II are presented in this section. Since different tests have been done, as explained in Section 5.2, the results are described separately in the following sub-sections. Then, an overview is given from the obtained experimental results for both part A and part B. Finally, some more general findings are considered Experiment II A In this sub-section the results of the glue test and the polished edge treatment test are described. Experiment II A.1 the glue The results of the glue test demonstrate that bonding a glass column by Hercuseal (i.e. an adhesive with low Young s modulus, 1.6 N/mm 2 ) is a feasible concept. Both prototypes (assembled from plates 10, 4 and 2 and assembled from plates 23, 3 and 32) showed a higher structural capacity compared to the results of a glass column bonded by Araldite (i.e. an adhesive with high Young s modulus, 2550 N/mm 2 ). These results are illustrated in Figure compressive strength [kn] araldite 17,1,21 hercuseal 10,4,2 hercuseal 23,3, applied displacement [mm] Figure 74 Load-displacement plot of the glue test results (the numbers correspond to the used glass specimens) In Table 22 the maximum load and the maximum occurring stress for each prototype are listed. The stress value of the Hercuseal bonded columns is on average 58.3% higher than the stress value of the Araldite bonded columns. Araldite versus Hercuseal specimen area [mm 2 ] force [kn] stress [N/mm 2 ] [%] Araldite Araldite Hercuseal Hercuseal Table 22 Experimental results of the glass columns assembled by different adhesives 14 prototype tested in Experiment I (Section 3.4.3) 117

118 It is good to realize that the costs for an H profile column bonded by Hercuseal are about three euro s, whereas the costs for the same column bonded by Araldite are about fifteen euro s. Photographs of the cracking sequence are shown in Figure 75. It illustrates the difference in failure behaviour between the two columns, which can be attributed to the stiffness of the glue. The Araldite bonded glass column, on the one hand, starts to break in the flange and has some residual strength left. The Hercuseal bonded glass column, on the other hand, fails more quickly and abruptly, but at a higher loading capacity. At the top of the column the web breaks to pieces and in less than a second the total column is broken. Araldite ( ) Hercuseal ( ) 1. column before loading 2. flange breaks 1. column before loading 2. cracking noises and top column breaks to pieces 3. immediately total failure column Figure 75 Cracking sequence of an Araldite bonded glass column and an Hercuseal bonded glass column From the cracking patterns it is observed that the stresses are more evenly spread over the column for the Hercuseal option than for the column glued with Araldite. The occurrence of local peak stresses has been reduced by the glue with lower stiffness, which results in a higher load bearing capacity of the column. Although it seems that Hercuseal is a good solution for the bonding of glass plates in a structural column, considering the strength capacity and the price of the column, it should be noted that these tests do not take into account aspects like load duration, temperature and humidity. Further research to the structural capacity of the polymer Hercuseal is therefore recommended. 118

119 Experiment II A.2 polished edges The effect of edge treatment on the load bearing capacity of a rectangular single glass plate can be derived from a comparison of the results of the compression tests on the series unpolished single glass plates (Figure 79 and Table 23) and on the series polished single glass plates (Figure 80 and Table 24). From this comparison the following is observed. Firstly, the series unpolished and polished single glass plates display a marginal difference in load bearing capacity. The average stress of the tested specimens equals for both series about 10 N/mm 2. From this observation it seems that polishing the bottom and top edge of waterjet cut glass plates does not have a significant effect on the structural capacity of glass plates. However, it is observed that both the polished and unpolished specimens failed by Euler buckling, which is illustrated in Figure 76. The two cracking patterns that have been observed in the middle of the buckling length are illustrated in Figure 77 and Figure 78. Whether the unpolished glass plates were more sensitive to Euler buckling than to very fine imperfections at the edges, is uncertain. Not a single one has failed by gradual crack growth from the top or bottom edge. Therefore, it cannot be concluded what the influence of the polished edge treatment on the strength of waterjet cut glass plates is. Secondly, the failure load of a rectangular single glass plate is found to be higher than expected. It was calculated that it would fail at a load of 4.7 kn by Euler buckling (Appendix I). It is observed that the average failure load was 8.03 kn (Table 23) for the unpolished glass plates and 8.46 kn (Table 24) for the polished glass plates. This is an increase in strength of about 75%. By using the Euler buckling formula the obtained strength value is below the real strength of a single glass plate. A buckling load of 8.0 kn would equal a buckling length of 607 mm instead of the 790 mm between the top boundary and the applied substructure. Possibly, the real buckling length is lower than the estimated value of 790 mm. However, it still seems that for a structural single glass plate of these dimensions the Euler buckling formula results in a good estimation of the failure load of the glass plate. Thirdly, the applied displacement at the moment of failure varies between 3.9 mm and 7.9 mm for all the specimens, see Figure 79 and Figure 80. It is assumed that this is caused by the material properties of the interlayer material, which is in this case felt. It is recommended to further investigate the influence of polished edges on the load bearing capacity of glass plates and glass columns. The exploratory investigation (see this section) into this topic has demonstrated that the strength of a single glass plate under compression is promising. The glass plates showed that, compared to the assembled glass columns, more load bearing capacity than expected according to theory. However, due to the unexpected strength capacity of a single glass plate, the influence of the edge treatment is still uncertain. This aspect should be further investigated in future research. 119

120 Figure 76 Buckling behaviour of a single glass plate under compression Figure 77 Crack pattern of a specimen with unpolished top and bottom edge Figure 78 Crack pattern of a specimen with polished top and bottom edge 120

121 load [kn] applied displacement [mm] Figure 79 Load-displacement plot of the unpolished glass specimens unpolished rectangle specimen area [mm 2 ] force [kn] stress [N/mm 2 ] Table 23 Experimental results of the compression test for unpolished glass plates load [kn] A B C D E applied displacement [mm] Figure 80 Load-displacement plot of the polished glass specimens polished rectangle specimen area [mm 2 ] force [kn] stress [N/mm 2 ] A B C D E Table 24 Experimental results of the compression test for polished glass plates 121

122 5.4.2 Experiment II B In this sub-section the structural behaviour of glass columns with different load introduction systems are described. Experiment II B.1 lead and aluminium as the interlayer material The results from the compression tests with different interlayer materials demonstrate that applying felt between the test bench and the glass column, which has been done in the previous tests, gives the best results. Although lead and aluminium are materials with a lower hardness than glass (Section 5.2.3), the ultimate failure loads are very low. In Table 25 the different failure loads for three tests with different interlayer materials are listed. The test setup is illustrated in Figure 81. The table shows that the failure load for a column with lead as the interlayer material has decreased by about 54% in comparison with a similar column with felt as the interlayer material. For the column with aluminium as the interlayer material the decrease in strength is even 72% compared to a similar column with felt as the interlayer material. interlayer material thickness interlayer failure load [kn] [%] [mm] lead aluminium (99%) felt Table 25 Effect of the interlayer material on the load bearing capacity of the column a) lead b) aluminium Figure 81 Glass columns before performing the tests with different interlayer materials; a) lead; b) aluminium For both interlayer materials, lead and aluminium, initial cracks in the column edges have been observed (Figure 82). This assumes that lead and aluminium cause local peak stresses at the edges and reduce thereby the strength of the column. 15 derived from Section

123 The above illustrates that felt has some properties which make it a good interlayer material although the material properties are not homogeneous over the area. Probably the initially low stiffness of the felt enables the material to deform and prevent the glass column from local (tensile) peak stresses at the edges. The softness and flexibility of the felt also enables levelling of the column. As glass is very sensitive to tensile stresses, centrically loading of the column is very important. a) lead b) aluminium Figure 82 Initial cracks in the bottom edge of the glass column with different interlayer materials; a) lead; b) aluminium Experiment II B.2 connection fastened to the glass surface The experimental results from the glass columns with the connection system fastened to the surfaces of the glass flanges are very promising. From this test it is concluded that the transfer of the compressive forces in the glass column by means of shear forces increases the load bearing capacity of the glass column, see Table 26 compared to Table 25. Due to the bonding of the surfaces of the glass and air gap between the glass and the steel plate, local peak stresses in the glass edges are avoided. It is assumed that this causes the increase in structural strength of the column compared to the others described in this section. prototype [numbers of the glass plates] failure load [kn] Table 26 Experimental results of the compression test for glass columns with connection systems fastened to their surface According to the failure modes of the columns with the connection system fastened to the glass surface, it is demonstrated that these connection systems avoided peak stresses at the edges. Before failure of the column, cracking noises have been observed. Since there were no cracks visible, it is assumed that these sounds are originated from the adhesive. At the moment the column reached its ultimate bearing load, total failure occurred (Figure 83). This indicates that the peak stresses were located at a bigger area of the glass column than only locally at one of the edges as observed in Section From the experiment it is observed that the connection system was still intact after failure of the columns. The applied adhesive has demonstrated to have both the adhesive and cohesive qualities 123

124 for the available shear stresses. In indication of these shear stresses is obtained by dividing the maximum load by the contact area between the glass and the steel, which transfers the compressive forces by means of shear forces. The contact area is based on six steel connection elements per boundary, see Figure 68. In total, the area to transfer the shear forces was equal to mm 2 per column. Based on the assumption that the total connection area was transferring compressive forces by means of shear forces in the glass column, the resulting shear stresses in the epoxy were N/mm 2 and N/mm 2, which is far below the shear strength of Araldite (18 N/mm 2 ) [Huntsman cooperation, 2010]. a) before testing b) after testing Figure 83 The steel connection system fastened to the glass surface; a) before testing; b) after testing Experiment II B.3 column cast in polyurethane rubber Overall, the performance of the columns cast in polyurethane rubber was very bad compared to the previously tested columns. It is observed that this connection system fails by very low load values. The maximum failure load measured is only kn, see Table 27. Although there is a layer of 16 contact area 2 big steel elements = mm 2 contact area 4 small steel elements = mm 2 contact area per boundary: mm N/mm N/mm

125 rubber (about 5 mm thick) around the glass column, it is assumed that local peak stresses occurred at the edges of the glass column, which resulted in gradual crack growth from an edge. This is illustrated in Figure 84. Whether the rubber was not suitable for this connection system or the intermediate layer was not thick enough, could not be concluded from this test. prototype [numbers of the glass plates] failure load [kn] Table 27 Experimental results of the compression test for glass columns glued in polyurethane rubber a) gradual crack growth b) initial crack growth from an edge Figure 84 Failure mode glass column cast in polyurethane rubber 125

126 Comparison of results from Experiment II B As a summary, the structural behaviour of all the different connection systems tested in part B of Experiment II are illustrated in Figure 85. The slopes of the graphs (i.e. the stiffness) are different, which can be explained by differences in material behaviour of the interlayer materials. For example, aluminium has a very high stiffness compared to rubber. From this diagram it reveals that the connection system with the compressive forces transmitted by means of shear forces has the best structural load bearing capacity. Compressive strength [kn] Applied displacement [mm] lead (B.1) aluminium (B.1) surface (B.2) ( ) surface (B.2) ( ) cast (B.3) ( } cast (B.3) ( ) felt Figure 85 Overview compression test results of glass columns with different load introduction systems Overview experimental results This subsection gives an overview of all the data gathered from the tests in this chapter, see Table 28. The occurring stresses in the glass columns show high differences. They really depend on the applied bonding material and the connection system. The highest stress value measured in a glass column in Experiment II is N/mm 2 for a Hercuseal bonded glass column with felt as the interlayer material. 126

127 Araldite versus Hercuseal specimen area [mm 2 ] force [kn] stress [N/mm 2 ] [%] Araldite Araldite Hercuseal Hercuseal unpolished rectangle (A.2) specimen area [mm 2 ] force [kn] stress [N/mm 2 ] polished rectangle (A.2) specimen area [mm 2 ] force [kn] stress [N/mm 2 ] A B C D E different connections (B) specimen area [mm 2 ] force [kn] stress [N/mm 2 ] [%] felt lead aluminium (99%) cast rubber cast rubber felt glued sides glued sides Table 28 Overview of the experimental results gained from the tests performed in Experiment II 19 prototype tested in Experiment I (Section 3.4.3) 127

128 5.4.4 Other considerations This subsection deals with some other more general considerations observed from the tests in Experiment II. Imperfections: cracks During the preparation phase, a lot of cracks have been observed in both the H profiles and the single glass plates (Section 5.3.2). The tests demonstrated that these cracks had marginal influence on the strength of the plates. For none of them initial failure was observed to be caused by these imperfections. Levelling of the glass column or plate Compared to the test setup in Experiment I, the substructure to level the glass plate or column has been added in Experiment II. Since glass is very vulnerable for tensile stresses, placing the element under a straight angle and loading it in plane, is necessary. In the production process of a structural glass element and on the building site levelling is extremely important. It is recommended to take care of this aspect already in the design phase of a structural glass column. Design stress From the tests it is observed that different interlayer materials and different connection systems result in specific structural behaviour and occurring stress values. Therefore, in the design of a glass column the design stress depends extremely on the boundaries and the applied materials. It should be noted that the values in this chapter correspond to columns that are only one metre high. 5.5 Summary and conclusions The following sections provide the conclusions from test II A and II B that have been performed in this chapter to investigate the effects of the parameters glue stiffness, polished edge treatment and load introduction Glue stiffness From test A.1 it is concluded that the prototype assembled by Hercuseal (i.e. an adhesive with low Young s modulus, 1.6 N/mm 2 ) resulted in a higher load bearing capacity than the prototype assembled by Araldite (i.e. an adhesive with high Young s modulus, 2550 N/mm 2 ). With the same circumstances (i.e. felt as the interlayer material and loading both the flanges and the web) the maximum stress value of the Hercuseal bonded columns is on average 58.3% higher than the stress value of the Araldite bonded columns. Nevertheless, it is recommended to investigate the effect of load duration, temperature and humidity on the structural behaviour of the polymer. From the cracking patterns it is concluded that the adhesive with lower Young s modulus is able to distribute the peak stresses over a bigger area than the adhesive with higher Young s modulus. The column bonded by Hercuseal breaks very abruptly with cracks over the whole section, which leads to total failure. The column bonded by Araldite, on the other hand, shows local cracks, which after a while lead to total failure Polished edge treatment From the tests performed with rectangular single glass plates it is concluded that single glass plates under compression have more load bearing capacity than expected according to theory. It is observed that the glass plates both polished and unpolished (i.e. waterjet cut edges) failed at a compressive stress of about 10 N/mm 2 by Euler buckling. Due to the unexpected strength capacity of 128

129 a single glass plate, the influence of the edge treatment is still uncertain. This aspect should be further investigated in future research Introduction of forces From the tests with lead and aluminium it is concluded that felt would be preferred as the interlayer to transfer the compressive forces into the glass column above these materials. This superior performance of felt is assumed to be mainly the result from the initially low stiffness of the felt, which prevents the glass column from local (tensile) peak stresses at the edges. Also, the softness and flexibility of the felt enables levelling of the column. As glass is very sensitive to tensile stresses an eccentrically loaded column should be avoided as much as possible. From the tests with the connection system fastened to the glass surfaces it is concluded that transferring the compressive forces in the glass column (via the flanges) by means of shear forces increases the load bearing capacity of the glass column. It is assumed, by applying this design, that peak stresses at the edges due to fine imperfections are avoided and a difference in vertical position between the glass plates does not limit the structural strength of the column. The tested columns demonstrated that Araldite was a sufficient bonding material, i.e. the adhesive and cohesive qualities were sufficient. However, it should be noted that these columns were only one metre high. It is recommended to investigate the applicability of this glue for cases with higher shear stress values. From the test with the column cast in polyurethane rubber it is concluded that this connection system reduces the load bearing capacity of the column compared to other connection systems described in this chapter. It is assumed that probably the layer of rubber around the glass was to thin or the rubber was not sufficient as the interlayer material in this design. Overall, it is concluded that the connection system with the compressive forces transmitted by means of shear forces has the best structural load bearing capacity compared to the other systems that have been tested. 129

130 130

131 PART III Case-study pavilion 131

132 132

133 Chapter 6 Design structural glass column This chapter provides the structural design of a glass column for a pavilion, based on the experiences and knowledge gained from the experimental research and numerical analysis presented in Part II of this research. The preliminary design of the pavilion is meant as a case-study to get a realistic situation and to understand the forces that need to be transferred by the glass column. On the basis of these requirements the column boundary connections and the column section are considered. 133

134 6.1 Introduction This chapter focuses on the structural design of a glass column. The design is based on the practical experiences and knowledge gained from the experimental and numerical investigations done in this research (Chapter 3, 4 and 5). Section 6.2 provides the preliminary design of the pavilion that has been created to get a realistic situation and to understand the forces that need to be transferred by the structural glass column. An explanation of the three basic assumptions for the design concept precedes the structural design of the pavilion. The preliminary design comprises only the main structural aspects to understand the structural performance of the building. Additionally, the overall stability of the pavilion and the importance of an alternative load path have been discussed. Furthermore, the requirements for the structural glass column have been derived (i.e. the design load, the number of glass columns and the available height). As the requirements for the glass column are known, Section 6.3 investigates a concept for the column boundary connection and Section 6.4 investigates a concept for the column cross-section. Experiment I has resulted in an indication of the structural behaviour of the five tested cross-section configurations. To gain more insight in the qualities of different configurations for slender glass columns assembled from single glass plates, a non-experimental study is provided in Section 6.4. In general, the bearing capacity, the susceptibility to impact and the connectivity to load introduction systems have been studied. In addition, the problems that need to be studied before designing a structural glass column made of laminated glass have been discussed. Section 6.5 provides a safety concept for the column. Since glass is a very brittle material, the safety of the structural glass column is considered in a separate section. The final column design is presented in Section 6.6. The design is developed from the concepts for the boundary connection system, the cross-section and the safety of the structural column. Finally, an evaluation of the design process of the structural glass column is provided in Section Pavilion As the focus of this research is on the design of a glass column and not on the structural design of a pavilion with a glass column, a thorough structural design calculation of the pavilion will be omitted. However, to get a realistic situation and to understand the forces that need to be transferred by the glass column a preliminary design is required and is provided in this section Design concept The two-floors-high pavilion is 22.5 meters wide and 45 meters long, see Figure 86. The lower floor, 4 meters high, is enclosed by a glass façade and concrete roof, which results in an inner climate. The first floor, the roof, is more like a terrace and can be reached by an external staircase. 134

135 Figure 86 The pavilion 135

136 The design of the pavilion is based on three main aspects that are specifically of relevance for structural glass columns: - transparency throughout the pavilion It is especially the transparency property of glass that makes it a valued material when compared to other conventional structural materials like concrete, steel and timber. Therefore, it is chosen to enclose the building by a glass façade and, of course, use structural glass columns. The roof, on the other hand, will be designed in concrete. In this way, it seems that the concrete floor is floating in the air. - preventing the glass columns from tensile stresses as much as possible As the tensile strength of glass is much lower than the compressive strength, the design of the pavilion takes into account this weakness of glass by three structural solutions. a) Pin-ended columns are, in theory, only subjected to normal forces, which is preferred in glass columns. Applying this type of columns to the pavilion, however, means that the columns do not contribute to the stabilizing effect of the pavilion. As a result, the stability of the pavilion needs to be controlled by other structural elements. b) A roof designed in a thick layer of concrete, prevents the roof from wind suction. Tensile reaction forces in the glass columns due to this wind suction are thereby omitted. c) Glass columns located in an inner climate are not subjected to heavy wind loads. Bending in the columns due to the wind loads is prevented by the glass façade. When the sliding doors in the pavilion have a total area of less than 0.05 of the total façade area, the pavilion is considered as a closed building according to NEN durability of the adhesive Another advantage of locating the glass columns in an inner climate instead of outside, is that the influence of moisture and UV on the adhesive will be omitted. As a result, the adhesive will have a longer life time. The pavilion could serve as an exhibition hall or meeting room. The ground floor creates an open space illuminated by natural daylight. Via an outer glass staircase visitors can go to the roof where a terrace could be realized Preliminary design To create a feasible context for the glass column, only the main structural aspects are considered in this preliminary design. The calculation with the corresponding description for this initial design phase is provided in Appendix J. By considering the actions on the structure the main structure is designed and checked on stability. Finally, the requirements for the design of the glass column, like the design load, are provided. In this section two design aspects will be discussed: stability and second load path. As observed in the experiments glass is very sensitive to imperfections: it fails more quickly than expected. From literature it is known that the strength is not one value, but depends on several aspects, like dimensions, weathering and production tolerances. Therefore, the application of structural glazing in a building requires some safety measures. Two aspects related to the safety measures of the pavilion are described in this sub-section. 136

137 Stability The glass columns in the pavilion are assumed to be pin-ended columns to prevent the structural glass from tensile stresses (more about this topic in Section 6.3). As a result, it is checked in Appendix J whether the transparent glass façade is able to stabilize the pavilion by means of plate action. It is a feasible concept by considering the situation that no failure occurs. The glass façade has enough capacity to deal with the tensile stresses in the structure. Also, E.M.P. Huveners agrees in his doctoral thesis with the stabilizing capacity of glass panes [Huveners, 2009]. However, as the glass façade is sensitive to impact, the stability of the pavilion is not secure. In the previous the stabilizing effect of the glass façade is considered on the assumption that it is not damaged. Thereby, it is recommended to apply extra redundancy to the stabilizing elements of the pavilion. The following options could be considered to enhance the stability of the structure: - a core - a stabilizing wall - glass fins - wind bracings in the façade - a combination of these stabilizing elements. To retain the transparency throughout the pavilion the third option (i.e. glass fins) would be preferred. However, this is the fewest effective solution compared to the others. Alternative load path The other safety aspect is related to a second load path. If one column fails or a part of the structural façade, the load on the remaining structure increases. Therefore, the roof of the pavilion needs to be stiff enough to transfer the loads to the remaining glass columns and façade. As the roof is made of composite plank floors with a concrete layer on top, this probably would be sufficient. Some extra reinforcement could be added. It is recommended to check the residual capacity of the structure for several cases (i.e. a glass column fails or a part of the façade collapses). Solutions to create an alternative load path are: - if a stabilizing core or wall is selected, to locate this stabilizing element so that it could be part of the second load path of the most critical option of failure - to apply more structural glass columns than the ten that are required Requirements structural glass column From the preliminary design of the pavilion in Appendix J a few requirements for the design of the structural glass column are deduced. The design load for each of the 10 glass columns is equal to 789 kn. In this structural design calculation it is assumed that the columns are pin-ended and thus only loaded by compressive forces. Furthermore, the available height for the glass column including the boundary connection system is four metres. 137

138 6.3 Column boundary connections This section deals with the design concept of the boundary connections. First, the requirements for the boundary connection of the structural glass column in the pavilion are described in Section These requirements are related to the assumptions made in the preliminary design of the pavilion, see Section 6.2. Finally, on the basis of these requirements and the experimental results a concept is developed for the load introduction system and the type of support in Section Boundary connection requirements In general, the connection system should be able to transfer the load from the roof, which includes self-weight and variable loads, through the glass column to the foundation. The upper boundary of the glass column is connecting to the roof and the bottom part is supported by the foundation. As it is assumed in Section the column connections are exposed as real hinges. According to this, the glass panels in the glass column are subjected to in-plane compression only. Since glass is stronger when exposed to compressive forces, this pin-ended column with only normal forces is preferred. However, the situation of only normal forces in a column is very rare. Due to imperfections and eccentrically applied loads, the column will be exposed to bending and tensile stresses as well. To gain as much as possible the ideal situation of only compressive stresses in the glass, the design of the boundary connection needs to fulfil the following requirements as far as possible. Also, some requirements obtained from the experimental and numerical results (Chapter 3, Chapter 4 and Chapter 5) have been added to the list of requirements. The connection system should: - allow rotational movement, but avoid horizontal and vertical displacement - allow any production tolerances or a difference in vertical position between glass plates - allow levelling of the column - omit transfer of forces via the edges of the glass - omit rotation along the longitudinal axis - omit direct contact between glass and a metal like steel The sensitivity of glass for local peak stresses and the lack of calculation standards make it difficult to prove by calculation the strength of a connection. Therefore in practice almost all connections have been tested, after a finite element model is made to get a first idea of the structural behaviour of the connection. In this study only the first phase, the design, has been performed and the verification is recommended before applying this system in reality. Based on the preference to have pure compressive forces in a glass column (Section 6.2.3), the structural design calculation of the pavilion resulted in a design load of 789 kn for the glass column Boundary connection concept The boundary connections of a column have been divided in different aspects, see Figure 87. By considering these aspects, a design for the column boundary connections has been developed. The design choices for the aspects are based on the experimental and numerical results in the previous chapters and on the structural design of the pavilion. Part A, in Figure 87, corresponds to the glass column itself, which will be considered in Section 6.4. Parts C and E contain solutions for the transition between steel to steel or steel to concrete elements. This will be determined in Section 6.6, the final design of the glass column. This section 138

139 includes the selection of the right connection systems. The design concept for the load introduction from metal to glass, part B, and for the type of support, part D, will be considered separately in the following. A) glass B) transition glass-metal C) transition metal-support D) type of support E) transition support-concrete floor Figure 87 Deviation of the boundary connection into different aspects Transition glass-metal (part B) In Experiment II B (Section 5.4.2) different load introduction systems have been tested. It is concluded that the system with the forces transferred by means of shear forces in the glass flanges (Figure 69) has the best qualities compared to the other tested load introduction systems (Section 5.5.3). This system: - resulted in the highest structural capacity. The failure loads of the two tested columns were 204 and 222 kn (Table 26), where the other load introduction systems did not exceed a strength capacity of 174 kn (Table 28). - transfers the forces via the surfaces of the glass column and not via the edges. It is observed that no local peak stresses at the edges occurred, but total failure in the glass column (Section 5.4.2). Therefore, it is assumed that this load introduction system executes its function, to transfer the forces, very well. - avoids the problem of differences in vertical position between glass plates (Section 3.5). The air gap under the bottom edge and above the top edge of the glass column (Figure 69) enables a slight difference in vertical position due to not accurate assembling of the glass plates or due to a difference in length between the plates. In this way, slight imperfections in 139

140 the production process of assembling or cutting of the glass plates do not limit the structural strength of the column. The two tested columns demonstrated that both the adhesive and cohesive qualities of Araldite 2000 Plus 2013 were sufficient for a one-metre-high column with a maximum load of 222 kn (Table 26) to bond the steel with the Araldite and to transfer the shear forces of about 4.12 and 4.47 N/mm 2 (Section 5.4.2). The final column needs to transfer higher forces. The area to transfer these forces by means of shear between the glass and the metal should be sufficient to not exceed the shear strength of Araldite, which is 18 N/mm 2 [Huntsman cooperation, 2010]. Type of support (part D) In the engineering practice the most commonly applied support system is the hinge. Other support systems that have been considered in mechanics are the role and the fixed support. For each purpose special design variants have been developed to approximate these support systems as much as possible. As it is not the intention in this research to consider supporting systems in great detail, the emphasis of this sub-section is on the development of a support system that is in accordance with the requirements for the structural glass column in the pavilion. As explained in Section the basic assumption of the preliminary design of the pavilion is to create pin-ended columns to prevent the glass columns from tensile stresses as much as possible. In the following, two options for the support system will be considered: the ball-and-socket joint and the traditional column joint (see Table 29). An overview of the advantages and disadvantages is listed in Table Ball-and-socket joint Especially the hinge property of the ball-and-socket joint makes this support system a very valuable option for the structural glass column. Due to this system the column is only subjected to compressive forces and allows rotational movement. However, this joint also allows rotational movement along the longitudinal axis. From the experimental results it is found that the H profile column with fixed boundary connections (i.e. no rotation along the longitudinal axis of the test bench) showed a higher strength capacity than a similar H profile column where the lower part of the test bench was able to rotate. If this joint would be selected, a solution needs to be found to unable this rotation. Considering the resistance of buckling, this support results in a buckling length which is equal to the system length. Buckling would occur at a lower value than for the other support system considered in this sub-section. A very famous example of the application of the ball-and-socket joint is the Maeslantkering in the Netherlands. The joint allows movement of the big arms in several directions due to waves in the water and by opening and closing the doors. For further reading on the Maeslantkering is referred to Keringhuis [Keringhuis,-]. - Traditional column joint The second support system consists of a base-plate connected with bolts to the roof or floor. After leveling of the column by the bolts, the joint is filled with concrete. The ability to level the column on site is an advantage of this system. However, it requires good skills from the workmen on site. If the column is placed a bit out of position, the glass column is subjected to tensile stresses. Furthermore, 140

141 this system does not allow any rotational movement, which results in moments in the connection system. The column is not only subjected to normal forces. These traditional column joints are applied to steel structures at most of the train stations in the Netherlands. The steel columns that are part of the structures to fix the wiring for the trains are very often connected by this support system. side view top view advantages and disadvantages ball-and-socket joint (+) only normal forces in the column (-) column is able to rotate around the longitudinal axis (-) longer buckling length traditional column joint (+) common practice for steel columns (+) smaller buckling length (+) bolts enable levelling on site (-) connection system is unable for rotational movement, which results into moments in the connection system (-) requires good skills from the workmen on the building project Table 29 Comparison of two support systems: the ball-and-socket joint and a traditional column joint As observed in the experiments performed in Chapter 3 and Chapter 5, glass columns are very sensitive to imperfections and therefore never reach the theoretical strength value. It is not buckling that makes the H profile columns fail, but tensile stresses in the column due to imperfections in the glass, out-of-straightness of the glass or eccentrically introduction of forces. Furthermore, due to the sensitivity of glass it is important to develop a connection concept which prevents that the column fails by the previously described failure modes. In addition, it is not required that the quality of the glass column depends on the skills of the workmen on site. An extra facility on site to level the column to deal with inaccuracies would be preferred. Altogether, the main aspects of these systems are: - the ball-and-socket joint allows rotation and thereby reduces the tensile stresses in the structural glass column as much as possible - the traditional column joint enables leveling on site. Both aspects are preferred in the final boundary connection concept. Further optimization of the boundary connection system is necessary to fulfill the requirements considered in Section 6.3.1: 141

142 - The rotational movement along the longitudinal axis should be fixed. A joint system that fixes rotation along the longitudinal axis and at the same time allows rotation along the width of the column is illustrated in Figure 88. The cross consists of two axis, which enables the rotation along the width of the column. However, in case of heavy compressive forces the axis is subjected to bending and should be designed very stiff. Figure 88 Joint system [Armisoft, -] Based on the considered connection systems, a concept for the boundary connection system of the structural glass column for both the upper and lower side of the column has been developed, see Figure 89. Important aspects of this boundary connection system are: - rotation along the longitudinal axis is fixed by the cross; - rotation along the width of the column is allowed by the cross in combination with the ball. Between the ball and the steel plates a layer of Teflon enables a fluent rotational movement. Also the holes in the arches are finished with a layer of Teflon so that the axis are able to rotate in these circular holes; - the compressive forces are transferred by the ball; Furthermore: - the adjustment facility to level the column on site is applied in the transition between both the support system and the floor and the support system and the roof, see Figure 95. This facility contains adjustment nuts, as in the traditional column joint. Settlements of parts of the foundation will not be considered in this study. It is assumed in this design concept that the foundation of the pavilion is stiff enough; - preserving of the steel is possible through the open spaces; - for everyone interested, the boundary connection system is visible. It should be noted that besides all the advantages of this system, it probably will be an expensive solution. As the tolerance on the dimensions is very low, some of the steel elements need to be produced by casting, which is an expensive procedure. 142

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144 a) b) c) 144

145 d) e) Figure 89 Boundary connection concept for both the upper and lower edges of the final structural glass column: a) Base plate with hole is placed b) Ball with cross is positioned in the hole c) Lower arches are fastened d) Top plate is brought in position e) Upper arches are fastened 145

146 6.4 Column section This section gives more insight into the capabilities of different column section configurations. The configurations are built up from three or four plates of waterjet cut float glass 8 millimetres thick, 100 millimetres wide and 1000 millimetres long, which is similar to the tested specimens in Experiment I (Section 3.2.2) and Experiment II (Section 5.2.1). It is assumed that the cross-section does not change over the height of the column. As quoted in Section 1.1.2, the production aspects and aesthetics were the main factors considered when determining the right shape for the column section. In this case the columns are built up from single float glass elements. This is a very common building material. Difficulties with the production of the column section are therefore omitted. However, there are a lot of other aspects which can help a designer or architect by choosing the right configuration for their glass column. The final column will be made out of single glass for two reasons. Firstly, all the knowledge gained from the experiments is related to single glass specimens. Secondly, it is concluded from the experiments that the load-bearing capacity of a column assembled from single glass plates would be sufficient. An overview with the capabilities of the different column configurations is therefore based on single glass cross-sections. As it would be obvious to design a glass column in laminated glass due to safety this will be considered in this section as well. The safety of the single glass column is considered in Section Single glass In this sub-section several monolithic cross-section configurations will be compared by four criteria: bearing capacity, susceptibility to impact, connectivity and others. After an explanation of these criteria, the capabilities of each configuration on the basis of these aspects will be summarized. Nine different configurations for the cross-section of the column have been considered, which are shown in Figure 90. The glass elements are joined together at their edges. It is assumed that the junctions are able to be as strong as the glass elements. Figure 90 Column section configurations Some of the configurations consist of three plates of glass. Others are made out of four plates of glass. They have both their advantages and their disadvantages. Therefore, no distinction will be made between them. Bearing capacity The most important property of a column is the ability to carry loads. For a structural glass column this holds true to. Therefore the first criterion that should be considered in this analysis will be the 146

147 bearing capacity. This is the bearing capacity of the column without taking into account any influences that may reduce the strength. The bearing capacity will be split into the aspects: material, resistance to normal forces, resistance to buckling and resistance to torsional buckling. - Material The bearing capacity of a column depends on the chosen material and its properties. Since the glass plates considered in this analyses are all based on the same material, this aspect will not be considered in the comparison. - Resistance to normal forces The resistance to normal forces for a material is based on the size of the area where the loads are applied. Considering the maximum allowable stress, the column section is restricted to a minimum area to carry a certain load. The prototypes for the experiment are limited to three or four plates each. This means that the resistance to normal forces is higher for a prototype made out of four plates than the resistance to normal forces for a prototype made out of three plates. - Resistance to buckling The resistance to buckling needs to be taken into account in this analysis. This will be done by considering the values of the second moment of area in both directions. Since the structural application of the column is a pin-ended column, the lowest value of the second moment of area determines its resistance against buckling. For one of the configurations the principal directions did not coincide with the original axis of the cross-section. According to Appendix B the principal directions have been determined. - Resistance to torsional buckling The resistance to torsion has been taken into account by calculating the Euler torsional buckling strength (Section 2.2.1). In general, open sections are more susceptible to torsion than closed sections. Since the sections made out of three glass plates are all open sections, these show the lowest resistance against torsion. Susceptibility to impact As is discussed in Section 2.1, the material glass is able to carry heavy loads in theory. But, due to internal and external scratches or eccentric loading the bearing capacity of glass reduces. This makes that particularly for glass columns the susceptibility to impact is also very important to consider in the design. For example, if the structure has protruding edges and the floor is going to be cleaned by heavy machinery, then the column will be susceptible to scratches, which results in a reduction in strength. The aspects that will be considered for the criterion susceptibility to impact are: protruding edges and stamina. - Protruding edges Some glass sections have the appearance of protruding edges. While these edges are made in glass, the sensitivity to impact of these edges should be considered. An external layer to take up the external forces can prevent the structural layers from failure. Considering the cross-section, however, configurations with protruding edges are more sensitive to impact than others. 147

148 - Stamina Stamina means the capacity of the column to fulfil its target to transfer loads although it has been subjected to impacts and is not totally intact anymore. If one glass plate is partly broken, it is not as strong and stiff as it was before. The centre of gravity shifts slightly and the point of application of the normal force does not change. As a result, the column is eccentrically loaded, which makes the column more sensitive to bending. This is visualized in the table in Appendix K. In some cases there is still an axis of symmetry after one glass plate is broken. For these configurations the column is sensitive to bending in only one direction. But, in other cases, where there is no symmetry anymore, the column becomes sensitive to bending in even two directions. Then there is also the situation where there is no cohesion left after the failure of one glass plate. This counts for configurations like the Z profile (configuration VII) when the web is broken. This situation is very critical for the column. Connectivity The cross-section needs to be connected to the roof at the upper boundary and to the foundation at the bottom boundary. Some cross-section configurations will be easier to connect than others. Also, a connection transfers the loads into the column. For a glass column this introduction of forces needs to be executed carefully to prevent the column from tensile stresses or peak stresses. In this analysis just two types of load introduction from the connection into the glass and vice versa are considered. These are: glued to the sides by shear or cast by shear and compression. - Glued to sides For this aspect, it is important to know whether a cross-section is closed or open. A closed section, for example, is harder to bond by gluing the sides than an H profile section. - Cast A cast connection is much easier to connect. The shape of the cross-section has no influence. Choosing for this type of connection, therefore, does not influence the choice of cross-section configuration. Others Other aspects that can be applied to the structural glass columns are: neatness, number of junctions, surface use and aesthetics. - Neatness Since glass is transparent, it is necessary to keep the material clean. Dirt accumulation or the presence of insects should be avoided. For a closed section it is hard or maybe even impossible to clean the inside of a column. A hermetically sealed column should be the solution for this problem. It keeps insects, dirt and water vapour out of the cavity. Only the thermal stress should be verified. In Appendix A it is proven that the internal bending stress caused by a difference in temperature between the inside of a closed section and the outside will not be an issue for the column dimensions that are used for the experiments and for an extended column. However, a validation for each structure would be advised. In the analysis this aspect is taken into account by checking whether a column has an open or closed section. 148

149 - Number of junctions In this analysis this aspect is taken into account in the context of workmanship. Each junction is made by hand in a factory. The more junctions, the more time is needed to fabricate a certain column. - Surface use Some columns are bigger than others. If there is a shortage in space in a structure, some columns will be more suitable than others. The aspect surface use is considered to be the area that can not be used for other things than the column. - Aesthetics Actually this aspect is not considered in this analysis. It is just left blank for the reader. Aesthetics is something very subjective. And very often it is a real argument for the final choice of a cross-section of a glass column. Final comparison A summary of the aspects for the different configurations is visualized in Appendix K. The considered glass columns are assembled from glass plates, which are 8 mm thick, 100 mm wide and 1000 mm long. The values for the area, resistance against compressive forces, resistance against buckling and surface used are therefore related to these specimens. An architect or designer can use this table as a guide to compare the qualities of these configurations. The glass numbers will be different by considering other glass specimen dimensions. However, with this data the qualities of the different configurations can be compared Laminated glass Although this thesis only focuses on columns made of single glass plates, this subsection discusses some of the problems that need to be studied before designing a structural glass column made of laminated glass plates. The advantages of laminated glass compared to just single layered glass is the ability to protect one layer by another and to prevent pieces of broken glass from falling down. Considering a structural glass column the first argument is significant. For the implementation of laminated glass in a structural glass column more fundamental study is required. Not only its mechanical behaviour is just partly known, but also the design of the cross-section can place the designer in a dilemma. These topics and others will be clarified below. Buckling behaviour The buckling behaviour of a monolithic section compared to a laminated section will be different. In general, the total thickness of a composite can be higher compared to a monolithic section. This reduces the slenderness of the column and therefore increases its resistance against buckling. Moreover, the glass laminate is composed of two or more layers of glass with an interlayer in between. The buckling behaviour is therefore dependent on the properties of the interlayer as well. As explained in Section Blaauwendraad distinguishes two extremes: the interlayer has no stiffness, which results into two separate planes of glass, and the interlayer is infinitely stiff, which results into ideally coupled glass plates. The buckling behaviour of a laminated cross-section is according to this theory dependent on the mechanical behaviour of the interlayer. 149

150 Interlayer For the interlayer different types of material are used. The most common one is PVB. This one is temperature dependent and sensitive to long duration loading. Relaxation of the shear modulus can influence the stiffness of the interlayer and in this way the buckling behaviour of the column. [Belis,-] The thickness of the interlayer should be able to intercept the shape imperfections caused by the thermal treatment. Cross-section Each cross-section is assembled from several glass plates. During the fabrication of a laminated glass column, first the glass needs to be cut in the right dimensions. After that, the glass plates are laminated in an autoclave and finally the laminated glass panels can be glued together into the right configuration. This procedure is of importance by dividing the cross-section in separate elements. In the assumption that each structural layer of glass needs to be protected by an outer layer of glass, some options for the separation of three cross-sections have been made in Figure 91. The laminated cross-sections in this figure are not drawn to scale. They just give an idea about the separation of a cross-section into laminated components. In the third row the structural layer is not interrupted. As a result, especially for the H profile and the Star the laminated components are very complicated. High fabrication tolerances are not allowed. Otherwise, the components will not fit together or the symmetric sections are not symmetric. Also, the glue lines of the H profile and the Star are not that straight anymore. The third row shows the option where the structural layer is interrupted. Basis assumption was to keep the laminated components as simple as possible. The structural behaviour of a laminated glass column where the structural layer is interrupted by a protection layer should be investigated. Square H Profile Star Configuration Structural layer is not interrupted Structural layer is interrupted Figure 91 The separation of a cross-section in laminated glass components 150

151 The figure shows that some designs are more suitable for laminating than others. There are other options available for assembling laminated glass plates together besides just gluing, like metal connection systems. These systems and their mechanical behaviour will be left out of consideration in this thesis. Another aspect that should be taken into account by designing the cross-section of a laminated glass column is the effect of weathering of the interlayer. Moisture in the air or cleaning liquid are able to react with the interlayer material. For the configurations in Figure 91 it is for almost all sections possible to get in contact with the interlayer. It is known that water can cause delaminating of the pvb-interlayer material. Other consequences should be verified or prevented as much as possible by designing the column. In this brief analysis it can be concluded that the Square cross-section is more suitable for a laminated glass column assembled by gluing compared to the H profile and the Star. Connection Considering laminated glass, the structural layer is protected by an outer layer. As a consequence, the design of the boundary connections will be influenced. A shear connection (glued or cast) on each end is not connected to the structural layer, but is connected to the outer layer. A difference in structural behavior between the monolithic section and the laminated section will be the result. Some scientists, like Bennison already spend some effort on these topics. The book Glass Manual [Schittich, 1999] gives a lot of insight into laminated glass by both text and illustrations. But, still a lot of fundamental investigation can be done Selection column section The selection of the configuration and adhesive for the final column design are explained in more detail in the following subsections. Configuration In Section the glued boundary connection system is selected to transfer the compressive forces by means of shear forces from the steel in the glass column and vice versa. To be able to assemble the steel connectors from this system an open column section is essential. From the cross-sections, considered in Section 6.4.1, there are five open configurations, see Figure 92. By comparing the qualities of these configurations (Appendix K), it is found that the U profile (the third configuration in Figure 92) and the H profile (the fifth configuration in Figure 92) have good resistance against Euler buckling and torsional buckling compared to the other three open sections. Also, the surface use of these configurations is very low. Figure 92 Open sections However, the stamina of these configurations could be better. If the middle glass plate fails, there is no cohesion between the plates left. Compared to the other open section configurations, it is found that only the cross would be slightly better for this criterion. Since the load bearing capacity of a 151

152 column is important for structural application, either the U profile or the H profile is selected. As there is no big difference between the qualities of these two configurations, the designer has selected the H profile for the final column due to aesthetics. In the final design extra safety should be considered due to the stamina qualities of the configuration. Adhesive In Experiment II A.1 (Section 5.4.1) two different types of adhesive have been tested. It is concluded that the prototype assembled by Hercuseal (i.e. an adhesive with low Young s modulus, 1.6 N/mm 2 ) has better structural qualities than the prototype assembled by Araldite (i.e. an adhesive with high Young s modulus, 2550 N/mm 2 ). The glass column bonded by Hercuseal: - resulted in the highest load bearing capacity. The failure loads of the two tested columns were 212 and 256 kn (Table 22), where the prototypes bonded by Araldite under the same circumstances (i.e. felt as the interlayer material and loading both the flanges and the web) did not exceed a strength capacity of 174 kn (Table 22). - failed very abruptly with cracks over the whole cross-section of the H profile configuration, where the glass column bonded by Araldite showed local cracks. From this, it is assumed that the column bonded by Hercuseal is more able to distribute the peak stresses over a bigger area than the glass column bonded by Araldite, the adhesive with higher stiffness. Very important to consider is that the prototypes bonded by Hercuseal have been loaded at both the flanges and the web. The load introduction system, which transfers the loads by means of shear forces and is selected as the load introduction system for the final column (Section 6.3), however, has been loaded only in the flanges. As a consequence, to load the total cross-section, including the web, the adhesive needs to transfer the forces from the flanges into the web and vice versa. An adhesive with low stiffness has less shear strength capacity and is, therefore, probably not able to transfer the forces in the same way as the adhesive Araldite has done in Experiment II B.2 (Section 5.4.2). To avoid this uncertainty, in the final design not only the flanges, but also the web is loaded by means of shear forces Dimensions of the glass column The dimensions of the glass column have been determined by considering the strength, stiffness and stability of the column. For the first aspect, the strength, the design strength of glass has been determined initially. For the third aspect, the stability, the ratio between the expected failure load and the observed failure load has been included. The three basic structural design elements will be considered separately in the following. Finally, the obtained dimensions of the glass column are presented. Strength The design strength is obtained from a combination of the experimental results of three relevant tests that have been performed in this research: - configuration 3, the H profile, in Experiment I (Section 3.4.3) - connection fastened to the glass surface, in Experiment II B.2 (Section 5.2.3) - the glue, Hercuseal, in Experiment II A.1 (Section 5.2.2) On the basis of this data (for one metre high H profile slender glass columns) it is derived in Appendix K that the strength of glass for H profile glass columns bonded by Hercuseal and connected by steel 152

153 fasteners to the surface of the glass is equal to N/mm 2. As glass is a very brittle and sensitive material, it is chosen to include some safety by multiplying the obtained value by a safety factor of As a result, the compressive design strength is 27 N/mm 2. If more tests would have been performed, a normal distribution of the obtained results would have been made. For safety reasons, the design strength of, for example, the lowest five percent would have been selected. Due to the low number of tests, it is chosen to multiply the obtained stress value by Stiffness Since the glass column is pin-ended and located in an inner climate (i.e. no wind loads), the stiffness is not considered in the design process of the glass column. Stability By the determination of the dimensions, the same ratio between the thickness and the width of the glass plates is selected to prevent the column from other instabilities. In Experiment I and II this ratio has been 8 : 100. It is referred to Appendix L for a more detailed description of the determination of the compressive strength of glass for the final column and the structural design calculations to determine the dimensions of the glass column. The resulting dimensions of the cross-section of the glass column are illustrated in Figure 93. The thickness of the glass is slightly above the maximum deliverable thickness of 25 millimetres (Section 2.1.1). A lower thickness would be more economical. For this research project the dimensions are based on the experimental results and therefor the thickness of 28 millimetres has been selected. The height of the column will be below the available height of 4000 millimetres and will depend on the dimensions of the connection system. Figure 93 The dimensions of the final H profile glass column 6.5 Safety concept As already mentioned in some of the previous sections, safety should be considered for the design of the glass column. Since glass is a very brittle material and sensitive to impact, not only the safety of the pavilion as a whole should be considered by applying alternative load paths in the pavilion, but also the glass column itself. In the current design the glass column is monolithic. For example, if a cleaning-machine passes by and hits the glass column the structural glazing will be damaged. The protection of the glass column from lateral impacts can be provided by outer layers. The load bearing element is then sandwiched between a degree of redundancy. 153

154 According to the selected connection system, it is important that the steel connectors are bonded to the structural glazing to transfer the forces between the steel and the glass. From this, it is not possible to use a glass safety layer bonded to the total height of the structural glazing of the column. Figure 94 The safety concept for the structural glass column: a non-structural laminated glass column is placed around the structural one A solution would be, to place a non-structural column around the structural one, see Figure 94. The distance would be determined by the dimensions of the boundary connection system. Goal of this outer column is to protect the monolithic structural glass column from scratches or other lateral impact. Also, the protruding edges of the flanges become less vulnerable for impact with the outer protecting layer. The lower boundary of the outer layer should be fixed and the upper boundary should be able to allow displacement both horizontally and vertically. A non-structural aspect of the safety concept is to retain the transparency in the column. The outer layer needs to be closed to prevent the column from dirt, insects and water vapour accumulation (Section 6.4.1). Besides sealing of the non-structural column, it is recommended to apply laminated glass for the outer layer. The advantages of laminated glass compared to just single layered glass is the ability to protect one layer by another and to prevent pieces of broken glass from falling down. If the non-structural column is subjected to cracks, the glass does not fall down and the structural glass column is still protected by another layer of (single) glass. The dimensions of the laminated glass are 55.6 (two layers of glass with a thickness of each 5 mm and six layers of pvb in between with a thickness of each 0.38mm), which is based on safety glazing. 6.6 Final column design As a result from all the previously determined systems and dimensions, the final glass column is presented in this section, see Figure 95. To summarize, the design aspects that have been applied to the final structural glass column assembled from rectangular single glass plates are: - the H profile configuration of annealed float glass cut by the waterjet cutting technique; - the dimensions of the cross section of the glass, i.e. 350 millimetres wide and 28 millimetres thick per glass specimen; - the stiffness of the adhesive, to glue the glass plates together, similar to the stiffness of Hercuseal Sealer 302; - the load introduction by means of shear forces in both the flanges and the web; - the allowance of production tolerances or a difference in vertical position between the glass plates due to the assembling procedure by the air gap above and below the glass plates; - the support system at both ends of the column based on a cross connection to allow rotation along the width of the column and fix rotation along the longitudinal axis of the column; - the ability to level the column on site by the adjustment nuts in the base plate; - the safety layer around the column of the glass type 55.6 to prevent the column from impact. 154

155 Figure 95 Final design concept of the structural glass column for the pavilion 155

156 6.7 Evaluation In this chapter the preliminary design of a pavilion has been made and subsequently the lay-out of a structural glass column for the considered pavilion is presented. The pavilion serves as a context for the ten structural glass columns. The design of the columns is based on the results from the experiments performed in this research. By selecting the boundary connection concept, the crosssection and taking into account a safety concept, the optimal lay-out of the columns is created. The following key issues have been considered in the structural design of the glass column: 1. Specific aspects related to structural glass columns 2. Structural safety aspects 3. Aspects related to the boundary connection system of the column 4. Aspects related to the cross-section of the column 1. Specific aspects related to structural glass columns The design of the pavilion is based on three main aspects that are specifically of relevance for structural glass columns. - It is chosen to keep the lower floor as transparent as possible to emphasize the potential of transparency of structural glazing. - As the tensile strength of glass is much lower than the compressive strength, the design of the pavilion takes into account this weakness of glass by three structural solutions: a) Controlling the stability of the pavilion by other structural elements than the glass columns, enables to design the columns as pin-ended columns which are subjected to only normal forces. b) Designing the roof in concrete, prevents the roof from wind suction and thus the columns from tensile reaction forces. c) Locating the glass columns in an inner climate, avoids bending in the columns due to heavy wind loads. The façade consists of only one opening: a sliding door entrance. - Another advantage of locating the columns inside instead of outside the pavilion is that the influence of UV, humidity and weathering on the adhesive is avoided. 2. Structural safety aspects As observed in the experiments, glass is very sensitive to imperfections: it fails more quickly than expected. For structural applications of glass, safety is therefore very important to consider. In the preliminary design two aspects have been considered in relation to the safety of the pavilion as a whole: stability and alternative load path. - Stability It is desired, from an architectural point of view, to keep the lower floor as transparent as possible to enhance the transparency of the glass structural elements. In this way, the roof seems to float in the air. Therefore it is preferred to obtain the stability of the pavilion from a transparent element. Stabilizing the structure by means of plate action of the façade glazing is a feasible concept. However, due to the brittleness of glass extra stabilizing elements should be added to secure the stability of the pavilion also during impact. 156

157 - Alternative load path If one of the columns or a part of the structural façade fails, the load on the remaining structure increases. To prevent the pavilion from total failure, alternative load paths need to be considered for several failure cases. In this pavilion the roof is designed in composite plank floors with a concrete layer on top to be stiff enough to transfer the loads to the remaining structural elements. Solutions for alternative load paths are given. 3. Aspects related to the boundary connection system of the column From the assumption to have pin-ended glass columns in the pavilion and the experimental results a list of six requirements for the boundary connection system has been derived. These requirements were mainly focused on the development of a pin-ended column and on increasing the load bearing capacity of the total column by the design of the boundary connection system. In the phase of development of the boundary connection concept two main parts have been distinguished: the transition between the glass and the metal and the type of support. - The transition between the glass and the metal It is concluded from the experiments that the best structural performance is reached by transferring the compressive forces by means of shear forces in the glass column. Moreover, it avoids tensile stresses due to a difference in vertical position studied in the numerical analyses. In the experiment steel connectors have been glued to the glass surfaces of the flanges of the H profile. For the final column design this system is selected and not only the flanges, but also the web of the glass column is directly loaded by means of shear forces. - Type of support A support system is designed on the basis of three existing joints: the ball-and-socket joint, the traditional joint with base plate and the cross joint. The final design allows rotation along the width of the column and prevents rotation along the longitudinal axis and displacement both horizontally and vertically. As a result, the new support system increases the bearing capacity of the glass column by reducing the presence of tensile stresses as much as possible. Furthermore, it has been observed in the experiments that levelling of the column is important to increase the structural capacity of the glass column. The transition between the support system and the floor therefore contains an adjustment facility, both at the upper and lower side of the glass column. This facility contains adjustment nuts to level the column on site. 4. Aspects related to the cross-section of the column For the design of the column section two aspects have been considered: the configuration and the adhesive. Prior to the selection of the configuration of the final glass column, nine different crosssections have been compared on bearing capacity, susceptibility to impact, connectivity and some other criteria. - Configuration It is found that the H profile is the most suitable cross-section for the structural columns in the pavilion. The main qualities of this configuration were: the load bearing capacity and the connectivity of the open section. 157

158 The dimensions of the H profile have been determined on the basis of the experimental results. In the structural design the strength, stiffness and stability of the column have been considered. - Adhesive From the experiments it is concluded that the bonding material Hercuseal (i.e. a sealer with low Young s modulus) results in promising structural performances. Thereby, on the basis of this knowledge the selected adhesive to bond the rectangular single glass plates together, is Hercuseal. Additionally, it is discussed whether the quality criteria for the single glass plates could be applied to laminated glass configurations as well. In general, it is found that the structural behaviour of laminated sections will be different compared to monolithic sections due to the interlayer material. Furthermore, the design of the cross-section configuration and subdivision in laminated components causes difficulties. A design of a laminated structural glass column should focus more on these aspects. Finally, as the cross-section of the glass column is monolithic, safety is considered regarding the structural glass column itself. Impact should be avoided to serve the structural purpose of the column. An outer layer of toughened laminated glass has been developed to create a safety barrier for the column. 158

159 159

160 160

161 PART IV Retrospect and prospect 161

162 162

163 Chapter 7 Conclusions This chapter closes this research into the structural aspects of glass columns. It provides conclusions from the research presented in the preceding chapters. 163

164 7.1 Introduction This chapter provides the conclusions from the research done into the structural aspects of glass columns. Firstly, the conclusions from the experimental investigations are provided in Section 7.2. Subsequently, the conclusions from the numerical investigation are presented in Section 7.3. Finally, in Section 7.4, the conclusions derived from the structural glass column design process are evaluated. 7.2 Conclusions drawn from the experimental investigations The experimental investigations done in this research focused on the parameters that have an effect on the structural capacity of slender glass columns assembled from rectangular single glass plates. This was done by means of compression tests to investigate the main design aspects on the structural response of the one-metre-high glass columns. In Experiment I five columns with different cross-section geometries were tested to determine the main design aspects of these glass columns. Each prototype was assembled from rectangular monolithic flat glass plates 8 mm thick, 100 mm wide and 1000 mm long and loaded by increased applied displacement with felt as the interlayer material between the test bench and the glass column. An average stress value for columns assembled from four glass plates of 36.6 N/mm 2 was measured with a standard deviation of 8.3 N/mm 2. In Experiment II the main design aspects were investigated in more detail to study the effect on the load bearing capacity of the columns. The dimensions of the glass plates and the test bench were similar, but different adhesives and interlayer materials were studied. Also, in this experiment only the H profile-configuration was tested, which consisted of three glass plates. The highest ultimate stress value measured was N/mm 2 for a glass column bonded by Hercuseal and with felt as the interlayer material. The lowest ultimate stress value measured was 14.5 N/mm 2 for a glass column bonded by Araldite and cast in rubber. The following subsections provide the conclusions drawn from the experimental investigations. Design aspects From the results of the compression tests performed in Experiment I the main design aspects for these columns have been derived: - Difference in vertical position between glass plates It is concluded that a slight difference in vertical position between the assembled glass plates causes initial failure. In the compression tests four out of five prototypes showed the first crack in the displaced plate, which was first compressed. The reason for this type of imperfection could be the length deviation between the glass plates or the not very accurate assembling of the plates. - Susceptibility to peak stresses at the edges It was observed that the bottom and top edges of the glass columns are very sensitive to peak stresses. In the compression tests three out of five prototypes showed gradual crack growth from the top or bottom edge caused by local exceeding of the characteristic tensile strength of glass, which led to total failure of the column. However, this failure mode warns a few seconds before total failure occurs compared to columns that fail by displaying local buckling or torsional buckling. 164

165 - Glue stiffness The load-displacement diagrams of three out of five prototypes showed non-linear behaviour starting from an applied displacement of about 10 millimetres. The first 10 millimetres of the graph displays exponential growth, which seems to be originated from the material behaviour of the interlayer material felt. After an applied displacement of about 10 millimetres, the graph displays another type of non-linear behaviour. Since glass has linear material behaviour until brittle failure, it is assumed that the non-linear behaviour could be attributed to the redistribution of stresses by the adhesive. Considering the adhesive, it is concluded that the 2-component epoxy Araldite 2000 Plus 2013 has both good cohesion and adhesion qualities. None of the tested columns failed due to a lack of bonding qualities in the glue. However, it should be noted that only this very stiff adhesive is tested in Experiment I. Maybe a lower stiffness enables the glass columns to redistribute the stresses even more over the glass column. The influence of the stiffness of the glue is therefore studied in more detail in Experiment II. - Imperfections It was observed that most of the glass specimens were subject to imperfections (i.e. holes in the edges of the glass or scratches on the surface). However, it was not noticed that these imperfections had an impact on the structural response of the glass column. The imperfections did not cause cracks in the columns. From the results of the compression tests performed in Experiment II the influence of the glue stiffness, the polished edge treatment and the introduction of forces on the structural response of slender glass columns was studied. Glue stiffness The H profile slender glass columns assembled from single rectangular glass plates, bonded by Hercuseal Sealer 302 with a Young s modulus of 1.6 N/mm 2 and loaded over the total cross-section by an interlayer of felt consistently showed a higher load bearing capacity than the same column bonded by Araldite 2000 Plus 2013 with a Young s modulus of 2550 N/mm 2. Both of the adhesives showed good cohesion and adhesion qualities. None of the tested prototypes failed due to a lack of bonding qualities in the adhesive. Additionally, the prototypes bonded by the adhesive with lower stiffness failed very abruptly over the entire cross-section of the glass columns, where the prototypes bonded by the adhesive with higher stiffness failed due to local failure. Therefore it is assumed that the adhesive with lower stiffness is able to redistribute the stresses more uniformly over the column, which results in lower local peak stresses. As a result, the column bonded by Hercuseal and loaded by compressive forces shows the highest structural strength. Polished edge treatment The series unpolished and polished single glass plates displayed marginal differences in load bearing capacity. The average compressive stress of the tested specimens equals for both series about 10 N/mm 2. From this observation it seems that polishing the bottom and top edge of the waterjet cut glass plates does not have a significant effect on the structural capacity of the glass plates. 165

166 However, it is observed that both the polished and unpolished specimens failed due to global buckling. None of the specimens failed due to gradual crack growth from the top or bottom edge. Possibly, this would suggest that the slender single glass plates were more sensitive to Euler buckling than to peak stresses at the edges. Therefore, it is not known whether a polished edge treatment of a waterjet cut glass plate would increase the strength of the specimens or only have a marginal influence. Furthermore, the strength values obtained were 75% higher than expected. The unpolished and polished monolithic glass plates failed at an average load bearing capacity of 8.0 kn and 8.5 kn respectively, whereas the expected failure load was 4.7 kn. Possibly, the theoretical buckling length of the test-setup was lower than estimated. But that still suggests that for a structural slender single glass plate of these dimensions the Euler buckling formula results in a good estimation of the failure load of the monolithic glass plate. Finally, as the applied interlayer material between the test bench and the glass was the non-linear material felt, the load-displacement diagrams were influenced by this material. At the beginning of the graph increased stiffening was noticed. Introduction of forces A slender glass column loaded over the entire cross-section by vertical applied displacement with felt as the interlayer material performs better than a similar column with lead or aluminium (99%) substituted for felt. The two metals very quickly resulted in gradual crack growth from the edges, where the felt resulted in local buckling. This would suggest that felt, the softest material, compared to the metals is more able to distribute the stresses over the glass. Another load introduction system that was tested transfers the compressive forces by means of shear forces in the flanges of the H profile glass column. This system showed the highest structural capacity compared to all the other load introduction systems that were tested in this research. It was concluded that the concept of transferring the forces in the glass surface by avoiding the edges of the glass plates shows promising results. Moreover, this system takes into account any differences in the vertical position between the glass plates of a column and avoids contact with the edges of the glass. In this way the peak stresses at the edges were reduced and the bearing capacity of the total column increased. It was observed that Araldite 2000 Plus 2013 has good adhesive qualities to bond the steel with the glass in this load introduction system and cohesive qualities to transfer the shear forces for the tested prototypes. Furthermore, a glass column cast in polyurethane rubber was tested. Compared to the previously described columns this system has very low strength capacity. It is not known whether the interlayer material rubber was not suitable or the execution was not accurate enough, but several cracks developed very quickly in the glass from the boundary connection systems at the edges. Overall conclusions from the experimental investigations To summarize, it is concluded from the experiments that different design aspects play an important role in the structural response of slender glass columns assembled from rectangular single glass plates. Avoiding any contact with the edges and the chance of uneven loading due to a difference in the vertical position between the glass plates results in a higher structural capacity in the glass columns. Also, an adhesive with low stiffness is able to distribute the stresses more uniformly over the glass column than an adhesive with high stiffness. In addition, levelling the column and 166

167 preventing the support from rotating along the longitudinal axis showed that there was increased structural capacity and so that it should be considered as well in the design process of a glass column. However, compared to the strength expectations, analytically determined by considering Euler buckling, torsional buckling and pure compression, it was concluded that none of the prototypes have reached these strength values. Only the slender single glass plates failed by Euler buckling at almost the expected strength value. This would suggest that glass is a very sensitive material. Therefore it is essential to take into account some safety aspects by designing a structural glass column. 167

168 7.3 Conclusions drawn from the numerical investigations The investigations on a two-dimensional numerical model done in this research focused on two of the design aspects that were considered in Experiment I: a vertical difference in position between glass plates and the stiffness of the glue. The first parameter is modelled by changing the material properties of the felt below or above the protruding glass plate(s). Increased stiffness of the felt simulates that the protruding glass plates are already higher loaded than the non-protruding glass plates. The second parameter is studied by comparing an adhesive with very high Young s modulus (i.e N/mm 2 ) and an adhesive with very low Young s modulus (i.e. 1.6 N/mm 2 ). The following subsections provide the conclusions from the numerical investigations. A difference in vertical position between glass plates From the imperfection analysis it is concluded that the tensile stresses occurring in the glass are due to a difference in vertical position between the glass plates. In a perfect column these stresses are almost equal to zero. A difference in the vertical position between the glass plates of 2.0 millimetres in combination with an applied displacement of 20 millimetres, on the other hand, almost results in the characteristic tensile strength of glass (i.e. 8 MPa). Additionally, it is concluded that the location of the tensile peak stresses in the numerical model due to a difference in the vertical position between glass plates coincides with the origin of the initial crack in the tested H profile column in Experiment I. Due to the protruding edge, the glass column is loaded unevenly. As a result, shear stresses develop between the protruding flange and the web, which results in tensile stresses arising at the bottom edge of the web. Stiffness of the glue From the stiffness analysis it is concluded that the adhesive with reduced stiffness results in lower stresses. This applies especially to the tensile stress, which is the most critical one for the loadbearing capacity of a glass column. Furthermore, it can be concluded that the adhesive with low stiffness results in a more even distribution of the stresses over the column, which greatly reduces the tensile (peak) stresses in the column. Due to the lower shear modulus value of the adhesive, the distance to transfer the forces from the protruding edge into the web was increased. Overall conclusions from the numerical modelling The results from the numerical analysis show similarities to the experimental results: - the stresses are in the same order of magnitude, which suggests that the Young s modulus of glass is equal to MPa - the location of the tensile peak stresses coincides with the location of the initial crack in the H profile in Experiment I - the development of the stresses over the glass column for the different adhesives in the numerical model coincides with the observed failure modes: local failure of the adhesive with high Young s modulus and global failure for the adhesive with low Young s modulus. 168

169 7.4 Conclusions drawn from the design process of a structural glass column The structural design of the glass column is based on the practical experience and knowledge gained from the experimental and numerical investigations done in this research. In other words, the results of the fundamental study done into slender glass columns assembled from rectangular single glass plates under compression have served as a basis for the design of a structural glass column for a pavilion. In the design process a preliminary design of the pavilion was made to create a context for the glass columns. After that, on the basis of the pavilion requirements the structural glass column was then designed. Herein, three main topics can be distinguished: the boundary connection system, the cross-section and a safety concept. The following subsections include the key issues that followed from the design process. Preliminary design pavilion Three main aspects that are specifically of relevance for bonded structural glass columns were considered in the design concept of the pavilion: transparency, low resistance to tensile stresses and durability of the adhesive. And, more importantly, the brittle material behaviour phase of glass should be avoided by building enough safety into the structural design. - The potential transparency of structural glazing is emphasized by keeping the lower floor as transparent as possible. In this way it seems as if the concrete roof is floating in the air. - To reduce the tensile stresses in the column as much as possible, it is assumed, in the preliminary design phase, that the stability of the pavilion is realized by elements other than the glass columns. The columns are also located in an inner climate to avoid any tensile stresses due to bending caused by wind load. Furthermore, the roof is designed in concrete to prevent it from having to endure wind suction and thus the columns from tensile stresses. - Locating the glass columns in an inner climate instead of outside has another very important advantage. The influence of moisture and UV on the adhesive will be avoided. As a result, the adhesive has a longer life time. To secure the structural capacity of the pavilion and prevent the columns from having to endure unexpected increased stresses, the stabilizing capacity of the façade glazing was studied in this research under normal circumstances. In case of failure, the structural façade has some residual capacity. However, as glass is a very brittle and sensitive material much more safety is recommended for this pavilion, from which its structure is totally dependent on structural glazing. Stabilizing elements that should be considered are: - a core - a stabilizing wall - glass fins - the application of more structural glass columns to create an overcapacity (i.e. in this case more than ten) - wind bracings in the façade - a combination of these stabilizing elements. To retain the transparency throughout the pavilion the third and the fourth option (i.e. glass fins and more glass columns) were preferred in this research project. It should be investigated whether these stabilizing elements are sufficient to ensure the safety of the pavilion. 169

170 Boundary connection system The boundary connection system was split into a concept for the transition between the glass and the metal and a concept for the support system. - In the experiments it was found that the transition between the glass and the metal has an important influence on the structural response of the column. The best structural performance was achieved by transferring the compressive forces by means of shear forces in the flanges of the glass column. Therefore it was this concept that was selected for the final column. The only difference is that the final column will be loaded by means of shear forces in both the flanges and the web to introduce the forces more evenly over the column. - The support system for the final glass column was designed on the basis of different existing systems (i.e. the ball-and-socket joint, the tradition joint and the cross joint). As a result, the final design not only prevents movement both horizontally and vertically, but also rotation along the longitudinal axis. Furthermore, it allows rotation along the width of the column. To conclude, the boundary connection concept enhances the structural capacity of the glass columns in the pavilion as much as possible by reducing the presence of tensile stresses. Cross-section For the design of the column section two aspects have been considered: the configuration and the adhesive. - On the basis of a comparison between the qualities of nine different monolithic crosssections, the configuration of the final glass column was selected. Taking into account the selected boundary connection concept, the bearing qualities and aesthetics, it was the H profile that was selected. - The selected bonding material was Hercuseal (or another adhesive with low stiffness properties). From the experimental results it emerged that the columns bonded by this adhesive compared to similar columns bonded by an adhesive with higher stiffness, reached the highest load-bearing capacity. In addition, the quality differences between single and laminated glass cross-sections were discussed. It followed that the interlayer of a laminated section influences the buckling behaviour of the plates by its specific stiffness properties. Moreover, the structural behaviour of the interlayer is dependent on the temperature and the load duration. Furthermore, dividing the section into separate laminated elements gives rise to complications: - The continuation of the structural layer results, with some configurations, in difficult components. These components do not allow any tolerance, otherwise asymmetrical sections or non-straight angles will be the result. - A glued connection system needs to be connected to the structural glass layer of a crosssection. As laminated glass is surrounded by an outer non-structural layer, this connection system gives rise to some complications. One solution would be to leave the lamination at the edges. However, this gives again more complicated laminated components. The dimensions of the cross-section of the glass column have been determined by considering the strength, stiffness and stability of the column. The design strength of the glass was derived from the stresses in the experimental results. The buckling strength was reduced by a safety factor to include the difference between the expected failure load and the observed failure loads and the uncertainty of the results as only a few tests were performed. 170

171 Safety As the cross-section of the glass column is monolithic, safety was considered regarding the structural glass column itself. Impact should be avoided to protect the structural aspect of the column. An outer layer of toughened laminated glass has been developed to create a safety barrier for the column. Final column design To summarize, the results of the fundamental study of slender glass columns assembled from rectangular single glass plates under compression served as a basis in the design of the structural glass column that will be applied to all ten columns in the pavilion. The main aspects in the design of the structural glass column in this research were: - the concept of the transition of forces between glass and metal by means of shear forces in the boundary connection system - production tolerances or a difference in vertical position between the glass plates due to the assembling procedure - the desired stiffness of the bonding material for the glass plates - the design strength of the glass in the final column design and the ratio between the expected failure load and the observed failure load by considering the stability of the column - the selected H profile configuration of annealed float glass cut by the waterjet cutting technique - the support system based on a cross connection to allow rotation along the width of the column and fix rotation along the longitudinal axis of the column - the ability to level the column on site by the adjustment nuts in the base plate - the concept of safety to prevent the column from impact by an extra layer of safety glazing around the column 171

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173 Chapter 8 Recommendations This final chapter closes this research on the structural aspects of glass columns and provides recommendations for further research. 173

174 8.1 Introduction From this research various recommendations for further studies follow. Section 8.2 provides recommendations into various aspects considered in the experiments. Then, Section 8.3 describes recommendations for further development of the numerical model. After that, Section 8.4 takes notice of recommendations for further improvement of the final glass column design. Finally, Section 8.5 provides recommendations for alternative glass column concepts. 8.2 Experimental analysis During the experiments it is found that further studies into some different aspects are recommended: the glue stiffness, the polished edge treatment, the introduction of forces and some others. In the following these are presented separately. Glue stiffness It is recommended to investigate the structural response of glass columns bonded by an adhesive with low stiffness on aspects like load duration, temperature and humidity. Although it seems that Hercuseal is a good solution for the bonding of glass plates in a structural column, considering the strength capacity and the price of the column, it should be noted that the tests performed in this research did not take into account all of it. Polished edge treatment It is recommended to further investigate the influence of polished edges on the load bearing capacity of glass plates and glass columns. The exploratory investigation into this topic has demonstrated that the strength of a single glass plate under compression is promising. The glass plates showed, compared to the assembled glass columns, to have a load bearing capacity similar to the related Euler buckling strength. However, due to the unexpected strength capacity of a single glass plate in combination with failure due to buckling, the influence of the edge treatment is not accurately investigated in this research. Studies that are recommended to investigate this aspect in more detail are compression tests with an H profile, from which the dimensions make that it is not vulnerable for buckling, with: - polished top and bottom edge - all the edges of the different plates polished. Introduction of forces The current research has revealed that the introduction of compressive forces in the glass column by means of shear forces increases the load bearing capacity of the glass column compared to the other load introduction systems. During the tests only the flanges of the columns were subjected to the introduction of the forces. Thereby, it is recommended to investigate the structural behaviour of a glass column subjected to the introduction of forces by means of shear forces over the entire cross section, i.e. both the flanges and the web, by a numerical analysis. Others Finally, it is recommended to perform tests on the long term behaviour of the glass and the bonding material. Also, an increase in the number of tests is recommended to obtain more accurate statistics about the design strength of glass. 174

175 8.3 Numerical model It is recommended to further develop the numerical model that has been investigated in this research. The model considered in this study is a two-dimensional numerical model. By extending the model to a three-dimensional model, also the stress development in the third direction can be investigated. 8.4 Final glass column design Considering the design of the glass column and the pavilion, there are three recommendations for further development. - It is recommended to optimize the stiffness of the adhesive for each specific application by a numerical analysis. The final glass column has a height of about four metres and is subjected to higher compressive forces than the columns that have been tested in this research. An optimization into the requirements of the Young s modulus of the adhesive for this application is recommended. - It is recommended to perform full-scale tests to study the structural performance of the boundary connection concept and the total glass column. In addition, it should be verified whether the load bearing capacity of the column is in consistence with the predictions in this research. - The structural glass column consists of 28 millimetres thick glass plates on the basis of the experimental results. As the maximum deliverable thickness is 25 millimetres, it is recommended to optimize the design dimensions by investigating the influence of other ratios between the thickness and the width of the individual glass plates on the structural response of the glass column. - In the currently developed pavilion the stabilizing capacity of the glass façade is sufficient when the pavilion is not subjected to impact or failure of part of the structure. The façade has some residual capacity. However, it is recommended to investigate some different scenarios and check which stabilizing elements need to be added. This will provide more insight in the safety performance of the pavilion. Additionally, the consequences of fire on the structural capacity of the glass columns is not considered in this research as it is a very broad topic. In the design of structural applications it is essential to take into account the consequences of fire. Therefore, it is recommended for further studies to investigate this topic by performing tests and considering different scenarios. 8.5 Others This research has focussed on slender glass columns assembled from rectangular monolithic glass plates. For further studies it is recommended to study glass columns designed in laminated glass, toughened glass and other configurations. Laminated glass columns will have different structural behaviour compared to single glass columns due to the interlayer material. A similar research but then focussed on laminated glass will provide more insight in the advantages and disadvantages of laminating. 175

176 Toughened glass consists of pre-stressed glass elements. In the production process first the elements need to be cut and then the elements are heated and cooled again. This study will provide more insight in the consequences of toughening. Finally, as an alternative to the slender glass columns assembled from rectangular monolithic glass plates, it is recommended to investigate the structural response of other design concepts like: a bundle of massive glass bars that is glued together, cylinders and rectangular glass plates glued together to a massive laminated block. 176

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179 Bibliography ALSOP, D.J.A. 1999, et al. Structural use of glass in buildings. London: SETO. ARMISOFT -. Autotechniek 18 May 2011, BAGGER, A., PETERSEN R.I Structural use of glass: Cruciform columns and glass portals with bolted connections subjected to bending. Proceedings Glass Performance Days. Tampere: GPD, pp BEHLING, S., BEHLING, S., ACHENBACH, J Glass - Konstruktion und Technologie in der Architektur, Structure and Technology in Architecture. Műnchen: Prestel. BELIS, J., IMPE, R. VAN, MEESTER, B. DE, LAGAE, G., KATNAM, K.B. Stability approach of the dimensioning of glass beams. 1 March 2011, BLAAUWENDRAAD, J Buckling of laminated glass columns. Heron, pp BOS, F.P Towards a combined probabilistic/consequence-based safety approach of structural glass members. Heron, pp DELTA GLASS Production 12 December 2010, DERKINK, M.F.A., et al Cursus constructieve toepassingen met glas. Delft: Stichting Postacademisch Onderwijs. ESDEP Lecture 6.6.2: Buckling of real structural. ESDEP Course. 22 March 2011, FORABOSCHI, P Compression use of structural glass and glass structures. Proceedings Glass Performance Days. Tampere: GPD, pp GAMBHIR, M.L Stability analysis and design of structures. Berlin: Springer. GLASS AGC. Stratobel. 23 November 2010, GRAAF, A.V. van de, HENDRIKS, M.A.N., ROTS, J.G Sequentially linear analysis as an alternative to nonlinear analysis applied to a reinforced glass beam. 7 th fib PhD Symposium, Stuttgart. HALDIMANN, M Fracture strength of structural glass elements analytical and numerical modeling, testing and design. Lausanne: École Polytechnique Fédérale de Lausanne. HALDIMANN, M., LUIBLE, A., OVEREND, M Structural use of glass. Zűrich: International Association for Bridge and Structural Engineering HARTSUIJKER, C Toegepaste Mechanica deel 2 spanningen, vervormingen, verplaatsingen. Schoonhoven: Academic Service. HARTSUIJKER, C., WELLEMAN, H Toegepaste Mechanica deel 3 statisch onbepaalde constructies en bezwijkanalyse. Amersfoort: Drukkerij Wilco. HARTSUIJKER, C., WELLEMAN, H Mechanics of Structures Module: introduction to continuum mechanics. Delft: TU Delft HIBBELER, R.C Sterkteleer. Amsterdam: Pearson Education. HUNTSMAN COOPERATION Adhesive selector guide Araldite HUVENERS, E.M.P Circumferentially adhesive bonded glass panes for bracing steel frames in façades. Eindhoven: University Press Facilities. 179

180 JONG, H. de Staalconstructies II. Delft: TU Delft. KERINGHUIS. -. Het keringhuis - Constructie. 24 May KLEINMAN, C.S., BRAAM, C.R., DEES, W.C., van GEEST, F.P.J., KŐHNE, J.H., LAGENDIJK, P Glazen kubus voor showroom. Cement Glasconstructies. pp KRUYS, R.A.A Het gedrag van glas onder brandcondities. Delft: Stichting Postacademisch Onderwijs. pp. GL 6. LEHMAN, L.R., STEVENS, H Fundamentals of glass technology. The Hague: Center for Professional Advancement. LEUNG, C Reinforcing Glass with Glass. Delft: TU Delft. LOUGHRAN, P Falling glass problems and solutions in contemporary architecture. Basel: Birkhäuser. LOUTER, C Fragile yet Ductile Structural Aspects of Reinforced Glass Beams. Zutphen: Wöhrmann Print Service. LUIBLE, A Stabilität von Tragelementen aus Glas. Lausanne: École Polytechnique Fédérale de Lausanne LUIBLE, A., CRISINEL, M Buckling design of glass elements under compression. Proceedings International Symposium on the Application of Architectural Glass. Műnich MOCIBOB, D Linear connection system for structural application of glass panels in fullytransparent pavilions. Proceedings Challenging Glass. Delft, pp NIEUWENHUIJZEN, E.J., VEER, F.A., BOS, F.P The Laminated Glass Column. Proceedings Glass Processing Days. Tampere: GPD. NIJSSE, R Onderweg naar morgen. Cursus constructieve toepassingen met glas. Delft: Stichting Postacademisch Onderwijs. pp. GL 4. NIJSSE, R., et al Construeren met glas stand der techniek. Gouda: CUR Bouw & Infra/Kenniscentrum Glas. NIJSSE, R Glass in structures. Basel: Birkhäuser. NIPIUS, F Knikkracht (van Euler). Infrawiki. 22 March =view&id=749. OVERBEEK, K., KOSSE, M Lijmen. Enschede: Saxion Kenniscentrum Design en Technologie. PFÄNDER, H.G. (revisioned by H. Schroeder) Schott guide to glass (original title: Schott Glaslexikon, 1980). Berkshire: Van Nostrand Reinhold Company. PFLÜGER, A Stabilitätsprobleme der Elastostatik. Berlin: Springer. PILKINGTON Het floatproces. 14 October REES, D.W.A Mechanics of optimal structural design. Chichester: John Wiley & Sons. RENCKENS, J Gevels en architectuur. Rotterdam: Veenman Drukkers. ROEBROEK, F.J.A Design of a transparent column in glass and steel. Eindhoven: TU Eindhoven. SCHIPHOLT, R.L., BOONSTRA, J.M., LEEN, J.H.M., de MAN, G., ROLLOOS, A., SPIL, B.C.A., VOS, A.J.M Overspannend staal Construeren A. Rotterdam: Bouwen met Staal. Vol. 2. SCHITTICH, C., STAIB, G., BALKOW, D., SCHULER, M., SOBEK, W Glass Construction manual. Basel: Birkhäuser. 180

181 SHELBY, J.E Introduction to glass science and technology. Cambridge: Royal Society of Chemistry. SIMONIS, F Van veilig construeren in glas tot veiligheidsglas. Delft: Stichting Postacademisch Onderwijs. pp. GL 3. TIMOSHENKO, S Theory of elastic stability. New York: McGraw-Hill Book Company. Vol.2. TNO DIANA DIANA User s manual. Delft: TNO DIANA. Release 9.3. USINOUVELLE Cutting machines. 17 March VEER, F.A The strength of glass, a nontransparent value. Heron. pp VEER, F.A., BOKEL, R.M.J., TUISINGA, L Fire resistance of glass. Proceedings Glass Performance Days. Tampere: GPD, pp VEER, F.A., VOORDEN, M. VAN DER, RIJGERSBERG, H., ZUIDEMA, J Using transparent intumescent coatings to increase the fire resistance of glass and glass laminates. Proceedings Glass Processing Days. Tampere: GPD, pp VEER, F.A., NÄGELE, T., JANSSEN, M.J.H.C The possibilities of glass bond adhesives. Tampere: GPD. VEER, F.A., PASTUNINK, J.R Developing a transparent tubular laminated column. Proceedings Glass Processing Days. Tampere: GPD, pp VEER, F.A., ZUIDEMA, J The strenght of glass, effect of edge quality. Proceedings Glass Processing Days. Tampere: GPD, pp VRENKEN, J De invloed van de E-modulus op de sterkte van gelijmde overlapverbindingen. Alphen aan de Rijn: Mybusinessmedia. Vol.6. WELLER, B., SCHNEIDER, J., REICH, ST., EBERT, J. Kontaktmaterialien zur Einleitung von Druckkräften in Glas. Bauingenieur pp WELLERSHOFF, F., SEDLACEK, G Glass Pavilion Rheinback Stability of Glass Columns. Proceedings Glass Processing Days. Tampere: GPD, pp

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183 Appendices 183

184 Appendix A Internal stresses In this appendix the consequences of a difference in air pressure between the inside of a hermetically sealed column and the outside is calculated. The ideal gas law, also known as the law of Boyle and Gay-Lussac, is: Since the molar volume equals the volume divided by the amount of gas in mol, the equation for the pressure can be rewritten into: / J K mol To find a realistic value for the difference in pressure between the inside and the outside of the column, two different temperatures for the inside of the column are expressed in inner pressure: / / In the Netherlands the average value of the pressure is:, / (NEN 2608:2009) Although this value varies for different temperatures and weather situations, it is assumed that this results in a representative value for the difference in pressure between the outside and the inside of the glass column of: p / The height of this column is 1 metre, which results in a distributed load of 5 kn/m. 184

185 Column section 0.1 metre by 0.1 metre Structural modelling Nm 1 6 b h m / Compared to the ultimate bending strength of glass in Table 6, this would not be a problem. By using the ultimate bending strength of glass, the maximum allowable difference in temperature will be defined. The ultimate bending strength of glass for annealed glass under long term loading is: 17.3 / 2 With this value, the maximum allowable moment in the glass plate considered above becomes: This coincides with a distributed load of: Since the height of the structure is 1 metre, the maximum allowable pressure equals: 231 According to the law of Boyle and Gay-Lussac the maximum allowable difference in temperature can be: From this, it can be concluded that the internal bending stress in the glass caused by a difference in temperature between the inside of a closed section and the outside will not be an issue for this structure. However, a validation for each structure would be advised. If the dimensions were 185

186 different, for example the height is 4 metres, the width is 0.8 metres and the thickness is 0.04 metres, the maximum allowable difference in temperature would be: b h b h It shows that an increase in width, when at the same time the length and height do not change, reduces the maximum allowable difference in temperature drastically. The outcome of the fracture is therefore very important by designing a column with a closed section. 186

187 187

188 Appendix B Principal directions Principal directions are the axes that need to be used to find the minimum and maximum value of the second moment of area. In some cases the original axes of a cross-section coincide with these principal directions, but in other cases they do not. In case of reflection symmetry, the principal directions coincide with the original axes. But for point symmetry and rotation symmetry it is not that obvious. With the formulas in this appendix the principal directions with their extreme values for the second moment area can be obtained. Most of this information is gathered from the book Mechanics of Structures (Hartsuijker, 2005). Transformation rules to calculate the components of a tensor due to a certain rotation α of the coordinate system: = cos sin cos sin cos sin (1) = sin cos cos sin sin cos = sin cos sin cos sin cos = sin sin cos sin cos cos These transformation rules can be simplified with the double-angle goniometric relations: 2 cos 1 cos 2 (2) 2sin 1 cos 2 2sin cos sin2 Into: cos 2 sin cos 2 sin sin2 cos 2 (3) The extreme values of the tensor can be obtained directly with:, 1 2 1/2 (4) These values occur for an optimum angle of: 2 1/2 (5) In a graphical way these values can be obtained by Mohr s Circle. Coordination Mohr s circle [179] 188

189 189

190 Appendix C Measurements test specimens experiment I The nominal dimensions of the glass plates were 8 mm thick, 100 mm wide and 1000 mm long. The accuracy of the measuring device was 0.05 mm. The thickness is measured about 20 mm from the edge. specimen thickness [mm] t1 t2 t3 t4 t5 t6 t7 t8 tav 1 7,80 8,10 7,95 7,90 8,05 8,00 8,05 8,10 7,99 2 8,00 7,85 7,90 8,00 8,05 8,05 8,00 7,95 7,98 3 7,90 7,85 8,10 8,00 8,00 8,00 8,10 8,00 7,99 4 8,10 7,85 7,90 7,90 8,05 7,90 8,00 8,00 7,96 5 7,85 8,10 8,00 7,90 7,95 8,05 8,00 7,90 7,97 6 8,05 8,00 7,95 8,05 7,85 8,20 7,85 7,95 7,99 7 8,00 7,90 7,85 7,90 7,90 8,20 7,90 7,85 7,94 8 7,85 7,90 7,85 7,80 8,00 8,00 7,90 7,85 7,89 9 7,90 8,00 7,85 7,95 7,90 8,00 8,00 7,90 7, ,05 7,85 7,85 7,90 7,90 8,05 8,00 7,80 7, ,95 8,10 7,90 7,85 7,85 7,95 7,80 7,80 7, ,80 7,90 7,85 7,90 7,95 8,05 7,90 7,85 7, ,85 7,85 7,85 7,80 7,80 7,95 7,85 7,85 7, ,85 7,80 7,80 7,80 7,85 7,90 7,85 7,90 7, ,90 8,05 7,90 7,90 7,85 7,95 7,95 7,90 7, ,90 8,00 7,90 7,80 7,90 7,90 7,90 7,90 7, ,10 8,10 7,90 7,90 8,00 7,95 8,20 7,85 8, ,90 7,90 8,00 7,95 7,90 8,00 7,95 7,90 7, ,85 8,10 7,90 7,90 7,95 7,95 7,95 8,05 7,96 7,94 As a result from the measurements, it is found that there are some deviations in the different glass specimens. On average, the thickness of the panels was 0,75% lower than the nominal thickness of 8 mm. The largest value measured was 8.20 mm, whereas the smallest value measured was 7.80 mm. These deviations in the thickness are in accordance with the tolerances considered in NEN-EN (Table 1). The length of all the specimens was 999 mm. The accuracy of the measuring device for measuring the length was 1 mm. The width of the specimens is measured with the same accuracy as the thickness: 0.05 mm. The width is measured at three locations: once in the middle and twice at the edges. At the ends of the glass plates the width is measured about 20 mm from the edge. Since the edges were cut by waterjet, the width is measured at the top and lower side of the glass plate. In total, this gives 6 measurements for the width. 190

191 specimen width upper side [mm] width lower side [mm] w1u w2u w3u wuav w1l w2l w3l wlav 1 100,60 100,70 100,60 100,63 100,25 100,35 100,30 100, ,65 99,50 99,55 99,57 99,30 99,30 99,35 99, ,50 100,60 100,60 100,57 100,20 100,40 100,50 100, ,50 100,45 100,50 100,48 100,30 100,25 100,20 100, ,60 100,50 100,50 100,53 100,40 100,40 100,40 100, ,50 100,60 100,50 100,53 100,35 100,45 100,45 100, ,60 100,60 100,75 100,65 100,15 100,25 100,30 100, ,70 100,65 100,60 100,65 100,25 100,35 100,50 100, ,55 99,50 99,50 99,52 99,40 99,30 99,20 99, ,65 100,60 100,50 100,58 100,25 100,00 100,20 100, ,50 100,65 100,50 100,55 100,40 100,50 100,00 100, ,50 100,50 100,30 100,10 99,20 99,65 99,20 99, ,45 99,55 99,50 99,50 99,05 99,10 98,90 99, ,50 100,45 100,50 100,48 100,05 99,80 99,70 99, ,60 100,60 100,60 100,60 100,35 100,20 100,25 100, ,50 100,55 100,60 100,55 100,15 100,10 100,10 100, ,65 100,60 100,60 100,62 100,15 100,30 100,20 100, ,55 100,50 100,70 100,58 100,25 100,20 100,45 100, ,45 100,60 100,55 100,53 100,25 100,20 99,90 100,12 100,38 100,03 The average width at the upper side was 0.38% bigger than the nominal width, whereas the average width at the lower side was only 0,03% bigger than the nominal width. The lower side is on average 0.35 mm smaller than the upper side of the glass plates. This is caused by the cutting technique. The biggest value measured for the width was mm and the smallest value mm. The angles were found to be right angles. This is measured with a small steel element consisting of an angle of 90 degrees. The accuracy of this measurement tool was very rough. 191

192 Appendix D Expectation experiment I The expectations of experiment I are split up in two parts. The first one is an analysis of the glass columns on imperfections in vertical position, glue line and glass edges. The second part is more theoretical and is covered in this appendix. The strength of the column is analytically determined on the basis of a few formulas. Euler buckling, torsional buckling and compression will be described successively. In all these calculations no imperfections, like glass edge imperfections or out-of-straightness, will be taken into account. In this way, the strength values are maxima. Euler buckling The Euler buckling strength is calculated for both I yy and I zz in the following table. configuration I yy (mm 4 ) N euler (N) (kn) 1 Square , ,8 3690,5 2 Double web , ,0 1674,3 3 H profile , ,8 924,1 4 Star , ,9 2605,6 5 Plus , ,4 4150,4 configuration I zz (mm 4 ) N euler (N) (kn) 1 Square , ,8 3690,5 2 Double web , ,4 4150,4 3 H profile , ,8 3689,8 4 Star , ,9 2605,6 5 Plus , ,8 3690,5 Torsional buckling, I I I 2 1 I 1 3 ht open sections I 4 O s t closed sections 192

193 The parameters in the torsional buckling strength formula, or the related ones, are listed in the next two tables. Each cross-section has a different warping constant. The warping constant for the starshaped cross-section was hard to determine. Since it was found that the second part of the summation, between the brackets, is almost negligible, this warping constant is given the value of one. The buckling length is considered to be equal to the system length, while the boundary conditions are a hinge and a hinge/role. A figure with the buckling lengths for different boundary conditions is given in Figure 22. configuration Young s modulus Poisson value G I yy (mm 4 ) I zz (mm 4 ) 1 Square , Double web , H profile , Star , Plus , I p (mm 4 ) l w (mm 4 ) C w (mm 6 ) l buc A N θ,buc (kn) , , , , ,5 Compression The compression stress of glass is very hard to determine, while it is a value dependent on several criteria (Section 2.1.3). To get more an idea of the compressive strength of the glass columns the compressive stress is considered to be 900 N/mm 2, which results in the following failure loads due to compression only. configuration area (mm 2 ) sigma compression (N/mm 2 ) N c (N) N c (kn) 1 Square Double web H profile Star Plus

194 Appendix E Felt stiffness Felt is one of the materials that has been adopted in the numerical model. As the non-linear material behaviour of the applied felt in Experiment I is unknown, it is derived from the experimental results (Figure 34). Since the first 10 millimetres of applied displacement for these graphs show a similar increase in stiffness, it is assumed that these displacement values with the corresponding stress values have been influenced by the material behaviour of the felt. This data is listed in the following tables. displacement [mm] displacement [mm] double web F [kn] square F [kn] h profile F [kn] star F [kn] cross F [kn] double web σ [N/mm 2 ] square σ [N/mm 2 ] H profile σ [N/mm 2 ] star σ [N/mm 2 ] cross σ [N/mm 2 ] average σ [N/mm 2 ]

195 The obtained experimental results consist of the material behaviour of both the two layers of felt and the glass. The non-linear material behaviour of the felt has been derived by applying the equivalent felt constant formula for a system that is in series The stiffness of the glass has been determined on the basis of Hooke s law and the Young s modulus, which is equal to N/mm / 1000 The derived stress and displacement values are listed in the following table. Also, the material behaviour of the compressed felt has been added for 0.5, 1.0, 1.5 and 2.0 mm vertical imperfection. sigma difference in vertical position / compressed thickness felt [mm] [N/mm 2 ]

196 Appendix F Model files and command files DIANA Parameter I: Difference in vertical position between glass plates Model file 0 mm displacement, adhesive Araldite 2000 plus 2013 'DIRECTIONS' E E E E E E E E E+000 'COORDINATES' E E E E E E+000 [..] E E E E E E+000 'MATERI' 1 NAME GLASS YOUNG E+004 POISON E-001 DENSIT E NAME ARALDITE_GLUE DSTIF E E NAME FELT_WEB DSTIF E E-002 SIGDIS E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E NAME STEEL YOUNG E+006 POISON E-001 DENSIT E NAME FELT_WEB_COMPRESSED DSTIF E E-002 SIGDIS E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E NAME FELT_FLANGE 196

197 DSTIF E E-002 SIGDIS E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E NAME FELT_FLANGE_COMPRESSED DSTIF E E-002 SIGDIS E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+000 'GEOMET' 1 NAME ARALDITE_GLUE THICK E+000 CONFIG MEMBRA ZAXIS E E E NAME FELT_COMPRESSED_FLANGE THICK E+002 CONFIG MEMBRA ZAXIS E E E NAME FELT_FLANGE THICK E+002 CONFIG MEMBRA ZAXIS E E E NAME FELT_COMPRESSED_WEB THICK E+000 CONFIG MEMBRA ZAXIS E E E NAME FELT_WEB THICK E+000 CONFIG MEMBRA ZAXIS E E E NAME GLASS_FLANGE THICK E NAME STEEL THICK E NAME GLASS_WEB THICK E+000 'DATA' 1 NAME GLASS_FLANGE 197

198 198 'ELEMENTS' CONNECT 1876 L8IF L8IF [..] 4142 L8IF L8IF Q8MEM Q8MEM [..] 4068 Q8MEM Q8MEM MATERI / / 1 / / 2 / / 3 / / 4 / / 5 / / 6 / / 7 DATA / / 1 GEOMET / / 1 / / 2 / / 3 / / 4 / / 5 / / 6 / / 7 / / 8 'LOADS' CASE 1 DEFORM 2398 TR E+001 DEFORM 2447 TR E+001 DEFORM 2389 TR E+001 DEFORM 2390 TR E+001 DEFORM 2394 TR E+001 DEFORM 2435 TR E+001 DEFORM 2436 TR E+001 DEFORM 2437 TR E+001 DEFORM 2438 TR E+001

199 DEFORM 2439 TR E+001 DEFORM 2440 TR E+001 DEFORM 2441 TR E+001 DEFORM 2442 TR E+001 DEFORM 2443 TR E+001 DEFORM 2444 TR E+001 DEFORM 2445 TR E+001 DEFORM 2446 TR E+001 DEFORM 2454 TR E+001 'GROUPS' ELEMEN 3 MAP-MESH(2D) / / 5 MAP-MESH(2D)-1 / / 9 MAP-MESH(2D)-3 / / 11 MAP-MESH(2D)-4 / / 13 MAP-MESH(2D)-5 / / 37 MAP-MESH(2D)-7 / / 39 MAP-MESH(2D)-11 / / 41 MAP-MESH(2D)-17 / / 43 MAP-MESH(2D)-18 / / 45 MAP-MESH(2D)-19 / / 49 MAP-MESH(2D)-9 / / 51 MAP-MESH(2D)-10 / / 53 MAP-MESH(2D)-12 / / 55 MAP-MESH(2D)-13 / / 57 MAP-MESH(2D)-21 / / 69 MAP-MESH(2D)-2 / / 83 MAP-MESH(2D) MAP-MESH(2D) MAP-MESH(2D) MAP-MESH(2D) MAP-MESH(2D)-15 / / 96 MAP-MESH(2D)-20 / / 'SUPPOR' / (4) / TR 1 / (4) / TR 2 / (4) / TR 3 'UNITS' FORCE N LENGTH MM 199

200 MASS E+003 'END' Command file *FILOS INITIA *NONLIN EXECUT LOAD STEPS EXPLIC SIZES 0.05(20) BEGIN OUTPUT FXPLUS FILE " _GlasscolumnGlueFeltSteel" DISPLA TOTAL TRANSL GLOBAL FORCE REACTI TRANSL GLOBAL STRAIN TOTAL GREEN STRAIN TOTAL TRACTI LOCAL STRESS TOTAL CAUCHY STRESS TOTAL TRACTI LOCAL END OUTPUT *END Parameter II: Stiffness of the glue Model file 1.0 mm displacement, adhesive with low stiffness 'DIRECTIONS' E E E E E E E E E+000 'COORDINATES' E E E E E E+000 [..] E E E E E E+000 'MATERI' 1 NAME GLASS YOUNG E+004 POISON E-001 DENSIT E NAME HERCUSEAL_GLUE DSTIF E E NAME FELT_WEB DSTIF E E-002 SIGDIS E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

201 E E E E E E NAME STEEL YOUNG E+006 POISON E-001 DENSIT E NAME FELT_WEB_COMPRESSED DSTIF E E-001 SIGDIS E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E NAME FELT_FLANGE DSTIF E E-002 SIGDIS E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E NAME FELT_FLANGE_COMPRESSED DSTIF E E-001 SIGDIS E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+000 'GEOMET' 1 NAME HERCUSEAL_GLUE THICK E+000 CONFIG MEMBRA ZAXIS E E E NAME FELT_COMPRESSED_FLANGE THICK E+002 CONFIG MEMBRA ZAXIS E E E NAME FELT_FLANGE 201

202 202 THICK E+002 CONFIG MEMBRA ZAXIS E E E NAME FELT_COMPRESSED_WEB THICK E+000 CONFIG MEMBRA ZAXIS E E E NAME FELT_WEB THICK E+000 CONFIG MEMBRA ZAXIS E E E NAME GLASS_FLANGE THICK E NAME STEEL THICK E NAME GLASS_WEB THICK E+000 'DATA' 1 NAME GLASS_FLANGE 'ELEMENTS' CONNECT 1876 L8IF L8IF [..] 4142 L8IF L8IF Q8MEM Q8MEM [..] 4068 Q8MEM Q8MEM MATERI / / 1 / / 2 / / 3 / / 4 / / 5 / / 6 / / 7 DATA / / 1 GEOMET / / 1 / / 2 / / 3 / / 4 / / 5 / / 6 / / 7 / / 8 'LOADS'

203 CASE 1 DEFORM 2398 TR E+001 DEFORM 2447 TR E+001 DEFORM 2389 TR E+001 DEFORM 2390 TR E+001 DEFORM 2394 TR E+001 DEFORM 2435 TR E+001 DEFORM 2436 TR E+001 DEFORM 2437 TR E+001 DEFORM 2438 TR E+001 DEFORM 2439 TR E+001 DEFORM 2440 TR E+001 DEFORM 2441 TR E+001 DEFORM 2442 TR E+001 DEFORM 2443 TR E+001 DEFORM 2444 TR E+001 DEFORM 2445 TR E+001 DEFORM 2446 TR E+001 DEFORM 2454 TR E+001 'GROUPS' ELEMEN 3 MAP-MESH(2D) / / 5 MAP-MESH(2D)-1 / / 9 MAP-MESH(2D)-3 / / 11 MAP-MESH(2D)-4 / / 13 MAP-MESH(2D)-5 / / 37 MAP-MESH(2D)-7 / / 39 MAP-MESH(2D)-11 / / 41 MAP-MESH(2D)-17 / / 43 MAP-MESH(2D)-18 / / 45 MAP-MESH(2D)-19 / / 49 MAP-MESH(2D)-9 / / 51 MAP-MESH(2D)-10 / / 53 MAP-MESH(2D)-12 / / 203

204 55 MAP-MESH(2D)-13 / / 57 MAP-MESH(2D)-21 / / 69 MAP-MESH(2D)-2 / / 83 MAP-MESH(2D) MAP-MESH(2D) MAP-MESH(2D) MAP-MESH(2D) MAP-MESH(2D)-15 / / 96 MAP-MESH(2D)-20 / / 'SUPPOR' / (4) / TR 1 / (4) / TR 2 / (4) / TR 3 'UNITS' FORCE N LENGTH MM MASS E+003 'END' Command file *FILOS INITIA *NONLIN EXECUT LOAD STEPS EXPLIC SIZES 0.05(20) BEGIN OUTPUT FXPLUS FILE " _GlasscolumnGlueFeltSteel" DISPLA TOTAL TRANSL GLOBAL FORCE REACTI TRANSL GLOBAL STRAIN TOTAL GREEN STRAIN TOTAL TRACTI LOCAL STRESS TOTAL CAUCHY STRESS TOTAL TRACTI LOCAL END OUTPUT *END 204

205 205

206 Appendix G Distribution of stresses in the numerical analysis The distribution of stresses in the glass columns are presented in this Appendix for several situations. Firstly, the columns bonded by Araldite (Young s modulus is 2550 N/mm 2 ) are shown for both the x- direction and the y-direction and for 0, 0.5, 1.0, 1.5 and 2.0 millimetres of difference in vertical position. Secondly, the columns bonded by the glue with lower stiffness (E=1.6 N/mm 2 ) are shown for the same situations. The applied displacement is for all of these columns equal to the maximum applied displacement in the numerical model, which is 20 millimetres. E = 2550 N/mm 2 Legend stresses x-direction 0 mm 0.5 mm 206

207 1.0 mm 1.5 mm 2.0 mm 207

208 208 Legend stresses y-direction 0 mm 0.5 mm

209 1.0 mm 1.5 mm 2.0 mm 209

210 E = 1.6 N/mm 2 Legend stresses x-direction 0 mm 0.5 mm 210

211 1.0 mm 1.5 mm 2.0 mm 211

212 212 Legend stresses y-direction 0 mm 0.5 mm

213 1.0 mm 1.5 mm 2.0 mm 213

214 Appendix H Measurements test specimens experiment II For Experiment II different glass specimens have been measured. The glass plates that can be distinguished include: rectangles and polished rectangles. For the measurement of the thickness and the width up to 150 mm the accuracy of the measuring device was 0.05 mm. The thickness is measured about 20 mm from the edge. The accuracy of the measuring device for the length and the width from 150 mm was 1 mm. The measurements have been performed in a similar way as the specimens for Experiment I have been measured. Rectangles The nominal dimensions of the glass plates were 8 mm thick, 100 mm wide and 1000 mm long. The measured values are listed in the tables on the next two pages. From this it can be concluded that the average thickness of the specimens was 2.38% lower than the nominal thickness of 8 mm. Compared to the measurements of Experiment I, this percentage was only 0.75 (Appendix C). The rectangles of experiment II showed a higher deviation in thickness. The largest value measured was 8.00 mm, whereas the smallest value measured was 7.70 mm. These deviations in the thickness are in accordance with the tolerances considered in NEN-EN (Table 1). Also the glass plates of Experiment II showed a higher deviation in width. The average difference between the lower and upper side of the plates was found to be 0.56 mm compared to 0.35 mm for the specimens from experiment I. This difference in width is caused by the cutting technique as explained in Section The biggest value measured for the width was mm and the smallest value mm. The rectangular glass plates have been assembled to nine glass columns (H profiles). The selection of the glass plates for the columns has been performed by selecting glass plates with equal width, as the length of all the specimens was 999 mm. The remaining glass plates have been tested as singular glass plates or have been disapproved due to the quantity or quality of imperfections. 214

215 specimen thickness [mm] t 1 t 2 t 3 t 4 t 5 t 6 t 7 t 8 t av 1 7,85 7,80 7,80 7,90 7,90 8,00 7,95 7,80 7,88 2 7,85 7,85 7,80 7,90 7,85 7,90 7,85 7,85 7,86 3 7,75 7,85 7,85 7,90 7,80 7,75 7,75 7,75 7,80 4 7,75 7,75 7,90 7,90 7,95 7,75 7,95 7,90 7,86 5 7,80 7,70 7,75 7,75 7,75 7,70 7,75 7,85 7,76 6 7,80 7,75 7,75 7,80 7,80 7,80 7,80 7,80 7,79 7 7,80 7,80 7,80 7,85 7,75 7,75 7,80 7,80 7,79 8 7,80 7,75 7,75 7,85 7,75 7,80 7,80 7,80 7,79 9 7,90 7,75 7,75 7,80 7,80 7,75 8,00 7,75 7, ,70 7,70 7,80 7,90 7,75 7,75 7,80 7,70 7, ,70 7,80 7,75 7,80 7,75 7,75 7,75 7,75 7, ,80 7,75 7,75 7,75 7,80 7,85 7,85 7,80 7, ,75 7,75 7,75 7,75 7,70 7,70 7,75 7,75 7, ,75 7,70 7,80 7,90 7,80 7,75 7,70 7,80 7, ,85 7,70 7,70 7,80 7,75 7,75 7,85 7,80 7, ,70 7,75 7,70 7,80 7,85 7,70 7,75 7,85 7, ,75 7,70 7,80 7,85 7,85 7,95 7,70 7,80 7, ,70 7,75 7,85 7,85 7,90 7,80 7,75 7,80 7, ,80 7,75 7,70 7,70 7,75 7,90 7,70 7,80 7, ,75 7,80 7,80 8,00 7,80 7,75 7,90 8,00 7, ,75 7,75 7,80 7,80 7,90 7,70 7,80 7,80 7, ,75 7,80 7,90 7,90 7,80 7,75 7,70 7,75 7, ,80 7,85 7,80 7,85 7,80 7,80 7,80 7,80 7, ,80 7,80 7,90 7,80 7,90 7,80 7,80 7,85 7, ,90 7,80 7,90 7,95 7,85 7,70 7,80 7,75 7, ,75 7,95 7,90 7,90 7,85 7,85 7,75 7,75 7, ,80 7,90 7,90 7,90 7,85 7,80 7,80 7,80 7, ,75 7,80 7,80 7,80 7,85 7,80 7,80 7,80 7, ,80 7,85 7,85 7,85 7,85 7,80 7,80 7,75 7, ,70 7,90 7,90 7,90 7,90 7,75 7,80 7,95 7, ,85 7,80 7,80 7,85 7,85 7,90 7,80 7,95 7, ,75 7,90 7,85 7,80 7,95 7,85 7,80 7,75 7, ,80 7,80 7,95 7,90 7,95 7,90 7,80 7,80 7, ,85 7,80 8,00 7,90 7,90 7,75 7,80 7,80 7,85 7,81 215

216 specimen width upper side [mm] width lower side [mm] w1u w2u w3u wuav w1l w2l w3l wlav 1 100,10 100,20 100,10 100,13 99,40 99,70 99,35 99, ,25 100,20 100,20 100,22 99,70 99,60 99,45 99, ,10 100,10 100,10 100,10 99,60 99,50 99,60 99, ,10 100,00 100,00 100,03 99,65 99,40 99,30 99, ,35 100,30 100,25 100,30 99,65 99,75 99,90 99, ,25 100,25 100,20 100,23 99,75 99,45 99,35 99, ,30 100,40 100,30 100,33 99,70 99,45 99,65 99, ,00 100,50 100,00 100,17 99,30 99,30 99,45 99, ,45 100,35 100,30 100,37 99,90 99,65 99,90 99, ,20 100,25 100,20 100,22 99,75 99,70 99,65 99, ,30 100,35 100,30 100,32 99,60 99,90 99,75 99, ,40 100,35 100,25 100,33 99,75 99,75 99,70 99, ,40 100,45 100,35 100,40 99,45 99,90 99,80 99, ,10 100,00 100,05 100,05 99,55 99,35 99,40 99, ,35 100,35 100,35 100,35 99,65 99,80 99,75 99, ,30 100,25 100,25 100,27 99,75 99,55 99,65 99, ,25 100,30 100,35 100,30 99,80 99,70 99,65 99, ,50 100,20 100,25 100,32 99,55 99,95 99,75 99, ,10 100,10 100,20 100,13 99,50 99,70 99,55 99, ,20 100,25 100,25 100,23 99,65 99,80 99,85 99, ,40 100,30 100,30 100,33 99,75 99,70 99,70 99, ,25 100,20 100,25 100,23 99,70 99,65 99,50 99, ,35 100,30 100,35 100,33 100,10 99,70 99,75 99, ,30 100,30 100,30 100,30 100,00 99,75 99,45 99, ,25 100,30 100,25 100,27 99,90 99,95 99,90 99, ,15 99,80 99,80 99,92 99,75 99,20 99,15 99, ,50 100,50 100,20 100,40 100,10 100,00 99,80 99, ,40 100,40 100,40 100,40 100,00 99,50 99,45 99, ,30 100,20 100,25 100,25 99,80 99,90 99,60 99, ,20 100,25 100,20 100,22 99,90 99,75 99,75 99, ,60 100,40 100,30 100,43 100,15 99,95 99,80 99, ,35 100,30 100,30 100,32 99,80 99,90 99,80 99, ,30 100,20 100,20 100,23 99,85 99,70 99,85 99, ,25 100,15 100,25 100,22 99,75 99,50 99,70 99,65 100,25 99,69 216

217 Polished rectangles The nominal dimensions of the polished glass plates were 8 mm thick, 100 mm wide and 1000 mm long. Only the bottom and top edge were polished, as these were subject to the introduction of the forces in the glass column. The measurements of these specimens are listed in the following tables. specimen thickness [mm] t 1 t 2 t 3 t 4 t 5 t 6 t 7 t 8 t av A 7,80 7,85 7,85 7,90 7,90 7,85 7,75 7,75 7,83 B 7,85 7,80 7,80 7,80 7,80 7,80 7,80 7,75 7,80 C 7,80 7,85 7,80 7,80 7,85 7,90 7,80 7,85 7,83 D 7,80 7,90 7,85 7,90 7,90 7,80 7,80 7,75 7,84 7,83 specimen width upper side [mm] width lower side [mm] w1u w2u w3u wuav w1l w2l w3l wlav A 100,10 100,00 100,10 100,07 99,55 99,30 99,35 99,40 B 100,00 100,05 100,00 100,02 99,55 99,55 99,60 99,57 C 100,10 100,00 100,00 100,03 99,85 99,40 99,55 99,60 D 100,45 100,50 100,50 100,48 100,00 99,95 100,00 99,98 100,15 99,64 On average, the thickness of the plates has been found to be 2.13% lower than the nominal thickness of 8 mm. The thickness of all the specimens were below the value of 8 mm, but in accordance with the tolerances considered in NEN-EN (Table 1). The average value for the difference in width between the upper side and lower side of the specimens is measured as 0.51 mm. This is almost similar to the value measured for the rectangular plates without polished edges of this experiment, but again more compared to the specimens of experiment I. The length of the polished rectangles was 997 mm, which is less than the length of the other specimens. This is caused by polishing up the edges. 217

218 Appendix I Expectation experiment II Three failure modes will be distinguished in this appendix, namely: Euler buckling, torsional buckling and pure compression (Section 2.2.1). By calculating the failure load for each of these failure modes the lowest value of the obtained loads corresponds to the expected failure mode. This expectation has been performed in a similar way for experiment I (Appendix D). During experiment II two types of configurations are tested: single glass plates and assembled glass columns (H-profiles). An expectation for the latter is described in Appendix D and will not be described in this appendix. The single glass plates have a cross-sectional area of 800 mm 2 and are 1000 mm high (Figure 66). The calculated failure loads are listed in the table in this appendix. The compressive stress of glass is assumed to be 900 N/mm 2 in Appendix D. Since it has been found in experiment I that the average compressive stress was equal to 29.0 N/mm 2 (Section 3.5), the compressive stress value has been adapted to the lowest value to get a more realistic failure load expectation. Although this value has been derived from assembled glass columns instead of single glass plates. failure mode failure load [kn] failure load reduced buckling length [kn] Euler buckling 2.9 a 4.7 b torsional buckling c d compression 23.2 e 23.2e From the expected failure loads it can be concluded that a single glass plate is expected to fail at 2.9 kn. However, the applied substructure (Figure 72b) reduces the buckling length of the glass plates. At a height of 210 millimetres from the bottom edge the glass plates have been supported. Thereby, the buckling length becomes 790 millimetres and the expected location of buckling is 380 millimetres from the top. The expected failure load for each considered failure mode with reduced buckling length is listed in the next table. The failure load due to Euler buckling has increased. However, the difference in buckling length did not influence the failure load due to torsional buckling. For the assembled glass columns the ratio between the ultimate load and the expected failure load is known. However, for single glass plates it is not. The expected failure load is therefore considered below 4.7 kn for a single glass plate. a b c / / , d, e

219 219

220 Appendix J Preliminary design pavilion J.I Introduction The preliminary design of the pavilion is presented in different sections: K.II Overall dimensions pavilion K.III Actions on the structure K.IV Design beam K.V Stability of the pavilion K.VI Glass column requirements The calculations have been performed in accordance with NEN 6702:2007 and NEN-EN :2003. As it is not intended to design a pavilion, but to create a context for the glass column, only the main structural aspects are considered in this preliminary design. Finally, the requirements for the design of the glass column, like the design load, are provided. J.II Overall dimensions pavilion top view of the pavilion distribution of forces from the composite plank floor with concrete topping to the beams The pavilion has an area of 22.5 x 45 m 2 and is 4 meters high. The grid of vertical supports was based on a multiple of 2.5 meters, which is the standard width of the considered composite plank floors (see J.III). The top view of the pavilion is illustrated in the above figure (left). The small black squares are meant to be the columns (10 in total) and the horizontal and vertical lines the steel beams. The beams span in two directions and between them there are the composite plank floors. As concrete is 220

221 topped in situ on these composite plank floors, the floor as a whole acts like one monolithic plate to distribute the forces, see the above figure (right). At the edges there will be steel sections to transfer the forces from the floor into the glass façade. As the beams are considered to be all the same type and placed at the same height, every beam carries an equal part of the load from the roof (except for the edges). The area is m 2 per beam. This coincides with the forces of meters per meter length of the beam. 8 Therefore, w mean is 3.52 meters. J.III Actions on the structure The pavilion consists of a lower floor and a roof where people may congregate. The permanent forces of the structure are therefore divided in the weight of the composite plank floor, the concrete topping and the steel beams. The live load is based on the forces that may occur on the roof. Permanent load - composite plank floor (width=2.5m) Betonson weight composite plank floor per meter length on a beam: - steel THQ 265 beam properties profile f : h mm 265 t w mm 8 b o mm 240 b u mm 450 G kg/m I y cm W y;pl mm * / / - finishing layer of 50 mm concrete Total permanent load: 50 mm 25 kn 3.52m 4.4 kn/m m / f 221

222 Live load As already explained briefly, the roof is an area where people may congregate. There will be a café, furniture and receptions. The live load consists therefore of a load for the roof area. Also, snow load and wind load will be taken into account. The snow load as well as the wind load depend on the shape of the roof, the thermal properties of the roof and some climatic influences. For this structure, an insulated pent-roof in Delft is considered. In the following calculation the pavilion is considered to be a closed building. According to NEN a building can be considered as a closed building when the sliding doors have a total area less than 0.05 of the total façade area. As the roof is constructed out of heavy concrete and the building is considered to be a closed building, wind suction will not be governing. - roof area [NEN 6702: 2007] - snow [NEN-EN : 2003], , / - wind [NEN 6702: 2007], / Combinations of actions - ultimate limit state partial factors ; 1.2 ; permanent + roof area: / permanent + roof area x ψ roof + wind: / permanent + roof area x ψ roof + snow: / - serviceability limit state 222

223 partial factors ; 1.0 ; 1.0 permanent + roof area: / permanent + roof area x ψ roof + wind: / permanent + roof area x ψ roof + snow: / J.IV Design beam Strength ; ; 1 8 ; ; ; ; ; ; THQ 320 (t = 8 mm) with ; is sufficient Stiffness According to NEN 6702 art ; 5 ; THQ 320 (t = 8 mm) with is sufficient for the required stiffness. Stability No lateral torsional buckling for a THQ-beam. Also, as the beams span in two directions the steel frame will be very rigid. J.V Stability of the pavilion In this section it is checked whether it would be possible to stabilize the pavilion by means of plate action of the glass façade panes or not. As a result from stabilizing glass facades, the lower floor would be really transparent. Otherwise a core in the inner space, steel crosses or fins should be implemented, which take away the transparency. The mechanical scheme of this concept is illustrated in the figure. 223

224 If wind blows to the top side of the pavilion, which has a width of 22.5 meters, the long side should stabilize the pavilion. Also, if wind blows to the other side (see figure), which has a width of 45 meters, the short side should stabilize the pavilion. Since the latter is more critical, this situation will be considered. The wind pressure on the pavilion for the long edge per meter height is [NEN 6702: 2007]:, /, / Half of the calculated wind pressure goes directly to the foundation. The other half needs to be transferred by the structure and is equal to:, This wind pressure will be split between the two stabilizing walls on each end of the pavilion. Each stabilizing wall, therefore, needs to transfer 43.7 kn. According to the maximum deliverable glass panel sizes and the width of 22.5 meter, 4 meters high and 2.5 meters wide glass panels are selected. The slenderness of the panels is Therefore, the total glass façade is modelled as separate glass elements instead of as one big plate. This means that each glass panel should be able to withstand the compressive and tensile forces from the wind load. As there are 22.5/2.5= 9 glass panels these forces equal:,, , ,, The tensile force of about 8 kn is a bit conservative, since in practice there will also be a compressive force from the self-weight of the roof. After about 30 years the tensile strength of glass equals: 8 /, see Table 4.The required glass area of glass to handle these tensile forces is then: 224