G LASS AS A S TRUCTURAL M ATERIAL : S IMULATION OF AN I NTERVENTION ON THE N ATIONAL M USEUM S OARES DOS
R EIS , P ORTO
D
IOGOM
ANUELG
ONÇALVESD
IASDissertação submetida para satisfação parcial dos requisitos do grau de MESTRE EM ENGENHARIA CIVIL —ESPECIALIZAÇÃO EM ESTRUTURAS E GEOTECNIA
Orientador: Professor Doutor João Paulo Sousa Costa de Miranda Guedes
Coorientador: Professor Doutor Mauro Corrado, Politecnico di Torino
Coorientador: Professor Doutor Francesco Laccone, Università di Pisa
JANEIRO DE 2023
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MESTRADO EM ENGENHARIA CIVIL 2022/2023
DEPARTAMENTO DE ENGENHARIA CIVIL
Tel. +351-22-508 1901 Fax +351-22-508 1446
Editado por
FACULDADE DE ENGENHARIA DA UNIVERSIDADE DO PORTO Rua Dr. Roberto Frias
4200-465 PORTO Portugal
Tel. +351-22-508 1400 Fax +351-22-508 1440
http://www.fe.up.pt
Reproduções parciais deste documento serão autorizadas na condição que seja mencionado o Autor e feita referência a Mestrado em Engenharia Civil - 2022/2023 - Departamento de Engenharia Civil, Faculdade de Engenharia da Universidade do Porto, Porto, Portugal, 2023.
As opiniões e informações incluídas neste documento representam unicamente o ponto de vista do respetivo Autor, não podendo o Editor aceitar qualquer responsabilidade legal ou outra em relação a erros ou omissões que possam existir.
Este documento foi produzido a partir de versão eletrónica fornecida pelo respetivo Autor.
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“The physical history of architecture shows that throughout all centuries it conducted an untiring fight on the side of light versus the obstacle imposed by the law of gravity.”
- Le Corbusier
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v ACKNOWLEDGEMENTS /AGRADECIMENTOS
Confesso que escrever este capítulo revelou ser uma tarefa mais difícil do que contava. Não por questões de memória, mas por não existir vocabulário suficiente para descrever o meu profundo sentimento de gratidão.
Aos meus pais. É graças ao grande exemplo que tenho em casa que posso agradecer aos objetivos que consegui atingir até hoje. Sem o apoio deles, tenho a certeza de que o caminho seria muito mais difícil. Obrigado pelos conselhos e, principalmente, por estarem sempre ao meu lado.
Ao Professor João Paulo Miranda Guedes. Não posso deixar em vão todo o seu o esforço e dedicação ao longo deste ano de trabalho. Apesar de o estudo ter sido desenvolvido durante cerca de quatro meses, existiu muito trabalho prévio para conseguir uma parceria para a sua execução, para conseguir encontrar um edifício na cidade que pudesse servir como caso de estudo (uma história engraçada) e na procura de informação sobre o mesmo. Mesmo nesta altura o Professor esteve sempre presente e interessado com os avanços e sempre disponível para qualquer situação que pudesse surgir.
Nas visitas ao Museu Soares dos Reis para executar o trabalho de investigação e diagnóstico, nas chamadas telefónicas para atualização do trabalho, nas reuniões – já presencialmente, no Porto – o Professor transmitiu o seu conhecimento de forma clara, o que foi fundamental para a execução deste documento. Agradecer também à sua paciência, que merece um prémio.
To Professor Mauro Corrado. From the first day you received me with open arms and a positive attitude, making me feel welcome at the university and in Torino. Your enthusiasm to meet with me regularly to discuss my work and provide valuable feedback was greatly appreciated.
Additionally, the knowledge and expertise you shared about glass structures was fundamental to the success of the and I am truly grateful for your contributions.
To Professor Francesco Laccone. Your expertise and suggestions were extremely valuable and fundamental to the execution of this work. Also, the insights and guidance helped to improve the work in a substantial way.
Aos trabalhadores do Museu Nacional Soares dos Reis. Ao Dr. António Ponte, que nos concedeu autorização para aceder aos espaços do Museu. À Dra. Marília e à Dra. Paula, por transmitirem o seu conhecimento sobre o Museu e o edifício.
À Fundação Marques da Silva. Especificamente à Dra. Conceição Pratas, pela sua ajuda durante o processo de pesquisa de informação sobre o edifício.
À Sara, ao Moura e ao Vasco. Obrigado por me fazerem crescer.
Aos meus amigos que me acompanharem no percurso académico. À Mafi, ao Hélder, ao Duarte, ao Santos, aos Luíses, ao Daniel, à Lina, à Ru, ao Bernardo, ao Rui, ao VT, ao Peixe, a todos.
Obrigado por serem quem são.
À Cati, à Chica e aos Pedros. Pela ótima companhia em Turim.
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vii ABSTRACT
The applicability of glass as a structural material has been developed over the years and is a consequence of history itself. In Portugal, its study and use are still very scarce and limited. The main objective of this thesis is to explore the potential of introducing glass in the design of a structure that incorporates it as a secondary material. This structure uses timber as the main material and is incorporated in a building that belongs to Portuguese heritage, the National Museum Soares dos Reis.
The museum building has a currently empty and unused courtyard. The implementation of a transparent structure, supported by the load-bearing walls, that covers it - this structure consists of a roof and facade - leads to an increase in space without compromising natural light.
The methods used for design follow the CEN/TS 19100:2021 and EN 16612:2019 standards, that are technical specifications documents used as the basis for the Eurocode in development of Glass Structures. A numerical modelling of some components was also performed, both for glass and timber components, using the SJ Mepla and Autodesk Robot software. This strategy allowed the verification of the installed stresses and deformations according to the standards for glass components and Eurocode 5 for timber elements. Additionally, the metal connections between the elements of glass and wood are also analysed and designed.
The result of this work is a transparent structure that protects the space above mentioned, that verifies the conditions imposed by the standard and respects the resistance capacity of the walls of the building.
KEYWORDS: Intervention on Existing Buildings, Timber Structures, Glass Structures, Structural Analysis, Structural Design, Numerical Modelling.
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ix RESUMO
A aplicabilidade do vidro como material estrutural tem sido desenvolvida ao longo dos anos e é uma consequência da história em si. Em Portugal, o seu estudo e utilização é ainda muito escassa e limitada. A presente dissertação tem como principal objetivo explorar a potencialidade de introduzir o vidro no dimensionamento de uma estrutura que o incorpora como material secundário. Esta utiliza a madeira como material principal e está inserida num edifício que pertence ao património português, o Museu Nacional Soares dos Reis.
O edifício do Museu possui um pátio atualmente vazio que não é utilizado. A implementação de uma estrutura transparente, apoiada nas paredes portadoras, que o cubra – estrutura essa que consiste numa cobertura e fachada – conduz a um aumento do espaço, sem prescindir a luz natural.
Os métodos utilizados para o dimensionamento seguem as normas CEN/TS 19100:2021 e EN 16612:2019, documentos de especificações técnicas que servirão como base para o Eurocódigo de Estruturas de Vidro. Foram também realizadas modelações numéricas de alguns componentes, tanto em vidro como em madeira, recorrendo aos softwares SJ Mepla e Autodesk Robot. Tal permitiu a validação das tensões e deformações instaladas, consoante as normas anteriormente referidas para o caso dos componentes de vidro, e do Eurocódigo 5 para os elementos em madeira.
Adicionalmente, as ligações metálicas entre elementos e vidro e madeira são também analisadas e dimensionadas.
O resultado deste trabalho consiste numa estrutura transparente que protege o espaço referido, que verifica as condições impostas pelas normas e respeita a capacidade resistente das paredes portadoras do edifício.
PALAVRAS-CHAVE: Intervenção em Edifícios Existentes, Estruturas de Madeira, Estruturas de Vidro, Dimensionamento, Análise Estrutural, Modelação Numérica.
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xi TABLE OF CONTENTS
ACKNOWLEDGEMENTS ... v
ABSTRACT ... vii
SUMMARY ... ix
PREAMBLE ... 1
OBJECTIVE AND METHODOLOGY ... 1
OVERVIEW ... 2
INTRODUCTION ... 3
HISTORY AND ARCHITECTURAL CONTEXT ... 3
GLASS BEHAVIOUR ... 9
PRODUCTION:FLOAT PROCESS... 10
GLASS TYPES... 11
2.5.1.ANNEALED GLASS...11
2.5.2.HEAT STRENGTHENED GLASS ...11
2.5.3.FULLY TEMPERED GLASS ...13
2.5.4.CHEMICALLY TOUGHENED GLASS ...13
2.5.5.INSULATING GLASS UNITS...13
MATERIAL PROPERTIES ... 15
CONNECTIONS IN GLASS ... 15
STANDARDS ... 16
GLASS AS A STRUCTURAL MATERIAL ... 17
3.1.1.DESIGN BENDING STRENGTH OF GLASS ...17
3.1.2.EFFECTIVE THICKNESS ...18
3.1.3.DESIGN OF INSULATING GLASS UNITS ...18
Safety Coefficients...18
xii
Climatic Load ... 19
Partition of Loads ... 20
3.1.4.GLASS BEAMS ... 21
TIMBER AS A STRUCTURAL MATERIAL ... 22
INTRODUCTION ... 25
HISTORICAL DATA ... 25
4.2.1.INTERVENTIONS MADE BY FERNANDO TÁVORA ... 29
INSPECTION AND DIAGNOSIS ... 31
THE IDEA ... 32
INTRODUCTION ... 37
ESTIMATION OF THE LOADS ON THE LOAD BEARING WALLS... 37
SHAPE ... 38
DIMENSIONS ... 44
INTRODUCTION ... 47
ROOF:GLASS ELEMENTS... 47
6.2.1.INSULATING GLASS UNITS ... 47
Maintenance Load ... 48
Wind Load ... 48
Climatic Load ... 52
Load combinations ... 52
Modelling: SJ Mepla ... 53
Verification at Limit State Scenarios... 56
6.2.2.GLASS BEAMS ... 58
Loads and Load Combinations ... 59
Modelling ... 60
Verification at Limit State Scenarios... 63
FAÇADE:GLASS ELEMENTS ... 64
Wind Load ... 65
xiii
Verification at Limit State Scenarios ...66
STEEL CABLE MESH ... 67
PRIMARY STRUCTURE VERIFICATION ... 69
6.5.1.LOADS AND LOAD COMBINATIONS ...69
6.5.2.MODELLING ...70
6.5.3.TIMBER BEAMS ...72
6.5.4.TIMBER COLUMNS...74
CONNECTION DESIGN ... 74
6.6.1.IGU’S –GLASS AND TIMBER BEAMS ...75
6.6.2.GLASS BEAMS –TIMBER BEAMS ...76
FINAL VERIFICATIONS ... 78
GENERAL CONCLUSIONS ... 81
MAIN ACHIEVEMENTS... 81
DIFFICULTIES ... 82
FUTURE IMPROVEMENTS ... 83
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xv INDEX OF FIGURES
Figure 2-1: Roman cage cup. Collection Staatliche Antikensammlungen. ... 4
Figure 2-2: The several phases of the Crown Method. ... 4
Figure 2-3: The Sainte-Chapelle in Paris, 1243-1248. ... 5
Figure 2-4: The Cylinder Method. ... 6
Figure 2-5: The Crystal Palace in London, July 1850-December 1850 (Joseph Paxton). On the left, the exterior view and the garden that surrounded it. On the right, is the interior view. ... 6
Figure 2-6: The Farnsworth in Plano, Illinois, 1945-1951 (Mies van der Rohe). On the right, the front façade of the building. On the left, the detail of the column is mentioned in the above text. ... 7
Figure 2-7: The Apple Store, in New Work (TriPyramid). On the left, the structure before the renovation, made in 2011. On the right, the structure after the renovation. ... 8
Figure 2-8: Glass components... 9
Figure 2-9: Graphics of strain/stress for steel and glass. ... 9
Figure 2-10: Glass production processes, processing methods and glass products. ...10
Figure 2-11: Scheme of the production process for float glass. ...11
Figure 2-12: Residual stress profile in heat strengthened glass...12
Figure 2-13: Comparison of fracture patterns of different types of glass and their how it affects their structural performance. ...12
Figure 2-14: Stress patterns of different types of glass. From left to right: het strengthened, fully tempered. ...13
Figure 2-15: Comparison of buildings before and after IGU’s. On the left, the former Shelton Hotel in New York, 1922-1924 (Arthur Harmon). On the right, the Seagram Building in New York, 1956- 1957 (Mies var der Rohe). ...14
Figure 2-16: Common glass supports types. ...16
Figure 3-1: Effect of the climatic load on insulated glass. ...19
Figure 4-1: The building in 1800. On the left, a map of 1893 with the location marked in red. On the right, the wall that separated the main house and the factory. ...26
Figure 4-2: Façade of the building before the works (left figure) and after the works (right figure). ...27
Figure 4-3: History timeline of the Museu Nacional Soares dos Reis. ...28
Figure 4-4: Proposal for the intervention, December 1994. ...29
Figure 4-5: Before (left figure) and after (right figure) of the patios of the building. ...30
Figure 4-6: Front facade of the National Museum Soares dos Reis. ...31
Figure 4-7: Detail of one of the ceilings of the building. ...32
Figure 4-8: The new entrance of the Louvre in Paris, 1981-1989 (Ieoh Ming Pei). ...33
Figure 4-9: The entrance of the Universal Musuem Joanneum, 2016-2011 (Nieto Sobajo Arquitetos). On the right, a top view of the square mentioned above. On the left, a detail of the glass conic shaped windows. ...33
Figure 4-10: The roof of the cloister of the Monastery of São Bento da Vitória in Porto, 1985-1990 (Carlos Guimarães and Luís Carneiro). On the right, a detail of the column. On the left, the whole structure. ...34
Figure 4-11: Areal view of the back area of the National Museum Soares dos Reis. ...34
Figure 5-1: Computation of the load from each floor on each side wall. ...38
Figure 5-2: Comparison of the building and the 3D model. ...39
Figure 5-3: First proposal for the structure. ...40
Figure 5-4: Shortcomings of the first proposal. ...41
Figure 5-5: Second proposal for the structure. ...41
Figure 5-6: Shortcomings of the second proposal. ...42
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Figure 5-7: Third proposal for the structure. ... 43
Figure 5-8: Top view of the structure. ... 43
Figure 5-9: Structural system of the façade. ... 44
Figure 5-10: Spacing of the roof beams. ... 45
Figure 5-11: Dimensions of the façade. ... 45
Figure 6-1:Dimensions of the IGUs on the roof. ... 47
Figure 6-2: Reference height or dome shaped roofs. ... 49
Figure 6-3: Values for cpe for dome shaped roofs. ... 51
Figure 6-4: Cross-sections of the IGU's installed on the roof. On the top, the cross-section designated for the smaller panels. On the bottom, the cross-section designated for the larger panels. ... 54
Figure 6-5: Comparison of the values given by the softwares SJ Mepla (top figure) and Autodesk Robot (bottom figure). ... 56
Figure 6-6: Direction and way of the imposed loads and the climatic load on IGU's. ... 58
Figure 6-7: Dimensions of the glass beams on the roof. ... 58
Figure 6-8: Cross-sections of the glass beams. ... 59
Figure 6-9: Axial stresses maps for the several supporting conditions considered. ... 62
Figure 6-10: Dimensions of the IGU's on the façade. ... 64
Figure 6-11: Cross-sections of the IGU's installed on the façade. On the top, the cross-section of the elements between the columns. On the bottom, the cross-section of the rest of the elements. .... 65
Figure 6-12: Shape of the profile of velocity pressure and reference height value for the case study. . 65
Figure 6-13: Detail of the wired mesh. ... 67
Figure 6-14: Behaviour of the structure without the steel cable mesh (top) and with it (bottom) – results in millimetres. ... 68
Figure 6-15: Detail of the pre-tensioned cables... 70
Figure 6-16: Model of the structure. ... 71
Figure 6-17: On the left, connection between the IGUs and the glass beams (roof). On the right, connection between the IGUs and the timber beams (façade). ... 75
Figure 6-18: Connection between the glass and timber beams. ... 76
Figure 6-19: Numerical analysis of the connection between the glass and timber beams. ... 77
Figure 6-20: Location for the verification of the loads on the load-bearing walls. ... 79
Figure 7-1: Final structure. Comparison between the original building and the proposal. ... 83
xvii INDEX OF TABLES
Table 2-1: Mechanical properties of glass. ...15
Table 2-2: Characteristic strength of glass types...15
Table 3-1: Partial load factors. ...19
Table 3-2: Load partition for external loads. ...21
Table 3-3: Isochore pressure on each pane of the IGUs. ...21
Table 5-1: Equation of the parabola (oxy axis with origin at the centre of the arch and oy positive down) and inclination of the straight line at the extremity, of the roof timber beams. ...45
Table 6-1: Load combinations adopted for the IGU's on the roof. ...53
Table 6-2: Model characteristics for both softwares. ...55
Table 6-3: Verification for the IGUs 3,20x1,40m on the roof, for ULS. ...57
Table 6-4: Verification for the IGUs 3,20x1,85m on the roof, for ULS. ...57
Table 6-5: Verification for the IGU’s on the roof, for SLS. ...57
Table 6-6: Load combinations considered to design the glass beams. ...60
Table 6-7: Glass beams model characteristics. ...60
Table 6-8: Supporting conditions of the four models. ...61
Table 6-9: Maximum axial stress in the several considered cases...63
Table 6-10: Verification for the glass beams. ...63
Table 6-11: Verification for the IGUs 2,45x3,60m on the façade, for the ULS. ...66
Table 6-12: Verification for the IGUs 4,00x3,60m on the façade, for the ULS. ...66
Table 6-13: Verification for the IGU’s on the façade, for SLS. ...66
Table 6-14: Characteristics of the model for the steel cable mesh. ...68
Table 6-15: Load combinations considered for the timber beams. ...70
Table 6-16: Model characteristics for the primary structure. ...71
Table 6-17: Stresses applied to the timber elements...72
Table 6-18: Temperature variations imposed on the steel cables. ...72
Table 6-19: Verification for the timber beams...73
Table 6-20: Verifications for the timber beams. ...74
Table 6-21: Model characteristics of the connection...77
Table 6-22: Properties of the bolts. ...78
Table 6-23: Verification of the loads on the load-bearing wall. ...79
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xix SYMBOLS,ACRONYMS AND ABBREVIATIONS
a the length of the short edge.
A area of the cross section.
a* characteristic value of the unit length.
Aref reference area of the structure.
C1, C2 factors that consider the bending moment diagram.
cdir directional factor.
cH coefficient for the effect of altitude change on isochore pressure.
co(z) orography factor.
cr(z) roughness factor.
cscd structural factor.
cseason season factor.
cT coefficient for the effect of cavity temperature change on isochore pressure.
di distance of the mid-pane of the glass ply “i” from the mid-plane of the laminated glass.
E Young’s modulus.
fb,k characteristic value of glass strength after a strengthening treatment.
fc,0,d design compressive strength along the grain.
fc,90,d design compressive strength perpendicular to the grain.
Fd design value of the action.
fg,k characteristic bending strength of annealed glass.
fm,d design bending strength.
G shear modulus.
Gk permanent action.
H altitude of the zone that the IGUs is going to be installed.
h1 nominal thickness of pane 1 of an IGUs.
h2 nominal thickness of pane 2 of an IGUs.
hi nominal thickness of pane “i”.
HP altitude of production of the IGUs unit.
Iz,eff effective moment of inertia about the minor axis.
k1 turbulence factor.
kc,90 factor that takes into account the load configuration, the possibility of splitting and the degree of compressive deformation.
kc,z instability factor.
kcrit factor used for lateral buckling.
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ke edge or hole finishing factor.
ke,p edge or hole pre-stressing factor.
kmod modification factor for timber structures.
kmod modification factor.
kp pre-stressing process factor.
kr terrain factor.
ksp surface profile factor.
L length of the cable.
LLT buckling length.
Mcrl,LT critical moment due to buckling.
n plies number.
Nsd axial force applied.
p0 isochore pressure.
pa air pressure at the installation local.
pC;0 isochore pressure due to changes in the cavity pH;0 isochore pressure due to altitude change
pp pressure at sea level at the time of production of the glass component.
Qk,1 dominant variable action.
Qk,i non-dominant variable actions.
Rv,k shear capacity of the bolts.
s cavity space.
TC temperature of the geographical zone that the IGUs is going to be installed.
TP temperature of production of the IGUs unit.
vb,0 fundamental value of the basic wind velocity.
Vsd shear force imposed in the connection.
z0 roughness length.
z0,II minimum height defined for the zone II.
zmax maximum height, that should be considered 200m.
zmin minimum height.
α angle of the applied load.
α coefficient of thermal expansion.
γG partial factor for permanent actions.
γM coefficient for timber structures.
xxi γM material partial factor.
γP partial factor for pre-stress on the surface.
γQ partial factor for variable actions.
δ1 partition of the exterior pane.
δ2 stiffness partition of the interior pane.
ΔT variation of temperature.
η coupling parameter coefficient.
λ1 size effect.
λA size effect.
ρ density.
σc,0,d design compressive stress along the grain.
σm,d design bending strength.
σp value of pre-stressing.
σsd design value of capacity of the material.
σv standard variation of the turbulence.
ϒs safety factor for steel cables.
Φ insulating unit factor.
Ψ0,1 factors for combination value of the accompanying variable actions.
SLS Serviceability Limit State ULS Ultimate Limit State IGU Insulating Glass Units
1
INTRODUCTION
PREAMBLE
Glass has been used since Roman times, in different appliances: cups, vessels or even windows.
However, it is with the development of the Gothic Style in architectural that professionals start looking at it in other ways. The construction of big panels for the stained-glass windows needed more study and consequently more development on glass technology. Other applications and developments were performed upon the Modernism era, were buildings start to adopt large panels and better thermal and acoustic performances are required. However, comparing to the long history of glass, the use of this material for structural purposes is recent.
This thesis aims to investigate the potential of using glass as a structural element in building construction. The National Museum Soares dos Reis is used as a case study, and the goal is to design a structure that can be incorporated into the existing building. The structure will primarily be made of wood, with glass used as a secondary structural material.
As explained before, the use of glass as a structural element is still relatively new and under-explored, and this thesis aims to contribute to the development of this field by providing a practical example of how glass can be used in a real-world building.
This work was developed in partnership with the Politecnico di Torino (PoliTO), through the ERASMUS+ Traineeship program, through the Professor Mauro Corrado. It also had the consultancy of the Università di Pisa (UniPI), through the Professor Francesco Laccone.
OBJECTIVE AND METHODOLOGY
The objective of this work is to design a structure, using timber as a primary structural element and glass as a second one, that covers the existing patio on the National Museum Soares dos Reis.
The design starts with the conception phase, where a 3D model of the building was created using SketchUp. After this, several proposals are analysed in order to obtain a final product that can fulfil the requirements stipulated. Simultaneously, a verification of the loads that the bearing walls is performed in order to study the possibility of the new structure could or not be partially supported on the granite load-bearing walls of the building.
The design proceeds to the verification of the structure, for both the Serviceability Limit State and the Ultimate Limit State. The different loads that the structure will be subject to (self-weight, maintenance and wind) are computed and combined, according to the current standards. Using two numerical
2
modelling software (SJ Mepla and Autodesk Robot), all the elements are verified and changed, if needed.
Next, the connections between the elements involving are designed and at the end, the capacity of the walls is verified for the loads imposed by the new patio structure.
OVERVIEW
This document is organised in seven chapters, following the next format:
Chapter 2, Literature Review in Terms of “Structural Glass”, presents an overview of the use of glass as a structural material. The architectural context of this material is explored, and also its structural behaviour and abilities. Also, an introduction to the standards is presented.
Chapter 3, Design of Glass and Timber Structures, describes the guidelines defined by the current standards that have to be taken into account upon the design of these elements.
Chapter 4, Case Study, explains the case study chosen for the execution of this work and presents the results of the inspection and diagnosis performed to the building.
Chapter 5 and 6, Conception and Design, describe the several stages taken to the result of the structure, explaining in detail the conditions adopted and the decisions taken.
At last, Chapter 7, Final Conclusions, presents the final structure inserted on the already existing building and a reflection of the necessary adds in order to turn it into a real project.
Additionally, the document also includes three annexes that presents the necessary values upon the computation of the design bending strength of glass, some auxiliar compensations that are needed for the application of the effective thickness approach and the results of the damage assessment performed.
3
LITERATURE REVIEW IN TERMS OF “STRUCTURAL GLASS”
Before starting to work with specific materials, it is necessary to understand and study their evolution and uses. This chapter puts glass in the context of architecture, either in the past and present. It’s also given a short view of timber structures.
INTRODUCTION
Glass is arguably the most remarkable material ever discovered by man [1]. It combines high resistance capabilities with contradictory properties: it’s a transparent material and even water, which penetrates almost everything, cannot pass through. On one side is strong and almost unbreakable, but on the other, only one scratch can lead to its failure [2].
The way a material is seen as structural or non-structural has developed through the years. For instance, clay and stone were used as the most common way to support all the loads that a building is under, but now they are not [3]. However, all applications of glass can be seen as structural. A small pane of glass in a traditional frame has to resist wind pressures, thermal variations or even accidental loads. These applications have several guidelines and rules that are known for a long time in the glass industry.
However, when architects and engineers start thinking about the more widespread use of this material, such as large areas of panels and the use in areas that are traditionally reserved for other materials such as roofs, walls, staircases, slabs and columns, this definition is not applied anymore. In this case, the elements are subjected to much higher actions and complex states of stress [4], being referred to structural glass.
HISTORY AND ARCHITECTURAL CONTEXT
Archaeologists believe that the first man-made glass object was produced around 2300BC, in a region that in the present day is located next to Iraq. At the time, the craftsmen blew the high-temperature glass into a mould, which then cooled and got the desired shape [5]. Nevertheless, these first centuries of glass making are not very relevant, because there are a few known finds [6].
The Romans are the civilization that developed glass making in a further way, creating clear glass, similar to the one we know today. There are a lot of findings of vessels and cups used at that time - like the one presented in Figure 2-1 - since they could produce them in large quantities. It was also considered prestigious to have glass windows installed in their homes, such was the complexity to create and install them [7].
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Figure 2-1: Roman cage cup. Collection Staatliche Antikensammlungen1.
Even though the Romans had an important part in the development of the glass industry, and used it in their buildings, Northern European Gothic architecture is seen as the first age of glass architecture.
The Gothic style was born and developed in Paris and lasted from the end of the 12th to the 16th century [1]. It was also in France that the Crown Process for manufacturing glass was invented, in the 14th century. This was the process that could produce the first flat glass panes, which led to notorious developments of the Gothic style.
This process is represented in Figure 2-2and had three main phases: in the first phase, the workers blew a large bubble of glass and rapidly rotated it in a way to create a glass disc, which corresponds to the second phase. In the final phase, this disc was cooled gently. The problem with this method was that it produced small panes - they were cut in squares of 400 x 300mm [2] - and the thickness was very variable [7]. In the present days, this method is still used, but not on large scale. However, this was the main method to produce stained glass at the time.
Figure 2-2: The several phases of the Crown Method2.
Stained glass is arguably one of the most important aspects of Gothic architecture. This term is applied to coloured glass made with metallic oxides as well as painted glass. During the mid of 12th century, the
1 Picture from: ‘Roman glass - Wikipedia’. https://en.wikipedia.org/wiki/Roman_glass (accessed Aug. 25, 2022).
2 Picture from: ‘Glass and Glazing | Roger Mears Architects’. https://www.rmears.co.uk/our-publications/glass-and- glazing/ (accessed Aug. 26, 2022).
5 presence of this type of material was largely increased, and it had a major role in the way the population learned about religion. The windows became illuminated and created visual effects that may have had a greater impact on the words of the priest [8].
Transparency was not important. The openings in the stones were more significant for this job, therefore the window was the illuminator and the book for the illiterate population to read. In these stained-glass panes, the Bible was illustrated in an imponent way, as well as local stories that were worthy to remember. As described previously, the designers had to recreate these stories in very small pane sizes, leading them to create a construction system that could support the demands of large areas that they had to fill. With this, the glass windows became assembled by pieces held together with lead, made and held in place to the stonework through a secondary frame of metal [1].
The Sainte-Chapelle – presented in Figure 2-3 – is an example of this type of construction. 613m2 of stained glass was designed to store the collection of Passion Relics that belonged to king Louis IX, bringing the structural stone for the second plan and illuminating the space with light, colour, and religious images. This building is also a great example of the power that religion had at the time, demonstrating the influence that it had on the royal family, since they were the only ones who had the resources and economical capacity to build something like this [9].
Figure 2-3: The Sainte-Chapelle in Paris, 1243-12483.
Developments in structural engineering made possible the creation of even larger openings for the windows, stimulating the demand for bigger and better panes of glass [7]. With this, the lead frames were rather weak and didn’t allow a large span, so frames were improved and made from natural stone to ensure the stability of these elements.
The technical improvement that changed architecture again occurred in the next centuries, with the creation of the Cylinder Method (see Figure 2-4). Instead of blowing the glass in a shape of a bubble, like in the Crown Process, the workers would create a cylinder that was posteriorly cut open, then heated again and shaped flat, creating larger panes of glass. In the beginning, sizes were similar to the ones
3 Picture from: ‘Ingresso da Sainte-Chapelle e Conciergerie de Paris sem filas’.
https://www.tudosobreparis.com/atividades/ingresso-conciergerie-sainte-chapelle (accessed Aug. 25, 2022).
6
abovementioned, however, in 1750, the Method was improved and could produce sizes up to 1000 x 800mm [2].
Figure 2-4: The Cylinder Method4.
The 19th century invention of the Siemns-Martin Firing Method, which consists in recovering the heat from waste gases, made possible the higher temperatures that are needed to produce better quality glass [7]. Also, the idea of growing plants out of season or away from their natural environments, led to the creation of large glass buildings as homes for these plants, transforming architecture again.
The Crystal Place (see Figure 2-5), in London, is a well-known example of Victorian architecture. In 1850 the Royal Society of Arts launched a competition to discuss a project for a building that could host an international exhibition to celebrate industry. Joseph Paxton presented an idea of a big glass and steel building that had the instant approval of Prince Albert [1]. After a couple of days, a team of Victorian engineers was already working on the project, and after just five months the work was completed [10].
Figure 2-5: The Crystal Palace in London, July 1850-December 1850 (Joseph Paxton). On the left, the exterior view and the garden that surrounded it. On the right, is the interior view5.
4 Picture from: C. Schittich, G. Staib, D. Balkow, M. Schuler, and W. Sobek, Glass Construction Manual. Birkhäuser, 2006.
5 Picture from: ‘The Crystal Palace - Wikipedia’. https://en.wikipedia.org/wiki/The_Crystal_Palace #Construction (accessed Aug. 29, 2022).
7 This building was a masterpiece of engineering. Covering 71 793m2 of ground and measuring 564 x 139mit used around 83 000m2 of glass. The structural elements were prefabricated and mounted on-site, and the reason for the success of the rather fast construction was the repetition of the components. The columns were made from cast iron and had all the same diameter, so all the trusses could have the same length. Walls were made of glass and timber, and the glass worked as a finishing for the building.
Unfortunately, on 30 November 1936, the building had an enormous fire, and it was destroyed, supposedly caused by someone that dropped a cigarette between the gaps in the floorboards. The importance of the Crystal Palace lies not only in the evolution imposed in architecture and engineering, but also in the visitors that attracted [1], since only the Great Exhibition of 1851 attracted personalities like Charles Darwin, Karl Marx, Michael Faraday, and George Eliot [11].
It was at the beginning of the 20th century that occur the development of various flat sheet processes, such as the American Colburn Process. In these, molten glass from the furnace was placed in a thin stream and flattened and cooled between rollers [7]. The next step forward was the Pulling of Glass Method, developed in Belgium. In this process, a steel bar is lowered into a pool of molten glass and then pulled up slowly. This creates a thin molten glass sheet that follows the steel bar, making the material cool with the air and creating, theoretically, unlimited lengths. The outcome was significant:
large windows were used in new construction, which forced the growth of the glass industry [2] and generated one of Modern architecture's most remarkable aspects.
However, in the middle of the 20th century, the rise of fascism in Europe had a crushing effect on European culture. In the decade before the beginning of the war, many great names departed to the United States of America, as life became unbearable for them [1]. Mies van der Rohe is one of these personalities, and stelling in Chicago continued to be one of the pillars of Modern architecture.
The Farnsworth is one of the architect’s most notable works (see Figure 2-6). The house is located in a garden area parallel to the Fox river, and its complexity is not clear at first site. The structure of the building is all on the outside, with a large white slab of concrete supported by steel columns and raised due to the risk of overflow. The slab of the roof is supported by the same columns, and by moving them backwards the architect ensures that they perform better. By having free the corners of the structure, it reinforces the feeling of not being in an enclosed space [12].
Figure 2-6: The Farnsworth in Plano, Illinois, 1945-1951 (Mies van der Rohe). On the right, the front façade of the building. On the left, the detail of the column is mentioned in the above text6.
6 Picture from: ‘Casa Farnsworth - João Morgado - Fotografia de arquitectura | Architectural Photography’.
https://www.joaomorgado.com/pt/reportagens/casa-farnsworth (accessed Aug. 30, 2022).
8
The idea that Mies van der Rohe transmits is that the nature around the house is also inside of it. The glass facades create the feeling of accessibility, and it seems that the limit of the house is the trees instead of the glass walls. In this way, the material is the most important aspect of the building, conducting all the light from outside, inside. The light of a sunny rainy day creates the sensation that the user is in the surrounding space, transforming the interior into the outside environment [12].
It was also around this time that a patent for reinforced glass was registered, marking the beginning of glass as an element that could distribute loads. In the mid of this century Pilkington, a company that specialized in glass making, developed the Float Process, an important way to produce laminated glass [7] - this method is going to be described in depth in this chapter.
Glass has been used more actively as a structural material in recent years. Many research projects have been devoted to the use of glass in structural applications. Engineers are attempting to design load- bearing glass elements by pushing the material's strength boundaries, to potentialize the material by applying it to floors, beams, walls, columns, and roofs.
One example is the Apple Store on the 5th Avenue, in New York. A glass cube serves as the entrance of the store, that is located below the ground level. This structural is seen as the definition of glass structure:
all loads are caried by glass beams, fins, roof, and façade panels. It was first built in 2006, and at the time the glass fins and panels were the largest ever produced in the world. As the research on glass continued, the structure was improved and re-design in 2011. One of the changes made was in the number of panels in the façade, that went from ninety to fifteen. In Figure 2-7 is possible to see these changes [13].
Figure 2-7: The Apple Store, in New Work (TriPyramid). On the left, the structure before the renovation, made in 2011. On the right, the structure after the renovation7.
7 Picture from: ‘Projects | TriPyramid’. https://tripyramid.com/projects/ (accessed Dec. 25, 2022).
9 GLASS BEHAVIOUR
The term “glass pane” refers to a single sheet of glass. A glass pane, depending on the configuration that’s used, generates a glass component (see Figure 2-8). If a glass pane is used by itself, it’s called monolithic glass, and the set of two or more glass plies forms laminated glass. Also, the set of at least two panes of glass, separated by one or more spacers that create an air space between, is called insulating glass unit.
Figure 2-8: Glass components8.
Glass is a homogeneous and isotropic material, that exhibits linear elastic behaviour in both tension and compression, although the compressive strength is much higher than the tensile one. It cannot re- distribute stresses because it lacks yield strength, and the failure is fast and occurs suddenly with no warning signs, i.e., glass has a brittle failure.
When the tensile forces reach to a critical point, the glass element fails, and a macroscopic crack is formed. The propagation of this crack depends on the imposed load, implying that the longer the load is applied, the deeper the crack becomes, and a consequent reduction of the resistant capacity happens.
This means that the capacity is not constant: it depends on the type and duration of the load, on the geometry of the element – different geometries generate different fracture patterns – and on the humidity conditions of the environment [14], [15]. This is also a factor that as to be considered upon the design of glass elements.
Comparing to the design of steel structures, also the attention on glass structures is concentrated on the cross sections with maximum shear forces and bending moments, limiting the internal stresses to the capacity of the material/structural element. However, contrary to steel that has the ability to yield and support deformations and internal forces that go beyond the elastic behaviour of the material, glass has not this ability and its final capacity is controlled by the local material strength. Normally, the stresses are concentrated in the points of connection with other elements, so connection design is also an important part of the process (see Figure 2-9) [7].
Figure 2-9: Graphics of strain/stress for steel and glass9.
8 Picture from: Matthias. Haldimann, Andreas. Luible, and Mauro. Overend, Structural Use of Glass. International Association for Bridge and Structural Engineering, 2008.
9 Picture from: C. O’Regan and Institution of Structural Engineers (Great Britain), Structural Use of Glass in Buildings, Second Edition. 2015.
10
Regardless of how brittle glass is, structures must provide some evidence of rupture to allow for preventive intervention. So, engineers developed the glass laminating technique, which consists in
"gluing" glass piles together through an interlayer. Once a crack forms, it is impossible to stop it from spreading and increasing in size until it fractures. However, if the glass plie is part of a laminated glass, it is connected to another pane of glass that did not fracture and may withstand the imposed loads. The presence of an interlayer is also crucial for safety, since if one or more layers of glass break, the pieces remain bonded to it, reducing the risk of damage from falling glass fragments.
PRODUCTION:FLOAT PROCESS
As mentioned before, many processes are adopted to produce glass with the properties that are intended, and Figure 2-10 presents an overview of these production processes, the processing methods, and the glass products. It’s important to note that all production methods have the same steps: first, the material is melted, at a temperature that is between 1600 to 1800ºC, the second step is the shape, at temperatures between 800 and 1600ºC, and the end the cooling, at temperatures between 100 and 800ºC.
In the same figure as indicated before, marked in a bold rectangular is presented the Float Process. The reason is that this is the most popular primary manufacturing process, since about 90% of today’s flat glass is produced this way [4].
Figure 2-10: Glass production processes, processing methods and glass products10.
The Float Process consists of three main phases: melting, tin bath and annealing at the ther (special oven for glass manufacturing). These phases are presented in Figure 2-11.
10 Picture from: Matthias. Haldimann, Andreas. Luible, and Mauro. Overend, Structural Use of Glass. International Association for Bridge and Structural Engineering, 2008.
11
Figure 2-11: Scheme of the production process for float glass11.
The raw materials – sand, soda ash and limestone – are melted in a furnace that reaches temperatures up to 1550ºC, and this results in a viscous substance designed by molten glass. It is then poured into a tin bath in an inert gas atmosphere. Since tin melts at temperatures higher than the molten glass, the glass floats on top of the bath creating a smooth surface of a constant thickness between 6 to 7mm [4].
In the last stage, glass enters in the ther, which has a system of rollers that gradually cools down the material and gives a glass pane with a constant thickness, which, depending on the final intended product, may vary between 2 and 25mm; reducing the speed of the rollers results in a higher glass thickness and vice versa After annealing, the glass panels are inspected and cut to a typical size of around 3,20m (dimension of the rolling carpet) by 6,00m [2].
Because of this production process, the two faces of glass sheets are not identical, since one face has direct contact with the tin bath and the other with the inert gas atmosphere. The tin has been found to have lower strength and worse behaviour when glued; it can be detected because it glows when exposed to ultraviolet radiation [4].
GLASS TYPES
The process explained before can produce four base glass types. They vary in their bending stress capacity, which is modified by a post-treatment. In an ascending order of strength, they are referred to:
annealed, heat strengthened, fully tempered, and chemically toughened.
2.5.1.ANNEALED GLASS
Annealed glass is the product that comes directly from the Float Process, without any post-treatment – at the end of the tin bath, the glass is slowly cooled. As a result, it’s the type with less bearing capacity, and it may fail due to large temperature differences. It normally breaks into large pieces, which conducts to a good performance in terms of safety and post-breakage behaviour [16].
2.5.2.HEAT STRENGTHENED GLASS
Heat strengthened glass is also known as partially toughened or semi-tempered. It begins is life as annealed glass, but then is reheated and passes through the process of tempering.
11 Picture from: C. O’Regan and Institution of Structural Engineers (Great Britain), Structural Use of Glass in Buildings, Second Edition. 2015.
12
For structural applications, the tempering of glass is the most important process as it is the method to give higher capacity to the elements. The result of this process is the creation of residual stresses inside the glass panes, that keep the regions near the surface in compression and the inside in tension – as shown in Figure 2-12. As long as the exterior forces are low enough to keep cracks on the compressive zone, there is no tensile stress and consequently no crack propagation. This is accomplished by reheating the annealed glass pane and then cooling the glass surfaces faster than the interior. This causes the surface to solidify faster, and as the interior cools, it attempts to shrink. As it does so, the tension in the middle rises and the surfaces compress [4], [7]. The amount of residual stresses inside glass is determined by the rate at which the interior is cooled: more energy is kept inside if the colling is fast, and vice versa.
Figure 2-12: Residual stress profile in heat strengthened glass12.
The fracture pattern is directly influenced by the energy stored inside of the glass. As an example, in Figure 2-13 is possible to visualize the different fracture patterns of the types of glass. The size of glass cracks is directly related to the energy stored inside: higher residual stresses produce lower size of cracks.
Figure 2-13: Comparison of fracture patterns of different types of glass and their how it affects their structural performance13.
12 Picture from: K. C. Datsiou and M. Overend, ‘The strength of aged glass’, Glass Structures and Engineering, vol.
2, no. 2, pp. 105–120, Oct. 2017, doi: 10.1007/s40940-017-0045-6.
13 Picture from: Matthias. Haldimann, Andreas. Luible, and Mauro. Overend, Structural Use of Glass. International Association for Bridge and Structural Engineering, 2008.
13 2.5.3.FULLY TEMPERED GLASS
Fully tempered glass has a higher capacity than heat strengthened glass. This difference is caused by the surface's cooling: using cold air jets, the surface is cooled faster, resulting in higher creep at the inside zone and, as a consequence, higher residual stresses. When the pane is subjected to bending, and because the inside tension zone is smaller, in order for failure to occur, the imposed load must produce a crack that would overcome a much higher compressive zone than in heat strengthened glass. The comparison between the two stress profiles is presented in Figure 2-14. Fully tempered glass is also known as “safety glass”, since its fracture pattern is characterized by small pieces, as showed in Figure 2-13.
Figure 2-14: Stress patterns of different types of glass. From left to right: het strengthened, fully tempered14.
It is normal to assume that stronger glass is a safer option, but this is not always the case. One advantage of heat strengthened glass is that if it does break, it tends to crack into larger pieces and remain in the frame. Fully tempered glass, on the other hand, will break into small pieces to reduce the risk of injury, but it will tend to fall out of the frame. When falling from a height of several meters, even a small piece of glass can cause injuries. So as a result, in these situations heat strengthened is advised rather than fully tempered glass.
It's also important to note that any type of cutting or drilling for connections must be completed previous to the tempering process, as any change in the equilibrium of the residual stresses inside outcomes in an abrupt shattering of the glass [7], [16].
2.5.4.CHEMICALLY TOUGHENED GLASS
Chemically toughened glass is employed on rare occasions, typically in geometries where fully tempered glass cannot be used. The process is distinct from the previous ones by the fact that it doesn't involve thermic treatment, and the residual stress pattern is different. The panes are dipped in an electrolysis bath, which changes the ions on the surface, resulting in higher residual compressive stresses than in other glasses.
2.5.5.INSULATING GLASS UNITS
Insulating Glass Units (IGU’s) are designed to improve the energy efficiency of buildings. These elements consist of two or three panes of glass separated by a spacer, with the panes sealed together to
14 Picture from: C. Schittich, G. Staib, D. Balkow, M. Schuler, and W. Sobek, Glass Construction Manual.
Birkhäuser, 2006.
14
create an airtight cavity. The space between the panes is typically filled with an inert gas, such as argon or krypton, to improve insulation by reducing heat transfer through the glass component.
At first glance, IGU’s appear to be an easy system to implement, given that they are one of the most commonly used solutions in terms of infill panels. They do, however, represent a significant advancement in engineering and architecture.
The way that buildings were illuminated was through natural light or oil lamps since it was the only option. Architecture accomplished this by incorporating large skylights and windows into the spaces, allowing in as much natural light as possible. When electricity was invented near the end of the 19th century, it was a way to change that, but it was too expensive and not a viable option at the time.
So, the solution remained using glass. However, even though glass can be a good insulator, in order to let the light in it had to be so thin that it would lose this capacity. So glass was necessary but was a problem too. As electricity got cheaper and heating or cooling systems were invented, glass started to be less used – its lightning capability was not necessary anymore. But still, people wanted to see the outside and engineers were trying to find a solution.
In 1934, Thermopane developed the first prototype of an insulating glass unit: by doubling the amount of glass, it was possible to keep the light in, while also benefiting from the insulation properties.
Furthermore, installing a cavity with dry air between them proved to be an effective insulation solution [16]. This was one of the factors that changed architecture (see Figure 2-15).
IGU’s can typically go up to three distinctive glass panes, and each one can be composed by laminated glass. It can also contain any type of glass that was previously mentioned.
Figure 2-15: Comparison of buildings before and after IGU’s. On the left, the former Shelton Hotel in New York, 1922-1924 (Arthur Harmon)15. On the right, the Seagram Building in New York, 1956-1957 (Mies var der Rohe)16.
15 Picture from: C. Gray, ‘Mr. Houdini, Your Box Is Ready’, The New Work Times, Mar. 26, 2009.
https://www.nytimes.com/2009/03/29/realestate/29scapes.html (accessed Dec. 11, 2022).
16 Picture from: M. Lamster, ‘A Personal Stamp on the Skyline’, The New York Times, Apr. 03, 2013.
https://www.nytimes.com/2013/04/07/arts/design/building-seagram-phyllis-lamberts-new-architecture-book.html (accessed Dec. 11, 2022).
15 MATERIAL PROPERTIES
The properties of glass are defined in the EN 16612 standard (described in Chapter 2.8), as presented in Table 2-1.
Table 2-1: Mechanical properties of glass.
Properties for glass
Density ρ 2 500 kg/m3
Young’s modulus E 70 GPa
Poisson number μ 0,22
The same standard suggests values of characteristic strengths for the different types of glass presented before – see Table 2-2.
Table 2-2: Characteristic strength of glass types.
Glass type Characteristic
strength [MPa]
Annealed 45
Heat strengthened 70
Thermally toughened 120
CONNECTIONS IN GLASS
Glass design connections are crucial because they contribute significantly to the overall strength and stability of the structure. The connections must be able to transfer loads from one element to the next and resist all structural actions. It also takes a part on the general appearance of the structure: it should be seamless and blend with the elements, creating a cohesive and visually appealing design.
The general approach for dealing with connections between glass and other materials is to avoid direct contact between the two, using softer materials – such as plastic or rubber. This way, the loads or movements are diverted from the glass elements. This also controls the effect of local imperfections, that have an impact on the behaviour of glass [4], [7]. As stated before, normally the stresses are concentrated in the points of connection with other elements, so connection design is also an important part of the process.
Also, during the past years the objective is to maximize transparency when using glass. This is also noticed in connections: from linearly supported glazing (mid 20th century) to the silicone sealants (1970s) and to the bolted supports (1980 and 1990s) – these glass supports are represented in Figure 2-16 [4].
16
Figure 2-16: Common glass supports types17.
The structure that is going to be developed in this work is going to use two methods of connection: the clamp and the bolted one. In Chapter 5.7 these types are going to be explored and explained.
STANDARDS
As the demand for structural elements in glass has risen, some design standards, draft standards, and technical guidelines have already been created. All have the same objective: determine the resistant capacity of a glass element based on its geometrical and environmental conditions, using simple calculations. However, further research and technical work still has to be done, as most of these standards are directed to the analysis of rectangular elements supported at all ends [4].
In Europe, some standards are being used as design guidelines; to avoid an exhaustive overview of all, this subchapter will present the two that are used for this work:
CEN/TS 19100:2021 "Design of glass structures". This technical specification document – the conversion of CEN/TS 19100 into a new Eurocode compatible with the revised 2nd generation Eurocode suite is an ongoing task, and the corresponding EN document is expected to be published by 2025 [17] – is divided into three parts: the first is the basics of design criteria, which presents the requirements for resistance, serviceability, and glass component failure consequences. The second and third part are oriented to the determination of the resistance when an element is under out-of-plane or in-plane loaded glass components, accordingly.
EN 16612:2019 “Glass in building – Determination of the lateral load resistance of glass panes by calculation”. This European standard gives the general guidance for lateral load resistance of linearly supported glazed elements used as infill panels. The standard presented before does not cover the action of cavity pressure variations on Insulating Glass Units.
17 Picture from: Matthias. Haldimann, Andreas. Luible, and Mauro. Overend, Structural Use of Glass. International Association for Bridge and Structural Engineering, 2008.
17
DESIGN OF GLASS AND TIMBER STRUCTURES
In Portugal, wood was regularly used as a structural material century but has recently fallen into disuse. On the other hand, glass has been gaining structural capabilities. This chapter presents the main characteristics of both materials, as an introduction to the structure that will be designed under this thesis.
GLASS AS A STRUCTURAL MATERIAL 3.1.1.DESIGN BENDING STRENGTH OF GLASS
The use of glass as a load-bearing material is relatively recent, so there are many standards that present general methods to compute the bending strength of glass. Each standard defines different methods and research continues in order to find a common ground. Also because of this, the calculations involve more influence of material characteristics and higher safety factors. The next subsections present the design method of the European Standard – CEN/TS 19100-1:2021.
With this, the design value of the strength of glass (fg,d) is given by:
f , = k ∙ k ∙ λ ∙ λ ∙ k ∙f,
γ + k ∙ k , ∙f , − f ,
γ (3.1)
Where:
ke is the edge or hole finishing factor.
ksp is the surface profile factor.
λA is the first factor that takes into account the size effect.
λ1 is the second factor that takes into account the size effect.
kmod is the modification factor.
fg,k is the characteristic bending strength of annealed glass.
γM is the material partial factor.
kp is the pre-stressing process factor.
ke,p is the edge or hole pre-stressing factor.
fb,k is the characteristic value of glass strength after a strengthening treatment.
γP is the partial factor for pre-stress on the surface.
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The explicit method of computation, with all necessary tables, is available on the Annex A of this document.
3.1.2.EFFECTIVE THICKNESS
As stated before, a laminated glass is an element composed by two or more glass plies with one or more polymer interlayers, such as polyvinyl butyral (PVB). The interlayer affects the response of the element because it allows the transfer of shear stresses among the glass plies. So, the evaluation of the amount of connection offered by the interlayer is crucial for the design of laminated glass elements.
These elements' responses, such as beams and panels, can be modelled analytically or numerically, with the glass acting as a linear-elastic material and the interlayer acting as a linear viscoelastic material. To simplify numerical computations, the total thickness of the element can be defined by an effective thickness, which corresponds to the thickness of a monolithic ply with equivalent stress and deflection properties. [18].
The standard CEN/TS 19100-2 provides guidance for the determination of the effective thickness. The effective thickness for deflection calculations (hef,w) should be computed by:
h , = 1
η
∑ h + 12 ∙ ∑ (h ∙ d )+ 1 − η
∑ h
(3.2)
Where:
η is the coupling parameter coefficient. The computations of this parameter are given in Annex B of this document.
hi is the nominal thickness of pane “i”.
n is the plies number.
di is the distance of the mid-pane of the glass ply “i” from the mid-plane of the laminated glass.
Furthermore, the effective thickness of the ply “i” of the laminated pane for stress calculation (hef,σ,i) should be compute by:
h , = 1
2 ∙ η ∙ | |
∑ h + 12 ∙ ∑ (h ∙ d )+ ℎ ℎ ,
(3.3)
All the parameters were defined above.
3.1.3.DESIGN OF INSULATING GLASS UNITS
Safety Coefficients
As mentioned before, the standard to have in count when dealing with IGU’s is the EN 16612:2019, that considers the values for the partial load factors presented in Table 3-1.
