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Modelling of Curved Glass Elements - Cold-Bent Glass and Simplified Models

Baradey, Mohamad LU (2025) In TVSM-5000 VSMM01 20251
Structural Mechanics
Department of Construction Sciences
Abstract (Swedish)
Glasarkitektur utvecklas ständigt med ökande krav på estetik, funktionalitet,
och hållbarhet. Användningen av böjda glaselement blir allt vanligare i modern byggnation. Traditionellt tillverkas krökt glas av floatglas som upphettas över glasets transitionstemperatur och formas till önskad krökning. Denna teknik är tids- och energikrävande och därmed relativt kostsam. Av denna anledning används andra mer effektiva alternativ, nämligen kallböjt glas. Det innebär att glaselementen böjs på plats under monteringen utan någon värmebehandling.

Detta examensarbete undersöker modellering och spänningsanalys av kallböjda glaselement, där plana glasrutor elastiskt deformeras över en böjd ramstruktur utan uppvärmning, vilket leder till permanenta... (More)
Glasarkitektur utvecklas ständigt med ökande krav på estetik, funktionalitet,
och hållbarhet. Användningen av böjda glaselement blir allt vanligare i modern byggnation. Traditionellt tillverkas krökt glas av floatglas som upphettas över glasets transitionstemperatur och formas till önskad krökning. Denna teknik är tids- och energikrävande och därmed relativt kostsam. Av denna anledning används andra mer effektiva alternativ, nämligen kallböjt glas. Det innebär att glaselementen böjs på plats under monteringen utan någon värmebehandling.

Detta examensarbete undersöker modellering och spänningsanalys av kallböjda glaselement, där plana glasrutor elastiskt deformeras över en böjd ramstruktur utan uppvärmning, vilket leder till permanenta inre (intrinsiska) spänningar genom hela glaspanelens livslängd. Syftet med arbetet är att utvärdera hur kallböjt glas kan modelleras under dessa böjspänningar och i kombination med yttre laster, såsom vind, med hjälp av förenklade modeller som är praktiskt användbara, samt att identifiera vilka parametrar och villkor som är viktiga och avgörande.

Både monolitiska och laminerade glaspaneler studerades med analytiska metoder, nämnligen Euler-Bernoulli balkteori och Kirchhoff-Love plattteori, och validerades mot detaljerade finita element numeriska simuleringar i Abaqus. Studien fokuserar på glaspaneler med radier mellan 10–20 meter och tjocklekar mellan 6–12 millimeter, typiska för arkitektoniska tillämpningar. Resultaten visar att tunnare plattor och större böjningsradier minskar de inre spänningarna avsevärt. Laminerat glas med tjockare PVB-folier uppvisar förbättrad flexibilitet och lägre maxspänningar tack vare en bättre fördelning av spänningarna.


Studien visar att förenklade modeller kan utvecklas för att förutsäga spänningarna i glas som uppstår vid kallböjning med tillräcklig noggrannhet, särskilt för enkla monolitiska glas med användning av analytiska metoder. Även om de analytiska metoderna tenderar att överskatta spänningarna i laminerade paneler något, är de ändå användbara som konservativa verktyg i de tidiga skedena av konstruktionen, för att t.ex. utföra preliminära analys. Numeriska metoder är dock avgörande för att fånga komplexa effekter såsom kantförhållanden, icke-linjäriteter och en mer exakt PVB beteendet i laminerade strukturer. Rekommendationer för optimal paneltjocklek och mellanskikt-konfigurationer ges, tillsammans med förslag på framtida arbete, inklusive dubbelkrökta och isolerade glaselement.

Principen om superposition av spänningar visade sig vara giltig för glas, som uppvisar elastiskt beteende fram till brott. Numeriskt har det visats att det är möjligt att superponera yttre laster, såsom spänningar orsakade av vind, med kallböjningsspänningar, till exempel genom att simulera en sugkraft i motsatt riktning mot kallböjningen, vilket efterliknar vindens påverkan, och sedan superponera de maximala huvudspänningarna. Utmaningen låg i att approximera vindlaster på en krökt struktur med givna randvillkor i modellen med analytiska metoder, eftersom en förenkling där strukturen antas vara en plan rektangulär ruta med stöd längs alla kanter inte gav samma resultat. Med enkla ord, det är möjligt att superponera kallböjningsspänningar med externa laster, men att hitta en förenklad analytisk metod för att uppskatta de yttre lasterna kvarstår som oklart. (Less)
Abstract
Glass architecture continues to evolve with increasing demands for aesthetics, functionality, and durability. The use of curved glass elements is becoming increasingly common in modern constructions. Traditionally, curved glass is made of float glass that is heated above the glass transition temperature and formed into a curved shape. This technique is time- and energy-intensive, and consequently, relatively expensive. For this reason, other more efficient alternatives can be used, namely cold-bent glass. This means that the glass elements are bent during assembly on site without any heat treatment.

This thesis investigates the modeling and stress analysis of cold-bent glass elements, which involves elastically deforming flat glass... (More)
Glass architecture continues to evolve with increasing demands for aesthetics, functionality, and durability. The use of curved glass elements is becoming increasingly common in modern constructions. Traditionally, curved glass is made of float glass that is heated above the glass transition temperature and formed into a curved shape. This technique is time- and energy-intensive, and consequently, relatively expensive. For this reason, other more efficient alternatives can be used, namely cold-bent glass. This means that the glass elements are bent during assembly on site without any heat treatment.

This thesis investigates the modeling and stress analysis of cold-bent glass elements, which involves elastically deforming flat glass panels on a curved frame substructure without heat, resulting in permanent intrinsic stresses throughout the panel’s service life. The aim of this work is to evaluate how cold-bent glass can be modeled under intrinsic bending stresses and in combination with external loads, such as wind, using simplified models suitable for practical use, and to work out which parameters and conditions are crucial.

Both monolithic and laminated glass panels were studied using analytical methods (Euler-Bernoulli beam and Kirchhoff-Love plate theory) and validated against detailed finite element numerical simulations in Abaqus. The study focuses on glass panels with radii between 10–20 meters, and thicknesses between 6-12 millimeters, typical of architectural applications. The results show that thinner plates and larger bending radii significantly reduce internal stresses. Laminated glass with thicker PVB interlayers exhibits improved flexibility and lower peak stresses due to better strain distribution.

The study finds that simplified models can be developed to predict the stresses in glass induced by cold bending while maintaining sufficient accuracy using analytical methods, especially for simple monolithic glass, and although analytical methods have tended to slightly overpredict stresses for laminated panels, they still provide a conservative and useful tool for early design stages. Numerical methods remain essential for capturing complex effects such as edge constraints, nonlinearities, and complex interlayer behavior. Recommendations for optimal panel thickness and interlayer configurations are provided, along with suggestions for future work, including double-curved and insulated glass units.

The principle of stress superposition is found to be approximately valid for glass, which behaves elastically up to failure. Numerically, it has been shown that it is possible to superpose external loads such as stresses induced by wind with cold bending stresses by, for example, simulating a suction load in a direction opposite to the direction of the cold bending, resembling the behavior to that of wind, and then superposing the maximum principal stresses. The challenge was to approximate the wind loads on a curved structure with given constraints from the model using analytical methods, as simplifying the model by assuming it is a flat, rectangular pane and supported on all edges, did not give the same results. In short, it is possible to superpose cold bending stresses with external load stresses, but finding a simplified analytical method to approximate the external load stresses remains unclear. (Less)
Popular Abstract (Swedish)
Glasarkitektur utvecklas ständigt med ökande krav på estetik, funktionalitet och hållbarhet. Användningen av böjda glaselement blir allt vanligare i modern byggnation. Traditionellt tillverkas krökt glas av floatglas som upphettas över glasets transitionstemperatur och formas till önskad krökning. Denna teknik är tids- och energikrävande och därmed relativt kostsam. Av denna anledning används andra mer effektiva alternativ, nämligen kallböjt glas. Det innebär att glaselementen böjs på plats under monteringen utan värmebehandling.
Please use this url to cite or link to this publication:
author
Baradey, Mohamad LU
supervisor
organization
alternative title
Modellering av bågformade glaselement - Kallböjda glas och förenklade modeller
course
VSMM01 20251
year
type
H3 - Professional qualifications (4 Years - )
subject
keywords
Glass, Cold-bent glass, Curved glass elements, Simplified models, Structural glass engineering, Stress analysis, Finite Element Analysis, Abaqus simulation, Analytical modeling, Laminated safety glass, Monolithic glass, Glass deformation, Single curved glass, Structural mechanics, Glass treatments, Tempered glass, Glass bending, Euler-Bernoulli theory, Kirchhoff-Love theory, Principal stress, Glass in architecture, Wind load on glazing, Polyvinyl butyral (PVB), Properties of glass, Hot-bent glass, Glass effective thickness, Eurocode, Glass curvature
publication/series
TVSM-5000
report number
TVSM-5280
ISSN
0281-6679
language
English
id
9208876
date added to LUP
2025-08-01 14:04:42
date last changed
2025-08-01 14:04:42
@misc{9208876,
  abstract     = {{Glass architecture continues to evolve with increasing demands for aesthetics, functionality, and durability. The use of curved glass elements is becoming increasingly common in modern constructions. Traditionally, curved glass is made of float glass that is heated above the glass transition temperature and formed into a curved shape. This technique is time- and energy-intensive, and consequently, relatively expensive. For this reason, other more efficient alternatives can be used, namely cold-bent glass. This means that the glass elements are bent during assembly on site without any heat treatment. 

This thesis investigates the modeling and stress analysis of cold-bent glass elements, which involves elastically deforming flat glass panels on a curved frame substructure without heat, resulting in permanent intrinsic stresses throughout the panel’s service life. The aim of this work is to evaluate how cold-bent glass can be modeled under intrinsic bending stresses and in combination with external loads, such as wind, using simplified models suitable for practical use, and to work out which parameters and conditions are crucial.

Both monolithic and laminated glass panels were studied using analytical methods (Euler-Bernoulli beam and Kirchhoff-Love plate theory) and validated against detailed finite element numerical simulations in Abaqus. The study focuses on glass panels with radii between 10–20 meters, and thicknesses between 6-12 millimeters, typical of architectural applications. The results show that thinner plates and larger bending radii significantly reduce internal stresses. Laminated glass with thicker PVB interlayers exhibits improved flexibility and lower peak stresses due to better strain distribution.

The study finds that simplified models can be developed to predict the stresses in glass induced by cold bending while maintaining sufficient accuracy using analytical methods, especially for simple monolithic glass, and although analytical methods have tended to slightly overpredict stresses for laminated panels, they still provide a conservative and useful tool for early design stages. Numerical methods remain essential for capturing complex effects such as edge constraints, nonlinearities, and complex interlayer behavior. Recommendations for optimal panel thickness and interlayer configurations are provided, along with suggestions for future work, including double-curved and insulated glass units.

The principle of stress superposition is found to be approximately valid for glass, which behaves elastically up to failure. Numerically, it has been shown that it is possible to superpose external loads such as stresses induced by wind with cold bending stresses by, for example, simulating a suction load in a direction opposite to the direction of the cold bending, resembling the behavior to that of wind, and then superposing the maximum principal stresses. The challenge was to approximate the wind loads on a curved structure with given constraints from the model using analytical methods, as simplifying the model by assuming it is a flat, rectangular pane and supported on all edges, did not give the same results. In short, it is possible to superpose cold bending stresses with external load stresses, but finding a simplified analytical method to approximate the external load stresses remains unclear.}},
  author       = {{Baradey, Mohamad}},
  issn         = {{0281-6679}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{TVSM-5000}},
  title        = {{Modelling of Curved Glass Elements - Cold-Bent Glass and Simplified Models}},
  year         = {{2025}},
}