Article 2 : Calculation methods for glass panels

Article 2 : Calculation methods for glass panels

Calculation methods for glass panels

déplacement du vitrage sous chargement els

Moving the glazing under load (Service Limit State)

GENERAL

The calculation methods for the design of mechanical elements have evolved significantly in recent decades. It was in the 19th century that Continuum Mechanics (CM) began to develop, and a century later, the theorization of the Finite Element Method (FEM) emerged. The Finite Element Method (FEM) is a numerical technique used to solve engineering and physics problems involving complex structures. The theorization of the Finite Element Method involves defining the mathematical foundations on which this method is based. This theorization, coupled with the continuous improvement of numerical solution methods and the continuous improvement in processor power (Moore’s Law), has brought about a turning point in modern mechanical design methods.

 

Previously, structural calculations were always done by hand using tables (graphical models) and beam formulas from the strength of materials. With modern means and the use of dedicated finite element analysis software, it is now possible to perform calculations on complex geometries and predict mechanical behavior locally and accurately. Just imagine what a structure similar to the Eiffel Tower could look like today with modern resources! With more precise calculation models, it is possible, for example, to refine the behavior of glass in support zones, contact zones, drilling zones, and accurately determine stress levels in the glass and fixings. When well-mastered, these new techniques are very interesting as they reduce the number of assumptions and, ultimately, limit overdesign of structures and glass thicknesses.

The calculation methods for the design of mechanical elements have evolved significantly in recent decades. It was in the 19th century that Continuum Mechanics (CM) began to develop, and a century later, the theorization of the Finite Element Method (FEM) emerged. The Finite Element Method (FEM) is a numerical technique used to solve engineering and physics problems involving complex structures. The theorization of the Finite Element Method involves defining the mathematical foundations on which this method is based. This theorization, coupled with the continuous improvement of numerical solution methods and the continuous improvement in processor power (Moore’s Law), has brought about a turning point in modern mechanical design methods.

 

Previously, structural calculations were always done by hand using tables (graphical models) and beam formulas from the strength of materials. With modern means and the use of dedicated finite element analysis software, it is now possible to perform calculations on complex geometries and predict mechanical behavior locally and accurately. Just imagine what a structure similar to the Eiffel Tower could look like today with modern resources! With more precise calculation models, it is possible, for example, to refine the behavior of glass in support zones, contact zones, drilling zones, and accurately determine stress levels in the glass and fixings. When well-mastered, these new techniques are very interesting as they reduce the number of assumptions and, ultimately, limit overdesign of structures and glass thicknesses.

mascotte article be site web v2
mascotte article be site web v2

In general, the calculation methods for sizing glass panels are carried out using software that employs advanced mathematical models. It is possible to predict the movements of glass panels on facades and calculate their mechanical stresses. These calculations enable the optimization of structures and glass panels for top-notch projects!

In general, the calculation methods for sizing glass panels are carried out using software that employs advanced mathematical models. It is possible to predict the movements of glass panels on facades and calculate their mechanical stresses. These calculations enable the optimization of structures and glass panels for top-notch projects!

CALCULATION OF AN ATTACHED EXTERIOR GLAZING (AEG)

The commonly used method for sizing and predicting the strength of glass supported on one or two sides is to employ a beam bending model.

image tableau1 formulaire de poutre en flexion

Table 1: Bending beam form from strength of materials formulae

CALCULATION OF AN ATTACHED EXTERIOR GLAZING (AEG)

The commonly used method for sizing and predicting the strength of glass supported on one or two sides is to employ a beam bending model.

image tableau1 formulaire de poutre en flexion

Table 1: Bending beam form from strength of materials formulae

However, verifying an attached exterior glazing requires very specific assumptions, especially for assessing stress in the glass at support points. The assumption of a beam bending model is much less suitable for glass supported by fixing points. In France, tables (calculation models) are used in conjunction with tests to dimension Attached Exterior Glazings (AEGs) in most common cases. Furthermore, for glass with unusual shapes, dimensions, or positions of fixing points, the use of finite element analysis software is recommended.

However, verifying an attached exterior glazing requires very specific assumptions, especially for assessing stress in the glass at support points. The assumption of a beam bending model is much less suitable for glass supported by fixing points. In France, tables (calculation models) are used in conjunction with tests to dimension Attached Exterior Glazings (AEGs) in most common cases. Furthermore, for glass with unusual shapes, dimensions, or positions of fixing points, the use of finite element analysis software is recommended.

Using finite element analysis software:
The method involves taking a computer-drawn model, discretizing (numerically dividing) the panel into small elements, commonly known as meshing operation, and applying the desired support and loading conditions. Subsequently, the software solves the equilibrium equations (partial differential equations) and stores the results in the form of a table for each small element created during the meshing operation. This allows for recording in a spreadsheet and obtaining the displacements, forces, and stress levels for each small element of the glass.

All of these calculation methods enable us to study the feasibility of projects involving glass railings, cladding, or other glass fixtures. See the example below:

Using finite element analysis software:
The method involves taking a computer-drawn model, discretizing (numerically dividing) the panel into small elements, commonly known as meshing operation, and applying the desired support and loading conditions. Subsequently, the software solves the equilibrium equations (partial differential equations) and stores the results in the form of a table for each small element created during the meshing operation. This allows for recording in a spreadsheet and obtaining the displacements, forces, and stress levels for each small element of the glass.

All of these calculation methods enable us to study the feasibility of projects involving glass railings, cladding, or other glass fixtures. See the example below:

mascotte article be site web v2
mascotte article be site web v2

For the calculation of an Attached Exterior Glazing (AEG), we rely on existing assumptions that stem from previously conducted tests. However, for unusual glass structures or panels, it’s a different story. Specific methods will be employed to analyze each part of the glass in order to calculate the forces acting upon it.

For the calculation of an Attached Exterior Glazing (AEG), we rely on existing assumptions that stem from previously conducted tests. However, for unusual glass structures or panels, it’s a different story. Specific methods will be employed to analyze each part of the glass in order to calculate the forces acting upon it.

EXAMPLE OF ATTACHED EXTERIOR GLAZING CALCULATION

In the following example, we will study the bending stresses in VEA glazing for a very specific configuration. For example: a glass panel is held in place by just 3 fixing points and subjected to a wind pressure of 1000 Pa. The model is drawn in CAD, followed by meshing and the application of fixing points to hold the glass in place (boundary conditions).

In the following example, we will study the bending stresses in VEA glazing for a very specific configuration. For example: a glass panel is held in place by just 3 fixing points and subjected to a wind pressure of 1000 Pa. The model is drawn in CAD, followed by meshing and the application of fixing points to hold the glass in place (boundary conditions).

computer aided design modeling

Computer-Aided Design Modeling

meshing operation

Meshing Operation

application of boundary conditions

Application of Boundary Conditions

The results for glass deformation initially show that they are limited to 15mm. Furthermore, the bending stresses (outside the support zone) are lower than the allowable stresses for the glass (including load and material safety factors). The verification is carried out according to the criteria outlined in CSTB’s document 3574_v2.

The results for glass deformation initially show that they are limited to 15mm. Furthermore, the bending stresses (outside the support zone) are lower than the allowable stresses for the glass (including load and material safety factors). The verification is carried out according to the criteria outlined in CSTB’s document 3574_v2.

glass displacement

Glass Displacement

bending stresses in the glass

Bending Stresses* in the Glass

The dimensions of the glass (height, width, thickness), excluding drilling zones, are suitable for the project. However, it can be observed that localized stresses appear at the drilling locations. A more detailed analysis must therefore be conducted to assess the stresses in these areas.

To analyze the stresses in the glass’s drilling zones, a more detailed modeling of the glass and the contacting parts is performed. The materials, geometry of the parts, and contacts are defined in a precise numerical simulation model to accurately assess the stresses in the glass.

The dimensions of the glass (height, width, thickness), excluding drilling zones, are suitable for the project. However, it can be observed that localized stresses appear at the drilling locations. A more detailed analysis must therefore be conducted to assess the stresses in these areas.

To analyze the stresses in the glass’s drilling zones, a more detailed modeling of the glass and the contacting parts is performed. The materials, geometry of the parts, and contacts are defined in a precise numerical simulation model to accurately assess the stresses in the glass.

All the calculations performed are represented by colors and can be visualized on the image:

figure 1 contraintes principales de tractions
figure 1 contraintes principales de tractions
ingenierie verre

Main tensile stresses displayed at the drilling of an attached external glazing

In some cases, curvature radius tests are conducted on the glass panels to ensure deformation limits of the glass at the attachment points. These tests help verify the maximum allowable local stresses at the attachment points. The following figure illustrates the conductance of curvature radius tests and a comparison of the results obtained through calculations.

In some cases, curvature radius tests are conducted on the glass panels to ensure deformation limits of the glass at the attachment points. These tests help verify the maximum allowable local stresses at the attachment points. The following figure illustrates the conductance of curvature radius tests and a comparison of the results obtained through calculations.

In order to verify the relevance of the calculation models, a test comparison can be carried out to measure the differences between reality and the model. The following picture shows the comparison between tests and calculations:

In order to verify the relevance of the calculation models, a test comparison can be carried out to measure the differences between reality and the model. The following picture shows the comparison between tests and calculations:

verre test
casse verre essai gif anime (1)
verre casse test
test verre blanc
test verre colore

In addition to enabling the reduction of glass thicknesses, stress visualization helps design fittings and supports that are suitable for various projects (glass railings, structural glass, cladding, point fixings, etc.).

In addition to enabling the reduction of glass thicknesses, stress visualization helps design fittings and supports that are suitable for various projects (glass railings, structural glass, cladding, point fixings, etc.).

The visualization of stresses not only makes it possible to reduce the thicknesses of glazing, but also to design the most suitable fixings and supports possible for projects.

The visualization of stresses not only makes it possible to reduce the thicknesses of glazing, but also to design the most suitable fixings and supports possible for projects.

[1] History of strength of materials, Stephen P. Timoshenko, 1953. [2] Cahier 3574_v2, Attached External Glazing (VEA) with a Technical Notice, 2011.

If you would like to learn more about AEG façade design and dimensioning, our technical sales teams are at your disposal.

If you would like to learn more about AEG façade design and dimensioning, our technical sales teams are at your disposal.

ARCHICREE publication: Curtain up

ARCHICREE publication: Curtain up

Dear customers,

SADEV has been featured in the latest edition of the prestigious magazine ARCHI CREE.

The theme: Variance P, curtains up soon for SADEV’s latest innovation, the brand-new glass facade fixing system. This innovative technology offers solutions for VEA (Structurally Glazed Systems) with invisible fixings, creating glass facades that are both elegant and secure.

Stay tuned to our news page for more details about Variance P and other exciting upcoming projects. We are looking forward to sharing this adventure with you and continuing to shape the future of architecture together.

Read the article

The SADEV Team

Variance P – The new glass cladding solution

Variance P – The new glass cladding solution

A revolutionary glass cladding system

Discover the new glass cladding solution – Variance P

In the construction industry, glass cladding has become a popular trend for modern commercial and residential buildings. Owners and architects are constantly seeking innovative solutions to enhance the aesthetics of their building while meeting requirements for energy efficiency and durability. This is where the new product “Variance P” comes in.

Variance P is a glass cladding system designed to meet the highest aesthetic and functional requirements. This product uses tempered laminated glass, tempered monolithic glass, or photovoltaic glass panels that are connected together using invisible fixings. The innovative fixing system allows for easy and fast installation while providing maximum wind stability and resistance.

One of the most notable advantages of Variance P is its adaptability to all shapes and sizes of buildings. The system conforms to all shapes and inclinations of walls. Glass panels can be customized according to the customer’s needs in terms of color, texture, and transparency.

In addition to its aesthetic aspect, Variance P also offers functional benefits such as:

  • Ecological aspect: you have the possibility to fix photovoltaic panels and have thermal and acoustic insulation.
  • Minimalist appearance: the fixings are invisible once the glass is installed.
  • Customisable aspect: the glass can be customised to create unique facades.
Article 1 : Thermal expansion of facades with point fixed glazing system

Article 1 : Thermal expansion of facades with point fixed glazing system

Thermal expansion of facades with point fixed glazing system

Introduction:

In the field of construction, various climatic phenomena act throughout the life of facades with point fixed glazing system, which are directly exposed to the wind, snow, seismic events, and the effect of temperature variations. The expansion of different materials composing a facade can cause significant disorders if not taken into account early in the design stage. Therefore, it is essential to consider the effects of temperature during the design and sizing of a building facade. The temperature can change during the same day, and there can be significant differences between day and night. The temperature can also generally vary considerably from one season to another. The temperature range during the life of a facade is typically considered to fluctuate between -40°C and +60°C, representing a delta of 100°C.

dilatation verre gif anime

Different materials that make up a glazed facade have varying thermal expansion coefficients (*). Table 1: Some common values of thermal expansion [2

tableau article 6 couleurs

      ∆L= ∝L0 ∆T

 

  • ∆L  is the variation in length in metres [m]
  •  ∝  is the coefficient of linear expansion in Kelvin at power -1 [K-1]
  • L0  is the initial length of the element in metres [m]
  • ∆T  is the temperature change in Kelvin [K] or degrees Celsius [°C].

COMPATIBILITY OF DEFORMATION:

Facades with point fixed glazing system are often held by stainless steel fasteners, which themselves are supported by a steel or aluminum frame. Due to the different types of materials used, each element has different elongations due to thermal stresses. Given the fragile nature of glass, the glass panels of exterior point fixed glazing system are designed to be completely free of movement in their plane without constraints. These movements are allowed by functional clearances. Generally, the glass is suspended on two upper points, aiming to avoid phenomena of glass panel buckling (bending of the glass under its weight). The devices that allow functional clearance are the fixed, dilating, and free points provided in the attachments. All fastening points support forces perpendicular to the glass (wind direction for a facade glazing; weight, snow, and wind direction for a roof glazing). The fixed point fixes the panel in the plane of the glass. The dilating point fixes the panel in the vertical direction. Finally, the free points only support the loads normal to the panels.

The devices allowing functional clearances are the free and expanding points provided in the fasteners

image article 6 figure 1

All fixing points take up the forces in the direction perpendicular to the glazing (wind direction for a façade glazing; direction of weight, snow and wind for a glazed roof). The fixed point fixes the pane in the plane of the glass. The expansion point fixes the pane in the vertical direction. Finally, the free points only take up the loads normal to the panels. In practice, it is up to each design office to plan the position of the functional clearances adapted to the project, and to ensure that the dimensions of the functional clearances are in line with the climatic loads of the project.

In summary, temperature is a key factor to consider during the design and sizing of glass facades in buildings. The different materials that make up a facade have varying thermal expansion coefficients, which can cause significant disorders if not taken into account. To prevent buckling phenomena, glass panels are designed to be completely free of movement in their plane, thanks to the use of dilating and free points in the attachments. This allows for functional clearance to manage the different deformations caused by thermal stresses.

[1] Façades légères en détail, 2nd edition, Pierre Martin, 2017. [2] Cahier 3574_v2, Attached External Glazing (AEG) with Technical Opinion, 2011.

Visit us at BAU 2023

Visit us at BAU 2023

We are excited to be part of the world’s leading trade fair for Architecture, Materials and Systems in Munich this year.

From 17 to 22 April, our team will showcase our latest innovations in balustrades for buildings and glass industries.
Visit us at booth 520 in hall C3 at Trade Fair Center Messe Münchento see how our solutions increase the performance of your installations.

We look forward to seeing you!

Get your ticket here

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