Modeling of Point-Supported Glass Systems 1
Figure 01 - Model Including Dimensions
Figure 02 - Support Reactions - Local Results
Figure 03 - Stresses - Local Results
Figure 04 - Stress Analysis in Span Area
Technical Article
The transparency of glass material should not be missing in any building. In addition to the typical application areas such as windows, this building material is being increasingly used for facades, canopies, or even as a bracing for stairways. Of course, the planning architects often set a very high standard of transparency on fixation of the glass panes. This requires special glass fittings that couple the glass panes.
Background of Design
In addition to the general technical approvals of the individual producers, the design of point‑supported fittings is regulated in DIN 18008 [1]. This German standard specifies two different ways:
- Appendix B - Verification / Validation of finite element models
- Appendix C - Simplified method
Apart from the various design options, there are constructional provisions - especially for plate fittings - specifying the geometrical arrangement on a glass pane or the formation in the edge area.
Output Data for Analysis
Laminated safety glass from heat strengthen float glass 2 × 8 mm:
- Point fixing PH 793 by Glassline GmbH (Approval Z‑70.2‑99 [3])
- Cylindrical head Ø 52 mm
- Drilling Ø 25 mm
- Design load qd = 4.5 kN/m²
Figure 01 - Model Including Dimensions
Modeling in RFEM According to Simplified Method
In the case of the glass pane design according to the simplified method described in DIN 18008, Annex C [1], the pane may be analyzed without the drilling holes. The existing glass fittings are represented by springs. The existing spring stiffness is specified in the technical approval. In our example, it gives the following result:
$$\begin{array}{l}{\mathrm C}_{\mathrm Z,\max}\;=\;\frac1{24,372}\;+\;\frac1{3,015}\;=\;2,683\;\mathrm N/\mathrm{mm}\\{\mathrm C}_{\mathrm Z,\min}\;=\;\frac1{15,386}\;+\;\frac1{1,592}\;=\;1,443\;\mathrm N/\mathrm{mm}\\{\mathrm C}_{\mathrm Z,\mathrm{sel}}\;=\;2,000\;\mathrm N/\mathrm{mm}\\{\mathrm C}_{\mathrm V;\mathrm x,\mathrm y}\;=\;344\;\mathrm N/\mathrm{mm}\end{array}$$Based on these parameters, the following result values are obtained.
Figure 02 - Support Reactions - Local Results
Figure 03 - Stresses - Local Results
By using the formulas and parameters provided by DIN 18008, Annex C [1], all relevant stress ratios can be calculated now.
Stress component FZ
$${\mathrm\sigma}_\mathrm{Fz}\;\;=\;\;\frac{{\mathrm b}_\mathrm{Fz}}{\mathrm d²}\;\cdot\;\frac{\mathrm t_\mathrm{ref}^2}{\mathrm t_\mathrm i^2}\;\cdot\;{\mathrm F}_\mathrm Z\;\cdot\;{\mathrm\delta}_\mathrm Z\;=\;\frac{15.8}{25²}\;\cdot\;\frac{102}{82}\;\cdot\;1,964\;\cdot\;0.5\;=\;38.8\;\mathrm N/\mathrm{mm}²$$Stress component Fres
$$\begin{array}{l}{\mathrm F}_\mathrm{res}\;=\;\sqrt{\mathrm F_\mathrm x^2\;+\;\mathrm F_\mathrm y^2}\;=\;\sqrt{11²\;+\;4²}\;=\;12\;\mathrm N\\{\mathrm\sigma}_{\mathrm F,\mathrm{res}}\;=\;\frac{{\mathrm b}_{\mathrm F,\mathrm{res}}}{\mathrm d²}\;\cdot\;\frac{{\mathrm t}_\mathrm{ref}}{{\mathrm t}_\mathrm i}\;\cdot\;{\mathrm F}_\mathrm{res}\;\cdot\;{\mathrm\delta}_{\mathrm F,\mathrm{res}}\;=\;\frac{3.92}{25²}\;\cdot\;\frac{10}8\;\cdot\;12\;\cdot\;0.5\;=\;0.1\;\mathrm N/\mathrm{mm}²\end{array}$$Stress component Mres
Due to the hinged support about the axes x, y, and z, there is no additional moment Mres.
Stress concentration in the drilling hole area
$${\mathrm\sigma}_\mathrm g\;=\;{\mathrm\sigma}_\mathrm g(3\mathrm d)\;\cdot\;{\mathrm\delta}_\mathrm g\;\cdot\;\mathrm k\;=\;\frac{9.6\;\cdot\;8}{10.8\;\cdot\;1.6}\;=\;11.4\;\mathrm N/\mathrm{mm}^2$$The governing design stress value in the fitting area results then from the sum of the individual components.
$${\mathrm E}_\mathrm d\;=\;38.8\;+\;0.1\;+\;11.4\;=\;50.3\;\mathrm N/\mathrm{mm}^2$$As the final step, the moment in the span must be considered. In this case, the moment has to be determined on a statically defined system.
Figure 04 - Stress Analysis in Span Area
The governing stress in the span area is Ed = 16.5 N/mm².
The allowable stress for laminated safety glass is calculated as
$${\mathrm R}_\mathrm d\;=\;1.1\;\cdot\;\frac{{\mathrm f}_{\mathrm k,\mathrm{TVG}}}{{\mathrm\gamma}_\mathrm M}\;=\;1.1\;\cdot\;\frac{70}{1.5}\;=\;51.3\;\mathrm N/\mathrm{mm}²$$
and thus gives the result of the total design ratio of the glass η = 0.98.
In addition to the general stress analysis performed here, you can perform further additional designs for exact dimensions of the glass pane. For this, you can follow the standard.
Summary
Appendix C of the German standard DIN 18008 provides very simple tools for the design of point‑supported glass fittings. By using the table values, you can very quickly estimate the structural behavior of the glass pane and determine the design ratio. Another possibility is specified in Appendix B of the standard. This design method based on a finite element model will be explained in the next part of this article.
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