Modeling of Point-Supported Glass Systems 1

Technical Article

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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.

Basis of design

In addition to the general technical approvals of the individual manufacturers to be advised, the design of point-supported supports is regulated in DIN 18008 [1] . The standard basically lists two different options:

  • Appendix B - Verification/Validation of Finite Element Models
  • Appendix C - Simplified Procedure

In addition to the various design options, design measures such as the geometric arrangement on the glass pane or the design in the edge area have to be observed especially for the use of plate holders.

Used initial data of the analysis

Laminated safety glass made of TVG 2 x 8 mm
Point holder PH 793 of Glassline GmbH (approval Z-70.2-99 [3] ), plate Ø 52 mm, bore Ø 25 mm
Design load q d = 4.5 kN/m²

Figure 01 - 1 - Model Including Dimensions

Modeling in RFEM according to the simplified system

When designing the glass pane according to the simplified system of DIN 18008 Annex C [1], the pane may be viewed without its boreholes. The existing punk brackets are represented by springs. The existing spring stiffness is given in the approval and results in our example:

C Z, max = 1/24.372 + 1/3.015 = 2.683 N/mm
C Z, min = 1/15,386 + 1/1,592 = 1,443 N/mm
C Z, wt = 2,000 N/mm
C V; x, y = 344 N/mm

Based on the mentioned parameters, the following result values are calculated.

Figure 02 - 2 - Support Reactions - Local Results

Figure 03 - 3 - Stresses - Local Results

Using the formulas and parameters of DIN 18008 Annex C [1], all relevant stress components can now be calculated.

Stress component F Z :
$${\mathrm\sigma}_\mathrm{Fz}\;\;=\;\;\frac{{\mathrm b}_\mathrm{Fz}}{\mathrm d²}\;\cdot\;\frac{\mathrm t_\mathrm{ref}^2}{\mathrm t_\mathrm i^2}\;\cdot\;{\mathrm F}_\mathrm Z\;\cdot\;{\mathrm\delta}_\mathrm Z\;=\;\frac{15,8}{25²}\;\cdot\;\frac{102}{82}\;\cdot\;1.964\;\cdot\;0,5\;=\;38,8\;\mathrm N/\mathrm{mm}²$$

Stress component F res :
$$ \ begin {array} {l} {\ mathrm F} _ \ mathrm {res} \; = \; \ sqrt {\ mathrm F_ \ mathrm x ^ 2 \; + \; \ mathrm F_ \ mathrm y ^ 2 } \; = \; \ sqrt {11² \; + \; 4²} \; = \; 12 \; \ mathrm N \\ {\ mathrm \ sigma} _ {\ mathrm F, \ mathrm {res}} \; = \; \ frac {{\ mathrm b} _ {\ mathrm F, \ mathrm {res}}} {\ mathrm d²} \; \ cdot \; \ frac {{\ mathrm t} _ \ mathrm {ref}} {{\ mathrm t} _ \ mathrm i} \; \ cdot \; {\ mathrm F} _ \ mathrm {res} \; \ cdot \; {\ mathrm \ delta} _ {\ mathrm F, \ mathrm {res }} \; = \; \ frac {3.92} {25²} \; \ cdot \; \ frac {10} 8 \; \ cdot \; 12 \; \ cdot \; 0.5 \; = \; 0.1 \; \ mathrm N/\ mathrm {mm} ² \ end {array} $$

Stress component M res :
Due to hinged support about the axes x, y and z, no additional moment M res is generated.

Stress concentration in the borehole area:
σ g = σ g (3d) ∙ δ g ∙ k = 9.6 ∙ 8/10.8 ∙ 1.6 = 11.4 N/mm²

The governing design value for the area of the point supports is further calculated from the sum of the individual components.
E d = 38.8 + 0.1 + 11.4 = 50.3 N/mm²

As a final step, we have to consider the field moment. In this case, the moment must be determined on a statically determined system.

Figure 04 - 4 - Stress Analysis in Span Area

The governing loading of the system in the field zone results in E d = 16.5 N/mm².

The allowable loading for laminated safety glass is calculated
$$ {\ mathrm R} _ \ mathrm d \; = \; 1.1 \; \ cdot \; \ frac {{\ mathrm f} _ {\ mathrm k, \ mathrm {TVG}}} {{\ mathrm \ gamma} _ \ mathrm M} \; = \; 1.1 \; \ cdot \; \ frac {70} {1.5} \; = \; 51.3 \; \ mathrm N/\ mathrm {mm } ² $$
and thus a total utilization ratio of the plate of η = 0.98.

In addition to the pure stress analysis described here, further supplementary designs for the exact dimensioning of the pane must be performed. For further information, reference is made to the standard.

Conclusion and Outlook

Annex C of Standard 18008 provides very simple tools for designing punctual supports of glass panes. By using the table values, it is possible to quickly estimate the structural behavior and to determine the structural utilization. Another possibility is given in Annex B of the standard. This design and analysis using a finite element model is shown in the next part of this article.

Literature

[1]   DIN 18008-3: 2013-07
[2]  Weller, B .; Engelmann, M .; Nicklisch, F .; Weimar, T .: Glass Construction Practice: Construction and Design Volume 2: Examples according to DIN 18008, 3rd edition. Berlin: Beuth, 2013
[3]  General Technical Approval Z-70.2-99 of the 4th September 2014

Keywords

Point holder Modeling Point Holders

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