# Control of Climatic Load on Insulated Glass Panes of Glass Structures

### Technical Article

Loading panes of insulating glass due to climatic effects are clearly regulated in DIN 18008. In the case of the corresponding pane geometry, this load type can also be governing for the ultimate limit state design. The FE design on the entire structure with the space between panes represented as the volume of a gas provides exact results for the analysis. However, a plausibility check is also becoming more and more important. This article shows various options of how to perform these checks.

#### System basis

A vertical glazing with the dimensions h = 1,600 mm and w = 400 mm is considered. The pane is restrained without restraint, quadrilateral for the horizontal loads and selectively for the vertical loads. The pane structure of double insulating glass consists of two edge panes á 3.0 mm and a space of 16.0 mm. The considered load case is the climatic load case "Summer" of DIN 18008-1 [1] .

#### Check of resulting gas pressure

The relation between deformation and resulting pressure in the SDR can be described by the general gas equation.

$$\frac{{\mathrm t}_1\;\cdot\;{\mathrm V}_1}{{\mathrm T}_1}\;=\;\frac{{\mathrm t}_2\;\cdot\;{\mathrm V}_2}{{\mathrm T}_2}$$

The deformations calculated by means of the FE analysis result in a change of the gas volume. If you evaluate them for the system, the following values result:

• Load case 2, temperature difference: ΔV = 645.13 cm³
• Load Case 3, Atmospheric Pressure Difference: ΔV = 186.99 cm³
• Load case 4, difference in elevation: ΔV = 704.16 cm³

With the help of the initial volume and the temperature change, the resulting gas pressure can now be calculated.
With the values of

• p1 = 103 kN/m²
• V1 = 10,240 cm³
• T1 = 292 K.
• T2 = 312 K (load case 2)
• T2 = T1 = 292 K (load case 3 + 4)

results for

• Load Case 2: p2 = 103.53 kN/m²
• Load Case 3: p2 = 101.15 kN/m²
• Load Case 4: p2 = 96.37 kN/m²

The comparison with the FEM analysis in RFEM results in exactly the same values.

The difficulty of comparing the applied load on the entire system compared to a surface system consists in converting the surface load to be applied according to DIN 18008-1 to a surface system. In the literature, for example [2] , however, these correlations are documented so that you can always access them.

Based on the dimensions of the glass pane and the layer structure, a so-called insulating glass factor is calculated. Thus, you can describe the distribution of the load on the two panes.

The following parameters are considered:

$$\begin{array}{l}\frac{\mathrm a}{\mathrm b}\;=\;0,25\\{\mathrm B}_\mathrm V\;=\;0,07215\\\mathrm a^\ast\;=\;28,9\;\cdot\;\;\sqrt[4]{\frac{{\mathrm d}_\mathrm{SZR}\;\cdot\;\mathrm d_\mathrm a^3\;\cdot\;\mathrm d_\mathrm i^3}{\left(\mathrm d_\mathrm a^3\;+\;\mathrm d_\mathrm i^3\right)\;\cdot\;{\mathrm B}_\mathrm V}}\;=\;213,77\;\mathrm{mm}\\\mathrm\varphi\;=\;\frac1{1\;+\;\left({\displaystyle\frac{\mathrm a}{\mathrm a^\ast}}\right)^4}\;=\;0,0754\end{array}$$

In the climatic load case temperature difference (summer), a temperature change of 20 ° C is applied. The internal and external pressure is assumed to be 1.03 bar. This results in a load of q = 0.34 ∙ ΔT = 6.8 kN/m² as well as a load on a single pane of q = 6.8 ∙ 0.0754 = 0.513 kN/m².

Based on the surface loading on the single pane, it is now possible to perform a "manual" design. However, this is not pursued further here.

p end, in = 103.0 kN/m² + 0.513 kN/m² = 103.513 kN/m²

The atmospheric pressure difference is described by a pressure difference of 0.02 bar. This results in a load of q = 103.0 - 101.0 = 2.0 kN/m² on the entire system. The loading on a single pane of the same dimensions is therefore q = 2.0 ∙ 0.0754 = 0.151 kN/m².

The resulting gas pressure in the SDR also results from the sum of the final pressure and the applied surface loading:
p end, in = 101.0 kN/m² + 0.151 kN/m² = 101.151 kN/m²

In the case of the load difference in altitude, a difference of 600 m is assumed by default. The resulting loading is calculated as follows: q = 0.012 ∙ 600 = 7.2 kN/m². The conversion to the single system is as usual: q = 7.2 ∙ 0.0754 = 0.543 kN/m².

According to the assumption that the air pressure at the installation location is 7.2 kN/m² lower than at the production site, the resulting gas pressure in the SDR can also be calculated from it:
p end, in = (103.0 kN/m² - 7.2 kN/m²) + 0.543 = 96.343 kN/m²

#### Summary

The comparative calculation has shown that the results of the nonlinear FEM calculation are very similar to the analytical formulas. The described procedure shows a way in which the global, computer-aided calculation can be verified in a simple way. Furthermore, an attempt was made to clarify the correlations between the loads on the pulley and the pressure conditions in the SDR.

Using the loads calculated above, it would also be possible to check deformations and stresses in a further calculation. It should be noted that the computer-assisted calculation is usually nonlinear according to Theory III. The analytical formulas have been developed linearly according to the first-order analysis. Small differences in the results are therefore to be expected.

#### Reference

 [1] DIN 18008-1: 2010-12 [2] Albert, A. (Ed.): Schneider - Construction tables for engineers, 22. Edition. Cologne: Federal Gazette, 2016 [3] Feldmeier, F .: Climatic loading and load distribution in multi-pane insulating glass, Stahlbau 75, pages 467 - 478. Berlin: Ernst & Sohn, 2006