# 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 glass pane with a height of h = 1,600 mm and a width of b = 400 mm is examined. The pane is supported by restrained supports on four sides for the horizontal loads as well as by singular supports for the vertical loads. The insulated glass pane with double glazing consists of two edge panes of 3.0 mm each, and a space between panes of 16.0 mm. The examined effect is considered as the “Summer” climatic load case in compliance with DIN 18008‑1 [1].

#### Check of Resulting Gas Pressure

The relationship between the deformation and the resulting pressure in the space between panes can be determined using the general gas equation.

$$\frac{{\mathrm t}_1\;\cdot\;{\mathrm V}_1}{{\mathrm T}_1}\;=\;\frac{{\mathrm t}_2\;\cdot\;{\mathrm V}_2}{{\mathrm T}_2}$$Due to the deformations calculated in the finite element analysis, there is a change in the gas volume. If these are applied to the system, the following values are obtained:

Load case 2 | temperature difference: | ΔV = 645.13 cm³ |

Load case 3 | atmospheric pressure difference: | ΔV = 186.99 cm³ |

Load case 4 | local altitude difference: | ΔV = 704.16 cm³ |

Figure 02 - Deformed Structures

Using the initial volume and the temperature change, we can now calculate the resulting gas pressure. The following values are used:

Thus, the following results are obtained:

Load case 2 | p2 = 103.53 kN/m² |

Load case 3 | p2 = 101.15 kN/m² |

Load case 4 | p2 = 96.37 kN/m² |

In comparison with the FE analysis performed in RFEM, this gives exactly the same values.

#### Check Using Applied Surface Load

When comparing the applied load on the entire system with a surface system, the most difficult thing is to convert the surface load to be applied according to DIN 18008‑1 to the surface system. However, such cases are documented in technical literature (in [2], for example), so you can always find help there.

Based on the dimensions of the glass pane and the glass layer structure, the insulating glass factor is calculated. Thus, you can determine the load distribution in both panes.

The following parameters are taken into account:

$$\begin{array}{l}\frac{\mathrm a}{\mathrm b}\;=\;0.25\\{\mathrm B}_\mathrm V\;=\;0.07215\\\mathrm a^\ast\;=\;28.9\;\cdot\;\;\sqrt[4]{\frac{{\mathrm d}_\mathrm{SZR}\;\cdot\;\mathrm d_\mathrm a^3\;\cdot\;\mathrm d_\mathrm i^3}{\left(\mathrm d_\mathrm a^3\;+\;\mathrm d_\mathrm i^3\right)\;\cdot\;{\mathrm B}_\mathrm V}}\;=\;213.77\;\mathrm{mm}\\\mathrm\varphi\;=\;\frac1{1\;+\;\left({\displaystyle\frac{\mathrm a}{\mathrm a^\ast}}\right)^4}\;=\;0.0754\end{array}$$*Load Case of Temperature Difference*

In the climatic load case of the temperature difference (summer), a temperature change of 20°C is applied. The internal and external pressures are 1.03 bar. This results in a load of:

$$\mathrm q\;=\;0.34\;\cdot\;\mathrm{ΔT}\;=\;6.8\;\mathrm{kN}/\mathrm m^2$$The resulting load on the single pane is:

$$\mathrm q\;=\;6.8\;\cdot\;0.0754\;=\;0.513\;\mathrm{kN}/\mathrm m^2$$Based on the surface load on the single pane, it is now possible to perform a “manual” design. However, this is not further pursued in this article.

This surface load can be used to determine the relation between the load and the resulting gas pressure:

$${\mathrm p}_{\mathrm{end},\mathrm{in}}\;=\;103.0\;\mathrm{kN}/\mathrm m^2\;+\;0.513\;\mathrm{kN}/\mathrm m^2\;=\;103.513\;\mathrm{kN}/\mathrm m^2$$*Load Case of Atmospheric Pressure Difference*

The atmospheric pressure difference is specified by a pressure difference of 0.02 bar. This results in the following load on the entire system:

$$\mathrm q\;=\;103.0\;-\;101.0\;=\;2.0\;\mathrm{kN}/\mathrm m^2$$The load on a single pane with the same dimensions is therefore:

$$\mathrm q\;=\;2.0\;-\;0.0754\;=\;0.151\;\mathrm{kN}/\mathrm m^2$$The resulting gas pressure in the space between the panes also results from the sum of the final pressure and the applied surface load:

$${\mathrm p}_{\mathrm{end},\mathrm{in}}\;=\;101.0\;\mathrm{kN}/\mathrm m^2\;+\;0.151\;\mathrm{kN}/\mathrm m^2\;=\;101.151\;\mathrm{kN}/\mathrm m^2$$*Load Case of Altitude Difference*

In the load case of the altitude difference, the difference of the local altitude of 600 m is applied by default. The resulting load is thus calculated as follows:

$$\mathrm q\;=\;0.012\;\cdot\;600\;=\;7.2\;\mathrm{kN}/\mathrm m^2$$This is converted to the single system as follows:

$$\mathrm q\;=\;7.2\;\cdot\;0.0754\;=\;0.543\;\mathrm{kN}/\mathrm m²$$Assuming that the atmospheric pressure at the installation site is about 7.2 kN/m² less than at the production site, the resulting gas pressure in the space between the panes can also be calculated as follows:

$${\mathrm p}_{\mathrm{end},\mathrm{in}}\;=\;(103.0\;\mathrm{kN}/\mathrm m^2\;-\;7.2\;\mathrm{kN}/\mathrm m^2)\;+\;0.543\;=\;96.343\;\mathrm{kN}/\mathrm m^2$$Figure 03 - Gas Pressure Resulting from RFEM Calculation

#### Summary

The comparative calculation has shown that the results of the nonlinear FEM calculation are very similar to the calculation using analytical formulas. The described procedure shows a simple verification of the global computer-aided calculation. Furthermore, this article tried to clarify the relations between the loads on the glass pane and the pressure conditions in the space between the panes.

Using the loads calculated above, you can also verify the deformations and stresses. In this case, it should be noted that the computational calculation is usually based on the nonlinear, large deformation analysis where the analytical formulas were developed according to the linear static analysis. Therefore, there might be small differences in the results.

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