# Influence of Line Load on Insulated Glass Pane

### Technical Article

001527

11 July 2018

The proportion of glass when planning a building is increasing. Open, light-flooded buildings represent the modern art of architecture. However, specialized engineers have to face new challenges during their planning. Such an example are ceiling-high glass facades which are loaded by a handrail at the same time. The influence of this loading as well as the calculation of the deformation are shown in this article.

#### Analysis Model

An insulated glass pane with a height of 2 m and a width of 1 m serves as analysis model. The load application of the horizontal load of 0.5 kN amounts to 1.10 m. Insulated glass 5-16-5 has been chosen as pane structure.

#### Deformation Analysis

Due to the enclosed solid of the glass pane interspace, the design of both panes is rather complex. The loading of one pane inevitably causes also a loading of the second pane due to the linked system and therefore a load distribution on both panes. The size of the load distribution depends on the selected pane structure or the stiffness of the single panes.

An FEM software (such as RFEM, RF-GLASS) is usually used to analyze insulated glasses which solves the structural problem. However, in [1], formulas for the analytical view are also shown.

The following values result if the deformations are calculated manually for this example.

Calculation of solid under unit load
${\mathrm u}_{\mathrm p,1}\;=\;{\mathrm u}_{\mathrm p,2}\;=\;\mathrm b\;\cdot\;\mathrm h\;\cdot\;\frac{\mathrm a^4}{\mathrm E\;\cdot\;\mathrm d^3}\;\cdot\;{\mathrm B}_{\mathrm v\;}\;=\;1.0\;\cdot\;2.0\;\cdot\;\frac{1.0^4}{7\;\cdot\;10^7\;\cdot\;0.005^3}\;\cdot\;0.0501\;=\;0.01145\;\frac{\mathrm m^3}{\mathrm{kN}/\mathrm m^2}$
${\mathrm u}_{\mathrm q,1}\;=\;\mathrm b\;\cdot\;\mathrm h\frac{\mathrm a^3}{\mathrm E\;\cdot\;\mathrm d^3}\;\cdot\;{\mathrm C}_{\mathrm v\;}\;=\;1.0\;\cdot\;2.0\;\cdot\;\frac{1.0^3}{7\;\cdot\;10^7\;\cdot\;0.005^3}\;\cdot\;0.0365\;=\;0.00834\;\frac{\mathrm m^3}{\mathrm{kN}/\mathrm m}$

Calculation of auxiliary quantities
$\mathrm\alpha\;=\;\mathrm\alpha^+\;=\;\frac{{\mathrm u}_{\mathrm p,1}\;\cdot\;{\mathrm p}_\mathrm a}{{\mathrm V}_\Pr}\;=\;\frac{0.01145\;\cdot\;100}{1.0\;\cdot\;2.0\;\cdot\;0.016}\;=\;35.78$
$\mathrm\varphi\;=\;\frac1{1\;+\;\mathrm\alpha\;+\;\mathrm\alpha^+}\;=\;\frac1{1\;+\;35.78\;+\;35.78}\;=\;0.0138$
${\mathrm{ΔV}}_{\mathrm{ex},1}\;=\;{\mathrm u}_{\mathrm q,1}\;\cdot\;{\mathrm q}_1\;=\;0.00834\;\cdot\;0.5\;=\;0.00417\;\mathrm m^2$
${\mathrm{Δp}}_\mathrm{ex}\;=\;\frac{{\mathrm{ΔV}}_{\mathrm{ex},1}}{{\mathrm V}_\Pr}\;\cdot\;{\mathrm p}_\mathrm a\;=\;\frac{0.00417}{1.0\;\cdot\;2.0\;\cdot\;0.016}\;\cdot\;100\;=\;13.03\;\frac{\mathrm{kN}}{\mathrm m^2}$

Pressure in the glass pane interspace
$\mathrm{Δp}\;=\;\mathrm\varphi\;\cdot\;\left({\mathrm{Δp}}_\mathrm{ex}\;+\;{\mathrm{Δp}}_\mathrm c\right)\;=\;0.0138\;\cdot\;\left(13.03\;+\;0\right)\;=\;0.180\;\frac{\mathrm{kN}}{\mathrm m^2}$

From these values, it is now possible to determine the deflection in the mid-span.

$\mathrm f\;=\;\frac{\mathrm q\;\cdot\;\mathrm a^3}{\mathrm E\;\cdot\;\mathrm d^3}\;\cdot\;{\mathrm C}_\mathrm f\;=\;\frac{0.5\;\cdot\;1.0^3}{7\;\cdot\;10^7\;\cdot\;0.005^3}\;\cdot\;0.1045\;=\;0.006\;\mathrm m$
as well as from the internal load
$\mathrm f\;=\;\frac{\mathrm{Δp}\;\cdot\;\mathrm a^4}{\mathrm E\;\cdot\;\mathrm d^3}\;\cdot\;{\mathrm B}_\mathrm f\;=\;\frac{0.180\;\cdot\;1.0^4}{7\;\cdot\;10^7\;\cdot\;0.005^3}\;\cdot\;0.1151\;=\;0.0022\;\mathrm m$
results a resulting deformation of the loaded pane of
6.0 mm - 2.2 mm =3.8 mm.

This value corresponds almost exactly to the numerical calculation of RF-GLASS: uz = 3.5 mm. Small differences arise because the calculation formulas are linearized and the program is calculating according to the large deformation analysis as well as with applying a membrane effect.

The secondary loaded pane is deformed by the prevailing gas pressure in the glass pane interspace. Since both panes have the same stiffness, this value has been already calculated with uz = 2.2 mm.

#### Summary

The calculation theory of [1] shows that it is possible to check even linked systems manually. The manual calculation becomes more complex when changing the system, for example when using different pane thicknesses or even VSG on one side of the pane. Computer-supported calculation, for example with RF-GLASS, offers the designing engineer good support and facilitation.

#### Reference

 [1] Feldmeier, F.: Klimabelastung und Lastverteilung bei Mehrscheiben-Isolierglas, Stahlbau 75, Seiten 467 - 478. Berlin: Ernst & Sohn, 2006