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Dipl.-Ing. (FH) Ulrich Lex

2018-07-11

Influence of Line Load on an Insulated Glass Pane

The proportion of glass used 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 planning. One such example is ceiling-high glass facades loaded by a handrail. The influence of this loading, as well as the calculation of the deformation, are shown in this article.

Calculation Model

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

Structure

Calculation of Deformation

Due to the enclosed solid of the glass pane interspace, the design of both panes is rather complex. The loading of one pane inevitably also causes 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.

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

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

Calculation of solid under unit load

u_{p, 1} = u_{p, 2} = b \cdot h \cdot \frac{a^{4}}{E \cdot d^{3}} \cdot B_{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{m^{3}}{kN / m^{2}}

Formula 1

u_{q, 1} = b \cdot h \frac{a^{3}}{E \cdot d^{3}} \cdot C_{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{m^{3}}{kN / m}

Formula 2

Calculation of auxiliary quantities

α = α^{} = \frac{u_{p, 1} \cdot p_{a}}{V_{\Pr}} = \frac{0.01145 \cdot 100}{1.0 \cdot 2.0 \cdot 0.016} = 35.78

Formula 3

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Formula 4

{ΔV}_{ex, 1} = u_{q, 1} \cdot q_{1} = 0.00834 \cdot 0.5 = 0.00417 m^{2}

Formula 5

{Δp}_{ex} = \frac{{ΔV}_{ex, 1}}{V_{\Pr}} \cdot p_{a} = \frac{0.00417}{1.0 \cdot 2.0 \cdot 0.016} \cdot 100 = 13.03 \frac{kN}{m^{2}}

Formula 6

Pressure in the glass pane interspace

Δp = φ \cdot ({Δp}_{ex} {Δp}_{c}) = 0.0138 \cdot (13.03 0) = 0.180 \frac{kN}{m^{2}}

Formula 7

It is now possible to determine the deflection in the mid-span from these values.

From the distributed load

f = \frac{q \cdot a^{3}}{E \cdot d^{3}} \cdot C_{f} = \frac{0.5 \cdot 1 . 0^{3}}{7 \cdot 10^{7} \cdot 0 . 005^{3}} \cdot 0.1045 = 0.006 m

Formula 8

as well as from the internal load

f = \frac{Δp \cdot a^{4}}{E \cdot d^{3}} \cdot B_{f} = \frac{0.180 \cdot 1 . 0^{4}}{7 \cdot 10^{7} \cdot 0 . 005^{3}} \cdot 0.1151 = 0.0022 m

Formula 9

comes 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: u_z = 3.5 mm. Small differences occur because the calculation formulas are linearized, and the program calculates according to the Large Deformation Theory and uses an approach of membrane load-bearing capacity.

Results Deformation Pane 1

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 already been calculated with u_z = 2.2 mm.

Results Deformation Pane 2

Conclusion

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 design engineer good support and facilitation.

Author

Mr. Lex is responsible for developing products for glass structures and for quality assurance of the RFEM program. He also provides technical support for our customers.

Links

Structural Analysis and Design Software for Glass Structures

References

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

Downloads

RFEM Model File

2.47 MB

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