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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

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Knowledge Base Articles

Different glass types and layer structures are available for glass structures used for different purposes. The following types are usually used: float glass, partly tempered glass, and toughened safety glass.

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 govern 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 increasingly important. This article shows various options for performing these checks.

As mentioned in Part 1, according to the current standard DIN 18008-3, it is allowed in glass construction to represent point supports for glass components by means of FEM in order to design the adequate ultimate limit state. The rules are described in Annex B of the standard [1].

Product Features

The global calculation assigns the stiffness determined by means of the selected composition and the glass geometry to each surface. Then, the calculation proceeds using the plate theory. It is possible to select whether the shear coupling of layers should be considered.

In the case of the local calculation, you can further specify 2D or 3D calculation. Two-dimensional calculation means that the single-layer or laminated glass is modeled as a surface, whose thickness is calculated on the basis of the selected structure and glass geometry (using the plate theory). Similarly to the global calculation, you can optionally consider shear coupling of layers.

The 3D calculation uses solids in the model to substitute each composition layer. This way, the results are more accurate, but the calculation may take more time.

It is possible to model insulating glass only if local calculation is selected. The gas layer is always modeled as a solid element, so it is necessary to design individual insulating glass parts independently of the surrounding structure. The ideal gas law (thermal equation of state of ideal gases) is considered for the calculation and the third-order analysis.

In the add-on module, select the surfaces to be designed (for example, by using the Select function). The geometry of the glass pane, as well as the loads, is imported from the RFEM model.

Then, you have to decide if the calculation should be performed without the influence of the surrounding structure (local calculation) or with consideration of this influence (global calculation). If you select the local calculation, each surface selected for the design is detached from the model and calculated separately.

The global calculation considers the entire structure, including entered glass panes. All glass composition data and glass properties of individual layers are to be defined in RF-GLASS input windows. You can select layers of type glass, foil, and gas. The desired material can be imported directly from the library, which contains a large number of materials.

All parameters of individual layers, including their thicknesses, are editable. In addition, you can create a number of compositions in RF-GLASS, allowing you to design different types of glass together.

For insulating glass, you can consider external loads as well as loads due to temperature, atmospheric pressure, and altitude changes for the analysis. The module calculates these loads automatically on the basis of climatic load parameters. If you select the local calculation type, it is necessary to define line supports, nodal supports, and boundary members of the surfaces in RF-GLASS. These supports and members are considered in RF-GLASS only and have no influence on the model created in RFEM.

After the calculation, the results are displayed in clearly arranged result windows. Thus, you can easily find the maximum stress ratio. The stress diagram by composition is displayed as well.

Furthermore, RF-GLASS displays a parts list and, for insulating glass, the gas pressure. It is possible to display the results graphically in the RFEM model.

Both input and result tables of RF-GLASS, including graphics, can be added to the RFEM printout report. In addition, it is possible to export all tables to MS Excel.

RF-GLASS Add-on Module for RFEM | Analysis and Design of Glass Surfaces

Design of single-layer or laminated glass as well as gas layer insulating glass
design of curved glass
Option to select either local calculation without regard to the influence of a surrounding structure, or global calculation with regard to the influence of an entire structure
Calculation of limit stresses according to DIN 18008:2010-12 or TRLV:2006-08
Assignment of loads to load duration classes
Extensive material library including all common glass, foil, and gas types in compliance with the DIN 18008:2010-12, E DIN EN 13474 standards, and the TRLV:2006-08 regulation
Optional consideration of shear coupling of layers
Consideration of climatic loads
Calculation according to the linear static analysis or nonlinear analysis according to the large deformation analysis. analysis
Stress analysis, ultimate limit state design, serviceability limit state design
Graphical representation of all results in RFEM
Possibility to filter results and color scales in result tables
Direct data export to MS Excel