# Generating Wind Loads on Dome with Circular Base According to EN 1991-1-4 in RFEM

### Technical Article

Due to the structural efficiency and economic benefits, dome‑shaped roofs are frequently used for storehouses or stadiums. Even if the dome has the corresponding geometrical shape, it is not easy to estimate wind loads due to the Reynolds number effect. The external pressure coefficients (c_{pe}) depend on the Reynolds numbers and on the slenderness of the structure. EN 1991‑1‑4 [1] can help you estimate the wind loads on a dome. Based on this, the following article explains how to define a wind load in RFEM.

Wind loads of the structure shown in Figure 01 can be divided as follows:

- Wind load on walls
- Wind load on the dome

Figure 01 - Storehouse with Dome on Circular Base

#### Wind Load on Wall

For wall surfaces, the wind loads are determined according to [1], Chap. 7.9, which says the external pressure coefficients for circular cylinders depend on the Reynolds number, roughness and slenderness of a surface. In the case of the warehouse shown in Figure 01, the Reynolds number under the velocity pressure of 0.70 kN/m² results in 3.35 × 107. Based on [1], Figure 7.27, the external pressure coefficients for the Reynolds number of 1.00 × 10^{7} are used by approximation. These are required in RFEM in order to define the load factor as a function of the rotation angle α.

Figure 02 - Determination of Reynolds Number and Resulting External Pressure Coefficients

To define a load varying along perimeter, you can use the ‘Free Variable Load’ type, which can be found under the menu ‘Insert’ → ‘Load’. In the corresponding dialog box, you can select the wall surfaces first and define the projection direction. The wind acts on the local z‑axis of the surface, so it is necessary to adjust the load direction accordingly. You should select the load position so that all walls are surrounded by the plane projection. As a load value, the velocity pressure is defined according to [1], Chap. 4.5, or according to the national application document.

Since the load along the perimeter is not constant, you can select the ‘Along perimeter: Varying’ check box. Thus, it is possible to define a load factor at any angle along the perimeter, which factorises the load value from the previous dialog box. For the factor k_{α}, you can adopt the external pressure coefficient (c_{pe}) for the respective angle directly. The simplest way is to prepare a document in Excel and then import the parameters using the Excel Import. Before you confirm the input, the rotation axis and the initial angle must be defined.

Figure 03 - Dialog Box for Free Variable Loads

In order to check the applied loads visually, it is recommended to select the ‘Distribution of load’ check box in the Results navigator (see Figure 04). For this control, it is sufficient to calculate an iteration for the corresponding load case. This saves time in the case of larger structures with a fine FE mesh. The accuracy of the load distribution depends on the FE mesh. The finer is the FE mesh, the more accurate are the load values.

Figure 04 - Distribution of Load Along Perimeter

#### Wind Load on Dome

[1], Chap. 7.2.8 specifies the external pressure coefficients for domes with rectangular and circular bases. In the case of the domes with a circular base, the external pressure coefficients should be considered as constant along any plane perpendicular to the wind direction. As you can see in [1], Figure 7.12, the external pressure coefficients can apply to three areas (A, B, and C). The areas in between may be subjected to a linear interpolation.

The external pressure coefficient has a value of -0.65 for Area A, -0.80 for Area B, and -0.25 for Area C (see Figure 05). According to [1], Expression 5.1, the wind pressure result for the velocity pressure of 0.70 kN/m² is -0.46 kN/m² for Area A, -0.56 kN/m² for Area B, and -0.18 kN/m² for Area C.

Figure 05 - External Pressure Coefficients for Domes with Circular Base

This load can be easily defined in RFEM by using free rectangular loads, which can be generated in the menu ‘Insert” → ‘Loads”. In addition to defining the projection plane and the load direction, it is possible to consider a linear function for the load distribution, which covers the interpolation between the individual areas as mentioned in the previous paragraph. Now, two free rectangular loads are created. One is designated for Area A to B, the second for Area B to C (see Figure 06).

Figure 06 - Dialog Box for Free Rectangular Load

The load distribution function may help you control the applied wind load. For a better documentation of the load effect, you can optionally create a section (see Figure 07).

Figure 07 - Load Distribution on Dome

Figure 08 - Load Distribution on Dome and Walls

#### Further Information

Domes are very sensitive to the wind load action, especially when carried out on a membrane or shell structure, and when the dome diameter is very large (for example, in the case of stadiums) [2]. In this case, it is not sufficient to consider only a wind load, but the additional stress distributions must be analysed as well. Since [1] does not describe all unfavourable wind effects, the wind pressure coefficients should be verified by means of wind tunnel tests on the model. Therefore, you can also consider the effects of the dome position (for the surrounding buildings, for example).

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