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In the first example, we proceed with a preliminary design, particularly focus on calculating the total force. It is selected as 2D square plane. It belongs to Group 1 according to WTG-Merkblatt-M3 is:
- G1: Qualitative values with low accuracy requirements for use in the basic investigation or preliminary design. The effort and the requirements for the level of detail are reduced, as often not all boundary conditions are fully clarified.
- R1: Solitary (without surrounding buildings), analysis of individual important wind directions.
- Z1: Statistical mean values, provided it concerns stationary flow processes where fluctuations (e.g., due to approaching flow turbulence) can be sufficiently captured by other measures.
- S1: Static effects. It is sufficient to represent the structural model with the necessary mechanical detail, but without mass and damping properties.
The dimension of the example shows in Figure 1, and also the input assumption is illustrates as Figure 2:
In this example, we will compare wind force values in EN 1991-1-4 and RWIND. The formula of wind force in Eurocode section 5.3 is defined:
| cscd | Structural factor |
| cf | Force coefficient for the structure or structural element |
| qp(ze ) | Peak velocity pressure at reference height ze |
| Aref | Reference area of the structure or structural element |
Force coefficients (d=b=1 → Cf,0=2.10) of rectangular sections with sharp corners and without free end flow can be obtained in Figure 7.23 in EN 1991-1-4, and also reduction factor (ψr) for a square cross-section with rounded corners (r/b=0 → ψ r=1) can be obtained from Figure 7.24 in EN 1991-1-4. Indicative values of the end-effect factor ψλ=0.63 as a function of the solidity ratio φ=1 versus slenderness λ=2 can be obtained in Figure 7.36 in EN 1991-1-4.
The force coefficient cf of structural elements of rectangular section with the wind blowing normally to a face should be determined by Expression (7.9) in EN 1991-1-4:
| cf,0 | The force coefficient of rectangular sections with sharp corners and without free-end flow |
| ψr | The reduction factor for square sections with rounded corners |
| ψλ | The end-effect factor for elements with free-end flow |
- Mean wind velocity
The mean wind velocity vm (ze) at reference height z_e depends on the terrain roughness, terrain orography and the basic wind velocity vb. It is determined using EN1991-1-4 equation (4.3):
- Wind turbulence
The turbulence intensity Iv (ze) at reference height ze is defined as the standard deviation of the turbulence divided by the mean wind velocity. It is calculated in accordance with EN1991-1-4 equation 4.7 . For the examined case ze smaller than zmin:
- Basic velocity pressure
The basic velocity pressure q_b is the pressure corresponding to the wind momentum determined at the basic wind velocity vb. The basic velocity pressure is calculated according to the fundamental relation specified in EN1991 -14 §4.5(1):
where ρ is the density of the air in accordance with EN1991-1-4 §4.5(1). In this calculation the following value is considered ρ=1.225 kg/m3.
- Peak velocity pressure
The peak velocity pressure qp (ze) at reference height ze includes mean and short-term velocity fluctuations. It is determined according to EN1991-1-4 equation 4.8:
Then the wind force can be calculated:
The results in RWIND and comparison to Eurocode
In RWIND the results (in Figure 3 and Figure 4) of the total forces are available in the info tab of the edit model. The difference between RWIDN and Eurocode is about 2.5% (less than the criteria in WTG) which shows good agreement:
