# Wind Structural factor CsCd

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## What is the structural factor CsCd used for?

The structural factor takes into account the absence of pressures simultaneity to the surface of the construction and of vibration of the structure caused by the turbulence.

The cscd calculation is based on the building dimensions, construction location and the terrain's categories.

A minimum approved value of cscd = 0.85 is indicated in Appendix D.

## Normative references and national choices

EN 1991-1-4 §6.3.1 - Detailed procedure for structural factor cscd
EN 1991-1-4 Annex B - Procedure 1 for determining the structural factor cscd

In France (NF EN 1991-1-4/NA clause 6.3.1 (1) NOTE 3):
The procedure to use is the procedure 1 described in Annex B. Annex B is normative; Annex C does not apply.

In Belgium (NBN EN 1991-1-4 ANB §6.3.1 (1) NOTE 3):
The procedure 1 of Annex B recommended to calculate cscd is normative.

In United Kingdom (BS EN 1991-1-4 NA.2.21):
The recommended procedure given in BS EN 1991-1-4:2005 Annex B should be used.

## Building's fundamental frequency n1,x

An approched value of the structure's fundamental frequency can be calculated from:

• for a building height up to 28m, equation 4.6 of Eurocode 8 - Earthquakes:
This expression takes into account the nature of the structure (Ct) and its free vibration height (H).

• for construction height upper than 28m, equation F.1 of Eurocode 1 part 1-4 - Wind:
This expression only takes into account the free vibration height (H) of the structure.

## Turbulence intensity Iv(zs)

This is the standard deviation of wind turbulence divided by the average wind speed. It gives a mesure of the wind in the form of gusts. The recommended calculation procedure is given in EN1991-1-4 4.4(1) and the national annexes.

## Background factor B2

This coefficient reflects the lack of pressure correlation on the construction. The recommended calculation procedure is given in EN1991-1-4 B.2(2) and the national annexes:

with:

• h = total height of the building (in m)
• b = perpendicular dimension of the building to the wind (in m)
• L(zs) = turbulence scale according to EN1991-1-4 B1(1):
• Lt = reference scale (300m)
• zt = reference height (200m)

## Resonance response factor R2

This coefficient reflects the effect of turbulence in resonance with the considered vibration mode of the building. The recommended calculation procedure is given in EN1991-1-4 B.2(5) and the national annexes:

with:

• δ = logarithmic decrement of damping according to EN1991-1-4 Equation F.15:
• δs = logarithmic decrement of structural damping (0.05 for steel building, 0.06 for timber building, 0.10 for reinforced concrete buildings)
• δa = logarithmic decrement of aerodynamic damping for the fundamental mode (can be securely taken to 0)
• δd = logarithmic decrement of damping due to special devices (0 if no special device)
• SL(zs,n1,x) = non-dimensional power spectral density function according to EN1991-1-4 B.1(2):
• fL(zs,n1,x) = non-dimensional frequency according to EN1991-1-4 B.1(2):
• Rh and Rb = aerodynamic admittance functions according to EN1991-1-4 B.2(6).

## Peak factor kp

This factor is the ratio of the maximum value of the fluctuating part of the response to its standard deviation. The recommended calculation procedure is given in EN1991-1-4 B.2(3) and the national annexes:

with:

• ν = up-crossing frequency
• T = averaging time for the mean wind velocity, T=600 seconds.

## Structural factor cscd

The recommended calculation procedure is given in EN1991-1-4 6.3.1(1) and the national annexes: