# Wind Speed and Turbulence Intensity Profile for Determination of Quasi-Static Wind Loads According to Gust Concept

### Technical Article

Depending on stiffness, mass, and damping, structures react differently to wind action. A basic distinction is made between buildings that are prone to vibration and those that are not vibration-prone.

Usually, structures are not considered to be susceptible to vibrations if the deformations under wind action by gust resonance are not increased by more than 10 % [2]. In this case, the time variable wind action can be described as a static equivalent load.

Assuming that the turbulences within the wind flow are very large in relation to the building dimensions, a statically acting distribution of pressure p on a building geometry can be calculated with RWIND Simulation according to the "quasi-stationary method" or the so-called gust concept [3].

Basically, a stationary flow field around the analysis model is assumed for the turbulent speed fluctuation over the gust's duration [3]. The pressure fluctuation on the model surface from the inflow turbulence is thus seen as a state stationary over a certain time period t. Thus, the fluctuations follow exactly the course of the time-averaged pressure coefficients c_{p,mean} on the model surface.

The resulting wind-induced pressure Δp(t) on the model surfaces then depends purely on the inlet velocity v(t).

$\mathrm{\Delta p}\left(\mathrm{t}\right)=\frac{1}{2}\xb7\mathrm{\rho}\xb7{\mathrm{v}}^{2}\left(\mathrm{t}\right)\xb7{\mathrm{c}}_{\mathrm{p},\mathrm{mean}}$

ρ |
density of air |

v |
inlet velocity |

c_{p,mean} |
time-averaged pressure coefficient |

t |
time |

So, the value of the inlet velocity vector v(t) is:

v(t)² = (v_{x,mean} + v_{x,fluctuation}(t))² + v_{y,fluctuation}(t)² + v_{z,fluctuation}(t)²

If the squared terms only make a small contribution, an effective value of the inlet velocity vector v(t) is the result:

v(t)² = v_{x,mean}² + 2 ⋅ v_{x,mean} ⋅ v_{x,fluctuation}(t)

Using the effective inlet velocity in the equation of the wind-induced pressure results in:

Δp(t) = 1/2 ⋅ ρ ⋅ v_{x,mean}² [1 + (2 ⋅ v_{x,fluctuation}(t)) / v_{x,mean}] ⋅ c_{p,mean}

This transformation shows that the fluctuation of the wind pressure Δp(t) only depends on the fluctuation of the wind speed v_{x,fluctuation}(t) in the main inflow direction x.

If you replace the time-variable speed fluctuation v_{x,fluctuation}(t) by the maximum occurring speed fluctuation v_{x,fluctuation,max}, you remove the temporal variability from the system.

And if you then compare the term v_{x,fluctuation,max} / v_{x,mean} as a multiple g of the turbulence intensity I_{v}(z),

${\mathrm{I}}_{\mathrm{v}}\left(\mathrm{z}\right)=\frac{{\mathrm{\delta}}_{\mathrm{v}}}{{\mathrm{v}}_{\mathrm{mean}}\left(\mathrm{z}\right)}$

δ_{v} |
standard deviation from mean velocity v _{mean} |

v_{mean}(z) |
average velocity depending on altitude |

z |
height above ground |

you can describe the term in square brackets as gust factor G(z). Inserting the terms into the nominal wind load equation results in:

$\mathrm{W}=\frac{1}{2}\xb7\mathrm{\rho}\xb7{\mathrm{v}}_{\mathrm{mean}}^{2}\left(\mathrm{z}\right)\xb7\mathrm{G}\left(\mathrm{z}\right)\xb7{\mathrm{c}}_{\mathrm{p},\mathrm{mean}}$

ρ |
density of air |

v_{mean} |
average inlet velocity |

G(z) |
gust factor depending on altitude |

c_{p,mean} |
time-averaged pressure coefficient |

where

$\mathrm{G}\left(\mathrm{z}\right)=1+2\xb7\mathrm{g}\xb7{\mathrm{I}}_{\mathrm{v}}\left(\mathrm{z}\right)$

g |
factor for defining gust duration |

I_{v}(z) |
turbulence intensity as a function of altitude |

z |
height above ground |

For example in EN 1991-1-4, factor g is used for describing the gust duration 3.5.

RWIND Simulation calculates the mean values of the pressures p_{mean} on the model surface depending on an inlet velocity v_{x}(z) by means of a stationary solution of the RANS equations by using the SIMPLEC algorithm. Since the mean values of the pressure coefficients c_{p,mean} are based on the ratio between the determined mean pressure values p_{mean} to the undisturbed peak wind velocity pressure at the roof height q(height of roof),

c_{p,mean} = p_{mean} / q(height of roof)

it is possible to use the inlet velocity from the converted peak wind velocity pressure q(z) over the height to determine the nominal wind loads according to the gust concept [1].

v(z) = √(2 ⋅ q(z) / ρ)

Thus, this wind speed includes the mean wind velocity v_{mean} and the maximum fluctuation component v_{fluctuation}. In this case, the inflow turbulence intensity can be set constantly over the height to a very small value of about 5 % [4].

When considering effects of forces acting on the entire building or on large surface areas, this method provides a very good approximation to the natural wind loading [3]. The reason is that the small turbulence effects masked by averaging act only in partial areas and do not have any noticeable effect due to the global integration of the force values.

Furthermore, the concept reacts very well even for small partial areas with frontal inflow since here the effective pressure fluctuations are already very well recorded in the peak wind speed profile [3].

On the contrary, the system results in a poorer convergence to reality for surfaces with flow separation (side and rear wall). It is especially in these zones that the building-induced turbulence "faded away" by averaging using the gust concept has a greater effect than the inflow turbulence effect contained in the inlet velocity profile.

#### Author

#### Dipl.-Ing. (BA) Andreas Niemeier, M.Eng.

Product Engineering & Customer Support

Mr. Niemeier is responsible for the development of RFEM, RSTAB, and the add-on modules for tensile membrane structures. Also, he is responsible for quality assurance and customer support.

#### Keywords

Peak wind speed Gust wind speed Basic wind velocity Mean wind speed Turbulence intensity Wind pressure

#### Reference

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