# How to calculate the peak velocity pressure $q_{p}$

Last updated: November 20th, 2022

Before we start calculating anything, let’s start with the question: What do we need the peak velocity pressure for?

The value of the peak velocity pressure includes many parameters about the location, height of the building and some more. The unit is in $kN/m^2$, and we need the peak velocity pressure to calculate the wind forces which act on roof and facades/walls.

So, in this article we are going to show the exact steps how to calculate the peak velocity pressure $q_{p}$ according to EN 1991-1-4:2007.

Many of the parameters that we either derive from Eurocode or calculate do not have to be necessarily done in the order we suggest in this guide.

- First we are defining the height z of the building
- Then we get the fundamental value of basic wind velocity $v_{b.0}$
- Followed by the orography factor $c_{0}$
- Turbulence factor $k_{l}$
- The density of air $\rho$,
- The reference height terrain category II $z_{0.II}$
- The roughness length $z_{0}$.
- Then we calculate the terrain factor $k_{r}$
- The turbulence intensity $I_{v}$
- The roughness factor $c_{r}$
- The mean wind velocity $v_{m}$
- Before we finally calculate the
**peak velocity pressure $q_{p}$**

I also made a process chart in case you are like me and prefer visuals to text π

So let’s have a look at the structure we are going to calculate the peak velocity pressure for because we need some parameters for the calculation π

## Geometry of the structure

As you might have already figured out – I like to use examples. This time, we will calculate the peak velocity pressure for a precast concrete office building. The material does not matter for this calculation. We need the dimensions of the building.

As you can see from the picture, the building has the following dimensions

Height above ground | z = 17.1m |

## Fundamental value of basic wind velocity $v_{b.0}$

According to EN 1991-1-4 1.6.1 the fundamental value of basic wind velocity describes a 10-minute mean value at a height of 10 m above ground and in an open country terrain which includes annual risks and some more parameters.

For the exact definition, you can have a look at the mentioned Eurocode section.

This value must be found in the Nation Annex or you can use the Wind speed calculator made by ** Dlubal Software GmbH. **To do it with the online calculator simply click on the following link, click on the wind button, select your National Annex and enter your location.

Let’s assume our office building is located in Copenhagen, Denmark. Then we get a value of

$v_{b.0} = 24 \frac{m}{s} $

## Orography factor $c_{0}$

EN 1991-1-4 4.3.1 (1) recommends the Orography factor to be taken as 1.0.

$c_{0} = 1.0 $

## Turbulence factor $k_{l}$

As for the Orography factor, EN 1991-1-4 4.4 (4.7) recommends also the turbulence factor to be takes as 1.0.

$k_{l} = 1.0 $

## Density of air $\rho$

The recommended value for the density of air is given in EN 1991-1-4 4.5 (1) and it is 1.25 $\frac{kg}{m^3}$.

$\rho = 1.25 \frac{kg}{m^3} $

## Reference height Terrain category II $z_{0.II}$

The reference height of terrain category II is used to calculate the terrain factor $k_{r}$. The value can be found in EN 1991-1-4 Table 4.1.

$z_{0.II} = 0.05 m$

## Roughness Length $z_{0}$

The roughness length is also used to calculate the terrain factor $k_{r}$.

The value depends on the terrain category where our building or structure is located. The value can also be found in EN 1991-1-4 Table 4.1.

In our case, we assume that our office building is located in a suburban terrain with regular cover of buildings.

Therefore, the building falls into terrain category III.

$z_{0} = 0.3 m$

## Terrain factor $k_{r}$

The formula to calculate can be found in EN 1991-1-4 (4.5).

$k_{r} = 0.19 * (\frac{z_{0}}{z_{0.II}})^{0.07}$

Inserting the values of $z_{0.II}$ and $z_{0} $ leads to

$k_{r} = 0.19 * (\frac{0.3m}{0.05m})^{0.07} = 0.215$

## Turbulence Intensity $I_{v}$

The turbulence intensity is calculated with EN 1991-1-4 (4.7).

$I_{v} = \frac{k_{1}}{c_{0} * ln(\frac{z}{z_{0}})}$

leading to

$I_{v} = \frac{1.0}{1.0 * ln(\frac{17.1m}{0.3m})} = 0.247$

## Roughness factor $c_{r}$

The roughness factor is calculated with EN 1991-1-4 (4.4)

$c_{r} = k_{r} * ln(\frac{z}{z_{0}})$

leading to

$c_{r} = 0.215 * ln(\frac{17.1}{0.3m}) = 0.871$

## Seasonal factor $c_{season}$

The principle of the seasonal factor is that the wind load can be lowered because the wind is blowing less strong in some months.

In the case that you are designing a temporary structure such as a tent or a canopy that is built for a short time frame and then disassembled after a few weeks, you might be able to use a seasonal factor $c_{season}$ depending on the months it has to withstand the wind.

When you need to design your structure for the execution phase, then you might also be able to use $c_{season}$. We are designing an office building which is **NOT** temporary and therefore $c_{season}$ is taken as 1.0 and can be left out of the calculations.

$c_{season} = 1.0$

## Directional factor $c_{dir}$

The principle of the directional factor is that the wind is blowing less from certain directions and therefore the peak velocity pressure and then the wind load can be reduced for those directions.

The recommended value for the directional factor is given in EN 1991-1-4 4.2 Note 2 as 1.0.

However, it is also referred to the National annex, which might define $c_{dir}$.

$c_{dir} = 1.0$

In further calculations, $c_{dir} $ is not included because a value of 1.0 is neither increasing nor decrease the peak velocity pressure.

## Mean wind velocity $v_{m}$

The mean wind velocity is calculated by EN 1991-1-4 (4.3) as

$v_{m} = c_{r} * c_{0} * v_{b.0} $

leading to a mean wind velocity of

$v_{m} = 0.871 * 1.0 * 24 \frac{m}{s} = 20.9 \frac{m}{s} $

Finally, we can calculate the peak velocity pressure π

## Peak velocity pressure $q_{p}$

The mean wind velocity is calculated by EN 1991-1-4 (4.8) as

$q_{p} = [1 + 7 * I_{v}] * \frac{1}{2} * \rho * v_{m}^2$

leading to a peak velocity pressure of

$q_{p} = [1 + 7 * 0.247] * \frac{1}{2} * 1.25\frac{kg}{m3} * (20.9 \frac{m}{s})^2 = 0.746 Β \frac{kN}{m^2} $

## Summary

For a building with the height of 17.1 m in a suburban area in Copenhagen, Denmark, the wind load can be calculated with a peak velocity pressure of $q_{p} = 0.746 \frac{kN}{m^2} $.

And that is exactly what we are going to do in the next articles. We are calculating the wind force on walls and roofs.

- Wind load calculation of walls
- Wind load calculation of a flat roof
- Wind load calculation of a pitched roof
- Wind load calculation of an arched structure

Hope to see you there π