# How To Calculate The Peak Velocity Pressure {2023}

The calculation of the peak velocity pressure is the 1st step when calculating the wind load on roofs, walls and bridges. 💨🌬️

In this blog post we show, step-by-step, how to calculate the peak velocity pressure according to Eurocode. 🧮🔢

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 roofs and facades/walls.

Let’s get started. 🚀🚀

## Process of peak velocity pressure calculation

To calculate the peak velocity pressure, we have to do the following steps. 👇👇

- Height of the structure
- Fundamental value of basic wind velocity v
_{b.0} - Orography factor c
_{0} - Turbulence factor k
_{l} - Density of air $\rho$
- Reference height terrain category II z
_{0.II} - Roughness length z
_{0} - Terrain factor k
_{r} - Turbulence intensity I
_{v} - Roughness factor c
_{r} - Mean wind velocity v
_{m} - Peak velocity pressure q
_{p}

## 1. 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 |

## 2. 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: We can also use the wind speed calculator made by ** Dlubal Software GmbH. **Click here to open the online calculator. 👇👇

##### 1. Step: Click on the wind icon

##### 2. Step: Choose your country and national annex

##### 3. Step: Type in the location of the structure

Btw, Østerbro is the district in Copenhagen in which I live. ✌️😄

For an office building located in Copenhagen, Denmark, we get a fundamental value of the basic wind velocity of

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

## 3. Orography factor c_{0}

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

$$c_{0} = 1.0 $$

❗

This value may be defined differently in the National Annex of your country. So double-check if that is the case.

## 4. 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.

$$k_{l} = 1.0 $$

❗

Again also this value may be defined differently in the National Annex of your country. So double-check if that is the case.

## 5. 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 kg/m^{3}.

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

## 6. 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.

$$z_{0.II} = 0.05 m$$

## 7. 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.

$$z_{0} = 0.3 m$$

## 8. Terrain factor k_{r}

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

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

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

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

## 9. Turbulence Intensity I_{v}

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

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

leading to

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

## 10. Roughness factor c_{r}

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

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

leading to

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

## 11. 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.

$$c_{season} = 1.0$$

❗

The seasonal factors can be specified in the National Annex in case you are designing a temporary structure.

## 12. 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.

## 13. Mean wind velocity v_{m}

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

$$v_{m} = c_{r} \cdot c_{0} \cdot v_{b.0}$$

leading to a mean wind velocity of

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

Finally, we can calculate the peak velocity pressure. 👍👍

## 14. Peak velocity pressure q_{p}

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

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

leading to a peak velocity pressure of

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

## 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 kN/m^{2}.

And that is exactly what we did in the following articles: 👇👇

- 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

## Peak Velocity Pressure FAQ

**How do you calculate the peak velocity pressure?**You calculate the peak velocity pressure with formulas from Eurocode EN 1991-1-4 and its national annex.

**How does the height of a structure affect the peak velocity pressure?**The higher a structure or building is, the greater the peak velocity pressure. However, the calculated peak velocity pressure or wind load can often be reduced by CFD calculations or a wind tunnel test. But this is expensive.

As a semi-retired ( but still dabbling) UK Engineer I’m far more familiar with the “simpler” British Standard COP’s. Nevertheless I wanted to teach myself the Eurocode approach but was finding the Eurocodes a bit more difficult to follow until I stumbled across your excellent videos on Youtube. The videos and hardcopy notes are so clear so my thanks to all those responsible for the time taken to create them. I real benefit for my ageing brain!

Hi Trevor,

Thanks for the great feedback!

It’s great to hear that you think that the videos and posts are easy to understand. That’s the goal with it.

Best regards,

Laurin