Wind load calculation is required when buildings and structures are exposed to strong winds in order to evaluate the level of load they will experience during their service life as a consequence of the wind pressure.

Wind loads can be very significant, especially in high rise buildings and in geographical areas that are subject to strong winds and extreme weather conditions, like storms and tornadoes. In these cases wind load calculation should take into account not only the wind speeds but also the wind direction and unsteadiness. Wind load calculation can be carried out manually using equations or using Computational Fluid Dynamics (CFD), CFD calculation can complement the manual calculation by validating the original results.

The conventional approach in wind load calculation is to follow the formula required by the local building regulation. Typically the Wind Load   $$W_{L}$$ acting on a building is given by (1):

\begin{gather} W_{L}=C_{D}\;A\;\frac{1}{2}\rho v^{2} \end{gather}

where A the area of the building facing directly the wind (frontal area), $$\rho$$ is the air density – around 1.2 $${Kg/m^{3}}$$ – and $$v$$ is the wind speed (generally the maximum value recorded at the location of the building) and $$C_D$$ is the coefficient of drag, which depends on the shape of the building and is usually given by building regulations.

While this calculation is always required by law in combination with a specified safety factor, it includes a few simplifications:

1. The Coefficient of Drag $$C_D$$ is only assumed and not actually calculated, it can vary substantially as function of the building shape and it is difficult to know from tables as every building shape is different.
2. The pressure on the building is assumed to be constant, in reality it does vary across the building height and it is most of the times raising towards the top of the structure, therefore in reality the lever arm of the wind load is higher than the one assumed by the previous equation.
3. It does not take into account the terrain shape and the presence of other buildings around the calculated structure, those can potentially affect the flow and ultimately the level of loading on the main structure.
4. It assumes a constant wind direction without taking into account the extreme flow angularity deriving from a storm and their interaction with the building shape.

While it is worth stressing that the calculation above has to be carried out in order to comply with the relevant building regulations, it is important to complement it with a specific Computational Fluid Dynamics (CFD) analysis, which allows to evaluate the wind load in terms of forces and moments without the limitations listed above. It is possible to carry out both the wind loading calculation based on the formula as required by the building regulations and use a CFD model to validate the results, which gives increased confidence in assessing the structural integrity of the building.

## Wind load calculation using CFD

A Computational Fluid Dynamics (CFD) wind load calculation allows to estimate the structural load coming from a real wind load condition on a specific building. Generally, setting up a CFD model is relatively simple, as the building can be modelled with basic geometrical shapes, however the fidelity of the model can be increased by including relevant geometrical details of the building. SimWorks is a free CFD software which can help in streamlining the whole simulation process.

It is also important to include in the model the terrain and the surrounding buildings. After the geometry has been defined, it is then necessary to apply the correct wind speed to the front face of the computational domain of the model and select the model to use for the simulation (typically a steady RANS simulation).  Once the CFD simulation is completed, it is possible to visualise the wind flow field around the building as well as the actual load distribution and calculate the correct wind load on the building itself. In addition, it is possible to evaluate the CoP (Centre of Pressure) which is the point where the resultant force of the calculated wind load is to be applied, see an example of the wind load calculation on a group of buildings using SimWorks. Once the CFD model has been prepared, it is possible and fairly easy to change the wind speed and or directions to evaluate the wind loading for different weather conditions which the building can experience during its service life. This is particularly important when it is expected that the building will have to withstand extraordinary weather conditions are like tornadoes or heavy storms.

In fact the CFD model is capable to capture the effect of local flow variations and the actual flow angularity and vorticity and include these effects on the building wind load. Moreover CFD is the only available tool to evaluate the wind load on modern buildings with highly complex geometry.

The wind changes direction depending on the time of the day and on the month in the year. The effect of the direction change on the overall wind load can be significant because the coefficient of drag changes significantly because of the different section shape facing the wind and because of the variation of frontal area. To take into account those effect the worst case scenario has to be considered where the frontal area is maximum as well as the wind speed, applying this in manual calculation can be challenging as the coefficient of drag is not necessarily available for a given building shape at any wind direction. In this case a CFD calculation can help as it is possible to carry out a wind direction polar where multiple CFD simulations are carried out taking into account the all the possible wind directions in a specific location.

One of the most famous structural failures due to the wind load was the Tacoma Narrows Bridge accident in 1940, in that case a wind speed at 64 Km / h (40 mph) triggered an aerodynamic flutter effect on the structure of the bridge leading to its collapse.

The level of wind load was very low compared to the maximum load the structure could withstand, but unfortunately since the bridge was deforming under load its response to the flow field was changing as well producing an oscillatory wind load force. Finally the resulting wind load variation frequency was very close to one of the natural frequencies of the structure resulting in an ever growing level of displacement. The bridge movement was affecting the flow field around the structure contributing to the creating of a pulsating force on it (aerodynamic flutter). This is rarely the case in common buildings and structures as the structural stiffness is usually much higher than the one of a suspended bridge but even not taking into account the aerodynamic flutter effect, where the deformation of the structure is actually leading to a pulsating force, the wind load resultant force is still unsteady, meaning that it varies with time. There are two reasons for it to be unsteady, one is the actual variation of the wind speed which is not constant, but usually wind speed variation in time is relatively slow if compared to structural resonance (unless extreme weather conditions are taken into account, see storms section below) , the second reason is the fact that the flow field around a bluff body (like most of the buildings are) is by nature unsteady and this has to be taken into account in the structural and comfort calculations. A bluff body is shedding vortices from the backward facing shape corners which are varying with time, those structures are commonly called Von Karman vortices:

Coming back to the CFD model, it is possible to run an unsteady calculation (URANS or DES) and capture the natural frequency of the wind load simply changing the model analysis type. The first step is to define a time step small enough to capture the wind variation (see again the simulation type article to know how to choose a suitable time step) and a CFD simulation will be carried out at each time step. Once the analysis is completed all the time steps will be combined in a video showing the evolution in time of the flow field. In the same way it is possible to plot the wind load force resultant against time to get the force evolution across time. If required and if the aerodynamic load is high enough to be a concern a frequency analysis can be carried out on it to get all the force frequencies, finally it is possible to compare them to the natural frequency of the structures. Usually the difference between the structure first frequency and the aerodynamic load frequency are quite far and the aerodynamic load is small enough not to produce measurable displacements on the structures, if this is not the case than the user comfort and safety could be a concern. If in extreme weather conditions the wind load is high enough to deform the structure than a fluid structure coupled analysis has to be carried out to fully characterise the problem.

## Wind load effect on structure fatigue

Even if the wind load magnitude and unsteadiness (or variation of force with time) are not severe enough to damage the structure directly, they can still have an effect on the expected life of the structure itself. Most of the structures are subject to fatigue, where even a small load cycle if repeated enough times can lead to a catastrophic failure even if the maximum load is well within the maximum structural acceptable load. To take this effect into account it is necessary to know the fatigue life of the structural material used and assess the number of wind load cycles the structure will be subject to, once the number of cycles and the maximum load amplitude within each cycle are known the life expectancy of the structure can be derived directly from a fatigue graph like the one below:

A CFD modelling of the problem can help in determining the amplitude and frequency of the actual load the structure is subject to for a given wind speed and direction. It is also possible to monitor from existing weather historical data the variation of wind speed and direction which will be affecting the structure during an entire year. It is than possible to derive the number and amplitude of load cycles that the structure will experience during the year. Since the load cycles will change in amplitude and frequency the best praxis is to sum the equivalent damage from each load cycle to determine the structure predicted life, this can be achieved by using the Palmgren-Miner linear damage hypothesis.

## The case of extreme weather

Even if historical weather data in a specific places are known it is impossible to predict reliably whether extraordinary events will take place in the future, it is nevertheless possible to know which are the characteristic wind speed and directions of similar events which took place in other locations. If a CFD model of the building or the structure has been completed is then fairly straightforward to apply the exact conditions which would be experienced if such an event took actually place. For instance it is possible to define a load cycle which replicates all the wind speeds and directions experienced during a storm and apply those to the structure even if such an event is not expected in the area of choice.

Even if not required by law this analysis can highlight weaknesses in the structure which can be easily addressed in the design phase, or can highlight which areas of building would survive to an extreme event. Or simply can confirm that the structure as it is can withstand extreme atmospheric conditions. The result of a CFD simulation can predict in detail the flow structures and the instantaneous wind load in such conditions and most of the times it is possible to improve the structural integrity with minor design variations. This analysis is clearly very appealing for the building customer as it would be very difficult to simulate or even to take into account such events with the traditional approach described above. It is also possible for a company to produce a library of wind load cases deriving from storms and tornados which actually have happened in the past and automatically apply those conditions to all the structural and building designs considered.

## Conclusions

It is important to stress once again that a CFD model offers invaluable info about the wind load features and the structure reaction to it and it complements but it does not replace the traditional calculation required by the building regulations, but rather complements it. Once a CFD model is fully defined is fairly easy to simulate a whole variation of weather conditions, including extreme ones. This provides a wealth of information on how the building reacts to every possible condition it can be subject to during its service life. The analysis also contributes to the prediction of the expected structure life once the material fatigue is taken into account. For real life examples of how a CFD model can help to fully assess a building wind load refer to the IdealSimulations Architecture section.

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