# Wind load on buildings

The wind load on high rise building is calculated using the Cimputational Fluid Dynamics (CFD) free software SimWorks. The analysed building is part of a complex of buildings with a shorter one just in front of it. In this case the interaction between the two buildings is important in calculating the total wind load on the main one.

SimWorks is a free CFD software available for download at the following link. Also it is recommended to complete the SimWorks introduction tutorial.

## Load the geometry

The first step is to load the geometry:

1. Click on the browse geometry in the Simulation manager window and select the file Buildings.igs
2. Load the geometry
3. Rename the simulation as Building

Before starting the tutorial simply download SimWorks if you have not already and the tutorial geometry, it is free and there is no requirement for registration:

## Mesh parameters

1. The Outer domain size should be set to 150 100 50
2. The origin should be set at 5 -4 25

3. Make sure that the Point in mesh is out of the geometry, in this case the position is 30 0 0

4. Define the base cell size as 2

5. Increase the mesh refinement level on the buildings surfaces to 4 5 (min value – max value) and define 3 prism layers with expansion ratio 1.2 and initial thickness 0.005

## Reference values

The reference values are used to calculate the drag coefficient of the building and the overall momentum calculated with respect to the base. Insert the following coefficients:

Reference velocity: 25 m/s

Reference length: 26 m

Reference area: 204 m2

Centre of rotation: -3.75 -1 0

Once the coefficients are calculated it is possible to calculate the position of the centre of pressure which defines the overall load and its application point.

In the Output tab it is possible to define the output planes required for the post-processing analysis of the simulation. Define 30 planes in X between -25 and 50, 30 in Y between -25 and 25 and 50 in Z between 0 and 50

## Part group definition

1. Select the Part names layering from the layering menu
2. Select the Building_2 in the relevant part group in the Regions tab
3. click on the Create new part group icon to create an independent part group and get the aero coefficients of the taller building
4. Once the new part group is defined just call it Main building
5. Rename the remaining part group Secondary building

## Complete the run setup, mesh and run

1. Complete the Run setup, during this phase the geometry surface will be discretized in the background in preparation for the meshing phase so it can take a few minutes
2. Complete the Mesh phase, during this phase the live data will show the mesher progress
3. Run the simulation

## Flow field analysis

Once the simulation is complete it is possible to analyse both the flow field output and the resulting aerodynamic coefficients

1. To load the flow field right click on the completed simulation and select Fields → Load
2. Show the central plane normal to Y and a low plane normal to Z together with the two Buildings
3. Select the U variable in the Variable tab and select a range from 0 to 40 m/s
4.

The velocity field around the building is showing the interaction between the two building wakes and it is showing how much the flow is slowing on the wake of the main building. Also it is possible to note a small acceleration of the flow at the main building periphery.

1. Hide the plane normal to Y
2. Select Cp as the main variable in the Variable tab and define a range from -1 to 1
1.

This plot shows the pressure distribution on the buildings showing the high increase in pressure on the frontal face of the main building, while the lower portion of it is showing a reduced increase in pressure rise due to the presence and the wake of the smaller building.

## Wind load calculation

It is now possible to calculate the actual load on the two buildings, to do that we start from the drag coefficient of both and calculate manually the overall wind load and application point.

1. Right click on the completed simulation and select Plots → Load
2. Click on the Clear all plots button in the Plot window
3. Select the forces_Main_building part group from the Selected partgroup dropdown menu
4. Select Cd in the Selected variable menu and click on the Add plot button
5. Repeat the operation selecting the forces_Secondary_building part group
6. Click on the Zoom icon and select the last 300 iterations in both the plots
7. You can click Move graph icon if you want to analyse different areas of the plot
8. Alternatively you can click on the Reset view icon if you want to come back to the default zoom / position

The numerical values are still oscillating after 2000 iterations, this is because we are trying to simulate an unsteady flow with a steady state simulation. To have a more representative simulation we can run a fully unsteady CFD simulation, but this will be the object of a different tutorial. To be conservative in this case we take the maximum CD value across the last 300 iterations for both the buildings, and we obtain a maximum CD of 0.561 for the secondary building and 1.355 for the main one.

The final wind load can be then directly calculated using the definition of drag coefficient:

\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, see the wind load calculation blog post for more detailed info. So in our case we obtain:

\begin{gather}
W_{MB}=1.355*204*\frac{1}{2}*\;1.2*25^{2}\end{gather}

\begin{gather}
W_{SB}=0.561*204*\frac{1}{2}*\;1.2*25^{2}\end{gather}

The overall load on the Main building is 103660 N, the load on the Secondary building is 42920 N.

Please note that since we used the frontal area of the main building as reference area this is the value we need to input in all our calculations to get the correct load on both the main and the secondary building, as this is the value that the solver used for the Cd coefficient on each of the two buildings.

This quick calculation shows the overall load on both the building, now just repeat the same exercise to get the Cm_pitch:

The Cm_pitch is 0.76 on the main building and 0.21 on the secondary one. Very similarly to the wind load calculation we can now calculate the resulting bending moment due to the wind.The definition of pitching moment coefficient is different to the definition of drag coefficient because the value has to be multiplied by the chord c, this in our case was the height of the main building 26 m:

\begin{gather}
M_{W}=C_{D}\;A\;c\;\frac{1}{2}\rho v^{2}
\end{gather}

\begin{gather}
M_{MB}=0.76*204 *25\;*\;\frac{1}{2}*\;1.2*25^{2}\end{gather}

\begin{gather}
M_{SB}=0.21*204*25\;*\;\frac{1}{2}*\;1.2 *25^{2}\end{gather}

The final bending moment on the main building is 1444000 Nm and on the secondary building is 399000 Nm.

So if we want to calculate the CoP (centre of pressure) height where the resulting load is applied it is enough to divide one by the other.

CoP_height = Mw / W

CoP_{Height Main Building} = frac{M_{w}}{W} = frac{1444000}{103660} = 13.93 m

CoP_{Height Sec Building} = frac{M_{w}}{W} = frac{399000}{42920} = 9.29 m

This final value fully defined both the load and the application point on the building, it is then possible to carry out a structural calculation on the building structure based on this data. The results are aligned with the literature data.

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