The effect of wind on a building gets more significant as the height of the building increases. In this post, wind load analysis has been carried out on a 60m tall high rise building using the method described in EN 1991-1-4:2005 (*General actions – Wind action*). The structure is assumed to be located in an area with a basic wind speed of 40 m/s.

**Basic Data**

Height of building = 60m

Width of a building = 30m

Structure – Framed building

The structure is located at terrain category II (see Table below)

**Basic wind velocity**

The fundamental value of the basic wind velocity V_{b,0} is the characteristic 10 minute mean wind velocity irrespective of wind direction and time of the year, at 10 m above ground level in open-country terrain with low vegetation such as grass, and with isolated obstacles with separations of at least 20 obstacle heights.

The basic wind velocity V_{b,0} is calculated from;

V_{b} = C_{dir} . C_{season} .V_{b,0}

Where:

V_{b} is the basic wind velocity defined as a function of wind direction and time of the year at 10m above the ground of terrain category II

V_{b,0} is the fundamental value of the basic wind velocity

C_{dir} is the directional factor (defined in the National Annex, but recommended value is 1.0)

C_{season} is the season factor (defined in the National Annex, but recommended value is 1.0)

For the area and location of the building that we are considering;

Basic wind velocity V_{b,0} = 40 m/s

V_{b} = C_{dir}. C_{season}.V_{b,0} = 1.0 × 1.0 × 40 = 40 m/s

**Mean Wind**

The mean wind velocity V_{m}(z) at a height z above the terrain depends on the terrain roughness and orography, and on the basic wind velocity, V_{b}, and should be determined using the expression below;

V_{m}(z) = c_{r}(z). c_{o}(z).V_{b}

Where;

c_{r}(z) is the roughness factor (defined below)

c_{o}(z) is the orography factor often taken as 1.0

The terrain roughness factor accounts for the variability of the mean wind velocity at the site of the structure due to the height above the ground level and the ground roughness of the terrain upwind of the structure in the wind direction considered. Terrain categories and parameters are shown in Table 2.0.

c_{r}(z) = k_{r}. In (z/z_{0}) for z_{min} ≤ z ≤ z_{max}

c_{r}(z) = c_{r}.(z_{min}) for z ≤ z_{min}

Where:

Z_{0} is the roughness length

k_{r} is the terrain factor depending on the roughness length Z_{0} calculated using;

k_{r} = 0.19 (Z_{0}/Z_{0,II})^{0.07}

Where:

Z_{0,II} = 0.05m (terrain category II)

Z_{min} is the minimum height = 2 m

z = 60 m

Z_{max} is to be taken as 200 m

K_{r} = 0.19 (0.05/0.05)^{0.07} = 0.19

c_{r}(60) = k_{r}.In (z/z_{0}) = 0.19 × In(60/0.05) = 1.347

Therefore;

V_{m}(60) = c_{r}(z). c_{o}(z).V_{b} = 1.347 × 1.0 × 40 = 53.88 m/s

**Wind turbulence**

The turbulence intensity *I*_{v}(z) at height z is defined as the standard deviation of the turbulence divided by the mean wind velocity. The recommended rules for the determination of *I*_{v}(z) are given in the expressions below;

I_{v}(z) = σ_{v}/V_{m} = k_{l}/(c_{0}(z).In (z/z_{0})) for z_{min} ≤ z ≤ z_{max}

I_{v}(z) = I_{v}.(z_{min}) for z ≤ z_{min}

Where:

k_{l} is the turbulence factor of which the value is provided in the National Annex but the recommended value is 1.0

C_{o} is the orography factor described above

Z_{0} is the roughness length described above.

For the building that we are considering, the wind turbulence factor at 60m above the ground level;

I_{v}(60) = σ_{v}/V_{m} = k_{1}/[c_{0}(z).In(z/z_{0})] = 1/[1 × In(60/0.05)] = 0.141

**Peak Velocity Pressure**

The peak velocity pressure q_{p}(z) at height z is given by the expression below;

q_{p}(z) = [1 + 7.I_{v}(z)] 1/2.ρ.V_{m}^{2}(z) = c_{e(z)}.q_{b}

Where:

ρ is the air density, which depends on the altitude, temperature, and barometric pressure tobe expected in the region during wind storms (recommended value is 1.25kg/m^{3})

c_{e}(z) is the exposure factor given by;

c_{e}(z) = q_{p}(z)/q_{b}

q_{b} is the basic velocity pressure given by; q_{b} = 0.5.ρ.V_{b}^{2}

q_{p}(60m) = [1 + 7(0.141)] × 0.5 × 1.25 × 53.88^{2} = 3605.23 N/m^{2}

Therefore, q_{p}(60m) = 3.605 kN/m^{2}

**External Pressure Coefficients**

From Table 7.1 of EN 1991-1-4:2005 (E)

For the building, taking the height to width ratio h/d = 2.0

Pressure coefficient for windward side = +0.8

Pressure coefficient for leeward side = –0.6

The net pressure coefficient C_{pe10} = +0.8 – (–0.6) = 1.4

The net external surface pressure on the structure = q_{p}(z) C_{pe10} = 3.6057 × 1.4 = 5.05 kN/m^{2}

Therefore, w_{e} = 5.05 kN/m^{2}

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From these calculations, it is not clear that the wind profile varies with height….or the requirements that lead to your assumptions.

Congratulations for your contributions…keep up

The Eurocode National Annex to BS EN 1991-1-4 Allows the use of an coefficient which can be used to calculate the overall wind load on the building.

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