This article presents a comprehensive overview on wind action on structures to EN 1991-1-4-2005 + A1:2010, and the UK National Annex to EN 1991-1-4-2005 + A1: 2010. In this article EN 1991-1-4-2005 + A1:2010 is routinely referred to as “the standard” while UK National Annex is sometimes shortened as “UK NA”.

Scope of EN 1991-1-2005 + A1:2010

EN 1991-1-4:2005 + A1:2010 contains guidance on the determination of natural wind actions for the structural design of land-based structures, and elements attached to the structure, (e. g. components, cladding units and their fixings, safety and noise barriers).

According to Clause 1.1 (2), the standard is only applicable to

• Buildings and civil engineering works with heights up to 200 m.
• Bridges having no span greater than 200 m, provided that they satisfy the criteria for dynamic response.

Specific Exclusions

Clause 1.1 (12) of the standard makes specific exclusion of structures such as:

• torsional vibrations, e.g. tall buildings with a central core
• bridge deck vibrations from transverse wind turbulence
• wind actions on cable supported bridges
• vibrations where more than the fundamental mode needs to be considered.

Introduction

Wind is a mass of air in motion from areas of high pressure to areas of low pressure. When it encounters obstructions (structures), it exerts a pressure on those structures, thereby, in the process, converting its kinetic energy to pressure. This pressure is exerted on external surfaces of the structure due to direct contact and are also exerted on the internal surfaces due to porosity or openness of the structure.

From the foregoing brief overview of wind behaviour, the process of assessing wind actions on structures can be categorized broadly into three:

1. Calculation of wind velocity
2. Calculation of wind pressure
3. Calculation of forces/Loads exerted by wind on structures by means of aerodynamic coefficients (wind structure interaction)

However, each of these categories requires additional parameters to modify the main parameters (velocity, pressure, and load) to take account of peculiar environmental, terrain, and structural factors. Hence, for simplicity and clarity of thought each of these parameters shall be discussed in this article by grouping them under one of the three categories.

1. Calculating Wind Velocity (First Category)

The parameters necessary when determining wind velocity are the fundamental Basic Wind Velocity, Basic wind velocity, and the mean wind velocity (if orography is significant)

1. Fundamental Basic wind velocity (v_b,o)

The fundamental basic wind velocity is the 10-minute mean wind velocity with an annual risk of being exceeded of 0.02 (1 in every 50years) irrespective of wind direction, at a height of 10m above flat open country terrain and accounting for altitude effects (if required).

Besides stating the definition above that captures the model of fundamental basic wind velocity, the standard leaves the actual determination of the value to the National Annex of each member country as it requires specific meteorological data on national wind climate. The UK NA provides a map in NA.1 to supply fundamental basic wind velocity (v_b,map) and thereafter modifies it to account for altitude effect to obtain the actual “fundamental basic wind velocity” (v_b,o).

Considering that v_b,map in accordance with Eurocode 1-part 1-4 definition in clause 1.6.1 reflects the value of wind velocity at a fixed 10m height above the sea level, the altitude factor is necessary to account for the actual height of the structure on site.

The UK national annex gives the fundamental basic wind velocity in equation NA.1 as:

v_b,o = v_b,map × c_alt

The altitude factor (c_alt) as explained in NA.2.5 depends on:

The altitude (A) of the site above mean sea level or altitude of upwind base when orography is significant

Reference height (Z_s) as described in fig 6.1 of the standard for different structures (the figure is reproduced below) or reference height (Z_e) the height of the part above ground for vertical walls as defined in EN 1991-1-4:2005 Figure 7.4

The expression for calculating c_alt is reproduced below:

c_alt = 1 + 0.001. A; when Z_s ≤ 10m

c_alt = 1 + 0.001. A (10/Z_s )^0.2   Zs ≥ 10m

For simplification, the first equation for c_alt (Zs ≤ 10m) can be used for any building height.

2. Basic wind velocity (v_b)

The basic wind velocity is what is derived when fundamental basic wind velocity is modified to account for the direction of the wind being considered and seasonal effect (if required).

This means two factors are important for basic wind velocity:

• Directional factor (C_dir)
• Seasonal factor (C_season)

Directional factor (C_dir)

The standard refers users to National Annexes for the value of directional factor but recommends 1 if no alternatives. The UK NA gives values for directional factor in table NA.1. Twelve directions in degrees are given however, interpolation may be used to get any desired direction not included. Where the wind loading on a building is assessed only for orthogonal load cases, the maximum value of the factor for the directions that lie ± 45° either side of the normal to the face of the building is to be used.

For simplicity, the directional factor can be conservatively taken as 1 for all directions.

Seasonal factor (Cseason):

The seasonal factor is used for temporary structures. The standard refers users to National annexes but recommends 1 if no alternatives. The UK NA gives value for seasonal factor in table NA.2. It should be taken as 1 for permanent structures. It can generally be assumed as 1 as recommended by Eurocode1 part 1-4. It is largely insignificant when considering ultimate limit state and should be neglected (i.e.: taken as 1).

For simplicity, the seasonal factor can be conservatively taken as 1 for all directions regardless of situation.

The expression for basic wind velocity goes thus:

v_b= v_b,o . C_dir. Cseason (Equation 4.1)

 

(Note: After calculating basic wind velocity and if orography is not significant, the next step is to move on to the second category of the three categories which is to determine the wind pressure. However, if orography is significant, then the next step is to evaluate the mean wind velocity which will further modify the wind velocity by considering the effect of orography, and terrain roughness of the site).

3. Mean Wind Velocity (v_m^z) 

(Not necessary when Orography is not significant)

Recall the definition of the fundamental basic wind velocity, you would notice It is estimated for a structure which is 10m high above the ground in a country terrain. This is a general definition that does not give allowance for the peculiarity of individual site. The mean wind velocity is meant to correct this as it takes account of the peculiarities of the site and their environment.

In other words, the mean wind velocity can be said to be the 10-minute mean wind velocity at a specific height (z) (this is already taken care of by UK NA by c_alt) with an annual risk of being exceeded of 0.02 taking consideration of the specific orography and terrain roughness of the site a structure is to be founded. It is basically the effect of surrounding height (natural and artificial) on the site wind velocity.

From what has been established so far, the most significant of the factors required to modify the fundamental basic wind velocity to mean wind velocity are two:

1. Roughness factor
2. Orography factor

This is also apparent in expression (4.3) given in EN 1991.1-4-2005 for determining the mean wind velocity:

v_m^z = C_r^z .C_o^z . v_b    

Where:

C_r^z  is the roughness factor

C_o^z is the orography factor

v_bis basic wind velocity

Roughness Factor (C_r^z)

The roughness factor takes account of the impact of the terrain roughness on wind behaviour. Generally, terrain roughness (i.e.: how much the land surface around the site is clustered with buildings, forest, hills, etc.) decreases wind speed but increases its turbulence. This decrease in wind speed is caused by friction due to clustered land features which disrupt airflow and in turn leads to increase in wind turbulence.

The roughness factor is dependent on the terrain factor (K_r ) while the terrain factor is in turn dependent on the terrain length (Z_o). The formular for the two later factors are given in the standard.

The roughness factor is given in expression (4.4) of the standard as:

C_r^z = K_r.In(Z/Z_o )  Z_min≤ Z ≤ Z_max

C_r^z = C_r^zmin  when Z ≤ Z_min

Kr is the terrain factor defied in expression (4.5) of the standard.

Z_min is given in table 4.1 for the appropriate terrain category.

Z_o  is roughness length given in table 4.1 for the appropriate terrain category.

Z_max  is taken as 200m

Note: Terrain category 0 -IV are defined in Annex A of the standard.

Eurocode 1991-1-4 gives allowance for national annexes to stipulate an alternative procedure and the UK NA heavily exploits this has its approach substantially differ to that of the standard.

UK National Annex

The UK NA condenses the roughness terrain categories into three as oppose to five in the standard. The three categories are:

• sea
• country
• Town

Another apparent difference is that the UK NA considers the displacement height (h_dis) in evaluating roughness factor, an approach consistent with that of BS 6399-2. The displacement height (h_dis) accounts for sheltering effects created by surrounding closely spaced buildings or any other obstructions upstream of a structure in an urban environment. The displacement height (h_dis) should be taken as 0.8h_ave and its value should not exceed 0.6h. It is subtracted from the reference height (z-h_dis) of the structure on which wind action is to be calculated which leads to the overall reduction in wind action on the structure. This should not be taken to imply the structure is free from wind action below the displacement height. When there is not enough data on the density of the upstream structure, permanence, or height to guide the evaluation of displacement height, it can be ignored and conservatively taken as zero. The displacement height should always be taken as zero for site located in country terrain.

The combination of z-h_dis, and the distance up-wind to shoreline is necessary to extract the value of roughness factor while the combination of z-h_dis, and the distance from town boundary is needed for roughness correction factor, when applicable. Figure NA.3 should be used to determine the roughness factor of site in country terrain, while figure NA.3 multiplied by roughness correction factor (C_rT) in Figure NA.4 should be used for site in town terrain. For sea terrain, Figure NA.3 should be used to determine the roughness factor assuming that the distance upwind from the shoreline is equal to 0.1 km.

Orography factor (C_o^z)

Orography refers to the influence of mountains, hills and other huge landforms on wind speed. It increases mean wind velocity but does not affect wind turbulence. Both the standard and the NA agreed on using A.3 in the standard for calculating the orography factor when significant. However, their approach to determining whether orography is significant differs.

The standard requires orography to be considered when the velocity of the wind is increased by more than 5% according to clause 4.3.3(1)

As for the UK National Annex significant orography is defined in Figure NA.2 which is reproduced below

 

4. Wind Turbulence Intensity (I_v^z) 

(Not necessary when orography is not significant)

Wind turbulence causes increase and decrease in the wind value. This characteristic of wind to increase in speed abruptly is also described as gustiness which leads to an increase in the peak pressure of the wind. The turbulence factor (I_v^z ) is given in expression (4.7) of EN 1991-1-2004 as:

I_v^z   = σ_v / v_m^z   = K₁ / ( C_o^z  x In (z/z_o )       for Z_min≤ Z ≤ Z_max

I_v^z  =  I_v^zmin     for Z > Z_min

Where:

K₁ is the turbulence factor

z_o is the roughness length given in table 4.1 for the appropriate terrain category.

C_o^z  is the orography factor

Z_max  is taken as 200m

 

UK National Annex

The turbulence intensity of a flat terrain (I_v^z flat) is given in NA5 gives turbulence factor for site in a country terrain. For a site in a town terrain, the value obtained from figure NA.5 should be multiplied by turbulence correction factor (K_IT ) which can be gotten from figure NA.6.

 

2. Calculating Wind Pressure (Category 2)

5. Basic wind velocity Pressure

When wind movement is obstructed, it exacts pressure on the obstruction. This pressure has always been traditionally called “dynamic pressure”, however Eurocode 1 part 1-4 refers to it as “basic velocity pressure”. The dynamic pressure is a function of the wind speed and density. It can be expressed as:

q_b =  1/2 ρ v_b²  (expression 4.10 of the standard)

ρ is the density of air. Recommended value is 1.226Kg/m2 in the UK NA

v_b is the basic velocity pressure (evaluated earlier)

 

6. Peak velocity Pressure (q_p^z)

The peak velocity pressure account for the gustiness of wind. As Eurocode 1 part 1-4 does not account for gustiness when estimating wind velocity, this is made up for when estimating the wind pressure. The sudden increase in wind speed within a short time (gustiness) is accounted for by calculating the “peak velocity pressure”.

The peak velocity pressure composes of two parameters which are the basic wind velocity pressure (q_b ) and the exposure factor (C_e^z).

The standard recommends expression (4.8) for determining the peak velocity coefficient which is reproduced below:

q_p^z =( (1 + 7I_v^z ) x ρ v_m^{2 (z)})/2  = C_e^z x q_b

Where:

I_v^z is the turbulence intensity (discussed earlier).

q_b  is the basic wind velocity pressure (discussed earlier)

C_e^z is the exposure factor given in equation (4.9) of the standard as  q_p^z/q_b

However, when the terrain is flat (i.e. co(z) = 1,0) the exposure factor can be determined by using figure 4.2 of the standard as a function of terrain categories 0 to IV defined in table 4.1 and height (z) above the terrain.

 

UK National Annex

The UK NA has a substantially different approach to estimating the peak velocity pressure. In fact, the UK NA categorically states in NA.2.17 that expression (4.8) in the standard does not apply.

The UK NA gives different expressions for peak wind velocity for when orography is significant but reference height is less than 50m (Z < 50), when orography is significant and reference height is above 50m, and when orography is not significant.

Besides the exposure factor (C_e^z ), the UK NA also gives exposure modification factor (C_eT^z ) for site in town terrain when reference height is not greater than 50m. If the site is located within country, then exposure correction factor (C_eT^z ) is taken as 1. Exposure factor and exposure correction factor can be determined using Figure NA.7 and NA.8 respectively. The two parameters also take account of the sheltering effect of surrounding structure which is implemented in UK NA through the displacement height (h_dis). The displacement height can always be conservatively taken as 0 as explained earlier.

These expressions for peak velocity pressure in the UK national annex are reproduced below:

Peak Velocity Pressure when Orography is not significant

q_p^z = C_e^z •ce,(T) • q_b    (for town terrain)       equation (NA.3a)

q_p^z = C_e^z • q_b              (for country terrain)

 

Peak Velocity Pressure when Orography is significant (z ≤ 50m)

When orography is significant but building height is less than or equal to 50m, [(C_o^(z) + 0.6)/1.6] ² only needed to be added to the peak velocity pressure.

qp(z) = C_e^(z) •ce,T •q_b• [(C_o^(z) + 0.6)/1.6] ²     for z ≤ 50m; for sites in town terrain   (equation (NA.4a))

qp(z) = C_e^(z) •q_b• [(C_o^(z) + 0.6)/1.6] ²       for z ≤ 50m; for sites in country terrain

Where:

Ce(T) is the exposure correction factor

C_e^z    is the exposure factor

The value of exposure factor and exposure correction factor are given in fig NA.7 and NA.8 respectively of the national annex.

Peak Velocity Pressure when Orography is significant and for z ≥ 50m

$q_p{ }^{(z)}=\left\lceil 1+3.0 I_v{ }^{(z)}\right\rceil^2 \cdot \text { 0.5. } \rho . v_m{ }^2 \quad \ldots . \quad \text { Expression (NA.4b) }$

This can be simplified further for sites in town and country as shown below

$q_p{ }^{(z)}=\left(1+\left(3 \operatorname{Iv}_{(z), \text { flat }} \cdot\left(\frac{\mathrm{k}_{\mathrm{L}, \mathrm{~T}}}{c_{o(z)}}\right)^2 \cdot 0.613 \cdot v_m^2\right) \quad\right. \text { For sites in Town terrain }$

$q_p{ }^{(z)}=\left(1+\left(3 \operatorname{Iv}_{(\mathrm{z}), \text { flat }} \cdot\left(\frac{1}{c_{o(z)}}\right)^2 \cdot 0.613 \cdot v_m^2\right) \quad\right. \text { For sites in Country terrain }$

 

3. Calculating Wind loads and Forces on Structures using Aerodynamic Coefficients (category 3)

After determining peak velocity pressure of wind, the next steps in determining wind loads are structures specific. This category 3 shall only discuss the generic steps in calculating wind loads and then forces on structures, further application of the wind load on specific structures such as buildings, roof, bridges, canopies etc. are discussed in separate posts.

Wind force on a structure can generally be determined by multiplying the four parameters listed below

• Peak velocity pressure
• Area of structure/part of structure/elements under consideration
• Aerodynamic coefficients
• Structural factors.

The peak velocity pressure has been discussed earlier, we are left with aerodynamic coefficients and structural factors to discuss.

Aerodynamic Coefficients.

In order to correctly represent the interaction between wind pressure and a structure, some coefficients are needed. These coefficients are broadly categorized into two:

• Surface pressure coefficients
• Force coefficients

Section 7.1 of the standard gives aerodynamic coefficients appropriate for particular types of structures. Different structures like buildings, bridges, canopies etc. have different pressure or force coefficients appropriate for them. Some of these instances are mentioned below:

• Pressure coefficient (internal and external pressures) are appropriate for buildings, and circular cylinders. (Click here to read on application of wind load on Buildings. You should also click here to study a Worked Example on Wind Load on Frame Buildings).

 

• Net pressure coefficient is appropriate for canopy roofs, free-standing walls, parapets, and fences.

 

• Friction coefficients is appropriate for walls when the total area of all surfaces parallel with (or at a small angle to) the wind is not equal to or less than 4 times the total area of all external surfaces perpendicular to the wind (windward and leeward).

 

• Force coefficients is appropriate for signboards, structural elements with rectangular cross section, structural elements with sharp edged section, structural elements with regular polygonal section, circular cylinders, spheres, lattice structures and scaffoldings.

 

The reader can refer to section 7 of the standard for information on where each of this coefficient for each structure can be found.

 

Structural Factor

The structural factor (c_sc_d) has two components; ‘c_s’ which is the size effect factor, and ‘c_d’ which is the dynamic factor. The structural factor takes into account the effect of non-simultaneous occurrence of peak wind pressures on the surfaces of a structure (c_s) together with the effect of the vibrations of the structure in its fundamental mode due to turbulence (c_d).

The structural factor can be determined using clause 6.3.1 or Annex D of the standard. However, in most cases where the properties of a structure does not make them susceptible to dynamic excitation such as façade and roof elements with natural frequency greater than 5Hz, buildings with a height less than 15 m, framed buildings less than 100m high and whose height is less than 4 times the in-wind depth, chimneys with circular cross-sections whose height is less than 60 m and 6.5 times the diameter the value of c_sc_d may be taken as 1.

UK National Annex.

In the UK National Annex, ‘c_s’ and ‘c_d’ are evaluated separately using Table NA.3 and Figure NA.9 respectively. The values of size factors (c_s) given in table NA.3 depends on the sum of the breadth and height (b+h) of the structure or element.

In most typical framed buildings ‘c_sc_d’ can be taken as 1.0.

Wind Force on structures using Surface Pressure Coefficients

The wind force acting on a structure or a structural element may be determined by vectorial summation of external forces, internal forces and frictional forces (if applicable) over the structure or elements.

w_e =  c_sc_d q_p^Ze c_e

w_i =  q_p^Zi c_i

w_fr =  q_p^Ze c_fr

(The friction pressure act on the face parallel to the wind and are only significant when the area of the face parallel to the wind is large. Hence, according to clause 5.3(4) of the standard the effects of wind friction on a surface should be ignored when the total area of all surfaces parallel with (or at a small angle to) the wind is equal to or less than 4 times the total area of windward, and leeward surfaces).

The net wind pressure/load on a surface is:

w_k= c_sc_d q_p^(Ze) c_e + q_p^(Zi) c_i + q_p^(Ze) c_fr

Wind force on a surface or structure is obtained by multiplying the wind load by the area of reference (A_fr) of the structure or element. This is mathematically expressed below:

F_w= (c_sc_d q_p^(Ze) c_e + q_p^(Zi) c_i + q_p^(Ze) c_fr) A_rf

where;

w_e  is external wind pressure

w_i is internal wind pressure

w_fr is wind pressure due to friction

q_p^(Ze) is peak velocity pressure at a reference height (z) for external pressure

q_p^(Zi) is peak velocity pressure at a reference height (z) for internal pressure

c_e is external pressure coefficient

c_i is internal pressure coefficient

c_fr is the friction coefficient

A_rf is reference area of the structure or structural element.

Note: The standard confines the effect of structural factors (c_sc_d) to external pressures alone. This is however at variance with traditional UK practice where structural factors are applicable to both external and internal pressure.

 

Wind Force on structures using force coefficients

Wind pressure due to force coefficient is expressed as:

w = c_sc_d∑ c_r  q_p^(Ze)

The wind force is the product of wind pressure and area of reference which is expressed below:

F_w= (c_sc_d ∑ c_r  q_p^(Ze)) A_rf  (expression 5.4 of the standard)

c_r  is the force coefficient of the structural element

Other parameters remain as defined under wind pressure coefficient.

It should be noted that in accordance with the UK NA which implements the displacement height (h_dis), wind pressure for both external and internal surfaces at a reference height (z) can be rendered as q_p^{(Z – h_dis)} . This is applicable to expressions associated with both force coefficients and pressure coefficients.

 

References:

BS EN 1991-1-4:2005+A 1 :2010:  Eurocode 1: Actions on structures – Part 1-4: General actions – Wind actions.

UK National Annex to BS EN 1991-1-4:2005+A 1 :2010:  Eurocode 1: Actions on structures – Part 1-4: General actions – Wind actions.