This article presents an overview on application of wind load on building structures according to EN 1991-1-4-2005 + A1:2010 and the UK National Annex to EN 1991-1-4-2005 + A1: 2010.

This article shall build on a previous article titled “Wind Actions on Structures” where a detailed explanation is made on the steps required to calculate peak velocity pressure of wind. If you do not have a thorough background on wind actions, it is recommended that you visit the previous article and read up to “peak velocity pressure” before continuing with this article.

In “Wind Actions on Structures” the steps required to determine wind forces on a structure are broadly categorized into three. The first category is about determining the wind velocity. The second category becomes conclusive on determining the peak velocity pressure. The third category which is “calculation of wind forces on a structure” is explained to be structure specific. The main aim of this article is to revisit this third category in light of building structures.

Wind force on building structures or elements can be determined by multiplying the four parameters listed below.

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

Peak velocity pressure has been discussed in detailed in “Wind Actions on Structures”, we shall discuss the pressure coefficients and structural factors for building structures in subsequent paragraphs.

Wind Pressure and Pressure Coefficient for buildings

The standard considers the action of wind on both external and internal surfaces of building elements (walls and roofs) using external pressure and internal pressure coefficients. Section 7.2 of the standard is dedicated to pressure coefficients for buildings. Wind pressure is evaluated both for external and internal surface of building elements. The net pressure on the element (walls, roofs, and appendages) is then derived by vectorial summation of the external and internal surface pressure and also pressure due to friction if applicable. Pressure, directed towards the surface of the element is taken as positive, and pressure directed away from the surface, called suction is taken as negative.

Ie: w_k = w_e + w_i (+ w_fr , if applicable).

where:

w_k  = wind load/pressure

w_e = external wind pressure

w_i = internal wind pressure

w_fr = wind pressure due to friction

(NB: According to clause 5.3(4) of the standard, the effects of wind friction on the surface can be disregarded 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 all external surfaces perpendicular to the wind (windward and leeward).

Generally, wind pressure – both external and internal – on different part of a building is obtained by the product of the peak velocity pressure at a certain reference height (q_p^(Z)), and the pressure coefficient appropriate for that part of the building (c_p).

Ie: w_k = c_p q_p^(Z).

Where;

w_k is wind pressure.

q_p^(Z) is peak velocity pressure at reference height z.

c_p is pressure coefficient (either for external or internal pressure).

Consequently, the following sub-sections on external pressure and internal pressure coefficients provide three main information of necessary parameters required for computing wind pressure: The information are:

• How a building is to be defined into zones for pressure coefficients
• Reference height for peak velocity pressure on different faces of the building
• And lastly, reference to tables and figures where the pressure coefficients can be obtained for defined part of the building

External Pressure Coefficient

External pressures are created directly by flow of wind around structures. The values for external pressure coefficients according to the standard are based on the loaded area of the defined portion of the structure or elements.  Local coefficient (Cpe,1) is for loaded areas of 1.0m² or less, they are used for the design of small element; while overall coefficient (cpe,10) is for areas ≥ 10,0 m², they are used for the design of the overall structure. For defined portion of an element that has an area between 1.0m² and 10.0m², logarithmic interpolation can be done using figure 7.2 of the standard.

UK National Annex

The UK approach to external pressure coefficients which is implemented in UK N A differs from that of the standard. External pressure coefficients are only for two loaded areas, which are either ≤ 1.0 m² or greater. Clause NA 2.25 states that the cpe,1 value should be applied to loaded areas ≤ 1.0 m² and that the cpe,10 values apply to loaded areas > 1.0 m².

External Pressure Coefficients for vertical walls in rectangular Plan Building

Vertical walls in buildings are defined as A, B, C, D, and E in figure 7.5 of the standard which is reproduced below. The windward and leeward wall defines as D and E respectively are single zone of pressure coefficient. The sidewall is divided into several zones defines as A, B, and C from the corner of the windward face to that of the leeward face. The width of each zone on the sidewall is controlled by a parameter e which is b or 2h, whichever is smaller.

 

The pressure distribution for the leeward wall and the sidewalls should be taken as uniform over the height of the building as indicated in the Note in Clause 7.2.2(1) of the standard and Clause NA 2.26 of the UK NA. As for the windward face of a wall defined as D, it can be divided into different part depending on the aspect ratio of h/b as shown in figure 7.4 of the standard which is reproduced below. The top level of each part is considered as the reference height ‘Z_e’.

 

According to the figure above, the approach to getting the reference height is divided into three for external pressure

• When h ≤ b; then reference height = Ze
• When h ≤ 2b; then the reference height is divided into two here
  1. Ze = b (from the bottom)
  2. Ze = h (the remaining at the top)
• When h ≥ 2b then the reference height is divided into more than two here
  1. Ze = b (from the bottom)
  2. Ze = multiple strips at the middle (more findings about this)
  3. Ze = h (the remaining at the top)

The external pressure coefficient for each zone (A, B, C, and D) is dependent on the ratio d/h of a building and their values can be found in Table 7.1 of the standard. However, for slender building where h/d > 5, the total wind loading may be based on force coefficient in clauses 7.6 to 7.8, and 7.9.2 of the standard. The overall coefficient of the (drag coefficient) building can be derived by vectorial summation of the external windward and leeward coefficients.

w_k = q_p^(Z). c_net 

where;

c_net  is the net pressure coefficient provided in table NA.4.

Factor for accounting for lack of correlation between the windward and leeward faces may also be applied to the net pressure coefficients. For buildings with h/d ≥ 5 the resulting force is multiplied by 1. For buildings with h/d ≤ 1, the resulting force is multiplied by 0,85. For intermediate values of h/d, linear interpolation may be applied.

External Pressure Coefficients for Building Roofs

Roofs are defined as F, G, H, I, J, K, L, M, and N for flat roof, monopitch roof, duopitch roof, and hipped roof in figure 7.6 to 7.9 of the standard. The pressure coefficients for these types of roofs are also given within 7.2.3 to 7.2.6.

The pressure coefficients for vaulted roofs and dome roofs are given for only Cpe,10 in figure 7.11 and 7.12 respectively. The reference height for pressure distribution should be taken as Z_e = h + f as described in the figure below.

 

UK Annex

The standard only gives room for a National Choice of pressure coefficients for vaulted roofs and domes. The UK NA maintains that the recommended values given in Figure 7.12 of the standard should be used for dome roofs, however, it categorically states in NA.2.29 that figure 7.11 should not be used for vaulted roofs.

For vaulted roofs, external pressure coefficients are given in Figure NA.11 and Figure NA.12 for windward zone A and central zone B respectively. External pressure coefficients for leeward zone C should be taken as 0.5 for h/d ≤ 5.0 and f/d ≤ 0.5.

Internal Pressure Coefficient

Internal pressures are caused by openings and permeabilities in structures. The internal pressure coefficient, Cpi, depends on the size and distribution of the openings in the building envelope, and its value directly depends on whether the building has a dominant face.

According to clause 7.2.9(4), a face of a building should be regarded as dominant when the area of openings at that face is at least twice the area of openings and leakages in the remaining faces of the building considered. If this description is valid for a building, the value of the internal pressure coefficient should be taken as a fraction of the external pressure at the openings of the dominant face as given in the below expressions.

Cpi = 0.75 Cpe (when opening at dominant face = 2 x openings at remaining faces)

Cpi = 0.9 Cpe (when opening at dominant face ≥ 3 x openings at remaining faces)

When the area of the openings at the dominant face is between 2 and 3 times the area of the openings in the remaining faces linear interpolation for calculating Cpi may be used.

However, when a building is without a dominant face, the internal pressure coefficient Cpi should be determined from Figure 7.13 which is a function of h/d and μ (opening ratio for each wind direction). If there is not enough information to estimate μ for a particular case, then Cpi should be taken as the more onerous of +0.2 and -0.3.

When in at least two sides of a building, the total area of openings in each side is more than 30 % of the area of that side, then the building structure should be treated as a canopy and the actions on it should be calculated based on section 7.3, and 7.4 of the standard.

Additionally, the reference height (Zi) for the internal pressures should be equal to the reference height (Ze) for the external pressures on the faces which contribute by their openings to the creation of the internal pressure

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 ‘cd’ are evaluated separately. The values of size factor (c_d) are given in table NA.3 and they depend on the sum of the crosswind breadth and height (b+h) of the building or building element under assessment. If it is a frame building structure, the crosswind breadth is taken as the breadth of the whole building. However, for buildings like portal frame where each frame resists lateral load independently, crosswind breath can be taken as the bay width for gable frames and twice the bay width for internal frames.

The dynamic factors are given in figure NA.9 of the UK NA and they depend on the dimension ratio (h/b) of a building. Note 4 under figure NA.9 states that dynamic factor cd may be taken as 1.0 for framed buildings with structural walls and masonry internal walls and for cladding panels and elements.

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

 

Wind Force on Building and Building element

The wind force on a building element or structure can be said to be:

Wind Force = Wind pressure x Area of reference

Wind force on a building element equals:

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

If the frictional force is not significant, it can be reduced to:

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

Although EN 1991-1-4:2005 does not apply structural factor to internal pressure, however in line with traditional UK practice the wind force can be expressed as:

F_w=  c_sc_d q_p (c_e  – c_i ) A_rf

The overall wind force on a building using net pressure coefficient in table NA.4 of the UK NA can be expressed as:

F_w= c_sc_d q_p^(Z) c_net  A_rf

 

Click here to study a Worked Example on Wind Load on a 10-storey Frame Building

 

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.