Derivation of Wind Loads on Buildings | Worked Example

The subject of this post is the derivation of wind loads on buildings using Eurocode 1: Actions on Structures Part 1-4: General Actions- Wind Actions and the U.K National Annex. Kindly download the relevant codes from the links provided below before proceeding with this post, as references will be made where necessary to the relevant clauses in the codes.

Deriving wind load unto structures require the structural engineer to make sound sense of the environment in which the structure is to be constructed and the materials it will be clad in. The influence of opening within the building is also another major concern. To address this concerns Eurocode 1-1-4 creates some set of coefficients against which a base wind velocity will be factored. This is consequently converted to a pressure exerting a load on the building which can then be used for design by applying the appropriate partial factors.

The method presented in this post is based on the simplified method in the U.K National Annex, used for moderate rise buildings. Generally, for a building whose height is less or equal to 100m or 50m for buildings where the effect of orography (e.g. cliffs and escarpments) is significant.

Calculating the Wind Velocity

Wind loads are based on an expected velocity. In Eurocode 1-1-4, Clause 1.6.1 this is referred to as the fundamental wind velocity V_b,0 It is derived from a mean wind velocity of 10 minutes, which has a 1/10 chance of being exceeded over a one-year period. The height at which this speed happens is 10 m over flat, open countryside and allows for the effect of altitude.

The fundamental wind velocity is given in the national annex as:

{ v }_{ b,0 }={ v }_{ b,map }{ c }_{ alt }

In order to arrive at the wind pressure, some factors are applied to the fundamental wind velocity to obtain a base velocity which is used to determine the basic wind pressure and peak velocity pressure from which wind loads can be calculated. The full expression for the basic wind velocity may be written as

{ v }_{ b }={ v }_{ b,map }{ c }_{ alt }{ c }_{ dir }{ c }_{ season }

The factors upon which the basic wind velocity is dependent on are explained as follows

Location (V_b,map)

The location of the building determines the velocity from the map V_b,map. It is usually obtained from a map showing the isopleths of basic wind speed of a country. In Nigeria, this may be derived from the Nigerian Meteorological Agency wind documentation map.

Altitude Factor (C_alt)

The altitude factor C_altaccounts for the height above a reference datum the structure has been constructed from above the ground. Clauses NA. 2a and NA. 2b define how this coefficient is derived:

{ c }_{ alt }=1+0.001A\quad if\quad z\le 10m

{ c }_{ alt }=1+0.001A\left( 10/z \right) ^{ 0.2 }\quad if\quad z>10

z=0.6h

Where:

A is the altitude above mean sea level.
z is a referenced height based on the type of structure that is being considered. see figure 6.1 & 7 of EN 1991-1-1-4.
h is the height of the building above the ground.

However, the value of C_alt when z<10m is conservative and can be used for buildings of any height, the second expression is most beneficial when the height of the structure is relatively high.

Directional Factor (C_dir)

C_dir is derived from the table NA.1 in clause N.A 2.6 of the U.K National annexe, it depends on the angle to which the structure is oriented and the direction the wind has been considered. It is acceptable to conservatively take this factor as 1.0.

Season Factor (C_season)

The factor C_seasonseason is only used for temporary structures or structures under construction, its value may be obtained from table NA.2 in Clause NA. 2.7 of the UK National Annex. For non-temporary or finished structures it value may be ignored

Coefficients for Pressure due to Wind

Haven determined the basic wind speed V_b, the wind pressure from it can be calculated. This is known as the peak velocity pressure which depends on the roughness of nearby terrain and the structure’s proximity to the coast and how far it is located within a town. The peak velocity pressure is defined as

{ q }_{ p(z) }={ c }_{ o(z) }{ c }_{ e(z) }{ c }_{ e,T }qb

The variables listed in the equations upon which the peak velocity pressure depends on are explained below:

Basic Velocity Pressure (q_p)

The base pressure value due to the wind (q_b) is defined in Eurocode 1-1-4, equation 4.10 as

{ q }_{ b }=0.5\rho { v }^{ 2 }

where\quad \rho =air\quad density=1.226{ kg/m }^{ 3 }

{ q }_{ p }=0.613{ { v^{ 2 } } }_{ b }

Topography of Terrain (C_0(z))

The Eurocode refers to surface topography, such as hills and valleys, as ‘orography.’ Such features have a significant impact on wind speed, making C_0(z) a very significant coefficient. Figure NA.2, NA clause. 2.9 In the U.K. National Annex suggests a shaded area where the structures within it are influenced by land features, such as hills and escarpments. It explains how the effect of these features has an influence on the wind load derivation. If the structure is outside the shaded region, the value of C_0(z) is taken as 1.0.

Proximity to Shoreline (C_e(z))

Higher wind levels are usually seen in coastal areas. It is, therefore, necessary to allow this in the determination of the wind pressure applied to the structure. Figure NA.7 in the U.K National Annex is used to calculate the value of C_e(z) which is the variable added to the peak velocity wind pressure.

In order to use Figure NA.7, the height of the displacement (h_dis) must be known; this depends on the height of the adjacent buildings. Figure A.5 in Annex A.5 of Eurocode 1-1-4 explains how the height of the displacement is obtained. Note that, in the absence of reliable data on the heights of the surrounding buildings, it is appropriate to assume a value of 3 m for the factor (h_dis) in the city setting. If the building is in the countryside, its value may be taken as 0

Structures Within Towns Exposure Modified (C_e(T))

The further the structure is from the edge of the city, the more it is enclosed. This decreases the wind speed around the building and thus there is a resulting reduction in the applied pressure. To account for this reduction the factor C_e(T) is applied to the peak velocity pressure using figure NA 8 in the U.K national annexe. This figure is a diagram showing the height of displacement (h_dis) subtracted from the height of application of the wind pressure (z).

Calculating the Wind Load

Once the peak velocity pressure (q_p(z)) has been calculated, the wind load can be determined. This varies depending on what part of the structure is being assessed for wind loading. To determine the wind load, the coefficients explained in the next section is applied to the peak velocity pressure. These coefficients depend on the section of the building been assessed for the wind actions.

External Pressure Coefficient

There are two forms of the external coefficient of pressure (C_pe). (C_pe,1) refers to wind loads on distinct sections of the structure. Normally, this is used for the construction of cladding elements and is limited to an area not exceeding 1m2. Coefficient (C_pe,10) applies to larger portions of the structure and is specified in Clause 7.2.1 of Eurocode 1-1-4.

The values of these pressure coefficients are set out in Table NA.4 in the U.K Annex. These are based on the vertical walls of the building as defined in Figure 7.5 of Eurocode 1-1-4. (Also see figure one on this post)

Lack of Correlation Coefficient

There is normally a lack of correlation between wind pressures onto walls exposed to windward or leeward winds in contrast to those that are within the prevailing wind. To address this, Eurocode 1-1-4 clause 7.2.2(3) provides a factor that is applied to the wind forces to certain vertical walls. This factor only applies to walls that are within the windward and leeward wind areas and not those within the prevailing wind area.

For buildings with h/d greater than 5, the resulting force is multiplied by 1. For buildings with h/d less or equal to 1, the resulting force is multiplied by 0.85. For intermediate values of h/d, linear interpolation may be applied.
Clause 7.2.2(3) BS EN-1991-1-1-4

Provided all of these conditions are met, all forces on vertical faces within windward and leeward wind-exposed faces (e.g. areas D & E shown in Figures 1 can be multiplied appropriately with the factor

external pressure coefficient for rectangular building: wind loads — Figure 1: External Pressure Coefficient for a Rectangular Building

Internal Pressure Coefficient

The internal pressure coefficient (C_pi) is sensitive to the openings inside the walls of the structure to be considered for wind loads. Clause 7.2.9 of Eurocode 1-1-4 specifies how the coefficient is extracted by determining the structural openings inside the envelope.

When openings on opposite sides of the structure are greater than 30% of each surface area, the structure should be viewed as a canopy. It is at that stage that clauses 7.3 and 7.4 of the Eurocode 1-1-4 have to be complied with.

Where dominant faces are not present in a structure, Figure 7.13 of Eurocode 1-1-4 should be used in conjunction with table NA.9 that lists typical values of permeability. If there is a lack of certainty regarding the structure’s openings, then the value of (C_pi) should be taken as either +0.2 or -0.3, whichever provides the more onerous result. For more details on this see Clause 7.2.9(6) of Eurocode 1-1-4.

Structural Factor

The final factor applied to the peak velocity pressure is the size and dynamic factors also known as the structural factor (C_sC_d). Its value can be determined. by using either clause 6.2 (1) in Eurocode 1-1-4 or clause NA.2.20 in the UK National Annex. However, its value may be taken conservatively as 1.0 if the building is less than 15m in height

To determine the wind loads, both (C_pe) and (C_pi) are summed up with the structural factor C_sC_d and applied to the q_p(z)) peak velocity pressure described below

{w}_{z}={ q }_{ p(z) }({ C }_{ pe }-{ C }_{ pi }){ c }_{ s }{ c }_{ d }

This refers only to the zones in the structure as shown in figure 1 (rectangular buildings with flat roofs) and not the entire structure as a whole. For buildings with hipped, pitched roofs, there is some adjustment to the zones. See (figures 7.6 onwards in BS EN 1991-1-1-4).

Net Pressure Coefficients

While considering the separate zones of the structure for wind loads. The U.K National Annex allows for the generation of overall wind loads using net coefficients instead of summing the pressure coefficients of zones D (windward side) and E (leeward side). This is determined by using clause 2.27 in the U.K National Annex. In this section, there is a graph from which the net pressure coefficient C_net can be read and applied to q_p(z). The overall wind load is calculated as

{ w }_{ k }={ { q }_{ p(z) }c }_{ net }{ c }_{ s }{ c }_{ d }

Worked Example

Figure 1 shows a 12-storey permanent building located in the F.C.T. located 15km from the outskirts of the city. Determine the overall wind load on the building assuming the effect of orography is insignificant, and the site is at an altitude of 125m above mean sea level.

Basic Wind Velocity

The first step towards finding the wind load on this structure is to determine the basic velocity, to do that, we need the velocity from the map. This may be derived from the Nigerian Meteorological Agency wind documentation map.

Note that the velocity obtained from maps might be the fundamental velocity V_b,0 in such an instance, the altitude factor will not be applied.

{ v }_{ b }={ v }_{ b,map }{ c }_{ alt }{ c }_{ dir }{ c }_{ season }

{ v }_{ b,map }=36m/s (assumed)

Altitude Factor

z=0.6h=0.6\times 42=25.2m>10\\; A=125m

{ c }_{ alt }=1+0.001A\left( 10/z \right) ^{ 0.2 }\\ if\quad z>10

{ c }_{ alt }=1+0.001\times 125\left( \frac { 10 }{ 25.2 } \right) ^{ 0.2 }\\=1.1

Directional Factor: The wind load has been applied within 45 degrees of the normal face, therefore using the conservative value in table N.A 1 in the U.K National Annex.

{ c }_{ dir }=1.0\quad conservatively

Seasonal Factor: The seasonal factor is not relevant because the building is not a temporary structure.

{ v }_{ b }={ v }_{ b,map }{ c }_{ alt }{ c }_{ dir }

=36\times 1.1\times 1.0=39.6m/s

Peak Velocity Pressure

Since orography is insignificant, the equation for the peak velocity pressure reduces to

{ q }_{ p(z) }={ c }_{ e(z) }{ c }_{ e,T }qb

(C_e(z)) is obtained from figure NA.7 using z=42m and h_dis=3m. The distance upwind to the shoreline is greater than 100m because Abuja is not a coastal city