4 Wind load on structues

Wind forces are variable loads which act directly on the internal and external surface of

structures. The intensity of wind load on a structure is related to the square of the wind

velocity and the dimensions of the members that are resisting the wind (frontal area).

Wind velocity is dependent on geographical location, the height of the structure, the

topography of the area and the roughness of the surrounding terrain.

The response of a structure to the variable action of wind can be separated in to two

components, a background component and a resonant component. The background

component involves static deflection of the structure under the wind pressure. The

resonant component, on the other hand, involves dynamic vibration of the structure in

response to changes in wind pressure. In most structures the resonant component is

relatively small and structural response to wind forces is treated using static methods of

analysis alone. However, for tall or otherwise flexible structures, the resonant

component of wind should be calculated using dynamic methods of analysis. Such

structures are not considered further here.

Static effects of wind load on buildings

Reference wind velocity

The reference wind velocity for a locality is defined as the mean wind velocity at 10m

above farmland averaged over a period of 10 minutes with a return period of 50 years. It

is calculated using.

Vref = CDIRCTEMCALTVref, 0

Where Vref,0 is the basic reference wind velocity 10m above sea level and CDIR, CTEM and

CALT are factors relating to direction, seasonal variations in temporary structures and

altitude respectively.

The factors CDIR, CTEM and CALT will be specified for local conditions by individual

countries. For each of these factors, a value of unity may be assumed unless otherwise

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specified for a particular region. The direction factor, CDIR. Allows for the orientation of

the structure in relation to the direction of the prevailing wind. The seasonal variation

factor, CTEM, may be applied to structures of a temporary nature which are exposed to

wind for only part of a given year. It reflects the fact that storm winds are less likely in

the summer months in most European countries. (Temporary structures are subjected to

a reduced risk of exposure to strong winds simply by virtue of their reduced design life.

This phenomenon can be allowed for by means of a separate adjustment to the wind

reference velocity.) The altitude factor, CALT, allows for the altitude of the site on which

the structure is located. Wind speeds tend to be greater in sites located at high altitudes.

Exposure coefficient

Wind velocity tends to decease near ground level owing to frictional forces between the

wind and the ground. If the terrain is rugged, the decrease in velocity can be quite

substantial. The exposure coefficient takes account of the variation from the reference

wind velocity due to the roughness around the structure, the local topography and the

height of the structure above ground level. EBCS1 defines the exposure coefficient at

height z meters, using the relationship:

Where Cr and Ct are roughness and topography coefficients respectively and kT is a

terrain factor. The terrain factor is a function of the nature of the terrain and is given in

Table 4.1.

Table 4.1 Ground roughness categories and parameter values (from EBCS)

Category Terrain description krZ0

(m)zmin

(m)

1Rough open sae. Lakeshore with 5 km fetch upwind and smooth flat country without obstacles

0.17 0.01 2

2Farmland with boundary hedges, occasional small farm structures, houses or trees

0.19 0.05 4

3 Suburban or industrial areas and permanent forests 0.22 0.3 8

4 Urban areas in which 15% of the surface is covered with buildings and

0.24 1 16

2

their average height exceeds 15mThe topography coefficient, Ct, accounts for the increase in mean wind speed over

isolated hills and escarpments. Details for its calculation in such cases are given in

EBCS1 (Figure 3.6 and 3.7). For all other situations, Ct may be taken as unity.

(EBCS provisions)

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The roughness coefficient, Cr(z), accounts for the variability of mean wind velocity due

to the height of the structure above ground level and the roughness of the terrain. It is

defined by the logarithmic relationship:

Cr(z) = kr Ln(z z0) for z zmin

Cr(z) = Cr(zmin) for z zmin

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Where z0 is the roughness length and zmin is the minimum height. Both z0 and zmin are

dependent on the ground roughness and are given in Table 4.1.

External wind pressure

The wind pressure acting on the external surface of a structure is function of the

reference wind pressure which is given by:

Where = air density (kg/m3)

ref = reference wind velocity (m/s)

Fig. 4.1 Reference height, Ze depending on h and b.

The density of air varies with temperature, elevation and the expected atmospheric

pressure in the region during a storm. EBCS1 gives a recommended design value of at

200 C for different altitudes.

Table 4.2 Values of air densitySite altitude (m) above sea level (kg/m3)

0 1.20500 1.121000 1.061500 1.002000 0.94

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In order to determine the contact pressure on the outside of a structure or part of a

structure, the reference pressure, qref. of the wind must be multiplied by an external

pressure coefficient. cpe, and an exposure coefficient. Thus the external pressure is:

We = ce(ze)cpeqref

Where ce(ze) is the exposure coefficient evaluated at a reference height, ze. Reference

heights for the calculation of external pressure coefficients depend on the breadth to

height ration of the structure. For rectangular buildings whose breadth, b, is less than

their height, h, as illustrated in Fig. 4.1(a), the reference height equals the actual height.

When h exceeds b but is less than 2b, the building is considered in the two parts

illustrated in Fig. 4.1(b). When h exceeds 2b, the building is considered in multiple

parts. A lower part extends upwards from the ground a distance b. An upper part

extends downwards from the top a distance b. the rest of the building can be divided in

to any number of parts. With the reference height in each case calculated as the distance

from the ground to the top of the part.

The external pressure coefficient, Cpe, accounts for the variation in dynamic pressure on

different zones of the structure due to its geometry, area and proximity to other

structures. For instance, the wind acting on the structure in Fig. 4.2 is slowed down by

the windward face and generates a pressure on that face. The wind is then forced around

the sides and over the top of the structure, causing suction on the sides and on all

leeward faces. Suction can also be generated on the windward slope of a pitched roof if

the pitch is sufficiently small.

Fig. 4.2 Wind flow past a rectangular building. (a) plan; (b)end elevation

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With reference to Fig. 4.3, the external pressure coefficients for the various zones of the

walls of a rectangular building are given in Table 4.3. Similar tables are given in EC1

for other building shapes. The values in Table 4.3 are valid for surface areas in excess of

10m2 only. Values for lesser surface areas are given in the Euro code. External pressure

coefficients for the roof zones in a flat-roofed building are given in Table 4.4. Other

values are specified for areas less than 10m2, or when parapets are present, or when the

eaves are curved. Pressure coefficients are considered positive when the pressure is

action on to the surface of the structure and negative when the pressure is acting away

from that surface. Thus, the external pressure coefficient is positive when acting

inwards.

Fig. 4.3 External pressure coefficient zones (e = lesser of b and 2h): (a) de; (b) de

F

0.5e

d0.8e0.1e

0.2e

GF

0.25e 0.25eh

H

I

A

B

C

D

b

0.5e

d0.1e

0.2e

GF

0.25e 0.25eh

F

H

I

A

B*

D

b

E

E

7

The external pressure coefficient cpe for buildings and individual parts of buildings

depend on the size of the loaded area A. They are given for loaded areas A of 1m3 and

10 m3 in the relevant tables for the appropriate building configurations as cpe,1 and cpe,10

respectively. For other loaded areas the variation of the values may be obtained from

Fig. 4.4.

Figure 4.4 Variation of external pressure coefficient for buildings with size of the loaded area A

The figure is based on the following:

cpe = cpe,1 A 1m2

cpe = cpe,1 + (cpe,10 - cpe,1) log10A 1m2 < A < 10m2

cpe = cpe,10 A 10m2

Internal wind pressure

Internal pressure arises due to openings, such as windows, doors and vents, in the

cladding. In general, if the windward pane has a greater proportion of opening than the

leeward panel, then the interior of the structure is subjected to positive (outward)

pressure as illustrated in Fig.4.5 (a). Conversely, if the leeward face has more openings,

then the interior is subjected to a negative (inward) pressure as illustrated in Fig. 4.5(b).

Like external pressure internal pressure is considered positive when acting on to the

surface of the structure. Thus, internal pressure is positive when the pressure acts

outward.

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Table 4.3 External pressure coefficients for the walls of a rectangular building

(from EC1, part 2.3)

Zone (Fig.3.13) d/h1 1 d/h4 d/h 4

A -1 -1 -1

B,B* -0.8 -0.8 -0.8

C -0.5 -0.5 -0.5

D +0.8 0.8-0.067(d/h-1) +0.6

E -0.3 -0.3 -0.3

Table 4.4 External pressure coefficient for a flat roof (from EC1, part 2.3)

Zone (Fig. 3.13) Coefficient

F -1.8

G -1.2

H -0.7

I 0.2

Fig. 4.5 Internal pressures in structures

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Internal pressure on a building or panel is given by:

wi =ce(zi)cpiqref

Where zi is the reference height for internal pressure equal to the mean height of the

openings and cpi depends on the distribution of openings around the building. The

values recommended by EBCS1 are given in Fig 4.6 for a building without internal

partitions. In such a building, internal pressure is assumed to act uniformly over the

total area of the building. For buildings with internal partitions the extreme values, cpi =

0.8 and cpi = -0.5, may be used.

Fig. 4.6 Internal pressure coefficients, cpi, in buildings with openings (from EBCS1)

Wind force on structures

The total wind force action on individual zones of clad structures is proportional to the

difference in pressure between the external and internal faces. That is:

Fw = (we – wi) Aref

Where Fw is the total inward force and Aref is the reference area, generally equal to the

projected area of the zone normal to the wind direction. When calculating the total force

on (all zones of) a building, the forces on each zone can be calculated using the above

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equation (3.9) and summed. Alternatively, the total force on an entire structure (or an

exposed individual member) can be expressed as:

Fw = ce(ze)cf qref Aref

Where cf is a force coefficient. While, strictly speaking, the force coefficient is

approximately equal to the algebraic sum of the external pressure coefficients on the

windward and leeward faces, they are in fact slightly different owing to frictional effects

on the side walls. EC1 provides tables of force coefficients for common forms of

structures and sections used in structural frames.

Example 4.1 wind loads

Figure 4.5 The structure illustrated in Fig. 4E-1 is to be located in the centre of Paris on

a site surrounded by buildings of similar height. It is an apartment building

with internal partitions.

Fig. 4E-1 Building of example 4.1

Wind from the east and west is transmitted from clad faces to the north and south

masonry walls. Each external panel has opening windows equal in area to one tenth of

the total wall area.

(a) Determine the total moment due to wind at the base of the north and

south masonry walls.

(b) Calculate the maximum pressure on the east masonry wall.

Solution

The reference pressure and exposure coefficient are first calculated.

Reference pressure

12

NE

W

10

20

11

The basic reference wind velocity for Paris can be taken from the map and is 26m/s .

Assuming values of unity for cDIR, cTEM and cALT, the reference wind velocity is also 26

m/s. Hence the reference wind pressure is,

Qref = v

= (1.25)(26)2

= 423 Nm2

Exposure coefficient

As the height exceeds the breadth but is less than twice its value, the building is

considered in two parts, as illustrated in Fig. 4.1(b). The reference heights for external

pressure are thus:

ze = h = 20m

and

ze = b = 12m

As the building is located in an area of Roughness Category 4 (refer to Table 4.1), kT =

0.24, z0 = 1m and smin = 16m. Equation of roughness coefficient gives:

cr(20) = kTLn(20/z0)

= 0.24 Ln(20/1)

= 0.719

cr(12) = cr(zmin)

= 0.24 Ln(16/1)

= 0.666

Taking a topography coefficient of unity, the exposure coefficients become:

ce(20) = c (20) c (20)

= (0.719)2(1)2

= 1.725

ce(12) = c (12) c (12)

= (0.666)2(1)2

12

= 1.563

External pressure

It can be seen from Fig. 4.3 that only zones D and E are of interest in this example. The

ratio d/h is 10/20 = 0.5. Hence from Table 4.3:

cpe(Zone D) = +0.8

cpe(Zone E) = -0.3

At the reference height of 20m, the external pressure on zone D is (equation (3.7)):

we = ce(20)cpeqref

= 1.7250.80.423

= 0.584kN/m2

The corresponding force on the upper part of zone D is 0.584(128) = 56kN.

At the reference height of 12m, the external pressure on zone D is

we = ce(12)cpeqref

= 1.5630.80.423

= 0.529 kN/m2

and the corresponding force is 0.529(1212) = 76kN. The corresponding force for zone

E are -21kNand -29kN for the upper and lower parts respectively. These forces are

illustrated in Fig. 4E-2.

Fig. 4E-2 Forces due to east wind

20

8

10

16

676

29

56

21

12

E

W

N

12

13

(a) Internal pressure within a structure is self equilibrating. Thus, while it can cause

significant pressures on individual wall panels it results in no net force on the structure

overall. Accordingly, the overturning moment at the base of the north and south walls

due to wind is unaffected by internal pressure and is given by:

Moment = (56+21)16 + (76+29)6

= 1862 kNm

Of this, half will apply at the base of each of the two walls.

(b) To determine the total pressure on the east wall, it is necessary to calculate the

internal as well as the external pressure. As there are internal partitions, the worst value

for cpi is assumed, that is , cpi = -0.5. The maximum pressure will occur in the upper part

of zone D. In this part of the building the mean height of the windows will be assumed

to equal the mean height of the part. Hence:

Zi = 16m

The exposure coefficient at this height is calculated as before and is 0.666. Thus:

wi = ce(zi)cpiqref

= 0.666(-0.5)(0.423)

= -0.141

The net pressure on the upper part of zone D is the difference between the external and

the internal pressures, that is:

we – wi = 0.584 –(-0.141) = 0.725 kN/m2

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