Calculation of Wind Peak Velocity Pressure - Eurocode 1

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Wind Peak Velocity Pressure

Description:

Calculation of peak velocity pressure depending on the basic wind velocity and the terrain

category at the location of the structure. The wind action on the structure (forces and

pressures) can be derived from the peak velocity pressure.

According to: According to: EN 1991-1-4:2005+A1:2010 Section 4 EN 1991-1-4:2005+A1:2010 Section 4

Input

Illustration of Terrain categories reproduced from EN1991-1-4 Annex A Illustration of Terrain categories reproduced from EN1991-1-4 Annex A

Results

Project: Project: Subject: Subject: Designer: Designer: Date: Date:

Basic wind velocity

v

_b

=

4444 m/sm/s

Terrain category

=

II

Reference height from ground of

the examined part of the structure

z

=

1.25

1.25 mm

e

Orography factor at reference

height height z z

c

(

z

) =

1 1 e e

0

0 e

e

Wind peak velocity pressure

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Notes

1. The calculated peak velocity pressure q ( z ) is the wind pressure corresponding to the peak wind velocity. In order to calculate the nal wind actions on the structure (wind force or wind pressure) the appropriate force coecient or pressure

coecient depending on the type of structure must be applied, as specied in EN1991-1-4 §5.2 and §5.3

Details

p e

Input Data

Basic wind velocity: v = 44 m/s Terrain category: = I

Reference height from ground of the examined part of the structure: z = 1.25 m Orography factor at reference height z : c ( z ) = 1

Calculation of wind pressure

Basic wind velocity

The basic wind velocity v is dened in EN1991-1-4 §4.2(2)P as a function of the wind direction and time of year at 10 m above ground of terrain category II. It is calculated as:

v = c ⋅c ⋅v

where v is the fundamental value of the basic wind velocity which is dened in EN1991-1-4 §4.2(1)P as the characteristic 10 minutes mean wind velocity at 10m above ground level for terrain category II. The value of v is provided in the National Annex based on the climatic conditions of the region where the structure is located. The inuence of altitude on the basic wind velocity v may also be specied in the National Annex.

The directional factor c and the seasonal factor c are dened in EN1991-1-4 §4.2(2)P and they take into account the eects of wind direction and time of the year. Their values are generally equal to c = 1.0 and c = 1.0. The National Annex may specify values of c and c dierent than 1.0.

In the following calculations the basic wind velocity is considered as v = 44.00 m/s.

Terrain roughness

The roughness length z and the minimum height z are specied in EN1991-1-4 Table 4.1 as a function of the terrain category. For terrain category I the corresponding values are z = 0.010 m and z = 1.0 m.

The terrain factor k depending on the roughness length z = 0.010 m is calculated in accordance with EN1991-1-4 equation (4.5):

k = 0.19 ⋅ ( z / z ) = 0.19 ⋅ (0.010 m / 0.050 m) = 0.1698 m

The roughness factor c ( z ) at the reference height z accounts for the variability of the mean wind velocity at the site of the structure due to the height above ground level and the ground roughness of the terrain upwind of the structure. It is calculated in accordance with EN1991-1-4 equation 4.4.

b e e 0 e b b dir season b,0 b,0 b,0 b dir season dir season dir season b 0 min 0 min r 0 r 0 0,II 0.07 0.07 r e e

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For the case where z ≥ z :

c ( z ) = k ⋅ ln( z / z ) = 0.1698 m ⋅ ln(1.250 m / 0.010 m) = 0.8196

Orography factor

Where orography (e.g. hills, clis etc.) increases wind velocities by more than 5% the

eects should be taken into account using an orography factor c ( z ) dierent than 1.0, as specied in EN1994-1-1 §4.3.3. In general the eects of orography may be neglected when the average slope of the upwind terrain is less than 3° up to a distance of 10 times the height of the isolated orographic feature.

In the following calculations the orography factor is considered as c ( z ) = 1.000.

Mean wind velocity

The mean wind velocity v ( z ) at reference height z depends on the terrain roughness, terrain orography and the basic wind velocity v . It is determined using EN1991-1-4

equation (4.3):

v ( z ) = c ( z ) ⋅ c ( z ) ⋅ v = 0.8196 ⋅ 1.000 ⋅ 44.00 m/s = 36.06 m/s

Wind turbulence

The turbulence intensity I ( z ) at reference height z is dened as the standard deviation of the turbulence divided by the mean wind velocity. It is calculated in accordance with

EN1991-1-4 equation 4.7 .

For the case where z ≥ z :

I ( z ) = k / [ c ( z ) ⋅ ln( z / z ) ] = 1.000 / [ 1.000 ⋅ ln(1.250 m / 0.010 m) ] = 0.2071

where the turbulence factor is considered as k = 1.000 in accordance with EN1991-1-4 §4.4(1).

Basic velocity pressure

The basic velocity pressure q is the pressure corresponding to the wind momentum determined at the basic wind velocity v . The basic velocity pressure is calculated according to the following fundamental relation, as specied in EN1991-14 §4.5(1):

q = (1/2) ⋅ ρ _{⋅ v = (1/2) ⋅ 1.25 kg/m ⋅ (44.00 m/s) = 1.210 kN/m}

where the density of the air is considered as ρ = 1.25 kg/m in accordance with EN1991-1-4

§4.5(1).

Peak velocity pressure

The peak velocity pressure q ( z ) at reference height z includes mean and short-term velocity uctuations. It is determined according to EN1991-1-4 equation 4.8 as:

q ( z ) = (1 + 7⋅I ( z )) ⋅ (1/2) ⋅ ρ_{⋅ v ( z ) = (1 + 7⋅0.2071) ⋅ (1/2) ⋅ 1.25 kg/m ⋅ (36.06 m/s) =}

1.991 kN/m

where the density of the air is considered as ρ = 1.25 kg/m in accordance with EN1991-1-4

§4.5(1). e min r e r e 0 0 e 0 e m e e b m e r e 0 e b v e e e min v e I 0 e e 0 I b b b b2 3 2 2 3 p e e p e v e m e 2 3 2 2 3

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The exposure factor c ( z ) = 1.6458 is dened as the ratio of peak velocity pressure to basic velocity pressure:

c ( z ) = q ( z ) / q = 1.991 kN/m / 1.210 kN/m = 1.6458

Therefore the peak velocity pressure is calculated as q ( z ) = 1.991 kN/m .

Calculation of wind forces and pressures on the structure

The wind actions on the structure (forces and pressures) depend on q ( z ) as follows.

Wind pressures on surfaces

The wind pressure on surfaces are derived from the calculated value of q ( z ) = 1.991 kN/m by application of the appropriate pressure coecient, as specied in EN1991-1-4 §5.2.

For external surfaces the applicable wind pressure w is calculated as:

w = q ( z ) ⋅ c

where c is the appropriate pressure coecient for external pressure that is given in

EN1991-1-4 Section 7 depending on the type of structure. The appropriate reference height z for the external surface is given in EN1991-1-4 Section 7 depending on the type of

structure.

For internal surfaces the applicable wind pressure w is calculated as:

w = q ( z ) ⋅ c

where c is the appropriate pressure coecient for internal pressure that is given in

EN1991-1-4 Section 7 depending on the type of structure. The appropriate reference height z = z for the internal surface is given in EN1991-1-4 Section 7 depending on the type of

structure.

Total wind force on structure

The wind force on the structure F for the overall wind eect is estimated by application of the appropriate force coecient, as specied in EN1991-1-4 §5.3.

F = c c ⋅ c ⋅ q ( z ) ⋅ A where:

The structural factor c c takes into account the structure size eects from the non-simultaneous occurrence of peak wind pressures on the surface and the dynamic eects from the eect of structural vibrations due to turbulence. The structural factor c c is determined in accordance with EN1991-1-4 Section 6. A value of c c = 1.0 is generally conservative for small structures not-susceptible to wind turbulence eects such as buildings with height less than 15 m.

The force coecient c is given in EN1991-1-4 Sections 7 and 8 depending on the type of structure or structural element.

The wind reference area A is given in EN1991-1-4 Sections 7 and 8 depending on the type of structure or structural element. It is generally the projected area of the

structure loaded by the wind.

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