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Prof. Dr.-Ing. habil. Hans-Jürgen NiemannRuhr-Universität Bochum, Germany
Niemann & Partner Consulting Engineers, Bochum hans-juergen.niemann@rub.de
Niemann & Partner
Macedonian Association of Structural Engineers
MASE - Seminar on Eurocodes Skopje
30. March 2011
EN 1991-1-4:2005 (E) Eurocode 1: Actions on Structures
Part 1-4: General Actions - Wind Actions
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EN 1991-1-4 Wind Actions - Overview
Wind forces on structures, e.g. for overall wind effects
Wind pressures, e.g. for claddings, fixings and structural parts
Peak velocity pressure qp
Parameter
external pressure we = cpe ⋅qp (ze ) internal pressure wi = cpi ⋅qp (zi )
Fw = cs cd ⋅cf ⋅
qp (ze )⋅Aref
Calculation Procedure for Wind Actions
3
Wind Pressures: Internal and External Pressures
at
4
Wind Pressures Coefficients – Effect of Loaded Area
The size effect is considered for loaded areas A up to 10m².
for 1m²<A<10m²: cpe,A = cpe,1 – (cpe,1 – cpe,10 )⋅lgA
Example: Vertical walls of rectangular plan buildings
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mean wind velocity pressure
wind turbulence intensity
The peak velocity pressure includes the mean wind vm and the short term velocity fluctuations due to wind turbulence.
Peak Velocity Pressure qp
Time series of the wind velocity
, ρ = 1,25 kg/m²
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The exposure factor ce is defined through
where
roughness factor for the terrain category
[ ] )z(c)z(c)z(Ic orve2271 ⋅⋅+=
Peak Velocity Pressure: Exposure Factor ce
is the basic velocity pressure taken from the wind map
orography factor for the wind speed-up over hills and escarpments
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Flat Terrain
Top of a Hill
orography factor cO
Orography factor cO : the mean wind profile over orography
The mean wind velocity at height z above ground depends on terrain roughness and terrain contour, the so-called orography
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roughness length z0 = 0,003 m minimum height zmin = 1 m terrain factor kr = 0,156 roughness factor at z = 10 m
cr (10) = 1,266
roughness length z0 = 0,01m minimum height zmin = 1 m terrain factor kr = 0,170 roughness factor at z = 10 m
cr (10) = 1,173
roughness length z0 = 0,05 m minimum height zmin = 2 m terrain factor kr = 0,190 roughness factor at z = 10 m
cr (10) = 1
- reference terrain
Terrain factor cr : terrain categories (1)
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roughness length z0 = 1,0 m minimum height zmin = 10 m terrain factor kr = 0,234 roughness factor at z = 10 m
cr (10) = 0,540
roughness length z0 = 0,3 m minimum height zmin = 5 m terrain factor kr = 0,198 roughness factor at z = 10 m
cr (10) = 0,694
Terrain factor cr : terrain categories (2)
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Exposure Factor ce : profiles of the peak velocity pressure, qp
Exposure factor ce = qp /qb for flat terrain where co = 1
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Wind Map of Germany for the basic wind speed
vb,0 qb,0
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Calculation of Wind Forces
EN model for Wind Forces
structural factor
aerodynamic force coefficient
peak velocity pressure
reference area
at height ze
qp (z)
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Wind Forces – the Structural Factor cs cd
kp = ratio of the peak response and its standard deviation
It allows for the effect of non-simultaneous occurrence of the force peaks on the structure
≤
1
The structural factor (i) reduces the peak velocity pressure for the size effect, (ii) increases it for response amplification by resonance to turbulence.
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n1 natural frequency
Wind Forces – the Structural Factor cs cd (cont’d)
0,46 Hz
0,92 Hz
0,51 Hz
0,66 Hz
1,15 Hz
0,58 Hz
0,77 Hz
cs – decreases as height and width increase cd – increases as the height increases due to decrease of n1
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Wind Pressures on Large Roofs – Effect of Loaded Area
Windkanaleinbauten
MSV Arena Duisburg
BayArena Leverkusen
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Wind Pressures – Size Effect of Loaded Area
0 20 40 60Zeit in Sekunden
resu
ltier
ende
Win
dlas
t
Hinterkante
Vorderkante
Dachmitte
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Wind Pressures – Small Loaded Areas
-1,50
-1,60
-1,60-1,70-0,70
-0,70
-1,60
-1,50 -1,60-1,70
-1,20
-1,00
-1,00
-1,3
0
- 1,3
0
- 1,8
0
- 1,8
0
-1,20-0,80 -0,80
-0,80 -0,80
-1,50
-1,60
-1,60-1,70-0,70
-0,70
-1,60
-1,50 -1,60-1,70
-1,20
-1,00
-1,00
-1,3
0
- 1,3
0
- 1,8
0
- 1,8
0
-1,20-0,80 -0,80
-0,80 -0,80
Thank you for your attention
Prof. Dr.-Ing. habil. Hans-Jürgen NiemannRuhr-Universität Bochum, Germany
Niemann & Partner Consulting Engineers, Bochum hans-juergen.niemann@rub.de
Niemann & Partner