Transcript Slide 1

3.5 WIND LOADS
3.5.1 Wind phenomenology
Wind speed is experienced essentially at two different time
scales:
1: A slowly varying mean wind level; Vm. This wind component can
often be considered as constant for a short term period, say 3 hours.
2: A ”rapidly ”” fluctuating wind component, Vt, riding on the
mean wind speed. The period of fluctuations will be from
second to some few minutes.
Power
spectrum
Storm spectrum
Year
Few days
Hour
1 min.
1 sek
Turbulence
Speed
Mean wind speed
Time
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At a given point, the resulting wind speed can be written:
V(t) = Vm(t) + Vt(t)
The mean wind speed is typically the largest. Terrain
roughness govern the ratio. The ratio between standard
deviation of Vt and Vm is called turbulence intencity.
Typical turbulence intencity over ocean with storm
waves is about 0.12.
The wind speed varies with height, see eq(1a – 1d) in
Statoil metocean report.
For engineering purposes, the mean wind speed is
described by a distribution function often close to a Rayleigh
distribution. The mean direction is described by a probability
mass function for direction sectors (often) of 30 deg. width.
The mean wind speed corresponds to a given length of
averaging. Standard meteorological averaging is 10 min..,
in design the length of averaging is often taken to be 1 hour.
Wind speed will increase with decreasing length of averaging.
The ration between a 15sek average and a 1-hour average
10m above sea level is 1.37, see table in Statoil report for
other examples.
Example of a wind description for design purposes is shown
by Statoil Metocean report.
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For structures or structural components where the turbulent
wind may cause a dynamic behaviour, the frequency spectrum
for wind speed is given by Eq. (2a and 2b) of Statoil Report or
Norsok N-003.
This wind spectrum is deduced from wind measurements at
Frøya.
The turbulent wind is not fully correlated over the size of
structures. Coherence spectrum between two points are
given in Statoil report or Norsok N-003.
The loads on structures not exposed to dynamic behaviour
can be calculated considering the wind as static:
If structural dimensions are less than 50m, 3s gust should be
used.
If structures are larger, 15s gust can be used.
For structures which are exposed to simultaneous actions
from wind and waves, and where the wave loading is
dominating, the length of averaging of wind gust may be taken
to be 1 minute. Check with coming editions of Norsok for
possible changes.
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3.5.3 Wind forces
The wind force is proportinal to the wind speed squared:
F = k * (Vm + Vt)2 = Vm2 + 2VmVt + Vt2 =(ca) Vm2 +2VmVt
The mean wind gives a constant force on the structure,
while the turbulent wind yields a force proportional the the
turbulent wind speed.
Practical problems:
Offset and mooring line forces for ships and floating
platforms.
The natural periods of the surge, sway and yaw are often
in the order of 1-2 minute, i.e. a period band where the
wind frequncy spectrum has a considerable power density.
For this sort of problem, a dynamic analysis has to be
carried out involving the wind power spectrum.
Wind loading on flare towers and drilling towers. A quasistatic analysis is often possible accounting for some
dynamics by a proper dynamic amplification factor.
The wind loading on complicated structures are determined
by means of tests in wind tunel.
Remember that in all cases mentioned above, one will also
have to include the simultaneous affect of waves.
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The static wind force on a structural member or surface
acting normal to the member or surface is given by:
FW = ½ r C A V2 sina
C – shape coefficient, see DNV 30.5
r – density of air (= 1.225 kg/m3 for dry air)
A – projected area of member normal to force direction
a – angle between wind and axis of the exposed member
For the wind load of a plane truss, the load can be
calculated by using A as the enclosed area of truss if an
effective shape parameter is used, C=Ce, and the
transparancy of the truss is accounted for by multiplying
the area with the solidity ratio f. Ce is found in DNV 30.5.
If more than one member or truss are located behind each
other, shielding effect can be accounte for by multiplying
loads given above by the shielding factor, h. Values for h
are given in DNV 30.5.
Regarding the shape coefficicent, it is recommended that
DNV 30.5 or an similar reference are consulted.
NB: For structural sides not facing the wind, a considerable
suction force can occurr, see Fig. 3.14 b in kompendium,
Moan (2004).
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If structure or structural component can be exposed to wind
induced dynamics, the variability of the wind force is to be
accounted for:
FW(t,z) = ½ C r A (Vm(z)2 + 2* Vm(z)*Vt(z,t)) * sin a
It is seen that load is linear with respect to wind speed (since
Vt2 term is neglected). If the wind induced response is linear
function of load, the wind response may be obtained using
frequency domain analysis, i.e. the cross spectral density
for the dynamic wind load is multiplied by response transfer
function in order to obtain response spectra for dynamic
wind induced response.
Alternatively, wind histories for a number of load points may
be simulated from wind spectrum and corresponding time
histories for the response found by solving the equation of
motion in time domain.
The total extreme wind induced response can be found by:
F3h-max (Vm) = Fm + g * s(Vm)
g – extreme value factor for 3-hour maximum dyn. response
s – standard deviation of wind response under consideration
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Vortex Induced Vibrations (brief introduction)
Vortex shedding frequency in steady flow is given by:
f = St * V/D
St is the Strouhal number, V is wind speed and D is structural
diameter.
A critical velocity is defined as the velocity giving vortex
shedding frequencies equal to the natural frequency of
the structural member:
VC = 1/St * fN * D
fN – natural frequency of structural member.
St is a function of the Reynolds number, Re = VD/n, where
n is the kinematic viscosity of air, (= 1.45*10-5 m2/s at 15o
and standard atmospheric pressure. St is given in Fig. 7.1
in DNV 30.5.
A state of quasi-resonant vibriations of a member may take
place if wind velocity is in the range:
K1*VC < V < K2*VC
If possible, one should require: VC > 1/K1 *Vmax
Not always possible and maybe unnecessary strict criterium.
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3.6 Wave and Current loads
Water levels:
Maximum still water level
Positive
storm surge
Tidal
range
Highest astronomical tide (HAT)
Mean still water level
Lowest astronomical tide (LAT)
Negative
storm surge
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Minimum still water level
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