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friends let us discuss the tenth lecture title
environmental loads second part of the online
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course on offshore structures under special
loads we are discussing the complexities which
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arise from the conventional loads before we
understand the special loads in the responses
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of offshore platforms under the special loads
in the last lecture we were discussing about
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airys linear wave theory and complexities
arise from the linear wave theory in case
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of regular waves it is a practice to choose
. an extreme wave to represent . the effects
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of the set of irregular waves so the chosen
let see special regular wave which an extreme
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wave is governed by two parameters namely
the wave height and . the wave period however
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we agree that random wave is described .
by the energy density spectrum .
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random waves are generally used for design
of offshore structures when we understand
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this there are some basic terminologies which
we will understand in connection to the random
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wave lets say short term record length it
is ts which indicates the duration of . strum
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significant wave height hs which is average
height of highest one third waves in a short
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term record .
root means square . that is rms . of wave
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height which i call h rms this is root mean
square value . of individual wave heights
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.
in a short term record . the fourth one is
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peak frequency . which is omega zero which
is the peak frequency of the spectrum . .
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significant wave frequency .
which is omega s which is the average frequency
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corresponding to or corresponds to the significant
wave height . in a short term record . mean
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frequency which is omega bar which is mean
frequency of the individual . waves in short
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term record . . having said this the most
conventional spectrum use for estimating wave
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forces on offshore platform is pierson moskowitz
spectrum famously known as pm spectrum we
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have an interesting relationship between the
peak frequency and significant wave height
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which is given by peak frequency is point
one six one g by hs
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. so if i know one we can always find the
other one call also discuss and describe the
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peak frequency . in terms of mean wind speed
. which i call as uw so peak frequency can
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also be given by two third g by uw so one
may be interested why we are looking about
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the peak frequency because pierson moskowitz
spectrum is defined based on the peak frequency
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it says that the spectral energy s omega . is
given by alpha g square by omega five which
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is a variable e to the power of minus one
point two five . omega by omega zero to the
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power of minus four
so where in this case alpha is called as phillips
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constant which is given by zero zero eight
one for offshore application this spectrum
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is modified the pm spectrum what is being
described includes the peak frequency .
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which is omega zero in the equation which
is actually the function of mean wind speed
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. measured at a height of plus nineteen point
five meters above the mean sea level so the
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spectrum has only one parameter
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to specify which is . an independent parameter
it is either the peak frequency or uw because
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both of them are interdependent if you know
one i can find the other this spectrum is
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further modified . . which is now being used
in design of offshore platforms .
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this as two parameters namely significant
wave height and peak frequency this equation
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is given by . where in this equation the peak
. frequency is given by two third of u g uw
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hs is significant wave height .
and uw is the mean wind velocity
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the second spectrum we have is bretschneider
spectrum which again has two parameters namely
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significant wave height and significant frequency
. which is given by point one six eight seven
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hs omega s by omega e to the power of minus
point six seven five omega by omega s to the
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power minus four
alternative spectrum is given by international
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ship structures congers .
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which is issc spectrum which is again a two
parameter spectrum .
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which is hs and omega bar in this case the
spectral density function is given by . the
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following equation omega bar four by omega
five e to the power of minus point four four
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two seven omega to the power minus four this
is equation three . where omega bar is given
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by m one by m zero and m i . is called spectral
moments . m i can be simply given by . omega
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i s x plus omega d omega for i equals zero
one etcetera .
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people also use jonswap spectrum
which is for five parameters namely hs omega
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zero comma . the spectral density function
is given by alpha bar g square by omega five
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e to the power minus one point two five omega
by omega zero to power minus four of mu a
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omega . the mu is called peakedness parameter
which varies from one to seven usually an
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average value of . about three point three
is used in the design .
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this essentially have time based on experimental
studies .
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a w is given by exponential minus omega omega
zero square by two sigma square omega zero
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square .
where sigma dash is actually called spectral
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width parameter . which is actually zero point
zero seven for omega less than omega naught
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and zero point zero nine for all omegas more
than omega zero . alpha bar is a constant
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which is three point two five into ten power
minus three hs square omega zero four of one
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minus point two eight seven natural logarithm
of .
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interestingly for gamma equals one . the johnswap
spectrum
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actually reduces to the conventional pm spectrum
a mu is equal to five and for tp by root significant
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height is less than three point six gamma
is given by a separate equation which is five
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point seven five minus one point one five
tp by a root hs gamma can be taken as five
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if this value satisfied for any other value
of tp by root hs more than three point six
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this equation can be used . .
one can also compute the significant wave
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height . which is related to the variance
of waves spectrum
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significant wave height is related to zeroth
moment which is the variance because variance
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of the spectrum is also called zeroth moment
on the spectrum so if you know this zeroth
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moment of the spectrum you can always find
the significant wave height which is required
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in estimating the parameter gamma because
you have some hs here . and then substitute
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back in the johnswap spectrum to get this
spectral density function distribution for
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all bands of omega the next conventional load
what we will take will be the wind load . for
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estimating wind forces the most commonly used
engineering approach
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is based on few assumptions
so therefore one can say these assumptions
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lead to uncertainties or complexities in estimating
this wind forces assumptions are when a stream
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of air . flows with a constant velocity v
it will generate a force
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on a flat plate of area a so at a constant
velocity .
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the plate will be placed orthogonal to the
flow direction so wind forces or perpendicular
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. to the exposed surface area this force will
be proportional to a into v square . so the
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proportionality constant
depends on various factors but independent
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of area this is proved by . experimental investigations
.
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so therefore . wind force on a plate which
is orthogonal to the flow direction . can
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be estimated .
by net wind pressure which i call as p w pw
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is given by half rho a cw v square . where
rho a is the mass density of air . which is
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about one point two five kg per cubic meters
cw is called wind pressure coefficient . there
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is a very important assumption which is made
in estimating the wind forces and offshore
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platforms the assumption is mass density of
air increases significantly due to the splash
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happening on the members up to a height of
. twenty to thirty meters above mean sea level
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hence total wind . induced force on a member
or on the plate is given by . f w is this
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multiplied by the area .
if the plate is kept an angle if the plate
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is kept at an angle theta with respect to
the wind direction . for example let say . this
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is my plate . this is my angle theta i know
the projected area . i should say projected
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area this becomes my wind direction so the
wind force will be normal ok wind force will
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be normal to the plate so i have to find the
resolved value of this in the direction normal
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to the plate if you know the angle theta the
wind pressure coefficient cw is generally
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determined . under controlled stationary wind
flow conditions . usually is experiment is
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conducted in wind tunnel to estimate cw . it
of course depends on reynolds number .
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the value usually is point seven to one point
two for cylindrical numbers
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so wind force . will have two components . one
is . the drag force other is the lift force
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which is given by . this equations where drag
will act parallel to the wind direction and
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lift will acts normal to the wind direction
so its called drag this called lift force
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cdncl are respectably drag and lift coefficients
in both the cases area is measured normal
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to the wind surface . vz is given by an empirical
. . which is z by ten one over seven . which
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is called one seventh power law where v z
is called wind speed at zth location in elevation
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. z is called the location at which wind force
is calculated will be in meters v ten is called
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the wind speed at . ten meters above mean
sea level
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so this ten meter is called datum height or
reference height generally wind has two components
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the mean wind component
which is more or less is a static component
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the next one is the fluctuating component
which is called the gust component usually
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the gust component . is generated . by turbulence
in the flow field .
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this generally generated in three spatial
directions it
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is also a fact that the mean wind speed is
far greater than the gust component . v of
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t has the mean component plus the gust component
.
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it is interesting to note the spatial dependence
of the mean component .
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is only along the height . v of t is assume
to homogeneous both in space and time
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since wind velocity is got two components
to generally obtain load from gust component
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.
one can use the gust factor .
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the gust factor is generally multiplied . with
the sustained wind speed
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to obtain the gust speed
average gust factor . which we called as fg
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is about one point three five to one point
four five so there is an increase . thirty
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five to forty five percent in the gust speed
is very important to note that variation of
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the gust factor .
along the height is negligible . so people
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generally use sustained wind speed to calculate
forces on the offshore members we usually
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one minute average wind speed . this is . u
s weather bureau another interesting terminology
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which causes complexity in estimating wind
load is fastest mile velocity . is nothing
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but the sustained wind speed which we estimate
and multiply this with the gust factor . to
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obtain the fastest mile velocity usually in
design of offshore platforms people use hundred
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year sustained wind velocity of about one
twenty five miles per hour in design
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we all agree that wind is a dynamic process
because it varies with both space and time
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space in since both x y and z therefore few
parameters are important . .
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because these parameters cause complexities
in wind loads the first parameter is the length
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of record . the record can be continuous .
it can be intermittent with equal intervals
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between the observation can also measure the
record only when the value exceeds a threshold
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number so there are many ways by which we
can fix up the length of the record for the
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record to be continuous one looks for an average
value . let say v one for intermittent one
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looks for value v two you will see that generally
v two is greater than v one
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the second issue is average time of the record
is important to know that average time is
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different as the time at which or over which
the record is average the third issue is that
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the wind spectrum becomes input in structural
analysis
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therefore the fluctuating . component . should
be carefully defined .
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the fluctuation component sense the gust factor
the fourth issue is the cross spectrum variation
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in wind velocity along the height is taken
care of but along xy which is the variance
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or dependent on the special distribution .
is an important parameter .
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this is generally handled by considering aerodynamic
admittance function so friends the next lecture
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we will talk about various wind spectrum and
aerodynamic admittance function and then list
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the complexity that arrives from the wind
load on offshore platforms so in this lecture
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we discussed about various spectrum which
are used for various estimating wave loads
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then we also start understanding some important
limitations based on which wind forces or
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estimated on offshore members
thank you very much .