Wind Directionality Effects - Revisiting an Old Conundrum

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14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015

Wind Directionality Effects: Revisiting an Old Conundrum

Melissa Burton1, Yin Fai Li

2 and Stefano Cammelli

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1BMT Fluid Mechanics, New York City, U.S.A.

2BMT Fluid Mechanics, Kuala Lumpur, Malaysia

3BMT Fluid Mechanics, Teddington, UK

email: [email protected], [email protected] and [email protected]

ABSTRACT: There is no doubt that today, like perhaps never before, civil engineering is facing a wide range of new

challenges: buildings, not only tall buildings, are adopting more sophisticated envelopes with often non-orthodox geometries;

tall buildings not only are getting taller but designers are constantly pushing the boundaries of slenderness. In addition, new

high-tech materials are being explored by bridge designers, making some of these structures not only longer but lighter and

therefore far more wind sensitive. It is within this context that wind engineering is playing a vital role in allowing some of these

architectural and engineering visions to be successfully delivered. It is well recognized in the industry that uncertainties in the

assumptions made on wind speeds – that is strength as well as directionality – can have a non-negligible impact in the way they

propagate through the Davenport Chain. Historically, the debate over the treatment of wind directionality has always been

particularly lively, often dividing the two sides of the Atlantic. Today, after many decades of commercial practice, the authors of

this technical paper felt it appropriate to revisit this old conundrum. Making use of a number of commercial projects this article

will explore in depth the most commonly used approaches in regard to the treatment of wind directionality, highlighting

advantages and limitations.

KEY WORDS: Wind Tunnel Testing; Wind Climate Assessment; Up-Crossing; Sector Method; Storm Passage; Vortex

Shedding; High Frequency Force Balance; Dynamic Response; Wind-Induced Acceleration.

1 INTRODUCTION

The importance of wind climate – that is strength as well as directionality of the wind – in the assessment of the performance

of a structure under wind loading excitation is well recognised in the “Alan G. Davenport Wind Loading Chain” [1]. Davenport,

already in 1966 in his final report on the wind engineering works on the World Trade Center [2], stated: "Because of the

directional characteristics of wind pressures the probability distribution of wind pressure at a point on the exterior surface of the

building is only indirectly related to the probability distribution of velocity. A specific value of wind pressure can arise either

from a low wind velocity coming from a critical wind direction or a higher wind velocity coming from a less critical direction".

The importance of accurate predictions of site-specific wind speeds is paramount for tall and slender structures approaching

the Strouhal condition, especially when dealing with load effects entirely driven by resonant behaviour, e.g. wind-induced

accelerations. Misalignment of extreme wind speeds and their associated directionality can lead to large discrepancies on

wind-induced responses produced by different wind tunnel laboratories, as was exhibited when parallel testing of the World

Trade Center towers at two wind laboratories resulted in a 40% difference between predicted wind loads [3].

With this paper its authors would like to share their experience on commercial projects where different analysis methods in

current use for the treatment of wind directionality effects have been simultaneously considered and applied.

2 WIND CLIMATE

A vital part of the design of modern structures lies in the accurate assessment of design wind speeds. Designers typically rely

upon either codified values or results of wind climate analyses for the wind speeds to be used in design; both of which depend

upon accurate recordings of long-term wind records from meteorological sites. Unfortunately, almost always the wind speeds

needed for design are of a return-period which is significantly longer than the wind record itself. To confound the issue, wind

speeds in a specific location may be driven by a variety of storm mechanisms. Possibly the location is subject to one specific

mechanism, e.g. Miami (hurricanes), or perhaps two or more storm mechanisms drive the local wind climate, e.g. Shanghai

(synoptic events and typhoons).

There are a number of wind circulation mechanisms common to our planet: monsoons (driven by synoptic circulations), sea

breezes, thunderstorms, tropical cyclones (including hurricanes and typhoons), downslope winds, and winds that are particular

to rather localised areas of the globe, e.g. Shamals in the Middle East. Sea-land circulations (referred to as sea-breezes) are the

result of temperature difference between land and sea. The effect of this circulation can be significant

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relatively far in-land and is reversed at day and night. Phenomena such as thunderstorms are generally associated with weather

fronts but the interaction of topography and local solar heating can also be at the origin of these events (such as sea breezes

lifting moist air into mountainous regions). Thunderstorm events tend to be a local phenomenon with high gust speeds and are

observed in many areas around the globe, such as South-East Asia, areas in South America, most of the USA, etc. Downslope

winds are driven by local topography and occur when air flows over high mountain ridges with steep lee slopes. These types of

winds are referred to by many different names around the globe, such as: the Rocky Mountain Chinook, the Santa Ana winds in

California, the Föhn in northern Italy and Austria, and many many more. Hurricanes, typhoons, and tropical cyclones typically

form over large bodies of warm water in the middle latitudes. These types of storms are 3D structures with a low pressure center

called the ‘eye’ surrounded by rapidly rotating winds. These types of storms have the potential to generate some of the strongest

winds experienced on the globe. The general synoptic circulations that cause monsoon type winds in nearly all parts of the globe

are large pressure systems that can last for days, and sometimes even up to a week. Strength of these types of winds varies

seasonally and can consist of summer and winter trends separated by transition periods.

Where the design wind speed is based on well documented research by established experts it is possible to develop a wind

model that matches those speeds. Having said that, there are also numerous locations around the globe where research resources

have not been available to develop an accurate design wind speed mapping. In these cases local weather stations of wind

records, under the subject of the various wind mechanisms, can be analysed to determine a distribution that is characterized by

statistics. The parent distribution of wind speeds is most closely modelled by the Weibull distribution of the form:

k

V cVP /exp1

(1)

where c and k are empirical constants for a best fit to individual data sets and PV is defined as the probability that a velocity

will be less than V. Theoretically, for a set of data conforming to a Weibull distribution, the cumulative distribution function of

the extremes will converge towards a Fisher-Tippett Type I distribution of the form:

yPx expexp (2)

where the reduced variate y is given by:

)]ln(ln[ xPy

(3)

and Px is the probability that an extreme value will be less than a value x in any one year.

The number of years for which meteorological records are available is important in obtaining statistical reliability. More than

seven years is desirable and preferably more if available [4]. In some cases, the uncertainties connected with individual

meteorological stations can be reduced by examining more than one station in a given region. One of the potential issues in

simply using the Weibull parameters to define the parent distributions of a climate is that different wind mechanisms will follow

different distributions. Essentially a climate may have two overlaid distributions, one characterizing one storm mechanism and

another characterizing a second storm mechanism. For example, the lower return period wind speeds in Houston are controlled

by a mixed combination of synoptically driven storms and hurricanes whereas the longer return period events are exclusively

controlled by hurricanes. In this case it would be incorrect to utilize a single Weibull distribution to characterize both the longer

and shorter return period events and in doing so would potentially result in conservative predictions of either accelerations or

design wind loads for a tall building.

Originally explained by Cook [5] and later modified by Harris [4] the method of independent storms analysis, as

recommended in ESDU [6], makes use of wind speed maxima taken from independent storms of the same mechanism. The

advantage of this method over the traditional Gumbel extreme value analysis method is that many more wind records are

available to define the statistical parameters of a distribution, leading to a greater confidence in the estimation of design wind

speeds. The procedure for analyzing the independent storm data is similar to that for the Gumbel yearly maxima except that the

calculation of the reduced variate is modified. The probability that the extreme value will not be exceeded in any one year is

based on the rank of the wind speed compared to the total number of storms. The plotting positions are again modified based on

probability weighted least squares.

For the methods of analyses outlined above, there is an amount of uncertainty in the estimation and the precision of the wind

models and design wind speed estimates. Accurate estimates depend on both the quality and the length of the actual wind

records.

One item of importance in wind tunnel studies is that the wind model developed must be self-consistent in both the extreme

value analysis of the wind speeds and the description of the parent winds through the Weibull distribution. That is, considering

the winds from all directions, the model of the parent winds must provide the same wind speed for any given return period as the

extreme value analysis of wind speeds. If the developed models are not self-consistent this can lead to far greater difference in

predicted wind tunnel load effects than any difference garnished simply from different methods of analysis.

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3 UNCERTAINTIES IN WIND RECORDS

When using time histories of wind records in the prediction of extreme wind speeds and parent distributions it is prudent to

conduct numerous checks to reduce uncertainties. Understanding the effects of various types of measurement equipment, the

source from which the records have been taken, the effects of topography or terrain, or the impact of multiple wind mechanisms

can be crucial in ensuring that the inherent wind speeds entered into the various analysis procedures are accurate. In some cases

recorded wind maxima can fall outside confidence limits.

Depending on where in the globe one is studying design wind speeds greater uncertainties may exist; for example in India

where anemometers can be mounted on buildings where the local influence of the building itself may have a great effect on the

data, or in China where many anemometers have gaps in data recording during the cultural revolution, or in the Middle East

where at one point in time the anemometer would have been located in an isolated environment but with rapid city development

then became emerged in city terrain. In these cases it can often be misleading to rely solely on point estimates from extreme

value analysis techniques of longer return period events. There is a chance that the true longer return period wind speed is either

larger or smaller than the point estimate. This is a normal result of variability within the wind records (not even accounting for

the compounding variability when data uncertainties are factored in). There are three common reasons to account for this: firstly,

the value may originate from a storm with a different mechanism; secondly, the event may have a smaller probability of

occurrence than the analysis would indicate due to the finite record length not containing other intermediate storm events which

would occur eventually; thirdly, the value could be associated with a manual recording/rounding error. Carrying out an analysis

of artificially generated wind climate time histories from existing wind climate data records with consistent underlying climate

parameters Burton and Allsop [7] demonstrated that confidence limits on design wind speed predictions can result in +/- 10%

variability around that point estimate. That’s quite a substantial variability when considering wind loading on tall towers is

proportional to at least the wind speed squared but often to the wind speed cubed.

When conducting extreme value analysis, there are some quick and easy checks that can be carried out to determine whether

there is potentially a large skew in the predictions. When conducting extreme value analysis there is a greater reliability in the

prediction of the shorter return period events (or the mode). The slope of wind speed versus return period (or the way in which

the wind speeds vary with return period) is dependent upon the driving wind mechanism in the specific geographic location. For

example, knowing the one-year return period wind speed in London, and knowing that London winds are synoptically driven,

one can garnish a relatively reliable prediction of the design wind speeds at longer return periods as synoptic winds globally

follow a somewhat similar slope or variation against return period.

One of the biggest challenges and concerns in the development of a statistical wind model for a specific location is the

subjectivity involved when assessing wind records and deciding which records to ‘smooth’, which to ‘reject’ and which to

‘keep’. To erase all subjectivity from the assessment and prediction, and therefore the most accurate way to arrive at trusted

design wind speeds, is through Monte Carlo simulations. This type of simulation has become the standard internationally

accepted methodology for providing design wind speeds in hurricane or typhoon regions. Design wind speeds are predicted

using full-scale observation of previous event tracks and through the simulation of tens of thousands of additional probable or

possible events. Ultimately this means that there is a greater level of confidence in wind speeds predicted (and therefore load

effects predicted from those wind models) in areas where the driving wind mechanism is a hurricane or typhoon type of event. It

is possible to develop Monte Carlo simulations for the prediction of wind speeds in other climate types also, such as synoptic

climates, however at the moment the industry has not embraced this as a standard. It is of the opinion of the authors of this paper

that this is the direction that industry should be pushing to move.

4 WIND TUNNEL TESTING

Wind tunnel testing also plays an important role in the Davenport Chain [1]. Still today in the 21st century wind tunnel testing

is the most reliable and robust way to determine the response of structures to wind loading excitation. Information recorded in

the wind tunnel test is typically combined with the wind models developed above to predict the wind loads or the wind-induced

accelerations. The most commonly used wind tunnel testing techniques in tall building design are: high-frequency force balance

(HFFB, see also [8]); simultaneous pressure integration (SPI); and aeroelastic modelling.

HFFB wind tunnel models are constructed around a stiff and light central spine often manufactured using carbon-fibre with

light-foam to give the correct outer envelope of the tall building (Figure 1). These models are mounted on stiff load cells capable

of simultaneously measuring time-histories of wind-base shears, wind-base overturning moments and torsion. This technique

generally offers quick turnaround and a high degree of flexibility for re-analysis. The SPI technique makes use of wind tunnel

pressure models, typically constructed employing 3D printing technology (Figure 1). Similarly to the HFFB technique, the SPI

approach also offers a high degree of flexibility for re-analysis. As with this technology, measurements are simultaneously taken

over the entire surface of the building, the floor-by-floor wind loading distribution along the height of the structure can be more

accurately quantified and the contribution to wind loading from higher modes of vibration – particularly important in the realm

of super-tall buildings (see [9]) – thoroughly calculated. The only way to accurately assess the wind-structure interaction is to

employ the aeroelastic modelling technique (Figure 1): this is particularly important for super-tall buildings approaching the

Strouhal condition and any time the aeroelastic damping needs to be taken into consideration. Aeroelastic wind tunnel models

are designed and built to accurately match the structural arrangement of the real tall building and are instrumented with

accelerometers and strain gauges measuring in real time the structural response of the tall building to wind loading excitation.

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Figure 1: a) Boundary layer wind tunnel; b) HFFB model; c) load cells; d) pressure model; e) pressure data; f) surrounds model;

g) target model; h) aeroelastic model; i) flow visualisation.

Although there are numerous elements that go into a wind tunnel simulation, extending from the simulation of the atmospheric

boundary layer to the exact architectural representation of not only the tower in question but also of all of the surrounding

developments and the measurement equipment utilized, it is very rare to find differences in load effects predicted from multiple

wind tunnel laboratories when focusing solely on the experiment itself. In most cases, when the wind climate model is

standardized, two or more wind tunnel laboratories can carry out testing and produce very similar results. The majority of the

time when differences are observed they have arisen for two reasons: the wind climate models used by the two laboratories are

different or the analysis method to combine the wind climate model with the wind tunnel measurements is different.

5 COMBINING WIND STATISTICS WITH WIND TUNNEL MEASUREMENTS

Over the past 50 years a large number of studies on the directionality of extreme wind events have been undertaken:

Davenport [10], Melbourne [11] and Cook [12], just to name a few. These in turn led to a number of proposed methods to

combine full-scale wind statistics with model scale wind tunnel measurements. The most notable and widely used in the industry

are: i) the up-crossing method; ii) the sector method; and iii) the storm passage method. Both the up-crossing and sector methods

of analysis are sensitive to the underlying parameters derived from the wind climate analysis explained above and to the

treatment of uncertainties in wind data.

The up-crossing method, which requires the parent distribution of wind speeds and directions to be derived, was originally

formulated using theory developed by Rice [13] for a one dimensional random variable. Davenport [10] subsequently expanded

this equation for applications in the wind engineering field, arriving at:

dVpd

dV

VgN g

g

g

2

0

2

,1

12 (4)

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where N is the up-crossing rate for a specific load effect g and , , , and Vg are respectively the characteristic fluctuation of

wind speed, the mean cyclic rate of the wind climate of interest, the wind direction and the velocity at the response boundary of

the load effect.

The load effect in this case is determined by combining two models: the first which defines the fraction of time that the wind

can be expected to be greater than a specified value and the second which defines how frequently a specific wind speed is

exceeded. Due to the complex computational nature of the up-crossing procedure, detailed verification of its implementation can

often be difficult [14]. It is the implementation of the up-crossing approach that resulted in the use of the Kd wind directionality

factor in the ASCE7 guideline [15] to account for the probability that the strongest wind may not impact the structural system in

its weakest direction.

Lepage and Irwin [16] have re-formulated the up-crossing equation of Davenport [10] to allow for better integration with

climatic information. The usage of a characteristic rate of change of wind speed instead of the combination of a mean cyclic rate

and a characteristic wind speed fluctuation was introduced. In addition, the probability density function was described in terms

of directional Weibull coefficients. Furthermore, empirical relationships of time rate of change of wind speeds and wind

directions were also proposed.

The sector method requires extreme meteorological wind records to be fitted through extreme value distributions, on a sector-

by-sector basis. This method has been adopted as the basis for codification by a number of different countries across the globe:

Japan [17], Australia and New Zealand [18] and Europe [19]. The load effect for each wind direction is calculated using these

sector velocities and the highest load effect out of all the sectors defines the load effect for a given return period. The underlying

assumption when employing this methodology is that the correlation of wind speeds of adjacent wind sectors is generally weak.

In most climates this tends to be a fair assumption, however as aerodynamic effects can sometimes switch out more rapidly than

the change in sector wind strength there is always the possibility to overestimate the probability of having a specific load effect

occur. In addition, often engineering judgement is required to smooth out the sector by sector wind speeds determined from the

extreme value analysis.

The subjectivity of this smoothing out extends to the up-crossing method as well. Mixed climates become difficult to deal

with in the Lepage and Irwin [16] up-crossing method as a double humped Weibull distribution needs to be smoothed out,

thereby potentially losing or gaining conservatism for some of the return periods investigated. The other alternative is to use

multiple sets of wind parameters to describe the parent winds; one set at each return period in question. The sector method deals

with mixed climates by separating each climate mechanism and then probabilistically combining them, i.e. if a specific synoptic

event has a once-in-twenty-year chance of being exceeded and a typhoon event of the same magnitude also has a once-in-

twenty-year chance of being exceeded than the chance of the building seeing an event of that strength is once-in-ten-years. In

the sector method the mechanisms are combined wind sector by wind sector as each mechanism may have a different prevailing

wind direction.

The storm passage method combines, in the time domain, detailed information about the passage of extreme weather events –

often numerically simulated using Monte Carlo methods – with wind tunnel test data. The peak load effect for any year (or even

month) is then analyzed using standard extreme value analysis methods to compute the load effect as a function of return period.

This approach is particularly effective when working in hurricane / typhoon prone regions as Monte Carlo analyses of these

events are readily available.

The underlying driver for which analysis method is most appropriate relies on the quality of meteorological data and the

confidence that one has in the mathematical models used to describe those meteorological records. As noted in the ASCE

Manual for Wind Tunnel Testing of Structures, [20], different wind data sources can lead to different estimates of the wind-

induced response estimates. Because these differences can exist, it is often advisable to produce estimates of response vs. return

period using more than one representation of the local wind climate.

6 COMPARISON OF LOAD EFFECTS PREDICTED BY VARIOUS METHODS: POSSIBLE SCENARIOS

Over the course of the last decade, the authors of this technical paper have peer reviewed numerous wind engineering studies

of tall- and super-tall buildings where parallel wind tunnel testing has been involved. Experience has shown that if the same

experimental boundary conditions (such as mean wind speed and turbulence intensity wind profiles), the same wind tunnel

measurement technique, and if the wind tunnel measurements have been combined with the same site-specific wind speeds, then

the discrepancies between the final results of the two or more wind tunnel labs are very likely to be within 5%-10%.

Although small differences in wind tunnel predictions are often unavoidable due to the random nature of wind itself and finite

sampling time available in the wind tunnel, large discrepancies are almost always due to a misalignment of the characteristics in

the wind climate – often seen as being the weakest link within the Davenport Chain [1], and a chain cannot be stronger than its

weakest link. When comparing wind tunnel results obtained using different analysis methods to account for the directionality of

the wind, it is vital to ensure that the omnidirectional design wind speed is matched across the different analysis techniques, i.e.

that the parent wind distributions, the directional extreme wind speeds and the wind time histories for the up-crossing method,

sector method and storm passage method respectively are self-consistent in an omnidirectional sense. Within the up-crossing

framework this is achieved ensuring that:

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R) large(for 1

2

,1

122

0

2

RVp

dVpd

dV

VVN

bomni

bb

b

b

(5)

where Vb and R are respectively the omnidirectional reference wind speed and the return period of interest. Within the storm

passage framework, this is achieved ensuring that:

R) large(for

11

ReVvP bVvP

ba

(6)

where Pa, and P are respectively the annual probability of exceedance, the annual occurrence rate and the rank probability in

the time history.

It should be noted that in general the differences in terms of response prediction between the up-crossing technique and storm

passage method are relatively small as the former is essentially an analytical representation of the latter, specifically designed in

the 1970s when computer power was rather limited.

With the above in mind the following five possible scenarios have been studied:

i) non-directional building (that is aerodynamic shape + structural system) in a non-directional wind climate;

ii) non-directional building in a directional wind climate;

iii) directional building in a non-directional wind climate;

iv) directional building in a directional wind climate (prevailing wind direction ≠ the critical direction of the

building);

v) directional building in a directional wind climate (prevailing wind direction = the critical direction of the

building).

Two sets of wind statistics have been utilised to illustrate the various possible scenarios; the first one, shown in Figure 2a, is a

probability density formed from the Monte Carlo generated typhoon time histories for Shanghai, whilst the second one, shown

in Figure 3a, refers to the hurricane wind climate of Miami. Figure 2b and Figure 3b show the non-directional wind climate

fabricated from the two above mentioned directional climates by maintaining identical volumes beneath the respective surfaces.

Given in Figure 2c and Figure 3c is a comparison plot demonstrating the prevailing wind direction for each climate for the

extreme wind events relevant to serviceability: 140-150 in Shanghai and 60o-70

o in Miami. The one important difference

between the Shanghai and Miami tropical storm wind climates is the difference in strength associated with the prevailing and

non-prevailing winds. The mean hourly wind speeds associated with the non-prevailing directions in Shanghai are

approximately 65% of the ones associated with the prevailing directions, whilst in Miami this ratio is closer to 80%. It is

important to note here that Shanghai is a ‘mixed’ wind climate and for a realistic prediction of load effects in this climate the

mixed contribution from both synoptic and typhoon events is required.

050

100150

200250

3003500

20

40

0

0.5

1

1.5

x 10-5

Wind Direction [deg]Ref. Speed [m/s]

Pro

babili

ty D

ensity

a)

050

100150

200250

3003500

20

40

0

0.5

1

1.5

x 10-5


Pro

babili

ty D

ensity

b)

0 50 100 150 200 250 300 3500

5

10

15

20

25

30

35

40

Wind Direction [deg]

Re

f. S

pe

ed

[m

/s]

Non directional climateDirectional climate

c)

Figure 2: a) Probability density, Shanghai typhoon wind climate; b) probability density, non-directional wind climate;

c) comparison of reference mean-hourly wind speeds.

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050

100150

200250

300350

0

20

40

0

2

4

6

x 10-6


Pro

ba

bili

ty D

en

sity

a)

050

100150

200250

300350

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20

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0

2

4

6

x 10-6


Pro

ba

bili

ty D

en

sity

b)

0 50 100 150 200 250 300 3500

10

20

30

40

50

Wind Direction [deg]

Re

f. S

pe

ed

[m

/s]

Non directional climateDirectional climate

c)

Figure 1: a) Probability density, Miami hurricane wind climate; b) probability density, non-directional wind climate;

c) comparison of reference mean-hourly wind speeds.

Having established the wind climate, response characteristics – taking both aerodynamics and structural arrangement into

consideration – are required in order to determine load effects. Given in Figure 4a and Figure 5a are the response characteristics

for two tall buildings (‘Building A’ and ‘Building B’ respectively), both anonymous projects studied in BMT Fluid Mechanics’

large boundary layer wind tunnel utilising the HFFB technique. These two figures show the directionality of the measured wind-

induced peak acceleration, respectively occurring at 80o and 50

o. By applying the maximum response level to all wind

directions, one arrives at Figure 4b and Figure 5b, which are representative of a building that has an identical response level to

wind blowing from any wind direction; this condition might be observed in a circular stack. Given in Figure 4c and Figure 5c is

the building plan form that has generated the directional response characteristics.

050

100150

200250

300350

0

20

40

600

50

100

150

Direction [deg]Speed [m/s]

Acce

lera

tio

n [m

illi-g

]

0

50100

150200

250300

350

0

20

40

600

50

100

150

Direction [deg]Speed [m/s]

Acce

lera

tio

n [m

illi-g

]

a) b) c)

Figure 4: a) Directional building response; b) non-directional building response; c) floor plan for ‘Building A’.

a) b) c)

Figure 5: a) Directional building response; b) non-directional building response; c) floor plan for ‘Building B’.

By combining either the Shanghai wind climate (Figure 2) or the Miami wind climate (Figure 3) with the response

characteristic of ‘Building A’ (Figure 4) or ‘Building B’ (Figure 5), it is possible to investigate specific load effects using the

up-crossing method, the sector method or the storm passage method, for the various scenarios listed above in i) through v). In all

cases cited below, the load effect in question is the peak top-floor acceleration.

The magnitude of the load effect for a non-directional building (no bias of an aerodynamic and / or structural response to any

particular wind direction) in a non-directional wind climate (no bias of prevailing or non-prevailing winds) is the same across all

three analysis methods. This is the hypothetical case of a circular stack in the middle of a uniform open field in a wind climate

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with no prevailing direction. Although the up-crossing and storm passage predict a level of response regardless of direction the

response is plotted as a horizontal line in Figure 6 below for easy comparison with the results of sector method. This is the case

where the Kd factor from the ASCE7 wind code [15] would be equal to 1.0.

Figure 6: Non-directional building in a non-directional wind climate [scenario i)].

Figure 7 shows the prediction of the load effects for a non-directional building (no bias of an aerodynamic and / or structural

response to any particular wind direction) in a directional wind climate (a climate with prevailing and non-prevailing winds); a

scenario represented by tall buildings, often of very ‘organic’ architectural forms and featuring fundamental modes of vibration

with closely-spaced frequencies, a common feature of square central RC cores. Similarly to the case of a non-directional

building in a non-directional wind climate, the predictions from all three analysis methods collapse one on top of each other.

Shown in Figure 7 is the Shanghai typhoon directional wind climate with the non-directional building response. In this scenario

the directional reference wind speed peaks at 140-150 and therefore the load effect is also showing a peak at that same wind

direction. The total up-crossing probability for the same load effect remains the same, but directionally biased toward

140-150.

Figure 7: Non-directional building in a directional wind climate [scenario ii)].

For load effects that do not exhibit any directionality, i.e. in the case of a non-direction building, the Vg will be constant with

wind direction, hence d

dVgin equation (4) will be zero and

2

0, dVp g will reduce to gomni Vp , effectively extending

the consistency condition for the reference wind speed to any non-directional load effect between sector method and up-crossing

analysis. For the very same reason the rank probability of a wind record within a storm time history will be exactly the same as

the corresponding load effect, thus also extending the consistency condition to the storm passage method.

The load effect for the scenario where there is a directional building (bias of an aerodynamic and / or structural response to a

particular wind direction) in a non-directional wind climate is given in Figure 8. Figure 8 is produced by combining the

aerodynamic response of ‘Building B’ with the fabricated non-directional wind climate of Miami. The up-crossing and storm

passage methods demonstrate a reduction in the load effect when compared to the sector method. The sector method results in

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the same predicted load effect as scenario ii) given above; the non-directional building in a directional wind climate. The

directional response from the sector method peaks at 50o, the direction with a higher up-crossing probability. The sector method

prediction is therefore entirely driven by the critical building response at 50. The up-crossing analysis predicts a reduced load

effect as the weaker wind directions combined with a less onerous building response contribute to the total up-crossing

probability. The storm passage method should be seen to represent the most accurate way to predict the load effect as it is a time

history combination of the climate and building response. Interestingly, in this case, the up-crossing method shows a greater

reduction in the load effect prediction than the storm passage method, which potentially means an un-conservative consideration

of the load effect for the building. It should be noted that amongst the five possible load effect cases given, this case is the one

where the largest discrepancies between the sector method and the up-crossing method are likely to occur.

Figure 8: Directional building in a non-directional wind climate [scenario iii)].

For most wind engineering problems, both the wind climate and building aerodynamic response are likely to exhibit some

form of directionality and therefore the case of the directional building in the non-directional climate is somewhat academic.

Given in Figure 9 is the load effect predicted using the three analysis methods for a directional building (response of

‘Building A’) in a directional wind climate (Shanghai typhoon climate) for the case when there is no alignment between the

direction of strongest winds and that of most critical building response; i.e. the prevailing wind comes from the southeast and

the structure is aerodynamically and structurally most sensitive to winds coming from the northeast. In this particular example

the peak load effect (sector method) occurs at 180, which on its own is neither a prevalent wind direction nor a critical direction

for the building. For this scenario of the directional building in a directional wind climate the sector method has the potential to

generate lower responses than the other two methods.

Figure 9: Directional building in a directional wind climate, prevailing wind direction ≠ critical direction of building response

[scenario iv)].

Occasionally, the prevalent wind direction might coincide with the most critical direction of the building response, as shown

in Figure 10. In this scenario, the sector method predicts a highly directional response driven in this specific case by the north

easterly winds, and the results are comparable to those predicted in a non-directional wind climate. To produce Figure 10, the

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Miami hurricane directional wind climate was rotated to align the prevailing wind with the direction of the crtical building

response for ‘Building B’.

The up-crossing load effects are biased towards the north-easterly sector and predict lower load effects than the storm passage

method: previous studies [21] have if fact indicated the potential for the up-crossing technique to under predict load effects in

regions where extreme winds may subject a tall building to the storm’s maximum strength over a wide range of directions

(sometimes upwards to 180). In this case the storm may be more effective in exciting the building critically as it quickly

switches or swings across directions.

Figure 10: Directional building in a directional wind climate, prevailing wind direction = critical direction of building response

[scenario v)].

It is worth pointing out that for an infinitely directional building (i.e., a building that responds to only one wind direction) in

an infinitely directional wind climate (i.e., a climate with wind that blows from only one wind direction), the integral in

equation (4) will be dominated by a single small wind sector. In this case for the storm passage method, the rank probability will

be driven mostly by the single critical wind direction (which would make up most of the wind record in the storm time history),

and therefore the predicted load effects for all three methods will collapse to the non-direction results of scenario i.

7 COMPARISON OF LOAD EFFECTS PREDICTED BY VARIOUS METHODS: COMMERCIAL PROJECTS

In the authors’ experience in simultaneously using different analytical methods for the treatment of wind directionality, the

extent of the differences between up-crossing and sector methods is in general far from being large. Figure 11 for example

shows a comparison of the 10-year wind-induced peak accelerations for a number of selected projects, of varying height and in

varying wind climates (hurricane / extra-tropical depressions / typhoon / mixed), determined using both the sector method and

the up-crossing technique. In all cases the omni-directional 10-year wind speed has been matched across the analysis methods to

ensure consistency.

Figure 11: Comparison of sector and up-crossing method on selected projects.

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Although the list of projects presented in Figure 11 is perhaps far from being long and comprehensive, in most cases the

difference in the accelerations predicted using the up-crossing method versus the sector method is minimal and the values of

acceleration given are within 5% of one another. In about one third of the cases given above the sector method is predicting an

acceleration that is more than 5% greater than that predicted using the up-crossing method and for about 15% of the occasions

the reverse is true. There is little consistency in where the differences occur across wind climate or geographical location. The

biggest differences extend from the alignment or misalignment of the largest building response to the wind climate: the former

generally indicating that the sector method will produce higher results and the latter generally indicating that the up-crossing

method will produce higher results. As this alignment (or misalignment) between the climate and largest building response

becomes more significant the discrepancy between the two methods grows. However, this is not the only factor influencing the

difference in predictions of peak wind-induced acceleration response between the two methods of analysis as there is often the

bigger picture to consider.

In general, we design for an acceptable level of risk and there are various underlying reliability considerations in the

assessment of the wind climate that need to be accounted for prior to favouring one method over the other.

8 RISK CONSIDERATIONS AND CONCLUSIONS

Ultimately when a structure is being designed with the consideration of wind affecting the accelerations and loads, an

acceptable level of risk is defined. In many codes this level of acceptable risk might be defined as an event having an annual

probability of exceedance of 2%. When choosing which analysis method to utilize to solve for load effects having such a

probability of exceedance, one must weigh in many considerations. As Allsop [20] rather nicely put it when talking about the

effects of wind directionality on reliability: "[...] treatment of wind directionality continues to be highly controversial, ranging

from 'of course the wind can blow from any direction' to a blanket assumption that wind loads on a building can be reduced by

15% for directionality when using code methods, and without further calculation [...]".

One cannot ignore that still today most codes of practice make use of analytical models which are presented in a very

deterministic fashion. The beauty, for instance, of the sector method is that the concept of having reduced design wind speeds

for less probable wind directions is easy to grasp and it fits more naturally within the rather deterministic nature of most codified

approaches. There is no doubt that, when robust wind codes of practice are missing or do not contain any information on wind

directionality, wind engineers are left with having to use wind records obtained from airfields and / or weather stations, which -

for various reasons - are often imperfect in nature. It will be down to the ability and the experience of the wind engineer to make

good use of such imperfect data.

It is clear, at least in the authors' mind, that the more 'black box' nature of the up-crossing technique is far less suited to handle

sub-optimal wind records. In climates where only poor meteorological wind records are available, where the wind records

contain a significant number of uncertainties, it is often desirable to place a lower limit, or cut-off, on the non-prevailing wind

speeds. This lower cut-off can also be thought of as providing some protection against future potential changes in either

climatology or in surrounding building morphology and is very easy to implement in the sector method approach. In the

up-crossing method one is forced to place this cut-off on the loads themselves.

In North America, for instance, it is easy to access high quality extensive time histories of wind records, whereas in some

cities in India or China these same quality records may not be available. In the former case, where high quality wind records are

available one may lean towards the up-crossing technique, whereas in the latter case the more appropriate method of analysis

may be the sector method. The authors of this paper still remember a commercial project in northern China which attempted to

make use of the wind records collected from a nearby local airport which oddly showed that wind almost never blew from a

particular wind sector. Upon local inspection of the weather station, it was discovered that there was a small out-building

constructed very near to the anemometer, so near that it was sheltering completely winds from one wind sector and most

certainly influencing winds from adjacent sectors. In cases such as this, it would be impossible to utilize the storm passage

method and one would almost certainly be left with no options rather than making use of sector method approach.

In an ideal world one of course would always like to be in a position of utilising the storm passage method. At one point in

time generating a complete hour by hour time history of what a building would have experienced over the course of its life was

thought to be very computationally expensive. With the advent of high speed computing systems, systems that are now capable

of solving multiple equations with rapidity, it is hard to argue against the use of this straightforward approach. Now, whilst the

generation of artificial time traces of wind records is very practical and common industry standard in climates driven by

hurricanes / typhoons, the same is not true for climates driven by extra-tropical depressions. In such climates the development

of Monte Carlo based statistics would require time and budgets which cannot be borne by a single commercial project: only

large industry-driven organisations, perhaps at cross-country level, could stand the chance of putting together the funds required

for embarking upon such a project.

9 REFERENCES

[1] A.G. Davenport, Discussion of “Multivariate distributions of directional wind speeds”, Journal of Structural Engineering 113 (1987): 184-187.

[2] NIST document NCSTAR 1-2, Appendix D, dated 13 April 2004, submitted by Skidmore, Owings and Merrill LLP, Chicago, Illinois.

[3] http://www.iawe.org/about/Wind_Loading_Chain.pdf [4] R.I. Harris, “Control curves for extreme value methods”, Journal of Wind Engineering and Industrial Aerodynamics, Vol. 88, pp. 119-131, 2000.

[5] Cook, N, 1985, The Design Guide to Wind Loading of Building Structures. Part 1: background, damage survey, wind data and structural classification.

Butterworths, London, 1985. [6] ESDU, 1993, Strong Winds in the Atmospheric Boundary Layer. Part 2: Discrete Gust Speeds, Item 83045, Issued November 1983 with Amendments A

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and B April 1993. Engineering Sciences Data Unit, ESDU International, 27 Corsham Street, London N16UA.

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Conference on Wind Engineering, San Juan, 2009

[8] T. Tschanz, and A.G. Davenport, “The base balance technique for the determination of dynamic wind loads”, Journal of Wind Engineering & Industrial Aerodynamics, Vol. 13, pp. 429-439, 2000.

[9] S. Cammelli, and T. Wyatt, “Higher modes of vibration in response of super-tall buildings to wind”, 35th Annual Symposium of IABSE, London,

September 20-23, 2011. [10] A.G. Davenport, ‘The prediction of risk under wind loading,’ Proceedings of the Second International Conference on Structural Safety and Reliability,

Technical University in Munich, Munich, West Germany, pp. 511-538, September 1977.

[11] W.H. Melbourne, Designing for wind speed with direction, in The Structural and Environmental Effects of Wind on Buildings and Structures, Course Notes, Monash University, Melbourne, Chapter 20, 1981.

[12] N.J. Cook, “Towards better estimation of extreme winds,” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 9,: 295-323, 1985.

[13] S.O. Rice, Mathematical Analysis of Random Noise, Bell System Technical Journal, v23 p282-332, 1944 [14] E. Simiu, Design of Buildings for Wind; a guide for ASCE 7-10 Standard users and designers of special structures, 2nd Edition, John Wiley & Sons, 2011.

[15] ASCE/SEI 7-10. American Society of Civil Engineers. Minimum Design Loads for Buildings and Other Structures, 2010.

[16] M. F. Lepage, and P. Irwin, “A technique for combining historical wind data with wind tunnel test to predict extreme loads”, Proceedings of the U.S. National Conference on Wind Engineering, Lubbuck, Texas, November 1985.

[17] A.I.J. Recommendation for Loads on Buildings (AIJ-RLB), Architectural Institute of Japan, 2004.

[18] Australian/New Zealand Standard: Structural design actions: Part 2- Wind actions, AS/NZS1170.2:2002. Standards Australia, 2011. [19] EN1991-1-4: Eurocode 1: Actions on Structures – Part 1-4: General actions – Wind Actions, 2005.

[20] ASCE, “ASCE manuals and report on engineering practice, no. 67, wind tunnel studies of buildings and structures”, American Society of Civil Engineers,

1999. [21] P. Irwin, J. Garber, E. Ho, “Investigation of wind tunnel data with full scale wind climate”, Proceedings of the 10th Americas Conference on Wind

Engineering, Baton Rouge, Louisiana, May 2005.

[22] A. Allsop, “Reliability of super tall buildings against wind damage: a review of international practice”, 13th ICWE, Amsterdam, July 10-15, 2011.

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Wind Directionality Effects - Revisiting an Old Conundrum