NATL .INST. , OF , STAND &„TECH ^RXC.

AlllDH ^370^7

PUBUCATIONS

Nisr United States Department of Commerce

Technology Administration

National Institute of Standards and Technology

NIST Technical Note 1418

Probabilistic Estimates of Design Load Factors for

Wind-Sensitive Structures Using the "Peaks Over

Threshold" Approach

Timothy M. Whalen

QC

^00

1J5753

NO. 1418

1996
J

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NIST Technical Note 1418

Probabilistic Estimates of Design Load Factors for

Wind-Sensitive Structures Using the "Peaks Over

Threshold" Approach

Timothy M. Whalen

Building and Fire Research Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899-0001

April 1996

^^ATES O*

U.S. Department of Commerce

Michael Kantor, Secretary

Technology Administration

Mary L. Good, Under Secretary for Technology

National Institute of Standards and Technology

Arati Prabhakar, Director
National Institute of Standards U.S. Government Printing Office For sale by the Superintendent of and Technology Washington: 1996 Documents

Technical Note 1418 U.S. Government Printing Office

Natl. Inst. Stand. Techno!. Washington, DC 20402

Tech. Note 1418

30 pages (April 1996)

CODEN: NTNOEF
Probabilistic Estimates of Design Load Factors for

Wind-Sensitive Structures Using the "Peaks Over

Threshold" Approach

Timothy M. Whalen

Building and Fire Research Laboratory

National Institute of Standards and Technology

Bldg. 226, Room B158

Gaithersburg, MD 20899-0001

April 26, 1996

Abstract: The "peaks over threshold" method is used to estimate ratios of wind-induced

loads with various long mean recurrence intervals to loads with a 50-year mean recurrence

interval. The results support the conclusion that the load factor value of 1.3 specified in

the ASCE Standards 7-93 and 7-95 is adequate for extratropical storm regions. However,

for hurricane-prone regions, the results imply that the standard value of the load factor

(even after being augmented by an importance factor specified in the standards) leads to

nominal ultimate wind loads with considerably shorter mean recurrence intervals than is the

case for extratropical regions. This suggests that the 1.3 load factor value specified in the

ASCE Standards 7-93 and 7-95 is inadequate for wind-sensitive structures in hurricane-prone

regions.

Key Words: building (codes); building technology; climatology; extreme value theory;

hurricanes; load factors; structural engineering; structural reliability; threshold methods;

wind (meteorology)
1 Introduction

The nominal design wind load is an extreme load with a specified probability of being

exceeded during a specified time interval. For codes and standards in the United States,

this interval is usually 50 years, and the specified load is based upon a 50-year nominal

design wind speed. For example, for the inland Miami, Florida area, the ASCE Standard

7-93 [1] and 7-95 [2] specify a nominal 50-year load based on a nominal 50-year design wind

speed of 49.17 m/s (110 mi/h). It is expected, however, that a structure or element thereof

should withstand wind loads substantially in excess of the 50-year wind load without loss of

integrity. The wind load beyond which loss of integrity can be expected is referred to as the

ultimate wind load. The ultimate strength provided for in the design of a structure is based

upon an assumed nominal ultimate wind load equal to the nominal design wind load times

a wind load factor.

The wind load factor should be selected so that the probability of occurence of the

ultimate wind load is acceptably small. This probabilistic concept is important from an eco- nomic or insurance point of view. To the extent that evacuation or similar measures cannot

be expected to prevent loss of life, it is important also from a safety point of view. However,

attempts to estimate wind load factors on a probabilistic basis have so far not been successful. This may be due at least in part to the common use in reliability calculations of the

assumption that wind speeds are modeled by probability distributions with infinite upper

tails, e.g., Gumbel or Weibull distributions. In [3] and [12], it was assumed that the probability distribution of hurricane wind speeds is Weibull. However, the Weibull distribution is an

asymptotic model for the distribution of the smallest extremes. For extreme largest values,

the appropriate asymptotic model is either Gumbel, Frechet, or reverse Weibull [4, 9]. As

for the Gumbel distribution, it was found in [6] to yield what appeared to be unrealistically

high ultimate wind loads.

Recent studies [9, 10] have produced evidence in support of the assumption that extreme

wind speeds are modelled by the reverse Weibull distribution, which is tail-limited [i.e., has

a finite-length upper tail). The purpose of this report is to explore the potential offered by

this finding for estimating wind load factors on a probabilistic basis. This is done separately

for hurricane winds (sec. 2) and for winds in extratropical regions (sec. 3). In this work, wind

directionality effects are not taken into account. It is also assumed that the dominant load

is due to wind. Our results are therefore applicable to wind-sensitive structures for which

wind directionality effects are not significant. (Refer to [8] for a discussion of directionality

effects.)

2 Load Factors for Hurricane-Prone Regions

In this section, we are interested in the estimation of wind load factors for those portions

of the United States that have hurricanes and tropical storms as their most likely source of

extreme winds. This region encompasses the coastal regions of the Gulf of Mexico and the

Atlantic Ocean (see Fig. 1). Data for this study were obtained via simulation of hurricane

winds based upon censored probabilistic models of the climatological parameters that influ- ence hurricane structure. Consult [3] for a more complete discussion of the model. Censoring

1
Figure 1: Locator map for the hurricane-prone region of the United States (from [11]).

was based on physical considerations and is in principle consistent with a tail-limited probabilistic model of extreme wind speeds. The data represent fastest one-minute hurricane

speeds in knots at 10 m above ground over open terrain at the coastHne at 55 equidistant

locations. Data are available as maximum wind speeds within each of 16 half octants for

each of 999 simulated hurricane events. As indicated earlier, we analyzed datasets consisting

of the largest speed in each hurricane event regardless of direction. The estimated mean

annual rate of occurence of hurricanes at each location is also included in the dataset. The

data are available on tape and via anonymous file transfer.-^ Analysis of the data was performed via programs that implement the de Haan version of

the "peaks over threshold" method for estimating extreme value distribution parameters.'^ A

discussion of this method may be found in [5]. From the estimated distribution parameters,

we obtained estimates of wind speeds having specified mean recurrence intervals R. (The

recurrence interval R in years is the inverse of the probability that that wind speed will be

exceeded in any one year.) Under the assumption that a reverse Weibull distribution is valid,

^See [lO] for details on obtaining the data.

^These programs are also available via anonymous file transfer; see the previous footnote.
the probability of no exceedance of a given threshold speed is

G{y) = Prob [r < y] = 1 - {[1 + {cyla)]-"^] , (1)

where a and c are location and tail-length parameters, respectively, a > 0, c < 0, cy > —a,

Y = X — u^ X \s the windspeed, and u < X is a threshold assumed to be sufficiently high

[9]. (More precisely, this is the conditional probability, given that X > u ioi u sufficiently

large.) To obtain the estimate of the wind speed, let A represent the mean crossing rate of

the threshold u per year. Therefore, we can take

Prob[r<y] = l-l/(Ai?) (2)

as an estimate of the probability of no exceedances. Equating these two probability expressions and solving for y gives

y = -a[l-(Ai^r]/c, (3)

which in turn yields

XR = y^u (4)

as the estimated wind speed having a mean recurrence interval of R for the threshold u. The

wind speed with an infinite mean recurrence interval, i.e., the limiting upper wind speed as defined by the reverse Weibull distribution, is denoted by Xinf. Using eq (1) and setting

G{y) = 1, we can solve for y and thus obtain

X^nf ^ u- a/c. (5)

The wind load factor specified in the ASCE Standard 7-93 represents the ratio of the ultimate

wind load to the wind load based upon the 50-year nominal hurricane wind speed X50 times

a hurricane importance factor F. Since wind loads are proportional to the square of the

wind speed, we form an estimate of the wind load factor Lr according to:

Lr = [Xr/{F*Xso)]'. (6)

As specified on page 152 in the Commentary on ASCE Standard 7-95 [2], F = 1.05. Linf is defined by eq (6) with Xinf replacing Xr.

We show representative plots of the estimated wind speeds Xr and estimated wind load

factors Lr for various values of R in Figure 2 for simulated hurricanes at Milepost 300 (a

location near Matagorda Bay, Texas).^ Both the wind speeds Xr and wind load factors

Lr display a great deal of variability for low thresholds {u < 25 m/s, roughly speaking).

We note that inherent in the reverse Weibull model is the assumption that the thresholds u

correspond to high extreme wind speeds, and violations of this assumption may lead to poor

distribution parameter estimates. Also, both Xr and Lr display variability for very high

thresholds (u > 43 m/s, approximately). This is due to the relatively small sizes (fewer than

30 data points) of the wind speed data samples exceeding these thresholds. Between these

two bounding cases, the values of Xr and Lr are fairly constant, although some fluctuation

clearly exists.

^In all figures in this report, wind speeds are fastest-minute wind speeds at 10 m above ground over open

terrain in meters per second.

I
Milepost 300

20 25 30 35 40

Threshold windspeed u (m/s) 20

Milepost 300

4.5

-: :

'

4

L.500

- - L_2000

-

- -L_10000 3.5 LJnf -

3

2.5

2

1.5

' ^^ ^ / N

4. ^i-ii'v-j-.j-'-i

./"

1

^-^ ^

25 30 35

Threshold windspeed u (m/s) 40

Xr versus u. Lr versus u.

Figure 2: Representative plots of estimated wind speeds Xr and load factors Lr versus threshold speed u.

Graphs of estimated wind load factors versus threshold speed for various locations along

the Gulf of Mexico and Atlantic Ocean coastline are provided in Appendix A. Due to the

previously mentioned reasons, no results have been shown for thresholds having more than

300 exceedances or fewer than 30 exceedances. Also, estimated load factors larger than 2.5 are not shown. For comparison, we have included in these plots a dotted line at Lr — 1.3,

representing the ASCE Standard 7-93 value of the wind load factor.

The graphs of Appendix A show noticeable variability in the load factors as a function

of threshold, especially for the high recurrence intervals R = 10,000 years and R = oo. However, certain trends are discernable. For example, the load factor -L500, shown as a

solid line in the graphs, is close to or higher than the design standard value of 1.3 for most

mileposts. This result is in keeping with the conclusions of [10], which found that the load

factor standard value corresponded to winds with relatively short mean recurrence intervals.

This implies that the probability of exceedance of the nominal ultimate wind load (calculated

in accordance with the standard) is about 0.002 (or larger) per year or, assuming that the

design lifetime of the structure is 50 years, is equal to (or larger than) about

1- v50 (1-0.002)^ 0.095

during the structure's lifetime.

3 Load Factors for Extratropical Regions

We now turn our attention to the estimation of wind load factors for areas of the United

States in which tropical storms are not expected to occur. We use as our source of data
Moline.lL 60

r55-

DCSOI X

n45-

(U

0) #401- c

g

5351-

•Iso

25

' '

X_50

- - X_500

- - X_2000

X_inl

,

' //-}//:.

. .'v\^ ^._ >V~--\

X'/ .^ ^-^-^

<y^^^>^ -

12 14 16 18 Threshold windspeed u (m/s)

Xr versus u.

20

Moline.lL

4.5

4

- L_500

- - L_2000

3.5

1

- - LIOOOO

LJnf

3 :

2.5 • -

2 A

1.5

1

• ' *. _ y^

\\ } \}.

12 14 16 18

Threshold windspeed u (m/s)

Lr versus u.

20

Figure 3: Representative plots of estimated wind speeds X^. and load factors Lr versus threshold speed u.

the records of the largest daily wind speeds collected at 44 U.S. weather stations that lie outside of the area described in sec. 2. Each set contains approximately 20 years worth of

daily fastest mile wind data. We once again used the de Haan estimation method, and the

analysis proceeded largely as described in the previous section, with one additional step.'^ In

order to reduce possible correlations among the data due to a single storm producing strong

winds for more than 1 day, the records were broken into intervals of 8 days, and maximum

speeds in each interval were identified. If maxima of adjacent intervals (denoted by I\ and

I2) were found to be less than 4 days apart, the following procedure was used. Let I\ contain

the smaller of the two maxima. This maximum was replaced by the highest value in I\

separated from the maximum in I2 by 4 days or more. This procedure insured that all data

in the set were at least 4 days apart. The interval of 4 days was chosen because it represents a reasonable maximum duration of a strong wind storm. Analyses with interval lengths

of 4 days and correlation periods of 2 days were performed and were found to produce no

significant differences in the results. Previous studies [9] have shown that this procedure,

while reducing the total number of data points used in the estimation process, tends to

remove low wind speeds from consideration, resulting in a data set more representative of

extreme winds.

In Figure 3, we show representative plots of the estimated wind speeds Xr and wind load

factors Lr for data from Moline, IL, for which 15 years of daily wind speed data are available.

Note that Lr is still defined by eq (6) for extratropical regions, but the hurricane importance

factor F is now set to 1.00. As was true for the hurricanes, we note a downward trend for

the estimated variates with lower thresholds. We ascribe this trend to bias associated with

'Again, both the data sets and analysis programs are available. See [9] for further information.
the inclusion of relatively weak winds. For this reason, and to reduce sampling errors due

to small sample sizes due to very high thresholds, we have plotted in Appendix B results

only for thresholds having between 30 and 450 data points. Once again, we note that there

is significant variability both among the plots and within a given plot. We may, however,

state unequivocally that the load factor L^oo is considerably lower than was the case for

hurricane winds for the majority of the stations. A comparison of the graphs of Appendix A

and Appendix B also suggests that the tails of the load factor distributions are considerably

shorter for stations in extratropical regions than in hurricane-prone stations.

4 Discussion of Results

Questions may arise as to whether our analyses of the hurricane wind speed data are

affected significantly by the model used in the simulation that yielded the data. However,

we note that the models upon which our data sets were based are considered reasonable

for professional practice and that these data were used for the development of the ASCE

Standard 7-93 wind speed map. Our analyses are therefore consistent with that wind speed

map. The wind speed map of the ASCE Standard 7-95 differs from that of the ASCE

Standard 7-93 in that (i) it uses peak gusts instead of fastest mile wind speeds (a difference

of presentation rather than substance), and (ii) it uses a boundary layer model based on the

Shapiro approximation [7] rather than an empirical boundary layer model. As was pointed

out by Shapiro, this model does not describe the boundary layer structure in detail, especially near the eye wall of the hurricane where wind speeds are expected to be largest. Also,

according to Shapiro, since this approximation entails a truncated spectral representation

for the wind velocity, the resulting estimates can have errors of as much as 25%. For this reason it is not clear that simulations based upon Shapiro's approximation are necessarily an improvement over earlier simulations. Given the present state of the art, it is our opinion

that our results have an acceptable basis as far as the quality of the data is concerned.

Nevertheless, we point out that the high degree of fluctuation in the estimates is a difficulty

in the study of probabilistically determined wind load factors. This suggests the need for

further improvements in both the quantity and quality of the data used in the estimation

process and further study of probabilistic estimation techniques.

Finally, we recall that all of our results are applicable to wind-sensitive structures for

which wind directionality effects are not significant. This is true for both hurricane-prone

regions and regions not subject to hurricanes. An assessment of relative values of load factors

in these two regions thus has a consistent basis.

5 Conclusions

In this report, we have used the "peaks over threshold" method to estimate ratios of

wind-induced loads with various long mean recurrence intervals to loads with a 50-year

mean recurrence interval. According to our estimates, the load factor value of 1.3 specified

in the ASCE Standards 7-93 and 7-95 is adequate for extratropical storm regions; that is, it corresponds to nominal ultimate wind loads judged to have sufficiently long miean recurrence
intervals. However, in hurricane-prone regions, the 1.3 standard value of the load factor (even

after being augmented by an importance factor of (1.05) ) leads to nominal ultimate wind

loads with considerably shorter mean recurrence intervals than is the case for extratropical

regions. To these mean recurrence intervals there correspond in most cases probabilities of

exceedance of the nominal ultimate wind load on the order of ten percent during a 50 year

lifetime of a structure. According to our results, an increase in the wind load factor would

therefore be appropriate for structures subject to hurricane winds.

Acknowledgments: This work was completed during the author's tenure in the NIST/NRC

Postdoctoral Research Associateship Program at NIST. Partial support by the NATO Scientific Affairs Division is also acknowledged with thanks. The author would like to thank

Emil Simiu, who served as research advisor, for his suggestions and comments on this work.

His participation in this project was partially supported by the National Science Foundation

(Grant No. CMS-9411642). Also, the author would like to thank Alan Heckert of NIST for

his assistance with the data sets and programs used in this study.

References

[1] American Society of Civil Engineers. ASCE Standard 7-93. New York, 1993.

[2] American Society of Civil Engineers. ASCE Standard 7-95. New York, 1995.

[3] M. E. Batts, M. R. Cordes, L. R. Russell, J. R. Shaver, and E. Simiu. Hurricane wind

speeds in the United States. J. Struct. Div. ASCE, 100:2001-2015, 1980.

[4] E. Castillo. Extreme Value Theory in Engineering. Academic Press, New York, 1988.

[5] L. de Haan. Extreme value statistics. In J. Galambos, J. Lechner, and E. Simiu, editors,

Extreme Value Theory and Applications. Kluwer Academic Publishers, Dordrecht and

Boston, 1994. Vol. 1.

[6] B. Ellingwood et al. Development of a probability-based load criterion for American

National Standard A58. NBS Special Publication 577, National Bureau of Standards

(U.S.), Washington, DC, 1980.

[7] L. J. Shapiro. The atmospheric boundary layer flow under a translating hurricane. J. Atmos. Sci., 40:1984-1998, 1983.

[8] E. Simiu. Estimation of extreme wind loads. In Davenport Sixtieth Birth Anniversary

Volume, pages 109-123. International Association for Wind Engineering, 1995. Ninth

International Conference on Wind Engineering.

[9] E. Simiu and N. A. Heckert. Extreme wind distribution tails: A "peaks over threshold" approach. NIST Building Science Series 174, National Institute of Standards and

Technology, Gaithersburg, MD, 1995.
[10] E. Simiu, N. A. Heckert, and T. M. Whalen. Estimates of hurricane wind speeds by

the "peaks over threshold" method. NIST Technical Note 1416, National Institute of

Standards and Technology, Gaithersburg, MD, Feb. 1996.

[11] E. Simiu and R. H. Scanlan. Wind Effects on Structures. Wiley-Interscience, third

edition, 1996.

[12] P. J. Vickery and L. A. Twisdale. Prediction of hurricane windspeeds in the U.S. J. Struct. Eng., 121:691-699, 1995.
A Estimates of wind load factors versus threshold for

locations in hurricane-prone regions

1

Legend (L_R, R in years)

LJnf

L_10000

L_2000

L_500

ASCE Standard load factor
Mileposl 150 Mileposl 200

30 32 34 36 38 40 42 44 46

Threshold windspeed u (m/s) 28 30 32 34 36 38 40 42 44Threshold windspeed u (m/s)

Milepost 250 Mileposl 350

2 V

, ^

' \

1.5 /

28 30 32 34 36 38 40 42 44

Threshold windspeed u (m/s) 32 34 36 38Threshold windspeed u (m/s) 40 42

Milepost 400

1 [— Milepost 450

32 34 36 38 40

Threshold windspeed u (m/s) 30 35

Threshold windspeed u (m/s)

10
2.5

Mllepost 500

'

' ":

'

'

2

.s. 1 • A ^ ^ ,--/----

^ / '

1.5 ---"'

-

"

Milepost 550

; ; ^

;^ '^ /\ / \/

'_^ ' \ /

* y\ \

/ "^v ,. • s .-' "^

--_^

'

'^ '- \\

30 35

Threshold windspeed u (m/s) 30 35

Threshold windspeed u (nVs)

25

Milepost 600

-

/

,

/' ^ '

\

2

.'' " *" \ _/

\ /

,--'

^ , '

1.5 -.^^ -^-""^^

Milepost 650

26 28 30 32 34 36 38

Threshold windspeed u (m/s) 28 30 32 34

Threshold windspeed u (m/s)

Milepost 700 Milepost 750

26 28 30 32 34 36 38 40

Threshold windspeed u (m/s) 26 28 30 32 34 36 38 40

Threshold windspeed u (m/s)

11
2.5

Mllepost 800

/' A

' \

; '. >' ^ / ^

• '• ' . / V ' / V. 2

/

1.5 ' * — ^

.

':C

-

' >' '^^^^-.^^^-^-^—

c^--^—

--^

Mileposl 850

28 30 32 34 36

Threshold windspesd u (m/s) 30 32 34 36

Threshold windspeed u (nn/s)

Mileposl 900 Mllepost 950

30 32 34 36

Threshold windspeed u (m/s) 28 30 32 34Threshold windspeed u (rn/s)

Mllepost 1000 Mllepost 1050

28 30 32

Threshold windspeed u (m/s) 26 28 30 32

Threshold windspeed u (m/s)

12
Mileposl 1100 Milepost 1150

27 28 29 30 31 32 33 34 35 36 37

Threshold windspeed u (m/s) 28 30 32 34Threshold windspeed u (m/s)

Milepost 1200 Milepost 1 250

30 32 34 36

Threshold windspeed u (m/s) 34 36 38 40

Threshold windspeed u (m/s)

Milepost 1300 Milepost 1350

/ / -' '"\^~ \ :' :

34 36 38

Threshold windspeed u (m/s) 30 32 34 36 38

Threshold windspeed u (m/s) 40 42

13
Milepost 1400 Milepost 1450

35 40

Threshold wtndspeed u (m/s) 36 38 40 42

Threshold windspeed u (m/s)

Milepost 1 500 Milepost 1550

2

.5

'" ' ' ^~t^:' i :

// y\--

/ '' "^

"* —

__-— -^

36 38 40 42

Threshold windspeed u (m/s) 30 32 34 36 38

Threshold windspeed u (m/s)

Milepost 1600

2 5

1t^ilepost 1650

2

/

1.5 .,-- -- ^.'•^. ''

' A

'

. 'V'

v. '.' \

/ /

' ~ X

' '^''-^^^

24 26 28 30 32 34 36 38 40 42

Threshold windspeed u (m/s) 26 28 30 32 34 36 38 40 42

Threshold windspeed u (m/s]

14
Mileposl 1700 Milepost 1750

26 28 30 32 34 36 38

Threshold windspeed u (m/s) 26 28 30 32Threshold windspeed u (m/s)

Milepost 1800 Milepost 1850

26 28 30 32

Threshold windspeed u (m/s) 24 26 28 30 32 34 36 38 40Threshold windspeed u (nVs)

Milepost 1900 Milepost 1 950

24 26 28 30 32 34 36 38 40

Threshold windspeed u (m/s) 26 28 30 32 34 36 38 40 42

Threshold windspeed u (m/s)

15
Mileposl 2000

30 32 34 36 38

Threshold windspeed u (m/s)

Mileposl 2050

-T 1

. • \ /

26 28 30 32 34 36

Threshold windspeed u (m/s) 38 40

Mileposl 2100 Mileposl 2150

26 28 30 32 34 36

Threshold windspeed u (m/s) 30 35Threshold windspeed u (m/s)

Mileposl 2200 Mileposl 2250

26 28 30 32 34 36

Threshold windspeed u (m/s) 30 35

Threshold windspeed u (m/s)

16
Milepost 2300

—t r24 26

\ \ ' \ y

28 30 32 34

Threshold windspeed u (m/s) 36 38

Milepost 2350

^1 \ ' \ /' \ l"

22 24 26 28 30 32

Threshold windspeed u (m/s) 34 36

Milepost 2400

^ '

' : .' / ^

22 24 26 28 30 32 34 36

Threshold windspeed u (m/s) 24 26 28 30 32

Threshold windspeed u (m/s)

Milepost 2500 Milepost 2550

,(

i\ ;. /

',1 ^ \ ^_

I ,1

I i

I ^ -.-'< -

^ \ '

•'

, /•'"""

\ ^

/"

\

':

.. ' / ^y .//'wV-'

J

' V

-^

\\^ ^_/_ V/ -

24 26 28 30 32 34 36 38 40

Threshold windspeed u (m/s) 26 28 30 32 34 36 38 40 42 44

Threshold windspeed u (m/s)

17
Milepost 2600 Milepost 2650

:

'*.;

."'

s.

/ /

/ \

x \

/

\

/

-

^ \ /^- ^/^ y -^ y

"" """'

/ v^^

'^' ^ ^/ / - > ^ ^ ^

28 30 32 34 36 38 40 42 44

Threshold windspesd u (m/s) 30 32 34 36 38 40 42 44 46Threshold windspeed u (m/s)

Milepost 2700

2.5

2

Milepost 2750

\ /

\ ' , \ ;

\ \ \ .\ '.

^-^^'' l.b

30 32 34 36 38 40 42

Threshold windspeed u (m/s) 26 28 30 32 34 36 38 40 42 44Threshold windspeed u (m/s)

Milepost 2800 Milepost 2850

26 28 30 32 34 36 38 40 42 44

Threshold windspeed u (m/s) 26 28 30 32 34

Threshold windspeed u (rrVs)

18
B Estimates of wind load factors versus threshold for

locations in extratropical regions

Legend (L_R, R in years)

LJnf

L_10000

L_2000

L_500

ASCE Standard load factor

19
Abilene, TX Albany.NY

14 15 16 17

Threshold windspeed u (m/s) 14 15 16

Threshold windspeed u (m/s) 17

Albuquerque, NM Blllings.MT

16 17 18 19 20 21 Threshold windspeed u (m/s) 16 17 18 19 20

Threshold windspeed u (m/s)

12

Binghamton.NY Bolse,ID

13 14 15

Threshold windspeed u (m/s) 16 13 14 15 16 17

Threshold windspeed u (m/s) 18

20
Burlington, VT

2.5

5^

Cheyenne.WY

<2o

o

(0 u.

T351.5

1 iMM^_^^^.^ii:ii^^^%.^JM^

13 14 15 Threshold windspeed u (m/s) 16 18 20 22

Threshold windspeed u (m/s) 24

Concord.NH Dayton.OH

12.5 13 13.5 14 14.5 15 15.5 Threshold windspeed u (m/s) 14 15 16 17 18

Threshold windspeed u (m/s)

2.5 Denver.CO

^1 2

_J

/

i2

/ ' D

31.5

/ / J^ ,

Duluth.MN

15 16 17 18 19

Threshold windspeed u (m/s) 20 13 14 15 16 17

Threshold windspeed u (m/s) 18

21
Fort Smith.AK Fort Wayne, IN

11 12 13 14 15 16 Threshold windspeed u (m/s) 14 15 16 17 18

Threshold windspeed u (m/s) 19

2.5 Green Bay.WI

o

51.5-

/ \ / "\

12 13 14 15 16

Threshold windspeed u (m/s) 17

Greensboro, NC

2.5

/ »

5^

; ,

21

u.

51.5 ' /'' C">\

.1

'

. ,

\ /' ^ - ' y

. . .

10 11 12 13 14

Threshold windspeed u (m/s) 15

Greenville.SC Helena.MT

2.5

51.5

10 11 12 13 14

Threshold windspeed u (m/s) 15 16 17 18

Threshold windspeed u (m/s) 19

22
Huron.SD Lander.WY

n.o

: f ,» It

1 ' * 1 ' DC

1 2 ,

^.

* ' ,' I i'

,' ' ' / _l , ^

' \' / m

O /

- If ' ' /\ ^ ' o

(0 /y ' ( * I / \ ' u. /

/ ^^

1

' A '»' / \ ^^

T1

tn \ \ / / / \ / \ o—

1

1.5 "' / /\ '^^ /'7

^ \/

-y • \ \v " . - ^ '

14 15 16 17 18 19

Threshold windspeed u (m/s)

2.5

S1.5

, 'I i

I ; I '

:/\ '/ \w/. \/a V A'

14 15 16 17 18 19 20 21 Threshold windspeed u (m/s)

Lansing, Ml Loulsviile.KY

14 15 16 17

Threshold windspeed u (m/s)

2.5

S1.5

i I A ^ '

''

' / / \ V ''

/ / / \ / _ - - / / \

.* • • / -* J,* = • ......

11 12 13 14 15

Threshold windspeed u (m/s) 16

Macon.GA Milwaukee.WI

10 11 12 13 14 15 Threshold windspeed u (m/s) 14 15 16 17 18 Threshold windspeed u (m/s)

23
Minneapolis,MN

2.5

"=, 2

_i / 1 \ U) \ o ." u

(0 .' u. / / /\

T3 r / \

(0 / \ ii1.5 / \

H . ,

Missoula.MT

12 13 14 15 16

Threshold windspeed u (m/s)

2.5

2-

S1.5

'' -^^ '- , • y'

: ; 1

, , 1 14 15 16 17 18

Threshold windspeed u (m/s)

Mollne.lL 2.5

COS1.5

12 13 14 15 16 17 18 19

Threshold windspeed u (m/s)

Oklahoma CIty.OK

16 17 18 19

Threshold windspeed u (m/s)

Pocatello.lD Portland.ME

15 16 17 18

Threshold windspeed u (m/s) 12 13 14 15 Threshold windspeed u (m/s) 16

24
Portland.OR Pueblo.CO

2.5

(S 51.5

1 . ij

-

1 ,

\ /

: (

'

/

/ / ' y^^~\ '

,

.' / ^ \

" \ / /- / \ s :

.' '

it" ^ V :/j \ ' "*

'

' /

' / AA-;

,'>^' ^

^^-iixv' ^^V

13 14 15 16 17 18 19 Threshold windspeed u (m/s) 16 17 18 19 20 21 22 23

Threshold windspeed u (m/s)

Red Bluft.CA Richmond.VA

13 14 15 16 17 Threshold windspeed u (m/s)

11 12 13 14

Threshold windspeed u (m/s)

Salt Lake City.UT

15 16 17 18

Threshold windspeed u (m/s)

2.5 San Diego.CA

31.5

.

; 1

; J

i *

1 f

-•' 1

'•....•• \ / \ \

i /

-''/

\'~--":.^vc::>-^:'-Mf/ >^

\y

10 11 12 13

Threshold windspeed u (m/s) 14

25
Sheridan.WY Spokane.WA

14 15 16 17 18

Threshold windspeed u (m/s) 14 15 16 17

Threshold windspeed u (m/s) 18

Springfield.MO Toledo.OH

12 13 14 15

Threshold windspeed u (m/s) 16 13 14 15 16 17 18Threshold windspeed u (m/s)

Topeka.KS Tucson, AZ

2.5r

11.5-

: ' ''

I

• : \ ' '^

/

'

1 '

' /

:

^ ' 1 ' ' /

: : ' ^

' / /

' \ ' I /

! \ '

'

•

'

>

' /

12 13 14 15 16 17 Threshold windspeed u (m/s) 18 13 14 15 16 17

Threshold windspeed u (m/s)

26
Winnemucca.NV

2.5

11.5

• /

^

/ _ - - ^

13 14 15 16 17 1{ Threshold windspeed u (m/s)

Yuma.AZ

2.5 1 f n rz

y f\\ y * ; \ / /, I / \

"^1 2 / /' > > / \ ' _i / ^' \ \ / ^ '

(/I / / \ / \ -o / / \ >, . ' u

(0 u. . — "

" ' \ / ^ * ' •a / ' / y\ \ /

^ \' /

(0 .' / y' \ *' ' / 51.5 w^s-:'.vx>-

12 13 14 15 16

Threshold windspeed u (m/s)

27


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by the sponsor; public distribution is by the National Technical Information Service, Springfield, VA 22161,

in paper copy or microfiche form.
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