NAT'L INST OF STAND & TECH

A111D7 E1D703.

NBS BUILDING SCIENCE SERIES 100

Building To Resist The Effect Of Wind

VOLUME 2. Estimation of Extreme Wind

TA- Speeds and Guide to the

Determination of Wind Forces

.U58

NO .100 VRTMENT OF COMMERCE • NATIONAL BUREAU OF STANDARDS

V I L. m

C , L

NBS BUILDING SCIENCE SERIES 100-2

Building To Resist

The Effect Of Wind ::^^\

In five volumes 065 ^^^u^ : _ W -cxo ,\

*Wy I g 1377

VOLUME 2: Estimation of Extreme Wind Speeds and

Guide to the Determination of Wind

Forces

Emil Simiu

Richard D. Marshall

Center for Building Technology

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

Sponsored by: The Office of Science and Technology

Agency for International Development

Department of State Washington, D.C. 20523

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued May 1977
Library of Congress Catalog Card Number: 77-600013

National Bureau of Standards Building Science Series 100-2

Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 100-2, .29 pages (May 1977)

CODEN: BSSNBV

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 - Price $1.30

Stock No. 003-003-01718-3
ABSTRACT

The Agency for International Development sponsored with the National Bureau of Standards, a three and a half year research project to develop improved

design criteria for low-rise buidings to better resist the

effects of extreme winds.

Project results are presented in five volumes. Volume

1 gives a background of the research activities, ac- complishments, results, and recommendations. In Volume 3, a guide for improved use of masonry

fasteners and timber connectors are discussed. Volume 4 furnishes a methodology to estimate and

forecast housing needs at a regional level. Socio- economic and architectural considerations for the

Philippines, Jamaica, and Bangladesh are presented in Volume 5. Volume 2 consists of two reports. The first reviews the

theoretical and practical considerations that are perti- nent to the estimation of probabilistically defined

wind speeds. Results of the statistical analysis of ex- treme wind data in the Philippines are presented and

interpreted. Recommendations based on these results are made with regard to the possible redefinition of wind zones, and tentative conclusions are drawn

regarding the adequacy of design wind speeds cur- rently used in the Philippines. Report two describes some of the more common flow mechanisms which

create wind pressures on low-rise buildings and the

effects of building geometry on these pressures It is assumed that the basic wind speeds are known and a procedure is outlined for calculating design wind

speeds which incorporates the expected life of the

structure, the mean recurrence interval, and the wind

speed averaging time. Pressure coefficients are tabulated for various height-to-width ratios and roof

slopes. The steps required to calculate pressures and

total drag and uplift forces are summarized and an il- lustrative example is presented.

Key words: Building codes; buildings; codes and standards; housing; hurricanes; pressure coefficients; probability dis- tribution functions; risk; statistical analysis; storms; structural engineering; tropical storms; wind loads; wind speeds.

Hi

Cover: Instruments to mcnsiire wind speed and direction being installed on a 10 meter mast at the project test site in Quezon City, Philippines.

CONTENTS

1. ESTIMATION OF EXTREME WIND SPEEDS-APPLICATION TO THE PHILIPPINES

1.1 Introduction , 3 1.2 Wind Speed Data 2

1.2.1 Type of Instrumentation 2

1.2.2 Averaging Time 3

1.2.3 Height Above Ground 3

1.2.4 Distance Inland From the Coastline 4

1.3 Probabilistic Models of Extreme Wind Speeds 4

1.4 Assessment of Procedures Based on the Annual Highest Speed 4

1.4.1 Wind Climates Characterized by Small Values of opt(7 ) 5

1.5 Assessment of Procedure Based on the Highest Average Monthly Speed 6

1.6 Statistical Analysis of Extreme Wind Data in the Philippines 6

1.7 Interpretation of Results 7

1.7.1 Zone III 7

1.7.2 Zone II 8

1.7.3 Zone I 8

1.8 Conclusions 9

ACKNOWLEDGMENTS 9

REFERENCES 9

2. A GUIDE TO THE DETERMINATION OF WIND FORCES 13

2.1 Introduction 13

2.2 Aerodynamics of Buildings 23

2.2.1 Typical Wind Flow Around Buildings 24

2.2.2 Effect of Roof Slope 24

2.2.3 Roof Overhangs 24

2.3 Design Wind Speed 25

2.3.1 Mean Recurrence Interval 25

2.3.2 Risk Factor 25

2.3.3 Averaging Time and Peak Wind Speed 25

2.4 Design Pressures 25

2.4.1 Dynamic Pressure 25

2.4.2 Mean and Fluctuating Components of Pressure 25

2.4.3 Pressure Coefficients 26

2.4.4 Correction Factor for Height of Building. 27

2.5 Procedure for Calculating Wind Forces 27

ACKNOWLEDGMENTS 28

APPENDIX A

Illustrative Example 22 Comment 23

FIGURES

Fig. 1 Ratio, r, of Maximum Probable Wind Speeds

Averaged over t seconds to those Averaged over 2 sec 22

Fig. 2 Quantity B '22

Fig. 3 Probability Plots:

(a) Type II Distribution, y - 2 .'22

V
(b) Type I Distribution 12

Fig. 4 Typical Flow Pattern and Surface Pressures 14

Fig. 5 Vortices Along Edge of Roof 15

Fig. 6 Areas of Intense Suctions 15

Fig. 7 Typical Record of Wind Speed and Surface Pressure 16 Tables

Table 1 Suggested Values of Zq for Various Types of Exposures 3

Table 2 Maximum Annual Winds (1 minute average) 7 Table 3 Station Descriptions and Estimated Extreme Wind Speeds 7 Table 4 Mean Recurrence Interval 18 Table 5 Relationships Between Risk of Occurrence, Mean Recurrence Interval and Expected

Life of Building 18 Table 6 Pressure Coefficients for Walls of Rectangular Buildings 19 Table 7 Pressure Coefficients for Roofs of Rectangular Buildings 20

Table 8 Internal Pressure Coefficients for Rectangular Buildings 21 Table 9 Correction Factors (R) for Height of Building 21

Facing Page: A wind sensor is installed on the wall of a test house in Quezon City, Philippines. Pressures acting on

xvalls and on the roof of the test building are converted by

these sensors into electrical signals which are recorded on magnetic tape.

vi
1. ESTIMATION OF EXTREME

WIND SPEEDSAPPLICATION TO THE

PHILIPPINES

by

E. Simiu

1.1 INTRODUCTION

In modern building codes and standards [1, 2] basic design wind speeds are specified in explicitly probabilistic terms. At any given station a random variable can be defined, which consists of the largest yearly

wind speed. If the station is one for which wind

records over a number of consecutive years are

available, then the cumulative distribution function (CDF) of this random variable may, at least in theory,

2
be estimated to characterize the probabilistic behavior

of the largest yearly wind speeds. The basic design

wind speed is then defined as the speed corresponding to a specified value Fg of the CDF or, equivalently

(in view of the relation N=l/(l-FQ)in which N=

mean recurrence interval), as the speed corresponding to a specified mean recurrence interval. For example, the American National Standard A58.1 [l] specifies that a basic design wind speed corresponding

to a 50-year mean recurrence interval (i.e., to a value

Fg of the CDF equal to 0.98, or to a probability of ex- ceedance of the basic wind speed in any one year

equal to 0.02) be used in designing all permanent

structures, except those structures with an unusually

high degree of hazard to life and property in case of

failure, for which a 100-year mean recurrence inter- val (Fg = 0.99) must be used, and structures having no human occupants or where there is negligible risk to human life, for which a 25-year mean recurrence

(Fg = 0.96) may be used. A wind speed corresponding

to a N-year recurrence interval is commonly referred

to as the N-year wind.

The mean recurrence intervals specified by building

codes, rather than being based on a formal risk analysis—which is in practice not feasible in the present state of the art—are selected in such a manner as

to yield basic wind speeds which, by professional consensus, are judged to be adequate from a structural safety viewpoint. Nevertheless, it is generally

assumed that adequate probabilistic definitions of design wind speeds offer, at least in theory, the ad- vantage of insuring a certain degree of consistency

with regard to the effect of the wind loads upon structural safety. This is true in the sense that, all relevant

factors being equal, if appropriate mean recurrence

intervals are used in design, the probabilities of failure of buildings in different wind climates will, on the

average, be the same.

In the practical application of the probabilistic ap- proach to the definition of design wind speeds, cer- tain important questions arise. One such question pertains to the type of probability distribution best suited

for modeling the probabilistic behavior of the extreme

winds. The provisions of the National Building Code

of Canada [2] are based upon the assumption that this behavior is best modeled by a Type I (Gumbel) dis- tribution. The American National Standard A58.1 [1], on the other hand, assumes that the appropriate

models are Type II (Frechet) distributions with loca- tion parameters equal to zero and with tail length

parameters dependent only upon type of storm.

Finally, Thom [29] has proposed a model consisting of

a mixed probability distribution, the parameters of which are functions of (a) the frequency of occurrence

of tropical cyclones in the 5° longitude-latitude square under consideration and (b) the maximum average

monthly wind speed recorded at the station investi- gated. The question of selecting the most appropriate

distribution is one that deserves close attention: in- deed, as indicated in References 23 and 22, the magnitude of the basic design wind speed may depend

strongly upon the probabilistic model used. Assuming that the type of probability distribution best suited for modeling the behavior of the extreme winds is known, a second important question arises,

viz., that of the errors associated with the probabilistic

approach to the definition of design wind speeds.

Such errors depend primarily upon the quality of the data and upon the length of the record (i.e., the sample size) available for analysis.

These questions will be dealt with in this work, which

will also present results of statistical analyses of wind

speed data recorded in the Philippines. In the lighl of the material presented herein, possible approaches

will be examined to the definition of extreme wind

speeds for purposes of structural design in the Philippines.

1.2 WIND SPEED DATA

For the statistical analysis of extreme wind speeds to be meaningful, the data used in the analysis must be

reliable and must constitute an homogeneous set. The

data may be considered to be reliable if: • The performance of the instrumentation used

for obtaining the data (i.e., the sensor and the record- ing system) can be determined to have been adequate. • The sensor was exposed in such a way that it was not influenced by local flow variations due to the proximity of an obstruction (e.g., building top, ridge or instrument support).

A set of wind speed data is referred to herein as homogeneous if all the data belonging to the set may

be considered to have been obtained under identical or equivalent conditions. These conditions are deter- mined by the following factors, which will be briefly

discussed below: • type of instrumentation used • averaging time (i.e, whether highest gust, fastest mile, one-minute average, five-minute average, etc. was recorded). • height above ground • roughness of surrounding terrain (exposure) • in the case of tropical cyclone winds, distance inland from the coastline.

1.2.1 Type of instrumentation

If, during the period of record, more than one type of instrument has been employed for obtaining the data.

2
the various instrument characteristics (anemometer

and recorder) must be carefully taken into account and the data must be adjusted accordingly.

1.2.2 Averaging Time

If various averaging times have been used during the period of record, the data must be adjusted to a com- mon averaging time. This can be done using graphs

such as those presented in Reference 19 and included

in figure 1 in v^hich is a parameter defining the

terrain roughness (see, for example, Ref. 10).

1.2.3 Height Above Ground

If, during the period of record, the elevation of the anemometer had been changed, the data must be adjusted to a cbmmon elevation as follows: Let the roughness length and the zero plane displacement be

denoted by and Z^, respectively {Z^, Z^, are parameters which define the roughness of terrain, see

Ref. 10). The relation between the mean wind speeds

U(Zi) and LKZ^) over horizontal terrain of uniform

roughness at elevation Z^ and Z^ above ground,

respectively, can be written as

U(Z,)

U(Z)

Z„

fin Z.-Zrf ~77~

(1)

Suggested values of the roughness length Z^ are given

in table 1 (see refs. 10,21,7). For example, at Sale, Australia, for terrain described as open grassland with

few trees, at Cardington, England, for open farmland

broken by a few trees and hedge rows, and at Heathrow Airport in London, Z„ = 0.08 m [10, 21]. At

Cranfield, England where the ground upwind of the anemometer is open for a distance of half a mile

across the corner of an airfield, and where neighboring land is broken by small hedged fields, Z^ = 0.095m

[9]. The values of Z„ for built-up terrain should be

regarded as tentative. It is noted that Equation 1 is applicable to mean winds and should not be used to represent the profiles of peak gusts.

Table 1. Suggested Values of Z^ for Various Types

of Exposure

Type of Exposure Zj|( meters)

Coastal 0.005-0.01 Open 0.03- 0.10 Outskirts of towns, suburbs 0.20- 0.30 Centers of towns 0.35- 0.45 Centers of large cities 0.60- 0 80

The zero plane displacement Z^ may in all cases be

assumed to be zero, except that in cities (or in wooded

terrain) Z^ = 0.75 h, where h = average height of buildings in the surrounding area (or of trees) 1 10, 16]. Thus, for example, if in open terrain with Z,^ = 0.05 m,

L/(23) = 30 m/s, then adjustment of this value to the height Z^ = 10 m, using Equation 1, gives

U(10) = U(23)

10

0. 05

en

23

0. 05

5 30 = 30 = 25.9 m/s.

D. I J

It is noted that, in most cases, the roughness

parameters Z„, Z^ must be estimated subjectively, rather than being determined from measurements. Good judgment and experience are required to keep

the errors inherent in such estimates within reasonable bounds. In conducting statistical studies of the ex- treme winds, it is advisable that for any particular set of data, an analysis be made of the sensitivity of the

results to possible errors in the estimation of Z and

Zrf.

In the case of winds associated with large-scale extratropical storms, the mean wind U(Z) at height Z in terrain of roughness Z^, Z^ is related as follows to the mean wind (J,(Zj) at height Z^ in terrain of roughness

Z„.,Z^J21]:

U(Z) = /3 U,(Z|)

(2)

Cn z-z,

Zo.

The quantity, may be obtained from figure 2, which was developed in Reference 21 jn the basis of

theoretical and experimental work reported by

Csanady [4] and others [26]. (Note that Z^^<Z„)

Equation 2 may be applied if the roughness of the ter- rain is homogeneous over a horizontal distance from

the anemometers of about 100 times the anemometer

elevation [18, 24].

Let, for example, UZ,) = 29 m/s, Z,- = 10 m, Z^^ = 0.05 m, Z^j = 0. The corresponding speed U{Z) at Z - 40 m,

say, in open terrain of roughness Zo = 0.25 m, Z^^ = 0 is

U(10) = 1.12 X 29 Cni^

0.25 Cn

10 "005

= 31.1 m/s.

where 1.12 is the value of /3 for Z„, = 0.05 m, Z„ = 0.25 m, obtained from figure 2.

3
It is pointed out that, just as in the case of Equation 1, errors are inherent in Equation 2 that are associated with the subjective estimation of the roughness

parameters. Also, recent research suggests that in the

case of tropical cyclone winds Equation 2 underesti- mates wind speeds over built-up terrain, calculated as functions of speeds over open terrain, by amounts of the order of 15% or morell7l.

1.2,4 Distance Inland from the Coastline

The intensity of hurricane or typhoon winds is a decreasing function of the distance inland from the

coastline. Hurricane wind speeds may be adjusted to a common distance from the coastline by applying

suitable reduction factors. Such reduction factors have

been proposed by Malkin, according to whom the

ratios of peak gusts at 48, 96 and 144 km from the

coastline to peak gusts at the coastline are 0.88, 0.82 and 0.78, respectively [8, 14].

1.3 PROBABILISTIC MODELS OF EXTREME

WIND SPEEDS

The nature of the variate suggests that an appropriate

model of extreme wind behavior is provided by probability distributions of the largest values, the general

expression for which is [ll]:

F(i') = exp j-l(i'-M)/o'il"'^ I M<z'<°°

-00<jU<00

0<(T<oo

y>0

where i' = wind speed, /x = location parameter, cr —

scale parameter, y = tail length parameter. Equation 3 may be regarded as representing a family of distributions, each characterized by a value of the tail length

parameter y. As y becomes larger, the tail of the probability curve becomes shorter, i.e., the probability of occurrence of large values of the variate becomes

smaller. In particular, as y —* oo. Equation 3 may be

shown to become

F(i') = exp

I —exp[—d'—pi)/cr]

I — oo<t'<oo

-oo</x<oo (4) 0<cr<oo

The distributions given by Equations 3 and 4 are known as the type II and the type I distributions of the largest values, respectively.

Two basic procedures for estimating probabilities of occurrence of extreme winds are currently in use. The

first procedure consists in estimating the parameters

of a probability distribution of the largest values from

the series of annual highest wind speeds at the station considered. This procedure has been applied by

various authors as follows:

(a) In Reference 23, estimates are made of all three parameters, /x, cr and y in Equation 3, no specific

value being assigned a priori to any of these parameters.

(b) In References 27 and 28, the location parameter is assumed to have the value fi = 0. Estimates are then

made of the remaining parameters, cr and /jl. The ar- bitrary assumption that = 0 entails a sacrifice in goodness of fit; the justification for using this assumption is that it makes possible the application of Lieblein's well-known estimation procedure [13] to obtain values of cr andy [27]. However, in view of the recent development of alternative estimation pro- cedures applicable to type II distributions with fi^O

[23], the assumption that fj. = 0 becomes unnecessary.

(c) Court in the United States [3], Davenport in Canada [5] and Kintanar in the Philippines [12] have

assumed the universality of the type I distribution,

i.e., that the tail length parameter is always y = oo. Estimates are then made of the parameters /jl and a. The second procedure assumes the universal validity of the mixed distribution

Hv) =

p^ exp [-(^)'1 + p^ exp[-(^)-'-'] (5)

proposed by Thom in Reference 29. The First and the second term in the sum of Equation 5 represent the

probabilities that the winds associated with extratropical storms and with tropical cyclones, respectively, will not exceed the value, v, in any one year. The scale parameter, cr, is an explicit function of the maximum of the average monthly wind speeds

recorded at the station considered. The second

parameter of the mixed distribution, ppis an explicit

function of the frequency of occurence of tropical

cyclones in the 5° longitude-latitude square under consideration, and p£ = 1 — pj. Thus, in this second pro- cedure, the series of annual highest winds is not used

for estimating distribution parameters.

An assessment of the models described in this section

will now be presented.

1.4 ASSESSMENT OF PROCEDURES BASED

ON THE ANNUAL HIGHEST SPEEDS

To assess the validity of current probabilistic models,

statistical analyses of annual highest speeds were car- ried out using a computer program described in Reference 23. The results of the analyses, which are reported in detail in Reference 23, lend credence to the belief that a sufficiently long record of annual

largest speeds will provide an acceptable basis for probabilistic extimates of the N-year winds—even for

4
large values of N, such as are of interest in structural safety calculations—if the following conditions are

satisfied. First, the value of opt (y) for that record is large, say y ^ 40 (opt( y) = value of y Isee eq. 3] for which the best distribution fit of the largest values is obtained). Second, meteorological information ob- tained at the station in question, as well as at nearby

stations at which the wind climate is similar, indi- cates that winds considerably in excess of those

reflected in the record cannot be expected to occur ex- cept at intervals many times larger than the record

length. Wind climates which satisfy these two conditions will be referred to as well-behaved.

Assuming that the wind speed data are reliable, lower

bounds for the sampling error in the estimation of the N-year winds in a well-behaved climate may be

calculated on the basis of a mathematical result, the Cramer-Rao relation, which states that for the type 1 distribution (see ref. 11, p. 282)

,.,1.10867 , var(/A) >

n (6) „ 0.60793 , Var(a) > cr- n (7)

where var (/x), var {&) are the variances of jl and a, where fi and & are the estimated values of ^l and cr, respectively, obtained by using any appropriate

estimator consistent with basic statistical theory re- quirements; a is the actual value of the scale parameter and n is the sample size. Using Equations 6 and 7, lower bounds for the standard deviation of the sampling error in the estimation of the N-year wind,

SD[v(N}\, can be approximated as follows. Equation 4, in which the parameters fi, a are replaced by their estimates fi, cr, is inverted to yield

v(N) = /l-G(l-^)5- (8)

where

G(l-^) = -ln[-|n(l-J^)]= (9)

Then

SD[v(N)] > [var(/x) -I- [ai-Jj)]^ var (&}]^' (10)

Equation 10 is based on the assumption that the error involved in neglecting the correlation between fx and

cr is small. The validity of this assumption was

verified by using Monte Carlo simulation techniques.

Since the actual value of a is not known, in practical calculations the estimated value cr is used in Equations

6 and 7. For example, the distribution parameters cor- responding^to the wind speed data at Davao (« = 24,

see table 2), estimated by using the technique

described in Reference 23, are p. = 38.89 km/hr, a =

9.40 km/hr. It follows from Equation 8 that v (50) = 75 km/hr and from Equations 6, 7, and 10 that SD[v{5Q)\ > 5.18 km/hr. Subsidiary calculations not reported

here have shown that Equation 1 0 provides a good

indication of the order of magnitude of the sampling

errors.

1.4.1 Wind Climates Characterized by Small

Values of opt (y).

Occasionally, a record obtained in well-behaved

wind climates may exhibit small values of opt (y); this will occur if that record contains a wind speed that corresponds to a large mean recurrence interval. There are regions, however, in which, as a rule, the

statistical analysis of extreme wind records taken at any one station yields small values of opt (y). This is the case if, in the region considered, winds occur that are meteorologically distinct from, and considerably

stronger than the usual annual extremes. Thus, in the regions where tropical cyclones occur, opt (y) will in general be small, unless most annual extremes are

associated with tropical cyclone winds. An example

of a record for which y (opt) is small is given in figure

3a, which represents the probability plot with y = opt

(y) = 2 for the annual extreme fastest mile-speeds

recorded in 1949-73 at the Corpus Christi, Texas, air- port. For purposes of comparison, the same data have

been fitted to a type I distribution (opt ( y) = oo, or Eq.

4); the fit in this case is seen to be exceedingly poor,

i.e., the plot deviates strongly from a straight line (fig. 3b). As shown in Reference 23, a measure of the goodness of fit is given by the extent to which the probability plot correlation coefficient is close to unity;

this coefficient is printed out in figures 3a and 3b. To small values of the tail length parameter there fre- quently correspond implausibly high values of the estimated speeds for large recurrence intervals. In the

case of the 1912-48 record at Corpus Christi, for example, opt (y) = 2 and the estimated 5-minute average is 327 mph (155 m/s) for a 1000-year wind, which is highly unlikely on meteorological grounds. For 20- year records, the situation may be even worse: thus,

for the 1917-36 Corpus Christi record, which contains an exceptionally high wind speed due to the 1919 hurricane [3, 25j, opt (y) = 1 and the calculated 1000- year wind is 1952 mph (873 m/s) [23], a ridiculous

result. Also, the situation is not likely to improve sig- nificantly if the record length increases. From a 74- year record, a plot quite similar to figure 3 would

presumably be obtained, with twice as many points

similarly dispersed, to which there would correspond

a similar least squares line on probability paper.

It may be stated, consequently, that while in the case

of well-behaved climates it appears reasonable to in5
fer from a good fit of the probability curve to the data

that the tail of the curve adequately describes the ex- treme winds, such an inference is not always justified

if opt (y) is small.

It may be argued that one could avoid obtaining

unreasonable extreme values by postulating that the annual largest winds are described by a probability

distribution of the type I, i.e., by assigning the value y = oo to the tail length parameter. This has been done

by Court [3] and Kintanar [12]. As can be seen in figure 4, the corresponding fit may be quite poor. However, the estimated extremes at the distribution

tails will be reduced. The drawback of this approach

is that unreasonably low estimated extremes may be

obtained. For example, at Key West, Florida, if all three parameters of Equation 3 are estimated as in Reference 23, to the 1912-48 record there corresponds

I' (100) =99mph(44.2m/s)and y (1000) = 188 mph (84

m/s)—see Reference 23. If it is postulated that 7 = 00, then V (50) = 70 mph (31 ,7 m/s), y (100) = 77 mph (34.4 m/s) and y (1000) = 97 mph (38.8 m) [23], an unlikely

result in view of the high frequency of occurrence of hurricanes (about 1 in 7 years) at Key West.

It may also be argued that since the estimated ex- tremes resulting from small values of y (say y < 4) may be too large, and those corresponding to y = 00 may be too small, a probability distribution that might

yield reasonable results is one in which y has an in- termediate value, say 4< y < 9. Such an approach

has been proposed by Thom and will now be ex- amined.

1.5 ASSESSMENT OF PROCEDURE BASED

ON THE HIGHEST AVERAGE

MONTHLY SPEED

The procedure tor estimating extreme winds in hur- ricane-prone regions on the basis of annual highest

winds at a station was seen to have the following

shortcomings. First, because hurricane winds are

relatively rare events, the available data may not contain wind speeds associated with major hurricane oc- currences and are therefore not representative of the wind climate at the station considered (see the case of Calapan in Section 1.7 of this report). Second, in regions subjected to winds that are meteorologically

distinct from, and considerably stronger than the

usual annual extremes, implausible estimates may be

obtained.

The model proposed by Thom [Eq. 5j in Reference 29

represents an attempt to eliminate these shortcomings. It can be easily shown by applying the inter- mediate value theorem, that if this model is assumed,

the estimated extreme winds may be obtained by in- verting an expression of the form:

f(iO=exp l(-v/o-)-y(^')j

in which 4.5 < y (v) < 9. If the mean rate of arrival of tropical cyclones in the region considered is high,

then y ( v) will be closer to 4.5. Otherwise, y (f) will be

closer to 9; in regions where hurricanes cannot be ex- pected to occur, y(v) = 9. In order that estimates not be based upon possibly unrepresentative annual ex- treme data, Thom's model does not make use of annual extreme speeds. Rather, the parameter u is esti- mated from the maximum of the average monthly

wind speeds on record at the location considered,

presumably a quantity for which the variability is small.

While the quasi-universal climatological distribution proposed by Thom is tentative, it will yield results which, for a first approximation, may in certain cases be regarded as acceptable. This model has recently

been used by Evans l6j as a basis for obtaining design

wind speeds for Jamaica. Estimates of extreme speeds

obtained by Evans are substantially higher than the

results obtained by Shellard [20] in his 1971 analysis

of Commonwealth Caribbean wind data.

It was shown in the preceding section that the ap- proach which utilizes the series of annual largest

speeds may fail in regions in which hurricanes occur. For such regions, therefore, it may be that alternative approaches need to be developed. Among such ap- proaches is one in which estimates of extreme winds

are based upon the following information: • average number of hurricanes affecting the

coastal sector considered (per year) • probability distribution of hurricane intensities • radial dimensions of hurricanes • dependence of wind speeds upon central pressure and distance from hurricane center.

This approach appears to provide useful estimates of extreme winds corresponding to large recurrence in- tervals—which are of interest in ultimate strength

calculations—and is currently under study at the National Bureau of Standards.

1.6 STATISTICAL ANALYSIS OF EXTREME

WIND DATA IN THE PHILIPPINES

Through the courtesy of the Philippine Atmospheric,

Geophysical and Astronomical Services Administration (PAGASA), 16 sets of data were obtained consist- ing of maximum yearly wind speeds recorded during

at least 14 consecutive years. The data for each of the 16 stations are listed in table 2. Table 3 includes subjective station descriptions provided by PAGASA

personnel and the results of the analysis. In Table 3 are listed y^^v^h)= N-year wind based on the dis- tribution for which the best fit of the largest values is obtained and ^1^°° = N-year wind based on the type I distribution, N = mean recurrence interval in years.

6
TABLE 2. MAXIMUM ANNUAL WINDS (ONE MINUTE AVERAGES)

NO. Station Period of Record Maximum Annual Winds for Fach Year of Record (km/hour)

1 Davao 19 SO -7 3 39,52,40,39,40,37, 35, 35, 32,40,4(),40,H0,4«,48,48,56,46,52,5O,46,52,46, 46

2 Cagayan de Oro

1950-73 47,24,19,13,19,19,12,12,12,19,16,14,21,6,24,17,19,37,37,46,37,48,41,41

3 Zamboa nga 1950-73 48,64,40,39,48,61,43,40,48,45,48,72,48,48,50,56,68,67,70,56,61,74,61,78 4 Pasav City 1950-73 89, 1 03,89,92,72,72,64,72,97,72,8 1 ,66,69,74, 1 30,65,80, 1 1 1 ,83,74,200,80, 111,56

5 Manila 1949-70 72,105,97,89,101,97,100,105,81,72,97,89, 121,105,100,168,74,89,107,1 1 1,96,20(1 6 Manila

Central

1902-40 46,56,65,80,73,55,77,70,4 1 ,68,50,69,64,68,42, 4 1 ,67,54,70,83,58,53,60,5 1 ,45, 63,50,70,52,55,58,37,100,60,45,52,103,53,56 7 Mirador 1914-40 79,79,7079,1 21,1 02,94,72, 1 05, 1 07, 1 22,58,89, 1 07,93,63,77,92,63,53,93,73,75,

iri T(l t-O 49,,i9,6o,o,i 8 Baguio 1950-73 97, 1 05,56,97,97,8 1 ,64,64,6 1 ,48,97, 48,53,98, 111,1 07,80, 1 44, 1 07, 1 02, 1 37,85,89, 1 33

9 Caiapan 1959-73 145,1 85,97,72,40,68,40,96, 1 09,4 1 ,33, 1 1 1

, 1 02, 1 1 1 ,83 10 Surigao 1952-73 1 05,43, 1 1 3,40,40,40,43,48,64,64,89,39,74,52,78, 1 04, 1 67, 1 1 1 ,96, 1 07,96,74

11 Laoag 1949-73 34,72, 1 1 8,7 1

, 1 1)8, 1 (1( ),64, 8 1 ,8 1 ,64,8 1 ,79,64, 1 05,90, 1 44, 1 44,78, 1 20, 1 37, 1 ()0,67,K9,67,70 12 Iloilo 1949-73 97, 1 06,64,64,07 ,(i4,64,64,72,74,a,78,7S,M,74, 1 ^ 1 ,=^2,6 1 , 8<^, W,74

13 Cebu 1950-73 97,56, 1 2 1 ,48,8 1 ,64,48,48,48,43,48,43,64,64,56,48,56,70,93,65,56, 1 00,74,59

14 Legaspi 1955-73 40,97,97,48, 1 29, 1 85,97,82,89, 1 04,74,89, 1 48,74,70, 174,1 48,204,8

1

15 Tacloban 1949-73 137,58,106,1 13,56,68,60,47,48,69,87,42,105,93,74,1 1 1, 70, 1 94, 133,1 h7,63,8 1,155,1 04,67

16 Infanta 1960-73 60,43,45,50,128,39,133,126,46,46,189,85,104,83

TABLE 3. STATION DESCRIPTIONS AND ESTIMATED EXTREME WIND SPEEDS

No. station

Wins

/one

See Ref. 15

Period of RecordNo. of Years Anemometer

Flevalion (meters) Description

of Terrain opt (-y) v;;f"'^'"(km/hrl V~' (km/hr) N=50 N = 100 N = 10(I0 N=50 N=100 N=1000

1 Davao 111 24 III Town 75 82 105

-) Cagayan

de Oro

111 61 69 94

3 Zamboa nj^a 111 msii.yi 24 10 Open 88 95 117

•t I'asav Litv II 24 lO Air^»rt 22('i 292 820 164 m

5 Manila 11 I'<44-7(I Titp of S-*^lor\' building

Port Area 7 20K 238 365 192 212 276

f. Manila

Ct-nlral

11 19 (1jx-n (Park) 35 1113 1 12 144 nil no 1.38

7 Mirador

Baguu.

11 1'<I4-4(I 27 irf'

( 1 5111) ni aN>ve Mountain top

sea level)

139 151 192

8 BaRuu. II I4SI)-71 24 10 Mnutain top

( 1 500 m .iNive wa level)

164 IKO 2.30

9 Caiapan II |4S4-7'i IS 10 Top of hill; town on one

side

209 234 316

in Surigao 11 I4S2.71 ^2 7 Large City Top of 40m

lull

40 170 191 262 167 187 250

11 Laoag 11 1949-73 2"; 12 Open 174 192 252

12 Iloilo 11 19S0-73 24 25 (5m above 20m bldgj Town 2 180 235 640 138 152 192 n Cebu 11 l9sn-7.'< 24 10 Airpvirt 127 140 185

14 Legaspi I 19SS-71 19 12 Airport*- 90 235 2t>4 350 235 264 .340 1? Tacloban ! 1949-73 2? 12 {3m above 9m bidg.) Top of 1 5m

hill Military Campd

14 213 242 352 204 228 306

16 Intanta 1 IWfi-73 14 10 lown, Residential area

h 242 m m 2l4 542

^3 cup anemometer; mean speed averaged over one minute. ^Mean speed averaged over one minute.

'"Trees at East side of anemometer.

1.7 INTERPRETATION OF RESULTS

The results will be grouped into three classes, accorci- ing to the wind zone (as defined in Ref. 15) in which

the stations considered are located (table 3).

1.7.1 Zone III

"North and East; sea exposure.

^ Omitted if opt {y) = oo.

^ One minute averages.

It is noted that for all three Zone III stations listed in Table 3, opt (y) = oo. It is convenient to adjust the speeds at Davao and Cagayan de Oro to open terrain exposure. On the basis of the terrain descriptions of Table 3, if it is assumed Z„ = 0.30 m, = 0, Z„, = 0.08 m, Z^j = 0, it follows from Equation 2 that

7
U (10)

where UilO), L/j(10) are mean speeds above ground in town and open exposure, respectively. Thus, in Davao and Cagayan de Oro the calculated 50-year mean speeds at 10 m above ground in open terrain are 58 mph and 47 mph (94 km/hr and 76 km/hr) respectively, versus 55 mph, (88 km/hr) in Zamboanga. If the corresponding highest gusts are obtained by multiplying the one-minute means by a factor of, say, 1.20 (see

fig. 1), the estimated highest 50-yr gusts at Davao,

Cagayan de Oro and Zamboanga are at most 94 x 1 .20 = 113 km/hr, (70mph), i.e., considerably lower than

the value specified for design purposes by the National Structural Code of the Philippines [15] for Zone

III, viz., 95 mph (153 km/hr). This suggests that the re- quirements of Reference 1 5 regarding wind loading in the Zone III portion of Mindanao are conservative

and might be somewhat reduced. (It can be easily

shown, on the basis of Eq. 2 and figure 1, that this statement holds even if it is assumed that the errors in the estimation of the parameter values Z^ = 0.30 m

and Z = 0.08 m are of the order of as much as 50%.)

To validate such a conclusion it would however be

necessary to determine, from long-term records of

tropical cyclone occurences, that the 1950-73 data at the three stations analyzed are indeed representative

for southern Mindanao.

1.7.2 Zone II.

Several difficulties arise in interpreting the results for the Zone II stations in table 3. It is noted, first, that the

results obtained at stations in and near Manila (sta- tions 4, 5, 6 in table 3) are widely divergent. The dis- crepancies between the results for Pasay City and

Manila may be due to the different elevations of the respective anemometers. It may also be conjectured

that the discrepancies between these results and those obtained from the 1902-1940 Manila Central record

are due to differences in the averaging times and in the exposure, elevation and calibration of the instru- ments, as well as to possibly inaccurate estimates of the maximum speed in Manila and Pasay City in 1970

(200 km/hr, see table 2). The estimated wind speeds at Baguio based upon the 1950-73 record are higher than those obtained from

the 1914-40 data. No explanation is offered for these

differences; an investigation into their causes seems

warranted.

The record at Calapan illustrates the limitations of the approach to the definition of design wind speeds

based on the statistical analysis of the highest annual

winds. From the data covering the period 1961-72, the estimated 50-yr wind based on a Type I distribution is 88 mph (141 km/hr) [12], versus 1 31 mph (209 km/hr).

as obtained if the data covering the period 1959-1973

are used (see table 3). Since wind loads are proportional to the square of the wind speeds, the ratio be- tween the respective estimated winds loads is (209/141)2 = 2.2.

Although the record at Pasay City is best fitted by a type II distribution with opt (y) = 2, it is unlikely, as noted previously, that such a distribution correctly describes the behavior of the extreme winds. This is obvious, particularly in the case of the 1000-yr wind,

which, on physical grounds, could not possibly attain 509 mph (820 km/hr) (see table 3). The National Structural Code of the Philippines

specifies, for Zone II and elevations under 9.15 m, a design wind of 109 mph (175 km/hr). In the light of the data shown in table 2, the value appears to be

reasonable. It will be noted that tables 2 and 3, and

figure 13 of Reference 15 indicate that the extreme

speeds and the frequency of occurrence of tropical

cyclones, are considerably higher at Laoag than at Cebu. This suggests that Zone 11 could be divided, ac- cordingly, into two subzones, with wind load requirements higher in the northern than in the southern

subzone.

1.7.3 Zone I.

As indicated previously, if y(opt) is small , i.e., if the differences among maximum wind speeds recorded

in various years are large, the probability distribu- tions that best fit the data may not describe correctly the extreme wind speeds for large recurrence intervals. The minimum and the maximum winds for the period of record are, at Legaspi, 25 mph (40 km/hr)

and 127 mph (204 km/hr), respectively, and, at Tacloban, 26 mph (42 km/hr) and 120 mph (194

km/hr), respectively. In the writer's opinion, the

reliability of the N-year wind estimates obtained at these stations for N=50, 100 and 1000 is therefore

doubtful. The same comment applies to the estimates

for Infanta, where the record length is quite insuffi- cient (14 years). The writer therefore believes that the

results of table 3 should not be used to assess the ade- quacy of the design wind speed requirement for Zone

I specified in Reference 15. Rather, it is reasonable to base such an assessment on a comparison between

wind speeds in Zone I and in areas affected by hurricanes in the United States. In the light of U.S. ex- perience, it is the opinion of the writer that from such

a comparison it follows that the 124 mph (200 km/hr)

wind speed requirement for Zone I and elevations

under 30 ft. (9.15 m) is adequate for structural design

purposes.

8
1.8 CONCLUSIONS ACKNOWLEDGMENTS

From the analysis of available extreme speed data in the Philippines, the following conclusions may be

drawn:

1. The design wind speeds specified by the National

Structural Code of the Philippines for the Zone 111 part of Mindanao appear to be conservative and

might be somewhat reduced. For this conclusion to be validated, it would be necessary to determine,

from long-term records of tropical cyclone occurrences, that the data analyzed herein are representative for southern Mindanao.

2. Methodological difficulties and uncertainties with

regard to the reliability of the data preclude, at this time, the estimation for Zones 11 and 1 of N-year ex- treme winds that could be used, with a sufficient degree of confidence, as design values within the framework of an explicitly probabilistic code.

3. According to the data included herein. Zone 11 can

be divided into two subzones, with wind load re- quirements higher in the northern than in the southern subzone.

4. The data included herein suggest that the wind

speed requirement specified by the National Structural Code of the Philippines for Zone 1 is adequate

for purposes of structural design, except as noted

below.

5. Higher wind speed values than those specified by

the National Structural Code of the Philippines

should be used—except perhaps in the Zone 111 part

of Mindanao—in open, and in coastal exposure.

6. Improved design criteria for Zones II and I, includ- ing possible redefinitions of these zones, could in the future be achieved by applying the methodology briefly described at the end of the

section "Assessment of Procedure Based on the Highest Average Monthly Speed." This would re- quire, in addition to data on the frequency of oc- currence of tropical cyclones at various locations in the Philippines, that the following data be available:

a. Reliable wind speeds, carefully defined with

respect to terrain roughness, averaging time and

distance from shore line.

b. Approximate radial dimensions of tropical

cyclones.

c. Approximate dependence of tropical cyclone

speeds upon minimum central pressure and dis- tance from storm center.

The writer wishes to express his indebtedness and appreciation to Dr. Roman L, Kintanar, Mr. Manuel

Bonjoc, Mr. Bayani S. Lomotan, Mr. Jesus E. Calooy, Mr. Leonicio A. Amadore, Mr. Samuel B. Landet, and

Mr. Daniel Dimagiba, of the Philippine Atmospheric,

Geophysical Astronomical Services Administration

(PAGASA), for kindly permitting him to use the PAGASA records and facilities and for their effective and generous help. He also wishes to thank Dr. R. D. Marshall of the Center for Building Technology, In- stitute for Applied Technology, National Bureau of Standards, for useful comments and criticism of this work. The computer program used here was

developed by Dr. J.J. Filliben, of the Statistical Engineering Laboratory, National Bureau of Standards. REFERENCES

(1) Building Code Requirements for Minimum Design Loads in Buildings and Other Structures, A58.1-1972(New York: American National

Standards Institute, 1972).

(2) Canadian Structural Design Manual (Supplement

No. 4 to the National Building Code of Canada) (National Research Council of Canada, 1970).

(3) Court, A., "Wind Extremes as Design Factors," Journal of the Franklin Institute, vol. 256(JuIy

1953), pp. 39-55.

(4) Csanady, G. T., "On the Resistance Law of a Turbulent Ekman Layer," journal of the Atmospheric Sciences, vol. 24 (September 1967), pp. 467-471.

(5) Davenport, A. G., "The Dependence of Wind

Loads Upon Meteorological Parameters," Proceedings, Vol. 1 (International Research Seminar on Wind Effects on Buildings and Structures) (Toronto: University of Toronto Press,

1968).

(6) Evans, C. J., "Design Values of Extreme Winds in Jamaica" (Paper presented at Caribbean

Regional Conference, Kingston, Jamaica,

November 6-7, 1975).

(7) Fichtl, G., and McVehil, G., Longitudinal and

Lateral Spectra of Turbulence in the Atomospheric

Boundary Layer, Technical Note D-5584

(Washington, D.C.: National Aeronautics and

Space Administration, 1970).

(8) Goldman, J.L., and Ushijima, T., "Decrease in Maxinum Hurricane Winds after Landfall,"

journal of the Structural Division, vol. 100, no. STl, proc. paper 10295 (New York: American

Society of Civil Engineers, January 1974), pp. 129-141.

9
(9) Harris, R.I., "Measurements of Wind Structure At

Heights Up to 585 ft Above Ground Level,"

Proceec/;n^s (Symposium on Wind Effects on

Buildings and Structures) (Leicestershire:

Loughborough University of Technology,

1968). (10) Helliwell, N.C., "Wind Over London," Proceedings (Third International Conference of Wind

Effects on Building and Structures) (Tokyo,

1971)

(11) Johnson, N.L., and Kotz, S., Continous Univariate

Distributions, vol. 1 (Wiley, 1970)

(12) Kintanar, R. L., "Climatology and Wind-Related

Problems in the Philippines," Development of Improved Design Criteria to Better Resist the Effects of Extreme Winds for Low-Rise Buildings

in Developing Countries, BSS 56 (Washington,

D.C.: National Bureau of Standards, 1974). SD

Catalog No. C13. 29/2:56

(13) Lieblein, J., Method of Analyzing Extreme Value

Data, Tech. Note 3053 (Washington, D.C.: National Advisory Committee for Aeronautics,

1954).

(14) Malkin, W., "Filling and Intensity Changes in Hurricanes Over Land," National Hurricane

Research Project, vol. 34(1959).

(15) National Structural Code of the Philippines, (Sec- tion 206 in BSS 56: Development of Improved

Design Criteria to Better Resist the Effects of Extreme Winds for Low-Rise Buildings in Developing Countries) (Washington, D.C.: National Bureau of Standards, 1974). SD Catalog No.

C13.29/2:56

(16) Oliver, H. R., "Wind Profiles In and Above a Forest Canopy," Quarterly Journal of the Royal

Meterorological Society, vol. 97 (1971), pp. 548-553.

(17) Patel, V.Cand Nash, J.F., Numerical Study of the Hurricane Boundary Layer Mean Wind Profile (Report prepared for the National Bureau of Standards) (Sybucon, Inc., June 1974).

(18) Peterson, E. W., "Modification of Mean Flow and

Turbulent Energy by a Change in Surface Roughness Under Conditions of Neutral

Stability," Quarterly Journal of the Royal

Meteorological Society, vol. 95(1969), pp. 569-575.

(19) Sachs, P., Wind Forces in Engineering (Pergamon

Press, 1972).

(20) Shellard, H.C., "Extreme Wind Speeds in the Commonwealth Caribbean," Meteorological

Magazine, no. 100(1971), pp. 144-149.

(21) Simiu, E., "Logarithmic Profiles and Design

Wind Speeds," journal of the Engineering

Mechanics Division, vol. 99, no. EMS, proc. paper !0I00(New York: American Society of

Civil Engineers, October 1973), pp. 1073-1083.

(22) Simiu, E., and Filliben, J. J., "Probabilistic Models

of Extreme Wind Speeds: Uncertainties and

Limitations," Proceedings (Fourth International Conference on Wind Effects on Buildings and

Structures) (London, 1975).

(23) Simiu, E., and Filliben, J.J., Statistical Analysis of Extreme Winds, Tech. Note 868 (Washington,

D.C.: National Bureau of Standards, 1975). SD

Catalog No. 013.46:868

(24) Simiu, E., and Lozier, D. W., The Buffeting of Tall Structures by Strong Winds, BSS 74

(Washington, D.C.: National Bureau of Standards, 1975). SD Catalog No. 13.29/2:74.

(25) Sugg, A. L., Pardue, L. C, and Carrodus, R. L., Memorable Hurricanes of the United States, NOAA Technical Memorandum NWSSR-56

(Fort Worth: National Weather Service, 1971).

(26) Tennekes, H., and Lumley, J.L., A First Course m

TMr(7M/e;7ce (Cambridge: The MIT Press, 1972).

(27) Thorn, H. C. S., "Distributions of Extreme Winds

in the United States," Journal of the Structural Division, vol. 86, no. ST4, proc. paper 2433

(New York: American Society of Civil Engineers, April 1960), pp. 1 1-24. (28) Thom, H.C.S., "New Distributions of Extreme Winds in the United States," Journal of the Structural Division, vol. 94, no. ST7, proc. paper 6038 (New York: American Society of

Civil Engineers, July 1968), pp. 1787-1801.

(29) Thom, H.C.S., "Toward a Universal Climatological Extreme Wind Distribution," Proceedings,

vol. 1 (International Research Seminar on Wind Effects on Buildings and Structures)

(Toronto: University of Toronto Press, 1968).

10
I 2 4 6 10 20 40 60 100 200 400 600 1000 2000 3600

Time, t, seconds HGURE 1. RATIO, r, OF MAXIMUM PROBABLE WIND SPEEDS AVERAGED OVER t SECONDS

TO THOSE AVERAGED OVER 2 SEC.
I 95.0000000=MAX-

•I

X

89.0000000

83.0000000

77.0000000

71.0000000

65.0000000=MID

59.0000000

53.0000000

"(7.0000000

tl. 0000010

35.0000000=MIN- X

I-.5001281 2.2021567 3.903*8'i'? EXTREME VALUE TYPE 2 (CAUCHY TYPE) PROB. PLOT wtTH EXP. PAR. r 2.000000000

PROBABILITY PLOT CORRELATIOM COEFFICIE'^T = .97191 ESTIMATED INTERCEPT : 3 1.071809 FIGURE 3a. TYPE II DISTRIBUTION, 7=2.

I 1 1 1 1 1-

95.0000000=MAX89.0000000

5.60>tel39 7.3061 SAMPLE SIZE N = 3 ESTIMATED SLOPE = 9.38757i»7

83.0000000

77.0000000

71.0000000

65.0000000=MID

59.0000000

53.0000000

K7. 0000000

ifl. 0000010

35.0000000=iV|IN- X

X XXX

-1.3829817 -.Ot2ft807 1 EXTREME VALUE TYPE 1 (EXPONENTIAL TYPE) PROBABILITY PLOT PROBABILITY PLOT CORRELATION COEFFICIENT r ."WlOt ESTWATED INTERCEPT

2.637327"t 3.977'»3 THE SAMPLE SIZE N = ESTIMATED SLOPE = 9 . '•928209 FIGURE 3b. TYPE I DISTRIBUTION. Facing Page: This wind tunnel at the University of the Phillipines is used to study wind effects on scale-model

buildings. Shown is a model of the CARE, Inc., test house. The rows of blocks on the floor of the tunnel generate tur- bulence orgustiness similar to that observed in full scale.

12
2. A GUIDE TO THE

DETERMINATION OF

WIND FORCES

by

R. D. Marshall

2.1 INTRODUCTION

This paper deals with the nature of wind flow around

buildings, the pressures generated by wind and the determination of forces acting on building elements as well as on the overall structure. It is assumed that buildings designed in accordance with the procedures

outlined in the following sections and tables do not

exceed 33 ft (10 m) in height or 164 ft (50 m) in plan

dimension and have a height to width ratio (h/w) not exceeding four.

2.2 AERODYNAMICS OF BUILDINGS

The flow of wind around buildings is an extremely

complex process and cannot be completely described

13
by simple rules or mathematical formulae. Wide

variations in building size and shape, type of wind

exposure, local topography and the random nature of wind all tend to complicate the problem. Only by

direct observation of full-scale situations or by resort- ing to prop>erly conducted wind-tunnel tests can the

characteristics of these flows be established. In spite of these complications, guidance can be provided by

considering some typical flow situations.

2.2.1 Typical Wind Flow Around Buildings

A typical flow situation is illustrated in figure 4 where the wind is blowing face-on to a building with

a gable roof. The flow slows down or decelerates as it approaches the building, creating a positive pressure on the windward face. Blockage created by the build- ing causes this flow to spill around the corners and

over the roof. The flow separates (becomes detached

from the surface of the building) at these points and

the pressure drops below atmospheric pressure, creat- ing a negative pressure or suction on the endwalls and

on certain portions of the roof. A large low-pressure region of retarded flow is cre- ated downwind of the building. This region, called the wake, creates a suction on the leeward wall and

leeward side of the roof. The pressures are neither

uniform nor steady due to the turbulent character of the oncoming wind and varying size and shape of the

FIGURE 4. TYPICAL FLOW PATTERN AND

SURFACE PRESSURES.

wake. However, it has been established that the pat- terns of wind flow around bluff bodies such as the building in figure 4 do not change appreciably with a change in wind speed.

This allows dimensioniess pressure coefficients (to be

discussed later) determined for one wind speed to be

applied to all wind speeds. In general, the wind

pressure is a maximum near the center of the windward wall and drops off rapidly near the corners. Pressures on the side or endwalls are also nonuniform, the most intense suctions occurring just downstream of the windward corners.

2.2.2 Effect of Roof Slope

The pressures acting on a roof are highly dependent

upon the slope of the roof, generally being positive over the windward portion for slopes greater than 30

degrees. For slopes less than 30 degrees, the windward slope can be subjected to severe suctions which

reach a maximum at a slope of approximately 10 degrees. Under extreme wind conditions, these suc- tions can be of sufficient intensity to overcome the dead weight of the building, thus requiring a positive

tiedown or anchorage system extending from the roof

to the foundation to prevent loss of the roof system or

uplift of the entire building.

Intense suctions are likely to occur along the edges of roofs and along ridge lines due to separation or detachment of the flow at these points. For certain combinations of roof slope and wind direction, a conical vortex can be developed along the windward

edges of the roof as shown in figure 5. This is a "roll- ing up" of the flow into a helical pattern with very

high speeds and, consequently, very intense suctions.

If not adequately provided for in the design, these

vortices along the edges of the roof can cause local failures of the roofing, often leading to complete loss of the roof. Areas where intense suctions can be ex- pected are shown in figure 6.

2.2.3 Roof Overhangs

In calculating the total uplift load on a roof, the pressure acting on the underside of roof overhangs

24
must also be included. These pressures are usually

positive and the resultant force acts in the same direction as the uplift force due to suction on the top surface of the roof. Pressures acting on the inside of the buiding (to be discussed later) can also contribute to the total uplift force and must likewise be accounted

for.

VORTICES PRODUCED

ALONG EDGE OF ROOF,

WHEN WIND BLOWS

ON TO A CORNER

FIGURE 5. VORTICES ALONG EDGE OF

ROOF.

AREAS WHERE HIGH

SUCTIONS MUST BE ALLOWED FOR ON THE

CLADDING

FIGURE 6. AREAS OF INTENSE SUCTIONS.

2.3 DESIGN WIND SPEED

Several factors must be considered in selecting a wind

speed on which to base the design loads for a building

or other structure. These include the climatology of the geographic area, the general terrain roughness,

local topographical features, height of the building,

expected life of the building and acceptable level of

risk of exceeding the design load. The assessment of climatological wind data and the procedure for obtaining basic wind speeds are discussed in section 1.0. The selection of the basic wind speed and the deter- mination of modifying factors to obtain the design

wind speed are discussed in the following sections.

2.3.1 Mean Recurrence Interval

The selection of a mean recurrence interval, with

which there is associated a certain basic wind speed,

depends upon the intended purpose of a building and

the consequences of failure. The mean recurrence in- tervals in table 4 are recommended for the various

classes of structures.

2.3.2 Risk Factor

There is always a certain risk that wind speeds in excess of the basic wind speed will occur during the expected life of a building. For example the probability

that the basic wind speed associated with a 50-year mean recurrence interval will be exceeded at least once in 50 years is 0.63. The relationship between risk of occurrence during the expected building life and

the mean recurrence interval is given in table 5. It should be noted that the risk of exceeding the basic wind speed is, in general, not equal to the risk of

failure.

2.3.3 Averaging Time and Peak Wind Speed

It is well known that the longer the time interval over which the wind speed is averaged, the lower the indi- cated peak wind speed will be. The calculated design

loads will thus depend upon the averaging time used

to determine the design wind speeds. In this document, it has been assimied that all speeds used in pressure and load calculations are based upon an

averaging time of 2 seconds. Wind speeds for averaging times other than 2 seconds can be converted into 2-second average speeds using the procedure

described in section 1.0.

2.4 DESIGN PRESSURES

2.4.1 Dynamic Pressure

When a fluid such as air is brought to rest by impacting on a body, the kinetic energy of the moving air is converted to a dynamic pressure q, in accordance

with the formula

q= \llpU- (1)

where q = N/m-, p is the mass density of the air in kg/m ' and U is the free-stream or undisturbed wind

speed in m/s. The mass density of air varies with temperature and barometric pressure, having a value of

1 .225 kg/m^ at standard atmospheric conditions. In the case of tropical storms, the mass density may be 5

to 10 percent lower. However, this is offset somewhat

by the effect of heavy rainfall, and the value quoted

above should be used for all wind pressure calculations, i.e.,

(7 = 0.613L7- (2)

2.4.2 Mean and Fluctuating Components of

Pressure

As in the case of wind speed, pressures acting on a building are not steady, but fluctuate in a random

manner about some mean value. A typical recording

of wind speed and pressure at a point on the roof of a house is shown in figure?.

A close inspection of figure 7 reveals the following

characteristics:

15
(a) The average or mean pressure is negative (suc- tion)

(b) Pressure fluctuations tend to occur in bursts

(c) Maximum departures from the mean are in the negative (suction) direction

(d) The peak values far exceed the mean value

J r

LIT m SP 1 Ih

^1 p 20 0 iO riME SECONDS

»R :ss in tn r r 1

FIGURE 7. TYPICAL RECORD OF WIND

SPEED AND SURFACE

PRESSURE.

To quantify these pressures, it is essential that a suffi- ciently long time interval be used to obtain a stable mean, ft. The fluctuations are described by their stan- dard deviation or root-mean-square, taken

about the mean. Finally, the peak pressure fluctua- tions are described by a peak factor, <^', which indi- cates the number of standard deviations that the peak

pressure deviates from the mean. Thus, the peak

pressure can be expressed as

/'max =V + X /Vms /'min = V-g Prms

(3;

It should be noted that the peak factor,^', is a random

variable and has a probability distribution function

that depends on the geometry of the building and tur- bulent structure of the wind. The values of ^ are

selected so that the associated probabilities of being

exceeded are in line with the expected building life.

2.4.3 Pressure Coefficients

It is convenient to express pressures acting on the sur- faces of a building in terms of the dynamic pressure as follows

pressure, give the wind loads acting in a direction normal to those surfaces or elements. The total resul- tant forces and moments acting on a building can then

be determined by considering the appropriate components of these loads acting on each of the surfaces or elements. As discussed in the previous section, the instan- taneous peak pressure can be expressed in terms of the mean pressure and a fluctuating component. Since

pressure fluctuations are limited in spatial extent, it is necessary to consider the size of the building surface or element when selecting the pressure coefficient.

Pressures on Extended Areas: For the purpose of determining wind loads acting on sizeable surface areas such as the walls and roof of a building, the pressure coefficients listed in tables 6 and 7 should be

used. These coefficients have been determined experimentally from measurements taken on full-scale buildings and from wind-tunnel tests and they represent an upper limit of conditions likely to occur on the indicated building surfaces.

Pressures on Localized Areas: It is to be expected that the smaller the area considered, the larger the effec- tive peak pressure will be. In addition, there are cer- tain surface areas where intense suctions occur as pointed out in sections 2.2.1 and 2.2.2. To provide for these cases, pressure coefficients for localized areas are included in tables 6 and 7. These coefficients are

for the purpose of assessing wind loads on local clad- ding and roofing elements and should not be used to calculate overall loads on buildings. They should be

used in conjunction with the internal pressure coeffi- cients (where appropriate) as described in the following.

Internal Pressures: As indicated in section 2.2.3 the net load or force acting on the roof or walls of a build- ing depends not only on the external surface

pressures, but on the internal pressure as well. The

magnitude of the internal pressure depends upon the building geometry, size and location of openings, and

wind speed and direction. As with external pressures,

it is convenient to express internal pressures in terms

of the dynamic pressure and a pressure coefficient

Cp,-. These coefficients can be positive or negative as indicated in table 8. The net pressure acting on a building element is the algebraic sum of the external and internal pressures

P = Cpq (4)

where Cp is a pressure coefficient whose value de- pends upon the geometry of the building and local flow conditions. Pressure coefficients are specified for particular surfaces or elements of a building and,

when multiplied by the surface area and dynamic

p = q(Cp-Cpi) (5)

Thus a positive internal pressure will increase the loading on those areas of roofs and walls subjected to external suction.

16
2.4.4 Correction Factor for Height of Building

The pressure coefficii nts described above are based on

building heights of 33 ft (10 m) and peak wind speeds

at 33 ft (10 m) above ground, averaged over 2seconds.

Overall loads calculated for buildings appreciably less than 33 ft (10 m) in height (measured to eaves or parapet) will thus be overestimated if these coeffi- cients are used without modification. On the other

hand, tributary areas such as doors, windows, clad- ding and roofing elements will respond to pressure

fluctuations with duration times considerably less than 2 seconds. To account for this, the pressures must

be multiplied by the correction factors, R, in table 9. Thus the expression for the net pressure acting on a bui idi ng surface becomes

,> = ,/(C^,R-C,„R,) (6)

and the force acting normal to a surface of area A is

F= c?(CpR -Cp,R,) A (7)

where R and Rj are correction factors for external and

internal pressures, respectively.

2.5 PROCEDURE FOR CALCULATING

WIND FORCES

The procedure for calculating wind forces on a build- ing is summarized in the following steps.

1. Select the appropriate mean recurrence interval

from table 4

2. Check the associated factor of risk in table 5 and

select a longer mean recurrence interval if appropriate.

3. Determine the basic wind speed for this mean

recurrence interval and the appropriate terrain roughness and type of exposure as outlined in sec- tion 1.

4. Convert the resulting basic wind speed to a 2-se- cond mean speed using the procedure described in section 1.

5. Calculate the dynamic pressure (fusing the ex- pression

(/=0.613

6. Select the appropriate pressure coefficients from

tables 6, 7 and 8. 7 Select the appropriate correction factors from ta- ble 9.

8. Calculate the pressures from the expressions

or p = ^?(CpR-Cp,R,)

9. Multiply these pressures by the respective surface areas to obtain the wind forces.

10. Sum appropriate components of these forces to obtain net uplift and drag loads.

knots

VELOCITY V

DYNAMIC

PRESSURE ^

0 10 20 30 40 50 60 70 80 90 100 110

1 J 1 1 1 1 1 1 1 1 1 1

1 1 iJjOIl 1 1.1 11 1 I 1JJ.1.L 1 1 1 1

1 1 1 1 1 1' 1

1

'

' '

1 1 11 1

'

1

'

'

'

' 1 ' ' ''

1

,,,],,, il ' ' 1 ' '

'

' 1 ' ' '' 1 ' ' '

' 1 ' ' ''

1 ' ' '

'

1

m.p.h. 0 10 ImmImmIi, 20 30

1 1

'

1 1 1 1 1 1 1 1 1 " 1 1 1 '1

'

1

1

40 50

1 1

'

' 1' 1 1'

1 ' " 1

1

60 70

1 1 1 1 1 1 1 1 1 1 1 1 M 1 1 1 M 1 80

M,l,,,ll

90

,rl,i,

100 110 120 130

1 , 1 , , 1 1 , ) , 1 , 1 , 1 1 1 ! , , 1 1 , M 1 1 M 1 1 1 , 1 1 1

m/sec.

0 5

1 1 1 1 1 1

10 15

1 1 1 1 I 1 1 1 1

20

1 ! 1 1 1 1 1

25 30

1 1 1 1 1 1 1 1 1 .i.j

35

1 ,

. . 40

1 1

1

45 50 55

1 1 1 1 1 M 1 1 1 1 1 1 .Lnl-l-L

Ibf/ft^ 0

1

1 2 3

1 1 1

4 5 6

1 1

1

7 8 9 10 II 1 1

'

1 '

1

15

1 1 M

20

1 I 1

25 30 35 40

, 1

'

i

, , 1 , , , 1 1 1 , 1 1

0

1 , ,

100

1 1 1 1 1 1 1 1 1 200

1 , 1 400 600 ,1,1,1,1

800 ,1,1

1000

1 1

1200 1400 1600 1800 2000

, 1,1 ,1,1,1

kgf/m^

0

1 , ,

10

• 1 1 1 i , , 1 1

20 30

1 1 1

40 50 60 70

< 1 1 1 1 1 1 1

80 90

1 i 1 1

100

1 1

120 140 160 180 200

1 1 1 1 1 1 1 1 1 CONVERSION CHART FOR WIND SPEED AND DYNAMIC PRESSURE HEAD

17
ACKNOWLEDGMENTS

Acknowledgment is made to the Building Research

Establishment (UK) for the illustrations used in this document. The writer also wishes to acknowledge

useful comments and suggestions provided by members of the Philippine Advisory Committee and by

Dr. Emil Simiu of the Center for Building Technology.

TABLE 4 MEAN RECURRENCE INTERVAL

Class of structure Mean recurrence interval years

All structures other than those set out below. 50

Structures which have special post-disaster functions, e.g. hospitals, communications buildings, etc. 100

Structures presenting a low degree of hazard to life and other property in the case of

failure. 20

TABLE 5. RELATIONSHIPS BETWEEN RISK OF OCCURRENCE, MEAN RECURRENCE INTERVAL AND EXPECTED LIFE OF BUILDING

Desired

Lifetime Risk of exceeding in N years the wind speed corresponding

to the indicated mean recurrence interval

IN Years 0.632 0.50 0.40 0.30 0.20 0.10 Mean Recurrence Interval in Years

10 10 15 20 29 45 95

20 20 29 39 56 90 190 50 50 72 98 140 224 475

100 100 144 196 280 448 949

Note: From this table it will be seen that there isa lO'/J risk that the wind speed corresponding toa mean recurrence interval of 475

years will be exceeded in a lifetime of 50 years.

18
TABLE 6. PRESSURE COEFFICIENTS FOR WALLS OF RECTANGULAR BUILDINGS

Building

Height/Width

Ratio

Building

Length/width

Ratio

Wind Angle

Cp for Face Local

/\ ()

0 OH -U.S -0.6 -0 6 l<//w<1.5 -1.2 0 ^1 (1u.n^1 (1u.ok (1 ^ -u . r* n/ w <^u.r> n1

1

OK -OS -0.8 -0 8

1 ^ <^ Jl\A/ <r 1 -

1 1 1 - .1 90 -0.4 -0.4 0 8 -0 4

() 0.8 -o.s -0.7 -0.7 K//W < IS -1.4 90 -0.7 -0.7 0.8 -0 s n ^ ^ uixAj ^ 1 ^ u.r* *^ n/w I .D

(1yi OH -O.d -0.9 -0.9

1 , \ (/ W \ T 1 1 90 -0.4 -0.4 0.8 -0.^

O.H -O.S -0.8 -0.8 l<//w<I.S -l.s 90 -O.H -0.8 0.8 -O.S 1.5<h/w<4

0 O.S -0.6 -0.9 -0.9 1.5<//w<4 -1.5 90 -0.4 -0.4 0.8 -0.3

Notes: (l)h is the ineigiit to eaves or parapet, / is tine greater plan dimension of thie building and w is the lesser plan dimension.

(2) Local Cp values (last column) should be used in conjunction with correction factors for overall areas in Table 9.

19
TABLE 7. PRESSURE COEFFICIENTS FOR ROOFS OF RECTANGULAR BUILDINGS

Building

Meigni/wiatn

Wind Angle

Of Arc3 Roof Slope 0 Degrees

Ratio ^L/cgrees; 0 10 20 25

PFCr -1.0 -1.0 -0.4 -0.3

-0.6 -0.6 -0.8 -0.6 U IJ -1.6 -1.9 -1.9 -1.6 K -1.4 -1.4 -2.0 -1.6 h/w<0.5

-1.2 -1.1 -1.0 -0.8 FH -0.6 -0.6 -0.6 -0.5 QO"U I

J -2.0 -1.8 -1.8 -1.6 K -1.4 -1.4 -2.0 -1.6

FF -1.0 -1.0 -0.6 -0.4

V J 1

1

-0.6 -0.6 -0.8 -0.8 u

IJ -1.8 -1.8 -1.8 -1.8

0.5<h/w <4

K -1.4 -1.4 -2.0 -1.6

EG -1.2 -1.1 -1.0 -0.8 FH -0.6 -0.6 -0.5 -0.4 90 J -1.8 -1.8 -1.6 -1.6 K -1.4 -1.6 -1.6 -1.6

Notes: (1) The pressure coefficient on the underside of roof overhangs should be taken as that on the adjoining wall surface.

(2) Local Cp values (/ and K) should be used in conjunction with correction factors for overall areas in table 9.

f

h

1

w

£ G

F H

w

/ K

K b

b = lesser c f h or 0.15 w

w

Extended areas Local areas ELEVATION PLAN

20
TABLE 8. INTERNAL PRESSURE COEFFICIENTS FOR RECTANGULAR BUILDINGS

Condition Internal pressure coefficient Cpj

1 . Two opposite walls equally permeable, other walls impermeable:

(a) Wind normal to permeable wall

(b) Wind normal to impermeable wall

-1-0.3 -0.3

2. Four walls equally permeable -0.3 or +0,2 whichever is the more severe for combined loadings

3 Dominant opening on one wall, other walls of equal per- meability:

(a) Dominant opening on windward wall, having a ratio of permeability of windward wall to total permeability of other walls and roofs subject to external suction, equal to—

2

3

6 or more

(b) Dominant opening on leeward wall

(c) Dominant opening on side wall

(d) Dominant opening in a roof segment

+0.5

+0.6

+0.8

value of C^, for leeward external wall surface value of for side external wall surface value of C^, for external surface of roof segment

Notes: ( I ) Internal pressures developed within an enclosed structure may be positive or negative depending on the position and

size of the openings.

(2) In the context of table 8 the permeability of a surface is measured by the total area of openings in the surface under consideration.

(3) The value of C^,, can be limited or controlled to advantage by deliberate distribution of permeability in the wall or roof, or by the deliberate provision of a venting device which can serve as a dominant opening at a position having a suitable external pressure coefficient. An example of such is a ridge ventilator on a low-pitch roof, and this,under all directions

of wind, can reduce the uplift force on the roof.

TABLE 9. CORRECTION FACTOR (R) FOR HEIGHT OF BUILDING

Terrain Structural System Area h < 5 5 < h < 10

Smooth Zo < 0.12 m

Walls

Overall Elements0.85

1.00

1.00 1.20

Roofs

Overall Elements0.85

1.05

1.00

1.25

Internal Pressure 0.85 1.00

Rough Zo > 0.12 m

Walls

Overall Elements0.75

0.90

1.00 1.20

Roofs

Overall Elements0.75

0.95

1.00

1.25

Internal Pressure 0.75 1.00

Notes: (l)The term "Overall" refers to the entire area of a given wall or roof slope.

(2) The term "Elements" refers to roof and cladding elements, doors, windows, etc.

(3) The terrain roughness parameter Z„ must be estimated subjectively. The following values are suggested for various types of exposure. TYPE OF EXPOSURE Z„ (meters) Coastal 0.005-0.01 Open country 0.02-0.12 Outskirts of towns, suburbs 0.13-0.30 Centers of towns 0.40
APPENDIX A For wall A,

ILLUSTRATIVE EXAMPLE

A housing development is to be located in flat, open

country on the outskirts of Zamboanga, Philippines,

and will ultimately consist of several hundred singlefamily dwellings of quite similar geometry. The

period of construction is anticipated to be from 10 to 15 years. The basic plan dimensions are 6.2 x 7.5 m

and the height-to the eaves is 2.7 m. The gable roof has an overhang of 0.7 m on all sides and a slope of 10 degrees. Openings for doors and windows are evenly

distributed on the exterior walls.

Because the development is to be built over a period of several years, it would not be appropriate to assume a built-up area in selecting the basic wind speed and

flat, open country will be assumed here.

From table 4, a mean recurrence interval of 50 years

is selected and it is considered that the associated risk of exceeding the basic wind speed (0.632) in table 5 is acceptable.

From section 1, the 1-minute average wind speed

(N=50) for Zamboanga is 88 km/hr (Type 1 distribution). Since this is based on data obtained in open

country at 10 m above ground, this speed can be converted directly to the design speed. Also, from sec- tion 1 the ratio of the 1-minute speed to the 2-second

peak speed is 0.82. Thus the design speed is U = 88/0.82 = 107.3 km/hr = 29.8 m/s

The dynamic presure is calculated from equation 2 of section 2.4.1

= 0.613(7- =(0.613) (29.8)2 = 544 N/m2

Wind pressures are next calculated using equations

4-6 and the coefficients presented in table 6-9. Note

that

h/w = 2.7/6.2 = 0.44 and

//w =7.5/6.2 = 1.21 WALLS

Inspection of tables 6 and 8 reveals that the worst

cases are walls A and C with the wind blowing nor- mal to the ridge. For wall A, Cp = 0.8 and for wall C, Cp = -0.6. The local Cp is -1.2. The internal pressure

coefficients can range from 0.2 to -0.3. Table 9 indi- cates that the reduction factor is 0.85 for walls and in- ternal pressures and 1.00 for cladding elements, doors,

windows, etc.

p=(544)10.8-(-0.3)](0.85) = 509 N/m2

For wall C,

p=(544)t-0.6-(0.2)](0.85) = -370 N/m2

For cladding elements, the worst cases are

p= (544) 10.8 -(-0.3) (0.85)] = 574 N/m2

and

p = (544) 1-0.6 -(0.2) (0.85)] = -419 N/m2

For local pressures acting on strips of width 0.2 w =

1 .2 m at each corner,

p = (544) (-1.2 -0.2) (0.85) = -647 N/m2

ROOF

Inspection of table 7 reveals that the greatest uplift pressures on extended areas occur when the wind is blowing along the ridge.

For sections E and G,

f; = (544) 1-1.1 -(0.2)] (0.85) = -601 N/mFor sections F and H,

p = (544) 1-0.6 -(0.2)1 (0.85) = -370 N/mPressures acting on roofing elements in sections E a G are obtained as follows:

p = (544) l(- 1 . 1) ( 1 .05) - (0.2) (0.85)] = -727 N/mand for sections F and H,

p = (544) 1(-0.6)(1.05) - (0.2) (0.85)] = -438 N/mLocalized pressures act on strips of width 0.15 w =

0.93 m as shown in table 7. The worst case occurs fo area J with the wind blowing normal to the ridge.

Note that the uplift pressure under the eaves must

also be included.

22
p = (544) [-1.9 -(0.8)] (0.85) = -1.2k N/m^

For area K in section F, this negative pressure or suc- tion is slightly less

p = (544) [-1.4 -(0.8)] (0.85) = -1.0A:N/m='

Along the ridge (area K), the localized pressure is

p = (544) [-1.4 -(0.2)] (0.85) = -740 N/m'-

TOTAL UPLIFT FORCE

The total uplift force on the building is calculated for the wind blowing normal to the ridge as follows:

Area of one roof slope = [7.5 -I- (2) (0.7)] [6.2/ (2Cos 10°)

-1-0.7] = (8.9)0.85) = 34.2 m2

COMMENT

The loads calculated above are the loads that can

reasonably be expected to occur under the conditions

stated in the example. They should be considered as the minimum suitable loads for use with stresses and

load factors appropriate for the type of structural material used.

For geographical areas exhibiting large variations in annual extreme wind speeds, the basic wind speed

should be selected with caution. The application of

probabilistic models of extreme wind speeds and some of their limitations are discussed in section 1 .0.

Note that areas E, F, G and H include areas J and K

when calculating overall loads.

Uplift = (544) (1.0 + 0.6) (34.2) (Cos 10°) (0.85)

-I- (544) (6.2) (7.5K0.2) (0.85) = 29.2 kN

TOTAL DRAG FORCE

The total drag force (neglecting the roof) is calculated

as the sum of the loads on the windward and leeward

walls. Drag = (544) (2.7) (7.5) [0.8 - (-0.5)] (0.85) = 12.2kN

23

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