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Ser Tnt N21t2 nr. 88 c . 2 BI,DG

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UATIONAI, NESEARCH COI'NCIt CAI{ADA

DTVISIOtr OF BUIIJDINC NESEARCH

WTND LOADS ON STMICTUAES

by

A. G. Davenport

A N A L Y Z E D

Tecbntcal Papen So. 88 of ttre

DlvLelon of Butldlng Reaeanob

Ottawa I4arch L960

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PRET'ACE

Much attention has recently been given by the Building Structures Sectlon of the Divlslon of Bullding Research to the subject of loads on structures, with spe-cla1 referenee to thelr treatment in the National Building Code of Canad.a. Tmprovements ln the method.s of designlng structures must be paralleled by a more accurate assessment of the loads act1n6 upon them, slnce a destgn can be no more accurate than the load assumption made for the calcula-t i o n . .

TLre Buildlng Structures Seetion has begun a study of the action of wlnd on structures, in additlon to carrylng on an extensive study of snow loads on roofs, In view of the great varlation in cllmate and topography aoross Canaala and. the great varlatton of shapes of structures, much slm-pllflcatlon is neeiLed in codifying wind. loads for practlcal purposes. Part of the sinplificatlon ls the lnevltable

consequence of lack of knowledgeI there ls stiLl much room for improvement in the present wlnd load requirements.

Wind forces on structures depend on the velocity of the air on the one hand and the effect of the shape of the structure itself on the other, or in other wordsr oB meteorological as well as engineerlng lnfonnatlon. Iilre baslc infomatlon on wind. speeds in the National Bullding Code (L953) consists of a map showing rfcomputed. maxi.mum gust speedslt for aL1 of Canacla. TPrls TVas prepared. by the Meteorologi-cal- Dlvislon of the Departrnent of lransport wlttt which the Dirrision of Buildlng Research is forturrate to maintain the closest liaison.

lhe present stud.y on wind load.s was begun wlth an extenslve surr/ey of the literature on the'actlon of wind on structures, based upon which the author has made a number of recommend.atlons whlch lnevitably reflect to some de6ree hts personal opinions, fhe author of the paper is A.G. Davenport who, from July 1957 to September

:-958, was a member of the Buildlng Structures Section, the head of which is W.R. Schriever. Ihe author has slnce left the Divlsion of Buildlng Research to take up post grad.uate study at the Universlty of Bristol.

Ottawa

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TABLE OF CONTENTS

Present Wl.nd Load Requlreqen!s

I n t r o d u c t l o n . . . . Shape Factors . . o . . . . I n c r e a s e o f V e l o c l t y w l t h H e l g h t . . . . D e s i g n V t l l n d V e L o c l t l e s . . . .

The Detennlnatlon of Baslc Deslgn WtryL-Yelegl'b:Le.s

' 2.1 Structr:re of Natunal Wlnd . o . . . . .

2 . 2 I n c r e a s e o f V e l o c l t y w l t h H e l g h t ;

t h e E f f e c t s o f S u : : f a c e F n l c t l o n . . ' . .

2.3 The Estlmatlon of Extreme Mean Wlnd

2.b li:i::tgi ; ioitiui"'a.,,ui"sr,ie'ritJ"iui

Ttre Detenmlnatlon of Wlnd Pnessures on Stnuctures

Wlnd TunnoL Studles and ShaPe

C o o f f l c l e n t s . . . o . . o . . . The Valtdity of Wtnd Turvtel Results fhe Consequences of Klnematlc

D l s s l m l l a r i t Y . o . . . . S h t e l d l n g E f f e c t s . . . .

Formulation of Shapo Coefficlents .

a a a a a

Ir

Dynamlc Effects of Wlnd L 2 2 2 1 . 1 L,.2

1 . 3

1 . 4

h

6

t 0

16

3 . 1

3 . 2

3 . 3

. 1 8 . 1 9 . 2 0

. 2l+

, 2 5

3.1+

3 . 5

h . 1

LL.2

li.3

Causes of Dynamlc Pnessures . . . 26 G u s t A c t i o n q n d G u s t C o e f f l c l e n t s . . . 2 6 Vlbnatlon of Stnuotures . c . . . .

3?

Reconmendatlons

5 . L B a s l c D e s l g n W l n d V e l o c l t t o s . . . . . -5.2

Increase of wind Veloclty wlth Helght 5 . 3 S h a p e C o e f f l - c l e n t g . . . . 5 . 1 + G u s t C o e f f l c l e n t s . . o . . . r . . .

R e f g n e n c g s . . . . ' ' " " | "' 3 8 Appendlx I - Deta on Wlnd VeLoclty Proflles

A p p e n d k fI - gqp]lflcatlon f a c t o r s f o n V a n l o u s f d e a l H l l 1 s a n d Rldges

Appendlx IIr - Extract fnom standards of the swlss A s s o c t a t l o n o f E n g l n e e r s a n r i A r c h l t e c t s S e c t i o n o n W l n d L o a d s

.35

:38

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WIND LOADS ON STRUCTITRES by

A . G . D a v e n p o r t

T h e p u r p o s e o f t h l s p a p e r l s t o l n d l o a t e t h e b a s l s o f t h e p r e s e n t d e s l g n w l n d - l o a d requlrements of the NatlonaL

B u l l " d l n g Codo of Canada (172)*, to dlscuss thetr underlylng a s s u m p t l g n s r and to pnovide a survey of nesearch dealing wtth t h e subJect of wlnd 1oads. From thls reconrnendatlons wllL be o f f e r o d wlth regand to what lrnprovements might be effected ln t h e a n a L y s l s and fonmulatlon of wlnd-load nequlrements and tn t h e n e c o r d i n g o f m e t o o r o l o g l c a l d a t a a n d , t o t h i s e n d , t o s u g g e s t r e s e a r c h n e e d e d .

]-. PRESENT WIND LOAD REQUTREMENTS(S e c t l o n [ . 1 , 2 o ] , n e f e n e n c e L 7 2 ) l . L l n t r o d u c t l o n

P r e s e n t w l n d - I o a d n e q u i n e m e n t s a r e b a s e d o n ;

( a ) l l c o m p u t e d maxlmum gust speedsrt, Vg, which ane asswned

to nofer to a glven datum level of J0 ft above ground.

( b ) a c o e f f t c l e n t C 5 g l v i n g t h e l n c n e a s e i n t h l s v e l o c i t y f o n h e l g h t s g r o a t e 4 t h a n 30 ft. f t l s d e f l n e d b y t h e fonmuLa Cu = L\,1/7 r r , j O , (on the ollo-s€vonth powen law)

where h ts the height above gnound, ln feet.

( c ) a set of shape coefficients C " f n o m w h i c h t h e w l n d p r e s s u r e s o n d t f f e r e n t s u r f a c e s o f a s t n u o t u r e a s s u m e d u n L f o r m l y d l s t r i b u t e d , a n d a l s o i n t e n n a L p r e s s u r e s can be infenned,

Ihe unlt pressure q ls then glven by

s = cs x t/2 p (ch vs)2

l n w h l c h p , t h e d o n s l t y o f aln, ls assumed to have a value suoh that if V* is ln mph,

9 = o . o o 2 5 B c s . ( c p v * ) 2 L b / s q f t

n r : m b e r s in panentheses refen to l1st of nefenenco matenlal a t the end, of thls paper.

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2

-T h t s u n l f o r m p r e s s u r e l s a s s u m e d t o b e s t a t L c a l l y a p p L i e d

and to act normaL to the surface. In generel form thls fonmula

a n d t h e lnhenent assumptlons 1n tts appllcatlon a n e s l m l l a n t o t h o s e u s e d ln many other bulidlng codes (L69-f?B).

1.2 S.hgpe Factons

fhe values of the shape factons glven ln the Bnltlsh Standard. Code of Practloe (171) whlch, tn turn, were largely

based upon investlgatlons ln a lamlnan fl-ow wlnd tunnel. at the

N a t l o n a l P h y s l c a l Labonatony (t03, 151) have been ad.opted by the

N a t l o n a l Bulldlng Cod.e wlthout substantlal alteratLon. R e c e n t

studies appoar to show the need. fon some nevlslons,

1.J Inc[egge. of Veloclty wllh_4oieht

The oDo-s€v€nth power law whl-ch has been adopted by the

Code to descnlbe the tncrease ln rrmaxlmum computed gust speedfr

wlth helght is a famllJ.an aenodynamlc proflLe found tn wlnd.-tunneL

lnvestlgations of turbulent flow over smooth boundanles at relatlveJ.y

hlgh Roynold,s numbers, (5L, B5 (p.221, and L9B) tn noutnalf.y stable

cond,ltlons over open fLat ternatn. ft should be noted, however,

that the proflle nefens to the lncrease ln mean veloc5.ty wlth

hoight; the assumptton lmpIled tn lts adoptlon by the pnesent ood.e

that lt also descr.lbes the lncrease Ln rfmaxlmum computod gust

s p o e d t r w l t h h e l g h t 1 s n o t s u b s t a n t l a t e d . 1.[ Deslgn r,r'/lnd Velgcltles P r e s e n t d e s l g n w l n d v e l o c i t l e s ( 4 t ) w e r e o b t a l i r e d b a s l o a L l y f n o m a n e m o m e t e r r e c o n d s . T h e s e r e c o r 3 d s a n e a v a l l - a b L e f o n a b o u t t w o h u n d n e d , s t a t L o n s a c r o s s C a n a d a ( 2 2 O ) . M o s t o f t h e l n f o n m a t i o n l s u s e d l n c o n n e c t l o n l v l t h t h e m e t e o r o l o g l c a l s e n v l c e s n e n d e n e d b y

the Department of Transpont to avlatlon and shlpping and tt ls not

s u n p r l i l n g t o flnd that the maJority of statlons are eLthen at

a L n p o n t s r o ? h a n b o u n s a n d o t h e r p L a c e s a l o n g t h e c o a s t l L n e .

The anemometers, usually sltuatod, on top of buJ-ldings'

are of the Roblnson cup-type - the lmproved three-cup lnstrument h a v l . n g g n a d u a l l y replaced-the less accunate foun-cup lnstrument.

R e c o n d s a r o a v a i L a b L o f r o m t h e s e s t a t l o n s f o n p e n l o d s

nanglng from one to thinty years. Tho records from these

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3

-the ansmometer Ln an hour, To thls a cornectton facton ls

some-tln:e s applted which may be about 5 per cont at 60 rnph (22O\ t y l e l d l n g t h o r ? t r u o r r h o u n l y m i l e a g e . T h l s c o r r e c t i o n f a c t o r i s a f u n c t l o n o f t h e g u s t l n e s s w h i c h l s a s s u n e d . to b e c o n s t a n t I n a p p l y l n g t h e c o n r e c t i o n . I n t h e l a s t f e w y e a r s n o c o n r e c t l o n s h a v e b e e n a p p L l e d .

Durlng the preparatlon of the 1953 code 1t was d.eclded

t h a t d e s l g n w i n d v e l o c i t i e s f o n t h e n e q u l r e m e n t s o f t h e C o d o

should conslst of the maxlmum gust veloclty measured by these

partlcular lnstnunronts over a thtrty-yean perlod. At that tlme

blnes anomometer recol3ds wene avaiLable for five statlons fon two

years. These instruments are of the pressure tyPe and necond on

Lnomographs tho average veloc|ty of gusts whose dunatlon ls

betwe6n irbout 2 and L0 seo (depondlne on the laesponse tlme of the lnstnument ).

UnfontunateLy, howover, roeords frorn all other stations

wero readlly availabie onl-y ln-terms of mean hounly wlnd speeds.

I t w a s t h e n o f o r e d e c l d e d t o s s t l m a t o t h e g u s t s p o e d s a t t h e s e

statlons by correlatlng maxtmum gust spoeds wlth hourl-y_wind

mil-eages at the four statlons fon whlch there wore slrnultaneous r o c o r d s o f b o t h v e l o c l t i e s , f o r t v r o y e a r s . I n p e r f o n m l n g t h l o

-correlatlon, gust speeds of over 65 mph occurrtng stmultaneously

wlth hourly mlleages over 35 mph wone used; aLL others were omlttod fnom tho computatlon.

T o t h e s e n e c o r d s , s h o w n l n F l g . I r a l i n e w a s f l t t e d b y least squares relatlng tire_,ttmost probabl-err gust volocltyr Vg, wlth

the mean hourly veLocity, V*, accordlng to

V g = 1 9 + L.22 Y^.

Panall-el to thts llne and enveloplng the d.ata was fltted the Llno V g ( m a x ) = 2 5 + L . 2 2 V m .

T h i s e q u a t l o n u r a s u s e d t o d e t e r m i . n e t h e m a x i m u m g u s t _ v e L o c l t l o s f o n a l i o t h e r s t a t l o n s . T h l s w a s t h e f i n s t s t e p l n d e t e r m i n i n g d o s L g n v e L o c i t i e s .

s t e p w a s t o e x a m l n e t h e r e c o r d s o f a l l s t a t l o n s d.etei.mlne for each the maxlmum reconded hounly The second a c r o s s C a n a d a a n d m 1 l e a g e . The thlnd n e c o r d e d m l l e a g e s s t e p w a s t o c o n r e c t e a c h o f t h e s e n u x l m r : m accbrctlng to the number of years necords had

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been kept. The fnom a study of V L c t o n l a :

-4-followlng standandlzlng

t h l n t y y o a r s neconds at factors were obtalnedTononto, Quebec, and

P e r c o n t a g e o f r n l l e a g e . t o b e

maxlmum to e ? a d d e d max].mumto pning a necorded

Yeans on recond. % to add, a r

5 L o

r.0

5

L5

3

L

2 5

2 0

30

0

The maxLmum gust speeds fon eaeh statLon wene then computed

fnom the connected maxlmum hounly mtl_ea.gee.

T o t h e s e nesults, with more welght glven to the

191g"T ponl.od, wero fltted the lsotaohs-shorvn tn Chant g

C l l m a t e , of the NatLonal Bulldlng Cod.e (tr'lg. Z).

The pnesent design velocity roqulnoments of the

d e f l n e d ( b y thls chart) fon ttordlniny t-emalntr.

2. TIM DETERMINAT]ON OF BASIC DESTGN IlUrND VELOCTTIES

2.1 Structure of Natural Wtnd

neconds of o f P a n t 2, C o d e a r e

Wlnds ane caused by the atmosphorlc pressure dlfferentlal-s

whlch arlse over tho sunface of the earth due to dlfferences ln

the amount of heat that ls reoelved fnom the srrrrr llhs acceLeratlon

p n o d u c e d by these pressure dlffenentlals 1 s a f f e c t e d , h o w e v e r , b y

anothen component of accelenatlon known ag the geostnophlc accolerq-tlon whlch ls caused by the notaaccolerq-tlon and cunvature of the eanth. Thus a pancel of aln mg-ylng on the nonthenn hemlsphere expenlenoes

a for"ce to the night 1ffiTght angles to the dlneirtlon of motlon)

propontlonaL to tho speed of motl.on, cal-Led the conloJ-ls fonce. If

ifnirtfy, hl" p""ssure system remalns the etame and sufflclont tlme 't

e l a p s e s fon the wlnd to neach a steady-state condltlon and. lf,

secondl-y, thene 1s no fnlctlon, then the wlnd wlLl flow at nlght

a g g l e s t o t h e p n e s s u r e g n a d l e n t ( 1 . e r p a f , a l l o L t o t h e l s o b a n s ) w l t h

the lowen pressure on the left. In othen words, the oonLol-ls fonoe

ls Just ln equlllbnium wlth the foroe due to tJrd pnessure dlffenentlal Above 1000 on 1100 feet these condltlons er4e often neanLy satlsfled,

end the wlnd blows neanly paralleL to the lsobars. Thls wlnd, whlch

1 s u n a f f e c t e d by fnlctton, i s o a l l - e d g r a d t e n t w l n d a n d l t s v e L o c l t y g n a d l e n t velocltv.

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-

-5-V g = P e w r s l n

' r . w .

stn2 A.

where = radlus of curvature of J-sobare = notatlonal speed of the earth = latltude

= pl3ossure gradlent = donslty of the aln

The equatlon lends ltself ldeaIly to sl-mple nomognaphlc solutlon as shown by Humphreys (S5l, and the gnadlent veloclty may be

e s t l m a t e d d l r e c t l y f r o n r lsobar chants such as that shown ln F1g. 3o A c c u r a t e e s t l m a t e s o f g n a d l e n t v e l o c l t y , h o w e v e r r Srro

d l f f l c u l t t o o b t a l n u n l e s s t h e g n l d o f m e t e o n o l o g l c a l s t a t i o n s m e a s u n l n g s u n f a c e p r e s s u r e s ls close. T h i g 1 s n o t p a r t t c u l a n l y the caso ln Canada and attempts made by the authon to flnd some c o n s i s t e n c y ln a comparlson of surface velocltles m e a s u r e d b y a n anemometer and simultaneous gradlent veloclty measured from tho s u n f a c e p r e s s u r e charts wene not successful, bocauso of the above r e e s o n s a s w e l L as a varlety of othors.

The velocity of tho gnadlent wind, however, ls attalned only at helghts ln the netghbourhood of 1O0O to 2000 ft above tho ground.. Closen to the gror:nd. the wlnd 1s netarded by frlcttonaL f o n c e s a n d o b s t r u c t l o n s a t t h e s u r f a c e a n d v t s c o u s f o r c e s t n a n g -n l t t e d u p w a -n d s b y t u r b u l e -n o e : 1 t s d t n e c t l o n t h e n i s n o l o n g e n p a n a 1 1 e 1 to the lsobars. T u r b u L e n c e a l s o c a u s e s n a p L d f l u c t u a t l o n s ln the veloclty ovor a wlde range of frequencies and ampll-tudes. T h e v e l o c l t y ' o i t h e w l n d a t l o w e r L e v e L s l s t h e r e f o n e e x p n e s s e d most usefully in tenms of lts mean speed. and the devlatlons fnou t h l s v o l o c l t y ( 8 5 ) .

The time on dlstance lnterval- over whlch the mean ls averaged deponds upon the purpose for whlch the wind ve1oo5.ty l s t o - b e u s e d o F o n r n a n y a p p l i c a t l o n s l t l s s u f f l c L e n t t o know tho avenage wind. speed durlng i-aay or qn hour (l+3). For the deslgn o f s t n u c t u r e s , h o w e v e r , it ls necossary to know the mean wlnd.

t e 1 f p t e o (f t a t y l he ) . y s t 1 s s f 1y t h

5)

sy ]-Und.er steady-b e d e t e r m l - n e d dlrect o f t h e l s o b a r s , a n d l s o b a r s ) ars known (3 w i t h a low-pressure g n a d l e n t veloclty Vg c o n d the e s s u o r z a n d ven e c f t pne F o e m g 1 v

A

l t l l a t re one vrl b y : ondlt he la s s u r e r z o n and vr en by s t ude a d l of s t d.p cln o n s l t u gra s o t h I (

3

h e g r t h e n t c v c 1y c r Pms t e n c y or: 1 t ur f g s ils o c c o ( a i n I l 1 o r f r8 r ( w i f v € u s o a c l n l n d s lgh nt 1u pa w 1 e n d l s p w h I a d l ra o13 n 1 c a n d , + gra he ( o lon s a e d c a n ture e l a t e the c l E y curva o f t h a g s o c n d s ) y c a v a t u the oc la ) ttr r w

A

dp dn

P

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- 6 *

speed during the peak of a storm lvhlch may last only a few m l n u t e s . T h e c h o l c e o f a s u l t a b l e t l m e o r d i s t a n c e l n t e r v a l f o r a v e r a g i n g n e a n v e l o c l t i e s 1 s d l c t a t e d b y c o n s l d e n a t l o n s

of the d;mamlc characterlstics of the urlnd, tho stnrrctuner and the anemometer. Fbom a rnorae detailed dtscusslonr whlch ls left w r t l l I a t e r , l t i s f o u n d t h a t t h e f a s t e s t m L n u t e o f w i n d o n t h e faetest rn-lle of wind represents roughly the opttmum averaglng l n t e n v a l f o r d e t e n m i n l n g a n d d e f l n l n g b a s l c d e s i g n w l n d v o l o c l t l e s .

2.2 I4c:'eage qf Velqelty wlt cts of Sunface

FFTATI6n-O n o o f t h e m o s t l m p o r t a n t f a c t o r s t o b e c o n s l d e n e d L s the lncrease of the mean wind^ velocity wlth hetght; a oorollany t o t h l s ls the notanding effect of the surface frlctlon o n w l n d v e l o c i t y n o a r e r t h e s u n f a c e o

V a n l o u s emplnlcal, seml-emplrlcal, and theonetlcaL formulae h a v e b e e n d e n l v e d t o represent the variatlon o f w l n d v e l o c l t y w t t ! h e l g h t . T h r e e o f t h e m b r e f a m t l i a r f o n m s a r e t h e s p l r a I , ( I 9 r _ 5 9 )

l o g a n l t h m l o , ( B l ) and exponenttaL (5) proflles. F o r s t n u c t u r a L punposes the exponentlal or pourer 1aw proflle has been used. most w l d e l - y b e c a u s e o f lts simpllcity. I t c a n b e s t a t e d a s f o l l o w s :

Y, = U zL/a

whono V, ls the velocity at helght z above ground and k and. V6-a r e c o n 6 t V6-a n t s ,

B y s u i t a b l e c h o l c e o f e x p o n e n t t h l s e r p r e s s t o n e a n b e m a d e to correspond closely over a consldenable nange to the other forms o f p n o f i l e w h l c h a n e l e s s e m p i r l c a l " T h e p o r r e r l a w 1 s h p p l l c a b l e only in the layer extending from the gnound up.to the helght at

w h l b h t f r e g r a d l e n t v e l o c l t y t s f l r s t a t t a i n e d ( u s u a l l y 1 n t h e n a n g e 1 O O O t o 2 O O 0 ft ) . A b o v e t h l s h e l g h t t h e w i n d v e l o c i t y m a y b e n e g a n d e d a s c o n s t a n t . f n h l s t n e a t l s e o n P h y s l c a l a n d D y n a m i c a l M e t e o r o l o g I r B r u n t ( 5 ) n o t e s t h a t r t ] f t h e _ v a r i q t l o n o f w l n d w i t h h e l g h t b e r e p r e s e i e t e d b y a l o w e n 1 a w z P t t i s f o u n d t h q t . p l s l n c n e a s e d b y a n lncnease 1n eithen noughnoss or stabllityrr ( z belng the height a b o v e g r o u n d ) " i i e r . e nefenence ls made by Brunt specifically t o a nang6 of helghts above roughly 1O metnes (33 ft) whlch ls of l n t e r e s t t o s t n u c t u r a l e n g i n e e r s .

A n attempt is now made to evalueto these tnfluences of s t a b l l l t y a n d suiface roughnoss on first, t h e r a t e o f l n c r o a s e o f m e a n v e l - b c i t y w l t h h e i g h t - a n d s o c o n d , o n t h e m a g n i t r r d o o f t h e m e a n s u n f a c e v e l o c i t y , b o t h o f v y h i c h a r e o f p n i m e l n r p o r t a n c e l n e s t l -m a t l n g b a s l c d e i i g n w i n d v e l o c i t i e s f o n s t n u . c t u r e s "

(13)

7

-rhe stabillty of a storm

i:#fl?"E;:

o{"tHeHt;in53t3ro"

oauses th-orough mlxlng the Lapso

c l o s e t o t h e a d l a b a t l c w h l c h s t a b i l l t Y ( 7 8 ' 8 5 ) . G e l g e r h a s r a 1 l Y a t t a l n e d a t . v e l o c l t L e s

. o b s e r v a t i o n s ( h 0 ) o f

ExcoptLons to thls statoment may be found howevonr_ ln severe local- storms such as thundenstorms and frontal squal3.s (and perhaps other largen storrns such as hurnicanes ln thelr early l n c l p i e n t l t a g e s b e f o r d f u } I m a t u r i r . t y l s r e a c h e d ) w h l c h a n o n o t a b l y unstiUle, alr-noar tho ground. belng wanmer than that a1oft. As a c o n s o q u e n c e o f t h l s i n s t a b l l i t y v i o l e n t t h e r m a l l n t e n o h a n g o t a k e s place bdtween the aln near the srrnface and the faster-movlng upper a l n w h i c h l s n o t r e t a r d e d b y f n i c t i o n n e a r t h e s u r f a c e . U n d e n clrcumstances of extreme tnltaUttlty the value of the exponent 1rl"( m a y a t t a l n t h e l l m l t i n g v a l u e o f z e r o c o r r e _ s B o 9 $ { n g to z e r o l n c r e a s e 1 n v e l o c l t y w i t h h e l g h f . A t A g r a , B a n k a t A 1 1 ( 1 ) m e a s u n e d a n

exponent oi O:ot

-677o.j-ro

lr"t!-uistabre condltlons and Sutton (85) suggests a valtre of lrl100.

From the fonegoing remarks the followlng_ general inferencos may be dnawn with regdra Eo the effects of stablttty on the proflle.

( f . ) Sevore local storms, such as thunderstorms, frontal s q u a l l s ( a n d p o r h a p l o t h e n s t o r m s s u c h ' a s h q r n l c a n e s tri tfretn early lnclptent stages ) ane extremelY un-s t a b L e a n d c o n un-s e q u e n t L y t h e i n c n e a un-s e o f m e a n v e l o c l t y urith helght ls very sraalL. Tho fnlctlonal

chanac-terlstici of the gi'ound surface may havo_ almost negl-1glbLe eff ects on the velocity prof 13-e n

' ( Z ) Large-scale rnatune storms of elthen troplc?l oT oxtna-troplcal d e s 6 r l p t i o n e x h l b l t n o a r l y n e u t r a l s t a b l l l r y w l t h

no manked tendency for vlolent thepntal lnterchan$€r The 4ominatlng iniluenco on the velocity proflle ln tlrose storfrs ls not stablllty but the surface roughne ss"

The ftnportant questlon nor,v arises how 8f?3t an effect doos surface noughniss have on the vrind veloclty pnoftle in storms of ths latter category, which ane probably far more lmportant? In comparlson to tfie vist amount wlricfr hai been wnltten in englnesrlng

(14)

B

-p a -p o r s on this genoral subJect scant attontlon has been given t o t h l s p a r t i c u l a n q u e s t l o n . I t a p p e a n s t o b e o f p a r a m o u n t

l m p o n t a n c e i n t h e a c c u r a t e e v a l u a t i o n o f w i n d v e l o c l t i e s .

f t s h o u l d f l n s t b e e m p h a s i z e d t h a t w h a t 1 s r e f e n r e d t o l n t h e t e r m I t s u n f a c e r o u g h n o s s t t ls neithen the shleldlng due to

indlvldual obstacl.es nor the onographlc effects lnfluenclng the

a l r f l o w ln mountaln reglons bu'b the cumulative statlsttcal d r a g

effect of many obstructlons on the wind. Tho induced notarding

foncos on the alrflow are due not only to the fnictlonaL dnag

a t t h e s u r f a c e b u t also to the much greaten vlscous forces a s s o c l a t e d wlth the tunbulence whlch extonds to a hoight fan g r e a t e n than the obstructions which causod Lt. T h e s u r f a c e r o u g h n o s s i s t h e n e f o r o chanacterlzod by the d.enslty, slze and h o l g h t o f the bulldlngs, t r e e s , v e g o t a t l o n , rocks, etc, on the

gnound, around and over whlch the wlnd must flow. Surface roughness

w111 bo a mlnimum oven the ocean and a maxlmum ovor" s lange clty.

The measurnement of wind veloclty profiles hag for somo

y e a r s been of ln'berest ln the flelds of meteorology, avlatlon, a g r l c u l t u n e and wind powero a s w e l l a s e n g i n e e r l n g ( s e e R e f o r e n c e s

on lltrlnd Structune, Nos. 1 to 100). A consldenable amor:nt of

i n f o n m a t l o n h a s n o w a c c u m u l a t e d f n o m w h l c h l t l s p o s s t b l e t o evaluate the tnfluence of the surface roughness on the wind v e l o c l t y p r o f i l e .

I n F l g . I ttre power laws correspondlng.to.the aocumulated experlmental" nesults of a numben of obsenvers (38) have been

p l o t t e d on a comparative basis nelatlng the natlo of mean velocltles at a glven height to that at 30 ft wlth the he:'"ght above gnound. TlLe data fnom which theso equlvalont powor law cunves are denlved a r e g i v e n 1 4 r e f e r e n c e s ] - 7 ; 2 2 r 2 5 , 3 9 , h B , 6 7 1 7 3 r 7 9 t 8 0 " 9 0 r 9 9 t

LOO,-and 156 (see also Appondlx f ). lllhone the results' were not

e x p l i c l t l y s t a t e d a s a p o l l r e l a l a w lt was found that in oach case a

power 1aw could be closely fitted to the data wlth only smal-l

d e v i a t l o n s . f t s h o u l d b e n o t e d t h s t t h e d a t a n e f e n s p e c l f l c a l l , y t o mean veloclty proftles p r e v a i l L n g above a height of l0 ft ln

s t n o n g w l n d s , o v e r f l a t g n o u n d s u r f a o e a t l a p s o r a ! 9 s _ w h l c h r _ 1 f .not

expllcltly stated, by the natune of the stonms studied. could not

h a v e d l f f e r e d g n o a t l y f r o m t h e a d i a b a t i c . T h e d a t a a r e t h e r e f o r o homogeneous witn tne exceptlon that the natr.re of the gnould._

roug[ness and the aggregate natune of obstructlons vary wldely from

the-smooth surface of the sea to the rough obstnucted surface of a l a r g e clty.

The exponent of the power law increase ls seen to vary

botvroen roughly I/) and 1 d.ependlng only on the surface noughness

c h a : r a c t e r i s t l c s " I t l s s e e n t h a t c u r v e s 1 t o 7 h a v e e x p o n e n t s

(15)

9

-t e n r a l n w a s charac-ter'ls-tloally f l a t a n d open. ILre avorago lles

close to t/7 wntch ls a familj.ar exponent- f ound at the bor.md.anieE

of plpes and wind tunnels ln whlch mechanlcal turbulenco

plto-domlnates and the fluld ls noutrally stable. The exponents of

curves B to f.l+ l1e between I/$ and. l/2.8 and average L/3.5.

Fon theso cutvos the tex'raln corresponded to the noughen chanao-t e n l s chanao-t l c s o f rough coasts, treed and wooded. f a n m l a n d . , t o v r n s , s c n u b t n e e s o etc. C u r v e s 1$ and 16 are dorlved fnom necords obtalnod i n l a n g o cltles, P a n l s a n d N e w Yonk, which pnobabLy represont

condltlons of oxtremo surf.ace noughnoss; tho correspondlng exponents

a r e L/2"o and. I/L.6,

I t s h o u l d b e n o t e d a t t h l s s t a g e t h a t v o l o c l t y l t s e l f m a y

be expected to havs a sltght socondary effect on the pnofile ln

that the valuo of the surface fnlctlon lncneases s1lghtLy with wlnd

veloclty; as a consoquence the nate of lncrease of moan wind,

v o l o c l t y w l t h h e J - g h t increases sltghtly w i t h veLoctty. T h l s l s q f a m i l l a r n e s u l t 1n wlnd tunnel wonk (85).

Numonical evldence of tho lndiroct J.nfluence of the

voloctty on the veloclty-helght nelatlonshlp ls funnlshed by

C o l l l n s t L n v e s t l g a t l o n s o f n f . n e s t o m r s , m a l n l y a t B n o o k h a v e n L a b o r a t o n y , Long Is1and. (11). f n t h t s l t w a s f o u n d b y e x a m l n l n g

the l-mlnuto mean veloclties at dlffenent olevations up to lp.0 ft

that the exponent of tho power law profile lncreased by appnoxlmatoly

0.O2 fon every 10 mph incn€ase ln sunfsce wind veloclty, at lO nph

t h e v a l u e b e l n g O " 2 7 ( l . e . l / 3 . 7 ) a n d t h e e x t r a p o l a t e d v a l u e a t B o m p h b e l n g 0 " 3 3 Q/Soo). T h e s e p r o f l 1 o s , a c c o r d l n g t o C o 3 - L 1 n s r .

fitted the experimentaL reconds extremoly well with the standard

d e v l a t l o n equalIlng 1"26 mph.

These nesults lndlcate hourever, that the effect of wlnd.

veLoclty (over the nange of maxlma encountered) is not nearly so gneat as that due to the d.lfferonces in surfaco roughn€e$r

Bearlng ln mind the influence of the wind veloclty on the

n a t e o f l n c r e a s e o f w l n d v e l o c i t y w i t h h e l g h t , l t 1 s n o w p o s s l b l o to suggest approximate vaLues fon porrexr law oxpononts correspondlng

to mone or less qualitative descniptlons of the surfaco roughnoss

o r aggregate lnfluence of the surfacs obstnuctlonsr as follot"rs: D e s c n l p t l g n o f t h e Terralg

F o n o p e n c o u n t n y , f lat coastal belts, s m s l l lslands situated 1n large bod.ies o f v ' r a t e r , p n a i n l e g r a s s l a n d , t u n d r a , e t c "

For viooded countrysido, panklando tovan$,

o u t s k i r t s o f l a r g e c i t j . e s n o u g h c o a s t a L b e l t s

r/3"5

(16)

1 0

-These flgures refer to the mean wlnd veloolty over level ground, to large-scare severe stonms (whlch exhlbtt ireanly

neutral stablllty) and to helghts between about 30 f t and,- the h e l g h t at whloh the gnadient veloclty Ls first a f , t a l n e d . f f t h o r e are areas tn wtrtch the hlghest-probable velocitles occup durlng severe local stortns such-as thunderstonms and fnontaL s q u a l l s ( w h l c h does not seem llkely) n o j . n c r e a s e in veloclty with height wou1d. seem appropriate.

2.J The Estlmatlon of Extremp Mean Wlnq_Vq.Iegl:by

ff nellable long-term anemometen neconds were avallabLe f o r all sreas exhibltin[ d l f f e n t n g c h a r a c t e n l s t l c s o f sunfaoe n o u g h n e s s and lnoLdence to sevene etorms the discusslon couLd b a s i c wlnd veloclty o o u l d b o L o c a t l o n r r b a s e d u p o i r a s t a t l s t l c a l snlod of I.rO on l0 yoansrr, and n o f l l o appnopniate to tho sunfaoe

U h f o n t u n a t e l y there are serlous obstacles to thls approaoh ( a t least ln a spans6ly populated cor.rntny such as canaaaj ;i;;;----m e t e o n o l o g l c a l r e c o n d s a n e n o t a l w a y s as satlsfaotory as thls approach wouLd nequine fo_n tho followtng reasorlso

Only a comparatlvely small numben of statLons would have r e c o r d s extendlng back a sufficLent numben of years (especlally l n C a n a d a ) ; at some locatlons the aneinometer his been moved soleral !i*"s durlng the penlod of necord, affectlng the exposuro and the homogenelty of the datq: on other: occastond severe storms havo blom the anemometor ayay on rendened lt Lnopenetlve thus J.osing cruclal lnfonmation. The anemometer" may also- glve neadlngs whlcfi a n e not representatlve of leveL c<

the anomomoton on or near a butldl example, suggest that the well-ex1 Empire State Bulldlng sltuated moi neads 2J pen eent hlghen than the

o f the bullding. J f , s t alrponts, anemometers were ralsed to a P3tisfactory helght to be fnee fnom ttre lnfluenco of the butldlngs t l t " y mlght pnesent a hazard. to alncnafto I n w l n t e n , t h e p e n l o d -of wonst storzns, Dlnes anemomotens sometlmes clog wittr bl-owlng snow and lce accnetlons sometlmes fonm on cup anemomef,ens; anemometen n e - a d l n g s taken Ln mountalns, valreys, and coastal cLiffs, and

s u b J e c t to orognaphlc effects somellmes nesuLtlng ln nnrcfr hlghen v e L o c l t l e s .

(17)

L l

-A l l t h e s e c o n s l d e r a t l o n s a d d o m p h a s l s t o S h e r l o o k r g n e o o r n n e n d a t S . o n , s h a r e d b y m a n y o t h e r s , t h a t d e s l g n v e l o o l t i e s

s h o u l , d be based rlon a statlstlcal a n a l y s l s o f w l n d r e c o r d s o v e r a p e r l o d o f [O to 50 yearstt (771. But not only thls, the results obtalned fnom the reconds of one statlon shouLd be nelated. to the results from other nelghbounlng statlons by a sultable numerloal method; only 1n thls way oan spunlous and systemattc e r r o r s a r l s l n g l n t h e r o c o r d s o f a n l n d l v i d u a l s t e t i o n b o m l n l m l z e d .

The noxt step, thenefor"e, ls to explone a sultable method w h e n e b y t h o a c c r m u l a t e d t o t a l o f a l l m e t e o r o l o g l c a l w i n d r e c o r d g m l g h t b e c o r r e l a t e d .

S t n c e tt ls not deslrable to restnlct t h e a d r n l s s l b L e d a t a solely to those obta:ined from anemomoters sltuated ln rf opon Level-countroyf' (77 ) (tfrf s ln certaln r.eglons of Canada wouLd doclmate t h e a v a l l a b I e d a t a ) , l t i s f l n s t n e c e s s a r y t o l n v e s t t g e t o m o r e ful1y the effects of sunfaco noughness on the velocltles meaeured near tho sunface ovor level ground.

f t h a s a l n e a d y b e e n n o t e d t h a t t h e n e l s s o m e h e l g h t a t

e lnfluence of the qnound fniction tnansnrltted upwards

whleh the lnfluence gnound fniction tnansnrltted upwards

t h n o u g h e d d y v l s c o s l t y , h a s a n e g l l g l b 1 e o f f e o t o n t h e v e l o o l t y of the wind as Lt responds to tlte pnessune d l e n t . I f t h o o f t h e w l n d a s l t r e s p o n a l s t o t h e p n e s s u n e g r a d l e n l r I I ' E l t o v e l o c t t y v g + v v t v J a t t h l s q v v r f l p h e l g h t l s d e n o t e d - b y V e ( t h e g r a d 5 . e n t v e l o c l t y )r r 9 * 6 r r u I 9 s v r l v u v s v r I t

s ,

a n d t h e h e l g h t a t w h l c h t h l s v e l o c l t y 1 5 f l n s t a t t a l n e d b y z E t h e n

qnq' Ene rleJ-gr]'t aE wIIJ_cn unlEr veI()gJ-uJ IU r J-r'n u q rrua4rrl'r4 vJ .tg urrr by refenencd to the powera law incneaie of ve3-ocity wlth hetgEtt

vz =

uu(+)

/ -, \L/6

z

Vn

'

To determlno the natlo of the veLocl-ty at helght z ebove t h e g n o u n d t o t h e g n a d l e n t v e l o c l t y i t l s f l r s t n e c e s s a r y t o

dotei'rnine values of zo eorrespondlng to the vanlous sunfaco noughi ness categonies alreaEy elaborated [pon. fhls wll]t now be attenpted

on the Uaits of such pertlnent experlmental data as are avalLabLe. Examlnatlon of Shenlookrs investlgatlons at Arur Anbon \73), lndicate that fon these conditLons of flat open countny the value o f z o ( t f r e h e t g h t a t w h l c h t h o g n a d l e n t v e l o a l t y L s f i r s t a t t a l n e d ) ls of tf,e ondei of lOO ft. Thls value agreos neasonab.ly cLose1y,y1th that obtalned Uy taffon at Saltsbr.rry Pl-ain (dlscussed by Pagon) !48) for slmllan teri'atn- in whlch avenage values sf zs to:r strong wLnds were 1:zt1 tt ln summer and B8l ft in wlnter. An"appnoximate valuo

of 9OO ft ls thenefore chossn for the value of zU tn flat open country.

(18)

' 1 2 t

f n l a n g e c l t l e s P a g o n ( h B ) o l t l n g T a y l o n t s s t u d l e s a t

the Etffel tower suggests a value of ?o for itrong winds in e

Iarge clty of 2O2A ft ln summer and Ih20 ft ln wlnten. An

approxlmate value of 17oo ft ls adopted for the pnesont. The

value of J,JOO ft ls chosen fon the lntenmedlate oonditlons of

nough wood.ed countny. These values of zo of 900, L3O0, and 1f00

f-t (together wlth the appropnlate exponefits) correspondlng to the thnee types of noughness condltlons glve the th:ree curves of F 1 g s . 6 a n d 7 .

At thls stager no suggestlon ls lntended that these curveg

a r e h l g h l y accunate l n d o e d t h e q u a l l t a t l v e a s p e c t s of the

p r o b l e m d.o not permlt gnoat exactness. It should be noted that 1n

these curves the vaLues of L/a, are founded upon a relatlvely

greaten emount of lnformatlon than ane the values of zo. The

enrors lnvolved ln the latter howeven (whloh may dtffeF Uy 2O0 ft)

a r e o f less consoeuerrcor

Some affLrmati-on of the rough accunacy of these cunves

ls afforded by the compantson of the sunfaco velocltles over

tenraln of dlfferent sunfqce noughness€so fn thel.n study of the

cllmate of Centnal Canada, Kend.rdur and Cur.rle (221+, p.15O) obeervg

I t t h e mean (annusL) wind sleed ln the pnalnles ls u6tweeir fe and 15

n p h .... T h e speed ls appreclably less ln panklands wtth means of

9-L2 mph and, agaln less Ln fonests 5-9 mph; the lncneased fnlotlon a m o n g t h e tiees ls.tho mal-n causert.

These neductlons ln wind veloclty corrpared to the archetypal

flat open countny of tlre pralnLes are entlnely oompatlble wtth those

s u g g e e t o d b y F E g . 7 .

A comparlson of mean wind spoed 1n nlne Canadlan cltles (22O')

a n d a t a l r p o r t s o n thelr outsklnts lndicates that the speed ln the

clty Ls 6$ pen cent of that near the outskLnts. (ffre value suggested

b y Flg. 7 ts 59 per cent. ) Elevatlon, shleldlngr and slttng of-the anemometers and penlods of observatlon vany ln every case but the t r e n d ls obvlous.

A study of hurrlcane winds at Lako Okeechobee (Ftorlda) t h e U . S o Conps of Englnoers (97) lndicated that the wlnd off lhe I a n d ( e v e r g l a d e s , coiered wltir scnub cypress, etc.) averagea 60

cent of the wind over the waten when the latter was l0 nph and 7

pen cent when the latten was B0 rnph.

An antlcLe ln rtThe Stnuctunal Englneerrt by Fenntngton ( f 8 t , p"5il+) dlscusslng the wind vel-ocltles found ln Gneat Brltatn ( l n genenal terms a terraln chanactenlzed by tneed, noIIlng'country a n d . s t n a g g l l n g u n b a n areas) oontalns the followtng lntore,*tlng

by

(19)

i 1 3 _

n o t e . t r O n one occaslon when the whol-e of the Bnltlsh Isles wes

c o v e n e d w i t h p a r a l l e L lsobars nunnlng nearly west to east, all

statlons on the westenn sldo gave the wlnd as fonce B 14e mph)

w h l l e those on the eaetonn slde gave force 5 (21 mptr) so that

lhe velocity was reduced by one-half ln oonsequence of the

. r f f n l c t l o n r r of the 1and. ff the veloclty at the exposed westenn s t a t i o n s be taken et two-thlrds the veloclty of the wlnd fnoe

fnom frlctlon, we get the followlng lnterestlng nesult whlch ls

p r o b a b l y correct enough fon pnactlcal uset one-thtnd of the

veloclty ls lost by the see fnlctlon on the western sJ-de, and

one-thlrd more by the land frlctlon of the country between west and

e a s t . l l

T l r e s e a g a i n a r e v 6 r y closo to the values suggested by F L g . 7 .

It is now posstble to retu::n to the pnoblem of detenmlnlng

d e s l g n v e l o c l t l e s a p p r o p n l a t e to dlfferent g e o g n a p h L c a L reglonso

T h e p n e d l c t l o n o f p n o b a b l l l t l e s a n d neturn penlods of

e x t n e m e w l n d v e l o c l t l e s h a s b e e n suggested many tlmes. T n 1 9 3 2

lfftng (ZO3) used the normal dlstnlbutton curvo to obtaln the

d l s t r l b u t l o n c u r v e s f o n e x t r e m e w l n d v e l o c l t i e s L n s e v e r a l L a n g e

A m e n l o e n aitles. A m o r e n e c e n t u n r ' l t e n J o h n s o n ( Z O Z 7 h a s r e m a n k e d ,

h o w e v e n , that thls type of dlstnibutlon r r g S - v e s a s l g n l f i c a n t

c t e v l a t l o n fnom obsenvod valuestt. S l n c e t h e d a t e o f W L n g t g

copP€s-pondenoe the extreme value dlstnlbutlon (due Largely to-Gumbel (201))

h a s been developedl Johnson analyzed the anemometer records for b o t h extneme lndlcated gusts and hourly mlleages at 1l statlons J.n

S w e d e n a n d slx ln the Brltish Isles and statos that trthe nesuLts obtalned do not contradLct the assumption that the dlstrlbutlon of extnerne values of type No. 1 ls !n close agreement wlth the

d l s t n l b u t l o n o f t h e a o t u a l w l n d v e l o c l t l e s r r ( 2 O Z t p . 1 1 9 ) . C o u n t

( 1 9 9 ) analyzed the neconds ot 2$ weathen stations in the Unlted

S t a t e s havlng 37 yeans of satisfaatory necords accondlng to the sane theory and. sf,ales-tfal1 of tho wlnd dala seems to fol].ovr-the theoryfl.

T h e f o n m t h l s d l g t r l b u t l o n f u n c t l o n t a k o s L s

d t*l = e-e-x

I

T h e n e d u c e d " v a r l a t e y ' = q ( x - u )

whene a ls the scale factor and u the mode of the extneme naluo datar S u p p o s e t h a t a l l a n e m o m e t o r r e c o n d s a r e a n a l y z e d t o o b t a l n the parameters a and u (tn terms of whlch the return perlod cf e x t r e m e s u r f a c e v e l o c l t L e s c a n b e c o m p L e t e l y d e t e r m i n e d a c c o n d t n g

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ilr

-t o -the ex-tneme value -theony). T h e n a n estlmato of the dtstrlbutlon

o f extreme gnadlent veloclties e t t h l s locatlon ls glven by the

p a n a m e t e n s ka and ku whene k ts a trnoughness coefflclentrr deftned by

zn belng the helght of the anemometer and zU and l/n belng glven

b ! F l g . 7 .

T h e o b j e c t n o w L s t o t n y t o c o r r e l a t e t h e s e e s t l m a t e e o f

t h e g n a d l e n t velocltles t o neduce the systematlc orrors whlch may

have occurued. ln the anemomoter reconds, impnove the esttmate of

e x t n e m e w l n d v o l o c l t l e s o c c u r r ' l n g a t s t a t i o n s w l t h s h o n t e r p o r l o d s

of necords, and mlnlmize the subJective elements lnvoLved ln the d e t e r n r i n a t i o n of deslgn wind velocltles.

Suppose that anemometer nnfr eltuated at latltude f ,, and

l o n g l t u d e 2,,., possesses records extendlng back a peniod of N11 y e a r s

w h l c h , by ex-tineme v a l u e a n a l y s t s , y l e l d s v a l u e s f o r t h e s c a l e f a c t o r

and mode of ar., and urr. Suppose that the best estimate of the rrroughness fadtorrr lii kn, then the correspondlng values of scale

f a c t o r a n d m o d a l v a L u e refernlng to the gredlent veloclty a t t h l s

p o l n t ane koar, = al' and kn un E ulnr

ft is now assumed. that these panametens folIow some mth degnee contoun sunface (where m 1s less than the total numben of r e c o r d s b e l n g a n a l y z e d ) o f t h e f o n m s l_ . \ ^ t J A

/r

- 1

/ J - t

,r1 =

T h e values of the coefflclents A 1 3 a n d BrJ are now obtained

P V f l t t l n g t h e observed values to these suniaces by the method of

l e a s t s q u a r o s ' T h l s p r o b l e m o f c o u r s e ls one sulted to electnonlc

c o t i t p u t e t i o n . f 1 f l t t i n g - t h e d a t a lt would be appropnlate to welght

t h e values fl:rst by the facton 1ffiwhlch p u t s lnbr"u^nellance on

-r e o o n d s of longen pe-rlod and second by e facton e detonmlned,

u n a v _ o l d a b l y ln m - o s t c a s e s , b y a s u b J e c t l v e evaluatlon of the'qua]ity o f t h e necords, havlng negand to th; sltlng of the anomometerr- the

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1 l L ' n u r n b e r o f t j m e s 1 t h a s b e e n n o v e d , t h e p o s s i b l e a m p l l f i c a t l o n e f f e c t s o f m o u n t a i n s , v a l 1 o y s , e t c . F o r e x a m p l e a f l r s t - c l a s s w e a t h e r s t a t i o n a t w h l c h t h e a n e m o m e t e r 1 s s l t u a t e d o n l e v e L g r o u n d v r e l l a w a y f r o m s h l e l d i n g a n d h a s n o t b e e n r n o v e d m l g h t b e [ t v e n a w e i g ] r t i - n g o f 9 o r ' 1 0 ( o u ' b o f a p o s s i b l e l 0 ) a n d a n a n e m o m e t e r s l t u a t e d c l o s e t t > t h e r o o f o f a b u l l d i n g r l n a s h l e l r l e d a r e a o r l n a v a 1 I e y , r n i g h t o n l y b e w e l g h t e d b y a f a c t o r o f 1 o r 2 . T h e l - e a s t s q u a r e s t f r o c e s s m i n l m i z e s t h e e r r o r s 1 n a l a n d u r o w i n g t o t h e m a n y c a u s e s c . j - t e d ( o n t h e a s s u m p t l o n t h a t t h o w o i g h t o d e r r o r s a r e n o r m a l l y d l s t r i b u t e d ) . T h i s p n o c e s s l e a d s d i r e c t l y t o t h e c o n t o u r s o f a t a n d u l f o r t h e t e r r i t o r y c o n s i d e r e d . T f n o w i t i s w l s h e d t o e r e c t a s t r r r c . b u r e a t a c e r t a i n l o c a t l o n t o l s s b a p e r l o d o f T y e a r s ( t > f O ) w i t h a r i s k o f q ( d t c t a t e d b y o o n s l d e r a t l o n s o f p u b l - l c l l a b i l l t y , t h e u s e a n d o c c u p a n c y o f t h e s t r u c t u r e , r e p l a c e m e n t c o s t s , e t c . ) t h a ' b t h e b a s i c d e s i g n r v i n d v o l o c i t y V i s e x c e e d e d w i t h j - n t h l s t l m e , t h e r e t u r n p e r i o d R o f t h l s w i n d v e l o c l t y V l s g l v e n b y - T

R = f6E;TI:qT

1 f q l s s m a l l r

=fr

Thls represents a pnobability of fr. By extneme v a l u e o f t h e r e q u i r e d g r a d i e n t v e l o c l t y

valuo theony tho

V . , =

o logo

loge + u l

w h e r o g I a n d u t a r e d e t e n m l n e d f r o m t h e c o n t o u r s o

The values of the velocliy noarer the surface correspondlng t o t h l s g n a < l i e n t v e l o c l t y a r e d e t o n r n i n e d f r o m F l g . 7 a c c o r d l n g t o t h e a p p r o p r l a t o r o u g h n e s s c o n d l t i o r l s r I f t h e s t r u c t u r e l s t o b e e r e c t e d o n a h 1 1 1 o r i n a v a l l e y a s u l t a b l e a m p L j - f l c a t t o n f a c t o n s h o u l d b e u s e d . ( E x a m p l - e s o f t h e s e g l v e n b y P a g o n ( l + B ) a n d P u t n a m ( 5 1 ) a n e _ t a b u l a t e d l n A p p e n d l x I T . ) d f t e n t h e o n f y w a y t o e v a l - u a t e t h i s w o u l d b e b y a c t u a l o b s e r v a t l o n o f w l n d v e l o c i t i e i a t t h e s l t e f o r a s h o r t p e r l o d a n d c o m p a r i n g t h e i r v a l u e ' w i t h t h o s o a t a n e a n b y a n e n r o m e t e r o n l e v e l t e r n a l n .

(-

1t-a'i I

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1 6

-2 . [ Cholce of a SultaPlo Avenaglng_Interval

It has alneady been noted that owlng to the wl.de f l u c t u a t L o n s ln wlnd veloclty whlch take plaoe over penlods n a n g l n g fnom fractlons o f a second to many centunles lt ls n e c e s s a r y t o m e a s u r e w l n d voloclty s b a t l s t i c a l l y l n t e r m s o f a meqn valuo and the devlatlons from the mean. The tlme or dlstance lntenval for whlch the mean ls obtalned depends upon t h e p u r p o s e for whlch lt ls requlred. T o c a l o u l a t e b a s L c wlnd veloclties for the deslgn of structuros certaln frrndqmental c o n s l d e r a t l o n s d e t e n m l n e u r h l c h lntorval l s m o s t a p p r o p n l a t o . T h e s e m a y b e s t a t e d a s f o l l o w s :

( 1 ) TLre lnterval should colnclde as far as posslble wlth s o m e natural penlodlclty o f t h e w l n d e

(21 The lntervaL should be rrlongrr cornpaned to both the natunal frequency of the stnucture and to the response -

tlme of the lnstrument: ln this way thene wlll be no dSmamlc lntenactlon betvrreen the structune and the mean w l n d and measuned wlnd velocltles w l l L b e r l t r u e r t .

(f) Ihe lnterval should be shont enough to record the " p e a k s r t o f g e v e n e s t o r m s .

(h) The lnterval should correspond to a body of alr of s r r f f l c l e n t s l z e t o c o m p l e t e l y e n v e l o p a s t r u c t u r e a n d lts vontex reglons.

It should be noted. that ln Canad.a the only wlnd v e l o c l t y s t a t l s t l c s r e c o r d e d o n a r o u t l n e b a s l s a r e t h o m e a n hounly mlleages necorded by cup anemometens and.the gu'st speeds

(noughly a 3-sec averiage speed) recorded by a small numben of f a l r l y r e c e n t l y e s t a b l l s h e d . D l n e s a n e m o m e t e r s . N e l t h e n o f t h e s e a v e n a g l n g lntervals l s s u l t a b l e f o r o b t a l - n i n g b a s l c d e s l g n w l n d v e l o c l t l e s f o r s t r u c t u r e s a s c a n b e a r g u e d f r o m t h e f a c t t h a t t h e h o u n l y a v e r a g e d o e s n o t s a t l s f y c o n d l t l o n s 1 a n d . 3 a n d t h e 3 - s e a a v e i a g e d o S s n o t s a t i s f y c o n b l t l o n s 1 , 2 t a n d I p .

On the othor hand, lt can bo argued that the ttmlle of wlndll or the rrmlnute of wj-ndrl both represent ldealIy

sultable, lf not optlmum, intenvals fon measunlng hlgh wlnd v e l o c l t l e s f o r p u r p o s e s o f s t r u c t u r a l d e s l g n . T h e r e a s o n s m a y b e s t a t e d a s f o l l o w s l n c o r r e s p o n d l n g o n d e n t o t h e s t l p u l a t e d c o n d l t l o n s .

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1 7 -( r ) B y m e a n s o f found that thermal 1n t o 5000 ft Lnterval or c o r r e l a t l o n c o e f f l c l e n t s , D u n s t ( 2 5 ' l l n s t o r m w l n d s m a J o n g r o u p s o f eddles, onlgin, had wavelengths of qbout l+000 - correspondlng closely to the mlle

the mlnute !.ntenval ln wlnds of 5O mph. ( 2 ) The natural perlod of most structures ls of the order

o f O.l to 3 sec Qg5) with that for the Emplre State B u l l d l n g o i 8 . 1 4 s e - c - ( 1 5 6 ) . w l t h the damping pnesent ' ln most structunes fLuctuatlons coruespondlng to one

mlle ln extnome wlnds would have lnfinlteslmel dynamlc a c t l . o n .

Shenlock and Stout, refenrlng to the response time of c o m m e r l c a l a n e m o m e t e r s , w n o t e - l n 1 9 3 7 r l t h a t b o c a u s e o f the lnertla of movlng parts of the instnr.rments the

r o c o r d s c o u l d o n l y b e a c c e p t e d a s a c c u r a t e t f t h e y w e r e a v e r a g e d oven l-O seconds or morert (72). T h u s e v e n e t 1!O rnpfr, the mlle of wtnd (or the mlnute of wlnd) s a t l s f l e s t h e s e c o n d naqulrement.

( : ) The mlle of wind also repnesents a body of alr fan l a n g e r t h a n m o s t s t n u c t u r e s , s o t h a t s t a t l c p n e s s u r e s a t Least equlvalent to this average speed can be

a n t l c l p a t e d .

(h) llhe mlIe of wlnd w111 be of sufficl.ently short duratlon to rocord the peak of a sudden severe local- thunderstonm o n s q u a l l .

These argunents justlfylng the use of the extrene mlIe o n m l n u t e o f , w l n d a s b a s l c - d e s l g n v e l o c t t l e s a r e e n d o n b e d f u r t h e n by the fact that the mlle of wlnd has been neconimended fon use ln

t h e U n l t e d S t a t e s ( 7 7 , l - 7 0 ) ( w h e n e n e c o n d s a r e a v a l l a b l e - f o r n a l Y y e a r s ) a s t h e b a s l s f 6 r d e s l g n w i n d v e l o c l t l e s a n d t h e m l n u t e o f w l n d ' ln the Brltlsh r s l e s ( 1 7 1 ) . T h e m o d l f l c a t l o n s t o t h e

enemometens at present ln use ln Canada which wouLd be necessary t o c o n v e r t f n o m * n e a d l n g s o f h o u r a v e r a g e s t o m l 1 e a v e r a g e s w o u l d Lnvolve llttle mor"e than the repLacement of the present reoorden t o o n e o f f a s t e r c h a r t s p e e d . f n v l o w o f t h e f a c t t h a t a t l e a s t 13 on il.r years of record.- should elapse before the wlnd veJ.oclty-a veJ.oclty-a t veJ.oclty-a veJ.oclty-a r e u s e f u l f o r s t veJ.oclty-a t l s t i c veJ.oclty-a l a n a l y s l s , t h e m o d l f l c a t l o n o f t h e present lnstruments would appoar to be of utmost ungency_. Ihe -cost

of these modlflcattons would be small compared to the gnoaten safety and economy whlch could thereby bo effected ln stnuctures throughout the country.

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L B

-THE DETERMINATION OF WIND PRESSI]RES ON STRUCfl'RES 3.1 Wlnd Tgnnel Studles altd Shape Coefflclents

Most of the knov,rledge r€latlng to shape ooefflalents and t h e d l s t n l b u t i o n o f p n e s s u r e s on structures has been acquired fnom numerous and often extenslve tests on models ln wtnd tunnels. A

s e l e c t l o n o f t h e p u b l t s h e d r e p o r t s o f t h e s e l n v e s t l g a t l o n s

orlglnatlng from niany countrl"es and covenlng a wido varlety of s h a p e s l s g l v e n l n r e f e n e n c e s 1 0 J - t o 1 5 8 .

s s e s f o r t o w o r s a n d o t h e n ner shapes (1h6) ! Internal.

r 1 d l n g ( f 0 3 , L36) have been the s u b J e c t s o f o t h e n s t u d l e s .

Figunes Ba, br and c show. tle chanacterlstic two-dlmenslonaL Flow patierirs eround a l+5o pttch roof stnuctune, a flat noof block stnucture and a semi-cl.ncular anch structure eactr standlng on a flat ground surface. It ls noted that the fLow lE d l v l d e d - l n t o t h r e e a f s t l n c t n e g l o n s - e w l n d w a r d v o r t e x r e g l o n -(A)r a leeward vortex reglon (B), separated firom the nonrotatlonal flow

(C) by a vontex layer (V) whlch envelopes the stnucture llke an Lmaglnary membrane, a4d.ln contact wlth the struptu:raI shape at the-sepai'atlon polnt (S). The wtndwand vontex neglon may be thought of as an extenslon of the boundany l-ayen. In regl-ons ln w h l c [ t h e v o r t e x l a y e r l s c o n v e x ( w i t h r e s p e c t t o t h e n e g t o n o f

nonrotatlonal florr) ihe pressune ls posltivo (to wlndward) and w h e n e concave, is negattve (to leeward). T h e s t a t l c p r e s s u r e - o n elthen slde oi tfre vdrtex layen ls the same (il+l). Much of the k l n e t l c e n e r g y w 1 t h 1 n t h o v o r t e x n e g l o n s l s d l s s l p a t e d L n t o h e a t by tunbulence. The pressures on surfaces of the structure are efuuaI to that at the- vortox layen modlfled by the degroe of t r r r b u l e n t a c t l v l t y r e m a l n l n g . H l g h s u c t l o n p r e v a i . l s Julp-behlld t h e p o l n t o f s e p a i a t l o n s . I n c u n i e d s t r u c t u i e s t h e p o s l t l o n o f S varles and ls d.ependent on the Reyrrolds number

( v e l o c l t y x c h a r a c t e r l s t l c d l m e n s l o n ) , t h e s u r f a c e n o u g h n e s s o f

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1 9

-the body, -the turbulence of the oncomlng fLow and the upstream

v e l o c t t y p n o f l l e . H e n c e t h e p r e s s u r e s a l s o d e p e n d o n t h e s e f a c t o n s . o n shanp-edged structures, h o w e v e r , t h e s e p a r a t l o n found nonmally occuns at one of the sharp edges, and the flow

patterns and hence the pressures are largely lndependent of

Reynolds number and surface noughness, but not of the upstneam v e l o c l t y p r o f l l e . E x c e p t i o n s t o t h l s s t a t e m e n t a r e f o u n d t

however, when the vontox layer approacheg tangency to one of the s u r f a c e s , l n w h t c h c a s e a f u r t h e r t u r b u l e n t z o n e _ . m 3 y b e s e t _ u p - o v e r thle sunf'ace wlth hlgh suctlons. In thls case Ny'tr<kentved obtalned dlrect proof of a strong Reynolds number dependence fon a deflnite type of bulldlng, broad ln pnopontlon to helght and wlth a flat n b - o r s l o p e , p a * E i c u l a r l y r r a i " t r e b w l t h a roof JLope of 2ooi(ilt9).

the same sltuatlon can anlse when the wlnd 1s incldent upon the

w a l l s o f a s t r u c t u r e a t s m a l l a n 6 1 e s .

The presence of the gnound surface oxerts a conslderable s t a b l l i z l n g l n f l u e n c e o n t h e p r a e s s u r e d l s t n i b u t l o n s w h l c h r -except J u s t t o t h e l e e o f t h e s e p a n a t t o n p o l n t , a r e f o r a l L p n a c t l c a l fu:rposes statlc lf the flbw ls steady. If the gnound pLane ls not p r e s e n t ( l ' ' 1 g . 9), as ls effectLvely the case ln tall slendor

s t n u c t u r e s s u c h a s s m o k e s t a c k s , m a r k e d l n s t a b i l t t y c a n a n l s e l n t h e p n e s s u r e d i s t n l b u t l o n : t h l s c a s e r o q u l r e s s p e c l a l c o n s l d e r a t l o n a n d w l 1 l b e d l s c u s s e d l n s e c t t o n [.3 whlch deals wlth the vlbnatlon

o f s t n u c t u r e s ,

3.2 The Valldlty ot_Wtnd firnnel Results

The nesults of wlnd tunnel tests on modeLs are genenally v a l l d f o n f u l l - s c a l e p r o t o t y p e s p r o v l d e d t h a t t h r e e c o n d l t l o n s a n e f u l f t l L e d ( r 9 5 ) :

( a ) t h a t t h e r e l s g e o m e t r i c a l s l m i l a r l t y b e t w e e n t h e m o d e l and pnototyPe

(b) that thene 1s oquallty of Reynolds nurnbers

( c ) t h a t t h e r e l s k l n e m a t l c s l m l l a n l t y l n t h e a p p r o a e h l n g f l o w s .

P r o v l d e d t h a t o n l y o v e p - 4 1 1 e f f e c t s a r e b e l n g s t u d l e d the flnst condltlon presenti no probJ-em. llre second condltlotr' h o w e v e r , l s n o t s o e a s y t o s a t l s f y s L n c e e g u a l t t y o f R e S m o l d s

nqmbens-noquires that lfre veloclty and characterlstlc dlmenslon

for the model and prototype be keit tn lnverse ratlo' That 4", tf the model fs f/iOOth scale, tha velocl-tV 11 the.wlnd tur:nel

should be one hundred t1me" a! great as that to vtrlch the protot;rpe l s e x p o s e d , p n o v l d e d , o f c o l r r s 6 , t h e f l u l d u s e d l n b o t h c a s e s l - s

atn at atmospher,lc temperature ana pressure. The slze of the

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2 0

-a r e -a s h o u L d n o t e x e e e d -a b o u t 5 pen bent of the cross-Sootlon-al area of the wlnd tr.urneI. The constnuctlon effects whloh result t f t h l s f l g u n e s l s e x c e e d e d c a n b e q u l t e l a r g e ( 1 _ 5 7 ) . _ T h e s e p r a c t l c a l r e s t r l c t i o n s g e n e r a l l y p r o h l b l t e q u a l l t y o f R e y n o l d s nrffrbers bolng achleved.

Fortunately, however, for most sharp-66964 structt11tes Lnequal-Lty of Reynolds nurnbers between model and protgtyPe ale l n c o n s e q u e n t l a l i s h a s a l r e a d y b e e n d e s c r l b e d . C u n v e d s t r u c t u r e s s u c h a s c y l l n d r l c a l s t a c k s , a r c h e d n o o f s , e t c . , n o r m a l l y e x h l b l t a falnly constant-pressune dlstrlbutlon between Reynolds numbons of LO4 bnd 2 x 105- at whlch polnt a transLtlon oocut?s produalng a d l f f e n e n t b u t a g a l n p r a c t l c a l l y c o n s t a p t p r e s s u r e d l s t n l b u t l o n for Rotrnolds numbens ln excess of 9 x JQ2 o The bordenllne Uetweeir--t[ese--two patterns ls prlm6n11y a visoous functlon and

transltion fnom one fLow pattenn to the othor can be antlflclally stLmuLated by rouglrenlng tfre surface of the body gr by- lncreaslng the tunbuLenle of-tho appnoachlng flow by means of mesh scroerrsr

In thls way the effects of lnequal-lty oi Re;molds_ numbens foy mod.els and prototypes wlth cu:rved surfaces can be kept to a mlnlmum as ln the case of sharp-edged stnuotunes.

T h e t h t n d n e q u l n e m e n t f o r t h e v a l l d l t y o f m o d e L t e s t s t namely, that thene ls klnematlc s

f l o w s , l s f a r m o r e d l f f l c u l t t o a t e s t s h a s t h l s n e q u l n e m e n t b e e n e t h e n e f o n e i m p o r t a n t t o l n d l c a t e t d l s s l m l l a r l t y 1 n t h e a p p r o a c h l n g

on fuLl-scale structuret dght alffer from those ln the wlnd tunnel.

3.3 Ttre Conseguences of Klnematlc Dlsslmlfgrlty

The klnematic pnopertles of the naturaL wlnd utrlch

nequlne slmulatlon ln the wind tunnel ar_er_baslcallyr the i,ncrease o f h e a n v o l o o l t y w i t h h e l g h t a n d t h e t u r b u l e n c e .

I t i s n o r m a l l n w l n d t u n n e l t e s t s t o t e s t m o d e l s a s f a r a s p o s s l b l e l n a u n l f o i m v e l c

mountlng the models on smooth bas near the centre of the tunnel awa nesr the wall. The shaPe coefflc

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- 2 1

v r h e r e P - Po repnesents the difference between the pnessure at t h e p o l n t o n t h e s u r f a c e o f t h e ^ s t r u c t u r e a n d t h e s t a t l c p n e s s u r e l n t h e u p s t r e a m f l o w a n d l / 2 P Y z l s t h e v e l o c l t y p r e s s u r e o f t h e . u p s t r e a m f l o w ,

S i m u l a t l o n o f a n y g l v e n r a t e o f i n c n e a s e o f v e l o c l t y with hetght in the wind tuimel can bo accompllshed, howeverr by u s l n g g n d d u a t e d . m e s h s c r e e n s p l a c e d l n t h o u p s t r e a m f l o w o r b y maklng uso of the natural proflle occr:rrlng at the walls of the w l n d tunnoL. O n e s u c h t e s t a l o n g t h e s e L i n e s w a s c a r r l e d o u t b y B a l l e y a n d V l n c e n t ( f 0 3 1 ; l n t h l d t h e m o d e ] w a s p l a c e d o n t h e

floon of the tunnel vrhene the nate of velocity lncrease corresponded closely wlth the VTfh potzsra Iarry. The shape coefflclents were ref-o r e n c e h t ref-o t h e v e l b c t t y p r e s s u r e a t a s c a l e h e l g h t ref-o f h9 ft abref-ove ground, at whlch polnt the veloclby pressure was some 4U pel- cent I e s s t h a n t h a t o c c u n r i n g a w a y f r o r y t h e w a l l s . I n s P l t e o f t h e l n c n e a s e l n v e l o c l t y w l f h h e i g h t t r t h e analysis of the nesults ... s h o v r e d that ln all

" " " " s t h e e f f e c t l s p r a c t t c a l l y e q u l v a l e n t to a unlform pressure o\rer the wholo pr-oSected he-lghirr.

T h l s s t a t e m e n t l s d i s t l n c t l y a t v a r l a n c o w l b h t h o a s s u m p t l o n c o n n n o n l y u s e d l n p r a c t l c e , t h a t t h e p r e s s u r e o n a stnucture at any gi-t"n helght ls dlnectly pnoportional to the v e l o c l t y p r e s s u i e - o f t h e o i c o m l n g f l o w s t t h e s a m e l e v e I . T h l s a s s u m p t i o i l r n a y b e t r u e f o n t a I 1 r - s l e n d e r s t n u c t u r e s o f _high- aspect n a t l o such as-nad1o towers, but ls evtdently not true fon the

m o r e u s u a f U u i l a f n g s h a p e s - . T h e t o t a l p r e s L u r e s l n 3 " b / s q f t a c t l n g o n t h e v a r i 6 u s s l n u c t u r a l s h a p e s lested^by Balley and V l n c e i l t a r e g l v e n l n F l g , 1 0 ( l n . t e r : i n s o f a n B o - m p h w i n d v e l o c l t y a t t h e r e f e r d n c e h e l g h t - o f [0 ft). I t l s a : o t e d t h a t t h e s e p r e s s u r o s lncrease with the hefght H of the structure ancl that al'L the

e x p e n l m e n t a l r e s u l t s i l e c l o s e t o t h e l l n e ( g ) e x p r e s s e d b y

q d- H

C o r n p a r e d w l t h t h i s n e s u l t 1 s t h e l n c r e a s e o f p r e s s u r e _ wlth helght given by the practical rule alneady^mentloned; namel-y,

that tho-pnelsure oir a structure at any helght ls propontlonal to the velocity pt"""""u of the wlnd at the same height. For the Vln potyen lalv lncrease ln helght thls corresponds to

q o < H 2 / 7 . T l r l s nelationship 1 s g l v e n b y } l n e ( B ) l n w h i c h t h e s h a p e c o e f f l c l e n t o f f . 5 a n O t h e v l l o c i t y o f B 0 n p h " ! [ 9 f t a r e a s s u m e d . T h e a i " 6 a " i i ) ' b ; t w e e n t h 6 t w o c u r v e s l s l m m e d i a t e l y n o t l c e d a n d " n g g " " t s t f i a t w h e n e t h e w l n d v e l o c i t y . p r o f i l e c o r ' l t € s -ponds to the tTitn power larv the assurnption that the pnessure on

Figure

TABLE  OF  CONTENTS
FIGURE II

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