2558 02 24 FInal Charnchai

WIND LOADS AND RESPONSES OF BUILDINGS WITH NONLINEAR MODE SHAPES

BY

MR. CHARNCHAI ORAPINPONG

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF CIVIL ENGINEERING

DEPARTMENT OF CIVIL ENGINEERING FACULTY OF ENGINEERING THAMMASAT UNIVERSITY

ACADEMIC YEAR 2014 COPYRIGHT OF THAMMASAT UNIVERSITY

.. 2558

( . )

( . )

( . )

( . )

( . )

(1)

//

()

. -

2557

.1311-50

: , , .1311-50

(2)

Thesis Title WIND LOADS AND RESPONSES OF BUILDINGS WITH NONLINEAR MODE SHAPES

Author Mr. Charnchai Orapinpong Degree The Degree of Master in Civil Engineering Major Field/Faculty/University Department of Civil Engineering

Faculty of Engineering Thammasat University

Thesis Advisor Thesis Co-Advisor (If any)

Assistant Professor Dr. Naret Limsamphancharoen -

Academic Years 2014

ABSTRACT

This research presents the correction factors for along-wind loads and responses of buildings with nonlinear mode shapes and the diaplacement of building. The formulation is compatible with DPT1311-50. The correction factors of along-wind are gust factor, maximum displacement and maximum accelation. These correction factors of across-wind are wind load, maximum displacement and maximum accelation. Result of analysis from dispalcement of building, The corrrection factor have a little bit effect to wind load and response. But the correction factor is neccessary individual for flexural building only. By the correction factors of along-wind, Gust factor isnt significant. Maximum displacement and maximum accelation have increase s significant. The correction factors of across-wind , maximum diaplacement, maximum accelation and wind load have increase s significant.

Keywords: wind load, nonlinear mode shapes, DPT1311-50

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.

. . .

(4)

(1)

Abstract (2)

(3)

(7)

(8)

1 1

1.1 1 1.2 2 1.3 3 1.4 3

2 4

2.1 4 2.2 11 2.3 17 2.4 23 2.5 27 2.6 37

(5)

3 40

3.1 40 3.2 42 3.3 42 3.4 56

4 57

4.1 57 4.2 58 4.3 60 4.4 61 4.5 62 4.6 67 4.7 0 73 4.8 .1311-50 78 4.9 84

5 87

5.1 87 5.2 88 5.3 92 5.4 z 94 5.5 95 5.6 99 5.7 0 101 5.8 .1311-50 104 5.9 109

(6)

6 112

118

120

129

(7)

2.1 (Gradient Height, gz ) (Exponential for Power Law, ) (Roughness Length, 0z ) 8 2.2 Turbulence Intensity, ( )uI z 9 3.1 41 3.2 54 4.1 , ,g DC a 82 4.2 1C 2C 82 4.3 1C 2C 83 4.4 85 4.5 1C 2C 85 4.6 , ,g DC a 86 5.1 , ,w w La P 107 5.2 4C 107 5.3 4C 108 5.4 110 5.5 4C 110 5.6 , , ( )w w La p H 111

(8)

1.1 2 2.1 4 2.2 5 2.3 autospectra New York (Dyrbye, Cla e and Hansen,1996 [4]) 6 2.4 6 2.5 11 2.6 30 2.7 2 0.14 34 2.8 2 0.25 34 2.9 2 0.36 35 2.10 2 0.14 35 2.11 2 0.25 36 2.12 2 0.36 36 2.13 37 2.14 Thanun (2006) 38 3.1 log 1 43 3.2 1 ( 100 ) 44 3.3 2 ( 114 ) 44 3.4 3 ( 128 ) 45 3.5 4 ( 128 ) 45 3.6 5 ( 128 ) 46 3.7 6 ( 80 ) 46 3.8 7 ( 140 ) 47 3.9 8 ( 130 ) 47 3.10 9 ( 149 ) 48 3.11 10 ( 84 ) 48

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3.12 11 ( 94 ) 49 3.13 12 ( 105 ) 49 3.14 13 ( 123 ) 50 3.15 14 ( 210 ) 50 3.16 15 ( 95 ) 51 3.17 16 ( 123 ) 51 3.18 17 ( 123 ) 52 3.19 18 ( 80 ) 52 3.20 19 ( 112 ) 53 3.21 55 3.22 56 4.1 1C 0.14 68 4.2 1C 0.25 68 4.3 1C 0.36 69 4.4 2C 0.14 70 4.5 2C 0.25 70 4.6 2C 0.36 71 4.7 3C 0.14 72 4.8 3C 0.25 72 4.9 3C 0.36 73 4.10 1 2 3, ,C C C 0.14 76 4.11 1 2 3, ,C C C 0.25 76 4.12 1 2 3, ,C C C 0.36 77 4.13 84 5.1 4C 0.14 100 5.2 4C 0.25 100 5.3 4C 0.36 101 5.4 4C 0.14 103 5.5 4C 0.25 103 5.6 4C 0.36 104

(10)

5.7 109

1

1

1.1

3 (Along wind load) (Across wind load) (Torsional load) 3

(. 1311-50) () 19 38 33 1 1 . 1 .

2

() ()

1

. 1311-50 z

1.2

0

4

8

12

16

20

24

1 0.5 0 0.5 1Measurement

BuildingNo.2

0246810121416182022

1 0.5 0 0.5 1Measurement

BuildingNo.21

BUAYHighlight

3

1.3 1.3.1

1.3.2

. 1311-50 1.4

4

2

2.1

Davenport (1975) (wind-chain) 5 2.1 1 2 3 4 5

2.1 .

5

1 2 3 (along wind speed, ( )U t ) (across wind speed, ( )V t ) (vertical wind speed, ( )W t )

2.2 2 (U ) ( ( )u t )

( ( )v t ) ( ( )w t )

2.2

t

U(t)

U

u(t)

6

2.3 autospectra New York (Dyrbye, Clae s and Hansen,1996 )

2.3

Brookhaven New York 100 4 5 10 1 (spectral gap) 10 1

2.4

7

gZ gU 2.4 (roughness)

(power law) (2.1)

g gU Z

ZU

Z < gZ (2.1)

U Z gU gZ gZ

Davenport (1960)

8 2.1

8

2.1 (gradient height, gZ ) (exponential for power law, )

gZ

()

1 1/8.5 245

2 1/7.5 275

3

1/6.5 300

4

1/5.5 335

5 4 2

1/4.5 365

6 ,

1/3.5 410

7

1/3 460

8

1/2.5 - 1/1.5 550

(boundary layer)

(normal distribution)

9

(turbulence intensity, uI ) u 2.2 2.2

)()()(

zUzzI uu

(2.2)

2.2

( )uI z 7-9 % 10-20% 15-25%

auto covariance function, )( t t

( , ) [ ( , ). ( , )]z E u z t u z t (2.3)

( , )uS z n

0

( , ) 4 ( , ) cos 2 .uS z n z n d (2.4)

n (Hertz) uS

2

0

( ) ( , ).u uz S z n dn

(2.5)

10 . 1311-50 (2550) Davenport- (1967)

20

10( , )( , ) 4u

R z nS z n Un

(2.6)

2

4/32

1220( )

( , )12201

( )

nU z

R z nn

U z

drag coefficient 0.005 - 0.05

010U 10 m

cross spectra density function, 1 2( , , )cuS z z n 1z 2z uS

1 2 1 2, , , ,cu u uS coh z z n S z n S z n (2.7)

1,uS z n 1z 2 ,uS z n 2z

1 2, ,coh z z n coherence function n 2 1 2, ,coh z z n 2.8

1 2, , fcoh z z n e (2.8)

1 2

1 112

zn C z zfU z U z

(2.9)

zC

11 2.2

3 4 Davenport 2.1

2.5

2.5 W D H i 1, 2 3 z t 3

1( , )F z t z t 2 ( , )F z t z

t 3 ( , )F z t z t

D

W

H

M3(t) M1(t)

M2(t)

WIND

F1(z,t)

F2(z,t)

12 z t

1 ,z t z t 2 ,z t z t 3 ,z t z t

1

m y t c y t k y t f t (2.10)

f t m c k y t y t

y t

20

H

i im m z z dz (2.11)

im z z i z z

13

202k n m (2.12)

0n

t

0

( ) ,H

i if t F z t z dz (2.13) 2 ( f )

0

( ) ( )H

i if F z z dz (2.14) ( )iF z z t f t

0

( , ) ( )H

i if t F z t z dz (2.15)

( , )iF z t z t

fyk

(2.16) .

14 2.15

1 2 1 2 1 2 1 20 0

( ) ( , ) ( , ) ( ) ( ) ( , , )i i

H H

f F F i iS n S z n S z n z z coh z z n dz dz (2.17)

,FS z n z n

2f 2.18

2

0

( )f fS n dn

(2.18) ( )y t 2 background resonant background 2B

2

22f

B k (2.19)

resonant 2R

0 022

( )4

fR

n S nk

(2.20)

2

2 2 2y B R (2.21)

15 2.18 , 2.19 2.20

2

0 022 2

( )4

f fy

n S nk k (2.22)

max( )y

max yy y g (2.23)

g peak factor 0.57722ln2ln

vTvT

T 3600 1-

v Effective mean crossing rate 0n

2.23

max gy C y (2.24)

gC (gust factor)

1 ygC g y (2.25)

z t

, ( ) ( )i iz t y t z (2.26) maxi z z

max max ( )i iz y z (2.27)

16 ( )yS

4

0(2 )y yS n S (2.28)

2

0(2 )y yn (2.29)

max yy g (2.30)

z

max max ( )i iz y z (2.31) ( )f

maxf k y (2.32)

2.24 2.32

gf k C y (2.33)

2.16

gf C f (2.34)

17 0y 0f f 2.23

yf k g (2.35)

( )iF z f 2.36

2

0

( ) ( ) ( )( ) ( )

ii H

i

m z zF z fm z z dz

(2.36)

( )im z ( )i zz H

2

3 ( )iF z f zH (2.37)

2.3

. 1311-50

NBC 2005 Davenport (1967)

2

11( ) ( ) ( )2 p

F z U z C z W (2.38)

1( , ) ( ) ( , )pF z t U z C W u z t (2.39)

1( )F z z 1( , )F z t z

pC

18 2.1 2.14

2

21 ( )2

H

H pzf U C W z dzH

(2.40)

2.1 2.39

1

22 2 2 2 2( , )

a

F H p UH xzS z n U C W S JH

(2.41)

UHS 2xJ Joint-acceptance function W 2.17 2.41

2 2 2 2 2 2 2( )f H p UH x zS n U C W H S J J (2.42)

2 1 2 1 2 1 2 1 220 0

1 ( ) ( ) ( , , )H H

z zz zJ z z coh z z n dz dz

H H H

(2.43) Joint-acceptance function z 2.18

2 2 2 2 2 2 2 2

0f H p UH x zU C W H S J J dn

(2.44)

19 2.40 2.44 2.16, 2.19 2.20

2 2

2 20

22 2 2

0

4

( )

UH x zB

HH

S J J dnH

y U z z dzH

(2.45)

0

2 22 2

22 2 2

0

3( )

UH x z nR

HH

n S J JHy U z z dz

H

(2.46)

2.6, 2.45 2.46

22

102 216B

H

U By U (2.47)

22

102 216R

H

U sFy U (2.48)

2

4/32

1220

12201

HH

H

nU

Rn

U

(2.49)

22 2

022

0

( )

H x z

H

H R J J dnn

Bz z dzH

(2.50)

20

0

2 2

22

0

14

( )

x z n

H

J Js

z z dzH

(2.51)

0HF R n (2.52)

2.1

22 010( ) ( )eU z C z U (2.53)

2010U 10

0 2

0

( )10

ge

g

zzC zz

(2.54)

gz

0gz 0

16 (10)eK C (2.55)

( )eH eC C H (2.56) 2.47 2.48

2

2B

eH

K By C (2.57)

2

2R

eH

K sFy C

(2.58)

21 2.25

y

eH

K sFBy C

(2.59)

2.59 3-5 . 1311-50 Davanport 2xJ 2.41 zcoh - 2.43

2 1

101x

H

J nWU

(2.60)

1 28

1 2( , , ) HnH z zU

zcoh z z n e (2.61)

2zJ 2.43

2

21 1

81 13

z

H

J nHU

(2.62)

( ) 3 zzH

22 2

20

3( )4 1

H z Hz dzH

(2.63)

,B s F 2.50, 2.51 2.52

0

4 1 1 110 83 1 1

3

H

H H

B R dnnW nHnU U

(2.64)

22

4/3204 1 13 1 1 1

457 122

zB dxzH zWz

(2.65)

01220H

nxU

0 0

1 18 103 1 13 H H

s n W n WU U

(2.66)

2

0

4/32

0

1220

12201

H

H

nU

Fn

U

(2.67)

,B s F 2.65, 2.66, 2.67 3-6, 3-7, 3-8 - . 1311-50

1( ) Bm z WD (2.68)

B

2.11 2.12

Bm WDH (2.69)

202 Bk n WDH (2.70)

23 2.16, 2.24 2.27

2

1max 2 2 20

32

4

w eH g p

gB

H I qC C CC

n D H

(2.71) 2.28 2.31

2 2 max

1max 04eH g

KsFn gC C

(2.72)

2.71, 2.72 3-12, 3-13 . 1311-50 2.4

. 1311-50 AIJ 2004 High Frequency Force Balance (HFFB) Tamura (1996) HFFB Tschanz Davenport (1983) aeroelastic HFFB 100 Hz balance system HFFB ( ( )f t 2.13)

1)

2)

z 3)

24

4) (motion induce force) -

5)

3 z z

2 20

( ) ( , ) ( )H

f t F z t z dz (2.73)

2 ( ) zz H

20

1( ) ( , )H

f t F z t zdzH

(2.74) 2.74 2 ( )M t 2.5

21( ) ( )f t M tH

(2.75) 2 ( )M t f

22

1f MS n S nH

(2.76)

25

2M

S n 2 ( )M t

2

2 22

1f MH

(2.77)

2

2M 2 ( )M t

fS n f n 2.76 2.77 - 2.22 2.27 LC

2

2 212

ML

H

CU WH

(2.78)

Hq

21

2H Hq U (2.79)

2.77 2.79

f H Lq WHC (2.80)

2.75 2.76

2

2

002 2

( )( ) Mff M

nS nnS n (2.81)

26 2.80 2.81 2.22

1H Ly Lq WHC R

k (2.82)

LR

4

LL

FR (2.83)

22

0 02

( )ML

M

n S nF (2.84)

2.35 2.82

1H L Lf g q WHC R (2.85)

2.85 2.37

2 ( ) 3 1H L LzF z q C W g RH

(2.86) 2.86 4-1 . 1311-50 m z BWD

3BWDHm (2.87)

202 3BWDHk n (2.88)

27 2.23 2.27 (2556)

2max 2 20

3( ) 14

H LL

B

q C gz Rn D

(2.89) 2.28 2.31

2max1( ) 3 H LB

z q C g RD (2.90)

2.90 4-11 . 1311-50 2.5

HFFB

() ( )fS n 2.17

2 ( )( )

f

f

S nS n

1 2 1 2 1 2 1 2

0 0

1 2 1 2 1 2 1 20 0

( , ) ( , ) , , ( ) ( )

( , ) ( , ) , , ( ) ( )

H H

F F

H H

F F

S z n S z n coh z z n z z dz dz

S z n S z n coh z z n z z dz dz

(2.91)

2 ( )fS n

28

( )z ( ) zz

H

( )z

( ) zzH

Holmes (1987) 2

1. (low correlation) z

1 2, , 1coh z z n 1 2z z 1 2, , 0coh z z n 1 2z z 1 2( , ) ( , ) ( )F F FS z n S z n S n 2.91

1 2 1 1 2 2

0 02

1 2 1 1 2 20 0

( ) ( , , ) ( ) ( )

( ) ( , , ) ( ) ( )

H H

F

H H

F

S n coh z z n z dz z dz

S n coh z z n z dz z dz

2 2 20

2 2 20

( ) ( ) ( )

( ) ( ) ( )

H

F

H

F

S n z z dz

S n z z dz

2

0

2

0

( )

( )

H

H

z dz

z dz

(2.92)

29

( ), ( )z z 2.92

2 32 1

(2.93)

2.93 2 low correlation

2. (high correlation)

z

1 2, , 1coh z z n 1 2( , ) ( , ) ( )F F FS z n S z n S n

2.91

1 1 2 20 02

1 1 2 20 0

( ) 1 ( ) ( )

( ) 1 ( ) ( )

H H

F

H H

F

S n z dz z dz

S n z dz z dz

2

02

0

( ) ( )

( ) ( )

H

F

H

F

S n z dz

S n z dz

2

02

0

( )

( )

H

H

z dz

z dz

(2.94)

( ), ( )z z 2.94 2

2 21

(2.95)

30 2.95 2 high correlation

2.6 2 low correlation high

correlation

2.6 (Holmes (1987)) 2.96 Holmes (1987)

20

43 1

(2.96)

Holmes (1987) ( )

Power law exponent of mode shape,

Mode

shap

e corr

ectio

n fac

tor

31 Xu and Kwok (1993) 2 Boggs (1989) ( )A z ( )B t

( , ) ( ) ( )F z t A z B t

0( ) H zA z A H Xu and Kwok (1993) 0 1

0 2

02

2( , ) ( )F H BzS z n A S nH

(2.97) 2.97 2.17

0 0

0 0

1 21 2 1 2 1 2

2 0 0

1 21 2 1 2 1 2

0 0

, , ( ) ( )

, , ( ) ( )

H H

H H

z z coh z z n z z dz dzH Hz z coh z z n z z dz dzH H

(2.98)

1. (low correlation)

1 2, , 1coh z z n 1 2z z 1 2, , 0coh z z n 1 2z z

2.98

0

0

22

2 02

2

0

( )

( )

H

H

z z dzHz z dzH

(2.99)

32

2 0 1 ( ), ( )z z 2.99

2 2 32 2 1

(2.100)

2.100 2 low correlation

2 0 2 ( ), ( )z z 2.99

2 4 34 2 1

(2.101)

2.101 2 low correlation 2. (high correlation)

1 2, , 1coh z z n 2.98

0 0

0 0

1 21 1 2 2

0 02

1 21 1 2 2

0 0

( ) ( )

( ) ( )

H H

H H

z zz dz z dzH H

z zz dz z dzH H

2

02

0

( )

( )

H

H

z z dzH

z z dzH

(2.102)

33 2 0 1 2.102

2

2 21

(2.103)

2.103 2 high correlation 2 0 2 2.102

2

2 2 22 1

(2.104)

2.104 2 high correlation

2.7 2.10 2 Holmes (1987) Xu and- Kwok (1993) 0.14, 0.25 0.36

34

2.7 2 0.14

2.8 2 0.25

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Mod

e sh

ape

corr

ecti

on f

acto

r (2

)

Power law exponent of mode shape ()

=0.14,alongwind

XuKwok L

XuKwok H

Holmes L

Holmes H

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Mod

e sh

ape

corr

ecti

on f

acto

r (2

)


=0.25,alongwind

XuKwok L

XuKwok H

Holmes L

Holmes H

35

2.9 2 0.36

2.10 2 0.14

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Mod

e sh

ape

corr

ecti

on f

acto

r (2

)


=0.36,alongwind

XuKwok L

XuKwok H

Holmes L

Holmes H

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Mod

e sh

ape

corr

ecti

on f

acto

r (2

)


=0.14,acrosswind

XuKwok L

XuKwok H

Holmes L

Holmes H

36

2.11 2 0.25

2.12 2 0.36

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Mod

e sh

ape

corr

ecti

on f

acto

r (2

)


=0.25,acrosswind

XuKwok LXuKwok HHolmes L

Holmes H

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Mod

e sh

ape

corr

ecti

on f

acto

r (2

)


=0.36,acrosswind

XuKwok L

XuKwok H

Holmes L

Holmes H

37

2 Holmes 2 Xu and Kwok 2.6 2.9 1 2 1 1 2 1

1 2 Holmes 2 Xu and Kwok 1 2 Xu and Kwok 2 Holmes

Xu and Kwok 2 0.14 2 0.25 2 0.36 2 2.6

2.13

2.13

38

Thanun (2006) (Linear regression analysis) 1 2.14

2.14 Thanun (2006)

1.420.701H ; 31.4H m (2.105)

H(m)

(m)

39 UB

1.454.262UB H ; 35.3H m (2.106)

LB

1.47.898LB H ; 27.9H m (2.107)

2.105 2.107

2.106 162% 2.107 62% H

40

3

Thanun (2006) 2 2 (shear type) 1 (flexural type) 1 () 3.2 3.1

1 19 () , 3.1

41

3.1

(m)

Direction

(m) 1

Direction (m) 2

1 26 100 33.0 33.0 2 29 114 23.6 32.7 3 32 128 22.4 65.0 4 36 128 38.2 43.8 5 32 140 33.0 45.0 6 23 80 27.5 50.0 Shanti sadan 75 7 27 88 34.0 37.7 Mahanakohn Gypsum 8 32 130 41.9 41.9 Kasemsun building 9 42 149 15.5 15.5 Baiyoke I 10 27 84 17.0 49.0 Pratunum Plestege 11 22 94 31.0 38.0 EngBuilding 12 30 105 20.8 46.4 13 35 123 20.0 52.8 SM Tower 14 54 210 35.1 38.2 ALL SEASONS

(CRD Tower)

15 27 95 25.5 30.3 ALL SEASONS (Capital Tower)

16 35 123 13.2 25.8 Rattanakosin View Mansion (A)

17 35 123 13.2 25.8 Rattanakosin View Mansion (B)

18 19 80 24.5 44.1 IBM TOWER 19 32 112 13.2 25.8 TWO PACIFIC PLACE

42

3.2 3.1

( ) 1 zzH

(3.1)

( )z z z H 3.1

() x log z

H y

( )log1i z

3.3

(

) 19 38 2 3.2 log 3.1 ()

43

3.1 log 1

31 >1 7

44

() ()

3.2 1 ( 100 )

() ()

3.3 2 ( 114 )

0

4

8

12

16

20

24

0 0.5 1 Measurement 0

4

8

12

16

20

24

0 0.5 1 Measurement

Direction2.030.29

0

4

8

12

16

20

24

28

0 0.5 1 Measurement

Direction10.940.03

04

8

12

16

20

24

28

0 0.5 1 Measurement

Direction2.060.01

Direction1.270.27

45

() ()

3.4 3 ( 128 )

() ()

3.5 4 ( 128 )

0

4

8

12

16

20

24

28

32

0 0.5 1 Measurement

Direction1.250.03

04

8

12

16

20

24

28

32

0 0.5 1 Measurement

Direction2.030.04

04

812162024283236

0 0.5 1 Measurement

Direction1=1.290.03

048121620242832

36

0 0.5 1 Measurement

Direction2=1.230.01

46

() ()

3.6 5 ( 128 )

() ()

3.7 6 ( 80 )

0

4

8

12

16

20

24

28

32

0 0.5 1 Measurement 0

4

8

12

16

20

24

28

32

0 0.5 1 Measurement

Direction2=0.96=0.03

0246810121416182022

0 0.5 1 Measurement


0246810121416182022

0 0.5 1 Measurement



47

() ()

3.8 7 ( 140 )

() ()

3.9 8 ( 130 )

0369121518212427

0 0.5 1 Measurement


0369

121518212427

0 0.5 1 Measurement


0

4

8

12

16

20

24

28

32

0 0.5 1 Measurement


04

8

12

16

20

24

28

32

0 0.5 1 Measurement


48

() ()

3.10 9 ( 149 )

() ()

3.11 10 ( 84 )

0369

1215182124273033363942

0 0.5 1 Measurement


0369

1215182124273033363942

0 0.5 1 Measurement


0369

121518212427

0 0.5 1 Measurement


0369

121518212427

0 0.5 1 Measurement


49

() ()

3.12 11 ( 94 )

() ()

3.13 12 ( 105 )

0

3

6

9

12

15

18

0 0.5 1 Measurement


03

6

9

12

15

18

0 0.5 1 Measurement


036912151821242730

0 0.5 1 Measurement


036912151821242730

0 0.5 1 Measurement


50

() ()

3.14 13 ( 123 )

() ()

3.15 14 ( 210 )

0

5

10

15

20

25

30

35

0 0.5 1 Measurement


05

10

15

20

25

30

35

0 0.5 1 Measurement


06

1218243036424854

0 0.5 1 Measurement


06

1218243036424854

0 0.5 1 Measurement


51

() ()

3.16 15 ( 95 )

() ()

3.17 16 ( 123 )

0369

121518212427

0 0.5 1 Measurement


0369

121518212427

0 0.5 1 Measurement


0

5

10

15

20

25

30

35

0 0.5 1 Measurement


05

10

15

20

25

30

35

0 0.5 1 Measurement


52

() ()

3.18 17 ( 123 )

() ()

3.19 18 ( 80 )

0

5

10

15

20

25

30

35

0 0.5 1 Measurement


05

10

15

20

25

30

35

0 0.5 1 Measurement


02468

1012141618

0 0.5 1 Measurement


02468

1012141618

0 0.5 1 Measurement


53

() () 3.20 19 ( 112 )

0

4

8

12

16

20

24

28

32

0 0.5 1 Measurement


04

8

12

16

20

24

28

32

0 0.5 1 Measurement


54

3.2

Direction 1

Direction 2

1 1.27 0.27 1.03 0.29 2 0.94 0.03 1.06 0.01 3 1.25 0.03 1.03 0.04 4 1.29 0.03 1.23 0.01 5 0.99 0.06 0.96 0.03 6 0.91 0.10 0.85 0.09 7 1.31 0.02 1.37 0.04 8 1.34 0.07 1.32 0.08 9 1.76 0.00 1.68 0.00 10 1.02 0.02 0.72 0.06 11 1.04 0.06 0.87 0.05 12 1.37 0.03 1.50 0.02 13 1.49 0.22 1.32 0.05 14 1.73 0.02 1.51 0.00 15 1.39 0.00 1.20 0.00 16 1.17 0.02 1.09 0.03 17 1.30 0.03 1.39 0.08 18 1.20 0.06 1.38 0.08 19 1.23 0.03 1.22 0.03

55

, 3.2 3.21 3.22

3.21

3.21 14 210.4 1.73 1 2 1.51 3.22 Thanun (2006)

y=0.0041x+0.7592

00.20.40.60.81

1.21.41.61.82

0 50 100 150 200 250Height(m)

56

3.22

3.4

3.2 0.72 1.76 1 1 0.00 - 0.29

y=0.0005x+0.1166

0

0.05

0.1

0.15

0.2

0.25

0.3

0 50 100 150 200 250

Height(m)

57

4

. 1311-50 Davenport (1967) . 1311-50 Davenport (1967) (Quasi-steady theory) (Gust factor),

4.1

, ,

2 ( )( )

f

f

S nS n

(4.1)

( )fS n ( )fS n

( )

2

n Holmes (1987) Xu and Kwok (1993)

58

kk

(4.2)

k k

ff

(4.3)

f f

4.2 4.4

1

ygC g

y (4.4)

y rms y

2.19 2.20 y y

2

0 022 2

( ) 4

f fy

n S nk k (4.5)

fyk

(4.6)

59

f rms

2

0

( )f fS n dn

(4.7) 4.1

2 2

0

( )f fS n dn

(4.8)

2 2 2 f f (4.9) 4.1, 4.2, 4.3, 4.9 4.5 4.6

22

0 022 2 2

( )

4f f

y

n S nk k

(4.10)

fy

k

(4.11)

4.10 4.11 rms y y

y y

(4.12)

y y (4.13)

60

y rms

y 4.12 4.13 4.4

1 ygC gy

(4.14)

4.3

z 4.15 4.16

max maxz y z (4.15)

max max z y z (4.16)

max z max z

z maxy maxy

max gy C y (4.17)

max gy C y (4.18)

61

4.17 4.18 4.15 4.16

max max gg

C zyz zC y z

(4.19) 4.13 4.19

max max

g

g

C zz z

C z

(4.20)

4.4 z 4.21 4.22

2max 02 yz g n z (4.21)

2max 0 2 yz g n z (4.22)

g peak factor 0.57722ln2ln

vTvT

4.21 4.22

max max y

y

zz z

z

(4.23)

62

4.12 4.23

max max zz z

z

(4.24)

4.5 4.14, 4.20 4.24 z z z z

zz

H (4.25)

1 zz

H

(4.26)

4.2

20

0

20

0

2

2

H

H

n m z dz

n m z dz

(4.27)

m

63

m

0

0

H

H

z dz

z dz

(4.28)

4.25 4.26 4.28

2

2 2 1 131 2 1

(4.29)

1 2.40

221 ( )

2

H

H pzf U C W z dzH

(4.30)

2

21 ( )2

H

H pzf U C W z dzH

(4.31)

4.3

2

02

0

H

H

z z dzHz z dzH

(4.32)

64

4.25 4.26 4.32

12 22 1 2 1

(4.33)

1 21 2 1 2 1 2

0 0

( ) ( , , ) ( ) ( )H H

fz zS n coh z z n z z dz dzH H

(4.34) 1 2

1 2 1 2 1 20 0

( ) ( , , ) ( ) ( )H H

fz zS n coh z z n z z dz dzH H

(4.35) 4.1

1 21 2

0 0

1 21 2

0 0

1 2 1 22

1 2 1 2

( , , )

( , , )

H H

H H

z zdz dz

H H

z zdz dz

H H

coh z z n z z

coh z z n z z

(4.36)

1 2( , , )coh z z n 1z 2z n

Holmes (1987)

2 (low correlation) (high correlation)

1 2, , 1coh z z n 1 2z z 1 2, , 0coh z z n 1 2z z

65

2 2

2 02

2

0

( )

( )

H

H

z z dzHz z dzH

(4.37)

4.25 4.26 4.37

222 2 1 12 3

2 1 2 1 2 2 1L

(4.38)

1 2, , 1coh z z n

2

022

0

H

HH

z z dzH

z z dzH

(4.39)

4.25 4.26 4.39

2

22 121 1H

(4.40)

66

low correlation high correlation L H L H

1

2 L H

(4.41)

1 2,C C 3C

1C

(4.42)

2C

(4.43)

3C

(4.44)

4.14, 4.20 4.24

11

ygC g C

y (4.45)

max 2 max

g

g

C zz C z

C z (4.46)

max 3 max

zz C zz

(4.47)

67

4.29, 4.33, 4.38 4.40 1 2,C C 3C

22

1

2 1 11 12 3 22 2 1 2 1 2 2 1 1 1

12 2

2 1 2 1

C

(4.48)

2 22

12 2

2 1 2 1

2 1 13

1 2 1

C

(4.49)

22

3 22

2 1 11 12 3 22 2 1 2 1 2 2 1 1 1

2 1 13

1 2 1

C

(4.50) 4.6

1 2,C C 3C 0 0.40 0.5, 1 2 4.1 4.3 1C 0.5, 1 2 ( = 0.14) ( = 0.25) ( = 0.36)

68

4.1 1C ( = 0.14)

4.2 1C ( = 0.25)

0.600

0.700

0.800

0.900

1.000

1.100

1.200

1.300

1.400

0.000 0.100 0.200 0.300 0.400

C1

B=0.5

B=1

B=2

0.5 1 2

0.600

0.700

0.800

0.900

1.000

1.100

1.200

1.300

1.400

0.000 0.100 0.200 0.300 0.400

C1

B=0.5

B=1

B=2

0.5 1 2

69

4.3 1C ( = 0.36)

1C 4.1 4.3 1C = 0.14, 0.25, 0.36

= 0 1C 4.4 4.6 2C = 0.5, = 1 =

2

0.600

0.700

0.800

0.900

1.000

1.100

1.200

1.300

1.400

0.000 0.100 0.200 0.300 0.400

C1

B=0.5

B=1

B=2

0.5 1 2

70

4.4 2C ( = 0.14)

4.5 2C ( = 0.25)

0.400

0.500

0.600

0.700

0.800

0.900

1.000

1.100

1.200

1.300

1.400

0.000 0.100 0.200 0.300 0.400

C2

B=0.5

B=1

B=2

0.5 1 2

0.400

0.500

0.600

0.700

0.800

0.900

1.000

1.100

1.200

1.300

1.400

0.000 0.100 0.200 0.300 0.400

C2

B=0.5

B=1

B=2

0.5 1 2

71

4.6 2C ( = 0.36)

4.4 4.6 = 0.5, = 1 = 2 = 2 1 2C = 0

4.7 4.9 3C = 0.5, = 1 = 2

0.400

0.500

0.600

0.700

0.800

0.900

1.000

1.100

1.200

1.300

1.400

0.000 0.100 0.200 0.300 0.400

C2

B=0.5

B=1

B=2

0.5 1 2

72

4.7 3C ( = 0.14)

4.8 3C ( = 0.25)

0.400

0.500

0.600

0.700

0.800

0.900

1.000

1.100

1.200

1.300

1.400

0.000 0.100 0.200 0.300 0.400

C3

1 0.5

2

0.400

0.500

0.600

0.700

0.800

0.900

1.000

1.100

1.200

1.300

1.400

0.000 0.100 0.200 0.300 0.400

C3

0.5 1 2

73

4.9 3C ( = 0.36)

3C 3 = 0.5, = 1

= 2 3C = 0 4.1 4.9 = 0 1 2,C C 3C 4.7 = 0

4.6 = 0

0 1 2,C C 3C = 0

0.400

0.500

0.600

0.700

0.800

0.900

1.000

1.100

1.200

1.300

1.400

0.000 0.100 0.200 0.300 0.400

C3

0.5 1 2

74

= 0 1 2,C C 3C 4.48, 4.49 4.50

11 2 3 2 2 12 2 2 1 1 2 2

C

(4.51)

2

2 2 2 12 1 3

C (4.52)

31 2 3 2 2 12 2 2 1 1 3

C

(4.53)

4.54

1 23 4

a aCa a (4.54)

1a 4a

1a 4a 4.55 4.63

11.6 2.05

1.37 2.28C

(4.55)

24.56 2.28

3 3.84C

(4.56)

3

3.2 1.61.8 3

C (4.57)

75

11.5 2.251.25 2.5

C (4.58)

25 2.53 4.5

C (4.59)

3

3 1.51.5 3

C (4.60)

11.5 2.58

1.36 2.72C

(4.61)

25.44 2.72

3 5.16C

(4.62)

3

3 1.51.5 3

C

(4.63)

4.10, 4.11 4.12 1 2,C C 3C 4.51 4.53 4.55 4.63

76

4.10 1 2 3, ,C C C ( = 0.14)

4.11 1 2 3, ,C C C ( = 0.25)

0.4000.5000.6000.7000.8000.9001.0001.1001.2001.3001.4001.5001.600

0.000 0.500 1.000 1.500 2.000 2.500

C1,4.51C2,4.52C3,4.53C1,4.55C2,4.56C3,4.57

0.4000.5000.6000.7000.8000.9001.0001.1001.2001.3001.4001.5001.600

0.000 0.500 1.000 1.500 2.000 2.500

C1,4.51C2,4.52C3,4.53C1,4.58C2,4.59C3,4.60

77

4.12 1 2 3, ,C C C ( = 0.36)

4.10 4.12 1. 1 2 3, ,C C C

1 2 3, ,C C C ( = 0.36) 2. 1 2 3, ,C C C 3

- 1 1 2 3, ,C C C 1 - 1 1 2 3, ,C C C 1 - 1 1 2 3, ,C C C 1 1 2 3, ,C C C

1 1 2 3, ,C C C

0.4000.5000.6000.7000.8000.9001.0001.1001.2001.3001.4001.5001.600

0.000 0.500 1.000 1.500 2.000 2.500

C1,4.51C2,4.52C3,4.53C1,4.61C2,4.62C3,4.63

78

4.8 . 1311-50

4.6 max ,gC z max z max ,gC z max z

4.7 0 1 1 2 3, ,C C C 1 1

1 zzH

(4.64)

4.64 1 4.45 1C 4.55, 4.58 4.61 gC

1 1gC g C

(4.65)

y

y

. 1311-50 1C 4.55, 4.58, 4.61

11.6 2.05

1.37 2.28C

(4.66)

79

11.5 2.251.25 2.5

C (4.67)

11.5 2.58

1.36 2.72C

(4.68)

4.25 4.26 0 4.46

1max 2 max g

g

C zz C zC H

(4.69)

max z 3-12 . 1311-50

2

1

max 2 2 2 20

3 24

W H eH g pg

g B

H I q C C CC zz CC H n D H

(4.70)

2

1

max 2 2 2 20

32

4

W H eH g p

B

H I q C C Czz CH n D H

(4.71)

80

max

.

2

max 2 2 2 20

32

4

W H eH g p

B

H I q C C CH C

n D H

(4.72)

2C 3

24.56 2.28

3 3.84C

(4.73)

25 2.53 4.5

C (4.74)

25.44 2.72

3 5.16C

(4.75)

4.25 4.26 0 4.47

1max 3 max zz C zH

(4.76)

81

3-13 . 1311-50 4.76

1 max2 2max 3 4 sD peH D g

zK Fzz C n gH C C

(4.77)

4.69 max z gC

1max max

2

g g

z z HC C C z

(4.78)

4.78 4.77

max2 23max

2

4 D peH D g

zC KsFz n gC C C

(4.79)

2C 3C 4.43 4.44

3

12

C CC

(4.80)

z

max2 2max 1 4 D p

eH D g

zKsFz C n gC C

(4.81)

1C 4.66 4.68

82

max

max2 2max 1 4 D p

eH D g

HKsFH C n gC C

(4.82)

4.1 .13111-50 Da . 1311-50

4.1 , ,g DC a

1g pC g

11g pC g C

2

2 2 20

32

4

W H eH g p

B

H I q C C C

n D H

2

2

2 2 20

324

W H eH g p

B

HC I q C C C

n D H

2 24D D peH D g

KsFa n gC C

2 21 4D D p

eH D g

KsFa C n gC C

1C 2C 4.2

4.2 1C 2C

1C 11.6 2.05

1.37 2.28C

11.5 2.251.25 2.5

C 1

1.5 2.581.36 2.72

C

2C 24.56 2.28

3 3.84C

25 2.53 4.5

C 2

5.44 2.723 5.16

C

83

4.3 1C 2C

1C 2C 1C 2C 1C 2C

1.0 1.00 1.00 1.00 1.00 1.00 0.98 1.1 1.01 1.02 1.01 1.03 1.00 1.01 1.2 1.01 1.04 1.01 1.05 1.01 1.04 1.3 1.02 1.06 1.02 1.07 1.01 1.07 1.4 1.02 1.08 1.02 1.09 1.01 1.09 1.5 1.03 1.09 1.03 1.11 1.01 1.11 1.6 1.03 1.11 1.03 1.13 1.02 1.13 1.7 1.03 1.12 1.04 1.15 1.02 1.15 1.8 1.04 1.14 1.04 1.16 1.02 1.17 1.9 1.04 1.15 1.05 1.18 1.02 1.19 2.0 1.05 1.16 1.05 1.19 1.03 1.21

84

4.9

4.13

180 30 45 200 0.25 / 0.015 25 / 1

pC = 1.3 4.4 4.5 1C 2C 4.2

y

x 45

30

85

4.4

. 1311-50

eHC 3-1, 3-2, 3-3 2.25 1.88 1.45

HV 3-5 37.47 34.3 30.14

B 3-6 0.62 0.62 0.62

s 3-7 0.083 0.073 0.060

0x 3-10 8.14 8.89 10.12

F 3-8 0.24 0.23 0.21

v 3-11 0.21 0.20 0.19 pg 3-9 3.80 3.79 3.77

K 3-5 0.08 0.10 0.10

3-5 0.264 0.304 0.318

4.5 1C 2C

1C 2C 1C 2C 1C 2C

1.0 1.00 1.00 1.00 1.00 1.00 0.98 1.5 1.03 1.09 1.03 1.11 1.01 1.11 2.0 1.05 1.16 1.05 1.19 1.03 1.21

4.4 4.5 4.1

,gC Da 4.6

86

4.6 , ,g DC a

gC

(m) Da

(m/s2) gC (m)

Da (m/s2)

gC (m)

Da (m/s2)

1.0 2.00 0.1015 0.0948 2.15 0.0833 0.0883 2.20 0.0594 0.0698 1.5 2.03

(+1.33%) 0.1125

(+10.81%) 0.1064

(+12.25%) 2.18

(+1.53%) 0.0940

(+12.81%) 0.1009

(+14.29%) 2.22

(+0.80%) 0.0677

(+14.03%) 0.0801

(+14.78%) 2.0 2.05

(+2.29%) 0.1203

(+18.51%) 0.1148

(+21.16%) 2.21

(+2.67%) 0.1018

(+22.23%) 0.1103

(+25.00%) 2.23

(+1.40%) 0.0739

(+24.44%) 0.0879

(+25.87%)

4.6 ,gC Da gC 3% Da 24.44% 25.87%

87

5

. 1311-50 Xu and Kwok (1993) . 1311-50 AIJ 2004 High Frequency Force Balance (HFFB) Tamura Boggs (1989) ( )A z ( )B t Xu and Kwok (1993) n . 1311-50 (2556) , z

5.1 ,

2 ( )( )

f

f

S nS n

(5.1)

88

( )fS n ( )fS n

( )

2

n Holmes (1987) Xu and Kwok (1993)

4 , ,w w LC a P (5.2)

k k

5.2

z 5.3 5.4

max maxz y z (5.3)

max max z y z (5.4)

max z max z

z maxy maxy max( )y

max yy g (5.5)

max yy g (5.6)

89

maxy maxy

2

0 022 2

( ) 4

f fy

n S nk k (5.7)

f rms 1

2

0

( )f fS n dn

(5.8)

5.1 5.8

2 20

( )f fS n dn

(5.9)

2 2 2 f f (5.10)

5.1, 5.2 5.10 5.7

22

0 022 2 2

( )

4f f

y

n S nk k

(5.11)

0 0

2 2

( ) ( )f Mf M

nS n nS n (5.12)

90

0MS n ( )M t 2M ( )M t LR

4

LL

FR (5.13)

LF

0 02( )M

LM

n S nF (5.14)

5.12, 5.13 5.14 rms 5.11

2 22

2 0 02 2 2 2

( )4

MM My

M

n S nk k

0 02 2( ) 1

4MM

yM

n S nk k

1My LRk

(5.15)

20

H

m m z z dz (5.16)

m z z

91

5.16 m BWD

3

BWDHm (5.17)

202k n m (5.18)

0n 5.17 5.18

202 3BWDHk n (5.19)

LC

2

2M

LH

Cq WH (5.20)

Hq 212 HU

5.19, 5.20 5.15

2 2

0

3 14

H Ly L

B

q C Rn D

(5.21)

92

5.21 rms

y y (5.22)

5.5, 5.6 5.3, 5.4

max max y

y

zz z

z

(5.23)

5.22 5.23

max max

zz z

z

(5.24)

5.3 z 5.25 5.26

max maxz y z (5.25)

max max z y z (5.26)

max max,y y

93

5.22 5.23

max yy g (5.27)

max yy g (5.28)

,y y rms

1

2 4 2 y y

4 0 00 2 ( )

2 4fn S nnk

(5.29)

5.12, 5.13 5.14 5.29

4 2 2 2

0 0 022 2 2 2

2

4f M

yM

n n S nk

2 20 4 My Ln Rk

(5.30)

5.19, 5.20 5.30

3 H Ly LB

q C RD

(5.31)

94

5.31 rms y

y y (5.32)

5.27, 5.28 5.25, 5.26

max max y

y

zz z

z

(5.33)

5.32 5.33

max max

zz zz

(5.34)

5.4 z z 5.35 5.36

max( ) eF z k z

(5.35)

max ( ) eF z k z

(5.36)

ek z 5.24, 5.35 5.36

( ) ( )

zF z F z

z

(5.37)

95

5.5 5.24, 5.34 5.37 z z z z

zz

H (5.38)

1 zz

H

(5.39)

5.2

20

0

20

0

2

2

H

H

n m z dz

n m z dz

(5.40)

m

0

0

H

H

z dz

z dz

(5.41)

5.38 5.39 5.41

22 2 1 131 2 1

(5.42)

96

Boggs (1989) ( )A z ( )B t ( , ) ( ) ( )F z t A z B t

0( ) H zA z A H Xu and Kwok (1993) 0 2

02

2( , ) ( )F H BzS z n A S nH

(5.43)

,FS z n z n ( )BS n n

1 2 1 2 1 2 1 20 0

( ) ( , ) ( , ) ( ) ( ) ( , , )H H

f F FS n S z n S z n z z coh z z n dz dz (5.44) 5.43 5.44

0 0

0 0

1 21 2 1 2 1 2

2 0 0

1 21 2 1 2 1 2

0 0

, , ( ) ( )

, , ( ) ( )

H H

H H

z z coh z z n z z dz dzH Hz z coh z z n z z dz dzH H

(5.45)

Xu and Kwok (1993)

2 (low correlation) (high correlation)

97

1 2, , 1coh z z n 1 2z z 1 2, , 0coh z z n 1 2z z 5.45

0

0

22

2 02

2

0

( )

( )

H

H

z z dzHz z dzH

(5.46)

0 2 5.38, 5.39 5.46

22

2 2 1 14 34 1 4 1 4 2 1L

(5.47)

1 2, , 1coh z z n

2

022

0

( )

( )

H

H

z z dzH

z z dzH

(5.48)

98

0 2 5.38, 5.39 5.48

2

22 12 22 1 2 1H

(5.49)

low correlation high correlation L H L H

1

2 L H

(5.50)

4C

4C

(5.51)

5.24, 5.34 5.37

max 4 max

zz C zz

(5.52)

max 4 max

zz C zz

(5.53)

4

( ) ( )

zF z C F z

z (5.54)

99

5.42, 5.47 5.49 4C

22

4 22

2 1 11 14 3 2 22 4 1 4 1 4 2 1 2 1 2 1

2 1 13

1 2 1

C

(5.55)

5.6

4C 0 0.40 0.5, 1.0 2.0

5.1 5.3 4C = 0.5, = 1 = 2 ( = 0.14) ( = 0.25) ( = 0.36)

100

5.1 4C ( = 0.14)

5.2 4C ( = 0.25)

0.500

0.600

0.700

0.800

0.900

1.000

1.100

1.200

1.300

1.400

0.000 0.100 0.200 0.300 0.400

C4

0.5

2 1

0.500

0.600

0.700

0.800

0.900

1.000

1.100

1.200

1.300

1.400

0.000 0.100 0.200 0.300 0.400

C4

1 2

0.5

101

5.3 4C ( = 0.36)

5.1 5.3 4C = 0.5, = 1 = 2 = 2 1 4C

= 0 4C

5.7 0

5.6 0 0 4C = 0

= 0 4C 5.55

4 4 31 2 2 2 12 4 2 1 2 1 3C

(5.56)

0.500

0.600

0.700

0.800

0.900

1.000

1.100

1.200

1.300

1.400

0.000 0.100 0.200 0.300 0.400

C4

0.5 1 2

102

4C 5.57

1 23 4

a aCa a (5.57)

1a 4a

1a 4a 5.58 5.60

4 3 1.51.5 3C (5.58)

4 2.9 1.451.35 3C (5.59)

4 2.8 1.41.2 3C (5.60)

5.4, 5.5 5.6 4C 5.56 5.58 5.60

103

5.4 4C ( = 0.14)

5.5 4C ( = 0.25)

0.4000.5000.6000.7000.8000.9001.0001.1001.2001.3001.4001.5001.600

0.000 0.500 1.000 1.500 2.000 2.500

C4,5.56C4,5.58

0.4000.5000.6000.7000.8000.9001.0001.1001.2001.3001.4001.5001.600

0.000 0.500 1.000 1.500 2.000 2.500

C4,5.56C4,5.59

104

5.6 4C ( = 0.36)

5.4 5.6 4C 4C 1 4C

5.8 . 1311-50

5.6

max max ,z z F z max max ,z z F z 5.7 0 1 4C 1 1

0.4000.5000.6000.7000.8000.9001.0001.1001.2001.3001.4001.5001.600

0.000 0.500 1.000 1.500 2.000 2.500

C4,5.56C4,5.60

105

1 zzH

(5.61)

5.61 1 5.38, 5.39 0 5.52

1max 4 max zz C zH

(5.62)

(2556) . 1311-50

'max 2 2

0

3 14H L L L

B

q C g Rz

n D

(5.63)

max z 5.63 . 1311-50

1 'max 4 2 20

3 14H L L L

B

q C g Rzz CH n D

(5.64)

max

.

'

max 4 2 20

3 14H L L L

B

q C g RC

n D (5.65)

4C 5.58 5.60

106

5.38, 5.39 0 5.53

1max 4 max zz C zH

(5.66)

4-11 . 1311-50 5.66 z

1max 4 3 H L L L

B

q C gzz C RH D

(5.67)

4C 5.58 5.60

max

max 4 3 H L L LB

q C gH C RD

(5.68)

5.38, 5.39 0 5.54

1

4 ( ) ( )zF z C F z

H

(5.69)

(2556) z . 1311-50

' ( ) 3 1H L L LF z q C g R (5.70)

107

5.70 . 1311-50 5.69 z

1'

4 ( ) 3 1H L L L

zF z C q C g RH

(5.71)

5.1 .13111-50 w (2556) wa . 1311-50

( )F z 5.1 , ,w w La P

'

2 20

3 14

w H L L Lw

B

I q C g Rn D

'

4 2 20

3 14

w H L L Lw

B

I q C g RC

n D

3 w H L Lw L

B

I q C ga RD 4 3 w H L Lw L

B

I q C ga C RD

'3 1L W H L L LzP I q C g A RH

1

'4 3 1L W H L L L

zP C I q C g A RH

4C 5.2 5.3

5.2 4C

4C 4 3 1.51.5 3C 4

2.9 1.451.35 3

C 4

2.8 1.41.2 3

C

108

5.3 4C

4C

1.0 1.00 1.00 1.00 1.1 1.03 1.03 1.04 1.2 1.06 1.07 1.07 1.3 1.09 1.10 1.11 1.4 1.12 1.13 1.14 1.5 1.14 1.15 1.17 1.6 1.17 1.18 1.20 1.7 1.19 1.20 1.22 1.8 1.21 1.23 1.25 1.9 1.23 1.25 1.27 2.0 1.25 1.27 1.30

109

5.9

5.7 180 30 45 200 0.25 / 0.015 25 /

1 5.4

y

x 45

30

110

5.4

. 1311-50

eHC 3-1, 3-2, 3-3 2.25 1.88 1.45

HV 3-5 37.47 34.30 30.14

Hq 4-2 877.48 735.3 567.66 'LC 4-3 0.198 0.198 0.198

1 4-7 0.367 0.367 0.367 1 4-9 2.313 2.526 2.875 LF 4-6 0.119 0.095 0.070

LR 4-15 6.23 5.00 3.66

Lg 4-14 3.79 3.79 3.79 5.59 4C 5.5

5.5 4C

4C

1.0 1.00 1.00 1.00 1.5 1.14 1.15 1.17 2.0 1.25 1.27 1.30

5.4 5.5 ,w wa LP 5.1 5.6 = 1.0

111

5.6 , , ( )w w La p H

(m)

wa (m/s2)

( )Lp H(N/m2)

(m)

wa (m/s2)

( )Lp H(N/m2)

(m)

wa (m/s2)

( )Lp H(N/m2)

1.0 0.280 0.410 3535 0.214 0.308 2698 0.145 0.204 1837 1.5 0.320

(+14.29%) 0.469

(+14.29%) 4040

(+14.29%) 0.247

(+15.42%) 0.355

(+15.42%) 3114

(+15.42%) 0.170

(+16.67%) 0.238

(+16.67%) 2143

(+16.67%) 2.0 0.350

(+25%) 0.513

(+25%) 4419

(+25%) 0.272

(+27.19%) 0.392

(+27.19%) 3432

(+27.19%) 0.188

(+29.63%) 0.264

(+29.63%) 2381

(+29.63%)

5.6 , , ( )w w La p H 4C

112

6

6.1

. 1311-50

( ) (1 )( )zz

H (6.1)

z H 6.1 1311-

50 = 0 >1 1

() 19 3 0.00 0.29 0.72 - 1.76

113

6.1.1 4.6

=0 4.7 =0 1

=1 1 >1 () , ,gC Da 4.1 1C 2C 4.2 4.3

4.1 , ,g DC a

1g pC g

11g pC g C

2

2 2 20

32

4

W H eH g p

B

H I q C C C

n D H

2

2

2 2 20

324

W H eH g p

B

HC I q C C C

n D H

2 24D D peH D g

KsFa n gC C

2 21 4D D p

eH D g

KsFa C n gC C

1C 2C 4.2

114

4.2 1C 2C

1C 11.6 2.051.37 2.28

C 1

1.5 2.251.25 2.5

C 1

1.5 2.581.36 2.72

C

2C 24.56 2.283 3.84

C 2

5 2.53 4.5

C 2

5.44 2.723 5.16

C

4.3 1C 2C

1C 2C 1C 2C 1C 2C

1.0 1.00 1.00 1.00 1.00 1.00 0.98 1.1 1.01 1.02 1.01 1.03 1.00 1.01 1.2 1.01 1.04 1.01 1.05 1.01 1.04 1.3 1.02 1.06 1.02 1.07 1.01 1.07 1.4 1.02 1.08 1.02 1.09 1.01 1.09 1.5 1.03 1.09 1.03 1.11 1.01 1.11 1.6 1.03 1.11 1.03 1.13 1.02 1.13 1.7 1.03 1.12 1.04 1.15 1.02 1.15 1.8 1.04 1.14 1.04 1.16 1.02 1.17 1.9 1.04 1.15 1.05 1.18 1.02 1.19 2.0 1.05 1.16 1.05 1.19 1.03 1.21

180 1 4.9 gC 3 Da

115

6.1.2 5.6

=0 5.7 =0 1

=1 1 >1 () ,w wa LP 5.1 4C 5.2 5.3

5.1 , ,w w La P

'

2 20

3 14

w H L L Lw

B

I q C g Rn D

'

4 2 20

3 14

w H L L Lw

B

I q C g RC

n D

3 w H L Lw L

B

I q C ga RD 4 3 w H L Lw L

B

I q C ga C RD

'3 1L W H L L LzP I q C g A RH

1

'4 3 1L W H L L L

zP C I q C g A RH

4C 5.2 5.3

116

5.2 4C

4C 4 3 1.51.5 3C 4

2.9 1.451.35 3

C 4

2.8 1.41.2 3

C

5.3 4C

4C

1.0 1.00 1.00 1.00 1.1 1.03 1.03 1.04 1.2 1.06 1.07 1.07 1.3 1.09 1.10 1.11 1.4 1.12 1.13 1.14 1.5 1.14 1.15 1.17 1.6 1.17 1.18 1.20 1.7 1.19 1.20 1.22 1.8 1.21 1.23 1.25 1.9 1.23 1.25 1.27 2.0 1.25 1.27 1.30

117

6.2

4.1 5.1 2 (Low correlation L ) (High correlation H ) L H L H 4.41 5.50

118

(2550). (.1311-50). : ...

, . (2548). . :

NBCC (2005). National Building Code of Canada. Canadian Commission on Building and Fire Codes. National Research Council of Canada. Ottawa. Canada.

Dyrbye, Clae s and Hansen, Svend Ole (1996). Wind Loads on Structures. John Wiley & Sons, Chichester, van der Hoven

AIJ (2004), Recommendation for Loads on Building. Architectural Institute of Japan

. (2556). . 18

Boggs, D.W. and Peterka, J.A. (1989). Aerodynamic Model Tests of Tall Buildings. J. Struct. Div., ASCE. Vol. 115, No. 3. page 618-635

Davenport, A.G. (1960). Wind Load on Structure. Technical Paper No.88. Canada : Division of Building Research. National Research Council

Davenport, A.G. (1961). The Spectrum of Horizontal Gustiness Near the Ground in High Winds Q.J.Roy Met. Soc.. Vol. 87. 194-211

Davenport, A. G. (1967). Gust loading factors. J. Struct. Div.ASCE,93(3). 11-34 Davenport, A.G. (1975). Perspective on the full-sclae measurement of wind effect.

Journal of Industrial Aerodynamic. 1,23-54

119

Holmes, J.D. (1987). Mode shape corrections for dynamic response to wind. Eng. Struct., Vol. 9. page 210-212

Tallin, A.D., and Ellingwood, B.R. (1985). Analysis of torsion moments on tall buildings. Journal of Wind Engineering and Industrial Aerodynamics. 18 . page 191-195

Tamura, Y.,et al. (1996). Wind load and wind-induced response estimations in the Recommendations for Loads on Buildings. AIJ 1993. Engineering Structures., Vol. 18. No. 6.page 399-411

Tschanz, T., Davenport A.G (1983) , The base balance technique for the determination of dynamic wind loads, Journal of Wind Engineering and Industrial Aerodynamics 13 : page 429-439.

Xu, Y.L. and Kwok, K.C.S. (1993). Mode shape corrections for wind tunnel tests of tall buildings. Eng. Struct., Vol 15. No.5. pp.387-392

Petcharoen, C. (2002). Identification of dynamic properties of low and medium-rise buildings in Bangkok by an ambient vibration method., Master thesis . No. ST02-14. Asian Institute of technology

Thanun, S. (2006). Effect of pile foundation flexibility on the dynamic characteristics of multi-story building in Bangkok., Master thesis. No. ST06-14. Asian Institute of technology

121

.1311-50

1.

1 1 ( ) ( )gF z C F z (.1)

1( )F z

211( ) ( )2 p

F z U z C W (.2)

1( )F z z ( )U z pC (externalpressure coefficient) 1.3 .1311-50 ( )U z

0( ) ( )eU z U C z (.3)

0U

122 eC (exposure factor) 3 A eC (.4)

[.(3-1)] 0.2810ezC

(.4)

B eC (.5)

[.(3-2)] 5.07.12

5.0

zCe (.5)

C 50 4 eC (.6)

[.(3-3)] 0.720.430ezC (.6)

gC

[.(3-4)]

pg gC 1 (.7)

pg (statistical peak factor)

123 (root-mean-square- loading effect) (mean loading- effect) (.8)

[.(3-5)] )(DeH

sFBCK

(.8)

K 0.08 A 0.10 B 0.14 C B (background turbulence factor) ( HW ) (.9) s (size reduction factor) (.10) Dn (fundamental natural frequency in along-wind direction) (Hz)

HnD

44

124 F (gust energy ratio at the natural frequency of the- structure) (.11)

D (damping ratio) 0.005 0.015

v (average- fluctuation rate) (Hz) (.14) FsB ,, pg

[.(3-6)] dzzz

zWzHB

H

342

914

0 1122

1

1

4571

134 (.9)

[.(3-7)] 1 18 103 1 13

D D

H H

s n H n WU U

(.10)

[.(3-8)] 34202

0

1 x

xF

(.11)

[.(3-9)] vT

vTge

ep log2577.0log2 (.12)

[.(3-10)] H

D

Vnx 12200 (.13)

125

[.(3-11)] BsF

sFnvD

D (.14) T = 3600 ( )

[.(3-12)] 2

2 2 2

324

w eH g p

D B

H I qC C C

n D H

(.15)

= 0.28 A = 0.36 B = 0.72 C

B (average density of the- building) () 150-300 () q

20

12

q U (.16)

( )Da /2

[.(3-13)] 2 24D D peH D g

KsFa n gC C

(.17)

126 2.

[.(4-1)] '2 ( ) 3 1H L L LzF z q C W g RH (.18)

(: .1311-50 LP A .(4-1)

W ) 2 ( )F z z

Hq

[.(4-2)] 212H H

q U (.19) HU

'LC

(root-mean-square of overturning moment coefficient in across-wind direction) (.20)

[.(4-3)]

WD

WD

WDCL 22.0071.00082.0

23' (.20)

Lg

[.(4-4)] )3600(log2

577.0)3600(log2We

WeL nng (.21)

127 Wn

(Hz)

HnW

44 LR

[.(4-5)]

W

LL

FR 4

(.22)

W W 0.005 0.015

LF WD 3.0 LF (.23) )1( N WD 3.0 LF (2.94) )2( N

[.(4-6)] 22222

1 41

6.014

jjj

jN

j

jjjLF

(.23) 1N 0.3WD 2N 0.3WD

02.085.0

2

1

j j

[.(4-7)] WDWD

WD

WD

WD

WD

WD

12.0

15.05.9182.94.2

3.2

234

24

1

(.24)

128 [.(4-8)] 34.02

28.0WD

(.25)

[.(4-9)] 0.8921 1 0.380.12 WHD W n W

U (.26)

[.(4-10)] 0.85

2 0.56W

H

D W n WU

(.27)

2max( ) 2

[.(4-11)] '3 H L Lw LB

q C ga RD (.28)

129

11 .. 2529

Documents

2558 02 24 FInal Charnchai