AERODYNAMIC DERIVATIVES FROM SECTION MODEL DECAYS - Theory of Bridge Aerodynamics - page 293

()

ˆ ½

*
2

N j

PV

§ ·

bc

1

i

jj

°

¦

¨ ¸

=−

ˆ ˆ D

°

¨

22

¸

3

Vc 1 V +

C

′

©

j ij = 1

¹

i

° ° ¾
°

D θ

D

B
PV

(D.27)

()

ˆ

*
3

N j

§ ·

b

1

i

¦

j

¨ ¸

1

°

=−

ˆ ˆ

22 2

D ¨ ¸

Vc 1 V

+ °

j ij 1

C

′

©

=

¹

i

D θ

D

° ¿

B

()

ˆ

½

*
2

HV

§

N j

·

bc

1

i

jj

°

¦

¨ ¸

=−

ˆ ˆ

¨

22

¸

3

C

′ °

Vc

+

1 V

©

j ij 1

¹

L

= i

° ¾ ° L

θ

(D.28)

()

ˆ

*
3

N j

HV § ·

b

1

i

j

¦

¨ ¸

1 =− °

ˆ ˆ ¨

22

¸

2

C

′

Vc 1 V

+ °

©

j ij = 1

¹

L

i

¿

L θ

()

ˆ

*
2

½

N j

AV

§ ·

bc

1

i

jj

¦

°

¨ ¸

=−

ˆ ˆ ¨

22

¸

3

°

C

′

Vc 1 V

+ M

©

j ij = 1

¹

i

° ¾ °

M

θ

(D.29)

()

ˆ

*
3

N j

AV § ·

b

1

i

j

¦

¨ ¸ =−

1

°

ˆ ˆ

¨

22

¸

2

C

′

Vc 1 V

+ °

j ij 1 M

©

=

¹

i

¿

M

θ

It is seen that the indicial functions are determined by the deviation between
aerodynamic derivatives and their quasi-static counterparts, as could be expected. It
should be noted that the aerodynamic derivatives are functions of the reduced velocity
ˆ V , i.e. experimentally they have been determined at various set values of ˆ V . The
determination of the constants

b and c for each of the indicial functions

N j

mDLM
nyz θ

, or
, or

- ® = cs

j

ˆ

b e −

Φ=− ¦ ,

()

s ˆ 1 , will therefore require a multiple task data

mn j

=

¯ j = 1

fitting type of approach. Often

N =

2

will suffice.