Environmental Engineering Reference
In-Depth Information
b width of structure exposed to the wind [m]
c
f
average aerodynamic force coefficient in direction of wind
v
m
(z
e
) average wind speed at effective height z
¼
z
e
(see above)
m
1,x
equivalent mass for fundamental vibration in direction of wind [kg/m]:
Z
L
2
m
ðÞF
1
ðÞ
½
ds
P
j
m
j
P
j
M
j
2
1
2
1
D
z
j
F
F
;
j
;
j
0
m
1
;
x
¼
P
j
D
¼
P
j
D
2
1
;
j
2
1
;
j
Z
L
z
j
F
z
j
F
2
½
F
1
ðÞ
ds
0
(see DIN 1055-4 [12] F.4)
m (s) mass per unit length at location of coordinate s
F
1
(s)
fundamental flexural vibration mode (see DIN 1055-4 [12] F.3):
z
z
s
L
z
h
F
1
ðÞ¼
or
F
1
ðÞ¼
where
z ¼
2 for towers and masts
s; z coordinate s on longitudinal axis of structure or structural member, or height
coordinate z
L; h span L, or height h of structure or structural member
n
1,x
natural frequency for fundamental vibration in direction of wind [Hz] (see above)
Additional damping decrement
d
d
([12] F.5 (4))
Where special measures are provided for increasing the damping (e.g. vibration
dampers),
d
d
is to be calculated with the help of suitable theoretical or experimental
methods.
Aerodynamic force coefficient for towers with a cylindrical cross-section ([12] 12.7.1 (1)):
c
fj
¼
c
f0
;
j
c
l
where
c
f0,j
basic force coefficient for segment j to DIN 1055-4 [12] Figure 19 associated with
Table 11 (see Figure 2.6 associated with Table 2.7)
c
l
slenderness reduction factor to DIN 1055-4 [12] Figure 26 (see Figure 2.7)
Reynolds number ([12] 12.7.1 (2)):
v
b
n
where v m
Re
¼
¼
p
p
q kPa
½
=
s
2
q
=r
¼
40
½
