Environmental Engineering Reference
In-Depth Information
where
n
1
;
x
L
i
z
ðÞ
v
m
z
ðÞ
N
1
;
x
¼
Aerodynamic transfer functions R
h
and R
b
([12] C.3 (8))
These are specified for the fundamental vibration mode with identical sign (defor-
mation in the same direction) and are calculated, starting from R
L
, as follows:
for
1
h
1
2
h
1
e
2
h
R
L
¼
2
>
0
R
L
¼
1
for
¼
0
where
:
6
N
1
;
x
h
L
i
z
ðÞ
4
R
h
¼
R
L
with
h
h
¼
4
:
6
N
1
;
x
b
L
i
z
ðÞ
R
b
¼
R
L
with
h
b
¼
Logarithmic damping decrement
d
([12] F.5)
Estimate of the logarithmic damping decrement for the fundamental flexural vibration
mode to DIN 1055-4 [12] F.5 (1):
d ¼ d
s
þ d
a
þ d
d
Structural damping
d
s
see Table 2.6.
Aerodynamic damping ([12] F.5 (3))
r
b
c
f
2
n
1
;
x
m
1
;
x
v
m
z
ðÞ
d
a
¼
where
r
r¼
1.25 kg/m
3
density of air:
Table 2.6 Structural damping (to DIN 1055-4 [12] F.5 (2))
d
¼a
1
n
1
þb
1
d
s
min
where
n
1
¼ fundamental
exural vibration frequency [Hz].
Parameters a
1
,b
1
,
d
min
to 1055-4 [12] Table F.2 (extract)
Type of structure
a
1
b
1
d
min
Reinforced concrete towers
0.050
0
0.025
Masonry/concrete chimneys
0.075
0
0.030
