Civil Engineering Reference
In-Depth Information
Applying Equation (6.10) for the Helmholtz resonance frequency and setting
p
0
=10
5
Pa (atmospheric pressure),
ρ
=1.2 kg/m
3
(air density), γ=1.4 (ratio of specific heats) and
ℓ
e
=1.0
√A,
we have the following approximate formula for
n
H
:
(6.12)
where
K
A
is the bulk modulus for air (=γ
p
0
) and
K
B
the volume stiffness of the building
structure (theoretically it is the internal pressure required to double the internal volume).
Equation (6.12) can be used to calculate
n
H
for typical low-rise buildings in Table 6.1
(Vickery, 1986).
Table 6.1 indicates that for the two smallest buildings, the Helmholtz frequencies are
greater than 1 Hz, and hence significant resonant excitation of internal pressure
fluctuations by natural wind turbulence is unlikely. However, for the large arena this
would certainly be possible. However, in this case the structural frequency of the roof is
likely to be considerably greater than the Helmholtz resonance frequency of the internal
pressures and the latter will therefore not excite any structural vibration of the roof (Liu
and Saathoff, 1982). It is clear, however, that there could be an intermediate combination
of area and volume (such as the 'concert hall' in Table 6.1), for which the Helmholtz
frequency is similar to the natural structural frequency of the roof and in a range which
could be excited by the natural turbulence in the wind. However, such a situation has not
yet been recorded.
Table 6.1
Helmholtz resonance frequencies for some typical
buildings
Type
Internal volume
(m
3
)
Opening area
(m
2
)
Stiffness ratio,
K
A
/K
B
Helmholtz
frequency (Hz)
House
600
4
0.2
2.9
Warehouse
5000
10
0.2
1.3
Concert hall
15,000
15
0.2
0.8
Arena (flexible
roof)
50,000
20
4
0.23
6.3
Multiple windward and leeward openings
6.3.1
Mean internal pressures
The mean internal pressure coefficient inside a building with total areas (or effective
areas if permeability is included) of openings on the windward and leeward walls of
A
w
and
A
L
,
respectively, can be derived by using Equation (6.3) and applying mass
conservation. The latter relation can be written for a total of
N
openings in the envelope:
