Page 104 - Dynamic Loading and Design of Structures

Page 81

that face. This gives

(3.25)

3
With material density ρ=8t/m and illustrative values C =1.2, V=3.2m/s, t=10mm and nj=0.8
D
s
Hz, the aerodynamic damping . A comparable tower of angle section members would
give about twice this value. For buildings, the conditions for the quasi-steady assumption will
be less well satisfied, but aerodynamic damping is also likely to be much less effective due to
the lower ratio of drag to weight. For a typical building with drag coefficient 1.0 and mass 4
2
2
t/m of face area (mass density 400kg/m and alongwind plan dimension 20m, say), V=32 m/s
and nj=0.8 Hz, the above formulation gives
Aerodynamic damping is commonly very important for the vertical or torsional gust
dynamics of bridges. Taking the deck width B as the reference dimension for coefficients and
reduced velocity, for vertical motion

(3.26)

The quasi-steady assumption is, however, significantly non-conservative for dCL/dα If
.
specific wind tunnel data are not available, the theoretical solution for an aerofoil with
harmonic perturbation generally gives a useful approximation (Walshe and Wyatt, 1983). The
effective value dC /dαof at practical frequencies is between 3 and 4. In strong winds a can
L
be significantly larger than s; for example, for a deck of width B=25 m, mass m=15 t/m and
natural frequency 0.5 Hz (typical for span 250m), in a wind of 30 m/s, . The
aerodynamic damping of bridge decks can also be expressed using the ‘derivatives’ as
discussed in Section 3.3.4.

3.2 AERODYNAMIC INSTABILITY

3.2.1 Introduction
‘Aerodynamic instability’ is a very convenient generic term to cover a wide range of dynamic
responses to wind, but means little more than a statement that the response in question is not
sufficiently described in terms of the gust action considered above. There are intrinsically two
distinct mechanisms:

●flow instability excitation, or simple ‘Vortex shedding’;
●aeroelastic excitation.
In the former, the flow pattern is unstable, even when the structure is stationary. In the
common example of a slender prismatic structure such as a chimney, vortices associated with
flow separation from the flanks of the structure grow until they are carried away by the flow.
The latter results from the changes of the aerodynamic