Page 103 - Dynamic Loading and Design of Structures

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the deck (‘spanwise’) follows the methodology introduced above, but it is usual to include a
further admittance factor which takes account of the width of the deck (‘chordwise’). The
theoretical solution for an aerofoil (Sears’ function) serves well in many cases (Walshe and
Wyatt, 1983). A comparative survey of published formulations is given by Hay (1992). Much
more sophisticated models are available for integration of gust action with the feedback of the
effect of structural motion on the forces, as discussed in section 3.2.5.

3.1.5 Aerodynamic damping

The alongwind response of skeletal structures such as lattice towers is commonly significantly
reduced by aerodynamic damping. The narrowband response is essentially harmonic
(sinusoidal), modulated relatively slowly, and the relative velocity (V+u−y) (wherey=dy/dt is
the velocity of the structure in the downwind direction) thus includes a sinusoidal perturbation.
For a tower of natural frequency n=1 Hz, comprising members of width d=0.3 m and in wind
of mean speed V=30m/s, the reduced velocity VR=V/nd is of order 100 (i.e. the fluid advance
in the duration of one cycle of oscillation is 100 times the significant reference dimension of
the structure). The induced perturbation of the drag force will therefore be closely quasi-static
with amplitude (2y/V)P, given the usual linearization. Examination of the equation of motion
shows this to be equivalent to a viscous damper with coefficient c=2P/V, thus making a
contribution to damping logarithmic decrement

(3.22)

in which use has been made of the standard result . In modal analysis this
becomes

(3.23)

where p and m are the mean load and mass per unit length and µj is the mode shape function.
Equation (3.22) can also be expressed in terms of a Scruton number (eqn (3.31), Section
3.2.2) and reduced velocity VR=V/nd (where d is the reference dimension for the drag
coefficient C ), i.e.
D

(3.24)

For a crosswind motion, the postulate ‘drag coefficient C constant, crosswind C zero’ gives
L
D
damping one-half of this value (cf. the comparison between v and u gust excitation, above).
To show the likely importance, consider a lattice tower of tubular steel members of wall
thickness t, having total mass (M) twice the mass of the members exposed in one face and
total drag coefficient CD=1.2 based on the shadow area (A) of