Page 109 - Dynamic Loading and Design of Structures

Page 86

with substantial damping derived from interwire friction; the device is thus a simple form of
inertial damper, albeit not optimized as a Tuned Mass Damper (TMD) for any one specific
mode. It is attached near the end of the cable, accepting a reduction of effectiveness overall in
order to avoid the circumstance of coincidence with a node in any of the modes for which
protection is required. Such augmentation of damping is only necessary for such a heavy
2
2
prism (equivalent density about 6t/m for steel spiral strand, 3.5t/m typical for composite
steel and aluminium conductors) because the structural damping at low amplitudes is
exceptionally low; values as low as logarithmic decrement δ=0.003 have been quoted. The
Reynolds number is also unfavourable.

3.2.4 Reynolds number, size number, lock-on

Reynolds number Re=VD/v, has a strong influence on vortex shedding from members where
flow separation takes place from a curved surface. The kinematic viscosity of air
2
−5
v=1.5×10 m /sec under normal ambient conditions, so the above basic definition gives
5
Re=0.7×10 VD. For a circular section a change in the mean position of separation tends to
5
occur at about R =3.5×10 . For a limited range above this value, the ‘supercritical range’,
e
vortex shedding tends to be less well organized, giving much weaker excitation than in the
subcritical range. Wootton (1969) pointed out that substituting the critical value of reduced
velocity to replace V in Reynolds number gave a ‘size number’ , such that the Reynolds
number at resonance is equal to the size number divided by VRC-With , the
condition is likely to ensure freedom from serious excitation. It will be noted that the
cable example gives a much lower value of size number; for 19 Hz,
2
Lighting columns and masts give low values of nD in the fundamental mode, and
generally also in the second mode. As an indication of the latter, a 15 m mast may have a
second mode frequency of 5 Hz. The crucial diameter for lock on is likely to be around the
2
mid-height, typically less than 0.2 m, giving nD <0.2. Chimneys, however, tend to give much
higher values. A concrete chimney of 2:1 taper and height ten times the base diameter will
have a natural frequency about 70/h (Hz, given height h in metres). 1.0 Hz would then be
associated with height 70 m and the diameter at, for example, 0.8 h above ground would be
4.2 m, giving . In this ‘transcriticaP range relatively well organized vortex shedding
is again observed. have been recommended for the subcritical range, 0.25–0.40
for the transcritical range.
The favourable range is of greatest significance for individual tubular members making up
lattice structures. The natural frequency for a circular steel tube member of length L can be
expressed by

(3.34)

in which t is the wall thickness and cf is a fixity factor, equal to unity for simple