Page 118 - Dynamic Loading and Design of Structures

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sections and conical transitions. Thus, for fB=25 N/mm (say, giving stress range 50N/mm to
limit fatigue damage) the response limit for a uniform diameter chimney is
(e.g. for h/D=20). For an unlined stack at D/t=200, the
Canadian formulation then requires K =16 (turbulent flow). For low turbulence conditions, the
s
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deterministic estimate with Č=0.3 (for high nD ) and the modified Canadian formulation
L
both require Ks=32.
For concrete chimneys, if unlined, . The American Concrete Institute
code ACI 307 allows presumption of 1 per cent of critical damping, δ0.063.
=
Thus with D/t=40, Ks=20; a 50 per cent addition to the mass by a refractory liner would
increase this to 30. Thus, ηvalues are comparable with the above steel example. However,
H/D values are commonly lower, and for an untapered multi-flue windshield at (say) h/D=14,
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the associated strains will be higher; η=0.03 then gives concrete stress (at E=35 kN/mm )
2.
fB=9N/mm A 1:0.6 diametral taper, retaining h/DB=14 and with IB/IT=8 (say, giving
.
Ctr=0.70), would reduce the stress to 4 N/mm2 Greater taper would lead to more than ±10
per cent change of diameter over the top third and thus to reduction of the predicted response
according to the above rules.
The final word of this section must be to highlight the importance in all assessments of
●the value of structural damping;
●the possibility of low turbulence wind at the critical speed.

The occurrence of low turbulence conditions varies very greatly according to location, and is
generally ill explored in engineering guidance.

3.2.9 Vortex shedding: bridges

The case of Tacoma Bridge has already been mentioned. However, the pursuit of improved
deck cross-section profiles to ensure freedom from strong torsional motion generally also has
the effect of reducing the strength of excitation by vortex shedding. Nevertheless, it is in
practice impossible to eliminate it entirely, and it is necessary to check both fatigue and the
subjective reaction of users of the structure. The subjective reaction criterion incorporated in
the UK Design Rules for Aerodynamic Effects on Bridges BD49/93 is an acceleration value,
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centred on an amplitude of 0.8 m/s , or 8 per cent of the acceleration due to gravity. The
corresponding structural stresses will be about 8 per cent of the stresses due to dead load;
although such stresses might pose a significant fatigue risk (depending on fatigue detail
classification and on the frequency of the wind condition for resonance) the subjective
reaction criterion is commonly more significant.
The amplitudes thus accepted are generally sufficient for lock on ensuring vortex shedding
correlated over a substantial part of the span, especially in the relatively low turbulence
environment typical of long spans (estuarial and/or high level valley crossings). The
deterministic model, giving a response inversely