Page 115 - Dynamic Loading and Design of Structures

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For a slender concrete chimney with h=12D and δ=0.04 (say), this factor is

. If furthermore D/t=40 (say) at the reference height for evaluation of Ks
(height z=5h/6 is suggested), then K =12 (taking structural mass only (i.e. unlined)) and the
s
given stochastic estimate is 40 per cent of the deterministic value.
For low turbulence conditions, the Canadian code gives doubled values for both the basic
exciting force coefficient and the negative damping factor. Ks must therefore robustly exceed
2×7.6=15; the above example would be unacceptable. The possibility of low turbulence must
clearly be approached with severe caution, with regard to the frequency of occurrence (or
upper limit of co-existent windspeed) of a stably stratified flow with temperature lapse rate
inversion. A deterministic check may particularly be advisable.
The CICIND (1999) recommendations for steel chimneys present a rather complicated
.
algebraic formulation for ηThis is based on curve fitting the foregoing stochastic model for

small amplitude response, combined with a sharp lock on effect as the tip amplitude exceeds
about 0.01 D (r.m.s.) but with a self-limiting reduction of excitation for amplitudes exceeding
about 0.2D (r.m.s.). Four different parameter sets are given to cover subcritical and
transcritical Reynolds number and normal and low levels of turbulence (threshold speeds for
the latter being specified). The larger amplitude response predictions are based largely on
experience in Denmark and in Poland where chimneys with very high slenderness h/D) have
allowed survival of such amplitudes (cf eqn (3.45)), but it is questionable how far this should
be exploited in design.
The guidance for concrete chimneys produced by the American Concrete Institute, the ACI
Manual of Concrete Practice part 307 (ACI 307–95) is another elaboration of this format. The
analysis remains essentially unchanged, but many of the parameters treated hitherto as simple
constants are now dependent on intensity of turbulence and/or aspect ratio. Guidance is given
on application to the second cantilever mode, and to combination with the effect of alongwind
forces when the critical speed is approaching the design windspeed. The net changes
operative in turbulent wind are typically modestly favourable, but the problems posed by low
turbulence appear to be viewed very lightly in this Code.
The Eurocode ENV 1991–2–4 informative Annex C presents a compromise procedure
developed by Ruscheweyh (1982, see also Ruscheweyh et al., 1988), supplemented in ENV
1993–3–2 for chimneys. The basic response equation (ENV 1991–2–4 equation C.4) has the
form of the deterministic model; the excitation is defined in terms of a coefficient for the r.m.s.
value of load per unit length (denoted c ) and a ‘correlation length’ (denoted L ) over which
j
lat
the modal force integral is evaluated following the deterministic format. L is a function of the
j
response amplitude, but unfortunately this parameter combines the consideration of
correlation and the factor to be applied to the r.m.s. to obtain a design value. The given values
are thus not readily comparable with other procedures; for response amplitudes less than 0.1D,
L =6D, but increases to 12D if the response amplitude is more than 0.2D. The high threshold
j
for the effect of motion on L j