Page 114 - Dynamic Loading and Design of Structures

Page 91

exceeding unity) it is arguable whether such refinement is appropriate, given the inherent
uncertainty in this problem.
BS 8100 (Lattice towers and masts) uses a deterministic model with a rather complex
notation and presentation. In the notation of this chapter, Č=0.3 (transcritical Reynolds
L
number is presumed) and primary resonance is assumed at V =5n D. To allow for lock on at
cr
j
higher speeds, a correction factor ke is presented graphically; the graphical presentation is
2
poor but it is apparently intended that windspeed 1.2Vcr gives an effective Č LV about 8 per
cent greater than the basic value
Stochastic models can be expected to give a smaller response. The negative aerodynamic
damping concept was implemented in Commentary B to the Canadian National Building
Code (NBC) in 1980. The parameter values suggested by Vickery, as given on page 89, are
supplemented by a formulation for admittance which can be written as J=JasKAR, in which J as
is the Davenport ‘diagonal’ value for the correlation factor, and KAR combines allowances for
the approximation therein and for the aerodynamic effect of the free end. The basic value
given is (but ), in which h is the height of the chimney (or, for
moderately tapered chimneys, three times the length deemed to have shedding locked on). A
closer approximation (but disregarding the end effect) would be given by (cf
the gust analysis, page 77); for a typical first mode shape this would agree at h/D=12 and be
somewhat smaller than the Code value for more slender chimneys.
The first mode resonance solution was expressed in the NBC Commentary by an equivalent
static load (PL, say, per unit length) acting over the top third of the height. This is set equal to
the theoretical inertial load intensity at the top of the chimney, which with the input values for
normal turbulence wind conditions, expressed in the notation of this chapter, is

(3.40)

in which the mass per unit length m is averaged over the top third. As noted earlier (Section
3.2.5), the denominator can be written in terms of the Scruton number, emphasizing the
importance of this normalized parameter. The corresponding normalized tip deflection can
then be written as

(3.41)

By comparison with the deterministic solution taking Č L=0.3, using the mode shape
approximation (which gives the modal integral quotient

, the stochastic result is smaller by a factor

(3.42)