Page 91 - Dynamic Loading and Design of Structures

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Any individual increments of inelastic deformation must therefore be kept very small, and a
linear structural analysis is sufficient, but a sophisticated treatment of the correlation of gust
actions over the extent of the structure is essential. The duration and random nature of the
process makes the power spectrum (see Chapter 10) an attractive analytical tool.
The ensuing presentation concentrates on the basic application of spectral analysis to the
gust loading problem pioneered by Davenport (1961, 1962), using the neutral ABL model,
although there is increasing recognition of the potential importance of convective effects
(Wyatt, 1995). This analysis further presumes simple ‘quasi-steady’ aerodynamics; the
companion problems of dynamic effects caused by flow-pattern instabilities or by feedback of
structural motion to the aerodynamic forces are considered under the heading of Aerodynamic
Instability, Section 3.2.

3.1.2 Spectral description of wind loading
The turbulent velocities are described by Cartesian components (u, v and w) superimposed on
the mean windspeed V; u is in the mean wind direction, w is commonly used for the vertical
component. It is generally presumed that the turbulence components can be treated for
analytic approximations as small compared to V; the instantaneous windspeed V(t) is thus
V(t)=V+u(t), and v and w can be treated as causing small changes in the instantaneous wind
direction. The notation is used throughout this chapter for the variance of quantity u, and
correspondingly for other input and response quantities.
In a severe temperate-climate windstorm, the mean windspeed and the associated statistical
description of the gusts carried by it remain constant (‘stationary’ in the statistical sense) for a
sufficient duration that analysis in the frequency domain using power spectra is the preferred
approach. Provided the gusts are the result of surface roughness over a long fetch, rather than
being substantially influenced by specific discrete obstacles in the immediate vicinity, the
input spectra take universal normalized forms. In this way, the spectrum of each turbulence
component is fully defined by the r.m.s. value and a timescale parameter (for normalization of
frequency), the Harris—von Karman algebraic formulation being widely accepted (see below,
especially Figure 3.2a, Section 3.1.3) . Cross-spectra describing the spatial correlations are
also crucial in this application (Harris and Deaves, 1981; ESDU, 1986b).
Given standard algebraic descriptions of the input spectra, the subsequent analytic steps are
straightforward in application, and ad hoc numerical Fouriertransform operations are not
normally required except for interpretation of wind tunnel data or full size monitoring studies;
such specialist aspects are not considered further here. Full description of spectral procedures
can be found in sources such as Newland (1993), in which the mathematical basis is
developed, crucially equations 10.20–10.22, and 10.71. Attention is specially drawn to the
discussion given with these equations. Generally good guidance can be drawn from the