EQUIVALENT WIND LOADING SPECTRUM TECHNIQUE
G. Piccardo(1) and G. Solari(1)
(1)
Istituto di Scienza delle Costruzioni, University of Genova,
Via Montallegro 1, 16145 Genova, Italy
ABSTRACT. Wind forces on structures are usually schematized by the sum of their mean
static part and a nil mean fluctuation generally treated as a stationary process randomly
varying in space and time. The multi-dimensional nature of such a process gives rise to
relevant numerical efforts in order to carry out the dynamic analysis of the structural response.
With the aim of drastically reducing the above computational burden, this paper introduces a
method by means of which the external fluctuating forces are schematized by an equivalent
identically coherent process, rather than by the actual cross-correlated process. This process is
identified by a power spectral density function, called the Equivalent Wind Loading
Spectrum, whose expression is given in closed form.
INTRODUCTION
Wind action is usually schematized by a suitable distribution of forces applied on the
structural surface. These forces are represented by the sum of their mean static part and a nil
mean fluctuation generally treated as a stationary process randomly varying in space and time
and schematized, in the frequency domain, by their cross-power spectral density function.
WIND LOADING MODEL
Time domain analysis
Using the model [3, 4], F , F' are given by:
F z  
1 2
u z b  Cu  u z 
2
(2)
'
z; t 
F' z; t     F
(3)
where C is the , component (=x,y,; =u,v,w,s) of the following matrix:
cd cd  c  cos 
C   c cd  c cos 
c m c m cos 
cd  c sin 
cd c sin 
c msin 
cds 
cs 
c ms 
(7)
Figures 7 show the rms values of the x alongwind and y crosswind displacements (a) and
of the  torsional rotation (b) of model 2 in the middle of its span. The solid lines correspond
to the rigorous solutions based on Eq. 16; the dashed lines are the obtained applying the
EWLST. As shown by the diagram of figure (b) there is a fairly good correspondence
between the two different solutions.
Figure 7. Dynamic response of model 2.
It is possible to verify that in the class of the usual mode shapes a suitable K value exists,
depending on 1 (z), making Eq. 20 an almost exact approximation of Eq. 22. Table 1 gives a
list of such values.
Table 1. Noticeable values of K for horizontal structures ( = /2).

1(z)
1
sin(z/  )
sin(z/2  )
[1-cos(2z/  )]/2
(z/  )0.5
(z/  )1.0
(z/  )1.5
(z/  )2.0
(z/  )2.5
K(=u,v,w,s)
0.50
0.39
0.40
0.32
0.44
0.38
0.33
0.29
0.26
CONCLUSIONS
Using the Equivalent Wind Loading Spectrum Technique proposed in this paper, the
external fluctuating forces are schematized by an equivalent identically coherent process,
rather than by the actual cross-correlated process. This process is identified by a power
spectral density function, the Equivalent Wind Loading Spectrum, whose expression is given
in closed form.
REFERENCES
[1] Davenport, A.G. (1961). The application of statistical concepts to wind loading of
structures. Proc. Instn. Civ. Engrs., 19, 449-472.
[2] Davenport, A.G. (1962). The response of slender, line-like structures to a gusty wind.
Proc. Instn. Civ. Engrs., 23, 389-408.
[3] Vellozzi, J., Cohen, E. (1968). Gust response factor. J.Struct. Div., ASCE, 97, 1295-1313.