Issue 69

A. Almeida et alii, Frattura ed Integrità Strutturale, 69 (2024) 89-105; DOI: 10.3221/IGF-ESIS.69.07

Wind modeling For the proposed problem, the procedures described in [48] are followed and, therefore, it deals only with synoptic winds (more complex models can be found in [49]). Thus, the wind load is given by:  D D D F F F   (1)

in which D F is the mean component and  of the drag force can be obtained by:

D F is the fluctuating component of the drag force, D F . The mean component



 2

p

2

0 i r F q C Ab z z  / D D i

(2)

in which i A is the effective area of exposure considered, orthogonal to the wind direction, b and p are meteorological parameters, r z is the reference height (10 meters), i z is the height under analysis and 0 q is the reference dynamic pressure of the wind, relative to the mean component, given by: D C indicates the drag coefficient that depends on the building shape,

1 2 a p V 

2



q

(3)

0

a  represents the specific mass of the air (equal to 1.225 kg/m³ at 15 ºC and 1013 mbar) and

p V is the design

in which

wind velocity, expressed by:

0 1 3 0.69 p V V S S 

(4)

in which 0 V is the base wind velocity, 1 S is the topographic correction factor and 3 S is the statistical correction factor. The fluctuating component of the drag force can be obtained by:   0 D i D F q C A  (5) in which  0 q is the reference dynamic pressure of the wind, relative to the fluctuating component, given by:

1 2

 0





p



2 Vpb z z v   /

q

(6)

a

i

r

in which   x y c ,c , v t  is the fluctuating component of the wind velocity, x c and y c are the horizontal and vertical coordinates, respectively, in a Cartesian plane, of the point under analysis, and t is the time. The fluctuating component of wind velocity is considered a normal random process with zero mean. The problem was formulated through the superposition of harmonic waves, in a process known as the spectral representation method [50]. Using this method, it is possible to convert the energy described by the spectrum in the frequency domain to the time domain and this implies the inclusion of a random component in the process, as shown in:

f n



 





    V t



f t 



S f

f

(7)

2

cos 2

Φ

s

i

i

i

i

i



i

1

in which , S i is the spectral density of the wind velocity, i f is the frequencies considered, f n is the maximum value of the considered frequency range, i f  is   s V t  is a fluctuating velocity signal at a given position in space, with  s   1,2,3,4

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