Keywords: wind dynamic response, method of Davenport, influence line functions, telecommunications towers and masts.

The analysis of the effect of the wind in structures can be of great complexity due to wind variability in space and time. This article presents a theoretical revision of a statistical procedure for the wind actions in towers and metallic masts evaluated by the method of Davenport [3], which uses influence line functions for determining any structural response decomposed into its resonant and non-resonant components. Examples of structural responses are presented using this methodology for a typical tower or metallic mast.

The average structural response is predominantly in the direction of the wind, but the fluctuation response occurs either in the direction of the wind or normal to the wind. The peek response, , can be obtained by the following expression:

in which corresponds to the average response, is the standard deviation of the fluctuation response and is the peek factor (the ratio between the maximum fluctuation response and the standard deviation).

The force of the wind can be decomposed into the sum of a constant part and a fluctuation part (Barros [2] and Holmes [4]):

For a telecommunications tower for which and are respectively the tower width variation and the wind speed variation along the normalized height , the average wind force in the structure at a normalized height can be obtained from the following expression

in which is the index of exposed area.

Any average response can be determined using the expression

where corresponds to the influence line of the intended response (any generalized force or generalized displacement of interest, pre-determined anywhere).

The fluctuation part (or standard deviation part) of the wind force at a normalized height , can be expressed by:

in which corresponds to the turbulence intensity at the top of the structure. Also the variance of the non resonant response (due to the wind forces at frequencies below the structure natural frequency) is expressed by the coefficient of vertical spatial correlation between the two forces F vertically apart by a distance .

Some structural responses of a typical metallic tower under wind actions, determined by Almeida and Barros [1], are presented herein using the procedure described previously. Results obtained are represented graphically showing the values of each one of the responses (average, resonant and non-resonant), as well as percentage-wise the portions of response (average constant and fluctuation dynamic) associated with base shear, base moment and the tip lateral displacement.

In the design of metallic towers the wind action is usually the more limiting one. The consideration of the dynamic fluctuation effects in the design of these structures is quite essential. The effect of the resonant component in the total response is quite significant and it cannot be neglected (namely in the determination of the top displacement, where this component of the response assumes values greater than those of the non- resonant response). This conclusion is coherent with regulatory codes that suggest the resonant response should be considered in structures with fundamental frequency less than 1 Hz.

1

Almeida, R.F. and Barros, R.C., "Análise do Efeito Dinâmico do Vento em Torres e Mastros Metálicos", V Congresso de Construção Metálica e Mista, Centro de Congressos de Lisboa, 24-25 de Novembro de 2005, Lisboa, Portugal (in portuguese).

2

Barros, R.C., "Dimensionamento estrutural de mastros metálicos", Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, Vol. 18, 3, pp. 351-365, 2002.

3

Davenport, A.G., "How can we simplify and generalize wind loads?", Journal of Wind Engineering and Industrial Aerodynamics, Vol. 54/55, pp. 657-669, 1995. doi:10.1016/0167-6105(94)00079-S

4

Holmes, J.D., "Along-wind response of lattice towers - II: Aerodynamic damping and deflections", Engineering Structures, Vol. 18, No. 7, pp. 483-488, 1996. doi:10.1016/0141-0296(95)00131-X

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