PDF格式（左键浏览，右键另存）：

A new framework for evaluating along-wind responses of a transmission tower

Vol.8, No.1 (2009)《Earthquake Engineering And Engineering Vibration》

Abstract：In this paper, an analytical framework to evaluate the along-wind-induced dynamic responses of a transmission tower is presented. Two analytical models and a new method are developed: (1) a higher mode generalized force spectrum (GFS) model of the transmission tower is deduced; (2) an analytical model that includes the contributions of the higher modes is further derived as a rational algebraic formula to estimate the structural displacement response; and (3) a new approach, applying load with displacement (ALD) instead of force, to solve the internal force of transmission tower is given. Unlike conventional methods, the ALD method can avoid calculating equivalent static wind loads (ESWLs). Finally, a transmission tower structure is used as a numerical example to verify the feasibility and accuracy of the ALD method.
Keywords：along-wind-induced dynamic responses; transmission tower; generalized force spectrum; equivalent static wind loads

Introduction
Lattice high-rise structures such as transmission towers are lightweight, very tall, flexible structures characterized by low damping and sensitivity to wind loads (Li and Bai, 2006). The wind load must be accurately calculated prior to structural design. The wind load can be qualified through multiple-point synchronous scanning of pressures on the surface of the structural model in a wind tunnel, or by high frequency fore balance (HFFB) measurement. However, unlike for ordinary buildings, the wind load on transmission towers is difficult or may be impossible to measure using multiple-point synchronous scanning of pressures due to its high hollowness rate, while the HFFB measurement is usually used to estimate the generalized force of the fundamental mode and fundamental mode generalized force spectrum (GFS). Then, according to random vibration theory, the variance of the responses including only the first mode can be further obtained. However, higher modes may provide noticeable contributions to the responses, especially for slender structures like transmission towers. Systematic studies on evaluating the along-wind responses of latticed towers were conducted by Holmes (1994; 1996a, b). To better understand the response of the transmission tower-line systems to wind, a novel approach for wind tunnel aero elastic modeling of conductors was introduced in detail (Loredo-Souza and Davenport, 2001; Loredo-Souz, 1996).
HFFB measurements on three semi-rigid tower models were performed in the TJ-1 boundary layer wind tunnel at Tongji University. The fundamental mode GFS of the transmission tower was obtained first, and then the higher mode GFS was expressed in analytical form (Zou, 2006). In order to obtain the structural internal forces, such as can be achieved with the conventional processing approach, the equivalent static wind loads (ESWLs) that include only the fundamental modal contribution of the transmission tower were also established (Yu, 2006). In this paper, a practical numerical higher mode GFS model is presented for applications in design practice. It was developed on the basis of the fundamental mode GFS obtained from a wind tunnel model experiment, and adopted the height-independent fluctuating wind power spectral density and Shiotami-Type spatial coherence function. Then, an analytical model for the displacement response is further deduced. In the formulation, the contributions of higher modes are included and the conversion relationship between the unilateral and bilateral power spectral densities is taken into account. Moreover, unlike the conventional method, the applying load with displacement (ALD) method, which will be described in the next section, is adopted to calculate the internal forces. The two models and the ALD method constitute a new practical analytical framework for use in the design of transmission towers.

Conclusions
A new framework has been presented to evaluate the along-wind-induced dynamic responses of transmission towers, in which a practical higher mode generalized force spectrum (GFS) model is deduced on the basis of a fundamental mode generalized force spectrum (GFS) obtained from a wind tunnel. The framework also adopts the height-independent fluctuating wind power spectral density and Shiotami-Type spatial coherence function.
In addition, based on random vibration theory, a practical algebraic formula is derived which includes higher mode contributions. The formula can be used to evaluate the RMS value of the displacement response through proper simplification.
Finally, a method called the ALD method is presented to calculate the internal force of a transmission tower by directly using the displacement response obtained from Eq.(34).
It is shown that the results obtained by the ALD method show good agreement with the conventional method. The advantage of this approach is that it is rational and avoids calculating the ESWLs, which makes it easier to use in engineering practice.

References：
[1] American Society of Civil Engineers (1999), “Wind Tunnel Studies of Buildings and Structures,” ASCE Manuals and Reports on Engineering Practice, ASCE, New York,.
[2] Chen XZ and Kareem A (2005a), “Coupled Dynamic Analysis and Equivalent Static Wind Loads on Building with 3-D Modes,” Journal of Structure Engineering, 131(7): 1071–1082.
[3] Chen XZ and Kareem A (2005b), “Dynamic Wind Effects on Buildings with Three-dimensional Coupled Coupled Modes,” Journal of Engineering Mechanics, 131(11): 1115–1125.
[4] Chen XZ and Kareem A (2007), “Equivalent Static Wind Loads on Low-rise Buildings Based on Full-scale Pressure Measurements,” Engineering Structures, 29(10): 2563–2575.
[5] Chopra, AK (2000), Dynamics of Structures: Theory and Applications to Earthquake Engineering, 2nd ed, New Jersey: Prentice-Hall.
[6] Holmes JD (1994), “ Along-wind Responses of Lattice Towers: Part I — Derivation of Expressions for Gust Response Factor,” Engineering Structures, 16(4): 287–292.
[7] Holmes JD (1996a), “Along-wind Responses of Lattice Towers: Part II — Aerodynamic Damping and Deflections,” Engineering Structures, 18(7): 483–488.
[8] Holmes JD (1996b), “Along-wind Responses of Lattice Towers: Part II — Effective Load Distributions,” Engineering Structures, 18(7): 489–494.
[9] Kareem A and Zhou Y (2003), “Gust Loading Factor-Past, Present and Future,”Journal of Wind Engineering and Industrial Aerodynamics, 91(12):1301–1328.
[10] Li HN and Bai HF (2006), “High-voltage Transmission Tower-line System Subjected to Disaster Loads,” Progress in Natural Science,16(9): 899–911.
[11] Loredo-Souza AM (1996), “The Behavior of Transmission Lines Under High Winds,” PhD Thesis, The University of Western Ontario, London, Canada.
[12] Loredo-Souza AM and Davenport AG (2001), “A Novel Approach for Wind Tunnel Modelling of Transmission Lines,” Journal of Wind Engineering and Industrial Aerodynamics, 89(11): 1017–1029.
[13] Yu XL (2006), “Wind-induced Dynamic Responses on Lattice Towers and Simplified Evaluation of Equivalent Wind Load,” MD Thesis, Wuhan University, Wuhan, China. (in Chinese)
[14] Zhang XT (2006), Engineering of Structure, Beijing: China Architectural Industry Press. (in Chinese)
[15] Zhou XY and Gu M (2006), “Analytical Approach Considering Modal Coupling Effects for Buffeting Resonant Response of Large-span Roof Structure,” Journal of Vibration Engineering, 9(12): 179–183. (in Chinese)
[16] Zou LH (2006), “Investigation on Model of Dynamic Wind Loads and Wind-induced Vibration of Lattice Highrise Structures,” PhD Thesis, Wuhan University, Wuhan, China. (in Chinese)