A closed-form solution for the wind-induced responses of transmission lines considering the failure of adjacent towers

Some towers in transmission lines may collapse first under the gust wind and have pulling effects on conductors, which may trigger the cascade failure when the unbalanced force on the adjacent tower is large. Thus, a closed-form solution is proposed to predict conductor responses induced by both the failed tower and wind loads. The total wind-induced response is divided into the mean component affected by support displacement and fluctuating component around the static equilibrium, which can be determined by nonlinear static analysis and influence line, respectively. The equilibrium iteration method and trapezoidal equivalent wind pressure are proposed to correct the response distortion caused by the large deformation and non-uniform wind pressure. Then, the power spectral density and root mean square of responses considering three-dimensional correlation are provided. Finally, parameter analysis investigates the influence of support displacement, initial horizontal tension, and horizontal span on reaction force and gust response factor (GRF). The results show that the proposed closed-form solution has high accuracy and efficiency, and the influence of large deformation and wind pressure forms on the wind-induced responses cannot be ignored. Moreover, both the lateral reaction force and GRF are significantly sensitive to the lateral support displacement.