Coupling between Torsional and Vertical Modes of Wind-Induced Nonlinear Vibrations in Suspension Bridges Due to Suspender-Loosening

Abstract

This chapter presents an important result that the maximum amplitude of vertical vibrations in suspension bridges under wind load may be underestimated by up to 500%, based on the numerical stimulations on Tsing Ma Bridge with a wind intensity equivalent to “Typhoon Signal No. 8” of Hong Kong. It discusses the nonlinear effect that may arise as the nonlinear terms for both large deflection and rotation and those for the suspender-loosening, are retained. For cases of steadily-blowing wind and fluctuated wind conditions, the nonlinear coupling because of torsional and vertical modes is virtually non-existent—that is, the main nonlinear effect is because of suspender-loosening. However, for sudden gusty wind condition numerical results suggest that the torsional vibrations set in as time evolves, despite the fact that there is no initial torsional deflection. As time increases further, the vertical vibration becomes extremely large. Such large deflection should damage structural components and eventually leads to the final collapse of the suspension bridge. This whole scenario closely resembles what actually happened in the case of the collapse of the Tacoma Narrows Bridge. This is the first time that the transition of vertical modes to vertical-torsional coupled modes is predicted in theoretical analysis.