Natural periods of long-span cable-stayed bridges

In this paper an analysis of the natural periods of long-span cable-stayed bridges is developed for both H-shaped and A-shaped towers. The analysis is carried out by using both an analytical and a numerical model of the bridge. The analytical developments refer to a continuous model of the bridge, which is founded on the assumption of diffused distribution of the stiffness of stays along the girder and of the prevailing truss behavior of the bridge. The dynamical equilibrium equations governing free vibrations are obtained considering the oscillations from the starting equilibrium configuration corresponding to the dead load action. Then, the tangent stiffness of the bridge corresponding to this configuration is considered. The analytical treatment of the dynamical equilibrium equations is based on the assumption that for long spans the bending stiffness of the girder is negligible compared to the global flexural stiffness of the bridge. Simple analytical results that are capable of capturing the main behavior characteristics of the bridge are obtained. Moreover, to give useful and suitable numerical comparisons, a discrete model of the bridge that accounts for the actual spacing of stays and the actual flexural stiffness contribution of the girder has also been developed. The numerical results obtained validate the simple analytical continuous model.