Fundamental Mode Estimation for Modern Cable-Stayed Bridges Considering the Tower Flexibility

Abstract

The design of cable-stayed bridges is typically governed by the dynamic response. This work provides designers with essential information about the fundamental vibration modes, proposing analytical expressions based on the mechanical and geometrical properties of the structure. Different bridge geometries are usually considered in the early design stages until the optimum solution is defined. In these design stages, the analytical formulation is advantageous, because finite-element models are not required and modifying the bridge characteristics is straightforward. The influence of the tower flexibility is included in this study, unlike in previous attempts on mode estimation. The dimensions and proportions of the canonical models proposed in the analytical study stem from the previous compilation of the dimensions of a large number of constructed cable-stayed bridges. Five tower shapes, central or lateral cable-system layouts and box- or U-shaped deck sections, have been considered. The vibration properties of more than 1,000 cable-stayed bridges with main spans ranging from 200 to 800 m long were extracted within an extensive parametric analysis. The Vaschy-Buckingham theorem of dimensional analysis was applied to the numerical results to propose the formulation for period estimation. Finally, the formulas were validated with the vibration properties of 17 real cable-stayed bridges constructed in different countries. The importance of the tower flexibility is verified, and the errors observed are typically below 15%, significantly improving the estimations obtained by previous research works.