Assessment of nonlinear structural vertical-torsional coupling in cable-supported bridges

Abstract

Using simplified mathematical representations of suspension bridges, mathematicians have demonstrated that a vertical dynamic forcing can cause large torsional vibrations due to geometric nonlinearities of the bridge that appear to be a structural dynamic instability. Compared to the extensive research that has been conducted on the dynamic behavior of cable-supported bridges, the approach used by the mathematicians appears too simplistic. This is due to the fact that the dynamic force considered by the mathematicians is approximate compared to actual dynamic loadings on bridges, especially those originating from wind. However, they raise a point that is not considered in the wind design of cable-supported bridges, i.e., a possible nonlinear structural coupling between the modes of vibration that could be detrimental to the bridge performance. Therefore, this paper presents a preliminary investigation of nonlinear vertical-torsional coupling in long-span bridges using a simplified practical approach. The proposed method relies on the finite element method and nonlinear pushover analyses. Using this approach, the nonlinear structural coupling is assessed for the numerical models of five suspension bridges and two cable-stayed bridges. The method allows determining the nonlinear stiffness parameters of equivalent systems having between one and three degrees of freedom (lateral, vertical and torsional). Since the proposed technique relies on the modes of vibration and can account for the interaction between the vertical and torsional effects, it can be used to judge which ones of the bridges considered are likely to be the most susceptible to nonlinear mode coupling under wind loads. The analysis results for the seven bridges shows that the suspension bridge system has a greater nonlinear vertical-torsional coupling in comparison to the cable-stayed system. Additionally, it is demonstrated that the span length has an influence on the vertical-torsional coupling. The results also show that the nonlinear coupling is slightly affected by lateral effects.