Dynamic Amplification Analysis of the Main Girder of Cable-Stayed Bridges After Cable Rupture Using the Modal Superposition Method

This study investigates the dynamic amplification effect of the main girder of cable-stayed bridges after cable rupture. The expression for the dynamic amplification effect is derived using the modal superposition method, and the influence of the duration of cable rupture on the dynamic amplification effect is investigated. The results indicate that, for a single-degree-of-freedom (SDOF) system without damping, the displacement dynamic amplification factor (DAF) can reach a maximum of 2.0. For the main girder of cable-stayed bridges, the dynamic amplification factor can exceed 2.0 and is related to the weight of the projection components of the response on the mode shapes. Using the modal superposition method of calculation, the higher-order modes have the greatest influence on shear force, followed by the bending moment, while they have the least influence on displacement. The theoretical derivation is validated using a simplified model, and it is shown that the commonly used equivalent static load calculation method with a factor of 2.0 for the static cable force poses potential safety risks. Furthermore, this study shows that the shorter the duration of cable rupture, the more pronounced the dynamic amplification effect. It is recommended that the duration of the cable rupture should not exceed 0.01 times the fundamental period of the structure when the maximum impact effect is calculated to ensure the rationality of the calculation results.

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