A structure is vulnerable if any small damage will trigger disproportionately large consequences, even leads to a cascade of failure events and progressive collapse. The structural vulnerability performance depends upon the properties, locations of damaged components and the way they are connected to the rest of the structure. In this paper, progressive failure analysis method is utilized for the vulnerability study of cable-stayed bridges. The goal of it is to identify various failure scenarios initiated from the sudden damage of some bridge components. Based on the analysis results, assuming that the behaviors of damaged components can be modeled using plastic hinges, the hybrid element model is introduced to derived the modified stiffness matrix considering both of the effects of bending moments and shear forces. Furthermore, the vulnerability index in terms of the nodal stiffness degradation can be analytically quantified, which could be regarded as an index to determine the bridge failure consequences, so that the vulnerability distribution graph for the whole bridge can be sketched to evaluate the bridge performances from vulnerability viewpoints. This quantitative approach is applicable for structural evaluation under unforeseen attack and illustrated on a typical long-span cable-stayed bridge.
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