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Cable supported bridges, such as suspension bridges, cable-stayed bridges and tied-arch bridges, play important roles in the transportation infrastructure systems. Failure of these bridges can lead to heavy casualties and significant economic losses. However, the resistance to system level failure under specified member loss scenario(s), also called structural robustness of these types of bridges and the key limit states for structural evaluation have not been adequately studied. In this paper, push down analysis is presented as a method to identify the key limits of cable supported bridges for structural robustness evaluation. The above analysis was conducted in LS-DYNA® on three disparate long-span cable-supported bridges, i.e., a suspension bridge, a cable-stayed bridge and a tied-arch bridge. The failure of key structural components of the bridges was monitored closely during push down analyses and several key limit states were identified. Bridges with single member loss were also pushed down and their response compared to the behavior of the corresponding intact bridges to evaluate the effect of member loss on push down capacity in the context of the identified limit states. The results show that the mentioned three cable-supported bridges exhibit a similar bilinear load displacement curve during push down analysis. Comparison on the overall performances of the identified key limit states indicate high capacity for the design live loads. The overall performance is affected negatively by cable loss and the effects varied depending on the location of the cable loss and the pattern of live load distribution. Despite these adverse effects, the capacities of the identified key limit states of these bridges under damaged scenarios are not reduced significantly.