Bridges: when is single mode seismic analysis adequate?

Single-degree-of-freedom (SDOF) models are frequently used in the seismic analysis of bridges, in particular in recent years when inelastic, SDOF-based push-over analysis has become increasingly popular. However, the scope of applicability of these models has not yet been clearly defined (e.g., in the Eurocode 8/2). Using SDOF models, displacements and forces could be significantly underestimated, especially in ‘irregular structures’. The authors have therefore proposed a more adequate criterion for the applicability of SDOF models, and a clearer definition of regularity. The seismic response of some typical European viaducts has been studied. Several different seismic analysis methods, both elastic and inelastic, were used, incorporating different levels of structural model simplification. Differences in the response obtained by using SDOF and multi-degree-of-freedom (MDOF) models were analysed. If these differences were significant, the response was considered to be irregular and the SDOF model unsuitable. For the quantitative estimation of the regularity and applicability of SDOF models a ‘regularity index’ has been introduced. The index is based on a comparison between the different displacement shapes obtained within two iterations of the single mode static analysis. Using this index the main parameters influencing the irregular response of the viaducts were identified and analysed.