EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS Earthquake Engng Struct. Dyn. 2003; 32:1639–1654 (DOI: 10.1002/eqe.292) Seismic response of multi-supported structures by proper orthogonal decomposition Federica Tubino ∗; † , Luigi Carassale and Giovanni Solari Department of Structural and Geotechnical Engineering; University of Genoa, Via Montallegro; 16145 Genova; Italy SUMMARY The seismic analysis of structures is usually carried out considering the ground motion as fully-correlated in space and determining the structural response by pseudo-deterministic methods such as the response spectrum technique. Actually, the partial correlation of the seismic acceleration may inuence heavily the behaviour of spatially extended structures, such as bridges, viaducts or pipelines. In order to take its partial correlation into account, the seismic ground motion is schematized as a stochastic process dependent on time and on space; the hypotheses of stationarity and homogeneity are used to obtain simple and general results. The inuence of the partial correlation of the seismic ground motion on the structural response is investigated by introducing suitable Equivalent Spectra. The acceleration of the support-points of the structure is represented by the Proper Orthogonal Decomposition (POD), dening the modes of the earthquake. The method is formulated for any kind of multi-degree-of-freedom system and is applied, as a case study, to an ideal single-storey multi-supported frame with an axially rigid beam. In the case of two supports, the POD decouples the pseudo-static and the dynamic contributions to the structural response. This property is preserved for structural systems with many supports, where only the lower modes of the earthquake, usually the rst two POD modes, are responsible for the structural response. Copyright ? 2003 John Wiley & Sons, Ltd. KEY WORDS: earthquake engineering; equivalent spectrum; multi-supported structure; proper orthogonal decomposition; structural dynamics INTRODUCTION Earthquake engineering commonly considers the seismic ground motion as fully correlated in space and represents it by single-point functions, such as time histories, response spec- tra, power spectral density functions (PSDF), or evolutionary spectra [1]. Single-supported structures are usually studied by expressing the equations of motion in terms of relative displacements between the structural elements (or lumped masses) and the ground. In this ∗ Correspondence to: Federica Tubino, Department of Structural and Geotechnical Engineering, University of Genoa, Via Montallegro, 16145 Genova, Italy. † E-mail: tubino@diseg.unige.it Received 20 February 2002 Revised 8 August 2002 and 22 November 2002 Copyright ? 2003 John Wiley & Sons, Ltd. Accepted 22 November 2002