Displacement limits and performance displacement proﬁles in support of direct displacement-based seismic assessment of bridges Donatello Cardone* ,† School of Engineering, University of Basilicata, 85100 Potenza, Italy SUMMARY Displacement limits and performance displacement proﬁles (PDPs) for the direct displacement-based assessment of existing bridges are proposed. The PDPs are deﬁned as the bridge inelastic deformed shapes associated with the attainment of selected damage states in some critical elements of the bridge. In the paper, displacement limits are provided for piers, abutments, joints, bearing devices and shear keys. Moreover, different approaches for the deﬁnition of the PDP are examined, including adaptive pushover analysis, effective modal analysis, and rational analysis of simpliﬁed bridge models. In the paper, the key aspects and modeling assumptions of the proposed direct displacement-based assessment procedure are presented ﬁrst. This is followed by some examples of application to typical Italian highway bridge conﬁgurations, differing in pier layout, deck type, and pier-deck connections. Copyright © 2013 John Wiley & Sons, Ltd. Received 1 June 2013; Revised 11 September 2013; Accepted 10 November 2013 KEY WORDS: seismic assessment; RC bridges; damage states; displacement limits; performance displacement proﬁle; effective damping 1. INTRODUCTION Traditional force-based seismic assessment approaches are basically based on the comparison between estimated base shear capacity and base shear demand speciﬁed by a seismic code. The base shear demand is found by reducing the elastic base shear corresponding to the elastic stiffness of the structure by a code-speciﬁed force reduction or behavior factor. The problem with this approach is that no assessment is made of the actual collapse mechanism, inelastic deformed shape and ductility demand of the structure. In the last two decades, a new generation of simpliﬁed nonlinear displacement-based methods for the seismic assessment of existing structures has been developed. All the methods combine the pushover analysis (POA) of a nonlinear MDOF model of the structure with the response spectrum analysis of an equivalent SDOF system, to provide an estimation of the global displacement response of structures for a given seismic intensity (PGA). The main nonlinear static methods (NSMs) are: (i) the capacity spectrum method (CSM), originally proposed in [1] and then adopted in the ATC-40 [2] and FEMA-440 guidelines [3]; (ii) the displacement coefﬁcient method (DCM), presented in the FEMA-273 [4] and then further developed in the FEMA-356 guidelines [5]; and (iii) the N2 Method [6], which has been implemented in the Eurocode 8 [7]. The common feature of NSMs is the use of POA to characterize the nonlinear behavior of the structure. The applicability of NSMs is then mainly limited by the implicit assumptions in POA. Thus, following attempts to improve NSMs basically consisted in improvements of POA, to account for the contributions of *Correspondence to: Donatello Cardone, School of Engineering, University of Basilicata, 85100 Potenza, Italy. † E-mail: donatello.cardone@unibas.it Copyright © 2013 John Wiley & Sons, Ltd. EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS Earthquake Engng Struct. Dyn. 2014; 43:1239–1263 Published online 17 December 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/eqe.2396