Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct Critical analysis of ultimate rotation formula for R.C. columns subjected to cyclic loadings Rosa Fusco, Rosario Montuori, Elide Nastri ⁎ , Vincenzo Piluso Department of Civil Engineering, University of Salerno, Via Giovanni Paolo II, 132 Fisciano, SA, Italy ABSTRACT Performance-based earthquake engineering relies on the availability of analytical models that can be used to predict structural performance, including collapse. Current code prescriptions allow evaluating the ultimate rotational capacity of hybrid (mechanical-empirical) or empirical formulations, for R.C. members both seismically and not-seismically detailed. The aim of the present work is to present a critical analysis of the empirical relationship proposed by Eurocode 8 Part 3 and Italian Seismic Code. These relationships formerly similar have been compared with the original formulations introduced by Biskinis and Fardis [1,2]. A databank of cyclic tests on rectangular column sections failing in flexure, shear and flexure-shear, have been selected from an available database and research reports. Their ultimate chord rotation corresponding to an ultimate strength of 80% has been compared with the results provided by the available relationships, to check the accuracy and the reliability of codes proposals. Finally, a new formulation based on an empirical approach is proposed. 1. Introduction In the European earthquake-prone Countries, the assessment of existing structures is a priority, since the vast majority of the building heritage was designed according to old seismic codes or even according to non-seismic codes. In current days Italy is crossed by a number of earthquake events, so that the topic of seismic safety evaluation for existing buildings assumes a relevant role, particularly in the case of a strategic building that has to avoid severe structural damage and to be effective immediately after the seismic event [3]. For these reasons, the assessment of an existing building has to be preceded by a phase in which performance objectives [4,5], seismic hazard [6] and determi- nation of deficiencies such as the material degradation [7,8], have to be taken into account. Obviously, first phases are pertaining to codes while the latter is devoted to the structural engineer. In most of these structures, the uncertainties about the nonlinear behaviour are relevant, in fact, the presence and location of potential inelastic zones, as well as their ductility capacity, are generally un- known. Even if the publication of Eurocode 8-Part 3 (EC8-3) [9], devoted to the seismic assessment of existing buildings, took place a decade ago, its application in engineering practices is still limited. The models introduced in EC8-3 have been proposed for the first time by Biskinis and Fardis [1,2]. They proposed models developed for beams, rectangular columns or walls and members of T-, H-, U- or hollow rectangular section, with or without detailing for earthquake resistance and with continuous longitudinal bars. The models employ simple, empirical expressions for practical applications without mo- ment-curvature analysis. They can be applied also to members with longitudinal bars lap-spliced in the plastic hinge region. The same model of EC8-3 [9] has been introduced in Italian Seismic code [10], even if with a slight difference. The issues addressed in this work regard the review and the im- provement of the empirical and hybrid mechanical-empirical formula- tion proposed in literature and in codes for the evaluation of ultimate plastic rotation of R.C. columns. For this scope, the equations proposed by Biskinis and Fardis [1], Italian Seismic Code [10] and Eurocode 8- Part 3 [9] have been applied to a databank of cyclic tests of R.C. col- umns. The aim of the work is on one hand to check the reliability of formulations proposed by codes and, from the other hand, to compare the results of these latter with the original relationship proposed by Biskinis and Fardis. In addition, only formulations able to provide the total rotation of members are considered, it means that formulation computing only the plastic part of chord rotation have been excluded from the comparison. Finally, a more effective relationship, suitable for all the failing moods has been proposed. 2. Considered databank A database of 342 rectangular columns was considered. Column tests involve cyclic and monotonic lateral loading of columns; with or without the axial load applied. The Pacific Earthquake Engineering Research Center (PEER) Structural Database [12] is the main source for the database. https://doi.org/10.1016/j.engstruct.2018.09.065 Received 27 April 2018; Received in revised form 13 August 2018; Accepted 21 September 2018 ⁎ Corresponding author. E-mail address: enastri@unisa.it (E. Nastri). Engineering Structures 177 (2018) 160–174 0141-0296/ © 2018 Elsevier Ltd. All rights reserved. T