PSI - Issue 62

Rossella Venezia et al. / Procedia Structural Integrity 62 (2024) 796–808 Rossella Venezia and Alessio Lupoi / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction The backbone of any country’s economy consists of its assets of transportation infrastructures, such as highways, bridges. The assessment of existing bridges has become a major issue in recent years. Many bridges in Italy are approaching their design life, therefore, verifying whether these structures are still “safe”, according to the current design standards, is crucial. The reliable detailed assessment of such existing bridges is important to evaluate their structural vulnerability, to address the ones requiring a seismic retrofit. Nowadays, retrofitting existing bridges to resist seismic actions that they were not originally designed for, is a common practice, but identifying which retrofitting solution is the most sustainable is a challenge for the next future. Nonlinear static analysis methods have become a popular tool for the assessment of various structural typologies, including bridges. Pushover analyses have been developed over the past three decades, such as the Capacity Spectrum Method (Freeman et al. 1975) and the single-mode N2 method (Fajfar, Gašperšič 1996) among the others, which represent the fundamentals of the method. They basically consist in identifying the structural performance applying a response spectrum approach to a bilinear representation of an equivalent SDOF model, derived from a pushover analysis of a MDOF model of the structure, under a force vector compatible with an assumed displacement profile (Casarotti, Pinho 2007). The N2 method is based on two main assumptions: (1) that the response of a structure is governed by one mode and (2) that the shape of this mode remains constant throughout the time history response (Krawinkler and Seneviratna 1998). To overcome the above-described limitations, a broad range of multi-mode pushover methods have been developed. They can be classified into two main groups: (1) the non-adaptive group and (2) the adaptive group ( Isaković et al. 2008). Several authors have examined the suitability of various pushover techniques for bridge analysis. These studies compared to those conducted on structures, however, are still in the minority. This study represents a further attempt to investigate the applicability of the N2 method to the analysis of bridges. The main goal of this study is to assess the accuracy of the maximum displacement demand prediction at collapse performance level when significant inelastic deformation of the structure is expected. Along this line, attention is focused on the influence of reference point choice for the construction of the pushover curve. In this paper, basic concepts of the method are first summarized. Then, the investigation is made on a real simply supported beams bridge of considerable length. Due to its irregular configuration, it may be a representative case to test the applicability of the procedure. The results have been compared with those of nonlinear dynamic time history analysis. 2. Pushover analysis of bridge structures The inelastic static analysis consists in determining the response of the structure subjected to a monotonically increasing pattern of static lateral forces compatible with an assumed displacement profile. In the single-mode pushover method, the N2 method, the vector of lateral loads P used in the pushover analysis is determined by Eq. (1), where M is the diagonal mass matrix. = (1) The magnitude of lateral loads is controlled by p . The distribution of lateral loads is related to the assumed displacement shape Φ . The response of a multi degree-of-freedom structure (MDOF) is the non-linear force displacement relationship, so-called static pushover curve (SPO). Obviously, the force-displacement relationship depends on the assumed distribution of lateral forces. The selection of an appropriate distribution of lateral loads is an important step within the analysis. Another important step is the selection of the representatives for force and displacement. In the N2 method, the representative for force is the sum of all lateral forces, that is equal to the base shear. The representative for displacement is the roof (top) displacement of the building structure (Fajfar and Eeri 2000). In the case of bridge structures, the choice of the representative for displacement, so-called the reference point, depends on the structural system. In the N2 method, the response of a MDOF system can be turned into the response of the equivalent single degree-of-freedom system (SDOF). The transformation from the pushover curve of the MDOF (the V - D diagram) to the capacity curve of the equivalent SDOF (the F ∗ - D ∗ diagram) is controlled by the constant Γ given by Eq. (2), that divides both force and displacement.