PSI - Issue 44

Alessandro Mei et al. / Procedia Structural Integrity 44 (2023) 2318–2325 Mei, et al./ Structural Integrity Procedia 00 (2022) 000–000

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However, they have peculiar mechanical features that make them different from ordinary steel buildings made of hot rolled sections. Columns (called uprights) have complex multi-folded open sections to reduce local and distortional buckling phenomena, Bertocci et al., 2017, caused by the small thickness of the sheets used for the cold-forming process (usually from 1.5 to 3.0 mm). Moreover, uprights are perforated along their height to provide layout versatility. The upright-to-beam joint is also affected by nonlinearities, like hysteretic pinching. This phenomenon is typical of dry joints made with a special connector welded to the horizontal beams and provided with a variable number of tabs that hook inside the spaced holes in the upright. In the capacity design, upright-to-beam joints are the leading cause of energy dissipation during seismic motion. However, evaluating the joint mechanical behavior is theoretically challenging because of the significant number of different upright-to-beam joints and profiles used in the engineering practice. For that reason, monotonic and cyclic tests have been carried out in the last two decades on rack joints (e.g., Aguirre, 2005, Bernuzzi and Castiglioni, 2001, Dai et al. 2018, Gusella et al. 2018, Yin et al. 2016), especially highlighting the pinching behavior of this kind of connection (Dai et al. 2018, Gusella et al. 2019, Jovanović et al. 2019, Peterman et al. 2014, Zhao et al. 2018). Rack building codes nowadays are divided into national/international and specialized codes. In the case of self supporting rack warehouses, national and European codes (such as the Italian Building Code C. S. LL. PP., 2018 or Eurocodes EN1998-1-1, 2004) are used to define external actions on structures, while specialized codes such as CEN European Committee for Standardization, 2009, and 2016 are used to evaluate design aspects not directly treated in general regulations. According to codes, static or dynamic analyses can be performed, and both can be done in the linear or nonlinear field for a total of four different analysis types. Nonlinear dynamic procedures can be impractical for design purposes because, among other reasons, failure criteria should be checked throughout time histories. The nonlinear static analysis (NSA) explicitly considers geometrical nonlinearities and the inelastic behavior of the structure. Avgerinou et al. 2019, Bernuzzi et al. 2017, Castiglioni, 2016, Comparini et al. 2017, Kanyilmaz, Brambilla, et al. 2016, Kanyilmaz, Castiglioni, et al. 2016, carried out full-scale pushover experimental tests to validate NSA for rack structures, investigating capacity curves, ductility factors, and behavior factors. However, NSA does not acknowledge the presence of more degrees of freedom as the system is supposed to respond with a single mode (although procedures that can go beyond this limitation exist), and since it is monotonic, it neglects the pinching of joints and its unstable hysteretic behavior. Moreover, classical pushover analysis is based on time-independent modal shapes, so it can be inaccurate for systems where higher mode effects are significant as rack structures as Mei et al. 2021 show. Finally, the equal-displacement rule for structures with considerable natural periods, on which the NSA analysis of the codes is based, may result in too small inelastic displacement demands in the case of hysteretic loops with significant pinching or stiffness or strength deterioration, as investigated by Fajfar and Gašperšič, 1996, Rahnama and Krawinkler, 1993. In this work, the problem of the cyclic response of rack structures affected by pinching is studied through single degree-of-freedom (SDoF) simulations, and by comparing linear and nonlinear responses, the latter evaluated using both elastic-plastic and pinching laws. The paper is organized as follows. Section 2 reports the constitutive models adopted together with the numerical procedure developed for the simplified response of an SDoF system. In Section 3, the seismic input selected as natural ground motion is reported. Section 4 reports the main results and case studies. Finally, in Section 5, the results are summarized and commented on. 2. Simplified Inelastic Response Restricting the analysis to a single degree of freedom system avoids the issues with higher mode contributions in the response evaluation and with overstrength in the evaluation of the behavior factor. NSA can only determine the system's displacement capacity and ductility ratio, so to evaluate the seismic assessment, it is necessary to define a procedure for determining the inelastic displacement demand at a given ductility.