PSI - Issue 77

Humberto Varum et al. / Procedia Structural Integrity 77 (2026) 665–672 Author name / Structural Integrity Procedia 00 (2026) 000 – 000

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analysis. For the first storey, the horizontal force was equal to 1/12 th of the weight above, and, for the 2 nd and 3 rd floors, equal to 1/8 th of the weight above (Fajfar, 2018). The first seismic code with a seismic coefficient of 10% emerged in Japan in 1924. Them, with a seismic coefficient that varies from 7.5 to 10% (depending on soil conditions) of the building's total dead and live loads, the Lateral Bracing Appendix was an optional appendix to the Uniform Building Code that introduced the first code regulations in the United States in 1927. Later, in 1978, the US began using new codes using ATC 3-06 recommendations, namely force reduction R-factors, probabilistic seismic maps (Fajfar, 2018). Despite R-factor or behaviour factor in EC8 make it possible to roughly account for the positive effects of the structure's nonlinear behaviour in a conventional linear analysis, describing the complex phenomenon of non-elastic behaviour for a structure with a specific average value has drawbacks and can lead to misunderstandings. As a result, this approach has been helpful to designers for decades and is beneficial for real-world applications. It only offers approximate solutions for the seismic analysis and design, nevertheless (Varum et al., 2022a). The modal response spectrum method was incorporated into the USSR's 1957 Standards and Regulations for Building in Seismic Regions, which made it the most crucial analysis technique. Later, this process was incorporated into several European seismic codes, and it is still used today for seismic analysis throughout Europe, as recommended by EN1998-1:2004 (CEN, 2004) and prEN1998-1-2:2024 (CEN, 2024). The Uniform Building Code (UBC) from USA, in 1991, was the first code to incorporate guidelines for the application of nonlinear response history analysis (NRHA) in seismic design for structures with passive energy dissipation systems and buildings that are base-isolated (Haselton et al., 2017). Nonlinear static (pushover) analysis was initially adopted in ATC 40 (ATC-40, 1996) and has been adopted in EN1998-1:2004 (CEN, 2004). Pushover-based techniques integrate the response spectrum approach with nonlinear static analysis. An inelastic response spectrum can be used to calculate seismic demand for an analogous single-degree-of-freedom (SDOF) system. The transformation of the multi-degree-of-freedom (MDOF) system into an analogous SDOF system, which represents the main limitation of pushover-based methods, would be exact only when the structure vibrated in a single mode with a deformation shape that did not change over time (Fajfar, 2018). EN1998-1:2004 (CEN, 2004) uses linear modal response spectrum analysis as its primary analytical method. There are some limitations on the usage of the comparable static lateral force procedure. Nonlinear analysis is allowed and can be either NRHA or pushover analysis. The second generation of Eurocode 8, prEN1998-1-2:2024 (CEN, 2024), introduces improvements, namely: • Introduction of new ductility classes: DC1, DC2, and DC3, which incorporate new aspects of wall structure design, such as the behaviour factor, design moment, and shear envelopes; • Definition of the behaviour factor as a composition of the product of the partial components: q R (overstrength due to the redistribution of seismic action effects in redundant structures), q S (overstrength due to all other sources) and q D (the deformation and energy dissipation capacity). Fig. 1 summarizes the seismic codes evolution discussed above.

Fig. 1. Seismic codes evolution.