PSI - Issue 64

Massimiliano Ferraioli et al. / Procedia Structural Integrity 64 (2024) 1017–1024 Ferraioli et al./ Structural Integrity Procedia 00 (2019) 000–000

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1. Introduction Torsional effects in buildings during seismic events stem from factors beyond just asymmetrical mass and stiffness distributions. Additional causes, such as variations in excitation at support points, non-structural element characteristics, and uneven live load distributions, contribute to generating eccentricities that are challenging to anticipate and quantify. These irregularities result in non-uniform plastic demand distributions due to floor rotations, leading to complex behavior, particularly under bidirectional seismic excitation due to torsional coupling effects. The torsional response can intensify in the inelastic range due to increased eccentricities caused by yielding at the structure's perimeter and torsional coupling effects, especially under bidirectional seismic excitation. Conversely, torsional effects typically diminish with increasing ground motion intensity and related plastic deformations. Linear analysis may not adequately account for this, particularly for the stiff edges of torsionally rigid buildings in the strong torsional direction and the weak edges of torsionally flexible buildings. Nonlinear static analysis of multi-story irregular buildings presents several challenges, including seismic excitation direction, lateral force distribution eccentricity, higher modes contribution, and node control for monitoring target displacement. Conventional pushover analysis with lateral force applied at the building's center of mass may underestimate seismic torsional response. Additionally, using the center of mass as node control may impact the accuracy. Furthermore, the dynamic response of irregular structures reveals that maximum displacement and rotation do not occur simultaneously. Consequently, a single pushover force distribution may not provide the most severe conditions for all structural elements. 2. Torsional effects in seismic assessment of buildings To address torsional effects, modern building codes have imposed restrictions on the design of buildings with irregular layouts and introduced the so-called accidental design eccentricity. This provision is based on studies carried out on simplified elastic multi-story buildings or simplified inelastic, one-story systems, while comprehensive conclusions regarding the inelastic torsional response of real multi-story buildings are still lacking. On the other hand, the validity and applicability of static pushover analysis were extensively studied in the literature. Nonlinear static procedures (NSPs) were implemented in procedures based on the Capacity Spectrum Method (CSM) or Displacement Coefficient Method (DCM), such as in FEMA 273 (1997), FEMA 356 (2000), ATC-40 (1996), Eurocode 8 (2005), Italian Code (2008), FEMA-440 (2005), and ASCE/SEI 41-13. However, several deficiencies were highlighted in the literature. No physical principle justifies the existence of a stable relationship between hysteretic energy dissipation and equivalent viscous damping, particularly for highly inelastic systems. Thus, procedures based on High Damping Elastic Demand Response Spectra (HDERS), may provide a very poor estimation of the target displacement. Moreover, the hypothesis of invariant lateral load distribution may be a very restrictive assumption for structures where higher mode effects are significant or local plastic mechanisms occur. The importance of these so-called "MDOF Effects" increases as the amount of inelasticity in the structure increases. Additionally, the application of pushover analysis to plan and vertically irregular building structures may create some problems due to torsional effects. Some authors observed that these effects generally decrease with increasing the plastic deformations and, thus, they can be conservatively estimated using elastic modal analysis. Chopra et al. (2004) suggested calculating the torsional response by combining the inelastic first mode contribution with the elastic higher mode contributions. Ferracuti et al. (2009) proposed a Force/Torque Pushover (FTP) analysis. These pushover methods tend to have some problems giving consistently good agreement with the Response History Analysis (RHA) results. Moreover, the differences tend to increase as the motion intensity increases and the response becomes more nonlinear. 3. Benchmark structure This paper examines a school gymnasium building (Fig. 1a) located in Vibo Valentia (Calabria-Italy) that is part of a larger school complex designed in the mid-1970s, with structural elements originally designed to bear only vertical loads. The school complex comprises four blocks of buildings separated by a seismic joint, including the gymnasium building, which has a planimetric shape resembling an "L" (Fig.1b). All structural units are constructed with reinforced