PSI - Issue 78

Danilo D’Angela et al. / Procedia Structural Integrity 78 (2026) 1617–1624

1618

1. Introduction Unanchored nonstructural elements (NEs) are highly vulnerable to seismic actions, and under relatively low seismic intensities, they can exhibit major damage (Chen et al., 2025a). Seismic damage of these elements, especially for strategic and critical facilities such as healthcare facilities (Guamán-Cabrera et al., 2023), can have critical consequences in terms of facility functioning interruption, economic losses, and treats for human lives (Chai et al., 2016). The seismic behavior of relatively slender elements is typically governed by rocking or rocking dominated motion (D’Angela et al., 2025) , and, once rocking mode is activated, large rocking amplitudes and heavily instable motion can be achieved even under relatively low intensities (D’Angela et al., 2022) . Rocking behavior (Housner, 1963) is heavily nonlinear and very challenging to estimate unless advanced models or time history analyses are carried out (Chen et al., 2025b; Dimitrakopoulos and Paraskeva, 2015; Fragiadakis and Diamantopoulos, 2020). Minor differences in terms of seismic input type and characteristics, block geometry, and boundary conditions can majorly affect the response, highlighting the complexity and instability of the dynamic phenomenon (Lagomarsino, 2015; Linde et al., 2020), as it is well known by early times (Housner, 1963; Ishiyama, 1982; Yim et al., 1980). Therefore, several studies attempted to define simpler analytical models (e.g., equivalent SDOF models) (Diamantopoulos and Fragiadakis, 2019; Priestley et al., 1978) or to develop capacity formulations (e.g., fragility curves) (Argenziano et al., 2023; Dimitrakopoulos and Paraskeva, 2015; Petrone et al., 2017) able to reliability predict rocking and overturning capacities under seismic actions; in some cases, displacement-based design and assessment approach were defined (Degli Abbati et al., 2021). However, existing approaches present significant limitations. For example, simplified models often neglect the influence of building dynamics, such as filtering and amplification effects, on the seismic demand acting on NEs, limiting the application to elements located at the ground (e.g., monumental elements). Most fragility models are derived for specific geometries or demand parameters, limiting their general applicability across a broader spectrum of element sizes, shapes, and installation heights. Additionally, traditional capacity formulations often focus solely on collapse or overturning thresholds, without adequately capturing intermediate damage states that are essential for performance-based assessments (D’Angela et al., 2025) . The present paper introduces a novel method for evaluating the seismic capacity of rocking-dominated NEs located within buildings. The proposed approach builds on fragility surfaces that explicitly consider the influence of building-induced filtering and amplification effects. A comprehensive set of incremental analyses on rigid blocks is conducted, accounting for variations in block geometry, engineering demand parameters (EDPs), including floor and ground motion intensity measures, and incremental damage states. Closed-form capacity surfaces are derived to facilitate rapid estimation of statistical capacities and associated uncertainties. 2. Modeling and analysis 2.1. Rigid modeling and numerical implementation The numerical analyses were performed by implementing the well-known Housner rigid block model (Housner, 1963), still widely used nowadays for assessing seismic response of slender NEs (Chen et al., 2025b; D’Angela and Magliulo, 2025; Fragiadakis and Diamantopoulos, 2020). Rigid block is depicted in Fig. 1, where O and O’ are the corner about which the block rotates, b and h are the semi-base and height dimensions, R is the semi-diagonal dimension, α is the critical angle, θ is the rotation angle.