PSI - Issue 78

Ebrahim Aminifar et al. / Procedia Structural Integrity 78 (2026) 1466–1473

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Fig. 1. Distribution of nave configurations across the “ rectangular ” subset

The chronological breakdown of construction periods (Fig. 2a) shows that the vast majority of churches were built between the 13th and 18th centuries, corresponding to the Gothic, Renaissance, and Baroque periods. This temporal concentration reflects both the extension of ecclesiastical construction and improved historical documentation during these centuries. Earlier periods (4 th -10 th centuries) are only marginally represented in the dataset, not necessarily due to architectural inactivity, but rather the low survival rate of early structures and limited archival records. This distribution forms the temporal backbone for interpreting changes in design, material use, and spatial articulation. In terms of construction materials (Fig. 2b), stone masonry dominates the known dataset (n = 465), aligning with the geological context of many regions and the long-standing tradition of quarry-based construction. Cut stone, associated with higher technique and used for ashlar or blockwork, was particularly prevalent in Romanesque and early Gothic churches, corresponding with Italy's medieval architectural peak. Conversely, brick use increases markedly in the 18th to 20th centuries. The shift reflects broader technological transitions and regional adaptation of materials, as confirmed in historical and vulnerability studies (De Matteis et al., 2019). Nevertheless, the fact that material information is missing for 42% of churches highlights a critical gap in the dataset, limiting temporal-material correlations and complicating modeling for mechanical properties in seismic assessments. Vault presence and vault typology (Figs. 2c-d) offer further insight into spatial articulation and structural load paths. Among known data, about 57% of churches lack vaults entirely, indicating either timber-trussed roofs or simpler, lighter coverings. Barrel vaults represent the most common structural vaulting method with or without lunettes. Cross vaults were also quite spread among the investigated sample, while others (such as vela and pavilion on spindles) account for smaller shares (DeFabrizio and Mallardo, 2023; Gaetani et al., 2015). The substantial portion of churches with unknown vault typology (32%) highlights documentation gaps and the need for supplementary survey efforts. To address this, future modeling will adopt a dual-scenario approach, incorporating both vaulted and non-vaulted configurations. Probabilistic thresholds based on known characteristics such as construction century or region will guide assumptions about vault presence. The strategy aims to reduce uncertainty propagation and ensure that both documented and undocumented structural configurations are adequately represented in the fragility analysis. Finally, spatial features such as apse and side chapel presence (Figs. 2e) help define functional and morphological complexity. The apse, a semicircular or polygonal termination of the nave, is present in over 53% of churches and plays both symbolic and structural roles; its curvature can enhance stiffness and mitigate overturning failures. Side chapels, on the other hand, are relatively rare (15%) in this typology, confirming the architectural simplicity and longitudinal dominance of single-nave churches. This reinforces their classification as structurally regular and morphologically constrained units, ideal for baseline fragility modeling . 3.3. Geometrical features of Single-Nave Churches The geometric ratios were analyzed to explore proportional logic. The area-to-height (A/H) ratio (Fig. 3a) showed a quite good linear relationship, with an average value of 1.91, indicating that taller churches generally had broader naves, suggesting a consistent volumetric rule aimed at preserving stability and aesthetic harmony. The associated histogram reveals a distinctly skewed distribution, indicating a predominance of proportionally compact configurations and a limited occurrence of geometrical extremes characterized by either excessive verticality or horizontal expansion (Fig. 3b).