PSI - Issue 78

Alessandro Pisapia et al. / Procedia Structural Integrity 78 (2026) 568–575

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However, diaphragms, namely, the floor systems that link these vertical elements, often receive insufficient attention in both design practice and structural education. This oversight persists despite diaphragms playing a fundamental role in ensuring the global seismic response of buildings. Moreover, it is important to highlight the evident difficulty in conducting adequate experimental investigations aimed at evaluating the in-plane deformability of floor diaphragms under horizontal actions. Therefore, the limited number of research studies available in scientific literature primarily relies on numerical simulations, such as those performed by Ju et al. (1999), Moeni et al. (2011), Zhang et al. (2016) and Pecce et al. (2017). Diaphragms represent the principal source of seismic mass and are responsible for transferring lateral inertial forces to the vertical resisting elements. They provide lateral support to columns and walls, resist out-of-plane forces from seismic and wind actions, and ensure the effective transfer of internal forces between vertical components, especially in buildings with structural irregularities or architectural complexities. In some cases, diaphragms must also resist thrusts from inclined columns or earth pressure in basement levels. Nevertheless, diaphragms are frequently simplified in design models using the assumption of in-plane infinite stiffness. While this assumption may be acceptable under specific conditions, it can result in inaccurate predictions of force distribution and, consequently, unsafe or uneconomical designs, particularly when diaphragms are irregular, perforated, or poorly connected to the seismic-resisting elements. Current European and national design standards, such as Eurocode 8 and NTC 2018, offer only limited and often vague guidance regarding diaphragm design. While some amplification of diaphragm demands is recommended (e.g., a 30% increase in design forces in the Italian code), these prescriptions may be inadequate when diaphragms are not intended to undergo inelastic deformation and must therefore be verified in the elastic range. According to the principles of capacity design, diaphragms should be proportioned to resist the maximum internal forces that dissipative vertical elements can develop under extreme seismic events, with due consideration for overstrength effects. Regarding the deformability check of the floor systems, the current codes also provide a quantitative definition of “infinite stiffness” by stating that diaphragms may be considered infinitely rigid if, when modeling their in-plane deformability, the differences in displacements compared to those resulting from the rigid diaphragm assumption do not exceed 10% at all points within the plane. This condition is generally considered satisfied though special care must be taken when diaphragms are supported by vertical macro-elements with very high stiffness and strength, such as shear walls and cores. The main goal of this study is to present a preliminary simplified theoretical model for evaluating the in-plane deformability of floor diaphragms under seismic actions. In particular, two single-storey configurations were investigated, each featuring three and four identical seismic-resisting frames along the direction of the seismic action. This model is intended to support engineers in critically assessing the validity of the infinite in-plane rigidity assumption, and to help identify cases where diaphragm flexibility may significantly alter the expected distribution of seismic forces within the structural system. 2. Theoretical model 2.1. Floor diaphragm with three vertical frames The assumption of an infinitely rigid diaphragm leads to a significant simplification of seismic analysis, as the dynamic degrees of freedom are reduced to two translational components and one torsional rotation for each floor level. However, it is evident that the assumption of infinite in-plane stiffness is a theoretical abstraction, since the diaphragm stiffness must be evaluated relative to the stiffness of the vertical seismic-resisting frames. Consequently, the design provisions reported in the introduction appear to lack rational basis, as the accuracy of the simplified modeling, resulting from the assumption of an infinitely rigid in-plane diaphragm, depends on the ratio between the in-plane flexural stiffness of the diaphragm and the lateral stiffness of the vertical resisting macro elements. This ratio, however, is not explicitly considered in the current design codes. More rational insights can be obtained through a simplified slab-beam model on elastic supports. To this scope, it is possible to consider the case of a perfectly symmetric building with a rectangular floor plan and three vertical seismic-resisting systems aligned in the transverse direction, subjected to seismic action along the same direction as shown in Fig.1. In particular, is the total dimension of the diaphragm and it is perpendicular to the direction of seismic action , is the dimension of the diaphragm along the loading direction, is the span length between the