## 1 Introduction  
The structural behavior of reinforced concrete (RC) buildings under seismic actions is influenced by floors' in-plane stiffness, which has a crucial role in the distribution of inertia forces to vertical structural elements. Such distribution of forces does not depend on the absolute floor stiffness but rather on the ratio between the floor stiffness and the lateral stiffness of vertical elements [1]. In order to guarantee that inertia forces arising in the building distribute among vertical resistan elements proportionally to their lateral stiffness, modern building codes recommend that floors subject to seismic actions are designed to behave as rigid diaphragms. The main geometric factors influencing floor in-plane stiffness are the floor thickness and shape ratio (length/width), the building plan geometry (i.e., rectangular, U-shaped, or L-shaped), the presence of openings within the floor, and the position of shear walls in the building plan [2, 3, 4, 5]. The main worldwide building codes [6, 7, 8, 9, 10, 11, 12, 13] provide qualitative and quantitative criteria to evaluate the adequacy of the rigid floor hypothesis. Qualitative criteria are primarily related to the shape of the diaphragm, while quantitative criteria set bounds to the in-plane deformation of the diaphragm. For instance, the Italian code mandates checking the rigid floor assumption when the building has an elongated- or noncompact-shaped plan or when there are shear walls with high lateral stiffness [8]. It also states that diaphragms can be considered infinitely rigid if, when their actual in-plane flexibility is modeled, the horizontal displacements nowhere exceed those resulting from the rigid diaphragm assumption by more than 10% of the corresponding absolute horizontal displacements. In existing Italian RC buildings, the most widespread floor typologies are the one-way joist systems made by a monolithic combination of a latticework of RC beams filled with regularly spaced ribs (joists) and a top slab with permanent light-weight fillers (usually hollow bricks) between the ribs. For this floor system, the code states that the rigid floor assumption can only be adopted if the slab thickness is not smaller than 40 mm. In existing buildings, designed only for gravity loads, this condition is not always satisfied, as it occurs in the two case-studies analyzed in [14]. Moreover, it is not unusual to deal with buildings having high length-to-width ratios [15], in-plan irregular structural patterns, and/or shear walls not uniformly distributed within the building plan [14]. For such buildings, the in-plane floor deformability could determine a larger demand of both strength and ductility to some structural elements as compared to the case of rigid floors [16; 17; 18; 19; 20; 21; 22]. In all the mentioned cases, the actual in-plane floor deformability may be not negligible. Furthermore, for buildings seismically retrofitted with external stiffening frames connected to the building structure along the perimeter, it may be necessary to take into account the effect of floor in-plane deformability to correctly evaluate the intervention effectiveness. For the seismic analysis of buildings, 3D FE models realized with frame and shell elements are commonly used due to their practicality and computational efficiency. In these models, the complex floor systems are represented by equivalent uniform orthotropic slabs discretized by shell elements with a prevalent membrane behavior (the bending plate part of the shell is not important). The problem of determining the characteristics of an equivalent orthotropic slab that reproduces the behavior of a ribbed plate (homogenization problem) is a rather old one. The method fundamentals were established in a 1914 paper by [PERSON] [23] regarding the bending behavior of reinforced concrete plates with steel ribs.