Equivalent Frame modelling of URM buildings: numerical validation and rules

Within the context of the seismic analysis of masonry buildings, the application of verification procedures based on nonlinear analyses is now widespread and requires reliable and computationally efficient modelling strategies. Among other possible techniques, the so-called “Equivalent Frame Method” (EFM) is one of the most used, especially in practice engineering. This simplified approach allows to describe the global in-plane behavior of the building and is based on the assumption that the nonlinear response of each wall is concentrated in specific masonry panels which are defined a priori (piers – vertical panels and spandrels –masonry beams that connect piers), while the remaining portions of the wall are usually idealized as rigid nodes. Despite of the large use of these models, there are many aspects that should be considered in order to verify their actual reliability, especially with regard to their application to existing masonry buildings. These last, indeed, are characterized by many irregularities that represent very hard-to-model features, making the application of the EFM complicated and even questionable: presence of flexible diaphragms (vaults, timber floors), different quality of the connection between the orthogonal walls, complex geometries and irregular opening patterns that are the result of several modifications during the years. All these aspects lead to several modelling uncertainties, which are not adequately addressed by the seismic codes, even if most of them explicitly suggest the use of the EFM for the seismic analysis of masonry buildings. Regarding these aspects, the collaboration to research projects developed at national scale has allowed to directly experience the not negligible consequences of the adoption of different plausible modelling choices on the outcomes of the seismic design and assessment of masonry buildings. Within this context, the objective of the present research is to provide a validation of the Equivalent Frame approach with regard to some of the critical issues related to its application. In particular, the attention is focused on the first step to deal with when applying this modelling approach, that is the a priori identification of the structural elements geometry. This last is usually related to the opening pattern of the considered wall: although it is rather straightforward in presence of regular walls with openings perfectly aligned, it may result difficult and arbitrary in presence of irregular opening patterns. The criteria proposed in the literature to this aim are mainly empirical and have never been validated in a robust way, especially with regard to their application to walls with irregular opening layouts. Furthermore, since no standardized rules are provided by the codes, professional engineers can use different criteria for the identification of piers and spandrels, thus potentially obtaining different outcomes of the seismic assessment. Hence, the research here presented firstly provides a systematic comparison between the different criteria available in the literature when applied to walls with different types of irregularity in the opening layout, aiming to explore their potentialities and their limits. To this aim, nonlinear static analyses are performed on case-studies structures represented by two-story walls, making comparisons in terms of global and local response as well as damage pattern between EF models and more accurate Finite Element models, whose results are considered as the reference solution. The obtained results are useful to provide specific indications about the rules for the EF schematization to be used (or avoided) depending on the types of irregularity characterizing the wall; moreover, some possible refinements are discussed, and specific original rules are outlined. Furthermore, since the seismic design and assessment of real buildings require to perform the analyses on 3D models, where the modelling of the connections between the orthogonal walls comes into play, the deepening of this aspect is deemed necessary in the view of a robust validation of the EF model. Indeed, as highlighted also by some preliminary analyses, the modelling of the flange effect may significantly affect, depending on the adopted assumptions, the obtained structural response. Therefore, some preliminary insights about this issue have been addressed. The obtained results, even if still at initial phase, already allow to highlight some potentialities and limits of the strategies commonly used by current EF models for the modelling of URM piers with flanges, outlining possible improvements and representing the starting point for future researches.