PSI - Issue 44

Stefano Bracchi et al. / Procedia Structural Integrity 44 (2023) 442–449 Stefano Bracchi, Maria Rota, Andrea Penna / Structural Integrity Procedia 00 (2022) 000–000

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building codes (e.g. the Commentary to the Italian building code, MIT 2019) allow the performance of analysis of single walls. However, no indications on the definition of the wall’s model in order to lead to a model fully consistent with the behavior of the wall of the entire building are generally given, without even recommending particular attention on this topic. Among the various factors, the behavior of single walls is influenced by orthogonal walls (i.e. the so-called “flange effect”). This works deals with the performance of nonlinear static analysis of buildings characterized by flexible floors, focusing the attention on the analysis of single walls extracted from entire buildings. In particular, comparison among code-based and refined approaches are performed, in order to understand if the current code specifications are sufficiently accurate to perform analyses in case of flexible floors. To this aim, it was also necessary to develop a strategy to carry out nonlinear static analyses of single walls fully consistent with the behavior of the wall inside the building, defining criteria for modeling and analyzing single walls extracted from entire buildings with flexible floors. The considered case study buildings are derived from two URM prototypes subjected to shake-table tests and characterized by timber floors and simple geometry (Magenes et al. 2014), whose seismic response was initially modelled by Penna et al. (2016). The work is limited to the equivalent-frame modeling strategy, where the behaviour of structural elements is modelled by means of macroelements representing piers and spandrels. In particular, the TREMURI software (Lagomarsino et al. 2013) was adopted, using three different macroelements implemented: the bilinear element proposed by Lagomarsino et al. (2013), the macroelement of Penna et al. (2014) and the improved macroelement proposed by Bracchi et al. (2021) and Bracchi and Penna (2021). The first one is an element compliant with the Italian building code NTC08 (2008), whereas the others represent refined mechanics-based elements. First, a strategy to carry out nonlinear static analyses of single walls fully consistent with the behavior of the wall inside the building was developed. Then, a comparison of the results obtained from the analysis of the entire building and the analysis of single walls was carried out, with a focus on the influence of the different macroelements adopted.

Nomenclature E

Young’s modulus of masonry shear modulus of masonry compressive strength of masonry shear strength of masonry

G f m f tu

efficiency parameter

η

elastic modulus of floor parallel to the spanning direction elastic modulus of floor orthogonal to the spanning direction

E 1 E 2

shear modulus of floor

G 1,2

2. Case studies The considered case studies are derived from the stone masonry prototypes subjected to shake table tests (Magenes et al. 2014, Penna et al. 2016). Despite three full scale buildings with timber floors were tested, in this work only two of them were considered. Hence, only the ones retrofitted improving the connections among orthogonal walls and stiffening the floors were studied (Building 2 and 3 according to the nomenclature of Penna et al. 2016). The buildings (Fig. 1) have the same geometric configuration with asymmetric distribution of openings and are made of two stories, flexible timber floors and two walls with openings in the directions parallel to the seismic excitation (West and East walls). Walls are made of two stone leaves with an internal core of rubble stone and mortar, with a total thickness of 32 cm. Furthermore, Building 2 was retrofitted adding steel beams at the first level and a r.c. beam at the walls-to-roof connection and stiffening the floors with additional timber panels. Building 3 was retrofitted adding a r.c. beam at the walls-to-roof connection, timber sheets to the roof diaphragm and r.c. slab to the original timber floor. Values of