PSI - Issue 44

Gaetana Pacella et al. / Procedia Structural Integrity 44 (2023) 1324–1331 Gaetana Pacella et al./ Structural Integrity Procedia 00 (2022) 000 – 000

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MODELLING ISSUES

GEOMETRYOF THEEF

LOCAL BEHVIOUR

LOAD CONDITION

Definition of the EF in the case of irregualr walls

Effect of strength and displacment capacity of piers and spendrels. Role of floors

Effect of axial force and horizontal actions patterns

Influence of the "flange effect"

Spandrels modelling

Fig. 1. Main modelling issues under studying

(Sandoli et al. 2021a). It requires the use of nonlinear structural modelling of masonry buildings subjected to seismic actions, topic which still represents an open problem in structural engineering (Quagliarini et al., 2017, Sandoli et al. 2020a; Ottonelli et al. 2022). Modelling issues of existing buildings are mainly related, on one hand, to in plan and elevation geometrical irregularities of the buildings and, on the other one, to uncertainties on material features due to construction rules and techniques developed over the centuries. To date, different methods and criteria to model the in-plane behavior of masonry walls are available in literature, based on the use of one-, two- or three-dimensional elements. Nevertheless, the Equivalent Frame (EF) approach is the tool suggested by the main national and international codes - both for research field and engineering practice - for carrying out linear and nonlinear static or dynamic analyses (Lagomarsino et al. 2013, Calderoni et al. 2016, Sandoli and Calderoni 2021). Through the EF model each wall is subdivided in three different elements - piers, spandrels and nodes – each of them represented with a Timoshenko beam element placed at the centerline of each structural member and having the same flexural and shear stiffness/strength of piers and spandrels. Rigid offsets are added at the edges of each beam to simulate the nodal panels (Dolce 1989). Despite the widespread use of the EF, many complexities affect its modelling criteria - especially in the case of irregular walls - and several of them are under studying in research field (Ottonelli et al. 2022). In Fig. 1, a summary of the main open issues which needs to be investigated more in detail or which are under studying are schematized. Among these, the geometrical modeling aspects of walls with irregular opening layouts represents one of the main unsolved problems. In fact, difficulties arise when automatized models will be developed because no unified approached have been yet developed, at least for the most recurrent types of irregularities. In this context, some modelling aspects concerning the in-plane seismic behavior of existing masonry walls have been investigated in this paper with reference to some Italian case study buildings. In particular, the attention was focused on the EF idealization of walls with irregular opening layouts, role of spandrels and flange effect (i.e. transverse walls). The outcomes of the different modelling strategies have been compared and, as a result, specific solutions have been proposed to implement within the EF approach. 2. Analyses of some irregularities 2.1. Effect of irregularities and role of spandrels Due to complex geometry of the walls in existing masonry buildings, characterized by vertical and horizontal misalignments, choice and modelling expedients are often not modifiable and repeatable with automatized procedures. Each irregularity should be analyzed and solved case by case based on an adequate engineering judgment, and the results should be correctly interpreted. To validate the effectiveness of the hypotheses adopted to define the EF, comparisons of its structural response with more advanced numerical models can be helpful. In Fig. 2, the EF schematization (Fig. 2b) of a masonry wall belonging to the Petrucci Palace (Fig. 2a), placed in Naples (southern Italy) is represented, developed through the software SAP2000 v18. Details about this case study can be found in Sandoli et al. 2021b. Firstly, the attention was focused on the pier of the ground story without openings: