PSI - Issue 44

Gaetana Pacella et al. / Procedia Structural Integrity 44 (2023) 1324–1331 G. Pacella, A. Sandoli, B. Calderoni, G. Brandonisio/ Structural Integrity Procedia 00 (2022) 000 – 000

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the EF model has been obtained by dividing the pier in a number of sub-piers coinciding with those coming from the upper story. The sum of inertial moment and cross-sectional area of the sub-piers must be equal to the total moment of inertia of the actual pier such that the flexural and shear stuffiness resulted not modified. Moreover, to ensure the kinematic compatibility among the sub-piers, both top displacements and rotations of each sub-pier must be equal among them (and to the real one); thus, a specific internal constrain (i.e., a couple of pendulums) to ensure such compatibility has been introduced. With regards to the spandrels, no effective tensile-resistant elements are in it included able to withstand seismic actions with an effective diagonal compressed strut behavior (Calderoni et al. 2010, Sandoli et al. 2020a). Thus, the spandrels should be considered as not effective with regards to flexural and shear behavior or, at least, its capacity should be limited to the reduced tensile strength of masonry (Beyer and Dazio 2012, Sandoli et al. 2020b). With the aim of providing a possible behavioral range, two limit behavior have been assumed for them spandrels in this paper: ( i ) Weak Spandrel (WS) and ( ii ) Resistant Spandrel (RS). WS means that they are not able to develop a coupling between the adjacent piers under seismic actions (i.e., variation of axial force over the piers). Therefore, the EF model substantially transforms in a series of full-height vertical cantilever walls connected at floor levels by means of an axially inextensible pendulum able to ensure the equality of the horizontal displacements only. Whereas, within the 2D-shell model - considered as a comparison model - the spandrels have been eliminated and the equality of horizontal displacements at floor level has been restored through internal constrains. In the case of RS, the spandrels are able to develop the coupling effect between the adjacent piers because considered provided with flexural and shear strength due to introduction of effective tensile-resistant elements or other reinforcement types. In this case, the EF transforms in a framed structure with beam-like spandrels. While the 2D shell model has spandrels modelled with shell elements having thickness and stiffness corresponding to the actual ones. Both linear-elastic and nonlinear static (i.e., pushover) analyses have been carried on the EF and 2D-shell model. For the pushover analysis, a triangular inverse distribution of seismic actions has been considered in both models. In Fig. 3, the result of linear-elastic analyses in terms of base shear (F) vs. top displacement (  ) curves are showed, for the EF modelled with WS (Fig. 3a) and RS (Fig. 3b). As it can be noted, a good matching between the two curves is resulted, highlighting the correctness of the EF idealization. To validate the effectiveness of the EF model also in nonlinear field, a nonlinear model of the walls has been developed both for EF and 2D-shell model. Within the EF model, the nonlinearity of the structural elements has been considered by means of a lumped plasticity model, i.e., through flexural and shear plastic hinges concentrated in specific cross-sections (where the maximum forces are expected) having an elastic-perfectly plastic behavior. As far as the 2D-shell model are concerned, the nonlinear behavior has been assigned to masonry material through a specific constitutive stress-strain law: elastic perfectly plastic behavior in compression and null in tension. In detail, a) b)

Fig. 2. (a) Plan of Petrucci Palace, (b) analyzed wall