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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The case studies were then modelled using the macroelement of Penna et al. (2014), which is a mechanics-based element able to model several aspects influencing the response, such as cracking of the section, toe-crushing, mechanics-based shear damage, uplift of the element and cyclic behavior. Therefore, it represents a refined model with respect to the code-compliant bilinear element. To characterize the material, the following properties have to be defined: Young’s modulus E , shear modulus G , density ρ , compressive strength f m , equivalent initial shear strength f v0,eq , shear drift capacity δ T , flexural drift capacity δ F , equivalent friction coefficient μ eq and the two parameters Gc t and β governing the nonlinear shear deformability (refer to Penna et al. 2014 and Bracchi and Penna 2021 for further information). The calculation of f v0,eq and μ eq is based on a linear approximation of the shear strength criterion around the point corresponding to the acting axial load (Bracchi and Penna 2021). The values of f v0,eq and μ eq adopted in this work were calibrated starting from characterization tests and in-plane cyclic tests. The case studies were finally modelled using the macroelement proposed by Bracchi et al. (2021) and Bracchi and Penna (2021), which is an improved version of the macroelement of Penna et al. (2014), solving some limitations regarding compressive behavior, flexural stiffness, shear strength and deformability. In particular, the element is able to calculate the shear strength according to different strength criteria, automatically calculating the equivalent shear strength parameters. In this work, the shear strength was calculated according to the criterion proposed by Turnšek and Sheppard (1980). For consistency with the macroelement of Penna et al. (2014), the adopted value of f tu was not obtained from characterization tests, but was calculated from the f v0,eq and μ eq used with the macroelement of Penna et al. (2014) using the formulas relating f tu to f v0,eq and μ eq (Bracchi and Penna 2021). The following values of f tu were obtained: 0.163 MPa for Building 2 and 0.142 MPa for Building 3. Finally, the macroelement of Bracchi et al. (2021) was adopted for piers only, whereas spandrels were modelled with the macroelement of Penna et al. (2014), using values of f v0,eq and μ eq adopted in the case where piers and spandrels were modelled with this element. 3. Modelling strategy The first step of the work consisted in the definition of a strategy to model and analyze a single wall, able to reproduce the same results obtained for the same wall when the analysis is performed on the entire building. This required to perform a pushover analysis on the entire building and on all its walls analyzed as single walls. The developed modeling strategy for the single wall analysis would ideally allow to obtain the same results obtained for that wall in the analysis of the entire building. To this aim, the original case study building had to be modified. First, all the walls (parallel and orthogonal to the seismic action) need to be fully symmetric. To this aim, the East wall was modified to have the same geometry of the West wall (characterized by the presence of two openings). Roof was modelled in a simplified way, by means of a plan diaphragm, as done at the first level. Openings in the North wall were eliminated to have the same geometry of the South wall. In this way, a first case study was defined assuming no openings in the walls orthogonal to the seismic action (Fig. 2). In addition, a second case study, characterized by the presence of a single opening at both levels of the two transversal walls was considered.

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Fig. 2. West/East (a) and North/South (b) wall for the first case study.

The strategy to model the single wall consisted in adopting a bi-dimensional modeling of flanges, i.e. the walls orthogonal to the in-plane loaded wall. Flanges are modelled as piers belonging to the considered in-plane loaded wall and defined along the entire interstory height. It was necessary to define a sufficiently small width (0.0001 m)