PSI - Issue 44

Sara S. Lucchini et al. / Procedia Structural Integrity 44 (2023) 2286–2293 Lucchini et al. / Structural Integrity Procedia 00 (2022) 000–000

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directions were analyzed separately (see Table 2) to consider the axial load increase due to global rocking involving the whole building. This increase corresponds to the weight of the areas of potential detachment of the adjacent transverse façade. The latter were identified by considering a failure angle inclined of 22 degrees with respect to the vertical plane and a band of constant width on the first floor. The global resistance of the building was estimated as the sum of the resistances of all the walls oriented parallel to the analyzed loading direction. As observed in the experimental test, the predicted in-plane resistance of the walls was governed by flexure (piers 1-3-4-6) and diagonal shear (piers 2-5). Only pier 5 did not show diagonal failure at the end of the test. The predicted seismic resistance of the unstrengthened building was equal to 129.1 kN and 129.7 kN in the positive and negative loading direction, respectively (see Fig. 1a). In both cases, the analytical prediction was on the safe side as it underestimates the experimental response by 28% and 27% respectively. Retrofitted building – positive loading direction (+X) The analytical model proposed by the Authors was used to determine the resistance of the six piers after retrofitting with SFRM coating on the external surface only. As discussed in Lucchini et al. (2021), a series of 700 mm long Φ8 steel rebars was used to connect the coating layer to the RC foundation and to prevent cracking of coating at the corners of the openings (see Fig. 2). Particular attention was paid to the schematization of the retrofitted piers, based on the fracture lines observed after testing. In fact, the SFRM coating and the reinforcing bars affect the failure mechanisms of the walls leading to fracture lines different from those proposed by Dolce (1991) for URMmasonry. The dotted lines represented in Fig. 2 represent the critical sections considered in the analytical calculation. In more detail, depending on the loading direction and on the geometry of the openings, the lower critical section was placed either at the interface with the foundation, where there is only the tensile contribution of steel rebars, or at the base of the windows, where there is only the continuity of SFRM (see Fig. 2a). The upper critical section, on the other hand, was placed at the intrados of the RC chord or at the upper end of the openings. Such an arrangement of the critical sections allows the prediction of the in-plane capacity to be on the safe side. Table 3 reports the resistance of the six longitudinal piers. Different axial loads and bending moments were considered for top (N t and M R,t ) and bottom (N b and M R,b ) ends of the piers, due to the different tensile contributions. An axial load increase was considered on piers 1 and 4 to consider the uplift of the adjacent transverse façade. Finally, V R, flex =(M R,t +M R,b )/(0.5·h) is the lateral load causing flexural failure of the pier. The global resistance of the retrofitted building in the positive loading direction, which was calculated as the sum of the resistances of the six piers of the ground floor, was 437.5 kN, corresponding to 72% of the peak load recorded in the experimental test (see Fig. 1a). As expected, the analytical prediction was on the safe side. The numerical predictions were calculated by keeping the initial axial load constant on each pier, assuming the wall ends to be free to vertically translate. On the contrary, during the test this translation was partially prevented by the rigid seismic floor diaphragm. In this configuration, as the horizontal load increases, the restrained vertical deformation causes the progressive increase of the axial load which, in turn, leads to a significant increment of the lateral resistance of the wall.

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(b)

Fig. 2. Retrofitted experimental building: schematization of resisting piers in (a) positive and (b) negative loading direction.