PSI - Issue 44

Ernesto Grande et al. / Procedia Structural Integrity 44 (2023) 582–589 Grande et al. / Structural Integrity Procedia 00 (2022) 000–000

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The mechanical properties of concrete and steel rebars were estimated from in-situ experimental tests: a mean value of the concrete compressive strength, f cm , equal to 24.5 MPa was evaluated, while an average yielding strength, f ym , equal to about 470 MPa, and an ultimate strength, f u , of about 735 MPa were obtained by testing steel rebars in tension. Pushover analyses were performed by applying lateral static displacements to the left nodes at the floor levels and considering a distribution along the height proportional to the mass. An axial load of 90 kN was applied at the top of the columns at the first floor, while a load of 180 kN was considered at the top of the columns at the second floor. Finally, a distributed load equal to 12 kN/m was considered on the beams. 3.2 Numerical analyses and results With reference to the accounted case of study, two different modeling approaches are herein presented, both obtained by using the OpenSees software framework (McKenna et al., 2010): • the first approach, herein denoted as “noJ”, where the nonlinear behavior is introduced only at the level of beams and columns without considering any models for the joints between beams and columns (i.e., according to a common modelling approach); • the second approach, herein denoted as “wJ”, where the scissors model is introduced for modelling the beam column joints in addition to the nonlinear behaviour of beams and columns elements. The nonlinear behavior of beam and column elements is introduced throughout a fiber discretization approach, where the uniaxial material model “Concrete04-Popovics” and the uniaxial material model “Steel02 – Giuffrè Menegotto-Pinto” are selected respectively for concrete and steel. The rotational springs introduced to simulate the shear behavior of the joint panel are modelled through the “Pinching4” uniaxial material by adopting the parameters proposed in Grande et al. (2021b). For both the structural models (“noJ” and “wJ”), pushover analyses are carried out. The gravity load patterns, those related to the distributed load on the beams and the axial forces acting on the top of the columns, are first applied. Subsequently, by keeping constant the gravity loads, a lateral load distribution is applied to the left side of the frame through a displacement control procedure with increase of 0.1 mm at each loading step. The pushover curves in terms of the base shear (V b ) versus the lateral displacement of the top floor (Disp) are reported in Figure 3 for both the modelling approaches (“wJ” model and “noJ” model). In the same figure is also reported the numerical curve obtained by Del Vecchio et al. (2016). The two modelling approaches lead to a difference in terms of the attained level of the lateral force: 143kN for the “wJ” model and 200kN for the “noJ” model. A not relevant difference concerns the lateral stiffness which shows a reduction in the case of the scissors model. The figure also shows that the curve obtained by Del Vecchio et al. (2016) lies between the curves here obtained by the two modelling approaches. In the figures are also reported the values of the base shear corresponding to the attainment of the first crack of the joints (marked with triangles) and the rotation capacity corresponding to the maximum shear strength (marked with squares). In order to investigate the deformability contributions also for beam and column members, on the capacity curves of Figure 3 are also reported the points (marked with cirlces) denoting the attainment of the following Limit States: collapse (CO), severe damage (DS) and limited damage (DL). They have been evaluated in terms of the chord rotation of beams and columns according to the current Italian codes (2018). As it can be noticed, the global mechanism governing the structural behavior of the frame is the same for both the modelling approaches; indeed, the three limit states are attained by the right column placed at the second level and at the same step of the analysis: 40mm for the DL, 73mm for the DS and 98mm for the CO limit state. For the “wJ” model, it occurs that the yielding (DL) of the first member of the frame is achieved after the first crack of the joints placed at the first level. Compared to the model that neglects the joint modelling, the “wJ” curve shows a variation of the lateral stiffness of the frame (corresponding to the beginning of the nonlinear behavior) for a value of V b equal to 66kN. This point represents the attainment of the joint first crack (τ 1 - γ 1 in the shear backbone multilinear law) at the right side joint of the first level, which is characterized by the largest rotational capacity among the four shear springs.