PSI - Issue 44

Samuel Barattucci et al. / Procedia Structural Integrity 44 (2023) 426–433 Barattucci et al./ Structural Integrity Procedia 00 (2022) 000–000

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target the cyclic response under the largest displacement amplitude, when infill panels provide negligible stiffness and strength. In this step, the numerical model included only the r.c. members. Then, the numerical model was integrated with the equivalent diagonal trusses that simulate the infill panel. In this second step, the features of the infill panel were determined so that the numerical model matched the response provided by the experimental test when low-medium displacement amplitudes are applied. 4.3. Cyclic response: numerical model Vs. experimental test In the first step, the calibration of the numerical model led to the determination of the mechanical parameters characterizing concrete and steel materials. In particular, the maximum compression strength of concrete F cm was set equal to 21.95 MPa, i.e. the mean compressive strength obtained from the concrete compressive tests. The corresponding Young’s modulus E cm was calculated as 2 F cm / ε c2 and it was equal to 21950 MPa. This value was assigned to the elastic part of columns, while it was reduced to 11475 for the elastic part of the beam. This reduction of the Young’s modulus takes into account that beams are cracked under gravity loads, even before the occurrence of the earthquake. The confinement effect on the core of the member cross sections was neglected because the specimen is representative of r.c. structures designed without seismic provisions, that generally have few stirrups in the r.c. members. Hence, the maximum concrete compression was set equal to 21.95 MPa also for the concrete core. The concrete strains corresponding to the maximum compression strength ε c2 and crushing strength were assumed equal to 2x10 -3 and 3.5x10 -3 , respectively. The concrete compressive strength at crushing, i.e. the residual strength, was calibrated based on the results of the full-scale experimental test carried out on the r.c. frame and set equal to 6 MPa. The tension strength of concrete is virtually zero. As for steel, the Young’s modulus E s was assumed equal to 210000 MPa and the yielding strength f ym and the kinematic hardening ratio b were equal to 400 MPa and 0.001, respectively. These parameters led to the cyclic response of the r.c. frame without infill panels plotted in Figure 6b by black line, which matches the experimental response of the frame (grey line) after complete crushing of infills. In the second step, the features of the diagonal trusses simulating infill panels were defined. The mechanical properties were assigned according to the data provided by the experimental tests. Hence, the thickness was equal to 12 cm, Young’s modulus and shear modulus were equal to 1979.7 and 791.9 MPa, respectively, while cracking strength was equal to 0.23 MPa. The parameters α and β, which rule the post-capping degrading stiffness and the residual strength, were calibrated to match the cyclic response of the infilled frame provided by the test and values α =0.006 and β =0.02 were found. Since the experimental results of the infilled frame showed cyclic degradation of strength and stiffness under cyclic loading, the parameters of the “Pinching4” material were set as follows. The value of 0.5 was assigned to (1) the floating point defining the ratio of the deformation at which reloading occurs to the maximum historic deformation demand and (2) the floating point defining the ratio of the force at which reloading begins to the force corresponding to the maximum historic deformation demand. The value of the floating point defining the ratio of strength developed upon unloading from negative load to the maximum strength developed under monotonic loading was set equal to 0. The same

100 125 150 175

100 125 150 175

Experimental Numerical

Experimental Numerical

Response of infilled frame

Response of bare frame

0 25 50 75

0 25 50 75

F [kN]

F [kN]

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0 25 50 75 100 125 150 175

Displacement [mm]

Displacement [mm]

(a) (c) Fig. 6. (a) Cyclic response of the infilled frame provided by experimental test, (b) calibration of numerical model of r.c. bare frame; (c) calibration of numerical model of r.c. infilled frame (b)