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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As emerged from the previous outcomes, the modelling of the joint shear mechanism (“wJ”) allowed to consider the nonlinear behavior of the joints even in the post-crack phase. Although the achievement of the cracking strength and the maximum strength of the joints leads to a reduction in the global stiffness and strength, a right evaluation of all the deformability contributions is performed. On the contrary, if the joint behavior is not properly accounted in the numerical model (“noJ”), it might be appropriate to limit the joint strength and the deformability at its first cracking, corresponding to a principal tensile stress of 0.3 √ fc, according to the Italian seismic codes (2018). This condition is achieved for a base shear value of 105kN in the case of the “noJ” modelling strategy. Downstream of the considerations made on the pushover analysis results, the seismic assessment of the analyzed frame is carried out in compliance with the nonlinear static procedure described in the current codes (NTC2018) and herein briefly summarized. In particular, the frame is converted to an equivalent single degree of freedom system (SDOF) through the introduction of the modal participation factor. Then, the SDOF capacity curve is idealized as a bilinear elastic-perfectly plastic force-displacement relationship. Once the main properties of the bilinear idealization system are evaluated in terms of elastic period, elastic stiffness and equivalent mass, the capacity curve in the acceleration-displacement (S a -S d ) format can be obtained. Finally, the procedure involves the comparison of the seismic capacity with the demand in the form of the acceleration-displacement response spectrum (ADRS spectrum) suggested by the code for the building site. Figure 5a shows the graphical procedure to estimate the displacement demand (performance point) of the SDOF system in the S a -S d format for the entire curves related to both the “wJ” and “noJ” models. Figure 5b shows the same procedure for the capacity curves limited to the joint first cracking.

(b)

(a)

Figure 5. Frame capacity vs. demand spectrum in the ADRS format: (a) entire pushover curves; (b) curves limited to joint first cracking.

If the entire capacity curve is considered (Figure 5a), the safety index (α=S d,cap /S d,dem ) is almost the same for the two approaches: 1.35 for the “wJ” model and 1.37 for the “noJ” model. Indeed, the slight difference in the elastic stiffness does not appear to affect the global performance of the structure. If the capacity of the system is limited to the joint first crack condition (Figure 5b), the approach without the joint modelling achieves a safety index α=0.25; on the other hand, the “wJ” model furnishes an index of 0.13, due to the lower value of the base shear attained. However, while in the former approach the deformability contribution of the joints should be limited to the first cracking condition, the latter allows considering the joint nonlinear behavior even beyond the cracking point and thus, the pushover curve can be followed until the ultimate limit state (CO). 4. Conclusions The present study is part of a research activity carried out by the Authors concerning the role of beam-column joints on the seismic vulnerability of RC-frames. In particular, starting from previous findings regarding a macro-