PSI - Issue 64

Sabatino Di Benedetto et al. / Procedia Structural Integrity 64 (2024) 983–990 S. Di Benedetto / Structural Integrity Procedia 00 (2019) 000 – 000

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As shown in Fig. 1, a numerical model of the analysed structure has been developed using SAP2000 software (CSI, 2021). All steel components have been represented by elastic beam elements, except for the bracings, which have been modelled as truss elements active only under tension. The pinned behaviour of the connections at beam to-column and column base joints has been simulated by applying rotational releases at the beam ends and the bases of the first-floor columns. Additionally, all nodes within the same levels have been constrained to move accordingly by implementing rigid floor diaphragms. Modal and linear static analyses have been performed. In particular, the modal analysis returned vibration periods of approximately 0.40 s for the first two modes. Meanwhile, the linear static analyses were conducted encompassing 84 load combinations at both the DL and LS limit states, covering all potential combinations of seismic actions. Based on these assumptions, the checks of the pinned beam-to-column joints shown in Fig. 3 were assessed under the ULS combination (1.3G k1 +1.3G k2 +1.5Q k ) with maximized gravity loads. The results revealed that the plates in bearing exhibited a maximum D/C ratio of 0.91, which represented the most critical check. Although this value is very close to the limit, the checks were deemed satisfied. Furthermore, considering that the bracings can withstand maximum axial forces of 381 kN and 150 kN at the first and second storeys, respectively, the connections between the diagonals and the columns were assessed with these actions, resulting in maximum D/C ratios of 0.78 and 0.31 at the respective levels for combined shear-tensile actions. Linear static analyses were conducted at the LS and DL limit states. At the LS limit state, collapse occurs if the yield stress, ultimate material deformations, or local/global instability phenomena are observed. Conversely, the DL state signifies the point at which structural deformations prevent the efficient utilization of the structure. The D/C ratios for resistance and stability, evaluated for the as-built configuration of the structural members, were found to be 0.95 for HE160 profiles and 1.76 for HEB160 columns. However, the same ratios for axial actions pertaining only to the diagonals resulted in a maximum D/C ratio of 3 at both storeys. Instead, regarding the checks at DL, it was observed that the maximum interstorey drift among all the analysed DL combinations was equal to 0.7%, which is below the 1% limit applicable to structures with infills designed to accommodate interstorey displacements without sustaining damage. Derived from the previous results, the seismic risk index (  E ) of the structure was determined to be 0.33. These findings facilitated the classification of the analysed structure into Seismic Risk Class D, as per the Guidelines for the classification of seismic risk of buildings D.M. 58 (2017). The previous analyses were conducted as elastic analyses, where all structural elements were modelled elastically. However, further investigations were undertaken by modelling the bracings as non-linear elements, employing links that act only under tension until reaching the ultimate resistance of the diagonals. This modelling approach allowed for non-linear static analyses characterised by Mass and Modal displacement distributions. The pushover curves depicted in Fig. 6 confirm that the as-built configuration of the examined structure exhibits limited displacement capacity upon reaching the peak base shear, indicating an inadequate seismic structural response. Another noteworthy aspect pertains to the irregular activation of plastic elements in the diagonals upon reaching the peak base shear values. Specifically, braces in tension on the second storey collapse in the Modal distribution, whereas in the Mass distribution, this occurrence is observed with braces on the first level. This irregularity arises from the non-uniform variation of brace overstrength along the building height, a factor not controlled during the design phase. This discrepancy stems from the absence of specific regulations in the design code used in 1982. In contrast, contemporary standards such as NTC2018 and EN1998-1 provisions (2004) address this issue by stipulating that, for new structures, the maximum overstrength factor Ω max (i.e., the maximum ratio between the plastic axial resistance of a given brace N pl,Rd,i / and the corresponding design seismic demand N Ed,E,i ) for tension braces should not exceed 1.25 times the minimum overstrength factor Ω min to ensure simultaneous brace yielding at all floors. 4. Retrofitted structure The analysis of the existing configuration of the school has revealed that the bracing system requires significant improvement. Consequently, it was decided to replace the existing diagonals with new braces equipped with innovative aluminium foam dampers (Fig. 5). The distinctive feature of this device is its ability to dissipate seismic