PSI - Issue 78

Giada Frappa et al. / Procedia Structural Integrity 78 (2026) 17–24

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modeled as a fixed support located at one-quarter of the socket depth below the top edge of the socket. Shell elements were adopted to model walls and staircases. The flat slabs at the first floor and roof levels were modeled solely as loads applied to the supporting beams. Additionally, since they are made of reinforced concrete with 45 cm thick solid slabs, and the openings do not significantly affect their in-plane stiffness, a rigid diaphragm constraint was assigned to the nodes of each floor level. The steel roof structures, installed during construction directly on the main beams and perimeter columns, were included in the model as non-structural permanent loads. Regarding the modeling of non-structural elements, the stiffening contribution of infill and partition walls was neglected; their influence was considered solely in terms of mass. Given the construction characteristics of the precast building and the nature of the loads it is subjected to, plastic hinges were implemented only at the base of the columns, as their behavior can be approximated as cantilever-like. For these hinges, the P-M2-M3 type was adopted, allowing the interaction between biaxial bending and varying axial force to be taken into account. No plastic hinges were assigned to the beams, as they exhibit a simply supported configuration between columns. 3.4. Modal analysis results The results of the modal analysis show that the first mode of vibration is purely translational in the X direction (Fig. 6a) , with a period T₁ = 0.492 s and a participating mass of 79.8%. The translational motion in the Y direction and the torsional motion about the vertical Z-axis are instead always coupled. For these coupled modes, the most significant are the 18 th mode (T₁₈ = 0.123 s) and the 36 th mode (T₃₆ = 0.095 s) , which activate 8.0% and 51% of the total mass for Y-translation, and 14.1% and 19.8% for rotation about the Z-axis, respectively. The coupling is attributable to the asymmetric layout of the structural walls in the building plan, and to the eccentric elevator core location within the penultimate structural bay at the northeast corner of the building (Fig. 1b). These factors generate a significant eccentricity between the center of mass and the center of rigidity, particularly in the Y direction. The minimization of coupling effects is one of the objectives of the retrofit intervention on the building, as it allows for a reduction of the internal forces in the structural elements located furthest from the center of rigidity.

(a)

(b) Fig. 6. (a) First vibration mode of the structure; (b) external steel bracing frames modeling.

3.5. Assessment of the safety indices ζ V and ζ E according to NTC 2018 The index ζ V expresses the level of safety with respect to vertical static loads. Its value is obtained as the ratio between the maximum live load that the structure can actually sustain and the live load that would be considered in the design of a new building with the same configuration. Evaluation of ζ V requires the examination of the results from bending and shear verifications on the beams, considering the most critical effects from all Ultimate Limit State (ULS) load combination. Only 5 beams located on the first floor (10%) out of a total of 48 beams of the building failed to meet the bending verification requirements, and 19 beams (40%) did not satisfy the shear verification criteria. On the basis of these results, it was obtained ζ V = 0.74. The index ζ E is a measure of the seismic safety level of the structure. It is defined as the ratio between the maximum ground acceleration that the existing structure is actually capable of withstanding and the design ground acceleration