PSI - Issue 44

Devis Sonda et al. / Procedia Structural Integrity 44 (2023) 115–122 Devis Sonda et al. / Structural Integrity Procedia 00 (2022) 000–000

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We can therefore write the equilibrium between input and absorbed energy: & . " . ! 0 % (4) The absorbed energy E A can be broken down into returned energy (elastic deformation energy E S ) and dissipated energy (hysteretic energy E H ): ! 0 ) . $ Assuming that a new equivalent structure, with the same geometric dimensions of the existing one, is designed to resist to the target site earthquake, the structure must absorb and dissipate an amount of energy equal to that transferred by the design earthquake ( % " ). As discussed above, to quantify the energy, the design requirements of the structure are more significant than the use of design spectrum in describing seismic action, since they also implicitly consider the duration of the seismic action. &' . "' . !' 0 % " (5) where N indicates the reference to the new equivalent structure. The equation expresses the balance between seismic input energy and energy that the structure can absorb in terms of kinetic, dissipated, and elastic energy. For an existing structure, not designed according to the seismic standards, the following applies: &# . "# . !# 0 % " (6) where E indicates the reference to the existing structure. Comparing the two equations we can write: &# . "# . !# 0 &' . "' . !' (7) The energy transferred by the earthquake to the structure is essentially transformed into: • elastic energy that induces deformations, displacements, and stresses; • energy dissipated by the structure through the damping of materials and dissipative mechanisms associated with structural ductility. Collecting the terms related to returned and dissipated energy we set: (#* 0 & . ) ; "%) 0 " . $ So, for an existing structure, we can write: (# #* . "# %) 1 (' #* . "' %) (8) which can be written in terms of energy ratio: . . 1 (9) Therefore, comparing the total energy (returned and dissipated) of an existing and new equivalent structure it is possible to quantify the seismic vulnerability, without necessarily considering the seismic input. 2. Industrial precast RC buildings Precast RC structures present usually a static scheme of columns fixed at the base and hinged to the beams at the top, with slender columns (especially in warehouses not designed for seismic action). The behaviour of the structure, when subjected to seismic action, can be described through a force-displacement curve, referring to a point at the top of the columns. A well-established procedure for deriving this curve is to carry out a push-over analysis. The relatively “simple” structural typology permits to refer to a single degree of freedom (SDOF) model. Assuming that the ideal behavior of the structure can be simplified as elastic-perfectly plastic, it is possible to obtain