PSI - Issue 78

Melina Bosco et al. / Procedia Structural Integrity 78 (2026) 441–448

442

Fig. 1. Extrapolation of the SDOF model from a multistory frame.

ratio is necessary for the application of non-linear static methods, e.g. the Capacity Spectrum Method (CSM) (Freeman 1998), or in Direct Displacement-Based Design (DDBD) procedures (Priestley et al 2007). The most known and used approaches to characterize a linear equivalent single degree of freedom system are based on the equal-area criterion stipulated by Jacobsen (1930, 1960) and the equivalent linearization proposed by Iwan (1979, 1980). Based on these approaches, several researchers obtained specialized expressions of the equivalent viscous damping ratio considering different hysteretic SDOF systems, see e.g. Kwan and Billington (2003), Blandon et al 2004, Blandon and Priestley (2005), Guyader and Iwan (2006), Landi et al. (2024). However, the use of literature expressions implies some subjective evaluations. In fact, all the examined literature formulations for the equivalent viscous damping ratio depend on the ductility ratio of the system under investigation. The evaluation of the ductility demand of a structure requires the idealization of its capacity curve. Since different idealization criteria could be adopted (e.g. the elastic-perfectly plastic bilinear idealization given in Eurocode 8 (EN 1998-1 2004) or the bilinearization with hardening stipulated in FEMA-356 (2000) or the multi linear idealization proposed by De Luca et al (2013)), the value of the ductility demand and, ultimately, the value of the equivalent viscous damping ratio depends on the selected criterion. Further, the choice of the most appropriate expression of the equivalent viscous damping ratio for the structure under examination is subjective. In this paper a new ductility-independent expression of the equivalent viscous damping ratio ξ eq of existing reinforced concrete (RC) frames is proposed. A parametric analysis is preliminary conducted on a large set of SDOF systems. Each SDOF system consists of an assembly of beams and columns whose cross-sections and material mechanical properties are consistent with those of RC framed buildings designed in Italy between the 1970s and the early 2000s. The equivalent viscous damping ratio is calculated for each SDOF system at the first achievement of the chord rotation capacity ϑ u of the members. Then, the proposed expression of the equivalent viscous damping ratio is fitted against the above results as a function of the ratio of the elastic to secant period of vibration of the SDOF system and of the chord rotation demand of beams and columns. 2. The SDOF system The SDOF system is intended as a part of a multi-story, multi-bay RC frame whose interstory height H and bay length L are equal to 3.20 m and 4.50 m respectively, as shown in Figure 1. It is assumed that at the intermediate stories of the frame the null point of the bending moment diagram in the columns is located at mid-height of these members (shear length L v = H /2). Further, it is assumed that seismic actions do not cause relevant axial forces in the columns of the central bay. In addition, it is assumed that the null point of the bending moments caused in the beams by the seismic actions is located at mid-length of the beams. With these hypotheses, the SDOF scheme is extrapolated by cutting off each column of two consecutive stories at the null point of the bending moment diagram and by cutting off the beams at the sides of the central bay at their mid-points. The cross-sections of the four columns of the SDOF model are assumed to be equal as well as the cross-sections of the three beams. In the side beams, the bending moment diagram due to the gravity loads is simulated by means of a fictitious concentrated external bending moment applied at nodes 8 and 9. The supports at nodes 1 and 2 consist of external hinges that