PSI - Issue 78

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

447

ξ eq [%] exp

R 2 =0.80

10 15 20 25 30 35

0 5

ξ eq [%]

0

5

10

15

20

25

30

35

Fig. 3. Predicted value ( eq  ) versus experimental ( exp

eq  ) values of the equivalent viscous damping ratio

5. Proposed expression of the equivalent viscous damping ratio Based on the trends highlighted in the previous section, an expression of the equivalent viscous damping ratio has been calibrated. The functional form of the proposed expression of the equivalent viscous damping ratio is constructed to include the parameters that more effectively influence the relationship between the lateral displacement of the inelastic SDOF system and the equivalent viscous damping ratio of the elastic SDOF system. The proposed expression is reported below ( ) ( ) 2.50 1.25 2.10 0.65 b 0.70 c 0 eq 0 max max sec 34 1 650 5000 −    = + − +   +     T T (4) where  0 is the viscous damping ratio associated with the energy dissipation in the elastic range of the structural behavior. For RC framed structures, the value of  0 is typically assumed equal to 5% of the critical damping. The dependency on the ratio T 1 / T sec accounts for the contribution to the equivalent viscous damping ratio due to the elongation of the period of vibration of the system. The contributions dependent on the maximum chord rotation demands account for the energy dissipated in beams and columns. The numerical values that appear in Eq. (4) have been determined so as to minimize the sum of squares of the differences between the equivalent viscous damping ratios given by the parametric analysis and the equivalent viscous damping ratios evaluated through the proposed equation. The optimization procedure has been performed by means of the MS Excel solver using the non-linear GRG method. Because of the nonlinearity of the mathematical problem, the optimization procedure has been repeated many times considering different initial values of the six constants. The value of the coefficient of determination R 2 resulting from the optimization process is equal to 0.80. The values of the equivalent viscous damping ratio obtained through the parametric analysis are plotted in Figure 3 Error! Reference source not found. against the corresponding values predicted by means of the proposed formulations. 6. Conclusions In this paper a new closed-form expression of the equivalent viscous damping ratio of existing RC frames is presented. The proposed expression is independent of the global ductility demand, whereas it depends on both global and local parameters of the analyzed system i.e., the ratio between elastic and secant period of vibration of the structure and the chord rotation demand of beams and columns. The influence of these parameters on the   