PSI - Issue 78

Marco Terrenzi et al. / Procedia Structural Integrity 78 (2026) 418–425

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Di ff erences between Rayleigh and Modal damping stem from how they capture sti ff ness changes due to plasti cization. Using k init in Rayleigh damping may cause overdamping, while k comm better reflects sti ff ness degradation, yielding results similar to Modal damping.In the IF model (Figure 7), trend lines in the X direction nearly overlap, in dicating similar results across damping approaches. In the Y direction, as with the BF model, modal damping leads to higher structural demands, with di ff erences more pronounced than in the BF case. The di ff erent damping approaches are compared by measuring the computational time needed to analyze two building models, BF (Figure 8a) and IF (Figure 8b).Modal damping extends analysis times by 15-20% compared to Rayleigh damping. Increasing the damp ing ratio ( ξ n ) with Rayleigh damping slightly decreases analysis times (2-5%). Conversely, with Modal damping, increasing the ξ n increases analysis times (5-7%). Analyzing the BF model consistently takes 10-15% longer than the IF model, regardless of the damping method.

(a)BF

(b) IF

Fig. 8: Total analysis time for di ff erent damping, normalized to analyses w / odamping.

4. Conclusion

This study investigated Rayleigh and Modal damping in nonlinear analyses of a 6-story RC building designed under older Italian codes. Two configurations were considered: with (IF) and without (BF) infills. The presence of infills was observed to significantly alter structural behavior, particularly as damage accumulates. Buildings were modeled using OpenSees through the STKO software, employing distributed plasticity for beams and columns, and equivalent struts for infills. Nonlinear Time-History Analyses (NTHAs) were conducted using 45 unscaled ground motions. A total of 41 convergent analyses were utilized for comparison. Di ff erences were assessed based on Roof Displacement (RD). • Rayleigh damping impacts the BF building more in the X-direction than the Y-direction. Using k init increases X-direction damping compared to k comm instead Y-direction di ff erences are minimal. For the IF building, k init and k comm yield negligible average di ff erences in Rayleigh damping, making the choice less critical than for BF. • Modal and Rayleigh damping di ff er more with increasing ξ in both BF and IF models. BF’s Modal damping better matches Rayleigh with k comm than k init . For IF, X-direction trends are similar, but the Y-direction shows Modal damping is lower than Rayleigh, causing higher demands, a much larger di ff erence than in BF. • Modal damping increases analysis times by 15-20% compared to Rayleigh damping, which has comparable computation times. For Rayleigh damping, higher damping ratios slightly reduce analysis time in both BF and IF buildings, whereas modal damping increases it. Regardless of damping type, BF models require longer analysis times than IF models. This article is intended only as a starting point for a broader and more extensive study, considering other engineering demand parameters (EDPs) such as the interstory drift ratio (IDR) and dissipated energy, and expanding the case study buildings.