PSI - Issue 78

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

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3.1. NTHAs with Rayleigh Damping

OpenSees o ff ers three Rayleigh damping variations based on the sti ff ness matrix: initial ( k init ), current ( k cur ), and committed ( k comm ), which uses the last converged time step’s sti ff ness. This study imposed damping ratios at two frequencies: the structure’s fundamental mode and the last mode with 5% mass participation (7 th forBF, 5 th for IF). Analyses ranged from ξ = 1% to 5%, in 1% increments. k cur results were excluded due to negligible di ff erences from k comm , significantly higher computational cost (e.g., 250 − 400% more). Figure 2 shows the impact of two Rayleigh damping cases on the BF model versus its undamped state. The damping e ff ect is more pronounced in the X-direction than in the Y-direction. A clear trend indicates di ff erences increase with damping ratio ( ξ n ). In the X-direction, average di ff erences range from 7% to 20% as ξ n increases from 1% to 5%. In the weaker Y-direction, di ff erences are almost negligible (2% to 6% as ξ n increases from 1% to 5%), as shown by linear trend lines.

Fig. 2: NTHAs of the BF model with Rayleigh damping: maximum RD in the X and Y directions with linear trend lines

Fig. 3: NTHAs of the IF model with Rayleigh damping: maximum RD in the X and Y directions with linear trend lines