## 2 Materials and Methods
### Seismic Input  
A set of 56 near-fault pulse-type ground motions with the closest distance from the recording site to the rupture plane less than 15 km have been selected for the dynamic analyses in this paper. These records are obtained from the strong motion database of the PEER Center [59] (last access 2024). Table 1 contains a list of specific ground motion details. Velocity pulses and intense displacement are commonly linked to near-fault seismic ground motions; furthermore, the two main sources of the velocity pulses observed in near-fault areas are usually forward directivity and permanent translation. Because they impose severe demands on structures that are not predicted by conventional measurements like response spectra, strong velocity pulses associated with near-fault ground vibrations are of interest to seismologists and earthquake engineers. The near-fault ground motion data set is carefully examined to find records that exhibit pulse-like signal effects; that is, records with notable velocity pulses are categorized as \"the pulse-like earthquake records\". These records are selected based on the pulse characterization algorithm proposed by [PERSON] [60]. An explanatory plot is presented in Figure 3 for pulse and no-pulse records.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline
**Earthquake** & **M** & **Station** & **Distance (km)** & **PGA (g)** & **FGV (cm/s)** & **Tp (g)** \\ \hline Cape Mendocino (1992) & 7.0 & Petrolia & 8.1 & 0.66 & 88.6 & 3 \\  & & Centerville Beach\_ Naval Fac & 16.44 & 0.48 & 51.18 & 1.967 \\ \hline  & & TCU065 & 0.57 & 0.79 & 125.3 & 5.74 \\ Chi-Chi Taiwan (1999) & 7.6 & TCU080 & 10.2 & 0.54 & 36.11 & 1.022 \\  & & TCU075 & 0.9 & 0.33 & 109.56 & 4.998 \\  & & CHY074 & 2.44 & 0.34 & 43.5 & 2.436 \\ \hline Denali, Alaska (2002) & 7.9 & TAPS Pump Sta. \#10 & 2.74 & 0.33 & 115.7 & 3.16 \\ \hline Dizce (1999) & 7.3 & Bolu & 12 & 0.822 & 62.1 & 0.88 \\ \hline Imperial Valley (1979) & 6.9 & El Centro Array \#6 & 1.35 & 0.45 & 113.5 & 3.77 \\  & & El Centro Array \#7 & 0.56 & 0.47 & 113.1 & 4.38 \\ \hline Iripina, Italy (1980) & 6.9 & Sturno & 10.8 & 0.32 & 71.9 & 3.27 \\ \hline Kobe (1995) & 6.9 & Takarazuka & 0.3 & 0.697 & 68.41 & 1.806 \\  & & Port Island (0 m) & 3.31 & 0.348 & 90.67 & 2.828 \\ \hline  & & Izmit & 7.2 & 0.23 & 38.28 & 5.37 \\ Kocaeli (1999) & 7.8 & Gebze & 10.9 & 0.244 & 50.3 & 5.99 \\  & & Yarrmca & 4.83 & 0.32 & 71.9 & 4.949 \\ \hline Landers (1992) & 7.4 & Lucerne & 2.2 & 0.79 & 133.5 & 5.12 \\ \hline  & & Saratoga Aloha & 8.5 & 0.51 & 41.6 & 4.57 \\  & & Gilroy Array \#2 & 10.38 & 0.37 & 34.76 & 1.729 \\ \hline Morgan Hill (1984) & 6.2 & Coyote Lake D.Southwest Ab. & 0.18 & 1.303 & 78.44 & 1.071 \\ \hline  & & Rinaldi Receiving Station & 6.5 & 0.87 & 148.08 & 1.25 \\  & & Sylmar Olive & 5.3 & 0.84 & 129.6 & 2.44 \\ Northridge (1994) & 6.7 & Pacoima Dam (upper left) & 7.01 & 1.58 & 54.86 & 0.84 \\  & & Pacoima Dam (downstr) & 4.92 & 0.434 & 44.29 & 0.588 \\  & & LA—Sepulveda VA Hospital & 8.44 & 0.93 & 77.67 & 0.931 \\ \hline Superstition Hills-02 (1987) & 6.5 & Parachute Test Site & 0.95 & 0.43 & 134.3 & 2.39 \\ \hline Tabas, Iran (1978) & 7.35 & Tabas & 2.05 & 0.86 & 123.5 & 6.19 \\ \hline \end{tabular}
\end{table}
Table 1: Pulse-like near-fault ground motions.  
Figure 3: Velocity spectra for **(a)** pulse (Imperial Valley—06 El Centro Array #6 (E06230)/Landers–Lucerne (LCN260)) and **(b)** no-pulse (Nahanni—Site 2 (S1280)/Gazli–Karakyr (GAZ000)) records.  
For SDOF structures with a period range of 0.1-3.0 s, five ductility values (\(\mu\) = 2, 3, 4, 5, 6), three strain hardening ratios (\(\alpha\) = 0, 5%, 10%), four energy dissipation ratios (\(\beta\) = 0, 0.25, 0.5, 1.0), one fixed-base case, three times for interacting systems with different aspect ratios (h/r = 1, 3, 5), and 56 ground motions, 403,200 analyses were performed in this study.