## 3 A Demonstration of the Proposed Framework: A Case Study
### Excitations and Responses  
A selection of NS-direction ground motion records were selected from JMA as the input excitations, as shown in Table 4. Taking the peak ground velocity (PGV) as IM, the above-ground motion records were input after amplitude modulation to study the seismic performance of cast-in situ PC and PCaPC frames. This dataset spans from 2000 to 2024. To represent three distinct seismic hazard levels corresponding to probabilities exceeding 50%, 10%, and 5% within 50 years, the records were scaled using PGV (i.e., PGV equals 18.6 cm/s, 36.5 cm/s, and 44.2 cm/s for three levels in the NS-direction). The PGV values for each hazard level were obtained from J-SHIS based on the location of the prototype building at Tohoku University's Aobayama Campus in Sendai, Japan. Table 5 shows the peak floor responses, including 'du,' the inter-story drift ratio at the i-th story, and 'ai,' the absolute floor acceleration at the i-th floor, as required in Table 4. The seismic response analysis shows that the maximum inter-story drift ratio of the PCaPC frame is 1.27%, compared to 1.86% in the cast-in situ PC frame. As structural damage in reinforced concrete systems is primarily governed by deformation demand, specifically inter-story drift rather than floor acceleration, both frames are expected to maintain structural integrity with only limited damage to load-bearing elements. The relatively small drift in the PCaPC frame indicates that its structural components remain within the elastic or lightly inelastic range, while the higher drift in the cast-in situ frame increases the likelihood of cracking and yielding in beams and columns. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Seismic** & **Earthquake** & **Mw** & **Depth** & **Station** & **Distance** & **Site** \\
**Hazard** & **Earthquake** & **Mw** & **(km)** & **Station** & **(km)** & **Amplification** \\ \hline  & Hokkaido Eastern Iburi & & & & & \\  & 21 February 2019 & 5.8 & 33 & Kanuma & 17.3 & 1.58 \\
50\% in 50 yrs. & Osaka Northern & & & & & \\ (PGV = 18.6 cm/s, & 18 June 2018 & 6.1 & 13 & Shin-Kotoni & 67.1 & 2.24 \\ RP = 73 yrs. & Near Awai Island & & & & & \\  & 13 April 2013 & 6.3 & 11 & Chayamachi & 18.7 & 2.09 \\  & & 18 June 2018 & 6.3 & 13 & Chayamachi & 16.3 & 1.72 \\  & & Near Awai Island & & & & \\  & 13 April 2013 & 6.3 & 11 & Kojdani & 11.8 & 1.48 \\  & & 13 April 2013 & 6.3 & 15 & Kakuuchi & 55.4 & 0.81 \\  & & 28 December 2016 & 6.3 & 15 & Kanamachi & 39.1 & 1.3 \\ \hline  & Noto Peninsula Offshore & & & & & \\  & 5 May 2023 & 6.5 & 12 & Misakacho & 11 & 0.96 \\
10\% in 50 yrs. & 5 May 2023 & 6.5 & 12 & Monzencho & 55.1 & 0.67 \\
(PGV = 36.5 cm/s, & Nagano Northern & & & & \\  & 22 November 2014 & 6.7 & 5 & Hakoshimizu & 27.4 & 0.81 \\  & & 22 November 2014 & & Otemachi & 55.7 & 1.77 \\  & & Yamagata-Oki & & & & \\  & 18 June 2019 & 6.7 & 14 & Fuyasu & 11.5 & 1.02 \\  & & Niigata Chuetsu & & & & \\  & 23 October 2004 & 6.8 & 13 & Kawaguchi & 33.1 & 1.35 \\ \hline  & Fukuoka Northwestern Offshore & & & & & \\  & 20 March 2005 & 7.0 & 9 & Maizuru & 26.1 & 1.44 \\
5\% in 50 yrs. & Miyagi Offshore & & & & & \\ (PGV = 44.2 cm/s, & 26 May 2003 & 7.1 & 72 & Tsuftukumotecho & 57.1 & 1.25 \\  & & & & & & \\  RP = 975 yrs. & Tottori Western & & & & & \\  for Sendai, Japan) & 6 October 2000 & & & & & \\  & Noto Peninsula & & & & & \\  & 1 January 2024 & 7.6 & 16 & Fugeshimachi & 35.2 & 1.75 \\  & & 1 January 2024 & 7.6 & Misakimachi & 9.3 & 0.96 \\ \hline \hline \end{tabular} Note: RP = return period.  
\end{table} 
Table 4: Ground motions selected for case study. In these frames, the structural damage remains minor. However, due to higher peak floor accelerations, nonstructural components such as compressors, sanitary waste piping, wall partitions, and stairs are more susceptible to damage, particularly in the cast-in situ system. The PCaPC frame, benefiting from its reduced floor accelerations, is less likely to experience extensive damage to nonstructural systems, thereby leading to a shorter expected recovery time.