# Vibration Response Characteristics of Prefabricated Frame Structures Around the Subway
## 5 Vibration Response Characteristics of Prefabricated Frame Structures Around Subways
### Influence of the Total Structural Stories Variation on the Structural Vibration Response  
To understand the vertical vibration propagation law of subway vibrations in structures, the vibration response of frame structures with semirigid joints of different total stories under subway environmental conditions were studied. The structural plan layout was the same as the baseline structure in Figure 3, and the basic design specifications were consistent with those of the baseline structure in Section 2. Only the total number of stories was changed: based on the 5-story baseline structure, 8-story and 11-story frame structure models with semirigid joints were designed, with a difference of 3 stories between each model. Since the change in the number of stories correspondingly altered the internal forces on beams, columns, and slabs, the parameters for the beams, columns, and slabs of the 8-story and 11-story models were selected according to the relevant requirements of Code [9], as shown in Table 12.  
The design specifications and sectional parameters were incorporated into the PKPM2025R2.3 software to derive reinforcement configurations for various models. To streamline structural analysis in the eight-story FEM model: beam reinforcement in floors 1-5 replicated the 1-1 section beam detailing from the first floor (Figure 7), while column reinforcement employed the first-floor central column cross-section. For floors 6-8, beam reinforcement adopted the sixth-floor 1-1 section configuration, with column reinforcement corresponding to the sixth-floor central column cross-section. In the 11-story FEM, the same simplification logic applied to beam-column reinforcement for floors 1-5 and 6-7. For floors 9-11, beam reinforcement followed the 1-1 section beam configuration from the ninth floor, with column reinforcement matching the ninth-floor central column cross-section. Slab reinforcement employed \(\Phi\)8@200 arranged bidirectionally. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multirow{2}{*}{ \begin{tabular}{c} **Beam Section** \\ **mm\({}^{2}\)** \\ \end{tabular}  } & \multirow{2}{*}{\ \begin{tabular}{c} **Column Section** \\ **mm\({}^{2}\)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Slab Thickness** \\ **mm\({}^{2}\)** \\ \end{tabular}  } \\ \hline
8-story model & \begin{tabular}{c} 1–5 story \\ 6–8 story \\ \end{tabular}  & \begin{tabular}{c} 250 \(\times\) 500 \\ 250 \(\times\) 500 \\ \end{tabular}  & \ \begin{tabular}{c} 550 \(\times\) 550 \\ 500 \(\times\) 500 \\ \end{tabular}  & \begin{tabular}{c} 100 \\ 100 \\ 110 \\ 110 \\ \end{tabular}  \\ \hline
11-story model & \ \begin{tabular}{c} 1–5 story \\ 5–8 story \\ 9–11 story \\ \end{tabular}  &
\begin{tabular}{c} 250 \(\times\) 600 \\ 250 \(\  
Calculation verification demonstrated that joints utilized four M20 (grade 8.8) high-strength friction-grip bolts in a dual-row symmetric configuration, accompanied by 12 mm splice plates with material properties identical to parent components, fulfilling all structural joint design criteria. Translational stiffness \(K_{\mathrm{v}}\) = 2.8 \(\times\) 10\({}^{9}\) N/m and rotational stiffness \(K_{\mathrm{r}}\) = 1.83 \(\times\) 10\({}^{8}\) N-m/rad were assigned, maintaining \(\gamma\) = 0.5. Schematic diagrams of finite element models with different story configurations are shown in Figures 4 and 21. Triaxial vibration data (X/Y/Z) from six-car Type B trains at 80 km/h along the tunnel axis were input via base-uniform excitation into all models. Vibration histories from midedge beam nodes were processed to obtain floor-specific weighted acceleration levels shown in Figure 22.  
Overall, the weighted acceleration levels across floors in semirigid jointed structures exhibited a decreasing trend with increasing total stories. This primarily stemmed from  
Figure 21: Schematic elevation diagrams of finite elements for models with different total numbers of stories: (**a**) 8-story model; (**b**) 11-story model.