# Nonlinear Dynamic Response of a Precast Concrete Building to Sudden Column Removal
## 4 Results and Discussion
### Summary of Results  
In this paragraph, the main findings of the present study are reported, particularly focusing on the events occurring during the different removal scenarios. The achievement of performance limit states for the PC system where the support loss is detected are reported in Table 3, indicating the corresponding time (t in s) and vertical displacement (\(\Delta\) in mm). From the previous table is clear how the support losses (PLS4) corresponding to catastrophic failures are a consequence of longitudinal tie fractures. This suggests the fundamental role played by continuous tying systems to prevent progressive collapse. It is worth to note that further studies are required to investigate the influence of material parameters as well as varying connection strengths and distributed tying systems. Table 4 outlines the chord rotations for the different PC systems and column removal locations in correspondence of the ultimate state condition. In detail, the ultimate limit state of the MRF system is related to the maximum displacement compatible with structural equilibrium, whereas the same condition for PCF systems is related to the loss of support or equilibrium, whatever occurs first. The associated load level is referred to the maximum magnitude corresponding to the previous considerations. It can be noted how the chord rotations reported for MRF systems generally meet the magnitudes derived from experimental results [54]. It is important to note that the MRF system is able to achieve greater chord rotations compared to PCF systems. This is indicative of the greater capacity of MRFs of redistributing the applied loads after the loss of a vertical elements compared to PCF systems. In addition, the use of illustrated modelling technique relies on the computational time. Indeed, an average time of 30 min was required to perform a single NLTHA instead of hours which could be required by refined FE models. Moreover, Seismostruct FE code [46] allows one to run multiple analyses at the same time, leading to a further computational advantage. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scenario** & **Model** & **Load level** & \(\Delta\) **(mm)** & \(\theta_{\text{L}}\) **(rad)1** & \(\theta_{\text{1}}\) **(rad)2** \\ \hline \multirow{4}{*}{Edge} & MRF & \(170\%\)-Q\({}_{b,e}\) & \(-3125.00\) & \(0.29\) & / \\  & PC\_1 & \(80\%\)-Q\({}_{b,e}\) & \(-2200.00\) & \(0.20\) & / \\  & PC\_1 & \(90\%\)-Q\({}_{b,e}\) & \(-2300.00\) & \(0.21\) & / \\  & PC\_2 & Self-weight & \(-2060.00\) & \(0.19\) & / \\ \hline \multirow{4}{*}{Interior} & MRF & \(100\%\)-Q\({}_{b,i}\) & \(-3180.00\) & \(0.29\) & / \\  & PC\_1 & \(60\%\)-Q\({}_{b,i}\) & \(-2250.00\) & \(0.21\) & / \\  & PC\_1 & \(70\%\)-Q\({}_{b,i}\) & \(-2500.00\) & \(0.23\) & / \\  & PC\_2 & Self-weight & \(-1950.00\) & \(0.18\) & / \\ \hline \multirow{4}{*}{Corner} & MRF & \(200\%\)-Q\({}_{b,c}\) & \(-1980.00\) & \(0.18\) & \(0.28\) \\  & PC\_1-1T & \(200\%\)-Q\({}_{b,c}\) & \(-1650.00\) & \(0.15\) & \(0.23\) \\ \cline{1-1}  & PC\_1-2T & \(200\%\)-Q\({}_{b,c}\) & \(-1800.00\) & \(0.17\) & \(0.25\) \\ \cline{1-1}  & PC\_2 & Self-weight & \(-1650.00\) & \(0.15\) & \(0.23\) \\ \hline \hline \end{tabular}  
* This value is related to the major span length \(L\) of 10.8 m. 2 This value is related to the minor span length \(l\) of 7.2 m.  
\end{table} 
Table 4: Summary of chord rotations for MCF and PCF systems for different removal scenarios. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Scenario** & **Model** & **PLS1 (t, \(\Delta\))** & **PLS2 (t, \(\Delta\))** & **PLS3 (t, \(\Delta\))** & **PLS4 (t, \(\Delta\))** \\ \hline Edge & PC1\_E-90\% & (0.25; \(-240\)) & (\(0.35;\)\(-500\)) & (\(1.00;\)\(-2200\)) & (\(1.20;\)\(-2300\)) \\ Interior & PC1\_I-70\% & (0.24; \(-225\)) & (\(0.34;\)\(-434\)) & (\(0.90;\)\(-2200\)) & (\(1.00;\)\(-2500\)) \\ Corner & PC\_1-200\%-1T & (0.25; \(-235\)) & (\(0.33;\)\(-290\)) & (\(0.80;\)\(-1800\)) & (\(0.85;\)\(-1650\)) \\ \hline \hline \end{tabular}
\end{table}