# A Parametric Computational Study of RC Building Structures under Corner-Column Removal Situations
## 2 Description of the Study
### FE Model Validation  
This section describes the validation of the FE model using experimental results [28] such as vertical and horizontal structural displacements, axial forces on columns and the structural damage after the column removal. It should be noted that the experimental measurements were obtained considering the column removal action only, so only displacement or force increments can be considered for comparison within experimental and numerical results. The vertical deformed shape of the first slab was measured during the test at 5 points along the corner-bay edge of the 1 st floor slab connecting columns P2 and P3 (the column that was removed). Displacements were also measured at the same points in the FE model. As can be seen in Figure 3, the FE model precisely reproduced the vertical displacements. The remaining or residual structural drift values were also compared in the test and the FE model. Figure 4 compares both sets of values. The FE model can be seen to match with the test results in the 1 st slab and is slightly different in the 2 nd slab. Nevertheless, the error is less than 1 mm, so the FE adequately reproduces the structural horizontal displacements. The peak structural dynamic response values were also measured after removing the column in both the test and the FE model for the drift and the vertical displacement in the position of P3. The results are given in Table 2 and include the error involved. The FE model comes closer to the experimental residual values than the peak values, although these errors are quite low. Figure 2: Finite Element (FE) model without the ground floor column P3 (column removed). Colours represent sections with different amounts of reinforcement according to the building details [28]. Figure 5 shows time-history comparisons between the axial force increments in the FE model (FEM) and the test for columns P1, P2/P6, P5 and P7. The comparison is shown from t = 0 s to t = 2 s, where t = 1 s is the start time of the column removal. Columns P2/P6 show a good correlation within experimental and numerical results. In this case, the average of these columns' experimental values (P2/P6 = (P2 + P6)/2) was calculated for correct comparison with the numerical values. The removal of corner column P3 increased the compressive axial load in columns P2 and P6 and decreased it in columns P1, P5 and P7. The comparison between the experimental and the FE model shows a good correlation, reaching similar load values with a dynamic response. Particularly, this is reproduced more realistically in columns P2/P6, P5 and P7 than in column P1. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Component** & **Value** & **Test** & **FE Model** & **Error [mm]** \\ \hline \multirow{2}{*}{Maximum vertical displacement [mm]} & Peak & \(-48.1\) & \(-41.9\) & \(6.2\) \\  & Residual & \(-42.8\) & \(-40.5\) & \(2.3\) \\ \hline \multirow{4}{*}{Drift [mm]} & \multirow{2}{*}{Floor 1} & Peak & \(1.40\) & \(0.84\) & \(0.56\) \\  & & Residual & \(0.40\) & \(0.38\) & \(0.02\) \\ \cline{1-1}  & & Peak & \(4.80\) & \(2.34\) & \(2.46\) \\ \cline{1-1}  & & Residual & \(2.40\) & \(1.53\) & \(0.87\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the peak and residual values of maximum vertical displacement and drift between the test [28] and the FE model. Figure 4: Comparison of the residual horizontal displacement/drift of the structure between the test [28] and the FE model. Positive values indicate horizontal displacement towards the removed column. Figure 3: Comparison of the residual vertical deformed shape of the first floor between P2 and P3 in the experimental test [28] and FE model. The level of damage sustained in the test was also compared with the FE model results. Figure 6 shows this comparison in terms of the computed damage in tension of the slabs and a picture of the cracks that appeared during the test. The different comparisons generally show good correlation between the test and the FE model results for displacements, forces and slab tensile damage.