## 3 Bending of Slab Supported by Column
the consecutive solutions, approaches the value of about 28.5 kNm. This is approximately 2 kNm less than the integral determined for the case of \(256\times 256\) elements without the use of reduction. The difference will be clarified by the following description of Figures 10-12. Figures 10-12 illustrate bending moments \(m_{xx}\) using both panel cut diagrams and contour plots. On the left-hand side, the original results, i.e., without the reduction, are presented. On the right-hand side, the reduction is employed during post-processing to represent the moments \(m_{xx}\) more adequately. The distributions for the last three finest \begin{table}
\begin{tabular}{r c c c c c} \hline \hline
**Division** & **FE Size** & \multicolumn{2}{c}{**Without Reduction**} & \multicolumn{2}{c}{**With Reduction**} \\ \(N\times N\) & \(h_{\text{FE}}\) & **max \(m_{xx}\)** & \(I_{mxx}\) & **max \(m_{xx}\)** & \(I_{mxx}\) \\  & **[cm]** & **[kNm/m]** & **[kNm]** & **[kNm/m]** & **[kNm]** \\ \hline \(8\times 8\) & 62 & 16.501 & 30.559 & 7.437 & 24.970 \\ \(16\times 16\) & 31 & 20.804 & 30.570 & 10.445 & 27.392 \\ \(32\times 32\) & 15.5 & 25.128 & 30.555 & 11.591 & 27.760 \\ \(64\times 64\) & 7.75 & 28.873 & 30.534 & 11.933 & 28.315 \\ \(128\times 128\) & 3.875 & 32.274 & 30.521 & 11.934 & 28.338 \\ \(256\times 256\) & 1.9375 & 35.569 & 30.513 & 12.327 & 28.518 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Influence of discretization on moment reduction in slab above column—results from Robot. Figure 11: Panel cut diagrams and contour plots of bending moments \(m_{xx}\) without (**left**) and with (**right**) reduction applied above column, results for Robot and mesh with 128 FEs along side. Figure 12: Panel cut diagrams and contour plots of bending moments \(m_{xx}\) without (**left**) and with (**right**) reduction applied above column, results for Robot and mesh with 256 FEs along side. Figure 10: Panel cut diagrams and contour plots of bending moments \(m_{xx}\) without (**left**) and with (**right**) reduction applied above column, results for Robot and mesh with 64 FEs alongside. meshes are shown. These figures confirm the numerical results listed in Table 2. Looking at the functions of \(m_{xx}\) for panel cuts, their character is similar for each mesh, respectively, for the unmodified results on the left and then for the results on the right when the reduction is applied. The maximum clearly grows with mesh density for the original results on the left. The distribution of contour plots is strongly localized above the column. The ones on the right are limited due to the introduced reduction. The patterns with the applied reduction have a more diffuse character, and the color gradient adjusts according to the scale. The panel cut for reduced moments looks truncated by the presence of the defined column size (here \(b=30\) cm). The introduction of such a limitation actually makes the results objective. Additionally, in the top right corner of the figures, the integral values for each case are shown. If a reduction is activated, the function of \(m_{xx}\) is limited, so the values of \(I_{mxx}\) are also lowered. The next aspect of the analysis focuses on the influence of the column size on the reduction in the slab's bending moments. The computations are carried out in Robot using the same mesh \(64\times 64\) with \(h_{\text{FE}}=7.75\) cm. The maximum value of \(m_{xx}\) is \(28.873\) kNm/m and corresponds to \(I_{mxx}=30.534\) kNm if the results are not corrected. Of course, these results are independent of the column size. Table 3 shows the reduction effect when the size of the column is changed. Here, both the moment \(m_{xx}\) and the integral \(I_{mxx}\) decrease as the column size increases. The ranges that are distinguished in the first row of the table refer to discrete values. For example, the same reduction degree is recognized for the column size of \(26\) cm as well as \(32\) cm.