## 3 Bending of Slab Supported by Column
The numbers in the subfigures of Figure 9 represent the deflection of the slab at the center and at all corners. When the column is introduced into the model, the deflection of \(-0.005\) cm is observed in the center. The column is actually very slightly shortened (compressed). When the full model is considered, the deflections in Midas (at the top) and in Robot (at the bottom on the left) are identical. It is noted that both packages are equipped with an implementation of so-called discrete Kirchhoff-Mindlin quadrilateral (DKMQ) FEs; see [14]. The difference between the central value and extreme deflections at corners equals 0.0770 cm. If the nodal support is assumed, as shown in Figure 9 at the bottom on the right, obviously, the central deflection equals zero. The difference in the deflection between the center and corners is now 0.0771 cm, which is almost identical to the full version of the model. It could, therefore, be presumed that both variants of the model are equivalent. Hence, the option with the nodal support can be adopted for the next analysis in Robot. Figure 8: Model of slab over column as structural element (**left**) or substituted by support at one node, where column size is defined additionally (**right**). It should also be mentioned that during the computations in Robot a so-called instability occurs in both types of the model, indicating the connection point as the cause of this perturbation. Global extremes of the displacement field should be verified in that case. If any excessively large values are noticed in the results, the model should be improved. Global displacement extremes in this benchmark do not produce unexpected results; consequently, the warning related to instability can be ignored. The computations in Midas do not involve any problems despite the challenging configuration of the model from a numerical solution perspective. Before displaying further results, one aspect arising from the theory should be mentioned. If this problem were reduced to the bending of a one-dimensional cantilever beam with a length equal to half the slab's span, by calculating the sum of the surface load from the entire slab's span to a resultant uniform load along the beam's axis \(q_{s}=\hat{q}_{z}\)\(L=9.92\)\(\mathrm{kN}/\mathrm{m}\), then the value of the fixed-end moment for such a cantilever with length \(L/2\) is  
\[M_{\mathrm{f}}=0.5\,q_{s}\,(L/2)^{2}=30.506\ [\mathrm{kNm}] \tag{17}\]  
This value of \(M_{\mathrm{f}}\) is consistent here with the integral \(I_{mxx}\) determined from the slab's bending moments along the centerline \(x=0\):  
\[I_{mxx}=\int_{-2.48}^{2.48}m_{xx}\ \mathrm{d}y \tag{18}\]  
Firstly, attention is focused on analyzing the bending moments for the slab depending on the mesh density, based on the solutions computed only in the Robot program. Table 2 shows the following in the respective columns: mesh division \(N\times N\), the size of square FE \(h_{\mathrm{FE}}\), and the results when the reduction option is turned off or on. In each case, the maximum value of the bending moment \(m_{xx}\) together with the value of the corresponding integral \(I_{mxxx}\) is listed. When the moment reduction above the support is not enabled, the maximum values of \(m_{xx}\) increase with the mesh density. This moment for the finest mesh is more than double that for the coarsest mesh. Such a rise is solely related to the mesh refinement pitfall and can lead to incorrect interpretation of the results. On the other hand, the values of the integral \(I_{mxxx}\) converge to the theoretical value \(M_{\mathrm{f}}\), ranging from 30.599 kNm to 30.513 kNm. When the reduction option is activated, moments \(m_{xx}\) for the refined discretizations tend to be more or less 12 kNm/m, except in the case of the coarsest mesh, where the value of \(m_{xx}\) is underestimated. The integral \(I_{mxxx}\), along with  
Figure 9: Deformation of slab—results for Midas (**top**) and Robot: model with column (**bottom left**), model with nodal support (**bottom right**).