## 5 Final Discussion and Conclusions
Convergence studies and other aspects of the analysis should be disregarded in regions close to the singularity since unprocessed FEM results (e.g., without additional smoothing or similar techniques) at such points are not objective. The second benchmark deals with out-of-plane bending in a slab supported by a column. An excessive increase in the slab's bending moment near the support is observed if only a standard numerical analysis is performed. This can be controlled in the post-processing phase by reducing the bending moment above the column. However, the application of the reduction function works differently in each software package. In Robot, it is accessible directly after the computations and depends on a column dimensions. In Midas, it can be enabled in the dimensioning module, where the reduction range is set directly by the user. The column dimensions or the specified reduction range influence the final limitation of the bending moment. It is also noticed that the FE size affects the reduction degree. In accordance with concrete structure design standards, the bending moment values should be read at the face of the support; hence, the application of the reduction is necessary during the analysis. It is suggested, for example, in [25; 43], to densify the FE mesh in the vicinity of a support such as the column and simultaneously introduce a reduction in moments. In this test, the adoption of uniform FE mesh densification over the entire slab area is intended to investigate the results for unbiased discretization, both without and with applied reduction. The third study concerns various types of modeling for the interaction between the beam and the slab. In this model, bending of the beam coincides with out-of-plane bending of the slab. Three variants of cooperation are analyzed: without an offset (\(z_{\rm I}=0\) cm), with a smaller offset, where the upper beam flange is aligned with the top slab plane (\(z_{\rm II}=12.5\) cm), and with a larger offset (\(z_{\rm III}=27.5\) cm), where the upper beam flange coincides with the bottom slab plane. Additionally, different methods for defining the offset are compared in Robot: either by simply selecting the option in the program menu, using rigid links, or inserting bar members between the beam and the slab. Each approach to introducing an offset leads to almost identical results. Moreover, instead of applying the offset option, a modification of the moment of inertia can also be effectively utilized. In Robot, a special coefficient must be activated with a value greater than 1.0. In Midas, a modified value of the moment of inertia is applied. The total bending moment, the value of which is commonly known and consistent with beam theory, is determined based on its moment diagrams \(M_{y}\) and axial force \(F_{x}\) (if \(z>0\)), as well as by evaluating the integral \(I_{mxx}^{\rm s}\) of the corresponding panel cut for the slab. The concise list of conclusions and remarks is outlined below:  
* The influence of transverse shear on the displacement field in the analytical solution of the cantilever beam problem is discussed. * Based on the numerical results for the cantilever beam in both programs, Robot and Midas, proper convergence to the analytical solution is demonstrated. * Finite elements with additional degrees of freedom, called drilling rotations, are included in the software. Shell elements in Robot deliver similar results to membrane elements with triggered extra in-plane rotations in Midas. * Stress singularities in FEM computations can occur in regions with geometric or material discontinuities. Such locations are not adequate to perform, e.g., a convergence study, and require different correction techniques, such as smoothing of the results. * The reduction process objectively improves the distribution of the bending moment in the slab above the column. The limitation in the reduction zone is governed by the column section size in Robot or a distance assumed by the user in Midas.