## 4 Interaction of Beam with Slab  
The third benchmark concerns the analysis of out-of-plane bending based on the model of a slab, which is in interaction with a beam. The configuration is presented in Figure 17. The slab has length \(L_{x}=6.0\) m, width \(L_{y}=5.0\) m, and thickness \(d=15\) cm. The beam span is \(L_{x}=6.0\) m, and it has a rectangular cross-section of \(b\times h=30.0\times 40.0\) cm. Both structural elements are made of concrete C30/37, with material properties as in the previous section: [PERSON]'s modulus is \(E=33\) GPa, [PERSON]'s ratio is \(\
u=0.2\), and shear modulus is \(G=13.333\) GPa. The edges of the slab along the width (\(L_{y}=5.0\) m) are simply supported, i.e., translations are constrained. Uniformly distributed load \(p_{Z}=1\) kN\(/\)m is applied along the beam, as shown in Figure 17. For the computations in both packages, two meshes consisting of rectangular FEs are employed: a coarser mesh with FEs \(1.25\times 1.20\) m and a finer mesh with FEs \(0.5\times 0.5\) m. A similar study, but much more concise, performed only on Robot and for a concrete slab with a steel beam, was demonstrated in [42]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Abbreviation** & **Applied** & **If** & **Column** & **Reduction** \\  & **Program** & **Reduction** & **Size \(b\)** & **Width \(W\)** \\  & & **Reduction** & **[cm]** & **[cm]** \\ \hline R-no & Robot & No & 30 & \\ M-no & Midas & No & 30 & \\ M-RC-0 & Midas & No & 30 & \\ M-RC-red50 & Midas & Yes & 30 & **50** \\ M-RC-red150 & Midas & Yes & 30 & **150** \\ R-red & Robot & Yes & **30** & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Types of moment reduction in slab supported by column illustrated in Figure 16.  
Figure 16: Comparison of bending moments \(m_{xx}\) in slab center for cases given in Table 6 (abbreviations explained in table and text). There are three variants of the connection between the beam and the slab, as depicted in Figure 18. The simplest version of the model, marked with the Roman numeral I, occurs when the beam axis aligns with the middle plane of the slab, i.e., no offset exists and \(z=z_{\rm I}=0\) cm. The second type of connection, marked by II, assumes that the upper flange of the beam coincides with the top plane of the slab, so the offset corresponds to \(z=z_{\rm II}=12.5\) cm. The last case of connection is presented in Figure 18 on the right-hand side and marked by III. Here, the upper beam flange faces the bottom plane of the slab, and the offset is \(z=z_{\rm III}=27.5\) cm. The study and comparison of these specified connections are described later in the section. Now, before discussing the aforementioned versions of the model and their results, the first aspect of the analysis is to determine whether the offset definition causes any changes in the obtained values. The study focuses only on type II connection with \(z=z_{\rm II}=12.5\) cm. Various options available in Robot for modeling connectors between the beam and the slab are investigated:  
1. Directly using the function offset;
2. Activating so-called rigid links for all nodes along the beam and their corresponding nodes of the slab;
3. Shifting down the beam by the distance \(z=12.5\) cm and inserting very stiff and stable members between the nodes of the beam and their counterparts on the slab. These members are artificially defined as round short pipe rods with high stiffness (\(E=300\) MPa and \(\
u=0.3\)) and an extremely large section: diameter \(d_{p}=1219.0\) mm and ring thickness \(t_{w}=25.0\) mm, leading to a cross-sectional area of \(A_{p}=93.776.54\) mm\({}^{2}\). The results obtained using the three options listed above are consistent with each other. Figure 17: Model of slab with beam, simply supported on two opposite slab edges, uniform load along beam axis, finer mesh. Figure 18: Types of connection between beam and slab: I. beam axis aligned with middle plane of slab—without offset \(z=0\) cm (**left**), II. upper flange of beam coincides with top plane of slab—offset \(z=12.5\) cm (**middle**), III.