# The Behaviour of Half-Slabs and Hollow-Core Slab in Four-Edge Supported Conditions
## 4 Computational Analysis
### FEM Calculations  
As shown in Section 4.1, deflections of the slab section calculated according to the standard procedure led to overestimating both short- and long-term deflections of reinforced concrete and prestressed slabs. Significant underestimations of the deflections were obtained for the slab model supported on four edges. Given the interaction between individual precast units was ignored, the results cannot be considered reliable. Therefore, FEM numerical models were prepared for the individual slab models. Numerical calculations were performed in the AxisVMX5 program based on the finite element method (FEM). The numerical representation of the analysed structures was carried out on shell models with various panel thicknesses. The thicknesses of the slabs were 200 mm (LGR), 160 mm (RP), and 160 and 120 mm for the shear keys between the panels. The HC model was 150 mm thick. The finite elements between the panels in the LGR and RP models had both a length and width of 50 mm, and the thickness was reduced by the thickness of the precast element to represent the presence of shear keys (flexibility). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Experimentally**} & \multicolumn{2}{c}{**Beam Model**} & \multicolumn{2}{c}{**Model of a Two-Way Slab**} \\ \cline{2-6}  & **Determined Deflection** & \multicolumn{4}{c}{**Calculated Displacement of the Model (mm)**} \\ \cline{2-6}  & **a\({}_{\text{obs}}\)** & **a\({}_{\text{cal}}\)** & **a\({}_{\text{obs}}\)/a\({}_{\text{cal}}\)** & **a\({}_{\text{cal}}\)** & **a\({}_{\text{obs}}\)/a\({}_{\text{cal}}\)** \\ \hline
**LGR** & 1.96 & 40.8 & 0.05 & 1.0 & 1.96 \\
**RP** & 3.90 & 11.0 & 0.36 & 2.0 & 1.99 \\
**HC** & 3.57 & 14.0 & 0.25 & 2.5 & 1.43 \\ \hline \hline \end{tabular} a\({}_{\text{obs}}\)—measured displacement; a\({}_{\text{cal}}\)—calculated displacement.  
\end{table} 
Table 6: Comparison of results from tests and calculations for short-term loading. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Experimentally**} & \multicolumn{2}{c}{**Beam Model**} & \multicolumn{2}{c}{**Model of a Two-Way Slab**} \\ \cline{2-6}  & **a\({}_{\text{obs}}\)** & **a\({}_{\text{cal}}\)** & **a\({}_{\text{obs}}\)/a\({}_{\text{cal}}\)** & **a\({}_{\text{cal}}\)** & **a\({}_{\text{obs}}\)/a\({}_{\text{cal}}\)** \\ \hline
**LGR** & 13.0 & 54.5 & 0.24 & 5.5 & 2.36 \\
**RP** & 12.0 & 38.4 & 0.31 & 6.8 & 1.75 \\
**HC** & 10.0 & 38.6 & 0.26 & 6.9 & 1.45 \\ \hline \hline \end{tabular} a\({}_{\text{obs}}\)—measured displacement; a\({}_{\text{cal}}\)—calculated displacement.  
\end{table} 
Table 7: Comparison of results from tests and calculations for long-term loading. Hinged connections between the elements were applied in the HC model. The decision as to the joint for HC panels was made based on a literature review, the recommendations of EN 1168. In particular, such a work model is indicated by a different shape of the presented (Sections 3.2 and 3.3) displacement curves. The slabs were supported linearly on four edges. The parameters of the stiffness of the supports corresponded to the stiffness of the walls supporting the structure. The basic size of the FEM element was 10 cm with twice the local compaction joint panels (5 mm FEM division). Finite four-node shell elements were used with six degrees of freedom for each node. An isotropic material model of concrete was used in the calculations. One of the objectives of the work was to assess the reliability of engineering calculations in estimating the actual vertical displacements (deflections) of panel slabs. Therefore, no complex material models, e.g., elastic-plastic or elastic-brittle, were used. The connection between the wall and the slabs was reduced to support stiffness, disregarding the interface parameters. The calculations were performed in the linear-elastic and nonlinear stages. Geometric linearity meant that the displacements remained in the small displacement theory.