# Numerical Analysis of the Impact of Thermal Spray Insulation Solutions on Floor Loading
## 4 Discussion  
By analyzing the available literature on the subject with the results obtained from the tests and calculations provided in the paper, the obtained results can be divided into two groups: results regarding the properties of the tested insulation material and the results of bending moments for designing floor slabs. Referring to the insulation material, it can be stated that the average value of the subgrade stiffness for spray-applied polyurethane foam is K = 32,000 kN/m\({}^{3}\). In the case of layer plates with a polyurethane foam core in an aluminum cladding laid as a subfloor, the average value of subgrade stiffness is K = 39,830 kN/m\({}^{3}\)[7; 23; 38]. The cited results show partial conformity; however, they clearly indicate that the insulation layer made of spray-applied polyurethane foam is a more deformable substrate, i.e., there will be greater values of deflections and bending moments than in the case of sandwich panels with a polyurethane foam core laid under concrete slabs.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Discretisation Grid**} & \multicolumn{2}{c}{**The Concrete Slab**} & \multicolumn{2}{c}{**The Concrete Slab**} \\  & **Resting on the** & **Resting on the** & \\
**Points** & **Subgrade Stiffness** & **Substrate Subgrade** & **Multiplier** \\  & **K = 32,000 kN/m\({}^{3}\)** & **Stiffness** & \\  & & **K = 50,000 kN/m\({}^{3}\)** & \\ \hline
157 & 0 & 0 & \\
158 & \(-\)0.833 & \(-\)0.811 & \\
159 & \(-\)1.388 & \(-\)1.316 & \\
160 & \(-\)1.723 & \(-\)1.582 & \\
161 & \(-\)1.889 & \(-\)1.732 & \\
162 & \(-\)1.931 & \(-\)1.834 & \\
163 & \(-\)1.970 & \(-\)1.886 & qs\({}^{2}\) \\
164 & \(-\)1.996 & \(-\)1.913 & \\
165 & \(-\)2.004 & \(-\)1.949 & \\
166 & \(-\)2.065 & \(-\)1.986 & \\
167 & \(-\)2.118 & \(-\)1.998 & \\
168 & \(-\)2.152 & \(-\)2.048 & \\
169 & \(-\)2.273 & \(-\)2.069 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: The values of bending moments for two variants of calculation.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Concrete Slab**} & \multirow{2}{*}{**Deflections [qs\({}^{4}\)/D]**} & \multicolumn{2}{c}{**Bending Moments [qs\({}^{2}\)]**} & **Decrease in the Value of** \\  & & \multicolumn{2}{c}{**M\({}_{\mathbf{x}}\) = M\({}_{\mathbf{y}}\)**} & **Bending Moment [\%]** \\ \hline Resting on the substrate & & & \\ with subgrade stiffness & \(\mathrm{w}_{169}=35.635\) & \(\mathrm{M}_{169}=-2.273\) & - \\ K = 32,000 kN/m\({}^{3}\) & & & \\ \hline Resting on the substrate & & & \\ with subgrade stiffness & \(\mathrm{w}_{169}=23.236\) & \(\mathrm{M}_{169}=-1.886\) & 17.03 \\ K = 50,000 kN/m\({}^{3}\) & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: The values of deflections and bending moments for two variants of calculation for the central point of the plate.  
It was noticed that with an increase in the subgrade stiffness reaction, which did not take into account the influence of underfloor insulation, lower values of deflections and bending moments were obtained. Consequently, this leads to accepting a too small reinforcement area. On the other hand, the slab cooperating with the underlying Winkler substrate receives higher deflections and bending moments, which results in the necessity of applying stronger reinforcement [38]. Damage to floor plates caused by the adoption of incorrect reinforcement or the faulty execution of reinforced concrete structures is a serious problem for the user of the facility. Numerous authors have considered this subject [4; 39; 40]. Although the literature includes papers discussing issues related to the bending of plates on an elastic foundation, they refer to the stratified soil below the floor [9; 13; 14]. This paper shows that it is also important to consider the layer directly under concrete slabs [41; 42].