## 4 Model Results
### Design Code and Empirical Formulas  
The equation for the punching shear resistance for RC flat slabs without shear reinforcement in ACI 318-19 [6] is as follows:  
\[V_{n}=\min\left[\frac{1}{3},\frac{1}{6}\left(1+\frac{2}{\beta}\right),\frac{1}{1 2}\left(2+\frac{\alpha_{s}d}{b_{o}}\right)\right]\lambda_{s}\sqrt{f_{c}^{ \prime}}b_{o}d \tag{7}\]  
The ACI 318-19 equation accounts for several crucial factors that affect the overall punching shear strength of the slab. These factors include the column-type-related factor (\(\alpha_{s}\)), ratio of the long to short sides of the column, concentrated load, or reaction area  
Figure 8: Comparison of the developed machine learning models in terms of RMSE and MAE. Figure 7: Predicted versus experimental shear capacities for the newly developed M5P model and other machine learning models. (\(\beta\)), and the size effect modification factor (\(\lambda_{s}\)). The inclusion of these parameters in the equation represents a significant update from the previous version of the code, ACI 318-14. The size effect modification factor (\(\lambda_{s}=\sqrt{2/(1+0.004d)}\leq 1\)) is particularly noteworthy as it acknowledges the impact of the slab depth (\(d\)) on the punching shear strength. This factor has a maximum value of 1, ensuring that the size effect does not overestimate the punching shear resistance. The column-type-related factor (\(\alpha_{s}\)) differentiates between interior, edge, and corner columns, assigning distinct values for each column type. In the given study, only interior columns are considered, resulting in an \(\alpha_{s}\) value of 40. This factor recognizes that the punching shear stress distribution around a column varies depending on its location within the slab. Finally, \(b_{o}\) represents the critical section perimeter (in mm) and is calculated as follows:  
\[b_{o}= \begin{cases}\begin{array}{c}4(c+d)\text{ for square columns}\\ \pi(c+d)\text{ for circular columns}\\ 2(c_{1}+c_{2}+2d)\text{ for rectangular columns}\end{array}\end{cases}  \tag{8}\]  
where \(c\) denotes the dimensions of the square column section or the diameter of a circular column. The equations from Eurocode 2 [7] for the punching shear strength for RC flat slabs without shear reinforcement is calculated as follows:  
\[V_{u}=\max\left\{ \begin{array}{c}0.18\cdot\xi\cdot(100\cdot\rho\cdot f_{c \kappa})^{1/3}\cdot b_{0}\cdot d\\ 0.035\cdot\xi^{3/2}\cdot\sqrt{f_{c\kappa}}\cdot b_{0}\cdot d\end{array} \right. \tag{9}\]  
The above equation considers the size effect factor (\(\xi\)), the characteristic cylinder strength of concrete (\(f_{ck}\)), and the reinforcement ratio (\(\rho\)) to determine the punching shear resistance (\(V_{n}\)). The size effect factor (\(\xi=\left(1+\sqrt{\frac{200}{d}}\right)\leq 2\)) accounts for the influence of the slab depth on the punching shear resistance, similar to the \(\lambda_{s}\) factor in ACI 318-19, but with a different formulation. The reinforcement ratio (\(\rho\)) plays a crucial role in Eurocode 2, whereas it is not explicitly included in the ACI 318-19 equation. This equation is valid when \(\rho\leq 0.02\). Additionally, the perimeter of the critical section (\(b_{o}\)) represented in Equation (9) is calculated differently in Eurocode 2 when compared to ACI 318-19:  
\[b_{0}= \begin{cases}4(c+\pi d)\text{ for square columns}\\ \pi(c+4d)\text{ for circular columns}\end{cases}  \tag{10}\]  
The equation for the punching shear resistance provided by BS 8110-97 [5] for RC flat slabs without shear reinforcement is calculated as the below:  
\[V_{c}=0.79k\bigg{(}100\rho_{t}\frac{f_{cu}}{25}\bigg{)}^{\frac{1}{3}}b_{0}d, \rho\leq 3\% \tag{11}\]  
This equation incorporates factors like the reinforcement ratio (\(\rho_{t}\)), cubic compressive concrete strength (\(f_{cu}\)), and effective depth of the slab (\(d\)) to determine the punching shear resistance (\(V_{c}\)).