## 4 Model Results
### Comparison with Previously Developed Models  
Table 5 provides a comparison of statistical error parameters for the M5P model and other available punching shear design equations described in the previous section. The inclusion of the mean value (\(\upmu\Omega\)) and coefficient of variation (COV\(\Omega\)) of the ratio of the actual punching shear strength to the model results (\(\Omega=V_{n,test}/V_{n,pred}\)) in addition to RMSE and R\({}^{2}\) values is important. These parameters help determine whether the model overestimates or underestimates the punching shear strength and provide an evaluation of the prediction model accuracy and precision, respectively. Accurate predictions must have \(\upmu\Omega\) values close to 1 and low COV\(\Omega\) values. The results in Table 5 indicate that the proposed M5P model outperforms all other models. While the performances of the Eurocode 2 [7] and Chetchotisak et al. models are reasonable, the M5P model shows significant improvements. Compared to the Chetchotisak et al. model, which is considered the most precise model among the design equations, the M5P model shows a significant reduction of 24.1% and 18.6% in terms of RMSE and MAEvalues, respectively. The \(\upmu\Omega\) and COV\(\Omega\) values for the M5P model are also notably lower than those from the other models, indicating a better model performance. The experimental dataset under consideration encompasses a diverse range of material properties and member sizes. To account for this variety, the normalized punching shear resistance was calculated based on the concrete compressive strength (\(f_{c}\)), effective depth (\(d\)), and critical section (\(b_{o}\)) of Eurocode 2 (EC2) [13] since this code performs better than the other two building codes evaluated in this study. For the M5P model and the experiments, the normalized punching shear resistance was determined using the method prescribed using Eurocode 2 (EC2) design code for identifying the critical section and concrete compressive strength. In order to evaluate the performance of the models, the Root Mean Squared Error (RMSE) value was employed as the assessment metric. Figure 9 presents the best-fit lines and their corresponding RMSE values for each model. Upon examining these values, it becomes apparent that the M5P model boasts a smaller RMSE compared to the Eurocode 2 (EC2) design code. This suggests that the M5P model demonstrates a superior accuracy in predicting the normalized punching shear resistance. The RMSE values for the M5P model and Eurocode 2 (EC2) stand at 0.0950 and 0.1568, respectively, indicating a significant difference in their predictive capabilities. This considerable gap in RMSE values highlights the improved performance of the M5P model in comparison to the Eurocode 2 (EC2) design code when it comes to predicting the normalized punching shear resistance. Furthermore, a closer look at the stress unit in Figure 9 reveals some considerable discrepancies between the experimental and predicted results. These differences suggest that the parameters utilized for normalization might not adequately represent the characteristics of punching shear strength. This observation underscores the need for the further investigation and refinement of the normalization parameters to improve their ability to capture the essential features of punching shear strength.