## 4 Results and Discussion
### Validation  
Experimental data in the training set, test set and validation set were used to validate the ANN model. Figure 6 shows a comparison of the predicted strength capacities by the ANN model and the experiments. It can be observed that the predicted values of the strength are in good agreement with the experimental values of the columns. For the normalized strength, the mean absolute error and goodness of fit are 0.0533 and 0.9304, respectively, for the training set, and 0.0133 and 0.9431, respectively, for the test and validation set. The results indicate that the ANN model can be effectively used to predict the strength of the RC columns under seismic excitations. Different types of explicit formulas have been proposed by researchers or adopted in design codes for calculating the strength of RC columns. In general, concrete and reinforcement contribute to the shear capacity of RC columns with shear failure mode. Therefore, the explicit formula has two distinct parts. \[V=V_{c}+V_{s} \tag{8}\]  
where \(V=F_{\text{max}}\) is the shear strength for shear-failed columns, while \(V_{c}\) and \(V_{s}\) are the contributions of concrete and steel reinforcement, respectively. In this study, three types of explicit formulas for predicting the shear strength of RC columns were adopted to validate the ANN model as summarized in Table 4.  
For flexural-dominated specimens, the lateral loading capacity is strongly dependent on the flexural strength (\(M_{c}\)) and the distance between the critical section of the plastic hinge and point of contra-flexure length (\(L\)), as follows:  
\[F_{\text{max}}=(M_{c}-P\cdot\Delta_{c})/L=\big{(}M_{y}\cdot M_{c}/M_{y}-P\cdot \Delta_{c}\big{)}/L \tag{9}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Reference** & **Concrete Contribution (\(V_{s}\))** & **Steel Contribution (\(V_{s}\))** \\ \hline Sezen and Moehle Sezen and Moehle (1996) & \(V_{c}=k_{\mu}\Big{(}\frac{0.5\sqrt{V_{c}}}{\lambda}\Big{)}\sqrt{1+\frac{P}{0.5 \sqrt{V_{c}}\cdot A_{c}}}\Big{)}\sqrt{1+\frac{P}{0.5\sqrt{V_{c}}\cdot A_{c}}} \Big{)}\sqrt{1+\frac{P}{0.5\sqrt{V_{c}}\cdot A_{c}}}\) & \(V_{s}=k_{\mu}\frac{M_{c}f_{\mu}D_{c}}{s}\) \\ \hline ACI 318-05 Moehle (1996) & \(V_{c}=\frac{1}{3}\Big{(}1+\frac{P}{13\lambda C}\Big{)}\sqrt{V_{c}^{2}}A_{c}\) & \(V_{s}=\frac{A_{c}f_{\mu}D_{c}}{s}\) \\ \hline FEMA 273 [PERSON] et al. (2018) & \(V_{c}=0.29\lambda\Big{(}k+\frac{P}{13\lambda C}\Big{)}\sqrt{V_{c}^{2}}A_{c}\) & \(V_{s}=\frac{A_{c}f_{\mu}D}{s}\) \\ \hline \hline \end{tabular} Note: \(k_{\mu}\) is the ductility-related strength degradation factor, and \(D^{\prime}\) is the distance from the extreme compression fiber to the centroid of the tension reinforcement. The meanings of other parameters in this table are the same as those in Table 1.  
\end{table} 
Table 4: Explicit formulas for estimating the shear capacity of RC columns. Figure 6: Comparison of experimental results and predicted results of the strength of RC columns. where \(\Delta_{c}\) is the capping displacement corresponding to the maximum lateral strength (\(F_{\text{max}}\)). [PERSON] et al. (2019) proposed a semi-empirical strength and deformation expression with good average agreement with test results.