## 4 Results and Discussion
### Comparison with the Different Provisions in Design Code  
In most design codes, the permissible moment redistribution \(\beta\) can be calculated using the neutral axis depth factor _c/d_ as a main parameter, as shown in Figure 14. It can be seen that the provisions for moment redistribution in various design codes are quite different, such as the upper bound of \(\beta\), the limited range of _c/d_, and the divergence between the predictions. In addition, the amount of moment redistribution is not only related to _c/d_ but also to the variation in the stiffness distribution and the bond between the reinforcement and concrete. However, the latter factors are usually not considered in design codes. The detailed provisions in the design codes are illustrated below. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Performance**} & \multicolumn{2}{c}{**ANN**} & \multicolumn{2}{c}{**SVR**} \\ \cline{2-5}  & **Training** & **Testing** & **Training** & **Testing** \\ \hline MSE & 0.0009 & 0.0009 & 0.0001 & 0.0008 \\ MAPE & 0.0989 & 0.0850 & 0.0079 & 0.0526 \\ \(R^{2}\) & 0.9521 & 0.9431 & 0.9950 & 0.9485 \\ IAE & 0.0694 & 0.0813 & 0.0080 & 0.0538 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Performance indices of ANN and SVR models. Figure 12: Comparison of predicted values with ANN model with experimental results: (**a**) training sets; and (**b**) testing sets. Figure 13: Comparison of predicted values with SVR model with experimental results: (**a**) training sets; and (**b**) testing sets. In CSA A23.3-14 [47], the negative moments at the supports of continuous flexural members can be increased or decreased by:  
\[\beta(\%)\leq 30-50c/d \tag{15}\]  
and \(\beta\) is no more than 20%. In BS 8100-1:1997 [48], the neutral axis depth of the cross-section subjected to the largest moment should be checked by the expression with the permissible percentage of moment redistribution as an independent variable. In other words, \(\beta\) can also be treated as a function of _c/d_:  
\[\beta\leq 0.6-c/d \tag{16}\]  
with a maximum of 0.3. The AS 3600-2009 [49] indicates that the elastically determined bending moments at any interior support of statically indeterminate members with reinforcement of Ductility Class N (the uniform elongation is no less than 5.0% and the tensile-to yield stress ratio is no less than 1.08) may be reduced or increased by:  
\[\beta(\%)=\left\{ \begin{array}{ll}30\%&c/d\leq 0.2\\ (30-75c/d)\%&0.2<c/d\leq 0.4\\ 0&c/d>0.4\end{array} \right. \tag{17}\]  
In the DIN 1045-1:2008 [50], fib Model Code 2010 [51] and EN 1992-1-1:2004 [52], the provisions for the moment redistribution are similar. The statically indeterminate members allowed for moment redistribution are predominantly subjected to flexure and the ratio of the adjacent spans is in the range of 0.5-2. Except for the neutral axis depth factor, the coefficient of the moment redistribution also depends on the ductility of reinforcement and concrete strength, as listed in Table 8.  
Figure 14: Comparison of various code provisions for moment redistribution. The ACI 318-14 [53] uses the net tensile strain \(\varepsilon_{\text{t}}\) as an indicator of the permissible moment redistribution, as given by:  
\[\beta(\%)\leq 1000\varepsilon_{\text{t}}\leq 20\% \tag{18}\]  
where \(\varepsilon_{\text{t}}\) is the tensile strain in the extreme layer of longitudinal tension steel at nominal strength, excluding strains due to effective prestress, creep, shrinkage and temperature and is required to be more than 0.75%. Notably, the coefficient of the moment redistribution specified in the design codes are calibrated through a safe envelope formed from the available experimental data with a certain probability and not from the real values such as the database values used in the present study for constructing the models. To study the performance of different approaches in design codes as well as the proposed ANN and SVR models, comparisons of their predicted results were conducted.