## 4 Simplified Model Using ANFIS  
The proposed ANFIS model provides more accuracy than do the other equations, but its practical application is difficult, because it consists of complex algorithms. Therefore, in this study, parametric studies of the virtual data were performed based on the previously constituted ANFIS algorithm, and a simplified equation for effective compressive strengths of corner and edge columns was proposed. Table 3 shows the range of variables to be assumed for the parametric study, and Figure 4 shows the tendencies in the effective compressive strengths of the column (\(f^{\prime}_{cc}\)) according to the concrete compressive strength of the column and the slab (\(f^{\prime}_{cc}\) and \(f^{\prime}_{cj}\)), and the aspect ratio of slab thickness to column width (\(h/c\)). The parametric studies found that as the \(f^{\prime}_{cc}\) and \(f^{\prime}_{cj}\) increase, the \(f^{\prime}_{cc}\) shows an overall tendency to increase. It was also found that the \(f^{\prime}_{cc}\) tends to decrease non-linearly with an increase in the \(h/c\). Based on the parametric studies, a dimensional analysis method [29] was used to derive the simplified equation for the effective compressive strength of the column. In this study, three dimensionless terms (\(\pi_{1}\), \(\pi_{2}\), and \(\pi_{3}\)) were set as shown below:  
\[\pi_{1}=\frac{f^{\prime}_{cc,pro}}{f^{\prime}_{cj}},\;\pi_{2}=\frac{h}{c},\; \pi_{3}=\frac{f^{\prime}_{cc}}{f^{\prime}_{cj}} \tag{5}\]  
where \(f^{\prime}_{cc,pro}\) is the effective compressive strength of the column by the proposed ANFIS model. In Equation (5), \(\pi_{1}\) is placed on the left side, while \(\pi_{2}\) and \(\pi_{3}\) are placed on the right side to constitute a relational expression as follows:  
\[\frac{f^{\prime}_{cc,pro}}{f^{\prime}_{cj}}=f(\frac{h}{c},\frac{f^{\prime}_{cc} }{f^{\prime}_{cj}}) \tag{6}\]  
Figure 3: Verification of proposed ANFIS model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(f^{\prime}_{cc}\) (MPa) & \(f^{\prime}_{cj}\) (MPa) & \(c\) (mm) & \(h\) (mm) \\ \hline Parameter range & 36–75 & 24–30 & 200–500 & 50–750 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Range of variables for parametric study. When it is represented by a dimensionless function for the \(h/c\) and the \(f^{\prime}_{cc}/f^{\prime}_{cj}\), it can be expressed in the form of an exponent with respect to the dimensionless terms \(\pi_{2}\) and \(\pi_{3}\), as follows:  
\[\frac{f^{\prime}_{cc,pro}}{f^{\prime}_{cj}}=K_{1}\left(\frac{h}{c}\right)^{ \alpha}\left(\frac{f^{\prime}_{cc}}{f^{\prime}_{cj}}\right)^{\beta} \tag{7}\]  
where \(K_{1}\) is the constant term, and \(\alpha\) and \(\beta\) are the exponential terms. The test results conducted by [PERSON] [9] and [PERSON] [12] showed that as the \(h/c\) increases, the \(f^{\prime}_{cc}\) decreases. The results of the parametric studies shown in Figure 4c also confirmed that the value of \(h/c\) is inversely proportional to that of \(f^{\prime}_{cc}\). The distribution of \(f^{\prime}_{cc,pro}/f^{\prime}_{cj}\) with respect to \(c/h\), which is the reciprocal of \(h/c\), is shown in Figure 5a, and the equation of a trend line for \(c/h\) can be obtained. When the equation of a trend line for \(c/h\) is reflected in Equation (7), it can be represented as follows:  
\[\frac{f^{\prime}_{cc,pro}}{A(c/h)^{0.27}f^{\prime}_{cj}}=K_{2}\left(\frac{f^{ \prime}_{cc}}{f^{\prime}_{cj}}\right)^{\beta} \tag{8}\]  
where \(K_{2}\) is the constant term. The distribution of \(\frac{f^{\prime}_{cc,pro}}{A(c/h)^{0.27}f^{\prime}_{cj}}\) according to \(f^{\prime}_{cc}/f^{\prime}_{cj}\) is shown in Figure 5b, and the obtained equation of a trend line is reflected in Equation (8) and then represented as shown below:  
Figure 4: Analysis results of parametric study.