## 3 Materials and Methods
### Evaluation of Models  
The strain model proposed by [PERSON] and [PERSON] [15] represents the performance on the previous experimental database with R\({}^{2}\) of 0.34 and RMSE of 4.6 which tell that the concept behind this model, i.e., the ultimate strain increases with the circumferential stiffness of confined concrete, was not accurate. [PERSON] et al. [16] model shows the performance with R\({}^{2}\) = 0.63 and RMSE = 2.37 which is a relatively good performance due to which this model was recommended by ACI 440-2R-02 [34]. Similarly, [PERSON] and [PERSON] [17] model shows the performance with R\({}^{2}\) = 0.66 and RMSE = 8.68; [PERSON] et al. [18] model shows the performance with R\({}^{2}\) = 0.35 and RMSE = 3.80; [PERSON] [19] model shows the performance with R\({}^{2}\) = 0.67 and RMSE = 4.32; [PERSON] and [PERSON] [20] model shows the performance with R\({}^{2}\) = 0.72 and RMSE = 2.74 and [PERSON] et al. [21] model shows the performance with R\({}^{2}\) = 0.73 and RMSE = 2.13. These evaluations represent that the model proposed by [PERSON] et al. [21] gave the best performance among the evaluated models. The values of R\({}^{2}\) and RMSE for all the evaluated models were also presented in Table 3. Therefore, the general form of this model was selected as final for the current study as given by Equation (14). After determining the constants of the selected form of strain model, the proposed nonlinear analytical model for strain of FRP confined concrete is given by Equation (15). \[\varepsilon_{cc}/\varepsilon_{co}\ =\ \alpha+\beta\rho_{k}^{\lambda_{1}}\rho_{ \varepsilon}^{\lambda_{2}} \tag{14}\]  
where \(\alpha\), \(\beta\), \(\lambda_{1}\) and \(\lambda_{2}\) are constants which were determined by using general regression analysis. \[\varepsilon_{cc}/\varepsilon_{co}\ =\ 1.85+7.46\rho_{k}^{0.71}\rho_{\varepsilon}^{1. 17} \tag{15}\]  
Figure 2: Performance of previously proposed and presently proposed strain models of confined concrete on the developed database. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Researcher** & **RMSE** & **R\({}^{2}\)** \\ \hline [PERSON] and [PERSON] [15] model & 4.6 & 0.34 \\ [PERSON] et al. [16] model & 2.37 & 0.63 \\ [PERSON] and [PERSON] [17] model & 8.68 & 0.66 \\ [PERSON] et al. [18] model & 3.8 & 0.35 \\ [PERSON] [19] model & 4.32 & 0.67 \\ [PERSON] and [PERSON] [20] model & 2.74 & 0.72 \\ [PERSON] et al. [21] model & 2.13 & 0.73 \\ Proposed model & 1.93 & 0.74 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Values of coefficient of determination (R\({}^{2}\)) and root mean square error (RMSE) for various previously proposed models on the developed database. The performance of the proposed analytical strain model is given in Figure 3 using the database of 678 points with the R\({}^{2}\) = 0.74 and RMSE = 1.93. These statistical indices show that the performance of currently proposed strain model is better than that of the previously proposed models with significant accuracy because the index of RMSE is less and index of R\({}^{2}\) is higher for the proposed model which is desirable. For a comparative study of the currently proposed and previously proposed strain models, the normal distribution curves and ratios of predictions were plotted. The normal distribution of confined concrete strains to unconfined concrete strains ratios of experimental predictions to theoretical predictions of different models for the previous database were presented by Figure 4 and the distribution of confined concrete strains to unconfined concrete strains ratios of the database was presented by Figure 5. The proposed analytical model and Lam and Teng [20] model performed well for the mean normalized values. The deviations of the proposed analytical model and Lam and Teng [20] model were 2.5% and 3% from unity, respectively. The normalized predictions of other previously proposed strain models were found to be conservative. It was observed that Toutanji [19] model presented most of \(\varepsilon_{cc}/\varepsilon_{co}\) ratios in the range 0.0-2.0.