# Simplified Plastic Hinge Model for Reinforced Concrete Beam-Column Joints with Eccentric Beams
## 4 Application of Simplified Plastic Hinge Model
### Comparison of Predictions to Test Results  
Figures 6-9 compare the test results (black cyclic responses) with the predictions by the simplified plastic hinge model (red envelope curves). It is noted that the comparison was made directly on the lateral load-drift ratio relationship. To examine the effect of the effective joint width, the predictions in each figure were made with a different design code: Figure 6 with ACI 318-19 [12] (or using Equation (1)), Figure 7 with ACI 352R-02 [13] (Equation (2)), Figure 8 with NZS 3101-2006 [14] (Equation (3)), and Figure 9 with Eurocode 8 [15] (Equation (4)). As shown in the figures, the predictions with different effective joint widths showed similar strength, which agreed well with the test results, but the deformation capacities (especially onset of strength degradation) varied. For concentric beam-column joint specimens (i.e., \(e/b_{c}=0\)), the predictions with ACI 352R-02 [13] showed relatively earlier strength degradation after the peak strength. However, except specimen C2 (Figure 7), the discrepancy was not significant. For eccentric beam-column joint specimens (i.e., \(e/b_{c}>0\)), the predictions with ACI 318-19 [12] underestimated the deformation capacity, showing early strength degradation (Figure 6,d,n,o,p). Compared to the predictions with ACI 318-19 [12], the predictions with ACI 352R-02 [13] showed better agreement, but slightly underestimated the deformation capacity in some specimens (Figure 7,d,o,p). Overall, the simplified plastic hinge model using the effective joint width of NZS 3101-2006 [14] showed the best predictions for all test specimens (Figure 8). Unexpectedly, the predictions with Eurocode 8 [15], which does not consider the effect of the beam eccentricity on the effective joint width, also showed quite good agreement, except the test specimens E0, E2, and E5 (Figure 9,n,o,p). From the comparison, it can be concluded that the simplified plastic hinge model with the effective joint width of NZS 3101-2006 [14] or Eurocode 8 [15] is considered acceptable for design purposes. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c} \hline \hline \multicolumn{13}{c}{**Specinences**} & \multicolumn{13}{c}{**Geometric Properties 1**} & \multicolumn{13}{c}{**Top Bar**} & \multicolumn{13}{c}{**Bottom Bar**} & \multicolumn{13}{c}{**Joint Hoop 3**} \\ \cline{3-13} \multicolumn{13}{c}{} & \(L\) & \(H\) & \(h_{b}\) & \(b_{b}\) & \(h_{c}\) & \(b_{c}\) & \(A_{s}\) & \(f_{y}\) & \(d_{b}\) & \(A_{s}\) &  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Speciness**} & \multicolumn{4}{c}{**Geometric Properties (mm)**} & \multicolumn{4}{c}{**Effective Joint width, \(b_{s}\) (mm)**} \\ \cline{2-9}  & \(\mathbf{b_{y}}\) & \(\mathbf{b_{c}}\) & \(\mathbf{e}\) & **ACI 318-19, Equation (1)** & **ACI 352R-02, Equation (2)  
Figure 6: Comparison between test results and predictions with ACI 318-19. Figure 7: Comparison between test results and predictions with ACI 352R-02. Figure 8: Comparison between test results and predictions with NZS 3101-2006. Figure 9: Comparison between test results and predictions with Eurocode 8. More specifically, the deformation capacity \(\delta_{u}\) by the predictions were quantitatively compared with the test results \(\delta_{T}\) in Table 4: the deformation capacity \(\delta_{T}\) of the test specimens was defined as the drift ratio corresponding to the nominal strength \(P_{y}\) (Equations (5) and (8)) in the post-peak response. As summarized in Table 4, the simplified plastic hinge model using the effective joint width of NZS 3101-2006 [14] or Eurocode 8 [15] matched well with the test results: the mean and COV (coefficient of variation) of \(\delta_{T}/\delta_{u}\) were 1.07 and 0.113 for the predictions with NZS 3101-2006, respectively, [14] or 0.97 and 0.177 for the predictions with Eurocode 8, respectively [15].