# Development of a New Rubber Buckling-Restrained Brace System for Structures
## 9 Results and Performance Evaluation
### Performance Evaluation
#### 9.4.2 Hinge Formation Results in Structural Pushover Analysis  
A plastic hinge zone is where the accumulation of inelastic deformation occurs. Most external input energy usually dissipates through continuous deformation of the plastic hinges in BRBs, RBRBs, and steel members. Therefore, the plastic hinge zone is critical, influencing the steel members of load-carrying, inelastic deformation, and energy dissipation capacity. Individually, plastic hinges are designed as a hinge with a discrete point. All deformation of materials, whether it is displacement or rotation, happens within the point of the hinge. For DBE and MCE hazard levels in the X and Y-directions, the plastic hinging in various members is observed to be formed first in braces, beams, and columns. Table 19 summarizes the plastic hinges formed under DBE and MCE-level earthquakes of bare, BRBF, and RBRBF configurations. As illustrated in the table, implementing a bracing system reduces the target displacement sufficiently and increases base shear slightly. For instance, in a DBE hazard level in the Y-direction, the target displacement decreases by 10.76 percent for BRBRF and 33.73 percent for RBRBF, and the same trend has happened in the other three cases. By comparison of the data collected from the results, it appears that the maximum number for BRB bracing failure under a MCE hazard level due to excessive loading was 37 out of 84 (44%). This number for RBRBs was only 9 out of 84 (10%), which improved its resistance and perfect behavior in load-bearing during various earthquake records. It shows the advantage of implementing RBRBs in the structure, which increases the capacity of the structure and mitigates the need for repairing or changing the braces after a severe earthquake simultaneously. Based on the ASCE code, the overall building response and the structural components should fulfill the \"Life Safety\" performance level at the DBE level and \"Collapse Prevention\" performance level at the MCE level. Figure 57 indicates the overall process of plastic hinges formed in bare frames, BRBFs, and RBRBFs. Tables 20 and 21, as well as Figures 58 and 59, indicate that about 45% of the hinges in a bare frame are more than life safety and are not able to fulfill the performance level. By implementing the BRB system, this amount is reduced by about 30% and reaches roughly 10%. The RBRB system illustrates a superior improvement among all; it decreases the percentage of unacceptable hinges to less than 1%. Similarly, Tables 22 and 23 and Figures 60 and 61 indicate the advantage of using a bracing system by making an enormous difference in reducing unacceptable plastic hinges under a MCE hazard level. BRBs reduce  
Figure 56: Dissipated energy under MCE in Chi-Chi TH. the number of plastic hinges for collapse prevention to less than 2%, and RBRBs declined it to less than 1%. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & **Percentage of Plastic** & **Percentage of Plastic** & **Percentage of Plastic** & **Percentage of Plastic** & **Percentage of Plastic** & **Hinges Formed in** & **Hinges Formed in** \\
**DBE** & **Hinges Formed in** & **A-IO** & **IO-LS** & **LS-CP** & **>CP** & **Total Hinges** \\ \hline BARE & 54 & 2 & 21 & 23 \\ \hline BRB & 77 & 12 & 10 & 1 \\ \hline RBRB & 83 & 16 & 0.6 & 0.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 20: Plastic hinge status in DBE-hazard-level X-direction. Figure 57: Plastic hinge formation. (**a**) Bare frame, (**b**) BRB frame, and (**c**) RBRB frame (MCE). Gray (A-IO), Green (IO-LS), Blue (LS-CP), Red CP.