# Development of a New Rubber Buckling-Restrained Brace System for Structures
## 7 Comparison of BRB and BRBR  
In Figure 39, both prototypes' full performance is shown. RBRBs' maximum capacity under tension was 177 kN (with 8 mm displacement), and their maximum displacement was 42 mm due to the aforementioned rubber components functioning after the failure of the RBRB core. Under compression, the maximum load was 224 kN (by 17 mm displacement), which had a maximum displacement of 42 mm as well, while the maximum BRB force reached 125 kN (by 16 mm displacement) and its maximum displacement was 26 mm. The comparison results for BRB and RBRB are shown in detail in Table 6 and Figure 40.  
Figure 38: Hysteresis curve in phase 2 of experimental RBRB. Figure 39: Comparison of experimental results for full BRB and full RBRB behavior. The higher compressive resistance of the RBRB, due to the rubber components, enhances stability by preventing global buckling during high seismic events. While this may slightly affect the dynamic behavior of the structure, the overall performance improvement outweighs these effects. Engineers should consider this behavior during design to ensure optimal load distribution and energy dissipation. This section presents the calculations for effective damping (Keffb), effective stiffness (\(\varphi\)), and dissipated energy (W) for both BRB and RBRB. The capacity of a structure to withstand earthquakes relies on its ability to dissipate the energy produced by ground motion. Due to the complexity involved in evaluating energy generated from ground motion, it is essential to adopt a structural design approach that ensures that the structure's energy dissipation exceeds the expected demand. The amount of energy dissipated by a structural system during seismic overloading is of paramount importance. The energy dissipated in a single hysteresis loop (W\({}_{i}\)) is estimated by considering the area enclosed by the hysteresis loop using Equation (2). In Figure 41, \(F_{i}(u)\) and \(F_{ul}(u)\) are forces at displacement '\(u\)' throughout the loading and unloading process. The summation of the total area enclosed by the hysteresis loop gives the cumulative energy dissipated in the specimen. The damping ratio was also calculated based on BS EN 15129:2009 [88] in Equation (3). The effective stiffness was calculated based on Equation (4), where V\({}_{\text{Ebd}}\) is the force corresponding to d\({}_{\text{bd}}\), obtained at the third load cycle. \[\Delta W_{i} =\int_{-v_{min}}^{v_{max}}\left(F_{i}(u)-F_{ul}(u)\right) \tag{2}\] \[\Phi =\text{W}\left(\text{d}_{\text{bd}}\right)/(2\pi\text{V}_{\text{ Ebd}}\text{d}_{\text{bd}})\] (3) \[\text{K}_{\text{effb}} =\text{V}_{\text{Ebd}}/\text{d}_{\text{bd}} \tag{4}\] \begin{table}
\begin{tabular}{c c c c c} \hline  & **MAX Dis Under** & **MAX Force Under** & **Max Dis Under** & **Max Force Under** \\  & **Tension (nm)** & **Tension (kN)** & **Compression (nm)** & **Compression (kN)** \\ \hline RBRB & 42 & 177 & 42 & 224 \\ \hline BRB & 26 & 129 & 26 & 125 \\ \hline \end{tabular}
\end{table} 
Table 6: Comparison of experimental results for BRB and RBRB. Figure 40: Comparison of experimental results for BRB and RBRB. Based on the aforementioned experimental result, it can be seen in the performance of both devices that there was an energy dissipation (the area of hysteresis loop) of 13,416 kN\(\cdot\)mm for BRB and 22,459 Kn\(\cdot\)mm for full RBRB behavior. The RBRB-dissipated energy was calculated as 13,416 kN\(\cdot\)mm before the core failure (in phase 1) and 12,432 kN\(\cdot\)mm after the core failure (in phase 2). It is concluded that the energy dissipated by RBRB increased by 41% due to the rubber's added resistance in comparison to BRB. The damping ratio also was based on BS EN 15129:2009 as shown in Equation (3) [88], and the BRB damped 60.3% of the income force while RBRBs' damping ratio was 64.8% and 52.1% in phases 1 and 2, respectively. The effective stiffness of both devices has been computed based on Equation (4), where V\({}_{\text{Ebd}}\) is the force corresponding to d\({}_{\text{bd}}\), obtained at the third load cycle.