## 5 Discussion
loops by providing confinement to the core concrete and delaying the onset of stiffness degradation [48]. The pinching effect, commonly observed in substandard structures, is attributed to poor shear capacity and inadequate bond strength between reinforcement and concrete [41]. Several mathematical models have been developed to simulate the cyclic response of RC structures, capturing key hysteretic characteristics such as stiffness degradation, strength deterioration, and pinching effects. The Takeda model [49] is one of the earliest models used to describe stiffness degradation in RC members based on empirical data from cyclic tests. The Bouc-Wen model [50] has been widely adopted for nonlinear hysteretic modeling, incorporating both material and structural degradation effects. The modified Clough model [51] extends these approaches by incorporating pinching effects in the hysteresis loops, making it particularly useful for simulating substandard structures. The graph presented in Figure 11a illustrates the hysteresis loops for the TnT frame in direct comparison to the X-type BRB frame. It is important to observe that the X-type BRB frame demonstrates considerably narrower hysteresis loops, which signifies a more rigid response under lateral cyclic loading conditions. The maximum displacement registered for the X-type BRB frame is approximately \(\pm\)0.010 mm, which is markedly lower than the displacement recorded for the TnT frame, ranging from \(\pm\)0.015 to \(\pm\)0.020 mm. Nonetheless, the peak forces attained by both structural frames remain within similar magnitudes, indicating that, despite the notable differences in stiffness, the ultimate load-carrying capacities are closely aligned. The graph in Figure 11b provides additional insights into the stiffness characteristics of TnT in comparison to X-type BRB. Notably, X-type BRB exhibits loops that are not only narrower but also more vertically aligned than those of the TnT. This observation suggests an increased stiffness and a diminished capacity for deformation in the X-type BRB model. Further, the initial graph presents the TnT frame, characterized by larger and more expansive loops, which indicate a greater capacity for energy dissipation during each loading cycle when compared to the X-type BRB frame. The increase in loop area signifies more considerable plastic deformation, resulting in a heightened cumulative energy absorption capability, an important factor in enhancing seismic resilience. This trend is further corroborated by the second graph, where TnT continues to encompass a larger area than X-type BRB. This observation leads to the conclusion that TnT frames, while exhibiting reduced stiffness, demonstrate superior energy dissip  
Figure 11: Hysteretic response of the specimens: (**a**) comparison of the retrofitted frames, and (**b**) comparison of the elements. them favorable for scenarios where energy absorption and deformation resistance are prioritized over elastic stiffness. Considering the noted distinctions, the selection between TnT frame and X-type BRB frame types is heavily influenced by specific design goals. In scenarios where increased stiffness and reduced deformation amplitudes are critical for mitigating displacements, such as in protecting non-structural components or for applications sensitive to deformation, the X-type BRB frames offer a significant benefit. On the other hand, in contexts where the focus lies on energy dissipation through deformation, alongside the necessity for ductility and resilience against more intense seismic activities, the TnT frame may be more advantageous owing to its larger hysteresis loops and enhanced capacity for energy absorption. Subsequently, the objective was to analyze the displacement traces of frames enhanced with TnT compared to those enhanced with X-type bracing. Additionally, the displacement traces of TnT and X-type brace components were plotted to facilitate comparative analysis.