## 5 Analytical Study and Model Calibration
### Approaches to Modeling  
FE models for the two tested RC were created utilizing Seismostruct V2025 [61], an advanced fiber-based platform capable of executing nonlinear static and dynamic analyses. Additionally, this software allows for the incorporation of both material and geometric nonlinearity effects in the modeling process. This is made possible through a total co-rotational formulation by [PERSON] and [PERSON] [45], accurately representing kinematic transformations tied to large displacements and three-dimensional rotations of beam-column members. This method allows small deformations in relation to the chord without losing general applicability, even with large nodal displacements and rotations. In the local chord coordinate system, six fundamental displacement degrees of freedom are presented in Figure 8a,b. On the other hand, distributed inelasticity elements are increasingly used in earthquake engineering for research and professional applications. Their advantages over simpler lumped-plasticity models, as well as their historical development and constraints, are documented by authors such as [PERSON] and [PERSON] [5] and [PERSON] and [PERSON] [7]. Notably, these elements do not require the complex calibration of empirical parameters against actual or ideal responses under simplified loading conditions, unlike concentrated-plasticity models. This fiber approach models cross-sectional behavior, linking each fiber to a uniaxial stress-strain relationship. The stress-strain state of beam-column elements is determined by integrating the nonlinear responses of typically 100 to 150 fibers in the section. Figure 8c represents a schematic illustration of the Gaussian integration procedure employed in this fiber-based FE analysis. This figure is pivotal for understanding the discretization strategy that underpins the accurate computation of the nonlinear behavior of RC beam-column elements. In this schematic, the RC element is depicted with its endpoints (0 and L), its midpoint (L/2), and, crucially, an integration point positioned at a distance of 0.3 L from the midpoint. This specific placement is not arbitrary; rather, it arises from an extensive sensitivity analysis and is consistent with the optimal Gaussian  
Figure 8: **(a,b)** Local Beam’s DOFs, and **(c)** Typical Gauss integration sections. integration schemes documented in the literature and is also recommended in the software manual employed in this study [4; 5; 61]. The rationale for selecting an integration point at 0.3 L from the midpoint is rooted in the need to accurately capture the spatial variability of stress and strain across the RC cross-section, particularly in regions where steep gradients may develop due to localized damage phenomena. By situating the integration point at this strategically determined location, the method ensures that the fiber-level responses, which collectively contribute to the global structural behavior, are computed with a high degree of precision. This is essential for modeling the complex nonlinearities inherent in seismic response, including material nonlinearity, bond degradation, and the evolution of damage under cyclic loading. Figure 9 provides a comprehensive graphical representation of the stress-strain relationships for the primary materials utilized in the analysis--namely, concrete, reinforcing steel, and the TNT-BRB system. The concrete curve is derived from the seminal Mander model [62], which rigorously characterizes the quasi-brittle behavior of concrete--from the initial linear elastic range to the onset of cracking and eventual post-peak softening. This model is widely recognized for its ability to capture the degradation of stiffness and the evolution of damage under increasing strain, which are critical for predicting seismic performance.