## 5 Analytical Study and Model Calibration
### Limitations of the Fiber-Based Finite Element Model  
At the core of the fiber-based FE methodology lies the discretization of an RC cross-section into a finite number of fibers, each endowed with a uniaxial stress-strain relationship that approximates the behavior of either the reinforcing steel or the concrete. This discretization enables the efficient summation of fiber responses to yield an overall sectional response; however, it does so by assuming a perfect bond between the steel and the surrounding concrete. Such an assumption, while expedient for computational purposes, neglects the intricate interfacial phenomena such as bond-slip, localized debonding, and the onset of micro-cracking that are inherently present in RC systems under cyclic loading conditions. The literature underscores that this assumption may lead to a systematic underestimation of stiffness degradation and strength loss during the post-yield phase. The phenomenon of bond deterioration, particularly under high-cycle fatigue conditions typical of seismic events, can precipitate significant deviations between the modeled and observed structural responses, especially in regions where bond failure governs the initiation of localized plastic hinges [64]. Furthermore, the inherent assumption of a uniform strain distribution across each fiber in the cross-sectional discretization tends to homogenize the actual material behavior. Concrete, characterized as a quasi-brittle material, exhibits highly localized cracking and crushing phenomena, particularly in zones of elevated stress concentration such as the vicinity of beam-column joints. In practice, these localized nonlinearities manifest as discrete regions of strain softening and damage accumulation, phenomena that are frequently averaged out in the distributed plasticity approach. It was shown that the distributed plasticity approach can mask the precise onset of inelastic behavior, thereby reducing the accuracy of the model in replicating critical localized damage mechanisms [65]. Figure 11: Comparison of displacement-time traces for specimens. The limitations of the fiber-based approach are further accentuated by the discretization strategy itself. In an ideal scenario, the division of a cross-section into fibers would capture the true heterogeneity of material properties and the spatial variability of stress and strain fields. However, practical implementations often necessitate a compromise between computational efficiency and resolution. Coarser discretizations may lead to an oversimplification of the complex stress distribution, especially in regions where steep gradients exist. This is particularly problematic when modeling the progression of damage in areas subject to concentrated plastic strains, where phenomena such as diagonal cracking or localized crushing are critical [66]. An additional point of concern is the calibration process of the fiber-based FE model against experimental data. While the present study demonstrates a commendable correlation between the analytical predictions and the global response characteristics observed during shake table tests, the calibration predominantly focuses on overall displacement and eigenfrequency metrics. Such calibration procedures, though effective in establishing the global accuracy of the model, may not adequately account for the evolution of localized strain concentrations and damage mechanisms. It is also important to consider the implications of the aforementioned limitations in the context of the intended application of the model. In seismic analysis, the accurate prediction of the energy dissipation capacity of RC structures is of paramount importance. The fiber-based approach, by averaging out localized phenomena, may overestimate the energy absorption capabilities of RC members, particularly in cases where local damage mechanisms such as bond-slip and localized cracking are predominant.