# Assessment of a Substandard Reinforced Concrete Frame's Beam-Column Joint Using Shake Table Testing
## 6 Discussion  
To assess the damage inflicted by an earthquake, it is essential to delineate the correlation between the intensity of ground motions and the resultant degree of damage to various structures. This correlation is commonly referred to in the technical literature as a damage function. To analyze the vulnerability of structures, various criteria have been developed to quantify damage [50]. These criteria provide a framework for assessing the extent of structural damage based on established theoretical principles, ultimately resulting in the calculation of a specific metric known as the damage index. A significant damage index is introduced by [PERSON] and [PERSON] [37]. This index is characterized as a linear amalgamation of damage attributed to energy dissipation and the peak deformation experienced. [PERSON] and [PERSON] [37] substantiated their proposed equation through empirical test results collected from various researchers examining concrete columns and beams. In this approach [37], the damage index (D) is defined as a combination of maximum deformation and cumulative energy dissipation, typically expressed as follows.  
\[D=\frac{\delta_{m}}{\delta_{u}}+\frac{\beta}{V_{y}}\frac{E_{h}}{\delta_{u}}\]  
Here, in the equation, \(\delta_{m}\) and \(\delta_{u}\) refer to the maximum experienced displacement and ultimate displacement capacity, respectively. \(E_{h}\) is the total hysteretic energy dissipated (area enclosed by the hysteresis loops), and \(V_{y}\) is the yield base shear strength value. Further, \(\beta\) is a constant defined in [37]. The assessed damage index stands at 0.89, categorizing it at the threshold of near collapse, yet still within the significant damage spectrum.  
The present experimental investigation elucidates critical seismic performance characteristics of substandard RC beam-column joints, explicitly highlighting pronounced stiffness degradation, strength deterioration, hysteresis loop pinching, and extensive shear cracking under seismic loading conditions. Specifically, the tested structural model demonstrated explicit numerical values that clearly articulate and quantify structural vulnerabilities, directly underscoring critical deficiencies typical of older, inadequately reinforced RC constructions.  
A comprehensive evaluation of recently published experimental studies involving similarly scaled tests corroborates our observations. [PERSON] and [PERSON] [51], through the detailed cyclic load testing of RC beam-column joints, reported notable strength losses exceeding 30%, stiffness degradation, and pronounced shear cracking--findings directly aligned with our experimental outcomes. Likewise, [PERSON] et al. [7] conducted cyclic loading tests on exterior RC beam-column joints, documenting significant shear cracking, concrete spalling, and severe joint deterioration. Their reported drift ratios and cyclic degradation trends remarkably parallel our observed data, emphasizing shared vulnerabilities and validating the reliability of our experimental approach.  
Detailed comparative analyses with prior shake table studies further reinforce the robustness and accuracy of our findings. [PERSON] et al. [16], in experiments on RC waffle-flat plate structures, documented substantial stiffness degradation of approximately 40%, and strength deterioration close to 30% under seismic actions--metrics closely corresponding to those observed in our current investigation. Similarly, [PERSON] et al. [17] investigated a three-story RC frame subjected to shake table tests, highlighting comparable cyclic hysteresis pinching and progressive stiffness reductions. Notably, the drift ratios recorded in their study, approaching values of around 0.055 radians, show significant quantitative similarities to our experimental data.