# Assessment of a Substandard Reinforced Concrete Frame's Beam-Column Joint Using Shake Table Testing
## 3 Experimental Study
### Criteria for Similitude Requirements  
Modeling theory delineates the parameters necessary for relating the geometrical aspects, material characteristics, initial scenarios, boundary constraints, and environmental influences of both the model and its prototype. This relationship is crucial for enabling the behavior of one entity to be articulated as a function of the behavior exhibited by the other. The foundational principle that facilitates the formulation of a comprehensive array of correlation functions, which articulate the correspondence between the model and the prototype, is referred to as similitude [33]. In this context, similitude can be understood as a conceptual framework that leads to the derivation of an extensive array of correlation functions, referred to as scaling laws. These scaling laws serve to define the dynamics of the relationship between the model and its corresponding prototype. Various methodologies exist to establish a relationship between the behaviors of full-scale prototypes and their reduced-scale counterparts. These methodologies encompass dimensional analysis, energy methods, similitude laws, as well as empirical similarity approaches [34]. According to [PERSON] and [PERSON] [35], dimensional analysis is an analytical method by which a dimensionally homogeneous equation, containing physical quantities and describing a physical phenomenon, is converted into an equivalent equation containing only the dimensionless products (\(\pi\)-factors) of the powers of the physical quantities. This type of analysis is based on the Buckingham \(\pi\) Theorem [36], which states that a dimensionally homogeneous equation can be reduced to a functional relationship between a complete set of independent dimensionless products (\(\pi\) factors). A structural model must be meticulously developed, assembled, and analyzed in accordance with specific similitude criteria that connect the model to the original prototype. These criteria stem from modeling theory, which can be established through a dimensional analysis of the physical phenomena that govern the structural behavior. In the context of dynamic model testing, dimensional analysis can be utilized to establish the principles that dictate the scaling laws associated with force, time, and other dependent dimensional quantities. This analytical approach provides a framework for understanding how these variables interact and scale in testing scenarios [37]. Table 2 presents a compilation of scale factors derived from similitude analysis, as discussed by [PERSON] and [PERSON] [33], specifically in the context of earthquake loading. In the realm of scaling applications, three primary physical models have been identified: the true replica model, the artificial mass simulation model, and the model that disregards gravitational forces. \begin{table}
\begin{tabular}{c c} \hline \hline
**Specifications** & **Biaxial Seismic Simulator** \\ \hline Table Dimensions & 3 \(\times\) 3 m \\ Degrees of Freedom & 2 \\ Simulation Frequency Range & 0–50 Hz \\ Maximum Actuator Displacement & \(\pm\)250 mm \\ Maximum Linear Velocity & 1000 mm/s \\ Maximum Specimen Turning Moment & 30 m-ton \\ Maximum Carrying Capacity & 10 ton \\ Maximum Table Acceleration & 1 g \#rated load \\ Maximum Table Speed & 1 m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Technical properties of the Allianz shaking table. This research employed an artificial mass simulation model specifically designed to fulfill the criteria of similitude regarding geometric and loading parameters. It is noteworthy that this model is compiled with nearly all material specifications, with the exception of its mass density. To rectify this deficiency, additional steel blocks were integrated into the roof structure, a maneuver that effectively preserved the overall stiffness of the model. Each steel block had dimensions of 1750 mm in length, 570 mm in width, and 60 mm in height, contributing an individual mass of 430 kg.