## 4 Configuration for Shake Table Testing
### Criteria for Similitude Requirements  
Modeling theory outlines key parameters for linking geometric features, material properties, initial conditions, boundary limitations, and environmental effects of models and prototypes. This interaction is crucial for understanding how one entity behaves in relation to another. The main principle enabling the formation of correlation functions, which depict the model-prototype relationship, is known as similitude [50]. In this framework, developing and analyzing a structural model requires a careful approach that follows specific similitude criteria connecting the model to the original prototype. These criteria stem from modeling theory, clarified through dimensional analysis of physical phenomena affecting structural behavior. In dynamic model testing, this analysis helps identify principles governing scaling laws for force, time, and other variables, enhancing understanding of their interactions and relationships during testing [51]. The concept of similitude is based on scaling factors that maintain the proportional relationship between a model and its prototype. This framework can be divided into three main categories: geometric similitude, kinematic similitude, and dynamic similitude. Geometric similitude guarantees that the scaled models faithfully represent the geometry of the actual prototype structures. As noted by [PERSON] and [PERSON] [52] and [PERSON] et al. [53], geometric similarity necessitates that all linear dimensions of the model be proportionately scaled from the prototype. In our investigation, geometric similarity was meticulously preserved by uniformly scaling the dimensions of structural components--such as beams, columns, joints, and reinforcing bars--by a factor of 1:3. This scaling factor was chosen after thorough consideration of practical limitations, encompassing laboratory space, instrumentation capabilities, and the ability to accurately capture intricate seismic responses. The geometric scaling upheld realistic reinforcement configurations, including bar diameters and spacing arrangements, thereby ensuring a faithful representation of actual RC structural layouts. Kinematic similitude pertains to the proportionality of time-variable attributes, encompassing displacement, velocity, and acceleration. In accordance with the comprehensive protocols established by the National Earthquake Hazards Reduction Program (NEHRP, 2011) [54], the attainment of kinematic similarity is vital for the precise simulation of seismic phenomena observed in authentic contexts [55; 56]. Within our shake table investigations, we maintained kinematic similitude by uniformly adjusting displacement and acceleration metrics in accordance with the principles of geometric and dynamic scaling. The resultant scaled seismic inputs effectively emulated typical earthquake motion, enabling us to accurately document critical structural response metrics, including peak accelerations, relative displacements, and deformation characteristics. Dynamic similitude encompasses the proportional relationships among mass, stiffness, and damping attributes to guarantee that the dynamic responses of scaled models accurately mirror the behavior of prototypes under seismic loads [50]. To accomplish this objective, we rigorously adhered to the principles of dynamic similitude, which included preserving mass and stiffness ratios in alignment with the geometric scaling factor. Additional mass was judiciously incorporated into our specimens utilizing steel blocks to replicate the requisite scaled mass density while maintaining structural stiffness. To compensate, steel blocks were added to the roof, preserving overall stiffness. Each block was 1750 mm long, 570 mm wide, and 60 mm high, weighing 430 kg. Fourteen blocks were welded together, creating a total weight of 6 tons.