# Assessment of a Substandard Reinforced Concrete Frame's Beam-Column Joint Using Shake Table Testing
## 3 Experimental Study
### Criteria for Similitude Requirements
In total, fourteen of these mass blocks were welded together to form a singular assembly, culminating in a comprehensive weight of 6 tons for this stacked configuration. The physical variables computed in association with this experimental approach have been detailed in Table 3. Table 2 delineates the similarity laws employed for scaling the prototype structure to the experimental model, whereas Table 3 systematically enumerates the specific experimental parameters adopted in this study. In designing a reliable 1:3 scaled model to investigate the seismic behavior of older, substandard RC frames, both the selection of materials and the dimensional scaling were approached with meticulous care. Foremost, concrete with a relatively low compressive strength of approximately 9 MPa was chosen to reflect the weak concrete quality commonly encountered in pre-1970s or otherwise deficient construction. This lower strength mix not only realistically mirrors the stress-strain characteristics of older buildings but also facilitates the accurate reproduction of cracking patterns, damage progression, and shear deficiencies observed in structures deemed subpar by modern design standards. Addition \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scaling Parameters** & **True Replica** & \
\begin{tabular}{c} **Artificial Mass** \\ **Simulation** \\ \end{tabular} &
\begin{tabular}{c} **Gravity Forces** \\ **Neglected** \\ \end{tabular} \\ \hline Length, \(l_{r}\) & \(l_{r}\) & \(l_{r}\) & \(l_{r}\) \\ Time, \(t_{r}\) & \((l_{r})^{1/2}\) & \((l_{r})^{1/2}\) & \(l_{r}\) \\ Frequency, \(\omega_{r}\) & \((l_{r})^{-1/2}\) & \((l_{r})^{-1/2}\) & \(1/l_{r}\) \\ Velocity, \(v_{r}\) & \((l_{r})^{1/2}\) & \((l_{r})^{1/2}\) & \(1\) \\ Gravitational acceleration, \(g_{r}\) & \(1\) & \(1\) & Neglected \\ Acceleration, \(a_{r}\) & \(1\) & \(1\) & \(1/l_{r}\) \\ Mass density, \(\rho_{r}\) & \(E_{r}/l_{r}\) & - & \(1\) \\ Strain, \(\varepsilon_{r}\) & \(1\) & \(1\) & \(1\) \\ Stress, \(\sigma_{r}\) & \(E_{r}\) & \(E_{r}\) & \(1\) \\ Modulus of elasticity, \(E_{r}\) & \(E_{r}\) & \(E_{r}\) & \(1\) \\ Specific stiffness, \((E/\rho)_{r}\) & \(l_{r}\) & - & \(1\) \\ Displacement, \(\delta_{r}\) & \(l_{r}\) & \(l_{r}\) & \(l_{r}\) \\ Force, \(F_{r}\) & \(E_{r}l_{r}{}^{2}\) & \(E_{r}l_{r}{}^{2}\) & \(l_{r}{}^{2}\) \\ Energy, \((EN)_{r}\) & \(E_{r}l_{r}^{3}\) & \(E_{r}l_{r}{}^{3}\) & \(l_{r}{}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Similitude laws for dynamic models [27]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Physical Quantity** & **Scale Factor** \\ \hline Length, \(l_{r}\) & \(3\) \\ Modulus of elasticity, \(E_{r}\) & \(1\) \\ Time, \(t_{r}\) & \(1.732\) \\ Gravitational acceleration, \(g_{r}\) & \(1\) \\ Strain, \(\varepsilon_{r}\) & \(1\) \\ Acceleration, \(a_{r}\) & \(1\) \\ Frequency, \(\omega_{r}\) & \(0.577\) \\ Velocity, \(v_{r}\) & \(1.732\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The calculated physical quantities for shaking table tests. ally, a smaller maximum aggregate size was employed to maintain geometric similarity in the aggregate-to-member size ratio and to prevent unrealistic over-strength phenomena. Parallel to this, steel reinforcement with a yield strength of 420 MPa was incorporated to emulate the reinforcement typically found in existing RC frames, without excessively elevating the model's ductility beyond that of the prototype. The bars were scaled in diameter and spacing to ensure that the overall steel ratio accurately paralleled full-scale conditions, thereby preserving the intended balance between tensile reinforcement and the surrounding concrete's capacity. In further alignment with established similitude principles, the scale factor for the modulus of elasticity for both concrete and steel was set to unity (\(E_{r}\)), as indicated in Table 3. This ensures stress-to-strain relationships correspond directly to the prototype, preserving accurate stiffness characteristics and deformation behaviors.