## 2 Materials and Methods
### Finite Element Modeling and Experimental Verification
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Group**} & \multicolumn{2}{c}{_Dor_**} & \multirow{2}{*}{**h/b**} & \multirow{2}{*}{**H (mm)**} & \multirow{2}{*}{\(f_{c}\) (MPa)} & \multicolumn{2}{c}{**Number of Longitudinal**} & \multirow{2}{*}{\
\begin{tabular}{c} **Number of Stirrups** \\ **at Ordinary Zones** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Number of Stirrups** \\ **at Specific Zones** \\ \end{tabular} } \\  & \multicolumn{2}{c}{_(mm)_} & & & & & \\ \hline A1 & 508 & N/ A \({}^{*}\) & \(1.1\) & 31.7 & 6 & 2 & 9 \\ \hline B1 & \(315\times 635\) & 2.0 & 1.4 & 30.2 & 6 & 3 & 9 \\ \hline C1 & \(457\times 457\) & \(1.0\) & \(1.0\) & 32.1 & 8 & 3 & 8 \\ \hline D1 & \(648\times 648\) & 1.0 & 1.4 & 30.7 & 12 & 4 & 13 \\ \hline E1 & \(324\times 324\) & 1.0 & 0.7 & 32.3 & 4 & 3 & 7 \\ \hline F1 & \(324\times 324\) & 1.0 & 1.4 & 31.5 & 4 & 5 & 12 \\ \hline G1 & \(914\times 914\) & 1.0 & 2.0 & 31.6 & 26 & 3 & 17 \\ \hline H1 & \(635\times 1270\) & 2.0 & 2.7 & 30.3 & 24 & 5 & 15 \\ \hline \end{tabular} \({}^{*}\)N/A: Sample A is circular with no ratio.  
\end{table} 
Table 1: Geometrical Properties of the experimental specimens. Figure 1: Geometry Properties of Reinforced Concrete Column, dimensions in mm. E is modulus of elasticity and \(f_{c}^{\prime}\) is the concrete compressive strength. It should be noted that the dilation angle of concrete is defined as 38-degrees. The steel material is considered as an isotropic hardening with a modulus of 200 GPa. Yield and ultimate stresses are considered according to the ASTM A370 as nominal values of 450 MPa and 600 MPa, respectively. Moreover, the connection of reinforcing bars and concrete is made by embedded region constraints. The nonlinear static analysis step is considered to simulate the models. The boundary condition of the bottom surface of the column is pinned (Ux = Uy = Uz = 0) and the top surface is loaded using displacement controls in which the loading rate is constant for all validations. The nonlinear static general analysis technique is employed to simulate the models. The loading stop rate is dependent on the yield stress of the bars and the failure of concrete. However, the Smooth-Step loading amplitude is applied to the load cell. The loading amplitude has 0.05 magnitude of failure load per second. To determine the appropriate mesh size for the analysis of the RC column, three sizes of finite element mesh were selected, and mesh sensitivity analysis was performed. Several attempts were made to reach the finite element results that coincide with the experimental results. However, independence to the mesh size will be considered by this technique. The discretization of concrete is shown in Figure 2.  
As stated previously, the experimental results of specimens are compared to finite element results. The strain-stress diagrams and the maximum corresponding values are shown in Figure 3 and Table 2. The results corresponding to specimen H are not reported in this table because of the inconvenience with the data acquisition system in the last step of the loading. Therefore, there is no record of the maximum axial strain [48]. In Figure 3 and Table 2, the difference of finite element compared with experimental results shows that the maximum stress and strain for specimen A (Figure 3a) is 11.5 and 2.5 percent, respectively. In Figure 3b, it is clear that the strain-stress diagram for both stress and strain parts is closely intertwined by having 4.9 and \(-6.6\) percent. It should be noted that the  
Figure 2: Discretization of concrete. It should be noted that the slop pattern of experimental and finite element ones for all specimens are almost match except Figure 3d,g. The reason of different slop pattern is due to dilatancy criteria of concrete. This means that the granular movements of fine and coarse aggregate of the laboratory admixture have a compact or loose condition. In compact condition, the stress causes an aggregate motion inside of the concrete core (volume).