## 2 Materials and Methods  
### Finite Element Modeling and Experimental Verification  
The experimental calibrations included several comparisons with the selected previous experimental results obtained by [PERSON] [48]. The research herein investigated large-size reinforced concrete (RC) columns subjected to axial loading. It follows the experimental program conducted by the University of California at San Diego and the Building Fire Research Laboratory at the National Institute of Standards and Technology. The cross-sections of the columns were circular, rectangular, and square. According to the experimental program, the specimens were divided into eight different groups with various variables. Figure 1 illustrates the geometry information of the experimental tests. Different dimension ratios had been considered to compare the results where h/b indicates the largest cross-section side (h) to the other side (b) [48]. Table 1 shows the geometrical properties of each group [48]. It should be noted that the longitudinal bars' diameter is 25.4 mm. The values of 9.5 mm and 12.7 mm are for the ordinary stirrups and specific zones, respectively. The material properties of the steel were selected according to ASTM A370 based on grade 60 with the yield and ultimate stresses of 450 MPa and 600 MPa [49]. To perform the simulation, the validation plays an indispensable role to ensure the accuracy of modeling. In this regard, the experimental data are employed to validate with the finite element results. Therefore, three-dimensional finite element (FE) models were built using Abaqus to simulate the behavior of the reinforced concrete columns. In this case, the RC columns (groups A to H) were modeled to validate the experimental results. In this 3D FE model, the concrete was modeled as a homogeneous-deformable solid using the C3D8R element type (3D 8-node linear isoperimetric elements with reduced integration). Both longitudinal and transversal steel bars were modeled as truss elements using the T3D2 element type (a two-node, 3-dimensional truss element). The concrete damage plasticity (CDP) model has been considered to simulate the properties of the concrete. Stress and strain properties can be defined by the CDP model including linear and nonlinear parts in which the plastic parameter must be used in CDP. In addition, stress-strain parameters should be computed in both compressive and tensile sides which both have their own damage parameters. The bottom line is to have enough data to calculate CDP parameters. This requires information that can be obtained through the experimental results. In other words, the compressive strength of concrete and failure strain should be known as the initial values of CDP. After computing those compressive and tensile stress-strain relationships and their corresponding damage parameters, the nonlinear parts should be separatedfrom the linear side. According to ACI 318 [50], 40 percent of the compressive strength can be considered as a boundary of plastic and elastic parts. In fact, these values have been computed for each group, and thus Equation (1) is used to calculate the modulus of elasticity of concrete ACI 318 [50]. \[E=4700\,\sqrt{f_{c}^{\prime}} \tag{1}\]