# Evaluation of Eccentric Compressive Behavior Between Active and Passive Preloading in CFST
## 2 Finite Element Modeling
### Verification of the Finite Element Model  
The finite element models for ordinary CFST columns and preloaded CFST columns under compression were validated by comparing the peak loads and the load-deformation curves determined by numerical calculations with the experimental results (Table 2 and Figure 8). As shown in Table 2, \(D\), \(t\), and \(l\) represent the diameter of the CFST, the thickness of the steel tub, and the full length of the specimen, respectively. \(f_{\text{cu}}\) and \(f_{\text{y}}\) are the cubic compressive strength of the concrete and the yield strength of the steel, respectively. Previous studies [11; 15; 23; 37; 38; 39; 40] conducted ordinary CFST and experimental/numerical research on preloaded CFST in compression. In general, a column with \(L/D\leq 4\) is defined as a short column. The above specimens approximated short columns and were similar to the model analyzed in this study. Therefore, these specimens were suitable for validation to confirm the correctness of the model. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Specimen Label**} & \multirow{2}{*}{_DIII (mm)_} & **Eccentricity** & \(f_{\text{cu}}\) & \(f_{\text{y}}\) & \(P_{\text{MT}}\) & \(P_{\text{PSM}}\) & \(P_{\text{PSM}}\) \\  & & & **(mm)** & **(MPa)** & **(MPa)** & **(MN)** & **(MN)** & **(MN)** \\ \hline \multirow{2}{*}{Zhao XL [37]} & C2 & 273/6/850 & 40 & 36.8 & 325 & 2504 & 2490 & 0.994 \\  & C3 & 273/6/850 & 80 & 36.8 & 325 & 2161 & 2158 & 0.999 \\ \multirow{2}{*}{[PERSON] [38]} & B4 & 219/4/1000 & 75 & 49.3 & 325 & 986.9 & 1055 & 1.069 \\  & C5 & 219/4/1000 & 100 & 54.1 & 325 & 825.2 & 875 & 1.060 \\ \hline \multirow{2}{*}{[PERSON] [23]} & C40T20(6) & 179/2350 & 0 & 40 & 235 & 1155 & 1149 & 0.995 \\  & C40T40(2) & 183/4350 & 0 & 40 & 235 & 1327 & 1511 & 1.139 \\  & C40T20(2) & 179/2/350 & 0 & 40 & 235 & 1072 & 1151 & 1.074 \\ \hline \multirow{2}{*}{[PERSON] [39]} & t2.5-a & 160/2.5/500 & 0 & 45.3 & 327.5 & 1600 & 1593 & 0.996 \\  & t2.5-b & 160/2.5/500 & 0 & 53.9 & 305.3 & 1690 & 1610 & 0.953 \\ \hline \multirow{2}{*}{[PERSON] and \(\;\)[PERSON] [15]} & SFC & 650/4.5/324 & 0 & 79.4 & 443 & 2201 & 2240 & 1.018 \\ \cline{1-1}  & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \\ \end{tabular}
\end{table} 
Table 2: Comparison between FEM analysis and literature results. Figure 7: Preloaded CFST calculation models. In Table 2, the peak loads determined from the finite element simulations (\(P_{\text{FEM}}\)) are compared with the experimental/numerical peak loads (\(P_{\text{Lit}}\)). A mean value (\(P_{\text{FEM}}\)/\(P_{\text{LIT}}\)) of 0.999 and a coefficient of variation (CoV) of 0.094 were obtained. The load-deformation responses of some typical specimens are shown in Figure 8, which includes four representative models and the abovementioned ordinary CFSTs. As can be seen from the figure, the finite element simulation results are not completely consistent with the test results. This may be because the finite element simulation is carried out under ideal conditions, while in reality there may be problems such as plastic yielding of steel bars, shrinkage creep of concrete, interface contact, and initial defects of the specimen, which lead to deviations between the simulation results and the test results. However, in general, the initial stiffness values, peak loads, and post-limit behavior (dashed lines) obtained by the finite element simulation are basically consistent with the results of the literature and this study (solid lines). Therefore, we believe that the finite element model can provide accurate calculation results. In practice, the effect of shrinkage on solid concrete cannot be ignored. In calculations, the shrinkage deformation of concrete can be simulated by relying on its temperature drop.