# Evaluation of Eccentric Compressive Behavior Between Active and Passive Preloading in CFST
## 4 Finite Element Analysis and Discussions  
### Load-Displacement History for Different Preloading Methods  
In this study, the preloaded specimens with an eccentric ratio of 0.2 were taken as an example, with a concrete cubic compressive strength of C25 (25 MPa), a steel yield strength of 275 MPa, and a steel thickness of 2 mm. To explore the longitudinal load-displacement response of CFST columns with different preloads, an ordinary CFST column was utilized as the reference for comparison. In Figure 12, the vertical coordinate is the longitudinal  
Figure 11: CFST-CC and CFST-SC with passive preloading: (**a**) CFST-CC; (**b**) CFST-SC. Figure 10: CFST-CP with active preloading. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Step Number** & **Specimen** & **Load Value** & **Component** & **Direction** \\ \hline \multirow{3}{*}{Step1-preloading} & CFST-SP & \(-60\)\({}^{\circ}\)C & Steel & Hoop tension \\  & CFST-CP & \(+63\)\({}^{\circ}\)C & Concrete & Three-way expansion \\ \cline{1-1}  & CFST-CC & 0.2 \(\varepsilon_{\mathrm{sy}}\) & Steel & Longitudinal \\ \cline{1-1}  & CFST-SC & 0.2 \(\varepsilon_{\mathrm{sy}}\) & Concrete & Longitudinal \\ \hline \multicolumn{1}{c}{Step2-service loading} & All specimens & \(\Delta L\) = 35 mm & The whole section & Compression \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Loading steps. load, which includes longitudinal preload and service load, while the horizontal coordinate is the longitudinal deformation along the direction of the eccentric load. In the curves, \"\(\bullet\)\" represents the peak load (\(P_{\text{u}}\)) of the curve, and \"\(\Delta\)\" and \"\(\circ\)\" denote 0.75 \(P_{\text{u}}\), and 0.85 \(P_{\text{u}}\), respectively. Moreover, the peak loads of the columns, the peak load ratios (a ratio of the peak load of a preloaded column to that of the ordinary CFST), and the ductility indexes are listed in Table 4.  
Figure 12: Longitudinal load versus displacement curves: (**a**) CFST-SP; (**b**) CFST-CP; (**c**) CFST-CC; (**d**) CFST-SC. According to Figure 12, all the curves included increment and decrement segments. However, each curve had a unique property due to the preloading in Step 1. As can be seen from Figure 12a and Table 4, CFST-SP had a higher peak load. This phenomenon could be ascribed to the influence of the active preload in the first step. In Step 1, the steel tube squeezed the concrete, making the steel and concrete work together in advance, while at the same time, according to equilibrium theory, CFST-SP was not loaded longitudinally at this step. Step 2 started with the respective initial stresses in the concrete and the steel tube. When the concrete in the compression bending zone was compressed by the initial radial preload and the service load, the local compressive strength of the concrete increased, which ultimately led to a slight increase in the peak load of CFST-SP compared to the ordinary CFST. As can be seen from Figure 12b, the peak load of CFST-CP appeared earlier than that of the ordinary CFST and had a peak load ratio of 1.15, which was the highest among the specimens. This was because, in the first step, the concrete was subjected to three-way pre-pressure due to the outward expansion of the self-stress concrete, which was constrained by the steel tube. In the second step, when CFST-CP was subjected to the servicing load, the concrete in the compression bending zone of the section had higher compressive strength, resulting in the highest load-bearing capacity for CFST-CP. Similar to CFST-CP, the concrete for CFST-CC was pre-compressed (Figure 12c). In Step 1, the preload was large and the concrete underwent early compression in three directions. In Step 2, the passive longitudinal compression of the concrete in the compression bending zone activated the confining effect of the steel tube and the concrete, ensuring that the two parts were tightly bonded from the beginning.