# Evaluation of Eccentric Compressive Behavior Between Active and Passive Preloading in CFST
## 5 Parametric Studies
### P-M Curves  
To further evaluate the eccentric compressive performance of the preloaded CFST, the _M-P_ envelope curves of the specimen considering the effects of different concrete strengths, steel strengths, and steel thicknesses were compared with the _M-P_ envelope curves of the ordinary CFST. The corresponding results are shown in Figure 21, where \(M\) and \(P\) represent the bending moment and the axial force at the bottom section of the specimen, respectively. As shown in Figure 21, the _M-P_ curves of CFST-SP and CFST-CP were more obviously convex than those of the ordinary CFST, and the carrying capacity of CFST-SC was slightly lower than that of the ordinary CFST. However, the difference between CFST-CC and the ordinary CFST was not obvious. Figure 22 interprets Figure 21 in terms of two different ratio indicators, which are given by  
\[a_{1}=(P_{max}-P_{max\;(CFST)})/P_{max(CFST)}, \tag{14}\]  
\[a_{2}=(M_{max}-M_{max(CFST)})/M_{max(CFST)}, \tag{15}\]  
In the expression, \(a_{1}\) represents the difference ratio of the maximum axial force between the preloaded specimen and the ordinary CFST. Similarly, \(a_{2}\) represents the difference ratio of the maximum bending moment between the preloaded specimen and the ordinary CFST.  
As can be seen from Figure 22, both CFST-SP and CFST-CP showed a significant increase in the maximum compressive and flexural load capacity, especially CFST-CP. Surprisingly, the difference ratios for CFST-CC were mostly positive, indicating that smaller passive preloads of concrete were not always detrimental to the carrying capacity. For CFST-SC, the restraining effect of the steel tube on the concrete lagged because the preload was only applied to the steel tube, resulting in reductions in the carrying capacity.  
Figure 21: _Cont._Figure 21: Effect of various parameters on \(M\)-\(P\) interaction diagram: (**a**) Effect of concrete strength; (**b**) Effect of steel strength; (**c**) Effect of steel thickness.  
Figure 22a shows the effects of the concrete strength, steel tube strength, and steel thickness on \(a_{1}\) for different specimens. It can be seen from the figure that except for CFST-CP, changing the parameter grades had very little effect on \(a_{1}\). The variation of \(a_{2}\) shown in Figure 22b was more complex compared to that of \(a_{1}\). For CFST-SP and CFST-CP, the effect of the parameter grade on \(a_{2}\) was small, but for CFST-SC and CFST-CC, the effect of the parameter grade on \(a_{2}\) was more evident. For CFST-CC, \(a_{2}\) decreased with the increasing concrete strength and even became negative. This phenomenon indicated that the greater the concrete strength was, the greater the preload was, and according to the principle of static equilibrium, the maximum bending moment became smaller instead and was even lower than that of the ordinary CFST. However, \(a_{2}\) increased with the increasing steel strength and thickness, which indicated that with the increase of the confinement coefficient related to the steel strength and thickness, the CFST-CC concrete strength in the compression bending zone was improved and the maximum bending moment was enhanced. Finally, for CFST-SC, the effect of the preload on the maximum bending moment was negative for any change in the parameter grade, with concrete strength and steel tube strength being the most prominent, and the pattern of change was consistent with that of CFST-CC.