## 4 Analysis of Influential Factors
### Deformation Performance  
The deformation performance of the concrete-encased CFST composite columns changed under exposure to high temperature, and could usually be evaluated with the deformation coefficient \(\mu\), which is the ratio of the ultimate displacement corresponding to failure load to yield displacement of the specimens. For the convenience of analysis, the heating temperature influence coefficient \(\xi(T)\) of deformation was introduced:  
\[\xi(T)=\frac{\mu(T)}{\mu_{0}} \tag{3}\]  
where \(\mu(T)\) and \(\mu_{0}\) are the axial compression deformation coefficient of the specimens subjected to high temperature and ambient temperature, respectively.  
Figure 9: Change laws of initial stiffness of specimens. (**a**) Influence of \(T\). (**b**) Influence of \(d\) and \(a\).  
Figure 10 shows the variation of the heating temperature influence coefficient of deformation. It can be seen from Figure 10a that with the increase in heating temperature, the deformation coefficient of the specimens takes \(T\) = 400 \({}^{\circ}\)C as the inflexion point, showing a trend of decreasing first and increasing later. When \(T\) = 400 \({}^{\circ}\)C, the deformation coefficient reached a valley value of 1.55, a decrease of 29.9% compared with specimens at ambient temperature. The main reason is that when the heating temperature was low (\(T\leq\) 400 \({}^{\circ}\)C), the initial damage to the outer RC was small, and its load proportion borne in the late loading period was large. However, due to the limited deformation capacity of the outer RC after the damage, the core CFST could not give full play to the deformation capacity of the specimen as a whole. When the heating temperature was high (\(T>\) 400 \({}^{\circ}\)C), the damage to the outer RC was large, and it worsened with the increase in the heating temperature. As a result, the load borne by the outer RC was small at the later stage of loading. The overall deformation of the specimen increased with the increase in heating temperature due to the CFST with excellent deformation performance bearing most of the load.  
It can be seen from Figure 10b that at both ambient temperature and high temperature (\(T\) = 600 \({}^{\circ}\)C), the deformation coefficient increased with the increase in steel tube diameter. The deformation capacity of the specimens with \(d\) = 114 mm and 138 mm increased by 6.25% and 12.5%, respectively, at the ambient temperature, while increasing by 23.12% and 27.74%, respectively, under exposure to high temperature (\(T\) = 600 \({}^{\circ}\)C) when compared to specimens with \(d\) = 89 mm. This shows that the diameter of the steel tube contributed to the slight increase in deformation capacity of specimens exposed to high temperature.  
Figure 10b reflects that the deformation capacities of the specimens with \(a\) = 20 mm and 30 mm were increased by 34.81% and 55.61%, respectively, under exposure to high temperature (\(T\) = 600 \({}^{\circ}\)C) when compared to specimens with concrete cover thickness \(a\) = 10 mm. The main reason is that the greater the concrete cover thickness was, which basically failed after exposure to high temperature, the stronger the deformation performance of the specimens was, due to the good ductility of the core CFST columns.