# Behavior of Circular CFST Columns Subjected to Different Lateral Impact Energy
## 4 Calculation Formula  
This paper has investigated the effects of these three experimental parameters (concrete compressive strength, impact energy and impact location) on the behavior of circular CFST columns subjected to lateral impact. The results find that the comprehensive corrected coefficient (\(\varphi\)) determined by the experimental parameters influences residual ultimate axial capacity. Hence, residual ultimate axial capacity (\(N_{\text{re}}\)) can be obtained by the following Equation (4):  
\[N_{\text{re}}=\varphi\times N_{0} \tag{3}\]  
where, \(N_{\text{re}}\) is calculated residual ultimate axial capacity of circular CFST columns subjected to lateral impact, and \(N_{0}\) is calculated ultimate axial capacity of circular CFST columns immune from the damage of lateral impact. The value can be obtained from the following Equations [39,40]:  
\[N_{0}=A_{\text{sc}}\times f_{\text{scy}} \tag{4}\]  
\[f_{\text{scy}}=(1.14+1.02\xi)\times f_{\text{cu}} \tag{5}\]  
\[A_{\text{sc}}=A_{\text{c}}+A_{\text{s}} \tag{6}\]  
\[\xi=\alpha\times f_{\text{y}}/f_{\text{cu}}\ (0.8\leq\xi\leq 4) \tag{7}\]  
\[\alpha=A_{\text{s}}/A_{\text{c}} \tag{8}\]  
where, \(A_{\text{s}}\) is area of the steel tube in cross-section, \(A_{\text{c}}\) is area of concrete in cross-section, \(f_{\text{y}}\) is the yield strength of steel tube, and \(f_{\text{cu}}\) is the compressive strength of concrete. According to Equation (3), the comprehensive corrected coefficient (\(\varphi\)) could be calculated by introducing it into the effected parameter \(M\) as following:  
\[\varphi=1.23M+0.026 \tag{9}\]  
Figure 16: Curves of \(\rho\)-concrete compressive strength: (**a**) Impact location is 0.50 H; (**b**) Impact location is 0.33 H; (**c**) Impact location is 0.25 H.  
where, effected parameter \(M\) has taken into account the effects of concrete compressive strength (\(f(\xi)\)), impact location (\(f(\alpha)\)) and impact energy (\(f(\beta)\)). The value of \(M\) is calculated as follows:  
\[M= f(\xi)\times f(\alpha)\times f(\beta) \tag{10}\] \[f(\xi)=-0.123\times\xi+1.08\] (11) \[N_{0}=A_{\text{sc}}\times f_{\text{scy}} \tag{4}\]0 (12) \[N_{0}=A_{\text{sc}}\times f_{\text{scy}} \tag{4}\]1 (13) \[N_{0}=A_{\text{sc}}\times f_{\text{scy}} \tag{4}\]2 (14) \[N_{0}=A_{\text{sc}}\times f_{\text{scy}} \tag{4}\]3  
where,\(f(\xi)\),\(f(\alpha)\) and \(f(\beta)\) are function of \(\xi\), \(\delta\) and \(\beta\), respectively. Impact location is represented by \(L\) and impact energy is represented by \(E\). The calculated and statistical results are presented in Table 6 and \[N_{0}=A_{\text{sc}}\times f_{\text{scy}} \tag{4}\]4 Table 6 presents the values (\(\lambda\)) of ratio of \(N_{\rm re}\) (residual ultimate axial capacity calculated according to equation) to \(N_{\rm r}\) (residual ultimate axial capacity obtained by test). The most calculated residual ultimate axial capacity values of circular CFST columns subjected to lateral impact are slightly smaller than residual ultimate axial capacity value of test results. This indicates that the calculated result satisfying the requirement of practical engineering has a strength reservation. The mean value (\(\lambda\)) is 0.97 and the variance value is 0.01365, which indicates that this equation is reasonably accurate to predict residual ultimate axial capacity of circular CFST columns subjected to lateral impact.