## 4 Finite Element Analysis  
### Subsection  
In steel-tube concrete, the constitutive model of core concrete has not yet formed a universally applicable constitutive model of concrete; the most representative constitutive models at home and abroad include those of [PERSON] [34], [PERSON] [35], [PERSON] [36], and similar models. In more than one study, when scholars analyzed the mechanical properties of steel-tube concrete by using ABAQUS 2021 software, they often adopted the constitutive model of concrete proposed by [PERSON], and the finite element simulation results were compared with the test results, the two damage forms, load-displacement curves, and the ultimate bearing capacity of the basic match.  
The modulus of elasticity of concrete refers to the provisions of ACI318 [37]. It is calculated as follows:  
\[E_{c}=4730\big{(}f_{c}^{\prime}\big{)}^{0.5} \tag{2}\]  
where \(f_{c}^{\prime}\) is the compressive strength of the cylinder (N/mm\({}^{2}\)), and [PERSON]'s ratio is taken as 0.2.  
The compressive stress-strain curve of the core concrete, concerning the relation described by [PERSON], which takes into account the restraining effect of the external steel tube on the core concrete, is obtained by using the restraining effect coefficient, expressed as follows:  
\[y=\left\{\begin{array}{ll}\dfrac{2x-x^{2}}{\delta_{0}(x-1)^{2}+x}&x\leq 1\\ \dfrac{x}{\delta_{0}(x-1)^{2}+x}&x>1\end{array}\right. \tag{3}\]  
where \(x=\varepsilon/\varepsilon_{c0}\), \(y=\sigma/\sigma_{c0}\), \(\sigma_{c0}=f_{c}^{\prime}\), \(\varepsilon\) is the strain of the concrete, \(\varepsilon_{c0}\) is the peak strain of the concrete, \(\varepsilon_{c0}\) is the peak stress of the concrete, \(\varepsilon_{c0}=\varepsilon_{cc}+800\cdot\xi^{0.2}\cdot 10^{-6}\), \(\varepsilon_{cc}=(1300+12.5\cdot f_{c}^{\prime})\cdot 10^{-6}\), and \(\beta_{0}=\left(2.36\times 10^{-5}\right)^{\left|0.25+\left(\xi-0.5 \right)^{\gamma}\right|}\cdot(f_{c}^{\prime})^{0.5}\cdot 0.5\geq 0.12\).  
The constraint effect coefficient \(\xi\) is expressed as follows:  
\[\xi=A_{5}f_{y}/A_{c}f_{cu} \tag{4}\]  
where \(f_{y}\) is the yield strength of the steel tube, \(A_{s}\) is the area of the steel tube, \(f_{cu}\) is the axial compressive strength of the core concrete, and \(A_{c}\) is the area of the core concrete.  
The steel principal structure uses the mathematical expression of the model described in the literature [38] for Q235, Q345, Q390, and other low-carbon soft steels and steels commonly used in construction projects. The stress-strain relationship curve is as follows:  
\[\sigma_{s}=\left\{\begin{array}{ll}E_{s}\varepsilon_{s}&\varepsilon_{s}\leq \varepsilon\\ -A\varepsilon_{s}{}^{2}+B\varepsilon_{s}+C&\varepsilon_{e}<\varepsilon_{s} \leq\varepsilon_{c1}\\ f_{y}&\varepsilon_{e1}<\varepsilon_{s}\leq\varepsilon_{c2}\\ f_{y}\Big{[}1+0.6\dfrac{\varepsilon_{s}-\varepsilon_{c2}}{\varepsilon_{c3}- \varepsilon_{c2}}\Big{]}&\varepsilon_{e2}<\varepsilon_{s}\leq\varepsilon_{c3} \\ 1.6f_{y}&\varepsilon_{s}>\varepsilon_{c3}\end{array}\right. \tag{5}\]  
where \(\varepsilon_{e}=0.8f_{y}/E_{s}\), \(\varepsilon_{e1}=1.5\varepsilon_{e}\), \(\varepsilon_{e2}=10\varepsilon_{e1}\), \(\varepsilon_{c3}=100\varepsilon_{e2}\), \(A=0.2f_{y}/(\varepsilon_{e1}-\varepsilon_{e2})^{2}\), \(B=2A\varepsilon_{e1}\), and \(C=0.8f_{y}+A\varepsilon_{e}{}^{2}-B\varepsilon_{e}\).