# Behavior of Two-Chord Steel-Concrete Composite Columns under Axial Compression
## 5 Numerical Modeling
### Material Models for Steel and Concrete  
An interaction between the concrete and steel tube can develop in CFST columns subjected to axial compressive force, and, due to the confinement effect provided by the steel tube, the concrete will have increased compressive strength. Tensile hoop stress will develop in the steel tube, which will lead to a reduction in the load-bearing capacity in the axial direction [39]. The confining stresses will change during the loading process, and local buckling of the steel tube's wall can also occur; all of these affect the interaction between the concrete infill and the steel tube. The mutual influence of the mentioned factors is fairly complex and must be considered in the modeling of the material's response. The steel tube was modeled as an elastic-plastic model with a strain-hardening effect. The elastic characteristics of the steel are presented in Table 3, while the plastic characteris  
Figure 17: Finite element model (**a**) and mesh detail (**b**). tics were defined as a multilinear isotropic function. The stress-strain curve is shown in Figure 18a. The load-bearing plates were also modeled as a steel material model considering only linear elastic properties. The calculation model for concrete requires a definition of the linear and multilinear isotropic properties [40]. In CFST columns, the steel tube provides the confinement necessary for an increase in the compressive strength and ductility of the concrete [2,41]. The confinement of concrete is passive in nature and relatively difficult to reflect. The confinement factor, \(\xi\), is often used to quantify the intensity of the concrete confinement [2]. The model used in this study was developed in [42,43]. The compressive part of the stress-strain curve of the concrete in the steel tube was determined via  
\[ \begin{array}{ll}f=\frac{A.X+B.X^{2}}{1+(A-2)X+(B+1)X^{2}}f^{\prime}_{cc}&X \leq 1\\ f=f_{r}&X>1\end{array}  \tag{12}\]  
where coefficient \(X\) is defined as \(X=\varepsilon/\varepsilon^{\prime}_{cc}\). The strength of the confined concrete and the corresponding strain are \(f^{\prime}_{cc}\) and \(\varepsilon^{\prime}_{cc}\), respectively. The residual stress is \(f_{r}\), while \(A\) and \(B\) are coefficients of the stress-strain curve. The increased concrete compressive strength due to the confinement effect was determined as follows:  
\[f^{\prime}_{cc}=f^{\prime}_{c}\Bigg{(}1+0.2\bigg{(}\frac{f_{y}}{f^{\prime}_{c }}\bigg{)}^{0.696}+\Bigg{(}0.9-0.25\bigg{(}\frac{D}{t}\bigg{)}^{0.46}\bigg{)} \sqrt{\xi}\Bigg{)} \tag{13}\]  
with the limits of the stress ratio \(1\leq f^{\prime}_{cc}/f^{\prime}_{c}\leq 3\). The value of \(f^{\prime}_{c}\) stress is set in MPa. The strain that corresponds to \(f^{\prime}_{cc}\) is defined in the micro-strains as follows:  
\[\varepsilon^{\prime}_{cc}=3000-10.4f^{1.4}_{y}\big{(}f^{\prime}_{c}\big{)}^{- 1.2}\Bigg{(}0.73-3785.8\bigg{(}\frac{D}{t}\bigg{)}^{-1.5}\Bigg{)} \tag{14}\]  
The residual strength of the confined concrete is  
\[f_{r}=f^{\prime}_{cc}\left(3.5\Bigg{(}\frac{t}{D(f^{\prime}_{c})^{0.7}}\bigg{)} ^{0.2}-\frac{0.2}{\xi^{0.3}}\right)\leq f^{\prime}_{cc} \tag{15}\]  
Coefficient \(A\), which describes the ascending part of the stress-strain curve, is defined as  
\[A=\alpha_{1}\frac{E_{c}\varepsilon^{\prime}_{cc}}{f^{\prime}_{cc}} \tag{16}\]  
Figure 18: Stress–strain curve for steel tube (**a**) and infill concrete (**b**). where correction coefficient \(\alpha_{1}\) with a value ranging from 1 to 1.3 is calculated via  
\[\alpha_{1}=1+0.25\xi^{(0.05+0.25/\xi)} \tag{17}\]  
Coefficient \(B\) defines the shape of the descending part of the stress-strain curve:  
\[B=2.15-2.05e^{-\xi}-0.0076f_{c}^{\prime}\geq-0.75 \tag{18}\]  
The compressive strength of the concrete used in the experiments was determined with the enhanced strength of the concrete due to the confining effect. The stress vs. strain relationship is shown in Figure 18b. In the presented FEM analysis, the negative slope of the stress-strain curve was omitted to avoid convergence issues [44].