## 5 Numerical Modeling  
### Simplification of STS Structure  
Considering the complexity of the STS structure, accounting for all its components in a numerical model is extremely complicated and greatly increases computational expense. To avoid this problem, an equivalent structure with a similar behavior is first established for the use in the subsequent numerical simulations. In order to obtain the mechanical behavior of the STS beam, a full-scale laboratory test is performed by the authors [33]. It was observed that the beam failed in flexure. In the early stage of the load application, the specimen was in an elastic state and no cracking was observed. Cracking started to occur along the interface between the steel tubes and the concrete in the mid-span at the level of about 7% of the measured peak load. As the applied load was increased, more flexural cracks appeared within both the pure bending and shear regions of the beam and the existing cracks were propagated toward the loading points with increasing width. The yielding of the bottom flange and connecting bolts began at the level of about 86% of the recorded peak load. During the loading, the crack propagation of the beam occurred slowly due to the constraining effect of the steel tube and flange plate. The flexural failure of the beam was initiated by the yielding of the bottom flange followed by the sudden rupture of the bottom flange and bolts, with crushing of the concrete. The cracks were developed mainly along the interface between the tubes and concrete in the region between the tubes. Several cracks were also formed along the interface between the tubes and the core concrete inside the tubes because of the tensile effect of the flange plate on the tubes. Based on the full-scale laboratory test a general load-deformation behavior of an STS beam can be established. The comparison results between the laboratory and numerical calculation were shown in Figure 17, the trend of laboratory test was familiar with numerical calculation. It indicates that element, interaction and stress-strain applied the model were valid. Figure 16: The value of bolts along with excavation sequence in monitoring sections: (**a**) Pilot tunnel construction; (**b**) Beam-column system construction; (**c**) Construction of the station hall; (**d**) Construction of the platform layer; (**e**) After the main construction. According to the construction schedule, the maximum free surface of the subway station are 7 steel tubes, considering the influence size-effect on calculation results. The model was established to study the effect welding of flange on bearing capacity (see Figure 18). Due to the STS structure being in the elastics stage in the construction of subway station, and according to the deflection formula of simply-supported beam [34], the equivalent stiffness of welding of bottom flange and no welding of bottom flange were 1.91 \(\times\) 108 N\(\cdot\)m\({}^{2}\) and 1.05 \(\times\) 108 N\(\cdot\)m\({}^{2}\), respectively (see Figure 19). Simplification model of the STS structure was divided into two materials (material 1 and material 2) to simulate the weak part of adjacent steel tubes, as shown in Figure 20. Not only can it ensure the whole stiffness of STS structure, but also retain the characteristics of STS structure. Considering the longitudinal direction of STS structure has a high stiffness, the longitudinal stiffness of material 1 is equivalent to longitudinal stiffness of concrete filled steel tube, and the stiffness is 92 GPa according to  
Figure 19: Load-deformation curve. Figure 17: Comparison of load-deformation curves between laboratory test results and numerical calculation. Figure 18: Finite element model with 7 steel tubes connected. Formula (5). Considering the effect of the steel tube with the hole on the whole stiffness, the stiffness was reduced to 70%, that is 65 GPa [35].