## 3 Modeling of the Steel-Concrete Composite Beam
### FE Model Verification 1  
The first FE model presented herein was calibrated on the results of a three-point bending test conducted by [PERSON] et al. [23]. The simply supported beam has a net span of 6300 mm and a total height of 700 mm. The headed studs have a diameter of 22 mm and  
Figure 3: Stress–strain relationship for the materials: (**a**) concrete; (**b**) headed stud and structural steel. a height of 150 mm. Detailed dimensions of the composite beam are shown in Figure 4a. Table 1 provides the detailed properties of the materials. In the solid-slipping beam model, all material parameters were defined based on the actual material properties. The dilation angle and the eccentricity parameter for the CDP model were taken as 20\({}^{\circ}\) and 0.1, respectively, and the ratio of the biaxial compressive strength and the uniaxial compressive strength was taken as 1.16. Figure 4b shows the three-dimensional finite element model developed in ABAQUS. A loading slab with the dimension of 60 \(\times\) 150 \(\times\) 50 mm and two supporting slabs with the dimension of 300 \(\times\) 200 \(\times\) 100 mm was modeled and tied to the upper surface of the concrete slab and the lower surface of steel flange, respectively, for the convenience of applying boundary conditions and avoiding over constraint. The initial elasticity modulus of the loading slab and supporting slab was valued at 1000 times that of the structural steel, to ensure the micro-distortion. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Yield** & **Tensile** & **Elastic** & **Thickness** & \\  & **Strength** & **Strength** & **Modulus** & **or Diameter** & **Elongation** \\  & **(MPa)** & **(MPa)** & **(GPa)** & **(mm)** & \\ \hline Steel beam & 320 & \(-\) & 210 & 14 & 34\% \\  & 400 & \(-\) & 208 & 16 & \(-\) \\  & 353 & 426 & 208 & 22 & \(-\) \\  & & & & & \\ Concrete & \(-\) & 49.4 & 36.68 & \(-\) & \(-\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material properties of FE model 1. Figure 4: Schematic and FE model of composite beams: (**a**) schematic of composite beams; (**b**) FE model of composite beams; and (**c**) boundary conditions and loading application. A general mesh size of 50 mm was defined for the overall structure, and a fine mesh size of 10 mm was adopted for the headed stud and the region around the head studs. The mesh sizes were also verified by carrying out the sensitivity analysis. Overviews of the finite element model and corresponding meshes are shown in Figure 4b, together with the coordinate system in which the \(X\) and \(Y\) axes define the cross-sectional plane, and the \(Z\)-axis is parallel to the longitudinal direction of the SCCB. The simply supported condition was applied at the supporting slabs, which were tied to the end of the steel beam, for which the translational displacements in the \(X\) and \(Y\) directions were restrained. The static solving was realized in the STANDARD module, by controlling the mid-span downward enforced (-\(Y\)) displacement at a specific rate. The interface slip was measured as the relative displacement between the nodes on the steel flange and concrete slab. The exact value of loads was measured as the total reaction acting on the loading surface. All boundary conditions are shown in Figure 4c. To simulate the damage process of SCCBs accurately, different friction coefficients have been tried; the most appropriate friction coefficients were determined as 0.1 for the interface between the steel flange and concrete slab and 0.45 for the surfaces of the headed studs and surrounding concrete. Figure 5 provides a comparison of the results of the experiment and FE model simulation. The FE model fairly predicts the initial stiffness, the ultimate strength, and the interface slip of the SCCB. The ultimate load obtained from the FE analysis was 729.54 kN, which is 3% less than the experimental test. The load-slip curve derived from the FE analysis also compares well with the test results.