# Research on the Fatigue Performance of Composite Girders with CSW and ST Truss
## 4 FE Analysis  
### FE Model  
An FE model of the test specimen was established by the software of ABAQUS. The concrete top slab was simulated with solid elements numbered by C3D8R, the chord, CSW, and cross bracing and truss brace were all simulated with shell elements numbered by S4R. The rebar was simulated with TRUSS elements, and the rebar was connected with the concrete top slab by the \"Embedded\" command. Relative slippage among the rebar, the concrete top slab, and the CSW were ignored. The concrete top slab connected with  
Figure 9: Developing process of fatigue crack: (**a**) developing process; (**b**) fatigue crack. the rebar and the CSW by the \"Tie\" command. To ensure the accuracy of FE model, the constitutive relationship of the concrete and the steel used in composite girders with CSW and ST truss should be determined. With reference to the literature [11], the constitutive model of the concrete could adopt the pattern shown in Equation (2), where \(f_{\text{cd}}\) and \(\varepsilon_{\text{c}}\) represent the compressive strength and the ultimate strain of the concrete. Equation (3) could be used to simulate the constitutive model of the steel including the chord, rebar, and other steel components, where \(E_{\text{s}}\), \(\varepsilon_{\text{s}}\), and \(f_{\text{s}}\) represent the elasticity modulus, yield stress, and yield strain, respectively. The parameters above were determined according to the test carried out in the materials. \[\left\{ \begin{array}{l}\sigma_{\text{c}}=f_{\text{cd}}\Big{[}2\frac{\varepsilon }{\varepsilon_{\text{c}}}-(\frac{\varepsilon}{\varepsilon_{\text{c}}})^{2} \Big{]}\quad(\varepsilon\leq\varepsilon_{\text{c}})\\ \sigma_{\text{l}}=f_{\text{cd}}\quad(\varepsilon>\varepsilon_{\text{l}}) \end{array} \right. \tag{2}\]  
\[ \begin{cases}\sigma_{\text{s}}=E_{\text{s}}\varepsilon\qquad(\varepsilon\leq \varepsilon_{\text{s}})\\ \sigma_{\text{s}}=f_{\text{s}}\qquad(\varepsilon>\varepsilon_{\text{s}}) \end{cases}  \tag{3}\]  
The hot spot stress distribution and stress concentration in steel structures have been demonstrated through physical testing and FE analyses to be relatively sensitive to the weld shape and structural detail geometry [29]. Thus, welds must be simulated in detail in order to ensure calculation accuracy. In the study, the size of the intersecting weld of the composite girder was simulated in accordance with the requirements [30], because the intersecting spatial curved surface of the intersecting weld was shaped using the high-precision NC cutting technology, and the two were welded using a fully automatic welding technique meeting the API requirements. As the material performance of a weld is usually superior to that of the parent metal, its strength was conservatively assumed to be the same as that of parent metal. It was ensured that the intersecting position between the CSW and the weld shared a joint with that between the weld and the surface of chord during mesh generation in the intersection zone between the CSW and the chord, in an effort to prevent the stress changes not caused by the stress-carrying or geometric mutation of the FE analysis model itself. Furthermore, the mesh along the pure bending segment, which was the focus of attention, was refined in order to improve the calculation accuracy. The fatigue performance test was consulted to determine the constraint conditions of the FE model. In the test model, a non-sliding hingged support was adopted at one end of the end crossbeam, while a sliding hinged support was used at the other end. A vertical load, symmetric with respect to the mid-span position, was applied to the concrete top slab. The mesh and constraint conditions of the FE model are shown in Figure 10a. The size of the FE mesh will influence the accuracy [31], thus, analysis on the mesh convergence of FE model should be conducted. In the study, the FE model with mesh sizes from 1 mm to 6 mm in the intersection zone were analyzed by considering the extrapolation method of hot spot stress, size of gradient strain gauges.