# Research on the Fatigue Performance of Composite Girders with CSW and ST Truss
## 2 Fatigue Performance Test Design
### Loading Rig  
The loading rig is shown in Figure 4. An MTS actuator with a capacity of 500 kN was used to apply vertical cyclic loads to the test model, and a distributing girder was used to  
Figure 3: Test model (unit: mm): (**a**) vertical plan; and (**b**) sectional plan. spread the load symmetrically to two points, so as to apply pure bending in a 2000 mm long section near the mid-span position. The loading method not only ensured that the stress state of all components of the test model was close to the stress state of actual bridges but made loading application easy. Integral FE analysis was conducted on the actual bridge to determine the fatigue load in the fatigue performance test by the software of MIDAS/CIVIL. All structural components in the integral model were simulated by beam elements. Rigid connections were used to simulate the connections between the CSW and the concrete top slab, chord and truss brace, chord and K bracing, etc. The general elastic connection was used to simulate the supports. There were a total of 1666 elements and 1101 joints in the integral FE model. The existing test results [11] were used to verify the correctness of the integral FE model. As shown in Table 2, the maximum deviation was 8.5%, indicating that the integral FE model could accurately reflect the overall stress states of the structure. Figure 4: _Cont._  
Combining the validated integral FE model and the fatigue load model given in the literature [24], the maximum stress range of 33.59 MPa was predicted at the welding region between the CSW and the chord under the action of live load located at the mid-span position. The welds between the CSW and the chord were viewed as the research object, so the fatigue stress range used in the fatigue performance test could be determined according to the damage equivalence principle and stress equivalence principle. Meanwhile, in consideration of the multi-lane effect and reduced scale, as shown in Equation (1), where \(\Delta\sigma_{\text{E2}}\) and \(\Delta\sigma_{2}\) represent the equivalent stress range corresponding to the condition that the number of loading cycles was 2,000,000 cycles and the stress range, respectively. \(\gamma\) represents the damage equivalence coefficient, and it was determined according to the literature [25]. \(\Delta\varphi\) represents the amplification coefficient, and it was determined according to the literature [25]. Combining Equation (1) and the result obtained from the integral FE model, it was proved that the equivalent stress range corresponding to the condition that the number of loading cycles was 2,000,000 cycles was 67.18 MPa. Moreover, combining the boundary, geometric parameters, and the FE model shown in Section 4, it was proved that when the equivalent fatigue load amplitude was about 300 kN, the fatigue stress range near the welds between the CSW and the chord was 67.22 MPa, and it was very close to 67.18 MPa. Thus, the equivalent fatigue load amplitude under 2,000,000 load cycles was determined as 300 kN. \[\Delta\sigma_{\text{E2}}=(1+\Delta\varphi)\gamma\Delta\sigma_{2} \tag{1}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Stress** & **Beam Model** & **Literature [11]** & **Deviation** \\ \hline Stress in chord & 173.2 & 164.5 & 5.3\% \\ Shear stress in CSW & 25.87 & 27.76 & \(-\)6.8\% \\ Stress in concrete top slab & \(-\)6.86 & \(-\)6.32 & 8.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Verification of integral FE model (unit: MPa). Figure 4: Loading rig for fatigue performance test: (**a**) sketch of loading rig; and (**b**) photograph of loading rig. Considering the nonlinear load-frequency relationship of the MTS actuator, the minimum value of the fatigue load needs more than 3% of the allowable peak load of the actuator. Hence, the maximum and minimum value of the fatigue load applied on the test model were taken as 350 kN and 50 kN, respectively. The loading frequency was taken as 3 Hz.