# Fatigue Performance Test and Numerical Analysis of Composite Girders with CSW-CFST Truss Chords
## 4 Non-Linear Numerical Analysis
### Sensitivity Analysis of Hot-Spot Stress  
According to the test results, the hot-spot stress obtained by the two-point extrapolation method not only provides structural safety and convenience, but is more reasonable; thus, the two-point extrapolation is recommended to determine the hot-spot stress. Combining the location of the gradient strain gauge, the interval between the unidirectional strain gauge on the gradient strain gauge and the mesh size of the finite element model, and the location of the point above that was used to extrapolate the hot-spot stress, can be found in the finite element model. Then the stress on the points was extracted, and, finally, based on the extracting finite element analysis results, the hot-spot stress was obtained by two-point extrapolation. The hot-spot stress distribution, and the maximum hot-spot stress envelopes on the left- and right-hand-sides of the intersecting weld between the corrugated steel web and the chord, are presented in Figure 20, where the origin of the horizontal axis corresponds to the mid-length section of the model. The ratio of the maximum value envelopes at the same section of the intersecting weld between the corrugated steel web and the chord in the composite girder with CSW-CFST truss chords to that in the composite girder with CSW-ST truss chords reported in [11] is given in Figure 21a, and hot-spot stress nephograms for the two types of composite girders are compared in Figure 21b. From Figure 20, it can be seen that, for both the left- and right-hand-side of the intersecting weld, the maximum hot-spot stress occurred near point S on the non-mold pressing side. In other words, within a single wavelength, the maximum hot-spot stress at the left- and right-hand-sides of the intersecting weld did not occur at point S of the same section, and the hot-spot stress in the inclined web segment was markedly greater than that in the straight web segment. Figure 19: Accuracy verification of non-linear numerical model: (**a**) comparison of load-displacement curves; and (**b**) comparison of hot-spot stress distribution. Figure 18: Mesh convergence analysis. It can be seen from Figure 21a that concrete in the chord influenced the hot-spot stress in the composite girder with the CSW-ST truss chords most obviously near the position of the maximum hot-spot stress (point S). It can be seen from Figure 20b that, compared to the composite girder with CSW-CFST truss chords subjected to the same external load, the composite girder with CSW-ST truss chords experienced a more obvious stress concentration, which occurred over a larger range, further indicating that concrete in the chord can effectively mitigate the extent of hot-spot stress concentration and improve the fatigue performance of composite girders with CSW-ST truss chords. The parameters to be included in the analysis of the corrugated steel web are the dip angle of the inclined web (\(\theta_{\text{w}}\)), the bend radius (\(R_{\text{w}}\)), and the thickness (\(T_{\text{w}}\)). In addition, as the chord formed the bottom of the cross-section, the diameter (\(D_{\text{c}}\)) and wall thickness (\(T_{\text{c}}\)) of the chords were also included among the parameters to be analyzed. The values of the analytical parameters for composite girders with CSW-CFST truss chords were determined based on the sensitivity analysis of composite girders with CSW-ST truss chords carried out in [11]. To enhance the representativeness of the analysis result, the parameters used in the Maluanshan Park Viaduct in Guangdong Province, China, were taken as the benchmark model, whose dip angle of the inclined web, bend radius, and thickness of the corrugated steel web and the diameter and wall thickness were 31\({}^{\circ}\), 300 mm, 20 mm, 720 mm and 20 mm, respectively. Combining the requirements of the value of the parameters in construction, a sensitivity analysis of hot-spot stress was carried out using a single variable method.