# 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
To analyze the influence of concrete in the chord on the hot-spot stress of composite girders with CSW-ST truss chords, which was the focus of the analysis, while ignoring irrelevant details, the location with the maximum hot-spot stress within a single wavelength  
Figure 21: Influence of concrete in chord on hot-spot stress: (**a**) distribution of coefficient \(\alpha\) along span length; (**b**) comparison of hot-spot stress nephograms. Figure 20: Analysis of hot-spot stress distribution: (**a**) hot-spot stress distribution; (**b**) envelope of hot-spot stress. of the mid-span section subjected to pure bending was taken for analysis. Each individual geometric parameter was varied in turn, while keeping the other parameters unchanged, to analyze the ratio of hot-spot stress in the composite girder with CSW-CFST truss chords to that in the composite girder with CSW-ST truss chords. The sensitivities of the ratio of hot-spot stress in the composite girder with CSW-CFST truss chords to that in the composite girder with CSW-ST truss chords to the chord diameter and chord wall thickness, thickness of the corrugated steel webs, and transition curve radius and dip angle of the corrugated steel web were analyzed, as presented in Figure 22. It can be seen from Figure 22 that the changes in the hot-spot stress in the composite girder with CSW-CFST truss chords resulting from changing any single geometric parameter essentially paralleled those in the composite girder with CSW-ST truss chords, and the variation range of \(\alpha\) was 0.399-0.815, demonstrating that concrete in the chords reduced the hot-spot stress in composite girders with CSW-ST truss chords by 18.5-60.1%. It can be seen from Figure 22a that coefficient \(\alpha\) was negatively correlated with the chord diameter. With increase in the chord diameter, the sectional area of concrete in the chord accounted for an increasing proportion of the whole cross-sectional area of the chord. As a result, the position of the neutral axis of the cross-section moved towards the axes of the chords. Moreover, concrete in the chords participated in force, which reduced the axial stress borne by the chord steel. Therefore, the reduction rate of coefficient \(\alpha\) gradually accelerated with increase in the chord diameter. When only the chord thickness was changed by the same amount, the ratio of axial rigidity of the interface between the corrugated steel web and the chord to the radial rigidity of the chord in composite girders with CSW-ST truss chords was affected by the change in the chord thickness more significantly than that in composite girders with CSW-CFST truss chords. However, when only the thickness of the corrugated steel web was changed by the same change ratio, the change in the thickness of the corrugated steel web had a greater influence on the ratio of axial rigidity of the interface between the corrugated steel web and the chord to the radial rigidity of the chord in composite girders with CSW-CFST truss chords than on that in composite girders with CSW-CFST truss chords. Therefore, as can be seen from Figure 22b,c, coefficient \(\alpha\) was positively correlated with both the chord thickness and the corrugated steel web thickness. Figure 22: Sensitivity of hot-spot stress at point S to geometric parameters: (**a**) chord diameter; (**b**) chord wall thickness; (**c**) corrugated steel web thickness; (**d**) transition curve radius; and (**e**) corrugated steel web dip angle. Although the sharp-corner stress at the intersection between the inclined and straight portions of the corrugated steel web could be further relieved and the stress flow made to transition more smoothly between the two by increasing the bend radius of the corrugated steel web, the axial rigidity of the interface between the corrugated steel web and the chord or the radial rigidity of the chord could not be effectively improved; thus, \(\alpha\) was weakly sensitive to the bend radius, as shown in Figure 22d.