# Research on the Fatigue Performance of Composite Girders with CSW and ST Truss
## 5 Hot Spot Stress Sensitivity Analysis
### Discussion of Sensitivity Analysis Results  
The sensitivity of the hot spot stress distribution to the geometric parameters, including the chord (\(D_{\rm c}\) and \(T_{\rm c}\)) and the CSW (\(T_{\rm b}\), \(R_{\rm b}\), and \(\theta_{\rm b}\)), was analyzed in Figure 13a-e. The results showed that the hot spot stress distributions obtained by changing a single geometric parameter were essentially similar to each other, implying that the geometric parameters had no influence on the distribution rule of the hot spot stress. The maximum hot spot stress occurred near point S of the CSW, the location of which was slightly influenced by the change in geometric parameters. In addition, Figure 13a showed that as \(D_{\rm c}\) increased, the wave crest at point S of the CSW became less sharp. The sensitivity of the hot spot stress at point S to the geometric parameters including the chord (\(D_{\rm c}\) and \(T_{\rm c}\)) and the CSW (\(T_{\rm b}\), \(R_{\rm b}\), and \(\theta_{\rm b}\)) was analyzed in Figure 14a-e. It was observed that the hot spot stress was negatively correlated with \(D_{\rm c}\), \(T_{\rm c}\), and \(R_{\rm b}\), and positively correlated with \(T_{\rm b}\), while it had a more complex relationship with \(\theta_{\rm b}\). The hot spot stress of the composite girders exhibited the strongest sensitivity to \(D_{\rm c}\), followed by \(T_{\rm c}\). Larger \(D_{\rm c}\), on the one hand, changed the position of the neutral axis, and it was gradually close to the chord surface. On the other hand, it reduced the ratio of the projection length of the inclined web in the chord section to the circumference length of the entire section, gradually approaching a flat steel plate and the chord, thereby reducing the out-of-plane bending moment borne by the inclined web, which was also the essential reason for the negative correlation of the hot spot stress with \(D_{\rm c}\). The wave crest at point S of the CSW became less sharp with the increase in \(D_{\rm c}\), and the hot spot stress distribution was gradually uniform along the length of the CSW. Parameters \(T_{\rm c}\) and \(T_{\rm b}\) separately affected the radial stiffness of the chord and the axial stiffness of the intersecting welds. The axial stiffness of the intersecting welds is usually larger than the radial stiffness of the chord. As \(T_{\rm c}\) increased, the radial stiffness of the chord increased, and the difference from the axial stiffness of the intersecting welds was reduced, thus the hot spot stress in the composite girders was negatively correlated with \(T_{\rm c}\). However, the axial stiffness of the intersecting welds increased with the increase in \(T_{\rm b}\), further amplifying the difference from the axial stiffness of the intersecting welds, thus the hot spot stress of the composite girders with CSW and ST muss was positively correlated with \(T_{\rm b}\). Moreover, the calculation methods of the radial stiffness of the chord and the axial stiffness of the intersecting welds were analyzed by Equations (4) and (5). Where \(I_{\rm c}\) and \(I_{\rm b}\) denote the radial stiffness of the chord and the axial stiffness of the intersecting welds, respectively, \(E_{\rm c}\) and \(E_{\rm b}\) are the modulus of elasticity of the chord and the CSW, respectively, and \(L_{\rm b}\) denotes the length of the intersecting welds. The results showed that when only \(T_{\rm c}\) or \(T_{\rm b}\) was varied, Equations (4) and (5) were both power functions, with the exponent of three and one, respectively, thus the sensitivity of the radial stiffness of the chord to \(T_{\rm c}\) was stronger than that of the axial stiffness of the intersecting welds to \(T_{\rm b}\). This was the main reason why the sensitivity of the hot spot stress to \(T_{\rm c}\) was stronger than that to \(T_{\rm b}\).