## 3 Equivalent Conversion of the Cross-Section
According to the conversion conditions of cross-section, Equation (1) could be derived based on the unchanged resultant force:  
\[\sigma_{s}A_{s}=\sigma_{c}A_{sc} \tag{1}\]  
Equation (2) could be derived based on the unchanged strain coordination condition:  
\[\frac{\sigma_{s}}{E_{s}}=\frac{\sigma_{c}}{E_{c}} \tag{2}\]  
The elastic modulus ratio (\(\alpha_{Es}\)) of steel and concrete materials could be expressed by Equation (3):  
\[\alpha_{Es}=\frac{E_{s}}{E_{c}} \tag{3}\]  
Based on Equations (1)-(3), \(A_{sc}\) could be expressed by either one of Equations (4)-(6):  
\[A_{sc}=\frac{\sigma_{s}}{\sigma_{c}}A_{s} \tag{4}\]  
\[A_{sc}=\frac{E_{s}\epsilon_{s}}{E_{c}\epsilon_{c}}A_{s} \tag{5}\]  
\[A_{sc}=\alpha_{Es}A_{s} \tag{6}\]  
Equation (7) could be given based on the unchanged overall dead weight of box girder before and after conversion:  
\[g_{s}=g_{c}=\gamma_{s}A_{s}l \tag{7}\]  
where \(g_{s}\) represents the dead weight of steel web in composite beam, and \(g_{c}\) represents the dead weight of the concrete web converted from \(g_{s}\). In addition, \(l\) is the length of the box girder length. On this basis, \(A_{sc}\) could be further expressed by Equation (8):  
\[A_{sc}=\frac{2g_{s}}{\gamma_{c}l} \tag{8}\]  
Assuming that \(t_{s}\) represents the thickness of the corrugated steel web plate section, and \(t_{c}\) represents the thickness of the converted concrete web. Based on the fact that the height of box girder cross-section remains unchanged, the thickness of the concrete web after conversion could be expressed by Equations (9) and (10):  
\[t_{c}=\frac{2g_{s}}{\gamma_{c}lh}=\frac{A_{sc}}{h}=\frac{\alpha_{Es}A_{s}}{h} \tag{9}\]  
\[\sigma_{s}A_{s}=\sigma_{c}A_{sc} \tag{1}\]0  
where \(h\) is the height of the box girder. In the modeling process, it is assumed that the corrugated steel web is completely connected with the concrete roof and bottom plate, and the slip between the corrugated steel web and the top and bottom plate is ignored. Assuming that the two parts are completely bonded, and then using the engraving function, the curve of the corrugated steel web is engraved on the concrete top and bottom plate, so that the corrugated steel web and the concrete top and bottom plate can be jointed. To verify the accuracy of the equivalent conversion method, a N4 cantilever segment was taken as an example. The bulk density of steel is about three times that of concrete. The elastic modulus of concrete is 3.55 \(\times\) 10\({}^{4}\) MPa and that of steel is 2.09 \(\times\) 10\({}^{5}\) MPa. The elastic modulus of steel is about 5.8 times that of concrete. The solid element model simulating the N4 cantilever segment is shown in Figure 3, and the linkage model after section conversion is shown in \[\sigma_{s}A_{s}=\sigma_{c}A_{sc} \tag{1}\]1  
According to the derived Equation (10), a 127.6 mm thick concrete web was modeled in the linkage model instead of the 22 mm thick corrugated steel web simulated in the solid model. Only the dead load was applied to the finite element models. The calculation results of the two models are extracted to obtain the longitudinal variation diagram of deflection along the whole bridge, as plotted in \[\sigma_{s}A_{s}=\sigma_{c}A_{sc} \tag{1}\]2  
As can be seen from Figure 5, after equivalent conversion of the cross-section with corrugated steel web, the deflection curve of the linkage model has the same distribution trend as that of the solid model. The maximum deflection occurs at the mid-span position, and the difference between the frame and solid models is greatest at the mid-span position. The maximum deflection at the mid-span position was 7.2 mm for the linkage model and 8.2 mm for the solid model, with a maximum deflection difference of 0.6 mm. The deflection of the solid model was 7% greater than that of the linkage model.