## 5 Bifurcation Segment Shear Lag Effect and Stress Distribution
### Stress Distribution Analysis of Single and Double Arch Rib Bifurcation Segment  
Figure 17 shows the vertical deformation of the local model. The vertical deformation trend is overall consistent with the global model established using the beam unit, but the vertical deformation on the same section appears to be unevenly distributed, and the section shows a regularity of larger displacement on both sides and smaller displacement in the middle, but this pattern is not obvious. The stress distribution on the bifurcated section of the whole arch rib is relatively uniform, and it is worth paying attention to the stress distribution state of the diaphragm in the anchorage area. Figure 18 shows the von Mises stresses in the diaphragm at the anchorage area under constant load in the 24 m local model, which is between 39 MPa and 77 MPa in most of the range, with only a local stress concentration at the location where the suspender is in contact with the diaphragm, with a maximum stress of 179.87 MPa. The arch rib bifurcation segment has the same distribution regularity under vehicle load or combined load. The von Mises stresses of the bifurcated segment model are analyzed under the five most significant design load combinations, which are (1) constant load + vehicle load + foundation settlement load, (2) constant load + vehicle load + overall temperature rise + foundation settlement load, (3) constant load + vehicle load + overall temperature fall + foundation settlement load, (4) constant load + vehicle load + crowd load + overall temperature rise + foundation settlement load and (5) constant load + vehicle load + crowd load + overall temperature fall + foundation settlement load.  
Figure 17: Vertical deformation of bifurcated segment of arch rib under constant load (unit: mm).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Section** & **\(\sigma\) (MPa)** & **\(\sigma\)0 (MPa)** & **\(\lambda\)** \\ \hline A-A & 73.1 & 59.0 & 1.24 \\ B-B & 73.0 & 60.3 & 1.21 \\ C-C & 60.1 & 61.7 & 0.97 \\ D-D & 77.2 & 68.9 & 1.12 \\ E-E & 78.4 & 70.0 & 1.12 \\ F-F & 71.4 & 72.3 & 0.99 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Calculation of shear lag coefficient.  
Figure 18: Von Mises stress in the suspender-anchored diaphragms of arch rib bifurcation segment under constant load (unit: MPa).  
Table 10 lists the von Mises stress variation ranges for the top slab, bottom slab and web of the bifurcated segment of the arch ribs. The von Mises stress of the bifurcated segment of the arch rib is mainly the distribution density of the combination of the axial force and bending moment of the arch rib in the cross-section, and the difference between the stresses of the single and double arch ribs is slight, but in general the stress of the double arch ribs is higher than that of the single arch rib. Under the action of load combinations (1)-(5), the stresses in the top slab, bottom slab and web of single and double arch ribs are all between 0 and 197 MPa, which are all less than the allowable stress of 320 MPa. Although there are local stress concentrations in the diaphragm in the anchorage area, the stress concentration range is small, which means that the current design of single and double bifurcation of arch ribs is reasonable. Noticeable shear lag effects were also observed on the top and bottom slabs of the thin-walled steel box arch ribs under the load combination, with a maximum shear lag coefficient of 1.4. The stresses in the arch ribs considering the shear lag effect have not exceeded the allowable stresses, and the installation of stiffening ribs and diaphragms reduces the probability of local instability of the thin-walled arch box due to the shear lag effect.