## 5 Bifurcation Segment Shear Lag Effect and Stress Distribution
### Analysis of Shear Lag Effect  
Although there are already formulas to consider the shear lag effect of a thin-walled concrete box girder, these formulas are not applicable to thin-walled steel box arch ribs due to the special characteristics of thin-walled steel box arch ribs, and thus the finite element method still has the advantage of a fast and accurate analysis of the shear lag effect. Six typical cross-sections in Figure 14 are selected to study the shear lag effect of thin-walled steel box arch ribs: cross-section A-A is the location of the suspender-anchored diaphragm on the side of the single arch rib, cross-section B-B is the location of the A-type diaphragm  
Figure 14: Boundary conditions and analytical sections. on the side of the single arch rib, cross-section C-C is the location of the B-type diaphragm on the side of the single arch rib, cross-section D-D is the location of the suspender-anchored diaphragm on the side of the double arch ribs, cross-section E-E is the location of the A-type diaphragm on the side of the double arch ribs, and cross-section F-F is the location of the B-type diaphragm on the side of the double arch ribs. Figure 15c,d respectively show the A-type diaphragm and B-type diaphragm. The a-type diaphragm is a hollow diaphragm on the complete section of the arch rib. The B-type diaphragm is not a complete one, but only half of the diaphragm. Under the action of symmetrical vertical forces, the positive stresses on the flange of the box girder are unevenly distributed along the section width direction. This phenomenon of uneven distribution of positive stresses along the width of the flange due to the lag in the transfer of shear forces from the web to the flange is called the \"shear lag effect\", which is usually measured by the shear lag coefficient, defined as  
\[\lambda=\sigma/\sigma 0, \tag{1}\]  
where \(\lambda\) represents the shear lag coefficient, \(\sigma\) represents the actual positive stress in the section, and \(\sigma 0\) represents the positive stress in the section calculated according to the elementary beam theory; when \(\sigma>1\), it is called \"positive shear lag\", and when \(\sigma<1\), it is called \"negative shear lag\". In bridge design, constant load, live load and preload all produce shear lag effects in the cross-section, but constant load is predominant. Figure 16 shows the distribution of axial compressive stresses in six typical sections of thin-walled steel box arch ribs under constant load, with the horizontal axis representing the transverse width of the steel box arch ribs in the figure. The positive shear lag effect occurs in sections A-A, B-B, D-D and  
Figure 15: Spatial finite element model of bifurcation segment of main arch rib: (**a**) overall bifurcation segment; (**b**) Y-block; (**c**) A-type diaphragm; (**d**) B-type diaphragm. E-E, and the negative shear lag effect occurs in sections C-C and F-F. Sections C-C and F-F are the locations where the B-type diaphragm is located, and the B-type diaphragm is not a complete one, but only half of the diaphragm; therefore, a significant shear lag effect is observed in both locations, complete and incomplete diaphragms. Sections A-A, B-B and C-C are located in the single arch rib with a wider arch box cross-section, while sections D-D, E-E and F-F are located in the double arch ribs with smaller arch box cross-section width; therefore, the shear lag effect observed in the single arch rib is more obvious than that in the double arch ribs, and the maximum shear lag coefficient is 1.24. The width of the thin-walled arch box with double arch ribs is only 2 m, and the shear lag effect is not obvious; in particular, the negative shear lag coefficient is relatively small. The curve fold in Figure 16 is the sudden change in stress caused by the longitudinal stiffening rib. The shear lag effect was also observed in the bottom slab for the thin-walled steel box arch ribs, and the distribution regularity is similar to that of the top slab, which is not repeated here.