## 8 Conclusions  
In this study, an analytical method from the perspective of shear flow was proposed to study the shear lag effect of thin-walled single- and double-cell box girders. Longitudinal displacement functions with cubic parabola form were built using the shear flow's zero points. Then, the governing differential equations were derived through the variational energy method, and analytical solutions of the shear lag effect under several common  
Figure 28: Transverse distributions of shear lag coefficients of Example 6: (**a**) \(z=2\) m; (**b**) \(z=20\) m. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Points**} & \multirow{2}{*}{**ANSYS**} & \multicolumn{2}{c}{**1 CD**} & \multicolumn{2}{c}{**2 CD**} & \multicolumn{2}{c}{**3 CD**} \\ \cline{3-8}  & & **2 m** & **20 m** & **2 m** & **20 m** & **2 m** & **20 m** \\ \hline \(a_{21}\) & & 1.22\% & 4.38\% & 2.43\% & 2.57\% & 8.17\% & 0.12\% \\ \(a_{22}\) & & 3.70\% & 2.86\% & 2.02\% & 1.67\% & 1.33\% & 1.14\% \\ \(a_{23}\) & & 0.93\% & 0.35\% & 0.44\% & 0.30\% & 0.81\% & 0.40\% \\ \(a_{24}\) & 0\% & 36.72\% & 13.41\% & 31.35\% & 11.14\% & 21.79\% & 7.31\% \\ \(a_{25}\) & & 13.51\% & 4.59\% & 12.57\% & 3.73\% & 9.79\% & 2.00\% \\ \(a_{26}\) & & 2.72\% & 0.13\% & 0.95\% & 0.85\% & 0.92\% & 0.55\% \\ \(a_{27}\) & & 2.51\% & 3.76\% & 0.26\% & 2.42\% & 2.53\% & 1.55\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Relative errors of shear lag coefficients of Example 6. Figure 27: Longitudinal distributions of shear lag coefficients of Example 6: (**a**) \(\lambda(a_{21})\) (top plate at \(x=0\) m); (**b**) \(\lambda(a_{22})\) (top plate at \(x=b_{11}\) m); (**c**) \(\lambda(a_{23})\) (top plate at \(x=5\) m); (**d**) \(\lambda(a_{24})\) (cantilever plate at \(x=8\) m); (**e**) \(\lambda(a_{25})\) (bottom plate at \(x=0\) m); (**f**) \(\lambda(a_{26})\) (bottom plate at \(x=b_{31}\) m); (**g**) \(\lambda(a_{27})\) (bottom plate at \(x=5\) m). boundaries and load cases were presented. Finally, some cases involving the simply supported beam were used to analyze the shear lag effect. The results obtained using the proposed method were validated via comparison with numerical results. Based on the present study, the following conclusions could be drawn:  
(1) The proposed method can provide reasonable predictions for the shear lag effect of single- and double-cell box girders. It is suggested that the 2 CS method is suited for solving the shear lag effect in single-cell box girders, and the 3 CD method is recommended for double-cell box girders. The analytical methods based on the shear flow distribution law proposed in this paper are more straightforward and practical. They also provide theoretical support for the subsequent development of finite beam elements. (2) For double-cell box girders, minimum stress locations on the top and bottom slabs do not coincide with the symmetry axis. Instead, they are near the zero points of shear flow. Therefore, it is rational to adopt the zero point of shear flow as the origin of the parabola. (3) The shear lag coefficients are varied at different webs of the double-cell box section. The magnitude of the coefficients is related to the distance from the web to the zero point of the shear flow. The further away from the zero point of the shear flow, the larger the value. (4) Considering the web's warping variation and the section's axial force balance can increase the accuracy of the calculation results. Y.S., conceptualization, data curation, formal analysis, methodology, visualization, writing--original draft, and writing--review and editing; S.Z., supervision, validation, and writing--review and editing; G.W., validation; and C.Z., visualization. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy. The authors declare no conflicts of interest.