# Shear Lag Effect of Ultra-Wide Box Girder under Influence of Shear Deformation
## 5 Correction of Cantilever Plate Displacement for Flexural Displacement Function  
Analyzing the finite-element numerical results of the box girder flexural space revealed that when the cantilever of the box girder cantilever plate was longer, the shear lag coefficients of the cantilever plate were significantly smaller than those of the top plate; the difference between the shear lag coefficients at the edge of the cantilever plate and those at the top plate was even larger. To reduce the effect of the stress concentration, the theoretically calculated and finite-element values of the shear lag coefficients in the section at position \(y=1450\) cm of the wing plate were compared; the results are shown in Figure 10. \begin{table}
\begin{tabular}{c c c c c} \hline
**Location** & **Key Point** & **Theoretical Value** & **Finite-Element Value** & **Measured Value** \\ \hline \multirow{6}{*}{\(L/2\) cross-section} & T6 & 0.972 & 0.846 & 0.877 \\  & T5 & 1.001 & 1.020 & 0.97 \\  & T4 & 1.030 & 1.644 & 1.098 \\  & T3 & 0.973 & 1.066 & 1.041 \\  & T2 & 1.037 & 1.663 & 1.093 \\  & T1 & 0.974 & 1.034 & 0.842 \\ \hline \multirow{6}{*}{\(L/4\) cross-section} & T1\({}^{\prime}\) & 0.995 & 1.025 & 1.323 \\  & T2\({}^{\prime}\) & 1.007 & 1.023 & 1.550 \\ \cline{1-1}  & T3\({}^{\prime}\) & 0.997 & 1.004 & 1.005 \\ \cline{1-1}  & T4\({}^{\prime}\) & 1.004 & 0.98 & 0.988 \\ \cline{1-1}  & T5\({}^{\prime}\) & 0.999 & 0.98 & 0.168 \\ \cline{1-1}  & T6\({}^{\prime}\) & 0.994 & 0.977 & 0.931 \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of the shear lag coefficients at the key points of the top plate of the \(L/2\) and \(L/4\) span sections under centralized loading. \begin{table}
\begin{tabular}{c c c c c} \hline
**Location** & **Key Point** & **Theoretical Value** & **Finite-Element Value** & **Measured Value** \\ \hline \multirow{6}{*}{\(L/2\) cross-section} & B4 & 1.127 & 1.153 & 1.093 \\  & B3 & 0.905 & 0.892 & 0.972 \\ \cline{1-1}  & B2 & 1.035 & 1.020 & 0.993 \\ \cline{1-1}  & B1 & 0.864 & 0.871 & 0.884 \\ \hline \multirow{6}{*}{\(L/4\) cross-section} & B1\({}^{\prime}\) & 0.969 & 0.965 & 1.116 \\ \cline{1-1}  & B2\({}^{\prime}\) & 0.980 & 0.964 & 0.97 \\ \cline{1-1}  & B3\({}^{\prime}\) & 1.003 & 1.012 & 0.996 \\ \cline{1-1}  & B4\({}^{\prime}\) & 1.033 & 1.041 & 0.977 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of the shear lag coefficients at the key points of the bottom plate of the \(L/2\) and \(L/4\) span sections under concentrated loading. As shown in Figure 10, there was a large difference between the finite-element numerical simulation values at the center of the cantilever plate and the top plate of the box girder and the theoretically calculated values in this study. The shear lag coefficients at the edge of the cantilever plate were smaller than the shear lag coefficients at the center of the top plate, mainly because the edge of the cantilever plate and the center of the top plate had different constraints. Because the cantilever plate at the cantilever end of the constraints did not exist, the top plate of the box chamber on both sides of the web connection was constrained by the different boundary conditions manifested in the difference of the force characteristics. Therefore, it is necessary to optimize the flexural displacement function derived in this study by considering the effect of the shear deformation of each plate and correcting the differences caused by the different boundary constraints. Accordingly, the degree of buckling of the cantilever plate that is corrected using the correction parameter is denoted as \(\varphi\); Equation (45) is corrected as follows:  
\[\eta_{\xi}(x,y)=