## 6 Example of Verification of Recommended Equations
### The Influence of Slab Thickness on the Effective Width  
The slab's effective width given by the current design specifications [12; 13; 24; 26] has nothing to do with the thickness of the slab. However, the last version of the Chinese design code GB 50017-2003 [38] included a clause related to the effective width and thickness of the slab, requiring that the slab's effective width cannot exceed 12 times the thickness of the slab. The author of this paper has designed the experiment's composite joint specimens [33] according to this clause [38]. Therefore, the slab thickness (\(h_{\text{c}}\)) in relation to the slab's effective width was still analyzed for this paper. The specimens' details are the same as the base model (\(L\) = 7800 mm, \(S_{0}\) = 1950 mm, and \(h_{\text{c}}\) = 100 mm) except for the slab thickness. The ABAQUS analysis data and the calculation results of Equations (7) and (8) are listed in Table 6.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multicolumn{3}{c}{\(L\) = 7200 mm} & \multicolumn{3}{c}{\(L\) = 7800 mm} & \multicolumn{3}{c}{\(L\) = 8400 mm} & \multicolumn{3}{c}{\(L\) = 9600 mm} & \multicolumn{3}{c}{\(L\) = 10,800 mm} \\  & \multicolumn{3}{c}{\(S_{0}\) = 1950 mm} & \multicolumn{3}{c}{\(S_{0}\) = 1950 mm} & \multicolumn{3}{c}{\(S_{0}\) = 1950 mm} & \multicolumn{3}{c}{\(S_{0}\) = 1950 mm} \\  & **Sagging** & **Hogging** & **Sagging** & **Hogging** & **Sagging** & **Hogging** & **Sagging** & **Hogging** & **Sagging** & **Hogging** \\ \hline ABAQUS: & & & & & & & & & \\ \(b_{\text{e}}\)/mm & 488 & 1407 & 500 & 1414 & 520 & 1423 & 529 & 1485 & 528 & 1490 \\ Equation (7): & & & & & & & & & \\ \(b_{\text{s}}\)/mm & 1869 & & 1950 & & 1950 & & 1950 & & 1950 \\ Equation (8): & & & & & & & & & \\ \(b_{\text{e}}\)/mm & 1818 & & 1950 & & 1950 & & 1950 & & 1950 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The effective slab width under changing \(L\).  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multicolumn{3}{c}{\(L\) = 7800 mm} & \multicolumn{3}{c}{\(L\) = 7800 mm} & \multicolumn{3}{c}{\(L\) = 7800 mm} & \multicolumn{3}{c}{\(L\) = 7800 mm} & \multicolumn{3}{c}{\(L\) = 7800 mm} \\  & \multicolumn{3}{c}{\(S_{0}\) = 1000 mm} & \multicolumn{3}{c}{\(S_{0}\) = 1500 mm} & \multicolumn{3}{c}{\(S_{0}\) = 1950 mm} & \multicolumn{3}{c}{\(S_{0}\) = 2500 mm} & \multicolumn{3}{c}{\(S_{0}\) = 3000 mm} \\  & **Sagging** & **Hogging** & **Sagging** & **Hogging** & **Sagging** & **Hogging** & **Sagging** & **Hogging** & **Sagging** & **Hogging** \\ \hline ABAQUS & & & & & & & & & \\ \(b_{\text{e}}\)/mm & 462 & 707 & 473 & 1064 & 500 & 1414 & 553 & 1658 & 567 & 1949 \\ Equation (7) & & & & & & & & & \\ \(b_{\text{s}}\)/mm & 1000 & & 1500 & & 1950 & & 2147 & & 2192 \\ Equation (8): & & & & & & & & & \\ \(b_{\text{e}}\)/mm & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 5: The effective slab width under changing \(S_{0}\).  
In Table 6, the \(b_{\rm e}\) of ABAQUS under sagging bending is from 0.928 times (464 mm) to 1.0 times (500 mm) that of the column width (500 mm). These ABAQUS finite element analysis results still maintain good consistency with the conclusions of [PERSON] et al. [29]. The data in Table 6 show that the calculation results of Equations (7) and (8) are very inclusive and completely cover the analysis results obtained by ABAQUS. Furthermore, the calculation results of Equation (7) are the same as those of Equation (8) because Equations (7) and (8) all do not consider the influence of slab thickness. Thus, the data in Table 6 reflect an objective fact--as the slab's thickness increases, the effective width decreases. However, the data in Table 6 also reflect that the influence of slab thickness is between \(-5.7\%\) and \(-7.2\%\), indicating that the impact of slab thickness on the effective width is not very large, and Equation (7) in the text is sufficient to cover the effect of slab thickness.