# Study on Shear Performance of Web-Embedded Composite Shear Connector
## 4 Calculation Equation of USBC
### General Equation of Shear Capacity  
The equation for calculating the USBC of the WECSC is expressed as follows:  
\[\begin{array}{ll}P_{n}&=\left(2t_{m}h_{m}-n\pi d^{2}/2\right)\left(-0.022f_ {c}+0.306\sqrt{f_{c}}-0.573\right)\\ &+0.69n\pi(d-d_{tr})^{2}A_{c}f_{cu}^{0.57}\\ &+0.29n\pi d_{tr}^{2}(1.76-0.0375d_{tr})A_{tr}f_{y}\\ &+0.29n_{s}\pi d_{s}^{2}f_{u}\left(\frac{E_{s}}{E_{s}}\right)^{0.2}\left(\frac {f_{cu}}{f_{u}}\right)^{0.1}\end{array} \tag{6}\]  
Equation (6) was used to calculate the WECSC specimens in this test and compared with the test and finite element simulation results (Table 8). The results show that there is minimal error between the results obtained using Equation (6) and the test results, with a maximum error of 9.66%. The variance in results was analysed, and the \(p\)-value was 0.91, indicating that there was no significant difference between the results obtained using Equation (6) and the experimental values. A correlation analysis was performed on the results, and the correlation coefficient R\({}^{2}\) = 0.99 was obtained, indicating that the results of the two groups were very similar, and results using Equation (6) were consistent with the experimental values.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Specimen Number** & **Test Value/kN** & **Value Based on Equation (6)/kN** & **Error\%** & \(p\)**-Value** & **R\({}^{2}\)** \\ \hline P-0 & 223.05 & 223.14 & \(-\)0.04 & & \\ \hline P-18 & 694.26 & 654.21 & 5.76 & & \\ \hline P-18-S & 821.43 & 822.64 & \(-\)0.15 & & \\ \hline P-14-S & 745.79 & 673.73 & & 9.66 & \\ \hline P-22-S & 952.37 & 961.29 & \(-\)0.94 & & \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comparison of the results of the derived equations with the experimental results.  
To further verify Equation (6) for the WECSC, it was necessary to compare it with a large amount of data. However, because the specific structure of the composite shear connectors with an embedded web was proposed in this study and no test specimen with the same structure has been found in the existing literature, 22 models considering different parameters were simulated using Abaqus. The model number was CxSyHzPm (x, y, z, and m represent the concrete strength, stud type, open-hole aperture, and diameter of the penetrating rebar, respectively). The simulation results are presented in Table 9.  
Figure 22 shows a comparison between the values calculated using Equation (6), the test value, and the finite element simulation value. It is evident these three values can be well matched with each other, with a correlation coefficient of R\({}^{2}\) = 0.93.  
In summary, Equation (6) derived in this study has a clear physical meaning, and through a comparative analysis, it was found that it can predict the USBC of the WECSC like those mentioned in this article.  
Figure 22: Comparison of the calculated value with the test and simulated values.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model Number** & **Simulated Values/kN** & **Model Number** & **Simulated Values/kN** \\ \hline C50S13H34P14 & 652.92 & C40S13H44P22 & 899.15 \\ \hline C50S13H54P14 & 761.15 & C50S16H44P18 & 837.45 \\ \hline C50S13H34P18 & 748.81 & C50S19H44P18 & 912.76 \\ \hline C50S13H54P18 & 833.12 & C50S10H44P18 & 783.37 \\ \hline C50S13H34P22 & 863.63 & C40S16H44P9 & 656.91 \\ \hline C50S13H54P22 & 934.83 & C40S10H44P9 & 533.47 \\ \hline C30S13H44P14 & 692.64 & C40S19H44P9 & 680.23 \\ \hline C40S13H44P14 & 699.84 & C40S13H44P9 & 584.98 \\ \hline C30S13H44P18 & 723.62 & C40S13H24P9 & 403.15 \\ \hline C40S13H44P18 & 729.68 & C30S13H24P9 & 384.96 \\ \hline C30S13H44P22 & 892.76 & C50S13H24P9 & 427.83 \\ \hline \end{tabular}
\end{table}
Table 9: Finite element simulation result.