## 8 Summary and Conclusions  
In this paper, the application of a URSP connector in the composite frame system was studied. Elaborate finite element models of side and middle joints, were built in MSC-Marc, in order to resemble the structural response of a composite frame under vertical and lateral loading conditions. The effects of URSP connectors on the structural performance of a composite frame based on the parametric analysis of several critical parameters were investigated. The ultimate load-carrying capacity of side joints and middle joints under a concentrated load and the crack performance under a vertical uniformly distributed load were discussed in depth. It has been demonstrated that the application of URSP connectors improves the crack resistance performance and has little influence on the lateral capacity and stiffness. In other words, applying URSP connectors in the composite frame has been demonstrated to:  
1. Maintain the ultimate capacity and overall stiffness under lateral loads, which are comparable to those of a composite frame with all stud connectors;
2. Improve the cracking resistance of an RC slab under vertical loads, compared with the composite frame with stud connectors only, and the improvement increases with the increased arrangement length of URSP connectors;
3. Only decrease the initial vertical stiffness a bit compared with the composite frame with stud connectors only under vertical loads.  
Furthermore, based on the FE results, the design recommendations of URSP connectors were given in terms of two factors, the amplification factor of the cracking load \(R_{F}\) and the stiffness amplification coefficient ratio \(R_{I}\). A distribution length of 0.4-0.5\(L\) (0.2-0.25 times of the whole frame beam length) is recommended for URSP connectors adopted near both beam ends for practical design.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**URSP Length (\(L\))**} & \multirow{2}{*}{**Formulas R\({}_{I}\)**} & \multicolumn{2}{c}{\(\mathbf{h_{s}}\) = 400 mm} & \multicolumn{2}{c}{\(\mathbf{h_{s}}\) = 450 mm} \\ \cline{3-6}  & & \(\mathbf{R_{I}}^{\prime}\) & \(\frac{R_{I}^{\prime}-R_{I}}{R_{I}}\) & \(\mathbf{R_{I}}^{\prime}\) & \(\frac{R_{I}^{\prime}-R_{I}}{R_{I}}\) \\ \hline
0.1 & 0.997 & 0.984 & \(-1.29\%\) & 0.985 & \(-1.20\%\) \\
0.2 & 0.986 & 0.975 & \(-1.11\%\) & 0.977 & \(-0.95\%\) \\
0.3 & 0.968 & 0.955 & \(-1.35\%\) & 0.958 & \(-1.09\%\) \\
0.4 & 0.943 & 0.936 & \(-0.74\%\) & 0.939 & \(-0.39\%\) \\
0.5 & 0.910 & 0.921 & 1.14\% & 0.925 & 1.56\% \\ \hline \hline \end{tabular}  
Notes: \(R_{I}\), and \(R_{I}^{\prime}\) are calculated by the proposed formula (9) and FE models of middle joints in Figure 21b.  
\end{table}
Table 5: \(R_{I}\) of middle joints under load case 2.  
**Author Contributions:** Conceptualization, X.N.; methodology, L.D. and L.Z.; software, L.D. and L.Z.; validation, X.N. and R.D.; formal analysis, L.D.; investigation, L.D. and R.D.; resources, X.N.; data curation, L.Z.; writing--original draft preparation, L.D.; writing--review & editing, X.N. and R.D.; visualization, L.D. and R.D.; supervision, X.N. and R.D.; project administration, X.N. and R.D.; funding acquisition, X.N.  
**Funding:** This research was supported by the National Key Research Program of China (Grant No. 2018 YFC0705704) and Key Research Program of China Railway Corp. (Grant No. K2018G018).  
**Acknowledgments:** The authors would like to thank the anonymous reviewers for their constructive comments and suggestions.  
**Conflicts of Interest:** The authors declare no conflict of interest.