## 3 Experimental Verification  
### Verification for the Nonlinear Interfacial Behaviors  
[PERSON] et al. [17] conducted eight simply supported steel-concrete composite beam experiments to test the influence of interfacial shear connection degree on the flexural behaviors. The compared specimens named NCB-4, NCB-5 and NCB-6 were built with different stud spacings, leading to the failure mode differences. The structural details of NCB-4, NCB-5 and NCB-6 are shown in Figure 9. The material properties are listed in Tables 1 and 2. According to the design details of shear connectors, the average shear capacity per unit length \(V_{u}\) can be calculated using Equation (23). The values of \(V_{u}\) for NCB-4, NCB-5 and NCB-6 were 860 N/mm, 383 N/mm and 688 N/mm, respectively. Additionally, the shear connection degree \(\eta\) was 1, 0.45 and 0.69 for NCB-4, NCB-5 and NCB-6, respectively. The analysis models of these three tests are built by OpenSees with the newly developed fiber beam element with interfacial slip effects. Meanwhile, the traditional fiber beam element is also employed to model the case without interfacial slip for comparisons. Figure 10a,b show the calculated results of load-deflection and load-slip curves, respectively. Some conclusions can be drawn by observing these comparisons. With an increase in shear connection degree, the stiffness and carrying capacity are both significantly improved. The proposed model and developed procedure can effectively capture the nonlinear interfacial slip behaviors, and the calculated results agree well with the tests. To further validate the prediction of the proposed model for the failure mode caused by nonlinear interfacial slip behaviors, the interfacial shear-slip curves are output from the models, as shown in Figure 11a,b, which shows the stress distributions along with the height of the failure cross-section at ultimate states. The failure modes observed by [PERSON] et al. [17] are shown in Figure 12. For the specimen with the lowest shear connection degree, NCB-5, the ultimate interfacial average shear almost reached the specified capacity. The ultimate stress of the top fiber in the concrete slab was lower than its compressive strength, meaning that the failure mode was caused by the interfacial slip rather than the concrete crushing. The observed failure modes caused by split cracks in Figure 12b validate this judgment. For NCB-4, the interfacial slip occurred but did not reach the ultimate states and the top concrete fiber reached its peak strength. The failure mode of NCB-4 is shown in Figure 12a. For the full shear connection model without slip effects, the top concrete fiber was in the stage of compression softening. The concrete slab was crushed and the steel beam showed full section yield, as shown in Figure 11b. The comparisons revealed that interfacial slip effects inevitably existed and significantly influenced the flexural behaviors of the steel-concrete composite beam, even when the shear connection degree was set to 1. The proposed model can effectively predict the flexural capacity, deformation and failure modes of composite beams with interfacial slip effects. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Components** & **Yield Strength (MPa)** & **Ultimate Strength (MPa)** & **Elastic Modulus (MPa)** \\ \hline Rebar \(\varphi\)6 & 440 & 524 & \(2.23\times 10^{5}\) \\ Steel Beam & 342 & 447 & \(2.23\times 10^{5}\) \\ Shear Studs & 488 & 552 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material properties of steel in NCB-4, NCB-5 and NCB-6. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Specimen** & **Cubic Compressive Strength (MPa)** & **Prismatic Compressive Strength (MPa)** & **Elastic Modulus (MPa)** \\ \hline NCB-4 & 30.0 & 22.8 & 22,800 \\ NCB-5 & 29.4 & 22.3 & 22,300 \\ NCB-6 & 35.6 & 27.1 & 27,100 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material properties of concrete in NCB-4, NCB-5 and NCB-6. Figure 10: Comparisons of analysis results with tests of NCB-4, NCB-5 and NCB-6.