# Study on Mechanical Properties of Simply-Supported Composite Beams Considering Creep and Slip
## 5 Conclusions  
1. When considering the creep effect of the combined beam at the same stud stiffness, the axial force of the concrete slab inside the combined beam was reduced by around 11.0-11.6%, and the slip was reduced by 7.32-11.67% at 407 d. However, the deflection of the combined beam increased by 39.91-41.3%, so the concrete creep effect reduces the flexural stiffness of the combined structure, increases the deformation of the combined beam, and adversely affects the combined structure. 2. The stud stiffness is an important factor affecting the long-term performance of steel-concrete composite beams. The stud stiffness was varied from 2000 N/mm to 10,000 N/mm, with other parameters unchanged. The change in axial force in the combined beam due to creep variation increased from 7.09% to 12.50%; the change in deflection increased from 31.97% to 46.60%, and the change in slip increased from 4.85% to 10.47% under long-term loading. The results show that the more strongly the studs constrain the concrete slab, the greater the adverse effect of concrete creep on the combined beam. 3. By comparing the theoretically derived formulation with the finite element numerical simulation results, the error was around 5%, which proves the validity of the formulation for the calculation of the axial force, deflection, and slip of simply-supported composite beams considering the coupling of creep and slip based on the principle of the energy variational method. The results show that the theoretically derived formulas are applicable to the solution of the axial force, deflection, and slip of simply-supported composite beams under different types of creep and slip coupling. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Time/d**} & \multicolumn{4}{c}{**Simulated Calculation Value**} & \multicolumn{4}{c}{**Values Calculated**} & \multirow{2}{*}{**Error 1**} & \multirow{2}{*}{**Error 2**} & \multirow{2}{*}{**Error 3**} \\ \cline{2-2} \cline{6-8}  & \(K_{1}=2\times 10^{4}\) & \(K_{2}=5\times 10^{4}\) & \(K_{3}=1\times 10^{5}\) & \(K_{1}=2\times 10^{4}\) & \(K_{2}=5\times 10^{4}\) & \(K_{3}=1\times 10^{5}\) & \\  & **N/mm** & **N/mm** & **N/mm** & **N/mm** & **N/mm** & **N/mm** & & \\ \hline
7 & 1.6644 & 0.7800 & 0.4290 & 1.7038 & 0.8182 & 0.4442 & 2.37\% & 4.90\% & 3.54\% \\
407 & 1.5836 & 0.7229 & 0.3841 & 1.5959 & 0.7408 & 0.3964 & 0.78\% & 2.48\% & 3.20\% \\ value & \(-0.0808\) & \(-0.0571\) & \(-0.0249\) & \(-0.1079\) & \(-0.0774\) & \(-0.0478\) & & \\ \hline \hline \end{tabular} Note: Error 1: between numerical solution and formula solution under stiffness of studs \(K_{1}\); Error 2: between numerical solution and formula solution under stiffness of studs \(K_{2}\); Error 3: between numerical solution and formula solution under stiffness of studs \(K_{3}\).  
\end{table} 
Table 6: Comparison of slip of composite beams with different stud stiffnesses (mm). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Time/d**} & \multicolumn{4}{c}{**Simulated Calculation Value**} & \multicolumn{4}{c}{**Values Calculated**} & \multirow{2}{*}{**Error 1**} & \multirow{2}{*}{**Error 2**} & \multirow{2}{*}{**Error 3**} \\ \cline{2-2} \cline{6-8}  & \(K_{1}=2\times 10^{4}\) & \(K_{2}=5\times 10^{4}\) & \(K_{3}=1\times 10^{5}\) & \(K_{1}=2\times 10^{4}\) & \(K_{2}=5\times 10^{4}\) & \(K_{3}=1\times 10^{5}\) & \\  & **N/mm** & **N/mm** & **N/mm** & **N/mm** & **N/mm** & **N/mm** & & \\ \hline
7 & 37.29 & 31.50 & 29.12 & 36.91 & 31.11 & 28.73 & 1.02\% & 1.24\% & 1.34\% \\
407 & 49.21 & 44.51 & 42.69 & 46.97 & 42.16 & 40.28 & 4.55\% & 5.28\% & 5.65\% \\ value & 11.92 & 13.01 & 13.57 & 10.06 & 11.05 & 11.55 & & \\ \hline \hline \end{tabular} Note: Error 1: between numerical solution and formula solution under stiffness of studs \(K_{1}\); Error 2: between numerical solution and formula solution under stiffness of studs \(K_{2}\); Error 3: between numerical solution and formula solution under stiffness of studs \(K_{3}\).  
\end{table}