# Study on Mechanical Properties of Simply-Supported Composite Beams Considering Creep and Slip
## 4 Analysis of the Result
### Comparison of Slip under Different Load Situations  
Since the slip at the end of the support is the largest among the simply-supported composite beams, we compare the slip at the end of the composite beam with the time. In Table 3, the beam end slips of the combined beam with time for different load forms and different calculation methods are listed. Table 3 shows that the slip at the end of the composite beam decreases with time, whether under a uniform or concentrated load. The maximum error between the calculated value of the formula and the simulated value is 4.67%. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Time/d**} & \multicolumn{2}{c}{**Simulated Calculation Value**} & \multicolumn{2}{c}{**Simulated Calculation Value**} & \multirow{2}{*}{**Error 1**} & \multirow{2}{*}{**Error 2**} \\ \cline{2-2} \cline{5-6}  & \multicolumn{2}{c}{**Uniformly**} & & & **Uniformly** & & \\  & **Distributed Load** & & & **Distributed Load** & & \\ \hline  
\hline \hline \end{tabular} Note: Error 1 is under uniform load; Error 2 is under concentrated load.  
\end{table} 
Table 3: Comparison of slip under different loads (mm). Figure 20: (**a**) Comparison diagram of mid-span deflection under uniform loads. (**b**) Comparison diagram of mid-span deflection under point loads. Figure 21 shows the curves of the slip size of the composite beam end calculated in the ANSYS finite element software, considering the creep change with time. It can be seen that when the loading age is 7 d under a uniform load, the end slip of the composite beam is 0.7800 mm, and the slip is reduced to 0.7229 mm at 407 d, which is reduced by approximately 7.32%. When the loading age is 7 d under a concentrated load, the end slip of the composite beam is 0.9901 mm, and the slip is reduced to 0.8746 mm at 407 d, which is reduced by approximately 11.67%. Figure 22 shows the curves of the slip size of the composite beam end considering the change in creep with time calculated by the formula derived by the MATLAB software. It can be seen that when the loading age is 7 d under a uniform load, the slip of the composite beam end is 0.8182 mm, and the slip decreases to 0.7408 mm at 407 d, which is reduced by approximately 9.46%. When the loading age is 7 d under a concentrated load, the slip of the composite beam end is 1.0323 mm, and the slip decreases to 0.9081 mm at 407 d, which is reduced by approximately 12.03%. Figure 23 shows the comparison of the slip curves of the composite beam end under the two methods. From the diagram, we can clearly see that the trend of the curves calculated by the two methods is the same, whether under a uniform load or concentrated load, but there are some minor errors. The error range is within 4.67% from the above table. Figure 21: (**a**) Beam end slip under uniform loads in ANSYS. (**b**) Beam end slip under different loads in ANSYS. Figure 22: (**a**) Beam end slip under uniform loads in MATLAB. (**b**) Beam end slip under point loads in MATLAB. Comparison of Axial Force, Deflection, and Slip of Composite Beams under Different Stud Stiffness Levels  
With the remaining factors of the example model unchanged, the stud stiffness is changed to \(K_{1}=2\times 10^{4}\)\(N/\)mm, \(K_{2}=5\times 10^{4}\)\(N/\)mm and \(K_{3}=1\times 10^{5}\)\(N/\)mm. The change in stud stiffness causes a change in interface slip between the composite beams. At this time, the changes in the axial force, deflection, and slip of composite beams with different stud stiffness levels under a uniform load are analyzed. In Table 4, the axial forces in the span of the combined beam at day 7 and day 407 of loading are listed for different stud stiffnesses and different calculation methods. Table 4 shows that regardless of the type of stud stiffness, the maximum error between the calculated value and the numerical simulation value is 0.71%. With the increase in stud stiffness, the axial force decreases more in the same creep time under the formula calculation results, which are 72.56 kN, 131.37 kN, 156.73 kN, respectively.