## 3 Simulation and Analysis of Structural Behavior
### Simulation Process and Results  
The three above-described models are used to simulate and calculate the response of the column-free QRST structure under test loads. Since these three models are all elastic models, the load pattern is completely consistent with Figure 6, using the direct calculation method. Taking the simulation results of the MBS model subjected to the 13 m service stage condition as an example, the distribution of internal forces, including bending moment, axial force, and shear force, is shown in Figure 12.  
Figure 11: Illustration of the joint influence zone: (**a**) Configurations of segments and distribution of stress zones; (**b**) Photo of segment in the joint vicinity.  
The calculated deformation results of the three models (ESHR model, BS model, and MBS model) under the same design condition (13 m service stage) are presented in Figure 13 and Table 4 for comparison. In Table 4, the positions of the long and short axes are indicated in Figure 7. The left short axis and the right short axis are both 2.55 m from the short axis.  
As depicted in Figure 13 and Table 4, all three models demonstrate efficient simulation accuracy. For comparison purposes, the simulation results calculated by the three models are analyzed based on different parts of the structure. Regarding structural deformations at the top of the structure, both the MBS model and the BS model effectively reflect the local deformation characteristics of joints, presenting higher simulation accuracy compared to the ESHR model. Concerning deformations at the bottom of the structure, the MBS model also achieves the best-fitting effect among the three models. As for structural deformations at the waist of the structure, the simulation results of the three models are relatively close. In  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Location**} & \multicolumn{2}{c}{**Experimental Results**} & \multirow{2}{*}{**ESHR Model**} & \multirow{2}{*}{**BS Model**} & \multirow{2}{*}{**MBS Model**} \\ \hline Short axis & \(-108.64\) & \(-108.69\) (\(0.04\%\)) & \(-105.55\) (\(-2.84\%\)) & \(-108.72\) (\(0.07\%\)) \\ Long axis & \(49.03\) & \(52.17\) (\(6.4\%\)) & \(51.56\) (\(5.15\%\)) & \(53.13\) (\(8.36\%\)) \\ Left short axis & \(-104.67\) & \(-106.99\) (\(2.22\%\)) & \(-102.26\) (\(-2.31\%\)) & \(-105.34\) (\(0.64\%\)) \\ Right short axis & \(-110.82\) & \(-106.99\) (\(-3.45\%\)) & \(-108\) (\(-2.54\%\)) & \(-111.25\) (\(0.38\%\)) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of convergence deformations of different axes between experiment results and simulation results based on three models (mm).  
Figure 12: Simulation results of the MBS model under the 13 m service stage condition: (**a**) Bending moment; (**b**) Axial force; (**c**) Shear force.  
Figure 13: Comparison of overall structural deformations between experimental results and simulation results based on the three models.  
addition, as shown in Table 4, both the BS model and the MBS model reflect the asymmetric deformation of the left and right short axes of the structure, while the ESHR model does not. Additionally, the MBS model has very good prediction results for the deformation of the three short axes compared with the other two models.  
In summary, due to the different simulation methods for joints, the ESHR model may not fully capture the local deformation characteristics near the joint, unlike the BS model or the MBS model. The MBS model, encompassing both joint deformation and joint-induced deformation in the vicinity of the joint, yields more precise simulation results compared to the ESHR model and the BS model. Therefore, it is recommended that the MBS model or BS model be used for the analysis of structural mechanics. Nonetheless, the ESHR model already provides adequate simulation accuracy for design purposes.