# Innovative Suspension Structures: The Role of Straight Elements Under Asymmetric Loads
## 3 Numerical Analysis of Suspension System Under Asymmetric Loads
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Stiffness**} & \multirow{2}{*}{**Load Factor \(\gamma\)**} & \multicolumn{4}{c}{\(\frac{N_{sym}}{N_{sym}}\)} \\ \cline{3-6}  & & **Bar 1–6** & **Bar 6–3** & **Bar 3–7** & **Bar 7–5** \\ \hline \multirow{3}{*}{I1} & 1.00 & 1.008 & 1.008 & 0.518 & 0.518 \\  & 1.50 & 1.011 & 1.011 & 0.418 & 0.418 \\  & 2.00 & 1.012 & 1.012 & 0.351 & 0.351 \\ \hline \multirow{3}{*}{P1} & 1.00 & 0.950 & 0.950 & 0.532 & 0.532 \\  & 1.50 & 0.935 & 0.935 & 0.444 & 0.444 \\ \cline{1-1}  & 2.00 & 0.923 & 0.923 & 0.364 & 0.365 \\ \hline \hline \end{tabular} \(N_{sym}\), \(N_{sym}\)—axial force under symmetrical and asymmetrical loading.  
\end{table} 
Table 3: The ratio of axial forces in the lower chord under symmetric and asymmetric loading for different load factors and stiffness types. Figure 13: Axial forces in the upper chord of the two-level system (SK-3) under symmetric loading (solid line) and asymmetric loading (dashed line), with \(\gamma=1.5\). It may seem that the most efficient design for minimizing bending moments occurs when the upper chord has a low bending stiffness (P1). However, a more accurate assessment of the suspended system's efficiency, particularly with a stiff upper bending chord, can be made by comparing the normal stresses of the upper chord cross-section. These stresses are calculated by combining the effects of axial forces and bending moments for various bending stiffness values, as illustrated in Figure 15. It is important to recall that the cross-sectional areas of the examined upper chords varied only slightly. The stress graphs in Figure 15 reveal that the most efficient cross-sections correspond to the highest stiffness values, where the maximum stress is \(\sigma=86.9\) MPa. In contrast, the lowest stiffness in the upper chord results in significantly higher stress values, reaching \(\sigma=316.5\) MPa. The effectiveness of suspension systems (SK-2 and SK-3) compared with suspension structures composed only of bending stiffness elements was previously demonstrated in the analysis of the SK-1 structure. However, it is also important to highlight the advantages of these systems over the conventional parabolic suspension system (SK-4) as shown in Figure 1. In the SK-4 structure, the vertical coordinates follow a quadratic parabolic distribution, typical of conventional suspension structures. Figure 16 presents calculation results for the SK-4 structure. Under asymmetric loading, even with the highest bending stiffness (I1), upward displacements occur on the left side of the structure. Additionally, with minimal bending stiffness (P1), which closely resembles a cable system, the upward displacements are significantly larger. It is important to note that, in all stiffness cases, the displacements of the conventional cable suspension structure are two to three times greater than those of the two-level suspension system. Figure 14: Bending moments in the upper chord of the two-level cable–strut system (SK-3) under symmetric loading (solid line) and asymmetric loading (dashed line), with \(\gamma=1.5\). Figure 15: Normal stresses at the bottom of the upper chord section in the two-level suspension system (SK-3) under symmetric loading (solid line) and asymmetric loading (dashed line), with \(\gamma=1.5\).