# Innovative Suspension Structures: The Role of Straight Elements Under Asymmetric Loads
## 3 Numerical Analysis of Suspension System Under Asymmetric Loads
These results confirm that a two-level system with a rigid upper chord is significantly more effective than one with a flexible upper chord. Figure 10: Vertical displacements of the single-level suspension system (SK-2) under asymmetric loads at different load ratios \(\gamma\). Figure 9: Vertical displacements of the single-level cable–strut structure (SK-2) under symmetric loads (solid line) and asymmetric loads (dashed line), with load ratio \(\gamma=1.5\). Figure 12 illustrates the influence of the load ratio \(\gamma\) on the displacement distribution. The numerical results for the two-level system, which are similar to those of the suspension single-level system, indicate that under asymmetric loading, the load ratio has minimal effect if the upper chord has sufficient stiffness (I1-R4). Only at very low bending stiffness (P1) does the load ratio significantly impact the displacements. The distribution of axial forces under asymmetric and symmetric loads is shown in Figure 13. The results reveal that the axial forces are nearly identical when the upper chord stiffness ranges from I1 to R4. Therefore, Figure 13 shows the results only when the stiffnesses are I1, R4, and P1. However, with very low bending stiffness, the axial forces increase with the largest differences reaching 9.0% (31.0 kN) under symmetric loading and 37.8% (52.1 kN) under asymmetric loading. Notably, under asymmetric loading, the axial forces are greater than under symmetric loading only on the less loaded side of the structure, closer to the central point \"5\". Therefore, it can be concluded that asymmetric loading does not significantly influence axial forces compared with symmetric loading. Figure 11: Vertical displacements of the two-level suspension system (SK-3) from symmetric loading (solid line) and asymmetric loading (dashed line) with \(\gamma=1.5\). Figure 12: Vertical displacements of the two-level system (SK-3) under asymmetric loading at different load ratios \(\gamma\). Table 3 presents the results of the influence of asymmetric loading on the bars of the lower chord of the SK-2 structure. It can be observed that, for any load factor \(\gamma\), the axial forces on the more heavily loaded side of the structure (bars 1-6 and 6-3) under asymmetric loading are very close to those under symmetric loading--especially when the upper chord is stiff (stiffness I1). When the upper chord has low stiffness (P1), the axial forces under asymmetric loading are lower than under symmetric loading, with the reduction becoming more significant as the load factor increases (variable loading dominates). On the less loaded side of the structure (bars 3-7 and 7-5), the axial forces under asymmetric loading are much lower compared with symmetric loading. However, this difference is smaller when the upper chord is stiffer (I1) and becomes larger as the load factor \(\gamma\) increases. Figure 14 shows the distribution of bending moments in the upper chord under asymmetric and symmetric loads. It should be noted that these bending moments are considerably lower than those observed in the single-level system. Additionally, the magnitude of bending moments strongly depends on the bending stiffness of the upper chord. For instance, under asymmetric loading, the bending moment values for I1 and P1 stiffnesses differ by up to 3.05 times, and under symmetric loading, by up to 5.19 times.