# Innovative Suspension Structures: The Role of Straight Elements Under Asymmetric Loads
## 3 Numerical Analysis of Suspension System Under Asymmetric Loads
Furthermore, Figure 8 highlights that suspension structures are significantly more sensitive to asymmetric loads than to symmetric ones, exhibiting larger displacements under asymmetric conditions. Significant displacements were observed in the two element suspension structure. To reduce these displacements, the stiffness of the rigid bars must be increased. However, this leads to large bending moments, necessitating a new design approach with additional bars to support the main rigid elements. The accuracy of analytical solutions was evaluated by performing numerical analysis on a suspension structure with two straight rigid elements. The analytical solutions demonstrated errors of no more than 2% for axial forces and approximately 4-5% for displacements and bending moments in asymmetrically loaded suspension structures with different bending stiffness in straight elements. The design scheme for the single-level suspension system (SK-2) is shown in Figure 1, with cross-sectional characteristics defined earlier in this section. Comparing results between the single-level suspension system (SK-2) and the two straight bar suspension structure (SK-1), the displacements (see Figure 9) at points \"2\" and \"4\" in SK-2 decreased compared with points \"a\" and \"b\" in SK-1 under asymmetric loads. Specifically, the vertical displacement at point \"2\" decreased by a factor of 7.72 to 13.01, depending on stiffness, while at points \"a\" and \"b\" of SK-2, the displacements decreased by a factor of 1.31 to 4.84. However, at low stiffness (P1), the displacements remained relatively large (0.432 m). At higher bending stiffness levels (I1 and R1), the vertical displacements at points \"a\", \"2\", and \"b\" were similar. The displacements of the central node \"3\" in the SK-2 system and node \"2\" in the SK-1 structure decreased by nearly half. However, at low bending stiffness in the upper chord (P1 and R4), the displacements due to asymmetric loads were larger than those from symmetric loads. At higher stiffness levels (I1, R1, and R2), the vertical displacements changed direction and moved downward. At point \"4\", the vertical displacements decreased by a factor of 1.51 to 7.64, but at low stiffness (P1 and R4), they changed direction and moved upward. This indicates that with minimal bending stiffness in the upper chord, the system is less effective against asymmetric loads. However, with medium stiffness (R1, R2, and R3), the single-level suspension system effectively minimizes displacement variations across all points of the upper chord, even under asymmetric loading. The influence of the ratio of permanent to variable loads \(\gamma\) on displacement distribution is illustrated in Figure 10. The numerical results indicate that under asymmetric loading, the load ratio \(\gamma\) has minimal  
Figure 8: Vertical displacements of a two-element structure (SK-1) under symmetric loads (solid line) and asymmetric loads (dashed line) when the load ratio \(\gamma=1.5\). impact if the upper chord is sufficiently stiff (I1, R1). Only at very low bending stiffness (P1) does the load ratio significantly affect displacements. The two-level suspension system (SK-3) is illustrated in Figure 1 with cross-sectional characteristics defined earlier in this section. This innovative two-level suspension system (SK-3) is more efficient than both the single-level system (SK-2) and two straight element (SK-1) suspension structures in terms of displacements and stress tension forces distribution. The displacements in the two-level suspension system (Figure 11) significantly decreased compared with the single-level system when the upper chord stiffness was set to I1, R1-R4. Under all examined bending stiffnesses, the central hinge \"5\" and other upper chord nodes shifted downward, even with asymmetric loading. However, when the upper chord had minimal stiffness (P1), the system became inefficient, with central node \"5\" and nodes \"6\", \"7\", and \"8\" shifting upward.