GEOMETRIC NONLINEAR BEHAVIOR OF SUSPENSION BRIDGES AND THE SUSCEPTIBILITY OF THEIR SUPPORTS TO DISPLACEMENT

ABSTRACT

This article provides a detailed study of the geometric nonlinearity of single-span suspension bridges and the tendency of their supports to undergo displacement. The research was carried out using computational calculations, theoretical analysis, and computer modeling. The results indicate that elastic displacements of the supports generate additional stresses, which may reduce the overall strength, stability, and long-term reliability of the bridge. The outcomes of the calculations and modeling scientifically justify the necessity of considering geometric nonlinearity and support deformations in the design process of suspension bridges. The findings of this study provide engineers and researchers with a scientific basis for designing suspension bridges that are safe, reliable, and durable.

АННОТАЦИЯ

В данной статье подробно изучены геометрическая нелинейность однопролетных подвесных мостов и склонность их опор к смещению. Исследование проводилось с использованием вычислительных расчетов, теоретического анализа и компьютерного моделирования. Результаты показывают, что упругие смещения опор вызывают дополнительные напряжения, которые могут снижать общую прочность, устойчивость и долговечность моста. Результаты расчетов и моделирования научно обосновывают необходимость учета геометрической нелинейности и деформаций опор при проектировании подвесных мостов. Данные исследования предоставляют инженерам и ученым научную основу для проектирования безопасных, надежных и долговечных подвесных мостов.

Keywords: Suspension, bridge, nonlinear, span, deflection, deformation, sloped, displacement, geometric, elastic.

Ключевые слова: Висячий, мост, нелинейный, пролёт, прогиб, деформация, паддатливый, cмещение, геометрический, упругое.

Introduction

Single-span suspension bridges are engineering structures designed to cover large distances. In their structural behavior, geometric nonlinearity is one of the key factors, as the applied loads cause significant deformations and lead to a redistribution of internal forces. In particular, the susceptibility of the supports to displacement generates additional stresses and unfavorable deformations[2]. This, in turn, requires special attention to ensure the stability, strength, and long-term reliability of the bridge. Therefore, nonlinear modeling techniques and modern computational tools are essential for the analysis of such structures[8].

The main objective of this article is to present the fundamental principles of calculating suspension bridges based on analytical and numerical methods.

Materials and methods

In the «Navruz» MCA of Samarkand city (Figure 1), the cables and anchors of a 132 meter (22.5 + 81 + 28.5) span suspension-cable-stayed pedestrian bridge crossing the Dargom canal were selected and tested.

The main load-bearing structures of the suspension-cable-stayed bridge were analyzed using the LIRA-SAPR software, considering the geometric nonlinear behavior of the structure and the susceptibility of its supports to displacement.

Figure 1. General view of the single-span suspension–cable-stayed bridge

The geometric nonlinear behavior of suspension bridges is influenced by the following factors:

-since the elastic modulus of steel cables (E = 160,000 MPa) is lower than that of bar-type structural elements (E = 210,000 MPa), the cables exhibit higher deformability[9].

-because the wound (helical) cables delivered to the construction site contain internal voids, they demonstrate 2-8% non-elastic elongation. The magnitude of stress that develops in suspension bridge cables is directly influenced by the cable sag (f) relative to the horizontal axis[10].

-If the supports of the suspension bridge are not fully rigid such as in the case of piled or non-piled foundations the overall structural behavior and internal force distribution require a geometric nonlinear analysis[11].

The susceptibility of suspension bridge supports to displacement is influenced by the following factors:

-large horizontal forces generated by cable tension.

-insufficient strength or uneven settlement of the soil beneath the foundation.

-inadequate strength of the foundation slab.

-thermal expansion and contraction resulting from temperature variations.

-horizontal effects and vibrations induced by wind, traffic, and seismic loads.

-erosion of the soil beneath the foundation due to river flow and slope washout[12].

Results and discussions

Taking into account the geometric nonlinear behavior of the suspension bridge and the susceptibility of its supports to displacement, numerical analysis was performed using a computer program, and the results were developed and compared. The comparison was carried out for three different geometric analysis schemes:

1) When the supports of the suspension bridge structure are assumed as rigid nodes.

Figure 2. Longitudinal N stress distribution of the suspension-cable-stayed bridge

Figure 3. General sag of the suspension-cable-stayed bridge in the Zg direction

Figure 4. Total displacement of the suspension-cable-stayed bridge in the Xg direction

2) When the foundation is assumed as non-piled (freely settling).

Figure 5. Longitudinal N stress distribution of the suspension-cable-stayed bridge

Figure 6. General sag of the suspension-cable-stayed bridge in the Zg direction

Figure 7. Total displacement of the suspension-cable-stayed bridge in the Xg direction

3) When the foundation is assumed to be reinforced with piles.

Figure 8. Longitudinal N stress distribution of the suspension–cable-stayed bridge

Figure 9. General sag of the suspension-cable-stayed bridge in the Zg direction

Figure 10. Total displacement of the suspension-cable-stayed bridge in the Xg direction

Table 1.

Comparison of LIRA-SAPR analysis results for the 81 m span suspension bridge

The results indicate that:

• Rigid supports provide the best performance, as theoretically no displacement occurs at the supports, resulting in minimal cable forces and pylon deformations. The structure transfers loads entirely to the rigid supports, so the bridge sag (Δf) is also minimized.
• Non-piled (freely settling) foundations produce significant deformations due to the compressibility and susceptibility of the soil to displacement: settlement occurs beneath the supports and lateral movements increase. As a result, the sag increases by +19%, and the lateral tilt of the pylons increases by up to +27%. The main disadvantage of this scheme is that the soil does not provide sufficient resistance to support the loads effectively.
• Piled foundations yield results close to the rigid support case. The piles enhance horizontal and vertical stiffness and limit excessive soil deformation. The sag (Δf) increases only by +5%, and the susceptibility of the supports to displacement remains small, indicating that the piles effectively transfer loads to deeper soil layers. Therefore, this scheme is considered the most practical solution.
• Comprehensive and detailed structural calculations should be carried out using numerical software such as LIRA-SAPR, since geometric nonlinearity, cable forces, and support deformations can only be fully captured through computational modeling.
• For further improvement of the study, it is recommended to incorporate monitoring data and experimental test results, which allows for comparison of the calculated outcomes with actual deformations under real conditions.

Conclusion

Geometric nonlinear analyses were performed in LIRA-SAPR for a single-span, 81-meter suspension-cable-stayed bridge using three different support schemes: rigid supports, non-piled foundations, and piled foundations. The results indicate that the susceptibility of the supports to displacement has a significant impact on the overall structural deformation and cable forces. The rigid support model exhibited the smallest displacements and the most favorable stress distribution, while the non-piled foundation resulted in increased displacements and maximum stresses. In the piled foundation scheme, secondary displacements were significantly reduced, achieving optimal structural performance.

Comparison of the results shows that, relative to the rigid support case, the non-piled foundation produced cable forces of 309 kN (−4.0%), sag of −2210 mm (+18.8%), pylon displacement of −178 mm (+27.1%), and maximum support displacement of 66 mm. In the piled foundation scheme, the corresponding values were 319 kN (−0.9%), −1960 mm (+5.4%), −143 mm (+2.1%), and a maximum displacement of 24 mm. Thus, equipping the foundation with piles yields results close to those of rigid supports and demonstrates significantly better performance than the non-piled variant.

The study confirms that accounting for the actual geotechnical susceptibility of supports to displacement is a critical factor for the safe and reliable design of suspension bridges. Performing structural analyses using modern computational software enhances both the safety and economic efficiency of bridge design.

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