An Investigation into the Impact of Time-Varying Non-Conservative Loads on the Seismic Stability of Concrete-Filled Steel-Tube Arch Bridges

Abstract

When the arch rib of the mid-bearing through and lower-bearing through arch bridges undergoes out-of-plane deformation, it is usually subject to the resilience force provided by the flexible hanger, which is known as the “non-conservative force effect” of the suspender. In contrast to the static condition, in the dynamic scenario, the time-varying non-conservative force exerted by the flexible suspender becomes more complex due to dynamic changes in external load. Moreover, the difference in fundamental frequency and vibration period between the bridge system and arch rib may influence the stress distribution within the arch rib during ground motion. This paper investigates the impact of time-varying non-conservative forces on the dynamic stability of arch ribs in concrete-filled steel tube (CFST) bridges under seismic loads. Specifically, it examines the influence of different seismic waveforms, frequency disparities between bridge slabs and arch ribs, and suspender stiffness on the non-conservative effect. The results reveal significant disparities in the impact of non-conservative forces exerted by the suspender during seismic events with identical intensity but varying frequency characteristics. The influence of non-conservative forces on the dynamic stability of bridges escalates as deck stiffness increases, while it remains relatively unaffected by changes in suspender stiffness.

1. Introduction

The concrete-filled steel tube (CFST) is a composite structure consisting of an external thin-walled steel tube and internal concrete filling, which effectively exerts the mechanical advantages of both materials. Due to its ease of construction and maintenance, CFST is a sustainable, low-carbon composite structure. The CFST arch bridge takes full advantage of the inherent advantages of this structural system, including its excellent compressive resistance, outstanding ductility, and light weight [1]. Moreover, it can well adapt to the requirements of modern engineering structures for large spans, high heights, heavy loads, and harsh environmental conditions [2]. Since the emergence of CFST arch bridges in the last century, their excellent performance has won great praise from engineers. Especially in the field of bridge engineering in China, CFST arch bridges are widely used in major cities, mountains, rivers, valleys, and other areas due to their light and beautiful linear design and excellent load-bearing capacity. Notably, mid-bearing through and lower-bearing through arch bridges have exhibited commendable economic benefits [3].

For CFST arch bridges, the deformation of the arch rib leads to a change in the direction of suspender force action; this phenomenon is called the “non-conservative force effect”. As early as 1923, the study of non-conservative forces in arch structures began. Based on the Saint-Venant’s theory of small deformations, Stephen Timoshenko derived analytical solutions for both uniform radial and non-conservative forces applied to thin circular arc strips experiencing out-of-plane elastic buckling [4,5]. Subsequently, Godden used the energy balance method to innovatively analyze the effect of non-conservative forces exerted by suspenders on the out-of-plane elastic stability of the tie-arch structure [6]. The investigation found that changing the direction of the suspender tension would significantly improve the out-of-plane stability of the arch rib, which was verified by the corresponding model test. Xiang et al. presented a finite element analysis method for evaluating the non-conservative force on single-bearing-surface arch structures [7]. The analysis results demonstrated that considering the influence of the non-conservative force, the elastic stability coefficient of circular arches could be increased by 2.5–3.0 times within a typical sagittal–span ratio range. Based on the aforementioned elastic analysis, Yang et al. developed analytical models to investigate the out-of-plane stability of bottom-bearing and top-bearing parabolic double-rib arch bridges [8]. They examined the influence of non-conservative force effects under various arch width–span ratios, sagittal–span ratios, and boundary conditions. The findings revealed that the impact of non-conservative force effects on stability performance was closely associated with the lateral bending stiffness of the bridge floor system while having minimal correlation with the torsional stiffness and vertical flexural stiffness of the arch rib.

Since the 21st century, with the widespread promotion and construction of steel-tube concrete arch bridges in China, the investigation into the non-conservative force effects on CFST arch bridges has attracted more attention from Chinese scholars. Pan et al. [9,10] studied the stability of a CFST double-rib x-arch bridge under non-conservative forces and determined the elastic stability load coefficient using the energy method. Wang et al. [11] selected Ganjiang Bridge in Jiangxi Province as the subject of analysis and developed ANSYS finite element models for CFST arch bridges with and without the influence of non-conservative forces. The findings indicate that non-conservative forces contribute to the overall stability of the bridge. Yun and Zhang [12,13], while investigating the static instability process of long-span and intermediate-span CFST arch bridges, discovered that the destabilizing effect exerted by the bridge deck system enhances both in-plane and out-of-plane stiffness of the structure, with a greater impact observed during its elastic stage. In order to further investigate the impact of suspender tension on the external ultimate bearing capacity, Wei et al. [14,15] conducted an out-of-plane stability test for a CFST single-rib-tube arch bridge and a CFST basket arch bridge, followed by finite element analysis. The findings from the analysis revealed that the non-conservative force effect of suspender tension significantly enhances the spatial mechanical performance of the arch structure. The degree of improvement is positively correlated with the suspension force. The results show that ignoring the non-conservative force effect will lead to a 22% reduction in the out-of-plane bearing capacity of the arch rib. Zhang et al. [16] conducted finite element analysis on the elastic stability of a long-span CFST railway arch bridge and concluded that an increase in the number of suspenders leads to a more significant favorable effect of non-conservative forces on suspenders.

According to the aforementioned studies, the non-conservative force provided by the suspender of the arch bridge contributes favorably to the static stability of CFST structures. This is attributed to the resilience force exerted by the flexible suspender, which effectively limits out-of-plane deformations of the arch rib. However, under dynamic conditions, the direction of the suspender force turns out to be variable and depends on the vibration characteristics of the structure. Therefore, a more comprehensive investigation is required to thoroughly examine how this non-conservative force affects dynamic stability problems. Currently, there is a lack of relevant research addressing time-varying non-conservative forces and their impact on structural dynamic stability; thus, further theoretical analysis is required.

2. Non-Conservative Force Effect Simulation Approaches of CFST Arch Bridges

2.1. Bridge Description

The Yajisha Bridge is an exceptionally large composite-structure bridge that connects the main channel and auxiliary channel of the Pearl River to Yajisha Island in the southwest section of Guangzhou Ring Highway. It has a span distribution of 76 m + 360 m + 76 m. The main span of this bridge features a self-anchored concrete-filled steel-tube arch design, with a calculated span length of 344 m and a rise–span ratio of 1/4.5.

The arch axis adopts a catenary form, with the arch axis coefficient m = 2 and k = 1.317. The bridge deck is designed with six lanes in each direction, providing a total width of 36.5 m. The center distance between the two arch ribs is 35.95 m, and there are eight groups of steel-pipe truss cross braces installed between the main arch ribs, including six groups of star-type braces and two groups of “K”-type braces. The arch rib section incorporates a novel design of six steel-pipe lattice sections, which represents the pioneering application in the field of international engineering. The bridge layout and arch rib section are illustrated in Figure 1. The arch rib is designed with equal-width and variable-height sections, featuring a section height of 8.039 m at the arch foot, 4.00 m at the arch top, and a width of 3.45 m.

The high-strength concrete with an axial compression strength of 50 MPa is poured into the chord tube and the joint plate of the arch rib. The steel properties at different locations in the arch rib section are slightly different, among which the 1#, 2#, 3#, and 5# steel pipes are made of steel with a yield strength of 345 MPa (referred to as “Q345”), and the 4# pipe is made of steel with a yield strength of 235 MPa (referred to as “Q235”). In terms of steel pipe (plate) size, the numbering rules are shown in Figure 1; the diameter of the 1# pipe and the 2# pipe is 750 mm, and the wall thickness is 18 mm and 20 mm, respectively. The wall thickness of the 3# steel string plate is 20 mm. The diameter and thickness of the 4# tube are 450 mm and 12 mm, respectively. The diameter of the 5# tube and the thickness of the steel pipe are 324 mm and 10 mm.

The side arch is a double-ribbed catenary arch with a calculated span of 71.0 m, where the ratio of vector to span is 1/5.2, and the axial coefficient of the arch aligns with that of the main arch. The ribs of the side arch consist of core concrete box beams measuring 4.5 m in height and 3.45 m in width, wherein the lower part forms a solid belly box beam, while at its end section, it adopts a stable space beam system structure.

2.2. Finite Element Model

The ABAQUS with version 6.14 finite element software [17] is employed to simulate and analyze the three-dimensional fiber beam model of Yajisha Bridge [18], while the common node double-element method is utilized to simulate the two material units in CFST. Previous studies have indicated that concrete debonding has negligible influence on the creep effect of CFST sections [19], and hence, bonding defects between them are not considered in this study.

The compressive behavior of confined concrete is simulated using the constitutive model proposed by Han [20], and the law of plastic flow is determined based on published study [21]. The tensile softening behavior of concrete is simulated using the power law softening model, and the creep model and algorithm are calculated using the step-by-step integral method introduced in the literature [22].

In terms of material properties, the main arch steel pipe exhibits an elastic modulus of 210 GPa, a yield strength of 345 MPa, and a mass density of 7850 kg/m³. Similarly, the core concrete possesses an elastic modulus of 34.5 GPa, a yield strength of 345 MPa, and a mass density of 2500 kg/m³. Additionally, the suspender wire bundle demonstrates a Young’s modulus value of 300 GPa. In this study, Timoshenko beam elements are employed to model arch ribs, bridge panels, wind braces, and spandrel columns. Each node is assigned 6 degrees of freedom to accurately capture the response of the beams under pressure, bending, and torsion. The influence of shear deformation is accounted for by incorporating actual shear stiffness values. T3D2 truss elements are utilized for tie bars and suspender units; specifically, the suspender unit solely bears loads without acting as a bearing unit in order to consider non-conservative force effects between the suspension arch rib and the bridge deck system. The spring element is used to simulate the axial movable-basin rubber support between the side arch, the column on the arch, and the side pier, and the spring stiffness is consistent with the axial stiffness of the support. The arch bridge model is shown in Figure 2.

The modeling details are summarized in

Table 1. Introduction to modelling details and assumptions used in this study.

Component	Structural Form/Material	Element Type	Assumptions
Arch Rib	CFST lattice sections/concrete and steel	Timoshenko beam	Plane cross-section assumption
Suspender	High-strength steel	Truss element	Only axial forces are transmitted
Bridge Deck	Q345 Steel	Timoshenko beam	Plane cross-section assumption
Star-type and K-type Brace	Q345 Steel	Timoshenko beam	Plane cross-section assumption
Spandrel Column	Q345 Steel	Timoshenko beam	Plane cross-section assumption
Tie Bar	High-strength steel	Truss element	Only axial forces are transmitted

for ease of following the simulation.

The above-established models have been compared with the measured data published in [23]. The measured value of crown displacement of Yajisha Bridge one year after opening to traffic is 0.12 m. The percentage difference between the predicted value and the measured value is as small as 4.1%, which can be seen in Figure 3. The comparison result verifies the accuracy of the established FE model.

2.3. Non-Conservative Force Simulation Approach

A complete bridge deck system and suspender model have been established above, and the non-conservative force effect provided by the suspender unit has been included in the model [11]. In order to analyze the effect of non-conservative forces on the dynamic stability of bridges, it is necessary to establish a comparison model of conservative forces. In the comparison model, the bridge deck covered by the main arch ring and the suspender element are passivated, and only the equivalent vertical force load is added. The amplitude of the external load consists of the gravity term of the bridge deck and the inertial force of the bridge deck caused by an earthquake. The structure and load characteristics are summarized in

Table 2. Introduction to structure and load characteristics of FE models.

Model Name	Structural Form	Initial Additional Load	Object
Original model	Deck systems and suspension units exist	No additional load	Consider the influence of the non-conservative force of the suspender
Comparison model	No deck systems and suspension units	Equivalent self-weight of deck systems and the vertical inertial force of the bridge deck caused by an earthquake	Consider the influence of vertical conservative force

, and the finite element model used for comparison is shown in Figure 4.

3. Analysis of Time-Varying Non-Conservative Forces on Yajisha Bridge

According to the analysis of the arch rib structure, it can be observed that the positions with the highest compressive stress and deflection deformation in an arch bridge are located at its bottom and top, respectively. In large-span arch bridges, the maximum out-of-plane displacement typically occurs in the segment of the arch rib with the greatest free length due to transverse connections. Therefore, investigating the impact of time-varying non-conservative forces on these specific locations holds significant engineering importance.

The influence of non-conservative force on the maximum transverse displacement of the arch rib and the stress–time history curve of the arch foot steel pipe under a Shanghai seismic wave with a peak ground acceleration (PGA) of 0.1 g is illustrated in Figure 5. As depicted in Figure 5a, when considering the non-conservative force of the suspender, most stress values in the time domain are smaller than those obtained under conservative force conditions. In the case of a vertical conservative force, the maximum amplitude of out-of-plane displacement for the arch rib is 2.29 cm, whereas in the case of a non-conservative force model, it is 2.12 cm. The immediate change in non-conservative force does not significantly enhance transverse displacement amplitude at the position of the arch roof due to a reduction in calculated length for a pair of K-supports installed at the top of the arch. These findings demonstrate that under seismic load, non-conservative forces provided by suspenders can partially mitigate out-of-plane deformation development in Yajisha Bridge’s arch rib.

Local analysis is carried out on the arch rib–suspender joint segment and part of the arch foot steel pipe at the lower position facing the arch top. Dimensionless stress $\overline{\sigma }$ and dimensionless displacement $\overline{\omega }$ are introduced. The degree of amplitude change in stress and displacement in the above position is investigated, which is denoted as follows:

$$\begin{array}{cc}\overline{\sigma }={\sigma }_{\mathrm{t}}/{\sigma }_0;& \overline{\omega }={\omega }_{\mathrm{t}}/{\omega }_0\end{array}$$

(1)

where ${\sigma }_t$ and ${\omega }_t$ are the current moment of steel-pipe stress and lateral displacement, respectively, and ${\sigma }_0$ and ${\omega }_0$ are the stress and displacement corresponding to the initial moment, respectively. The fluctuation of dimensionless parameters is shown in Figure 5b, where the horizontal segment at the initial time of the curve represents the transmission process of seismic waves from the base to the arch rib. The analysis results demonstrate that the stress amplitude of the arch foot position exhibits a more pronounced effect when considering non-conservative forces, as compared to neglecting them. This can be attributed to the time-varying impact of suspender forces on the arch rib structure. Similarly, by examining the variation pattern of dimensionless displacement, it is evident that the percentage change in lateral displacement of the arch is greater in absence of non-conservative force effects, indicating that these effects also impose certain limitations on out-of-plane deformation amplitudes.

According to the seismic stability analysis method proposed by Xu et al. [24], load–response curves for two different working conditions are determined, as depicted in Figure 6. Similarly, based on the energy relationship satisfied by dynamic stability, it can be inferred that the structure reaches a critical state of dynamic instability when the peak seismic acceleration reaches 0.166 g under conservative system assumptions. Comparatively, compared with the non-conservative force condition analyzed in the previous chapter, it is observed that the seismic stability performance of the bridge decreases by 12.6%. In other words, employing non-conservative forces on the suspender can enhance to some extent the dynamic stability performance of the arch rib.

The analysis results reveal that the inclusion of deck elements in the non-conservative force model not only amplifies the counterweight of arch ribs but also alters the distribution of stiffness mass within the system. Moreover, the suspender’s non-conservative force introduces a significant out-of-plane inertia force, thereby enhancing overall stability.

By comparing the maximum deformation of the arch rib under two conditions, it is evident that for all PGA conditions, the maximum displacement of the arch roof under non-conservative force conditions is smaller than that under conservative force conditions. Furthermore, as ground motion intensity increases, the disparity in displacement between these two conditions widens, indicating that non-conservative forces restrict structural vibration when subjected to Shanghai seismic waves. In fact, comprehending the intricate influence mechanism of non-conservative forces on spatial deformation of the arch rib necessitates considering not only structural frequency but also seismic wave frequency. Different stiffness ratios and various forms of seismic waves may result in distinct deformation discrepancies, which will be thoroughly discussed in the subsequent analysis.

4. Seismic Stability Performance and Sensitivity Analysis under Different Non-Conservative Force Conditions

The vibration problem of a long-span concrete-filled steel-tube arch bridge can be approximated as the coupling vibration problem of a double-layer structure composed of an arch rib and bridge panel [25]. The vibration characteristics of the system are related to the external load frequency, the natural frequency of the structure, and the connection stiffness between them.

In order to further investigate the impact of non-conservative forces on the long-term dynamic stability performance of CFST arch bridges, this section examines the seismic performance differences under the aforementioned three operational conditions from a structural seismic stability perspective and analyzes the sensitivity of time-varying non-conservative forces on seismic stability performance.

4.1. Seismic Stability of Bridges under Different Superior Frequency Excitations

The vibration equation reveals that the structural vibration characteristics vary with different external excitation frequencies. To investigate the influence of non-conservative forces from suspension cables on the dynamic stability performance of CFST arch bridges under varying vibration frequencies, this section initially selects three distinct seismic waveforms for spectral density analysis: El-Centro wave, Shanghai artificial seismic wave, and Shenzhen seismic wave.

Fourier transform analysis was performed on the time–history curves of the above three kinds of ground motion acceleration, and the obtained power spectral density function was shown in Figure 7.

According to the results of power spectral density analysis, the energy distribution of the primary excitation frequency in Shanghai’s artificial seismic wave falls within the range of 0–100 Hz, indicating a low-frequency vibration characteristic. In comparison, both El-Centro and Shenzhen seismic waves exhibit slower energy attenuation rates, with their dominant frequencies primarily distributed in the range of 0–150 Hz. This frequency distribution is similar to that observed in Shanghai’s seismic wave and represents a middle-to-low-frequency load excitation issue. In summary, it is evident that the energy distribution of seismic waves in Shanghai is predominantly concentrated in the low-frequency range, while the frequency characteristics of El-Centro waves resemble those of Shenzhen seismic waves, with vibration frequencies primarily concentrated in the middle- and low-frequency bands.

To compare the impact of structural non-conservative force effects under different excitation frequency properties, time–history analysis was conducted separately using Shanghai and Shenzhen seismic wave records. The aforementioned seismic waves were compressed along the time axis with a period compression factor of 2.50 s.

The nonlinear dynamic response analysis of Yajisha Bridge under two working conditions, with and without non-conservative force effects, is depicted in Figure 8 under the excitation of Shenzhen seismic waves.

By comparing the results of nonlinear dynamic analysis in Figure 8, it can be observed that, for most operational conditions, the vault displacement considering vertical conservative force is smaller than that considering non-conservative force of the suspender. Moreover, as ground motion intensity increases, the disparity between these two displacements gradually diminishes. However, when PGA is less than 0.1 g, their distinction becomes inconspicuous. These aforementioned phenomena deviate from the distribution pattern depicted by the dynamic analysis curve under Shanghai seismic wave excitation as illustrated in Figure 6. It can be concluded that the limiting deformation effect of the non-conservative force effect on the arch bridge structure is closely related to the frequency distribution range of the main seismic energy. The deformation constraint effect of the non-conservative force effect is prominent in the low-frequency vibration, but the effect provides a poor constraint effect in the seismic condition with higher excellent frequency.

The critical PGA of Yajisha Bridge is 1.003 g and 0.725 g, respectively, under the two conditions of non-conservative force and vertical conservative force. It can be found that the critical acceleration of dynamic instability of the Shenzhen seismic wave is much higher than that of the Shanghai seismic wave. The Shanghai seismic wave belongs to the category of soft-ground seismic waves, characterized by a low superior frequency that closely aligns with the spectrum characteristics of long-span structures. Consequently, these structures exhibit heightened sensitivity to vibration frequencies and experience an amplification effect in their vibration response, which increases the likelihood of overall structural instability. Additionally, Figure 8 illustrates that under seismic wave excitation in Shenzhen, there is a 27.7% difference in critical PGA percentage between the two conditions, surpassing the 12.6% observed under seismic wave excitation in Shanghai. This indicates that as the frequency of excellent seismic excitation increases, non-conservative force effects contribute significantly to enhancing the gain effect on suspender’s seismic stability.

Based on the above analysis, it is evident that in soft soil seismic wave sites, the optimal frequency of seismic waves tends to be lower. Therefore, during the design process, careful consideration should be given to the seismic stability performance of structures. If necessary, damping and isolation devices should be installed at bridge supports and arch foot positions while flexible dampers should also be incorporated into structural designs following a “three-stage” principle to enhance dynamic stability performance.

4.2. Seismic Stability of Bridges under Different Deck-Rib Frequency Ratios

In order to investigate the influence of the disparity in vibration characteristics between the arch rib and bridge deck, this study employed a fixed seismic wave form and selected the Shenzhen seismic wave with similar soil conditions to that of the Yajisha Bridge site for conducting sensitivity analysis on stiffness differences. To account for the variation in vibration characteristics, we introduced a dimensionless analysis parameter called the “deck–rib frequency ratio”, which represents the natural frequency ratio between the bridge deck and arch rib. Five sets of frequency ratios (1:19, 1:22, 1:25, 1:28, and 1:31) were chosen to analyze the impact of these disparities.

Figure 9 shows the distribution of seismic dynamic analysis curves under different deck–rib frequency ratios, where NC in the legend represents non-conservative force and C represents conservative force. From the development trend of the curve, it can be found that the distribution law of the vault displacement of the non-conservative force and the conservative force under different frequency ratios is generally the same. When PGA is less than 0.2 g, there is little difference between the two maximum spatial displacements, and the arch rib displacement in the non-conservative force condition is slightly less than that in the conservative force condition. With the increase in seismic acceleration, the increase rate of arch rib displacement under the non-conservative force condition is gradually greater than that under the conservative force condition, and its displacement is also larger than that under the conservative force condition. This is mainly because the in-plane displacement of arch rib increases faster when considering the non-conservative force operation of the suspender compared with the vertical conservative force condition.

The results of long-term dynamic stability analysis under conservative and non-conservative conditions are summarized in

Table 3. Critical peak ground accelerations with different deck–rib frequency ratios under Shenzhen seismic excitations.

Deck–Rib Frequency Ratios	1:19	1:22	1:25	1:28	1:31
Non-conservative force condition critical PGANC [g]	1.35	1.08	0.96	0.90	0.80
Conservative force condition critical PGAC [g]	0.78	0.75	0.73	0.69	0.66
PGANC/PGAC	1.73	1.44	1.32	1.30	1.21

. By observing the results in the table, it can be found that irrespective of considering the time-varying non-conservative force, an increase in deck stiffness leads to an increase in the critical peak seismic acceleration of the structure. Moreover, when considering the non-conservative force, the critical PGA exceeds that obtained under conservative conditions. This observation reflects that both the non-conservative force provided by the suspender and lateral stiffness offered by the deck significantly enhance the overall seismic performance of arch bridges.

The ratio of critical peak ground acceleration (PGA) under non-conservative force conditions and conservative force conditions directly reflects the impact of non-conservative forces on the overall structural performance. By comparing the critical acceleration ratios for different stiffness levels, it is evident that the contribution of non-conservative forces to dynamic stability is positively correlated with bridge deck system stiffness. Increasing the stiffness of the bridge panel not only enhances seismic stability performance but also amplifies the influence of non-conservative forces on structural stability.

4.3. Sensitivity Analysis of Axial Stiffness of Suspender

The elastic moduli of three commonly used prestressed steel strands were selected as 200 GPa, 300 GPa, and 400 GPa, respectively. An analysis was conducted to investigate the influence of these parameters on the axial stiffness of the suspension element. The corresponding working conditions for each modulus were denoted as DG-0, DG-1, and DG-2 in sequential order. Figure 10 presents the IDA analysis curves under two seismic wave excitation conditions for each working condition.

The figure demonstrates that the maximum displacement of the CFST arch bridge decreases as the Young’s modulus of the suspender increases. When comparing Guangzhou and Shanghai seismic waves, both within a 10% range, the average reduction in displacement is 8.0% and 5.3%, respectively. This reduction in displacement primarily arises from variations in vertical deformation within the bridge deck plane. In conclusion, it can be inferred that the stiffness of the suspender does not significantly impact the maximum displacement of the bridge.

The critical peak ground acceleration (PGA) values for all conditions under two types of seismic action are presented in

Table 4. Critical peak ground accelerations of CFST arch bridges with three different axial stiffnesses of suspenders.

Suspender Conditions	Shenzhen Earthquake Wave			Shanghai Earthquake Wave
	DG-0	DG-1	DG-2	DG-0	DG-1	DG-2
Non-conservative force condition critical PGANC (g)	0.940	0.962	0.988	0.181	0.187	0.194
Conservative force condition critical PGAC (g)	0.732	0.732	0.732	0.166	0.166	0.166
PGANC/PGAC	1.284	1.314	1.350	1.090	1.127	1.169

, based on theoretical analysis. The results indicate that a higher stiffness of the suspender contributes to the seismic stability of the structure; however, there is still a limited increase in PGA. Comparing the two seismic waves, the variation in PGA between adjacent working conditions remains within 5%. From the perspective of structural stiffness distribution, the above phenomenon can be explained as follows: the main function of the hanger component is to assemble the arch rib stiffness matrix and the bridge deck stiffness matrix to form an integrated structure. Compared with the arch rib, wind bracing, bridge deck, and other components, the hanger stiffness contribution is very limited, so changing the hanger stiffness has little effect on the eigenvalue of the overall stiffness matrix. As a result, the impact on its PGA will inevitably not be too great. Therefore, it can be observed that enhancing the stiffness of suspenders does not significantly impact the seismic performance of the structure.

5. Conclusions

Due to the time-varying characteristics of the non-conservative force provided by the suspender under dynamic excitation, the influence of the non-conservative force on the internal force and deformation of the structure is totally different with the static case. In this paper, the mechanism of the non-conservative force effect and the law of the influence of the non-conservative force on the dynamic stability of the structure under seismic excitation are studied. According to the coupled-vibration theory, three kinds of parameters affecting the dynamic characteristics of the structure are determined, which are the seismic wave frequency, the ratio of channel to rib frequency, and the axial stiffness of the suspender. The results of structural response and stability analysis under different working conditions are demonstrated in detail, and the sensitivity analysis of the above parameters is carried out. The results show that the contribution of the non-conservative force to the dynamic stability of the bridge increases as the deck stiffness increases, but it is not sensitive to change in the suspender stiffness. The excellent frequency of seismic waves has a significant effect on the dynamic stability of the CFST arch bridges. For the site condition with low excellent frequency of seismic waves, the seismic design should be strengthened for the seismic stability of structures.