Elastoplastic dynamic instability criteria of Chang Qing CFST truss arch bridge

Abstract

This research has focused on Chang Qing concrete-filled steel tube (CFST) truss arch bridge, addressing potential elastoplastic dynamic instability issues due to the replacement of hangers and deck system during maintenance. An energy conversion criterion was first proposed based on discrete Lyapunov functional. The vibration responses, energy conversion patterns, and plastic deformation characteristics of truss arch bridges under different load-release conditions (1/4 g, 1/2 g, and 1 g) were studied through finite element analysis. The obtained results indicated that under a load release of 1/4 g, the system presented stable periodic energy conversion (alternating decay of kinetic and strain energy), with the absolute Lyapunov exponent value of less than 1, proving the dynamic stability of the structure. With the increase of load release to 1/2 g, energy conversion process exhibited abrupt changes, with plastic hinges forming in arch ribs and diagonal braces, which resulted in asymmetric degradation of structural stiffness. Lyapunov exponent diverged and the system entered a nonlinear dynamic instability state. Complete release of gravity load resulted in asymmetric distribution of plastic hinges along both sides of the truss arches, compete interruption of energy conversion, and significant vibration amplitudes of Poincaré section, giving rise to loss of load-bearing capacity. This research revealed the effectiveness of discrete Lyapunov function in exploring dynamic stability, providing a theoretical basis for safety control in the engineering of bridge maintenance.

Introduction

Concrete-filled steel tube (CFST) arches have been extensively applied due to their numerous advantages including large span capability, high load-bearing capacity, and rapid construction, making them great candidates as critical load-bearing components for long-span railways, highways, and municipal arch bridges. From the completion date of the 115-m-span Cang Wang bridge in Sichuan in 1990 to 575-m-span Pingnan third bridge in Guangxi in 2020, China has constructed more than 395 CFST truss arch bridges. ¹ However, during this rapid development period, several defects have been reported in CFST arches. ² Extensive engineering practices have revealed that these defects could decrease the safety and serviceability of these structural systems. After 30 years of operation, many CFST truss arch bridges face maintenance and repair challenges. ³

In order to decrease thermal and bearing stresses, old CFST arch bridges, such as Chang Qing bridge in Shenyang city, adopted suspended systems. In this design, CFST truss arch bridge deck system lacked longitudinal girders; instead, crossbeams were suspended directly from arch nodes using hangers. However, with further application of such systems, it was found that these bridges did not have sufficient lateral stiffness, which resulted in the generation of out-of-plane vibrations. To solve this problem, longitudinal girders were added to transform truss arches from hingeless arch systems into tension systems. ⁴ This modification enhanced bridge overall lateral stiffness by increasing deck system connection rigidity. ⁵

Following long-term bridge service, components such as hangers and deck systems, which were directly exposed to dynamic loads, required removal and replacement once they reached their service life. During replacement processes, truss arches could release the strain energy stored due to bridge dead load, causing them to enter dynamic vibration states. However, this could pose dynamic instability risk. Therefore, it is essential to conduct elastoplastic dynamic stability analyses of truss arches during the maintenance processes of replacing hangers and deck systems to ensure bridge construction safety. ⁶

The first type of static stability problems in arches arouse when equilibrium state bifurcated, resulting in the disturbance of the stability of the original equilibrium state and transition to a new equilibrium state. This process included in-plane and out-of-plane buckling. ⁷ Like Euler critical load for centrally compressed columns, mathematical solution of the first type of stability problem for arches involved solving the eigenvalue problems of elastic equilibrium differential equations for each arch micro-element under internal and external forces. ⁸ During solving process, the geometric boundary conditions of homogeneous equations were derived based on geometric relationships and arch deflection curve deformation, while internal force-deformation relationships were established by constitutive equations based on the physical relationships between internal forces and deformation. ⁹

The second type of arch static stability was a nonlinear plastic analysis problem, similar to second-order elastoplastic buckling of eccentrically compressed columns with P-Δ influences. It resulted from simultaneous action of material and geometric nonlinearities. ¹⁰ The spatial equilibrium equations of the arch were established by introducing a local coordinate system for the arch into the elastic equilibrium differential equations. Due to the above-mentioned nonlinear characteristics, Newton–Raphson iterative method was applied to solve these equations.

Due to the large span and high load-bearing capacity of CFST truss arches, conventional structural laboratories are unable to conduct full-scale structural experiments and can only perform scaled model tests, supplemented by numerical analysis methods to verify the stability theories of various CFST truss arches.^11,12 Additionally, in-situ testing experiments are challenging to conduct during large deformations or even failure stages, and can only analyze the elastic stage. ¹ Partial model-based damage identification was employed to evaluate the stability of a long-span steel truss bridge (New Yellow River Bridge), while the stiffness separation method was utilized to reduce the computational time associated with damage identification in the bridge. ¹³

Unlike static stability, a clear concept had not been established for dynamic stability criteria. Instead, D’Alembert inertial force was introduced based on the elastic equilibrium equations of the planar deflection curves of arches and the linear equations of simple harmonic motion were applied to obtain fundamental equations for the natural vibrations of arch planar deflection. ¹⁴

Truss arch static stability analysis involved first equivalent truss stiffness to that of a single arch, followed by applying the aforementioned equilibrium equations to analyze single-arch stability. Generally, stiffness equivalent methods are applied: for Warren trusses, the weighted product of chord cross-sectional area and modulus is commonly applied as the computational stiffness of the truss, while for Pratt trusses, the weighted product of the first moment of chord cross-section and modulus is employed as computational stiffness. For dynamic instability due to cable rupture in high-potential-energy truss arches, dynamic relaxation method could be applied to derive dynamic equilibrium equations, which could then be solved through central difference methods.^15,16 Regarding large-scale deployable truss arches in aerospace applications under thermal excitations, various approaches such as L-chain transfer, center manifold, and feedback shape control methods could be combined with Routh–Hurwitz criterion to explore dynamic stability.^17–21

Existing theories on arch static stability generally rely on differential equations of elastic equilibrium and under homogeneity and elasticity assumptions, analytical solutions to the equations could be obtained. However, when considering geometric or material nonlinearities, analytical solutions are no longer obtainable. The concept of arch dynamic stability analysis is not well-defined and introduces inertial forces and assumes simple harmonic motion when deriving vibration solutions, but fails to obtain clear instability criteria. Therefore, the existing arch stability theories cannot take into account nonlinearities, let alone non-uniform stiffness. ²² To analyze truss arch large-deformation dynamic stability, the assumptions of elastic deformation theory for differential equations no longer hold. Furthermore, truss arch non-uniform stiffness characteristics invalidate the requirement for constant stiffness in equilibrium equations. ²³

A discrete Lyapunov functional was proposed since a critical theorem analogous to Euler’s cannot be established for truss arches. This method utilized a multi-scale numerical analysis platform to provide parametric variables, making it possible to establish elastoplastic dynamic instability criteria.^24,25

Due to the inherent geometric nonlinearity of the spatial structures of truss arches, material nonlinearities of members and nodes, and nonlinear properties of boundary conditions such as earthquake, wind, vehicle load, blood pressure, and thermal shock, both model experiments and theoretical calculations for arch stability based on elastic equilibrium were significantly limited. ²⁶ On the other hand, numerical algorithms such as finite difference method (FDM) and finite element method (FEM) can discretize nonlinear space into linear subspaces. By incorporating nonlinear constitutive equations, such as elastoplastic material models, and using multi-field coupling calculation methods, these methods possessed inherent advantages in solving truss arch dynamic stability problems.^27,28

Researchers had developed several finite element software packages and computational programs, including vehicle bridge interaction program based on ANSYS, which could be integrated with multi-body dynamics software such as UM to significantly enhance computational efficiency. For vehicle–bridge coupled vibration problems, vehicle and bridge can be divided into two separate subsystems and vibration equations for each subsystem can be derived separately. Then, cyclic coupling analysis can be performed. ²⁹ Research has revealed that bridge deck irregularities had significant effects on arch bridge dynamic responses. Improving bridge deck maintenance could decrease vehicle–bridge coupled vibration responses and extend bridge service life. ³⁰

Analyzing truss arch instability process showed that instability started with the failure of non-uniform materials, decreasing structural component stiffness, in turn causing overall instability in truss arches. This process presented the following cross-scale evolution characteristics: non-uniform materials -> component stiffness softening -> truss arch system dynamic instability. During this evolution, periodic conversions of strain energy (SE) and kinetic energy (KE) in the truss system was attributed to dynamic stability. Hence, a mathematical model for truss arch elastoplastic dynamic instability criterion was developed based on discrete Lyapunov functional. Using Python to drive ABAQUS, a truss arch bridge numerical analysis model was developed to provide computational parameters for the mathematical model.^31,32 This ultimately allowed to determine elastoplastic dynamic stability of CFST truss arches.

Overview and dynamic testing results of Chang Qing bridge

Shenyang Chang Qing CFST arch bridge (Figure 1) was constructed in 1997. It is a three-span half-through truss arch bridge with main span of 148 m. The main arch of the bridge is consisted of four spiral-welded Q345 steel tubes, each with wall thickness of 10 mm and diameter of 700 mm, forming the ribs of truss arch. A horizontal bracing is installed at arch crown, with K-bracings on both sides. Horizontal bracing and main arch are filled with C50 concrete. It is noteworthy that pump-lifting construction techniques and self-compacting concrete were not employed during construction.

Figure 1.

Chang Qing bridge.

An out-of-plane displacement of 0.7 m was measured at the crown after truss arch closure. An inspection in 2019 revealed cracks in the columns near the hangers on both crown sides. Dynamic testing of the entire bridge presented the following modal properties:

The first vertical bending mode (antisymmetric vertical bending) had a damping ratio of 1.212% and a frequency of 0.84 Hz while the second vertical bending mode (symmetric vertical bending) had a damping ratio of 0.979% and a frequency of 1.16 Hz. Also, the first torsional mode had a damping ratio of 1.152% and a frequency of 1.58 Hz.

Construction and service inspection data revealed that truss arch dynamic stability was essential to ensure safe bridge operation. Therefore, the following research was performed to investigate truss arch dynamic stability.

Dynamic instability critical state of CFST truss arch bridge

Since the dead and live loads of the bridge were transmitted to truss arch through hangers, truss arch stored high SE, placing it at the bottom of a high SE potential well and reaching a critical stable state. When the deck system or hangers were removed, truss arch SE oscillated at the bottom of the potential well. Based on the law of conservation of mechanical energy in the system, the minimum free energy of each component $U_r$ was obtained as follows:

$U_r={KE}_r-{SE}_r+W_r$

(1)

$W_r$ was the work done by external forces on a rod. Truss arch free energy ( $U_{truss}$ ) was obtained by summing the mechanical energy of each component in the spatial and temporal domains as:

$U_{truss}=\sum U_r$

(2)

Although equation (2) was conceptually clear, it could not be directly solved due to the complexity of truss arch spatial structure. Therefore, Lyapunov functional was applied for analysis. Instead of directly solving the differential equations, their convergence was evaluated.

Asymptotic solution $x\left(t,x_0\right)={\mathrm{e}}^{\mathbf{A}t}{x}_0$ of linear differential equations $\dot{x}=\mathbf{A}x$ plays a key role in algebraic methods for the determination of dynamic system stability. ³³ A system of linearly independent differential equations could be solved by coefficient matrix, which in turn could be directly solved through linear algebra. If the eigenvectors and eigenvalues of matrix “A” were known, an explicit solution could be obtained for the differential equations. The real part of Jordan matrix was primarily applied to solve differential equations. Also, the real part of eigenvalue, λ, determined solution exponential growth characteristics, which could be described using Lyapunov exponent λ and its corresponding Lyapunov subspace $L\left(\lambda \right)$ . ³⁴

λ is commonly applied to characterize systems evolving over time. Considering $x\left(·,x_0\right)$ as the solution to the linear differential equation $\dot{x}=\mathbf{A}x$ .

$\lambda \left(x_0,A\right)=\lim \hspace{0.17em}{\sup }_{t\to \infty }\frac{1}{t}\log \Vert x\left(t,x_0\right)\Vert$

(3)

Substituting $x\left(t,x_0\right)={\mathrm{e}}^{At}{x}_0$ into equation (3) gave

$\underset{t\to \pm \infty }{\lim }\frac{1}{t}\log \left|{\mathrm{e}}^{\lambda t}{x}_0\right|=\underset{t\to \pm \infty }{\lim }\frac{1}{t}\log \left({\mathrm{e}}^{\lambda t}\right)+\underset{t\to \pm \infty }{\lim }\frac{1}{t}\log \left(x_0\right)=\lambda$

(4)

where (−λ) is the Lyapunov exponent of the equation $\dot{x}=-$ λx. Equation (4) could be applied to solve Lyapunov functional in both discrete-time sequences and continuous-time systems.

$\underset{n\to \pm \infty }{\lim }\frac{1}{t}\log \left|{\lambda }^n{x}_0\right|=\underset{n\to \pm \infty }{\lim }\frac{1}{n}\log \left({\left|\lambda \right|}^n\right)+\underset{n\to \pm \infty }{\lim }\frac{1}{n}\log \left|x_0\right|=\left|\lambda \right|$

(5)

Model validation

For the verification of dynamic instability critical state in CFST truss arches, Lyapunov exponents about SE-KE conversions were incorporated into CFST truss arch bridge FEM models. This integration facilitated the derivation of the fundamental physical equations required for dynamic stability analysis in truss arches. Specific analysis covered the following aspects.

General conditions of FEM analysis

ABAQUS software was applied for FEM analyses. Chang Qing CFST truss arch bridge model was constructed by Python-driven program of Truss_ABAQUS_Py (developed by our research team). Simulation of trusses was performed using 2-node linear beam elements in space (B31). To avoid element singularity impacts, element size was set at 10 mm. This discretization technique ensured uniform model number, thereby enhancing computational efficiency.

To accommodate the vast number of CFST truss arch members, CFSTs were treated as singular entities and the relationship between average stress and longitudinal strain was derived, as illustrated in Figure 2. ³⁵ Curves were constructed by four sections. In the curves, point “d” represents CFST member tensile ultimate strength ( $f_{sc}^t$ ), “d-a” segment denotes elastic deformation stage, and point “a” marks the end of elastic stage and represents composite proportional limit ( $f_{sc}^p$ ), when CFST is exposed to axial compression. At this point, steel tube equivalent stress reached steel material proportional limit. Furthermore, “a-b” segment represents plastic development stage, point “b” marks composite yield point, and $f_{sc}^y$ is the standard value of CFST composite compressive strength. A parabolic relationship was observed between $f_{sc}^y/f_{ck}$ and confinement coefficient ( $\xi =\alpha f_y/f_{ck}$ ), where $\alpha =A_s/A_c$ is steel content ratio, $A_s$ and $A_c$ are steel tube and concrete column cross-sectional areas, respectively, and $f_{ck}$ is the standard value of concrete compressive strength.

$f_{sc}^y=\left(1.212+B\xi +C{\xi }^2\right)f_{ck}$

(6)

where the coefficients “B” and “C” reflect the roles of steel tube and concrete, respectively.

$\begin{array}{l}B=0.1759f_y/235+0.974\\ C=-0.1038f_{ck}/20+0.0309\end{array}\}$

(7)

Figure 2.

CFST stress–strain relationship.

The analysis showed that $f_{sc}^p$ and corresponding combined proportional strain ${\epsilon }_{sc}^p$ were basically related to steel yield point $f_y$ , but almost independent from concrete strength and steel content ratio. Based on statistical analyses, the following equation was derived.

$\begin{array}{l}{f}_{sc}^p=\left(0.192f_y/235+0.488\right)f_{sc}^y\\ {\epsilon }_{sc}^p=0.67f_y/E_s\end{array}\}$

(8)

“b-c” segment represents strengthening stage, which basically followed the linear relationship described as:

$E_{sc}^{\prime }=\{\begin{array}{l}5000\alpha +550\left(\xi \ge 0.96\right)\\ 400\xi -150\left(\xi <0.96\right)\end{array}$

(9)

Table 1 summarizes the key material parameters.

Table 1.

Material parameters.

α	ξ	E s MPa	f y MPa	E c MPa	f ck MPa	E sc MPa	E sc ’ MPa	f sc y MPa	f sc p MPa
0.061	0.42	2.1E5	345	3.5E4	50	5.9E4	17.1	84.3	64.9

FE analysis results

Since Chang Qing Bridge has been in service for 30 years, it is essential to replace components such as cross beams, hangers, and deck pavement. If all aforementioned components were replaced at once, construction speed would be increased, traffic closure time would be shortened, and social and economic benefits would be enhanced. However, this approach might result in instantaneous release of the strain energy stored within CFST truss arch, posing a dynamic instability risk to truss arch. Therefore, this research explored the sequence of scientifically and rationally replacing components to maintain CFST truss arch stability. Firstly, the initial stress of the main arch of Chang Qing Bridge before component replacement was calculated, as illustrated in Figure 3.

Figure 3.

Initial stress state of CFST truss arch.

Mises stress distribution within CFST truss arch members was generally uniform. The maximum stress value of 38.71 MPa occurred in the upper rib at arch top, while the corresponding stress in the lower rib was 22.58 MPa. All stress values in other members were less than 10 MPa. Compared to the parameters given in Table 1, truss arch was in an elastic stress state under these conditions. In order to analyze the impact of initial stress release caused by maintenance activities such as replacing hangers, updating the bridge deck system, and replacing cross beams on the dynamic stability of the bridge, the following analysis will involve the instantaneous removal of 1/4, 1/2, and 1 gravity, respectively.

Release of 1/4 gravity induced free vibration in truss arch. The time history SE to KE conversion is illustrated in Figure 4. The SE and KE of the truss arch underwent periodic conversions at a constant frequency, demonstrating the full capacity of the structure for energy transformation. This phenomenon confirmed that truss arch operated within its elastic working state.

Figure 4.

Release of 1/4 gravity: time history of truss arch SE and KE conversion.

Based on discrete Lyapunov functional equation (5), Lyapunov exponent was defined as the normal of the difference between SE and KE at the cross-section of each time series, where buckling deformation SE and truss arch KE undergo periodic transformations.

$\lambda =\frac{1}{n}{\displaystyle \sum }_{i=1}^n\log \frac{\left|{KE}_i^{peak}-{SE}_i^{peak}\right|}{\left|{KE}_0^{peak}-{SE}_0^{peak}\right|}$

(10)

As shown in Figure 4, the variable “i” in equation (10) represents the i-th half cycle intercept of the energy conversion time curve. ${KE}_i^{peak}$ and ${SE}_i^{peak}$ represent the peak values of strain energy and kinetic energy at the i-th half cycle intercept, while ${KE}_0^{peak}$ and ${SE}_0^{peak}$ represent the strain energy and kinetic energy under initial conditions, respectively. The parameter $\left|\lambda \right|<1$ , which corresponds to equation (5), and converges to a bounded value according to probability 1. The physical significance of this is that the SE and KE of the CFST truss arch are considered as a random process during the conversion. As the number of conversions “n” increases, the difference between ${KE}_i^{peak}$ and ${SE}_i^{peak}$ gradually decreases compared to the initial difference between ${KE}_0^{peak}$ and ${SE}_0^{peak}$ , indicating that this random process is in a steady state. ³⁶

The calculated values of λ by equation (6) are given in Table 2. λ remained within an absolute value of less than 1 and exhibited a steady-state reducing trend after i > 3, which indicated that truss arch structure demonstrated a convergent vibration process with dynamically stable properties. From Table 2, it can be seen that the energy conversion period is approximately 0.23 s. Based on this, during the maintenance process, accelerometers can be arranged along the arch axis to collect the acceleration response of the bridge under natural or vehicle-induced excitation. By applying integral transformation, the velocity response of the truss arch can be obtained, leading to the derivation of the KE-SE conversion curve of the truss arch, and the calculation of the Lyapunov exponents.

Table 2.

Lyapunov exponent of truss arches energy conversion λ.

	1/4 g		1/2 g		1 g
I	λi	Time	λi	Time	λi	Time
1	−0.396	0.118	−0.416	0.118	−0.9534	0.127
2	−0.803	0.225	−1.130	0.200	−1.3168	0.222
3	−0.989	0.321	−1.972	0.260	−1.2145	0.349
4	−0.991	0.433	−1.802	0.320
5	−0.783	0.557	−1.639	0.445
6	−0.688	0.678	−1.671	0.569
7	−0.651	0.792	−1.590	0.683
8	−0.686	0.887	−1.688	0.779
9	−0.697	0.979	−1.571	0.865
10	−0.673	1.088	−1.5159	0.974

At i = 5, truss arch KE reached its maximum. Figure 5 shows velocity distribution, which exhibited central symmetry among all members with peak value of 152.6 mm/s in K-brace which was substantially decreased elsewhere.

Figure 5.

Release of 1/4 gravity: i = 5 truss arch velocity.

Lateral and vertical amplitudes corresponding velocities at upper rib intersection nodes on the exterior side of arch crown with vertical columns were adopted to construct Poincaré sections, as illustrated in Figure 6. The sections clearly revealed the presence of strange attractors due to the dissipation existing in truss arch systems. Lateral amplitude U1 was 6 mm with 60 mm/s vibration velocity, while vertical vibration amplitude U3 and velocity were 25 mm and 220 mm/s, respectively.

Figure 6.

Release of 1/4 gravity: Poincaré sections of arch top node: (a) lateral amplitude U1 and (b) vertical amplitude U3.

Free vibration induced by the release of 1/2 gravity in truss arch. The time history of SE to KE conversion is illustrated in Figure 7. Continuous energy conversion between KE and SE failed to persist in this state. At i = 3, a discontinuous transition between KE and SE was emerged, accompanied by distinct dynamic characteristics shown in truss arch velocity contour plot (Figure 8). It is noteworthy that plastic hinges developed in the upper and lower rib members on one side of the arch, giving rise to subsequent stiffness loss. In addition, the periodic pattern of KE to SE conversion revealed increasing irregularity, indicating the onset of dynamic instability in truss arch system when i > 3.

Figure 7.

Release of 1/2 gravity: time history of truss arch SE and KE conversion.

Figure 8.

Release of 1/2 gravity: i = 3 truss arch velocity.

Figure 9 illustrates Poincaré sections corresponding to the node similar to those presented in Figure 7. In this state, emergence of plastic hinges triggered the loss of load-bearing capacity in certain truss arch members, resulting in asymmetric degradation of truss arch stiffness. Hence, neither the lateral nor the vertical vibrational amplitudes of the truss arch presented chaotic attractors which resembled characteristic strange attractors. The lateral amplitude U1 was in the range of −150 to 110 mm with vibration velocity range of −1100 to 1000 mm/s, while vertical vibration amplitude U3 and velocity were in the ranges of −120 to +130 mm and −800 to +600 mm/s, respectively.

Figure 9.

Release of 1/2 gravity: Poincaré sections of arch top node: (a) lateral amplitude U1 and (b) vertical amplitude U3.

Free vibration in a truss arch resulting from the release of strain energy caused by gravitational potential energy. The time history of SE to KE conversion is illustrated in Figure 10.

Figure 10.

Release of 1 gravity: time history of truss arch SE and KE conversion.

Similar to Figure 7, continuous energy conversion between KE and SE failed to persist in this state. Figure 11 shows the plastic hinges developed in the two sides of the arch. However, the positions of plastic hinges presented geometric asymmetry, characterized by rib members arranged on one side and diagonal braces positioned on the opposite side. This spatial non-uniformity induced asymmetric stiffness distribution within the truss arch system, demonstrating differential load-transfer mechanisms across its cross-section.

Figure 11.

Release of 1 gravity: i = 3 truss arch velocity.

Poincaré sections at identical locations further revealed asymmetric vibrational properties between lateral and vertical directions. Furthermore, a significant amplification was observed in vibration magnitude, indicating pronounced nonlinear dynamic responses within the system (Figure 12).

Figure 12.

Release of 1 gravity: Poincaré sections of arch top node: (a) lateral amplitude U1 and (b) vertical amplitude U3.

The above analysis focuses on the vibration analysis of bridges caused by the one-time release of strain energy in truss arches. During actual maintenance, the presence of vehicles and other loads is unavoidable. Therefore, loads such as vehicles can be treated as mass blocks coupled with the bridge structure to obtain the initial strain energy of the bridge, which can then be released proportionally, allowing vehicle dynamics to interact with the load-release instability mechanism. Related content will be continuously refined in subsequent research.

Conclusions

In this study, a Lyapunov function–based dynamic stability criterion on energy conversion conservation was developed for CFST truss arches. Assuming critical state for dynamic stability in CFST truss arches, FEM revealed effective conversion between SE and KE. The vibration energy half-cycle attenuation rate of the system, denoted as λ, should be defined. In addition, in this research, a novel theoretical framework and quantitative criteria was developed to ensure the structural safety of CFST truss arch bridges during maintenance, which is of great significance for extending their service life. The main findings of this research are summarized as follows:

(1) CFST truss arch dynamic instability was triggered by abnormal energy conversion, demonstrated as inability to sustain periodic conversions between KE and SE. When load exceeded a critical threshold (e.g., 1/2 g), localized components (such as arch ribs and diagonal braces) entered plastic phase, forming asymmetric plastic hinges that induced abrupt degradation in the stiffness of the system.

(2) By the calculation of Lyapunov exponent during energy conversion, the dynamic stability of the structure could be effectively identified: If the absolute value of the exponent converged and remained below 1, the system was in a stable state. If the value of the exponent diverged with alternating sign changes, the system was transited to an unstable state. FEM analysis demonstrated that under a 1/4 g load, λ exhibited stable attenuation, while after a 1/2 g load, λ rapidly diverged, validating criterion applicability.

(3) Replacement of bridge components during maintenance was essential to avoid abrupt release of excessive SE. Formation of plastic hinges (for example, in arch ribs) was closely related to load distribution, necessitating targeted reinforcement of vulnerable zones. Numerical simulations confirmed that FEM integrated with discrete Lyapunov theory served as an effective tool to predict dynamic instability, providing valuable reference for safety assessments in similar bridges.