Cable-stayed bridges, recognized for their substantial spanning capacity and adaptability to diverse topographical conditions, represent one of the primary structural types for long-span bridges [1–3]. With rapid economic development, the demand for crossing large rivers and valleys has driven significant advancements in cable-stayed bridge technology, leading to the construction of numerous super-long-span cable-stayed bridges [4–6]. However, as the length of the bridge increases, the impact of certain disasters or accidents, such as earthquakes, typhoons, and ship collisions, on the bridge will significantly increase [7–9]. For cable systems, failures caused by factors such as fatigue and corrosion also impose higher demands on bridge constructors [10–12]. This requires us to further ensure the safety and rationality of the overall structural design of the bridge.

A cable-stayed bridge primarily consists of three components: the girder, towers, and stay cables. Mechanically, the main girders are subjected to combined bending moments and axial forces. For spans exceeding 600 m, steel truss girders or steel box girders are predominantly employed. Long-span steel box girder cable-stayed bridges are highly statically indeterminate structures [13], offering advantages such as long spans, lightweight yet high strength, and construction efficiency [14–16]. Furthermore, they demonstrate superior performance in service life, construction speed, maintenance management, and economic efficiency [17,18]. The towers, functioning primarily in compression, are typically constructed from concrete to utilize its high compressive strength, substantial stiffness, and cost-effectiveness [19,20]. The girder sections often utilize closed steel box designs, while the tower sections are generally made of concrete box structures. Stay cables commonly consist of parallel high-strength steel wires or strands [21–23]. During bridge construction and service, variable actions such as vehicle loads, wind loads, and thermal effects must be comprehensively considered, as these constitute critical load cases in bridge design [24–26].

Extensive research has been conducted on the static and dynamic characteristics of cable-stayed bridges. Hiroshi et al. [27] applied the updated Lagrangian formulation and discretized the towers using closed box sections, analyzing the ultimate bearing capacity during construction and service stages by considering material nonlinearity while neglecting shear deformation. Qiu et al. [28] investigated static and dynamic behavior of a cable-stayed bridge with main span of 1800 m, examining the influence of parameters such as the rise-span ratio, the suspension-to-span ratio, the constraint condition of the stiffened girder, the number of auxiliary piers at side spans, the layout of suspension cables, and the elastic modulus of suspension cables. To reduce the internal stresses in the bridge towers and main girders, cable-stayed bridges employ floating or semi-floating systems. However, this results in insufficient longitudinal restraint of the main girders, necessitating the use of devices such as isolation bearings or elastic restraints to limit longitudinal displacement. Xu et al. proposed a novel vibration control system to constrain the longitudinal displacement of the levitation system based on the traditional tuned viscous mass damper and negative stiffness amplifying damper [29].

This paper systematically studies the static and dynamic structural performance of the Huangmaohai Bridge, focusing on optimizing the comprehensive system for the distribution of internal forces within the bridge, thereby ensuring more reasonable stress during service and enhancing the bridge’s resistance under seismic effects. A finite element model is established to analyze structural stiffness, bearing internal forces, and stresses in the main girder and stay cables under various service conditions. Furthermore, dynamic characteristics and seismic responses are examined, comparing the internal forces and displacement responses of the towers in the baseline model and the comprehensive model under E1 and E2 seismic events. This research provides valuable technical references for the design and seismic optimization of similar super-long-span cable-stayed bridges.

In the section on research gaps and contributions, this research confirms that the static performance of the Huangmaohai Bridge meets the code requirements and demonstrates the structural rationality. It also shows that the integrated structural system significantly enhances seismic performance, providing a viable seismic resistance strategy for long-span cable-stayed bridges. However, the finite element model used in this research simplifies the boundary and damping conditions, which require further investigation. Additionally, the performance of the integrated structural system under other types of disasters needs to be further validated.

The Huangmaohai extra-long-span three-tower cable-stayed bridge is recognized as the largest span bridge of its type both domestically and internationally, and is characterized by its innovative structural design. The structure is configured with single-column towers, separated steel box girders, and a spatial cable system with dual cable planes, while high aesthetic requirements are also imposed. The variable-cross-section and irregular tower shapes result in complex structural forces and significant construction challenges. The Huangmaohai Bridge is designed with a span arrangement of 100 + 280 + 2 × 720 + 280 + 100 m as a steel box girder cable-stayed bridge. The main girder is composed of two separate steel boxes connected by transverse cross girders. Parallel wire cables are employed, and vibration dampers are installed on the stay cables. The towers are constructed as concrete single-column structures. The pile caps are designed with circular shapes, while the transition piers and auxiliary piers are configured as full-width T-shaped sections. A rendering of the completed bridge is shown in Fig. 1. Key design issues are addressed through systematic and structural innovations aimed at enhancing the vertical stiffness of the main girder, optimizing thermal stress distribution, achieving superior overall bridge performance, and ensuring economic efficiency in component dimensions.

This study systematically investigates the static and dynamic structural behavior of the Huangmao Sea Bridge through refined finite element modeling. It explores the contributions of critical structural components, including the elastic restraints of the central tower, the dampers of the side towers, and the transverse seismic isolation system, in structural modeling and response analysis. The findings contribute to innovative approaches in seismic design and structural optimization of long-span sea-crossing bridges. The main conclusions are summarized as follows:

(1) The static performance is verified to satisfy code requirements. Under static load combinations, the maximum stress in the main girder is controlled at 222 MPa, which remains below the design strength of Q345 steel. The vertical deflection-to-span ratio is determined as 1/426, confirming adequate stiffness compliance. The safety factors for stay cables and auxiliary cables exceed 2.7 and 3.5 respectively, demonstrating that the overall structure is confirmed to be within the safe range. These results not only validate the structural design but also provide a refined reference for the static performance evaluation of long-span sea-crossing bridges with similar configurations.

(2) The comprehensive structural system is demonstrated to significantly improve seismic performance. Compared with the benchmark model, the internal forces at critical tower sections are generally reduced under both E1 and E2 seismic events. Under longitudinal-vertical seismic excitation, bending moment reductions of 23%–54% are achieved at key sections of both side and central towers. Under transverse-vertical excitation, the bending moments at tower bases are reduced by 20% and 30% for side and central towers respectively, demonstrating effective seismic mitigation. These results highlight the effectiveness of the proposed system in mitigating seismic impacts and offer valuable insights for the seismic optimization of long-span cable-stayed bridges.

(3) Significant displacement control is achieved through the integrated structural measures. Under longitudinal-vertical seismic excitation, the end displacements of the main girder are reduced by approximately 20% in the comprehensive model, with similar reductions observed at the tops of the towers. The overall structural displacement response is effectively suppressed, demonstrating the effectiveness of the implemented damping and restraint systems. These findings validate the proposed control strategy and offer practical guidance for enhancing the seismic resilience of long-span bridges.

While this study provides valuable insights into the seismic performance of long-span sea-crossing cable-stayed bridges, certain shortcomings remain. For instance, the current analysis focuses primarily on the structural response under idealized boundary conditions and simplified damping models. This research lays the groundwork for future research. Subsequent studies will focus on the development of key energy dissipation and restraint devices tailored for multi-tower, ultra-long-span sea-crossing cable-stayed bridges, as well as the investigation of critical parameters influencing energy dissipation and restraint strategies. These efforts aim to further enhance the seismic resilience and design precision of complex bridge systems.