A networked suspension cable arch bridge is a type of truss arch bridge system where at least two inclined suspension cables intersect, replacing the traditional vertical suspension cables. The cross-arranged networked suspension cables can effectively enhance the vertical stiffness and overall mechanical performance of traditional arch bridges, which has attracted attention in the field of bridge engineering. However, with the increasing span of arch bridges and the widespread use of thin-walled steel structures, structural stability issues have become more prominent. In particular, the risk of instability in steel arch ribs, which are primarily under compression, has become a key factor limiting its engineering application. To systematically analyze the stability performance of a networked suspension cable arch bridge and to explore the impact of different structural arrangement parameters on the overall stability of the structure, this study comprehensively considered geometric nonlinearity, material nonlinearity, and structural initial defects. A parametric spatial bar finite element model was established using nonlinear finite element methods to analyze the effects of varying cable tension forces on the overall stability. The displacement response and nonlinear instability critical load of key nodes on the arch ribs under load were calculated. The results from national and international standards were compared with those obtained using nonlinear finite element methods. Additionally, the study investigated the influence of different rise-to-span ratios, arch rib inclination angles, and cable inclination angles on the stability of the networked suspension cable arch bridge. Results show that variations in the suspension cable tension have little impact on the overall stability of the networked suspension cable arch bridge. The ultimate capacity of arch ribs based on standard methods is more conservative than that obtained through the nonlinear finite element method. The lateral overall stability of network arch bridges improves with increasing rise-to-span ratio and arch rib inclination, while it first increases and then decreases with the increase in cable inclination angle. The lateral stability performance of the bridge is optimal when the cable inclination angle is set between 50° and 60°.

To accommodate the alignment of approach roads on both banks, some long-span cable-stayed bridges with plate-truss composite girders adopt a laterally asymmetric lane arrangement. However, eccentric loading induces significant torsional effects in the main girder, which traditional cable force optimization methods struggle to account for effectively. To mitigate the adverse effects caused by lateral asymmetry, this paper proposes a stepwise optimization strategy for the finished bridge cable forces considering lateral asymmetry, based on the decoupling characteristics of vertical bending and lateral bending-torsion coupling in left-right symmetric cross-sections. Firstly, an equivalent single-beam model is established under the condition of consistent bending and torsional stiffness to facilitate cable force optimization analysis. The displacement response error between the simplified equivalent model and the refined model is within 6%. Subsequently, a stepwise cable force optimization procedure is proposed, consisting of two stages: average cable force optimization and cable force difference optimization. The first stage aims to minimize the bending strain energy to determine a reasonable distribution of average cable forces, while the second stage adjusts the cable force difference between the two sides to counteract the eccentric torque induced by the self-weight of the main girder. To reduce the variable dimensionality, B-spline curves are employed to replace the original dense cable force variables, with the control points of the spline curves serving as optimization variables. A gradient-based algorithm is used for solution. The results demonstrate that cable force difference optimization effectively balances the eccentric torque caused by the girder self-weight and significantly reduces the torsional angle of the main girder, thereby enabling the bridge to achieve the desired reasonable internal force state and configuration. Moreover, the stepwise optimization strategy significantly reduces computational cost through problem decoupling and dimensionality reduction, reducing the number of finite element analyses by approximately one-third while maintaining optimization accuracy and convergence stability.