A robust implicit dynamic analysis procedure based on the equivalent-node secant properties was developed by Lee et al. [1,2]. A highway tied-arch bridge collapsed in Taiwan in 2019. According to the investigation report, the main reasons for the collapse are the corrosion of the cable anchorage and the overweight truck. In this study, the robust procedure is extended to reproduce the progressive failure of the bridge, taking into account material deterioration and moving loads. In the simulation of the progressive loss of prestress and cable rupture, the corrosion effects are explicitly introduced by degrading the axial stiffness and ultimate strength of anchorage-related components. To accurately capture cable behaviour, a special cable element has been developed that incorporates initial pretension as an internal force state, rather than an external load, allowing for the consistent evolution of axial force throughout the dynamic analysis. In addition, a moving-load algorithm is developed to simulate the vehicle traveling on the bridge deck. Unlike conventional moving-load formulations, the proposed algorithm is capable of accounting for torsional effects induced by eccentric loads of trucks running on wide-deck bridge systems. All potential nonlinear and failure-prone components, including cable anchorage zones, deck segments, and pier connections, are idealized using nonlinear link elements. The robust procedure can capture post-failure load redistribution and interaction between structural components. Numerical results demonstrate that the combined effects of anchorage corrosion, pretension loss, cable rupture, and torsion-sensitive moving loads have a significant influence on the global stability and progressive collapse of the bridge. Numerical analysis also provides practical insights for evaluating bridge safety during the maintenance period.