Risk−Based Cost−Benefit Optimization Design for Steel Frame Structures to Resist Progressive Collapse

The design of structures to resist progressive collapse primarily focuses on enhancing structural safety and robustness. However, given the low probability of accidental events, such designs often lead to a negative cost–benefit. To address this problem, this paper uses risk analysis to optimize the progressive collapse resistance design of steel frame structures. The elements’ cross-section design for the progressive collapse resistance of steel frame structures is optimized using genetic algorithms and SAP2000 23, which identify the structural model with the minimum robustness index while ensuring safety. The results show that the risk-based robustness index can effectively assess the cost of progressive collapse design. More importantly, the optimization model can rapidly identify the most cost-effective structural design solution that complies with progressive collapse resistance guidelines, enhancing the simplicity and usability of the structure design optimization process. Additionally, the integration of the SAP2000 API with Python 3.8 automation streamlines the parameterization process, minimizes manual errors, and enhances the precision and efficiency of the structural design optimization. Finally, the model’s effectiveness is validated through a case study, where the refined single-frame structure shows a reduction in initial construction and collapse-related costs by 2.4% and 9.1%, respectively. Meanwhile, the three-dimensional frame shows a 2.9% rise in initial costs but a 13.5% decrease in total collapse-resistant design costs, illustrating the model’s ability to balance safety with cost-effectiveness.