This study investigated the structural progressive collapse using finite element (FE) and theoretical methods. Firstly, an FE model was established based on the component method and layered shell element method. The reliability of modeling approaches was evaluated by comparing them with the previous experimental tests by the author. The NIST building was taken as an example to investigate the structural collapse behavior and the failure modes after different component failure scenarios including single column, double columns, multiple columns, and horizontal components based on the alternative path method. The results indicated that the failure of gravity columns and joints more easily triggered the progressive collapse of the structure. After the failure of double moment-resisting frame columns, the structure still demonstrated considerable robustness. The impact of floor fragments played a controlling role in the process of collapse propagation. A method for achieving rapid collapse of structures was proposed based on the structural collapse characteristics. The study found that a demolition strategy based on gravity columns can facilitate the rapid collapse of structures. After comparing the different simplified modeling methods, it was revealed that the 2D models underestimated the anti-collapse performance of structures compared to the 3D models. Under the same scenarios, the predicted structural collapse response of the 2D model was several times greater than that of the 3D model (up to 7 times). Meanwhile, the structural collapse occurred earlier in the 2D model. The anti-collapse performance of structures adopting different design codes also was compared. It was revealed that GSA 2016 has put forward requirements for higher collapse resistance of buildings. In this study, a new calculation method was proposed, namely the Collapse Probability Prediction Method Based on the Randomness of Structural Load (CPPM-RSL). In the CPPM-RSL, load reliability theory was employed to ensure that the structural collapse resistance design fell within the realm of structural engineering theory. Meanwhile, the CPPM-RSL offered greater engineering interpretability compared to previous methods. Additionally, a new simplified mechanical model was proposed to predict the collapse resistance of structures. The new simplified model did not depend on the computational results obtained from the finite element method (FEM) unlike the existing model. At the same time, the simplified method also exhibited high reliability as revealed by comparisons with the FEM. To solve highly nonlinear problems, machine learning (ML) algorithms were established to predict the anti-collapse performance and the collapse probability of structures based on the proposed theoretical model. Meanwhile, the applicability and performance of the multiple ML algorithms in estimating the structural collapse behavior were compared and evaluated. The results indicated that the LightGBM model exhibited stronger robustness and predictive ability.
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