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This paper proposes an improved analysis method based on the theory of structural vulnerability, which incorporates structural redundancy and comprehensively analyzes structural vulnerability and robustness by considering the changes in structural stiffness and redundancy after damage to structural members under conventional loading. The improved method takes into account the changes in the strain energy of the structure after the damage of the structural members, which can be more in line with the actual situation of continuity collapse, and solves the complex process of traditional structural vulnerability theory that requires clustering and unclustering, greatly reducing the workload as well as solving the problem of not being able to find the critical members of the structure. The improved method is used to analyze the vulnerability of a 5-story dropped-story steel frame structure, to find the critical members of the structure based on the test data simulated by ABAQUS, to evaluate the robustness, and to propose improvement measures. The results show that the improved vulnerability assessment method is more reasonable and effective and can be applied to different steel frame structures.

The steel frame structure plays an important role in strategic deployments and is widely used in heavy machinery, metallurgy, military, and other important industries. To study the impact of explosive loads on the anti-progressive collapse performance of steel structures, this paper proposes to establish the vulnerability characteristics of steel frame structures and provides a method for calculating vulnerability characterization indicators. A finite element model is used to analyze the dynamic response of steel frame structures under the action of close-range explosive loads, and factors influencing the anti-progressive collapse of steel frame structures are proposed, including the number of stories and diagonal bracing. A comparison is made between the various column types of steel structures under explosive loads, such as corner columns, long-edge middle columns, short-edge middle columns, inner columns, also in various coupling conditions. The results show that the progressive collapse of steel frame structures is greatly influenced by the position of the explosion and less affected by the amount of explosive material. The simultaneous failure of corner columns and long-edge middle columns is more likely to cause overall structural failure. The addition of diagonal bracing significantly improves the anti-progressive collapse ability and prevents the lateral displacement of steel frame structures; increasing the number of stories provides more alternative load transfer paths for steel frame structures, thereby preventing their collapse.

In order to study the effect of the support mode of a staggered truss system on the continuous collapse resistance performance of a steel structure, four finite element models were established based on the bracing arrangement of a five-story steel frame structure. The situations of different columns on the first floor removed were classified into eight scenarios, and five models of each scenario were analyzed with nonlinear dynamic analyses. Finally, a computational metric based on energy robustness was proposed to evaluate the robustness of the structure. The results of nonlinear dynamic analyses indicated that the staggered truss system significantly improved the resistance to progressive collapse of steel frame structures and effectively increased the redundancy of steel frame structures. All four bracing methods effectively reduced the vertical displacement at the point of failure, with the peak displacement at the point of failure reduced by a maximum of 84 percent and a minimum of 41 percent compared to a pure frame structure. Moreover, the staggered truss system can reduce some axial force peaks in the adjacent columns adjacent to the failed columns. The structural robustness coefficients of Model A, Scheme 1, Scheme 2, Scheme 3, and Scheme 4 are 1.144, 1.339, 1.306, 1.584, and 1.176, respectively, according to the proposed robustness calculation method, which shows that the braced steel frame structure has improved robustness over the original structure. The staggered truss system improves the robustness of the steel frame structure so that the steel frame structure has better resistance to progressive collapse.

We aimed to investigate the extent to which the initial state generated by unexpected loads, such as explosions and impacts on the remaining structure, affects the dynamic response of the structure. The study used the orthogonal test method to obtain orthogonal table L25 (53) by combining five levels of each of the three factors of column removal time and initial velocity, and the initial displacement of the remaining structure under three failure scenarios of the corner, side, and internal columns at the ground floor of the reinforced concrete frame structure. The degree of influence of different factors on the structural dynamic response, and the result of the unifactorial impact of initial velocity and initial displacement of the remaining structure on the structural dynamic response in the case of failure of the bottom side columns, were obtained by the polar difference method. The results show that the analysis using the orthogonal test polar difference method revealed that the initial displacement has a more significant influence on the dynamic response of the structure, forming the main influencing factor. At the same time, the failure time and initial velocity have a smaller influence on the dynamic response of the structure as secondary influencing factors. In the case of unifactorial influence, the initial upward displacement and initial upward velocity are detrimental to the structure, leading to progressive collapse. In contrast, the initial downward velocity and initial downward displacement are favorable.

The conventional sensitivity analysis method unanimously takes all remaining elements except the damaged ones as statistical objects, and element importance is evaluated by the mean value of the sensitive indices of statistical objects. However, from the perspective of resisting progressive collapse, the method is not sufficiently targeted, and the evaluation results have some mistakes. The shortcomings of the traditional sensitivity analysis method in element importance evaluation were analyzed and compared through finite element investigations of two types of planar trusses. Based on the anti-progressive collapse mechanism of the planar truss, the sensitivity analysis method with lower chords as statistical objects was proposed to evaluate the importance of planar truss structural elements. This method is conceptually straightforward, and the assessment results are beyond-compare regarding accuracy via comparison against the results of other evaluation methods. Furthermore, based on identifying important elements, the structure’s bearing capacity can be improved by targeted anti-progressive collapse design.