In the current work, a probabilistic assessment method of a steel framed building under abrupt removal of a column due to catastrophic events is developed. A multi-storey steel framed model taking into account the influence of catenary effect has been analyzed. Uncertainties in the structural variables are incorporated in the probabilistic simulation approach. Based on the changes of component internal energy, the progressive collapse sensitivity to abrupt removal of a column has been investigated. Besides, a simplified beam damage model is proposed to analyze the energies absorbed and dissipated by structural beams under large deflections. In addition, the correlation incorporating catenary action between bending moment and axial force in a beam during the whole deformation development process is studied. With the methodologies adopted for progressive collapse assessment under removal of a column, a deterministic method has been developed, framed within the Advanced First Order Reliability Method (AFORM). A robustness index (RI) is proposed to evaluate the structural robustness performance based on the acceptable probability of global failure and structural collapse probability.
Based on the traditional mechanical model of straight beam element, the paper makes a systematic analysis and research on the pre-twisted beam finite element numerical model. Firstly, the paper proposed the pre-twisted Euler beam element mode, the mode uses 2 node and 12 freedom degrees, the element axial and torsion displacements use 2 nodes Lagrange interpolation function, bending displacement still use the cubic displacement. Secondly, the paper studies a new pre-twisted Timoshenko beam element mode, the proposed new Timoshenko beam element takes separate interpolation polynomial functions both flexure bending and rotation displacement. According to the relationship between bending moment and shear, the relationship between of bending displacement and angle displacement is derived, which is more accurate to consider the effects of shear deformation. Finally, by calculating the pre-twisted rectangle cantilever beam example, and contrasting three-dimensional solid finite element using ANSYS, the comparative analysis results show that pre-twisted Timoshenko beam element mode has good accuracy.
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