Simplified theoretical model for prediction of catenary action incorporating strength degradation in axially restrained beams

Catenary action is one of the structural mechanisms that could develop in a laterally restrained beam when subjected to large deformation, and it is a primary mechanism in the resistance to progressive collapse of frame structures in the typical scenario of a column removal. Analytical methods for the analysis of the catenary action exists for idealised beams with simple non-degrading yielding conditions. However, in a realistic beam assembly, especially under a column removal scenario, intermediate failure events such as failure of weld or a bolt component at the connection can occur; consequently, the strength of the beam in the plastic region degrades abruptly. This paper presents a simplified theoretical model taking into consideration the degradation of strength in the plastic regions. The basic model is formulated for a generic beam assembly axially restrained with a variable restraining stiffness (flexible axial support), and involves a middle connection. The strength degradation is represented by degraded yield functions. The model subsequently generates a realistic vertical load-deflection relationship, i.e. the resistance function. Comparison of load-deflection relationship so generated with corresponding finite element analysis shows good accuracy. Further comparison of the theoretical model with an existing laboratory experiment also exhibits good agreement. With the generated resistance functions, analysis of the actual dynamic response of beam assemblies in a progressive collapse scenario can be carried out using a standard procedure such as the energy method.