A Simplified Theoretical Model for Progressive Collapse Resistance of Steel Girders: Focusing on Load–Displacement Behavior Under Three Concentrated Loads

Progressive collapse is characterized by disproportionate structural failure triggered by localized damage, such as column loss under extreme loading conditions. The objective of this study is to develop a simplified analytical model that is applicable in engineering practice without the need for high-fidelity nonlinear finite element analysis. Although current design guidelines (GSA and DoD) provide analytical procedures and acceptance criteria, they do not explicitly address the tensile resistance of girders after the acceptance criteria are satisfied, particularly under large deformation and connection failure. To address this limitation, this study proposes a simplified theoretical load–displacement model for a fixed-end girder subjected to three concentrated loads, considering the effects of secondary beams and focusing on the local girder response under a column-removal scenario. The proposed model incorporates moment–axial force interactions at plastic sections in the large-deformation range. Based on one-dimensional finite element analysis results, an early-developed axial force of 0.15Fp at the onset of the transition stage and a residual bending moment of 0.3Mp during the catenary action stage are explicitly introduced to better represent actual structural behavior. The girder response is idealized using five characteristic points: yielding (Y), full plasticity (P), transition initiation (T), pure catenary action initiation (C), and collapse governed by connection failure (Fconn). Stress distributions at plastic sections are analyzed using three-dimensional finite element models to establish stress-based formulations and a rational procedure for estimating axial force at collapse. The validity of the proposed model is verified through comparisons with finite element analysis results for girders with different span-to-depth ratios. The results demonstrate reasonable agreement in terms of collapse load and displacement, particularly for slender girders, confirming the applicability of the proposed model for progressive collapse assessment.