A Framework for Collapse Vulnerability Assessment of Steel Beams Subjected to Increasing Loads and Nonuniform Longitudinal Temperature

Steel beams are susceptible to large deformation and capacity reduction when subjected to elevated temperatures. Determination of collapse loads for structural steel members under fire is critical for realistic assessment of system vulnerabilities. Such determination, however, should be conducted within a probabilistic framework that allows for the integration of various uncertainties influencing the behavior. In addition, the assessment should address realistic fire exposure that arises due to typical fire scenarios. To date, evaluation of the collapse load of beams in the presence or absence of uncertainties under nonuniform temperature is lacking. This paper presents a new analytical formulation, based on virtual work, for calculating the collapse load of beams subjected to nonuniform longitudinal temperature distribution. Moreover, a new probabilistic framework is devised to generate fragility surfaces for beams under combined fire and applied loads. Randomness in load and resistance including applied mechanical loads, compartment ventilation, compartment geometry, and thermal characteristics of surrounding surfaces are accounted for by including the statistical variations in these parameters. Comparisons of collapse loads calculated using the proposed approach and those calculated using a commercial finite element software show excellent correlation. The outlined framework can allow structural and fire engineers to rapidly evaluate the collapse load and mechanism of beams under a nonuniform temperature distribution.