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Unprotected steel columns exhibit a rapid deterioration in strength with increasing temperature. A method for the analysis of unprotected steel columns in fire conditions is presented. Beam finite elements are used to model the columns that are concentrically loaded with initial out-of-straightness and temperature-dependent elasto-plastic material properties. The accuracy of the model was determined by comparing it with available experimental results for column strength at elevated temperature and for time of collapse with time-varying temperatures. A study of the time to collapse of unprotected steel columns was undertaken for a range of load levels, slenderness ratios and column section sizes.