Building-specific loss assessment methodologies utilize component fragility curves to compute the expected losses in the aftermath of earthquakes. Such curves are not available for steel columns assuming they remain elastic due to capacity design considerations. Nonetheless, first-story steel columns in moment-resisting frames (MRFs) are expected to experience damage, through flexural yielding and formation of geometric instabilities. This paper utilizes an experimental database that was recently assembled to develop two sets of univariate drift-based column fragility curves that consider the influence of loading history. Ordinal logistic regression is also employed to develop multivariate fragility curves that capture geometric and loading parameters that affect the column performance. The implications of the proposed fragility curves on building-specific loss assessment is demonstrated using a case of an 8-story office building with steel MRFs. It is shown that structural repair costs in this case may increase by 10%, regardless of the seismic intensity, when column damage is considered. Similarly, the contribution of structural component repairs to expected annual losses may double over the building lifespan.