In this study, nonlinear dynamic response of 4, 7, and 10-story moment frame steel structures is investigated under seismic ground motions. An incrementally increasing intensity is accounted for to evaluate the Collapse Fragility curves of the same buildings under different values of torsional eccentricity. The site soil of the buildings is assumed to be composed once of a firm and then of a soft soil. As a distinction of this study, the realistic maximum possible value of eccentricity ratio for moment frames, including both stiffness and mass eccentricities, is shown to be 10-15% that is much less than peak values of the past studies. Because of the three-dimensional aspect of the study, the eccentricity is selected to be bi-directional and the horizontal components of the earthquake motion are applied concurrently. It is exhibited that while torsional eccentricity lowers the median Collapse probability of the studied buildings, it does not have a sensible effect up to the eccentricity ratios not larger than 10%. Besides, the taller structures on the firm soil are affected more strongly from torsional eccentricity, as the median Collapse acceleration decreases up to 46% for the 10-story building suffering from 15% eccentricity ratio on the firm soil.