In Japan, a series of destructive earthquakes (magnitude 7.0) occurred in a short period, resulting in a considerable interest in the low-cycle fatigue resistance of beam-end welds of beam-to-column connections with full-penetration welding. In the existing literature, various fatigue damage evaluation methods have been proposed based on the experimental results of stiffened beams aimed at preventing local buckling at the beam ends. However, because local buckling is expected to occur at the beam-ends of steel-framed structures, this study focused on conducting cyclic loading tests on I-shaped steel beams, allowing local buckling to occur at the beam-ends. In this study, we proposed novel fatigue curves based on the experimental results obtained from these tests. The experimental variables were the cross-sectional shape and constant amplitudes. Several constant loading amplitudes were applied to the same cross-sectional shape to investigate the effects of the constant amplitude and cross-sectional shape on the collapse mode. Based on these cyclic tests, when local buckling occurred, three collapse modes could be classified. These collapse modes were observed to vary depending on factors, such as the amplitude of the loading history and width-to-thickness ratio of the cross section. Additionally, this study revealed that the specimens that allowed for local buckling had larger deformation capacities until fracture than those that prevented local buckling at the beam ends.