Beams and beam-columns of many steel frames fractured in a brittle manner in the 1994 Northridge Earthquake and the 1995 Kobe Earthquake. In this study, the cracking and the following brittle fracture of rectangular steel tube beam-columns and H-shaped beam-columns subjected to a tensile axial force mainly and the repeated horizontal force were investigated by tests and analyses. Initiation of cracking at the place by a welded part of the beam-column to the base plate and its rapid propagation up to the fracture could be predicted qualitatively well by the critical axial force-axial displacement curve for convergence of the damage accumulation proposed before.