Top beam flange fractures were observed in the post-earthquake steel frame building inspections. Both seismic loads and gravity loads have effect on top beam flange fractures. The objective was to quantify the variation of stress intensity factor to weld root flaw sizes on top of the beam flange at column face in steel frame connections under gravity loads. Finite-element analyses were used to study fracture toughness in welded beam-column connections. Investigations of fracture behavior mainly focused on the standard pre-Northridge connection geometry. Finite element analysis was performed using the ANSYS computer program. Stress intensity factor was calculated through a J-integral approach. The parametric study was conducted to quantify elastic fracture demands as a function of beam geometries. Results show that the distributions of stress intensity factor tend to be even across the flange width under gravity loads. The thickness of beam web has little effect on stress intensity factors. Stress intensity factor increases nearly linear with the increase of flaw size, and it increases with the increase of depth of beam and width of beam. Stress intensity factor reduces with the increase of thickness of beam flange.