Brittle fracture was identified in many of prequalified weld joints in steel moment frames in the 1994 Nothridge earthquake. Then analyses of response and damage mechanism of beam-to-column connections under seismic load were widely studied in the world, but few people conduct the research on seismic-resistant behavior of beam-to-column web connections. To quantify the variation of stress intensity factor to weld root flaw sizes beam-to-column web connections with tapered beam flange plates, detailed 3D finite element analyses is used to study fracture toughness requirements in beam-to-column web connections, considering the large deformation, large strain, bolts pretension, bolt contact-slide, as well as material harden and soften. Fracture toughness demands are evaluated in terms of the mode I stress intensity factor. The stress intensity factor is calculated through a J-integral approach. The fracture toughness demands are studied for the flaw on the top of the beam flange and the bottom surface, respectively. Results indicate that the likelihood of top flange fractures is smaller than that of bottom flange fracture. Stress intensity factor is not uniform and is largest in the edge of beam flange. The fracture toughness in the edge of beam flange for web connections with step beam flange plates is 15% less than that for tapered beam flange plates.