This paper concerns the applicability of the Weibull stress approach, instead of toughness scaling model approach, for prediction of brittle fracture initiated at defects existing at the weld terminations. Beam-to-diaphragm joint models, which were designed to represent a connection of an I-section beam to RHS column member with through diaphragms, were tested under cyclic loads. Complete joint penetration groove welds were used for the connection between the beam flange and the diaphragm. Specimens had those discontinuities at the roots of welds to the beam bottom flanges, which were created by inserting copper plates into the grooves before welding or by using wire electrical discharge machining. The prediction of brittle fracture with a variety of defect sizes by using the FE analysis was conducted. The fracture moment predicted by using the critical Weibull stress accorded with the test results of specimen with defects such as the blowhole.