Welded connections between beams and built-up box columns in steel moment frames require the attachment of a continuity plate to the inside of the box column using complete joint penetration welds. Electroslag Welding (ESW) is often used to weld one of the sides of this continuity plate to the inside box column. These welds are susceptible to fracture owing to decreased material toughness and the installation of containment plates that create a notch condition. Finite element based fracture mechanics simulations are presented to examine the effect of various design and detailing parameters on the fracture toughness demands in these connections. The results indicate that the use of improved bevel details in the containment plate, and the use of a Reduced Beam Section (RBS) connection strongly mitigate fracture toughness demands, whereas eccentricity in the weld (with respect to the continuity plate) and mismatch between the beam and column flange widths exacerbate fracture toughness demands. The beam and column size, as well as weld access hole details are determined to have only a modest effect on the fracture toughness demands. Simulations also conducted to examine column wall thickness limits beyond which continuity plates may not be required. These suggest that using similar limits for wide-flanged columns may not provide adequate performance. Limitations of the study are presented, along with directions for future work.