The present research evaluates the ultimate shear capacity of a beam-to-beam shear and moment connection comprising a 3-bolted clip-angle and a 3-bolted clip-angle with a flange strip, based on 48 laboratory tests. The flange strip connecting the flange portions of the loading beam and supporting beam converts the 3-bolted shear connection (3BS) into a 3-bolted moment connection (3BM). For the 3BS connection, the ultimate shear strength increased by 62% with thickness and 37% with depth, while a 20% decrease was observed with increasing width. The flange strip effectively resists the transverse deformation of the 3BM connection and increases its shear strength. Following the conventional approach, an empirical shear-strength equation is proposed for the chosen 3 BS and 3BM connections. In addition, a new design method is introduced, along with a relevant design shear equation for the 3BM connection. The new design method introduces a rigidity coefficient that accounts for the material and geometric details of both the clip angle and the flange strip of the 3-bolted clip angle. The shear performance of the 3BM connection is 2.26 times that of the 3BS connection due to the addition of a flange strip. Design factors for the Load and Resistance Factor Design (LRFD), Limit State Design (LSD), and Allowable Strength Design (ASD) methods are derived from reliability analyses of experimental data.