Advances in timber engineering and the manufacturing of laminated timber products have facilitated the adoption of mass timber as a sustainable construction material with a reduced carbon footprint in taller construction projects. Special detailing is essential at beam-to-column connections in these buildings to support both gravity and lateral loads while minimizing damage to the timber columns and beams. In general, the gravity connections between beams and columns are designed to withstand shear forces. Nevertheless, in the event of an earthquake, these connections must exhibit the ability to undergo substantial lateral deformations and rotations, while preserving their load-carrying capacity. Limited research has been dedicated to BTC connections subjected to both moments and shear forces. This paper aims to assess the behavior of glulam BTC connections under both lateral and gravity loads with the objectives of quantifying the impact of gravity load on the lateral stiffness of the system and examining the deformed shape of connection components. To achieve this goal, a three-dimensional numerical model of the glulam BTC connection has been developed. Results showed the ductile performance of connections due to yielding of clip angle screws. The predicted large stresses implied the high risk of screw withdrawal and splitting in glulam columns under lateral loads. The developed model not only enables designing future large-scale experiments but also overcomes limitations associated with experimental testing.