This manuscript explores the stiffness and strength of Square Hollow Section (SHS) tubes subjected to localised transverse actions applied to the open side of a rectangular hole created using 3D laser cutting technology (3D-LCT). Understanding the behaviour of this specific detail is crucial as it is a key component in the connections between SHS columns and passing-through IPE beams. The methodology employed in this manuscript involved developing analytical equations to predict both stiffness and strength of this structural element. The provided equations are presented in a straightforward manner and were deduced by applying elasticity principles to structural components. To validate these equations, a parametric analysis was conducted, simulating the response of 27 distinct geometric configurations of the analysed structural detail thanks to the Finite Element (FE) software. Their accuracy was confirmed by comparing the results of these simulations with the outcomes derived from the formulated equations. The primary findings indicated that the proposed equations could predict the stiffness and strength of the studied detail with an average ratio close to 1 when comparing predicted and numerical results, and a coefficient of variation of approximately 10%.