Nowadays, despite the substantial increase in structural design knowledge, the semi-rigid connections steel design is still facing resistance from the structural engineers. This fact can be in part explained by few design standards that allows and explains their use, suitable computer programs and the lack of detailed information of the economical advantages of the semi-rigid design philosophy. This work presents a parametric analysis performed on a residential low-rise steel building considering all the steps necessary to a semi-rigid design. This analysis considered parameters like: beam-to-column connection stiffness and strength,structural system (steel or composite) and lateral frame stability (sway and non-sway frame solutions). The analysed structure consisted on a standard four pavements residential building proposed by a Brazilian Steel Mill Usiminas for low-cost popular constructions. Initially all the structure beam-to-column connections adopted a standard connection stiffness. The study continued with optimised connection stiffness for each of the designed structural frames. The first part of the present work is devoted to a full description of the design procedures proposed in the Eurocode 3, revised annex J for semi-rigid connection design. Based on this methodology a simple design model was proposed and implemented with the aid of the finite element program Ansys. The model included geometrical and material non- linearities and considered the connections semi-rigid behaviour avoiding the conventional approximations suggested in several current steel design standards. The results of this investigations are presented, discussed and compared to standard designs like the Usiminas proposal as means to access the economic potential and efficiency of the semi-rigid solutions. The best structural solution for the investigated construction was a non-sway composite semi- rigid (40 percent of the rigid capacity). The economy achieved were: 48 percent and 10 percent when compared to other semi-rigid solutions and the conventional Usiminas solution, respectively. This figures changed to 53 percent and 15 percent when optimised connections were used in each structural frame. The presented results confirm the advantage of the use of this connections kind in residential buildings in steel of low height.