###### Abstract  
In the present paper an improved formulation devoted to the optimal design problem of a special moment resisting connection device for steel frames is proposed. This innovative device is called a Limited Resistance Plastic Device (LRPD) and it has been recently proposed and patented by some of the authors. It is thought to be preferably located at the extremes of the beam, connecting the beam end cross section with the relevant column. The typical device is a steel element characterized by symmetry with respect to three orthogonal barycentric planes and constituted by a sequence of three portions with abrupt cross section changes. The main novelty of the present proposal is related to the design of special geometry for the optimal device ensuring that it possesses a reduced resistance with respect to the relevant connected beam element, is characterized by an equivalent bending stiffness equal to the one of the connected beam elements and exhibits full plastic deformations avoiding any local instability phenomenon. The optimal design is formulated as a minimum volume one and is subjected to suitable constraints on the geometry of the device and on its elastic and plastic behavior. The optimization problem is a strongly non-linear programming one and it is solved by adopting an interior-point algorithm that is available in the MATLAB Optimization Toolbox. The numerical simulations are devoted to the most used standard steel profiles (IFE, HE) and the results prove the great reliability of the proposed device. In addition, the relevant elastic and plastic domains of the designed devices are defined, and the expected behavior of the device is verified by appropriate 3D finite element models in the ABAQUS environment. than that available in shear wall systems and braced frames. Many issues are related to the formation of plastic hinges in MRF and to the linked structural consequences; for a discussion on these issues see, e.g., [1; 2; 3; 4]. A very important aspect to be considered in MRFs is the problem of connection performance and many papers address this topic [5; 6; 7; 8; 9; 10] starting from the extensive damages to the beam-to-column connections of the MRFs occurred during the 1994 Northridge and 1995 Kobe earthquakes. Basically, these studies resulted in the development of pre-qualified connections for use in seismic areas [11], which includes the reduced beam section (RBS) connections. In fact, the connection between beam and column must ensure the occurring of plastic curvature in the beam extreme, preventing local buckling phenomena and brittle rupture of the connection itself. A very large bibliography is available in literature regarding the connections between beams and columns and related issues, see, e.g., [12; 13; 14; 15; 16; 17; 18; 19; 20]. The plastic curvature capacity of the involved cross section preventing local buckling phenomena can be evaluated making reference to the cross-section classification reported in the international standards. The role of cross section classification is to identify the extent to which the resistance and rotation capacity of cross sections is limited by its local buckling resistance. To properly define such a limit, the international standards [21; 22; 23; 24] define four different classes. Class 1: ductile cross-sections are those possessing rotation capacity able to develop plastic hinges and wide plastic rotation capacity; Class 2: compact cross-sections are those that can reach their plastic moment resistance but show limited plastic rotation capacity; Class 3: semi-compact cross-sections are those that can reach just their limit elastic moment resistance without any plastic rotation; Class 4: slender cross-sections are those in which the buckling phenomena strongly influence the limit elastic moment resistance value. Consequently, plastic analysis can be conducted only for structural members whose cross-sections belong to Class 1 or 2.