The present paper concerns a new formulation of the optimal design problem of I-shaped multistep steel beam elements, based on the study of the plastic strain spread occurring in the relevant elements, with the aim of determining the length involved by the plastic deformation related to assigned load conditions and different constrained beam schemes. Material behavior is assumed as elastic–perfectly plastic, and the hypothesis of plane cross-sections is accepted. The functions defining the plastic strain spread are analytically obtained in the framework of Euler–Bernoulli beam theory. The proposed optimal design problem is a minimum volume one and the new constraint imposed on the length of the plasticized portion ensures that the minimum volume beam element also represents a maximum plastic dissipation one. Furthermore, the solution to the optimal design problem guarantees that the obtained multistep beam element ensures protection against brittle failure of the beam end sections, provides optimal cross-sections of the different portions belonging to Class 1 and ensures a suitable minimum value of the elastic flexural stiffness to respect the constraint on the deflection. Explicit reference is made to the so-called Reduced Beam Section (RBS), which characterizes the described multistep beam elements. Actually, the proposed formulation represents an innovative approach to obtaining an optimal beam element that really satisfies all the resistance, stiffness and ductility behavioral requirements. Some numerical applications conclude the paper, and their results are confirmed by appropriate FEM analyses in ABAQUS environment.
Benfratello et al. (Mon,) studied this question.