For a beam with rectangular section the evolution of the plastic zone is analytically followed from the beginning of the plastic strains until the theoretical collapse.
Deflection analysis of beams with rectangular cross sections is considered under specific loading conditions and assuming elasto-plastic behaviour with no hardening. Within the framework of small strain and small displacement approach analytical solutions are derived, which enable elasto-plastic analyses of beams to be performed in a closed analytical form. In consequence, clear tracing of the elasto-plastic response evolution with a propagation of the plastic zone through the volume, i.e. its spreading along the beam's longitudinal axis as well as its penetration through the cross section, is enabled as loads increase, from the appearance of a first plastic yielding in a structure till its collapse.
HALILOVIČ, Miroslav, ŠTOK, Boris. Analitično spremljanje razvoja elastoplastičnega stanja med upogibom nosilcev pravokotnega prereza = Analytical tracing of the evolution of the elasto-plastic state during the bending of beams with a rectangular cross-section. Stroj. vestn., 2007, letn. 53, št. 12, str. 806-818.