Analytical expressions for a deflection curve of a partially plastically loaded beam of rectangular section was derived.
Deflection analysis of beams with rectangular cross sections is considered under specific loading conditions, resulting in at most quadratic bending moment distribution, 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. With the derivation of the general solution, listed explicitly by equations in the article, which was never presented in any article or book before, the presented article fills the gap in the analytical non-linear mechanics of beams.
ŠTOK, Boris, HALILOVIČ, Miroslav. Analytical solutions in elasto-plasto bending of beams with rectangular cross section. Appl. math. model.. [Print ed.], 2009, issue 3, vol. 33, str. 1749-1760.