An analytical assessment of the length of plastification of partially restrained RC beams

In designing reinforced concrete frame structures under seismic and static gravity loads, the ductility is as important as the strength. Plastic analysis, taking advantage from the redistribution of the bending moment, allows the ultimate load to increase, leading to a more efficient use of the material. Regions designed to undergo plastic deformations, need to provide the required ductility, exploiting their post-elastic capacity. The plastic rotation depends on the physical plastic hinge length, which is deeply investigated here. The definitions and the literature equations proposed for its estimation are explained highlighting their use and abuse. Referring to a reinforced concrete beam, partially restrained at both ends and under a concentrated load at the mid-span, a reliable closed-form equation to predict the length of plastification, as impacted by the failure mechanism, is provided. The accuracy of the analytical equation is checked through a comparison with both literature results and existing formulas. The proposed equation well reproduces the influence on the length of plastification of those parameters neglected by current equations, such as the steel hardening behavior and the steel yielding strength, which cannot be ignored for an accurate prediction of the nonlinear capacity of reinforced concrete beams.