Effect of yield penetration on column plastic hinge length

The required confined zone in critical regions of columns and piers undergoing lateral sway during earthquakes is related to the plastic hinge length where inelastic deformation and damage develops. The exact definition of the plastic hinge length stumbles upon several uncertainties, the most critical being that the extent of the inelastic region evolves and spreads with the intensity of lateral displacements. Design codes quantify a reference value for the plastic hinge length, through calibrated empirical relationships that account primarily for the length of the shear span and the diameter of primary reinforcing bars. The latter term reflects the effects of bar yielding penetration in the support of columns. Here a consistent definition of plastic hinge length is pursued analytically with reference to the actual strain state of the reinforcement. Strain penetration extending bilaterally on the reinforcing bars from the critical section towards the column shear span and towards the bar anchorage is evaluated. Considering that bar yielding is synonymous to degradation of interfacial bond between bar and concrete over the yielded area, the field equations of bond are solved explicitly along the column primary reinforcement over the shear span, following the process of gradual crack formation along the member. Boundary effects and important design variables are considered, such as the shear span aspect ratio and the stress-resultants (axial load and flexural moment) carried by the column. Using this solution, the parametric sensitivities of the plastic hinge length are illustrated and compared with other alternatives that have been obtained through experimental calibration. Analytical estimations are also compared with experimental evidence from a number of column specimens tested under axial load and reversed cyclic lateral drift histories reported in the literature.