Modeling strain demands in longitudinal steel bars of concrete columns

Fracture of longitudinal bars, due to high-strain low-cycle fatigue, is a common failure mode in seismically detailed reinforced concrete columns. The issue has recently attracted increased scrutiny due the national push to introduce high-strength reinforcing bars with yield strengths exceeding 80 or 100 ksi in concrete construction. Recent tests on columns with high-strength reinforcement have indicated that high-strength bars can experience significantly larger strain demands than their lower strength counterparts, and therefore may be more susceptible to low-cycle fatigue failures. A computational model coupled with empirical relations are proposed to estimate the global deformation behavior of reinforced concrete columns and provide reliable estimates of the strain demands on longitudinal bars through the full range of expected inelastic deformations during seismic demands. The model was calibrated using data from experiments conducted on seven concrete columns reinforced with bars having yield strengths from 64 ksi to 106 ksi. The columns were pushed to large damage states and monitored using a high-resolution optical strain measurement system. The computational model consists of a distributed plasticity fiber-section element with five Gauss-Lobatto integration points, and is bounded by zero-length elastic shear and rotational springs that simulate shear and bar slip deformations, respectively. The fiber-section computational model was found to provide reliable strain estimates for longitudinal bars up to the initiation of cover spalling. Two equations are proposed, one to estimate the lateral drift at first spalling and the associated bar debonding, and the other to adjust longitudinal-bar strains obtained from the fiber-section element after bar debonding. Critical parameters that affect strain demands were found to be the reinforcement tensile to yield strength ratio, the maximum applied shear stress, the axial load, the reinforcement yield strength, and reinforcement bond demand.