Fiber beam–column element model considering reinforcement anchorage slip in the footing

Abstract

A simple and computationally efficient fiber beam–column element model is developed to consider reinforcement anchorage slip in the footing, which may cause the fixed-end rotation and greatly influence the seismic response of a reinforced concrete column. First, on the basis of an effective macro model for calculating anchorage slip and a classical uniaxial stress–strain relationship of rebar, the reinforcement anchorage slip in the footing is formulated. The macro model assumed a stepped bond stress to deal with the bond–slip relationship, and the slip is derived by integrating the strain over the development length. Then, the derived anchorage slip is introduced into the framework of the conventional fiber element model. By considering the rebar fiber strain in the footing fiber element as the sum of the rebar deformation and the anchorage slip, the stress–strain skeleton curve and the hysteretic law of rebar are modified. After that, the developed fiber model is validated by simulating two quasi-static tests of reinforced concrete columns. The developed model shows good accuracy in simulating the moment capacity and column stiffness, whereas the conventional fiber model may significantly overestimate the column initial and unloading stiffness. Finally, the shake-table test of a full-scale flexure-dominated bridge column is simulated to further validate the developed model. Comparisons indicate the considerably improved accuracy of the developed model in simulating the column displacement time-histories, base moment–column displacement responses, and base moment–base curvature responses. In addition, the rebar anchorage slip and the lateral displacement ratio owing to this slip effect are well predicted by the developed model. Therefore, the model is validated at structural, sectional, and micro levels.