"Models of Critical Regions in Reinforced Concrete Frames under Earthquake Excitations"
by N. Zulfiqar and F.C. Filippou

Abstract: This study endeavors to develop rational and computationally efficient models for predicting the hysteretic behavior of inelastic regions in reinforced concrete moment resisting frames that are subjected to severe seismic excitations.

A new approach in describing the hysteretic behavior of inelastic regions in reinforced concrete moment resisting frames is proposed. This approach consists of subdividing the inelastic region into slices called critical regions at locations where cracks form. Each inelastic region is thus made up of several critical regions. The response of each critical region to loads or deformations that are applied at the cracked end sections of the region is determined separately. This analysis yields the concentrated rotations at the cracks of the inelastic region, which are then summed up for all critical regions to yield the rotation of the entire inelastic region.

The model of a critical region is composed of a top and bottom reinforcing layer which describe the transfer of stress from reinforcing steel to concrete through bond. The interaction between the top and bottom reinforcing layer is established at the cracked end sections of the critical region by satisfying the equilibrium of axial forces and bending moments. To this end a new section layer model which accounts for the relative slip of reinforcing steel with respect to the surrounding concrete at the crack is proposed. To describe the stress transfer within the critical region a piecewise linear bond stress distribution is assumed along the reinforcing bar. The bond stress values of the distribution are established iteratively by satisfying the equilibrium and compatibility equations of the stress transfer problem along the reinforcing bar. The model is thus capable of describing the tension stiffening effect between cracks under cyclic load reversals.

Efficient numerical algorithms are developed for the iterative solution of the stress transfer within the critical region and the force and moment equilibrium at the cracked end sections. Since any combination of force and deformation boundary conditions can be specified at the cracks, analytical experiments can be conducted under either force or deformation control. The model can also be incorporated in a nonlinear dynamic analysis program that is based on the stiffness or flexibility method.

The accuracy of the analytical results depends to a significant extent on models for the relation between steel stress and strain and bond stress and relative slip of the reinforcement under cyclic loading. A relatively simple model that expresses steel stress as an explicit function of strain and steel strain as an explicit function of stress is proposed. The model is capable of describing quite accurately several aspects of the monotonic and hysteretic behavior of reinforcing steel. A nonlinear bond stress-slip model which accounts for bond deterioration under cyclic load reversals is used. The model simulates bond conditions in confined concrete regions of interior and exterior joints as well as those near flexural cracks in girder inelastic regions.

The validity of the proposed models is established by comparing the analytical predictions with available experimental evidence from the hysteretic behavior of anchored reinforcing bar, beam inelastic regions and interior and exterior beam-column subassemblages with or without slab.

The study concludes with a series of parametric studies aimed at assessing the sensitivity of the models to changes in key parameters and at studying the effect of variables such as anchorage length and bond strength on the hysteretic behavior of critical regions in reinforced concrete frames.

If you are interested in a copy of this report, please contact the EERC Library at eerclib@shake.berkeley.edu or send e-mail to Professor Filippou