"Model for Anchored Reinforcing Bars under Seismic Excitations"
by G. Monti, E. Spacone and F.C. Filippou

Abstract: This study presents a finite element model for reinforcing bars anchored in concrete and subjected to severe cyclic excitations. The solution to the problem of stress transfer between reinforcing steel and concrete is based on the flexibility method. In this case the governing differential equations are solved by force interpolation functions that strictly satisfy equilibrium along the anchored reinforcing bar. This solution method results in a very robust and stable nonlinear algorithm, particularly, for systems that exhibit severe stiffness and strength deterioration, as is the case for anchored reinforcing bars.

In the systematic derivation of the proposed solution method the model is viewed as a simple mechanical system that is made up of two components in parallel. The first component is the reinforcing bar and the second is the interface between reinforcing steel and surrounding concrete. The nonlinear hysteretic behavior of the model derives entirely from the nonlinear constitutive behavior of these two components. The hysteretic behavior of the reinforcing bar is described by a cyclic steel stress-strain relation, while the hysteretic behavior of the interface derives from a cyclic bond stress-slip relation that includes a damage parameter for representing the progressive deterioration of bond.

In formulating the finite element solution of the governing differential equations of the stress transfer problem, two different methods are discussed and compared. In the first method the governing differential equations are solved by approximating the displacement field with interpolation functions. The selection of appropriate displacement shape functions that are compatible with the node displacements is straightforward. In the second method the governing differential equations are solved by approximating the stress field with interpolation functions. In this case the selection of appropriate interpolation functions is not straightforward. In a parallel system the total stress field results from the superposition of the component stress fields. In this case the force interpolation functions in the components of the proposed model must satisfy the requirement that the steel force distribution be in strict equilibrium with the bond force distribution along the element. The proposed model is based on the second method, since this offers significant numerical advantages over the first.

The integration of the flexibility based finite element model in a conventional stiffness based finite element program faces several challenges that are addressed in this study with a new iterative algorithm. This algorithm is characterized by robust and stable numerical behavior even under conditions of significant strength and stiffness loss of the anchored reinforcing bar.

The study concludes with correlation studies between analytical and experimental results and several parametric studies. The former are intended to establish the validity of the proposed model, while the latter serve the purpose of identifying the significance of key parameters on the local and global response of anchored reinforcing bars and for providing some guidance for their design in regions of high seismic risk.

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