"A Fiber Beam-Column Element for Seismic Response Analysis of Reinforced Concrete Structures"
by F. Taucer, E. Spacone and F.C. Filippou

Abstract: This study proposes a reliable and computationally efficient beam-column finite element model for the analysis of reinforced concrete members under cyclic loading conditions that induce biaxial bending and axial force. The element is discretized into longitudinal steel and concrete fibers such that the section force-deformation relation is derived by integration of the stress-strain relation of the fibers. At present the nonlinear behavior of the element derives entirely from the nonlinear stress-strain relation of the steel and concrete fibers.

The proposed beam-column element is based on the assumption that deformations are small and that plane sections remain plane during the loading history. The formulation of the element is based on the mixed method: the description of the force distribution within the element by interpolation functions that satisfy equilibrium is the starting point of the formulation. Based on the concepts of the mixed method it is shown that the selection of flexibility dependent shape functions for the deformation field of the element results in considerable simplification of the final equations. With this particular selection of deformation shape functions the general mixed method reduces to the special case of the flexibility method. The mixed method formalism is, nonetheless, very useful in understanding the proposed procedure for the element state determination.

A special flexibility based state determination algorithm is proposed for the computation of the stiffness matrix and resisting forces of the beam-column element. The proposed nonlinear algorithm for the element state determination is general and can be used with any nonlinear section force-deformation relation. The procedure involves an element iteration scheme that converges to a state that satisfies the material constitutive relations within the specified tolerance. During the element iterations the equilibrium and the compatibility of the element are always satisfied in a strict sense by the assumed force and deformation interpolation functions. The proposed method proved to be computationally stable and robust, while being able to describe the complex hysteretic behavior of reinforced concrete members, such as strain hardening, "pinching" and softening under cyclic nodal and element loads.

A new scheme for the application of element loads in flexibility based beam finite elements is also presented in the report. The procedure is a natural extension of the element state determination algorithm and is based on the use of the exact internal force distribution under the applied element loads. The corresponding fixed end forces at the element ends are determined during iterations of the element state determination.

Correlation studies between the experimental response of several reinforced concrete elements and the analytical results show the ability of the proposed model to describe the hysteretic behavior of reinforced concrete members. The response sensitivity to the number of control sections in the element and the effect of the selected tolerance on the accuracy of the results is discussed in a few parameter studies.

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