Advanced Nonlinear Formulation for Reinforced Concrete Beam‐Columns

Abstract

This is the first of two papers addressing the efficient and simulta- neously accurate analysis of reinforced concrete frames through the use of adaptive nonlinear analysis techniques. The present paper discusses the requirements of adaptive analysis and highlights the essential need for a beam-column formulation that accurately models the behavior of reinforced concrete members in the range where the response can be considered elastic and fully recoverable. A new elastic formulation is therefore proposed for reinforced concrete beam-columns; it assumes a quartic shape function for the transverse displacements and differs from conven- tional finite-element formulations in the use of the constant-axial-force Criterion. The quartic formulation is capable of modeling a typical reinforced concrete mem- ber of arbitrary cross-sectional shape and reinforcement layout with only one ele- ment, including the effects of concrete tensile cracking, the nonlinear compressive response of concrete, and the beam-column action. Verification examples using the nonlinear analysis program ADAPTIC demonstrate the accuracy of the pro- posed formulation and its ability to model an entire reinforced concrete member using one element.