Advanced nonlinear formulation for reinforced concrete beam-columns

This is the first of two papers addressing the efficient and simultaneously 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 conventional finite-element formulations in the use of the constant-axial-force Criterion. The quartic formulation is capable of modeling a typical reinforced concrete member of arbitrary cross-sectional shape and reinforcement layout with only one element, 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 proposed formulation and its ability to model an entire reinforced concrete member using one element.