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This paper presents a simplified method based on direct and energy formulations for nonlinear analysis of reinforced concrete frame structures. In the simplified method, a reinforced concrete member is modeled by an equivalent member of homogeneous nonlinear material with a derived stress-strain relationship, which satisfies the requirement that the equivalent member has the same moment-curvature behaviour as the original member. One advantage of the simplified method is its simplicity which can be easily implemented in most structural analysis computer programs with nonlinear modeling capabilities. The developed model can accurately predict the nonlinear hysteretic responses of reinforced concrete structures with frame members of arbitrary shapes and reinforcing details under severe earthquake excitations. Numerical examples of a cantilever beam and a new bridge pier system of double-skinned concrete filled tubular (DSCFT) members, recently developed in Taiwan for seismic construction, are analyzed under monotonic and cyclic loadings. The effects of concrete confinement, steel hardening, stiffness degradation, strength deterioration, and pinching are simulated in the developed simplified method. Modules of the method are developed for implementation in the Open System for Earthquake Engineering Simulation framework (OpenSees). Results from the simplified method agree well with finite element and fibre layer models, as well as with experimental testing results.

A simplified method for nonlinear cyclic analysis of reinforced concrete structures: direct and energy based formulations