An energy-based computational scheme for the analysis of reinforced concrete structures with geometric and material nonlinearities

Abstract

This paper proposes a new energy-based numerical technique for the nonlinear analysis of reinforced concrete beam elements. The mathematical concept and equations are presented in detail for a general nonlinear quasi-static problem. This method can create a physical sense of the types of energy in a system for an analyst to easily consider any material type and geometric nonlinearity effects from the analysis of reinforced concrete members. The governing equations of this computational scheme have a quadratic form, which leads to proving a complementary relationship for a stability check. In other words, a distinguishing feature of the proposed method is paving the path for selecting the optimum size of displacement increments during a nonlinear numerical analysis. In the proposed method, the steps have been made easier for analysts. Unlike several existing methods, the formulation has also considered the shear and normal deformations, making the analysis results closer to experimental realities. Moreover, the results obtained from solving, evaluating, and comparing several examples demonstrate the acceptable accuracy and convergence of this energy-based approach for reinforced concrete beams. In addition, the quadratic nature of its formulation provides an analyst with information about the accuracy and stability of the obtained structural responses.

Keywords

• nonlinear analysis
• reinforced concrete
• numerical method
• energy-based method
• stability