Reinforced Concrete Membrane Element Formulations

Abstract

Finite‐element formulations are presented for the analysis of reinforced concrete membrane structures. Cracked reinforced concrete is treated as an orthotropic material based on a smeared, rotating crack model. Secant‐stiffness moduli are defined for concrete and reinforcement, and these are used in the development of linear displacement rectangular and triangular membrane finite elements. Procedures are discussed by which these elements can then be incorporated into a nonlinear analysis algorithm. Extensions to the formulations are also described that permit the consideration of prestrain effects in the component materials such as prestressing of the reinforcement, shrinkage of the concrete, or thermal expansion. The constitutive relations currently utilized are those of the modified compression field theory, although the element formulations are sufficiently generic to easily accommodate other constitutive models. A numerical example is provided to illustrate the simplicity of the calculation procedure and the good convergence characteristics and numerical stability of the formulations. Corroboration with experimental data is also discussed. Finally, the capabilities and application potential of the analysis procedure are demonstrated in sample analyses.