Closed-Form Moment-Curvature Expressions for Homogenized Fiber-Reinforced Concrete

Abstract

The authors present, for cement-based composites with homogeneously distributed reinforcement moment-curvature response, a closed form solution. The derivation has a uniaxial material constitutive response using quadratic and piece-wise linear segments' parametric representation. The authors studied compressive and tensile constitutive relational effects on moment-curvature response and observed that the most important parameters were tensile stiffness from first cracking to ultimate tensile strength to ultimate tensile strain. A beam's flexural load-deformation response under four-point loading conditions is simulated by combining crack localization rules with the moment-curvature relations. Underprediction of flexural results through direct use of uniaxial tension stress-strain response is indicated through model simulations, and is attributed to effective volume differences in material subjected to critical stress. Model simulations can match experimental data when a single scaling factor is applied to material models.