Closed-form solutions for flexural response of fiber-reinforced concrete beams

Abstract

The foundational closed-form moment-curvature solution for fiber reinforced concrete beams based on a bilinear tension model and strain compatibility. This formulation underlies the parametric design method presented in ACI 544.4R-18 and the analysis engines of the HRC Designer software.

Summary

This paper derives closed-form expressions for the moment-curvature response of fiber reinforced concrete beams. The material model uses a linear elastic range followed by a constant post-cracking residual stress in tension, with elastic-perfectly-plastic compression.

By enforcing strain compatibility and force equilibrium in normalized form, the neutral axis depth and bending moment are obtained explicitly at every curvature level, eliminating iterative sectional analysis. The resulting expressions convert flexural test data into design parameters and scale from material characterization to member design.

The formulation became the basis of the parametric design procedure for FRC in flexure and continues to anchor the group's design software and subsequent generalizations.