Closed-form solutions for flexural fatigue mechanical degradation of steel fiber reinforced concrete beams

Present research brings a novel methodology to estimate FRC mechanical degradation throughout closed-form solutions for FRC beams. The first step consisted on deriving the constitutive relations for tension and compression. While a quad-linear model was used for tension, an elastic perfectly plastic model was applied for compression aiming to reach the moment-curvature with the closed-form solutions. Crack opening is, subsequently, verified using the characteristic length and the evaluated tensile strains, which allows to evaluate crack increase under quasi-static loading. With the complete composite quasi-static mechanical characterization, the next step is to evaluate CMOD increase under fatigue loading with the proposed power law equation and the material S-N curve. Finally, the CMOD evolution under fatigue is estimated and the back-calculations bring the evolution of the other mechanical parameters along the cycles. The methodology was applied for three distinct concrete compositions in the literature and the results correctly fitted the observed CMOD evolution along the cycles.