Empirical equations for flexural residual strengths in concrete with low volumetric fractions of hook-end steel fiber

Abstract

The characterization of steel fiber concrete in a flexural test or tensile uniaxial test requires greater control of loading rate by the speed applied in the test machine, to be able to report more accurately the behavior of displacements or crack openings in micro-scale possible. In general, in the pre-dimensioning process, it is often discarded the characterization tests and the main standards do not provide theoretical design recommendations concerning the residual strengths of fibrous concrete. Some empirical models in the literature attempt an approximation of the theoretical design values, but they present greater dispersion in the results. This article proposes empirical equations for predicting the residual strengths of the steel fiber reinforced concrete (SFRC), for small fiber volume fractions (approx. < 0.8%). Experimentally notched beams subjected to three-point bending tests were collected, with the concrete matrix composed of hook-end steel fiber and the experimental residual strengths presenting the softening behavior in the load-opening ratio curve of the crack. The experimental residual strengths were compared with other empirical models found in the literature. The results showed that the maximum stress of the steel fiber pullout model established satisfactory relationships with the residual stresses in flexure. The empirical proposed residual strength model presented lower variability of dispersion around 10%, the mean absolute percentage error of 8%, compared to other usual empirical models and had the same material class with the experimental results, proving to be a viable alternative for pre-design and dosage optimization for SFRC.