Deriving stress–strain relationships for steel fibre concrete in tension from tests of beams with ordinary reinforcement

One of the most critical points in the theory of steel fibre reinforced concrete (SFRC) is quantifying the residual stresses in tension. Due to concrete interaction with fibres, a cracked section is able to carry a significant portion of tensile stresses, called the residual stresses. Because of a great diversity in the shape and aspect ratio of fibres and, consequently, varying bond characteristics, there are no currently available reliable constitutive models. In present practices, residual stresses needed for strength, deflection and crack width analysis are quantified by means of standard bending tests. However, such tests require relatively sophisticated and expensive equipment based on the displacement-controlled loading. Besides, the test results are highly scattered. This paper investigates an alternative approach for defining the residual stresses. The approach aims at deriving equivalent stress–strain relations of cracked tensile concrete using test moment–curvature relationships of flexural concrete members with ordinary reinforcement and steel fibres. Tests on eight lightly reinforced beams (reinforcement ratio 0.3%) with different contents of steel fibres (0%, 0.5%, 1.0%, and 1.5% by volume) have been carried out. Based on the proposed technique, equivalent stress–strain relations were defined for each of the beams and further used for curvature and crack width analyses.