Upper and Lower Bounds to Pull-Out Loading of Inclined Hooked End Steel Fibres Embedded in Concrete

Steel fibre-reinforced concrete (SFRC) consists of short, hooked steel fibres that are randomly distributed and oriented within the cementitious matrix. This paper presents a new analytical load-bounding approach that captures the tensile response of misaligned fibres embedded in the matrix. The contribution of fibres in bridging cracks to provide the required stress transfer relies on the orientation of the fibres in the concrete. Bridging fibres aligned with a crack are less effective than those inclined to it. Therefore, understanding the pull-out behaviour of misaligned fibres is a key factor in quantifying and optimising the design of SFRC in structural applications. In the laboratory, a single-oriented fibre embedded in a solid cylinder of concrete was subjected to a pull-out test, where the axis of the tensile force is aligned with the axis of the cylinder. Based on the observed behaviour, this paper presents a new analytical bounding approach to capture the pull-out response of misaligned hooked-end steel fibres embedded in a concrete matrix. The analysis was based on a transversely isotropic failure criterion assumed for the plasticity that occurs in the cold-drawn fibre. Lower and upper bounds to the loading failure were derived from fibre pull-out and fibre fracture, respectively. The division between bounds depended upon the fibre orientation, fibre diameter and the combined strengths of the steel and concrete. Bounding predictions were drawn from ratios between a fibre’s shear strength and its transverse and axial uniaxial strengths, as found from a novel testing proposal. The two bounds were compared with new data and other experimental results published in the literature. The results showed that the region between the bounds captured the failure loads of embedded fibres with effective load-bearing orientations. A critical orientation was observed at maximum strength. The present interpretation of the plasticity occurring within off-axis, hooked-end steel fibres suggests that it is possible to optimise the strength of concrete using this method of reinforcement.