Analysis and modelling of mechanical anchorage of 4D/5D hooked end steel fibres

Abstract

This paper represents an analytical model to predict the influence of the fibre geometry on the pull-out behaviour of various geometrical hooked end steel fibres. The model is established based on the concept of a frictional pulley along with two, three and four plastic hinges to simulate the mechanical anchorage effect provided by the hook. The mechanical contribution of the hook is a function of the cold work needed to straighten the fibre during the pull-out. The input parameters used in this model are directly related to geometrical and mechanical properties of each fibre. Model predictions are validated against experimental results for single fibre pull-out tests, and very good agreement is shown.

Comparisons Between Pull-Out Behaviour of Various Hooked-End Fibres in Normal–High Strength Concretes

“…The elastic-plastic moment expression was advanced to represent the actual the plastic penetrations involved in the unbending required. Here again when taken with the frictional pulley concept (Abdallah et al 2016a) this paper shows how plasticity explains the pull-out behaviour of 3D, 4D and 5D fibres embedded in a specific concrete matrix. It is shown how this approach is applied to experimental results for each hooked end fibre and three concrete matrices in normal-high strength range.…”

“…The elastic-plastic moment expression proposed above (step 7) has been incorporated into frictional pulley model (Abdallah et al 2016a) in order to predict the forces at each stage of pull-out for all hooked end fibres. From static force and moment equilibrium, the pullout force P in each pull-out stage has been determined (Abdallah et al 2016a) as given by Eqs. (21)-(24).…”

“…The rising applications of 4D and 5D hooked end fibres in modern structural applications have created the need to simplify theoretical analyses. For example, a semi-empirical pull-out analysis of these fibres was proposed by the authors to match observed behaviour satisfactorily (Abdallah et al 2016a). This model adopted Alwan's frictional pulley (Alwan et al 1999) to account for variations in mechanical and geometrical properties of the fibres as well as the matrix strength.…”

“…This model adopted Alwan's frictional pulley (Alwan et al 1999) to account for variations in mechanical and geometrical properties of the fibres as well as the matrix strength. Previously the authors (Abdallah et al 2016a) examined fibre-matrix conditions for a pull-out force where a full straightening of the fibre was observed. This paper investigates the conditions when the hook is not fully straightened during the pull-out as has been often observed.…”

Anchorage mechanisms of novel geometrical hooked-end steel fibres

“…Otherwise, if the bond is too strong, the fibre rupture may happen before they can fully contribute to the post-crack strength [13]. Therefore, the investigation of the bond mechanisms is a key factor to understand the tensile behaviour of SFRCCs [14,15].…”