Analytical approach to quantify the pull-out behaviour of hooked end steel fibres

An analytical modelling approach is developed in this article to simulate the pull-out behaviour of a single straight/hooked end fibre that is embedded in concrete matrix. The partial-interaction model is used to simulate the interfacial bond between the fibre and matrix along the entire fibre length throughout all stages of loading where additional axial and frictional forces due to straightening a hook is incorporated by simulating it as plastic hinges at the apex of bends. The analytical model is presented in a concise matrix form that helps to minimise the number of solution steps for the involved individual cases and provides a monolithic simplified implementation. A significant advantage of the approach is that it does not require fitting of a smoothing polynomial to show the full-range of fibre load-slip behaviour as it simulates the forces for straightening the fibre as it pulls through a bend and directly couples this to the interfacial bond forces.