Modelling of concrete corbels and hammerhead bridge piers

Abstract

The present work investigates the shear strength prediction for reinforced concrete corbels and hammerhead bridge piers. Reinforced concrete corbels could be seen as inverted deep beams loaded by wide elements. This type of reinforced concrete members are typically subjected to high shear forces and are susceptible to shear failures along diagonal cracks.

The main goal of this thesis is to introduce and define the fundamental theory of the kinematic model (2PKT), developed by Mihaylov et al. (2013), for deep beams and extend it to reinforced concrete corbels. The key feature of this theory are the compatibility conditions which are derived from a simplified kinematic representation of the deformation patterns observed in deep beams. The shear strength of the element is obtained by intersecting two curves: a shear capacity curve which is obtained as the sum of the four components of shear resistance across the critical diagonal crack and a shear demand curve that is derived from the tension force in the flexural reinforcement by using the moment equilibrium of the shear span. However, the kinematic model for deep beams supporting columns is not directly applicable to reinforced concrete corbels. According to the expression of the effective width of the loading/supporting plate, if the column is widened the critical crack will still be assumed to propagate towards its middle. This however is not consistent with the test observations where the cracks propagate close to the edges of the supporting elements. Therefore, if the kinematic model is applied without modifications, it will significantly overestimate the size of the critical loading zone, and thus will overestimate its shear resistance.

The extended kinematic model concluded that stress concentrations occur at the edges of wide loading and supporting elements which results in the propagation of critical diagonal cracks towards these locations as well as in the formation of narrow diagonal struts. To account for this effect, the kinematic model was extended by Boyan et al. in a simple manner by modifying the effective width of the loading plates which determine the inclination of the critical cracks and the size of the critical loading zones. The extended 2PKT method will be applied to all specimens found from literature and described in this report, and the main results will be summarized. The calculations were performed based on the procedure described above, where the intersection of the shear capacity and shear “demand” curves was found iteratively by using the bisection method.