Stirrup Effectiveness in Reinforced Concrete Beams under Flexure and Shear

Abstract

The so-called shear failure of slender beams is known to be due to combined action of flexure and shear which causes beam failure moment to be lower than ultimate moment in pure flexure, even for beams with stirrups. Current design procedures for shear strength analysis provide simple superposition of stirrup and concrete capacities, hence ignoring any stirrup influence on concrete mechanisms and/or any dependence of stirrup action on the failure mode. By contrast concrete shear resisting mechanisms, made of the beam and arch action contributions, can interact with stirrups in different ways. Latter interaction results in a truss mechanism variable contribution and in some enhancement of beam action contribution. A stirrup effectiveness function is introduced, which provides the ratio of effective mean shear stress increase due to stirrup inclusion and the conventional one drawn from 45 deg truss model. On these bases a mechanical model is proposed to provide mean ultimate shear stress ofRC beams with stirrups. By testing the proposed model against available experimental results from different authors, more accurate prediction is obtained than ACI Code, Eurocode, New Zealand Code and Zsutty's formula. Thus, a design formula is proposed which is simple and results in a reasonably conservative design.