Overstrength requirements to avoid brittle shear failure in RC slender beams with stirrups

Abstract

In this paper, an analytical expression was derived for the prediction of shear strength of slender reinforced concrete (RC) beams with stirrups. Failure occurring in B and D regions of the beam was considered. An expression derived for the shear strength of the B region was based on a modified constant angle truss model. The analytical expression derived consisted of three terms. The first one was related to the concrete contribution expressed through the square root of cylindrical compressive strength, geometrical ratio of longitudinal bars, and depth to width ratio. The second one was relating to the shear force induced by yielding of stirrups to the inclination of the main crack occurring at failure; its value depends on the geometrical ratio of longitudinal bars, transverse stirrups, and modulus of elasticity of concrete and steel. Finally, the third term was related to the shear force induced by the flexure of steel bars in the space s, which depends on the number and diameter of longitudinal bars and the yielding stress of longitudinal bars. Failure of the D regions was related to the concrete crushing of loaded joint under the effect of shear force and compressive force, including also the confinement effect due to the presence of stirrups. The original contribution of the paper was the determination of the maximum mechanical ratio of longitudinal and transverse steel to ensure over strength in shear respecting the strength hierarchy.Expressions derived and some of those available in the codes were verified against three different data banks of experimental researches available in the literature. The data banks utilized considered a very wide range of the geometrical ratio of longitudinal bars and transverse stirrups, including, for the latter, very high value producing brittle failure due to concrete crushing.