Determination of crack spacing and crack width in reinforced concrete beams

Abstract

In this paper spacing and width of flexural cracks in reinforced concrete beams are determined using two-dimensional finite element analysis. At early loading stages on the beam the primary crack spacing is based on the slip length, which is the development length required to resist the steel stress increment that occurs at a cracked section on the formation of the first flexural crack. A semi-empirical formula is presented in this paper for the determination of the slip length for a given beam. At higher load levels, the crack spacing is based on critical crack spacing, which is defined as the particular crack spacing that would produce a concrete tensile stress equal to the flexural strength of concrete. The resulting crack width is calculated as the relative difference in extensions of steel reinforcement and adjacent concrete evaluated at the cracked section. Finally a comparative study is undertaken, which indicates that the spacing and width of cracks calculated by this method agree well with values measured by other investigators.