Spacing of Cracks in Reinforced Concrete

Abstract

The spacing and width of cracks in a parallel crack system is approximately analyzed using the energy criterion of fracture mechanics as well as the strength criterion. The energy criterion indicates that the crack spacing is a function of the axial strain of the bars and also depends on bar spacing, bar diameter, fracture energy of concrete, and its elastic modulus. Both the energy and strength criteria yield a minimum strain necessary to produce any cracks. The energy criterion and the bond slip conditions further yield a lower bound on possible spacing of continuous cracks. The rules for the formation of shorter, partial length, cracks are also set up. Approximate expressions for the crack width at, and away, from the bars are derived. Numerical comparisons indicate satisfactory agreement with existing test data, and lend theoretical support to one aspect of the empirical Gergely‐Lutz formula obtained by statistical regression analysis of test data. Finally, formation of skew cracks in a biaxially stressed and biaxially reinforced plate is analyzed and a crack spacing formula is derived for one typical case.