CRACK-GROWTH IN FLEXURAL MEMBERS - A FRACTURE-MECHANICS APPROACH

ACI 318 contains several empirically based provisions regarding cracking and minimum flexural reinforcement of concrete beams and slabs. These provisions can be significantly improved by application of fracture mechanics principles. Rational analysis methods for concrete beams, which demonstrate a size effect, are developed using a simplification of the Hillerborg fictitious crack model. Without using numerical methods, the fictitious crack model is difficult to apply. Several simplifying assumptions are introduced to the fictitious crack model that allow beams to be simulated in an approximate analytical, rather than numerical, context. These assumptions are found to be justified by comparison with a finite element simulation of fictitious crack propagation in an unreinforced beam. Using fracture mechanics concepts, a method is developed to predict not only crack widths and lengths, but also the strength and cracking stability of reinforced concrete beams. Design equations and charts are presented.