Flexural deformability of reinforced concrete beams

In reinforced concrete beams, the sectional definition of the moment-curvature relationship is not straightforward owing to the presence of cracks. In general, this problem has been solved by considering a representative portion of the beam and by defining the curvature 1/r as the ratio between the rotation of the portion considered and its length. Large portions of the beam with many cracks lead to "average" moment- curvature relationship, while small portions delimited by two consecutive flexural cracks lead to "local" moment-curvature relationship. The difference between these two definitions is studied in this paper introducing a "general model." With this model the entire beam is modeled through a succession of blocks divided by flexural cracks taking into account the bond between steel and concrete. Due to the practical impossibility of univocal definition of the crack pattern evolution, it is proposed to use a "range model." This "range," delimited by the curves of maximum and minimum deformability, includes the moment-curvature relationship (locals and average) obtained from all possible crack patterns.