A fracture mechanics model for a composite beam with multiple reinforcements under cyclic bending

The flexural behaviour of a composite beam (e.g. a reinforced concrete beam) with multiple reinforcements under cyclic loading is analysed through a fracture mechanics-based theoretical model which considers a cracked beam subjected to an external bending moment and the crack bridging reactions due to the reinforcements. Assuming a rigidperfectly plastic bridging law for the reinforcements and a linear-elastic law for the matrix, the statically indeterminate bridging forces are obtained from compatibility conditions. Typical phenomena, such as elastic shake-down and plastic shake-down, in the composite beam under cyclic bending are described in terms of applied bending moment against beam cross-section rotation. Further, by employing a fatigue crack growth law (e.g. the Paris law), the mechanical behaviour of the examined beam up to failure can be captured. Some numerical examples to illustrate the capabilities of the proposed theoretical model are presented.