Stress-strain state of bending reinforced beams with cracks

The work is dealing with studying the stress-strain state of bending pre-stressed concrete beams with cracks. The problems of determining preliminary stresses in a reinforced concrete element, determining the moment of crack formation, and determining the stress in a section with a crack are successively solved. The problems were solved for a general section with the vertical axis of symmetry, taking into account the non-linear relationship between strain and stress in concrete. The resolving system of two transcendental algebraic equations is obtained from the equilibrium conditions of a part of the beam on one side of the section with a crack. Analytical expressions have been obtained for determining preliminary stresses, the external bending moment at which a crack normal to the axis appears, as well as the stress state parameters in the section with a crack, including the crack height. The results obtained make it possible to predict the bearing capacity of reinforced concrete structures at the design stage by two groups of limiting states, and to evaluate the real technical condition of the structures in operation. These results can be used to determine the parameters of fracture mechanics and evaluate crack resistance of a reinforced concrete beam.