Determining stress intensity factor in bending reinforced Concrete beams

Abstract

There has been analytically solved the problem of determining the stress state in the cross section of bending reinforced concrete beams with a crack in a linear formulation. For this, the beam is cut along the crack line and the equilibrium condition of the cut-off part of the beam determines the height of the compression zone and the tensile stress at the crack tip. The remaining parameters of the stress state are expressed in terms of these values. The value of the bending moment is determined, above which there takes place increasing the initial length of the crack. For this case, the length of the operational crack is determined. The solution is valid for beams of arbitrary section shape. Determining the stress intensity factor (SIF) is based on the assumptions that the longitudinal forces at the tip of the crack are equal with and without taking into account stress concentration. The size of the stress concentration zone is determined from the condition that the local stress is equal to the nominal stress. On this basis a formula has been obtained for determining the stress intensity factor in rectangular beams. The paper analyzes the dependence of the stress intensity factor on the crack length, the moment and other geometric and operational factors. The obtained results allow estimating the bearing capacity of beams with a crack, as well as their crack resistance by a stress intensity factor.