Assessment of Bending Reinforced Concrete Beams Crack Resistance

Abstract

The problem of determining the stress state in a section of bending reinforced concrete beams with an initial and operational cracks has been solved analytically. To this end, a system of two nonlinear algebraic equations has been obtained from the equilibrium conditions of the part of the beam cut along the crack line. From this system, for a beam with an initial crack, the height of the compression zone and the nominal stress at the crack tip are determined, and for an operational crack, the height of the compression zone and the length of the crack are determined. The remaining parameters of the stress state are expressed in terms of these values. There is also determined the value of the external moment above which an increase in the initial length of the crack occurs. Determining the stress intensity factor (SIF) is based on the assumptions that the longitudinal forces are equal at the crack tip, with and without 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, the formula for determining the SIF is obtained. The paper analyzes the SIF dependence on the crack length and the bending moment. The method of calculation is valid for beams of arbitrary cross-section, but explicit dependences are given for beams of rectangular cross-section most frequently encountered in production. The results obtained allow estimating the bearing capacity of beams with a crack, as well as their crack resistance according to the force criterion of fracture mechanics.