Effect of reinforcement on the crack resistance of concrete slabs

A preliminary analysis of the available publications devoted to the study of crack resistance of reinforced concrete structures showed the absence of established general patterns of influence of important geometric parameters inherent in reinforced concrete elements on the distribution of the characteristics of fracture mechanics along the crack front. Based on the analysis, the purpose of the study was formulated: to establish these regularities for a concrete slab reinforced with a system of longitudinal steel rods. When conducting the research, a linear and elastic model of concrete was used, and the stress intensity factor was considered as a characteristic of the fracture mechanics. A surface crack of constant depth located in the cross-section of the slab was postulated. It was assumed that its faces completely cover the cross-section of reinforcing rods. The crack depth, the depth of reinforcing rods, their diameter, and the distance between adjacent rods were chosen as dimensionless geometric parameters relative to the thickness of the slab. The slab was loaded with two types of loads applied to its ends: constant tensile stresses (pure tension) and linearly variable axial stresses (pure bending). The problem of determining the stress intensity coefficient depending on geometric parameters was reduced to the boundary problem of elasticity theory. The CalculiX finite element analysis package was used to solve it and obtain the stress-strain state of the slab. More than four hundred finite element models were constructed for various combinations of parameters. Based on the known displacements of the crack face points, the values of the stress intensity factor along the crack front were calculated using the relation obtained in the study. It is established that its values significantly depend on the diameter of the reinforcement, and therefore, when conducting practical calculations, it is not recommended to replace the action of reinforcement on concrete with concentrated force. Polynomial approximations with a relative error of 10% are obtained for extreme values of the stress intensity factor. The materials of the study can be useful in the design of reinforced concrete structures, and when studying or teaching a course in fracture mechanics