The modeling method of discrete cracks in reinforced concrete under the torsion with bending

Monitoring and testing of buildings and structures

The most famous of computer systems for the design of reinforced concrete structures in the world are taken into account only regular dispersed cracks. Completely different criteria should be used when analyzing the appearance and development of discrete cracks in reinforced concrete, the modeling methodology of which has not been developed to date. Therefore, the article provides working prerequisites, a methodology for simulating discrete cracks and calculating their rigidity. Several levels of cracking are considered. The development of spatial cracks is carried out on special bilinear surfaces. Then they fit in the approximating spatial finite elements that "expand", modeling a spatial crack, the opening of which is given in the form of a deformation effect with allowance for the discontinuity effect. When solving the inverse problem of determining the crack opening width, the deformation effect is not specified, and only the presence of a gap of the minimum possible width is modeled by means of an embossing; its opening, with appropriate loading, determines the width of the crack opening as the divergence of the shores of this gap. It is considered another variant of simulation of discrete spatial cracks in the article, in case of their implicit manifestation. Here pairs of finite elements adjacent to such a crack are distinguished from opposite sides. It is a special two-element design console model. These pairs are considered in two states: before their "expand" and after their "expand" taking into account the deformation effect and the discontinuity effect of concrete. It is introduced the classification of basic spatial cracks in spatial reinforced concrete composite constructions, cracks that develop to zones or from zones of geometric concentration; cracks that develop to zones or from zones of force and strain concentration of loading; cracks that develop in zones of inter-medial strain concentration. Their scheme is supplemented and based on these basic cracks by applying adjacent cracks, which are sought using the deformation criterion for their formation and the method of finding the extremum of a function of many variables using the Lagrange multipliers.