DESCRIPTION OF EMPIRICAL PROCESS OF CRACK FORMATION IN FRAMEWORK OF PROBABILISTIC THEORY

摘要

Theoretical accounts most frequently encountered in technical literature assume that the quantities describing the cracking process in beams, i.e. the cracking moment and crack spacing depend on the geometry of reinforced concrete section and on the mechanical properties of both constituent materials ― concrete and steel ― and are independent of the way of loading. Crack width is described either as a function of bending moment or shear force, often taking into account the influence of the duration of loading. Other factors are considered as secondary and are omitted in theoretical considerations. All descriptions are of deterministic character and for design purposes arbitrary factors of safety are introduced. The purpose of this paper is to confront some of these assumptions with the results of sufficiently numerous empirical investigations allowing to use the methods of mathematical statistics. The analyses carried out proved that crack density understood as the number of cracks per unit length of beam is not a constant quantity, but a random function. In the loading process not only mean value is varying, but also the form of function describing the distribution of crack density. The results of investigations indicate also that the influence of such factors as: method of curing, way of loading, joint action of bending moment and shear force, degree of shear reinforcement and kind of aggregate, influence appreciably the course of cracking process. Neglecting these influences in calculation methods requires the introduction of much higher factors of safety.