Abstract
In this paper an analytical model is developed to simulate crack initiation and propagation which is one of the most fundamental characteristics of reinforced concrete. The model is designed as follows. The ratio of the maximum principal stress to the modulus of rupture is designated the "crack ratio". The decision of which neighboring elements should be separated by a crack is based upon that the crack ratio is maximum over 1.0 at their common "side point". Once it has been determined that a crack should form along a particular grid line, the grid line is relocated perpendicular to the maximum principal stress and new nodes are introduced to express the new crack along the grid line. The discussion is made about the applicability of this analytical model by finite element calculations. The results are as follows : 1) The results of Analysis 1-1 in which crack initiation and propagation are considered obtain good agreement with the results of Analysis 1-2 in which cracks are preformed according to the crack pattern of Analysis 1-1. 2) The bond-slip model developed in the previous papers, Part 2 and Part 3, is introduced into this model and discussed by the linear analysis of a simple beam. When the bond is assumed to be nearly perfect, cracking is observed in a wide range, but in case of the nearly no bond only the flexural crack is propagated at the critical section. 3) The nonlinear bond-slip model is introduced into this model. From the analytical results of a simple beam, the following are recognized. (1) The less stress is transferred by the bond, the higher the flexural shear cracking load comes to be. (2) The pull out of the main bar and the dowel action are observed with the opening of the flexural shear crack. (3) When the flexural shear crack is propagated, the strain distribution of the main bar becomes uniform between the critical section and the crack surface. (4) There are two zones where the strain of hoop does not increase. These correspond to the previous experiments and theories.
