The free shrinkage deformation occurring in concrete members is generally restrained by members around one with different stiffness and shrinkage rate, and a restraining ratio which expresses degree of restraining has a major influence on state of shrinkage cracking. Therefore, in order to predict the shrinkage cracking, it is important to get the restraining ratio of concrete members in addition to free shrinkage strain of concrete.
With this background, in order to prepare eventually a design material for controlling shrinkage cracking with the organized distribution of restraining ratio, an experimental and analytical study to find out the regularity of distribution of restraining ratio in concrete walls was previously performed by authors. Additionally, it was noted that the restraining ratio in a wall with drying shrinkage should be reasonably considered by dividing it into the following two areas.
(1) Non edge area: the area whose restraining direction is horizontal and distribution of vertical direction of restraining ratio is linear because bending deformation is dominant and Bernoulli-Euler's hypothesis holds. The distribution of restraining ratio in this area can be calculated by replacing a concrete wall with a uniaxial model.
(2) Edge area: the area whose restraining direction is turbulent and distribution of vertical direction of restraining ratio is non-linear because shear deformation is dominant and Bernoulli-Euler's hypothesis does not hold. This signifies that the distribution of restraining ratio in concrete walls can be potentially predicted by the following policy: (1) First, the distribution of restraining ratio in a concrete wall is calculated by the uniaxial model, (2) Next, the position of areas to which the value calculated at above (1) can be not applied (i.e. edge area) and the value of restraining ratio in those areas is obtained from the design material prepared previously, considering various conditions of concrete walls.
In this study, the map of distribution of restraining ratio in concrete walls, which is the design material in line with above policy, was created. In particular, the distribution of restraining ratio in concrete walls with various conditions was calculated by FEM analysis. Moreover, the areas to which the value calculated by the uniaxial model can be not applied (peculiar areas) were shown by organizing that result, and restraining ratio and restraining direction in those areas were shown.
The distribution of restraining ratio shown in the map has the following characteristics.
(1) The peculiar areas occur at the upper and lower parts of both ends of a wall.
(2) The position and largeness of peculiar area at lower part of both ends of a wall hardly changes depending on stiffness balance between members. Additionally, the area extends vertically as the shape of a wall is horizontally long. Furthermore, though the area is decoupled by columns and beams with increased number of layer and span, the position of that entire area hardly changes.
(3) The average restraining ratio at the peculiar area at lower part of both ends of a wall is obtained by adding a constant value (approximately 0.4) to the restraining ratio calculated by the uniaxial model, and the average restraining direction at the area is 30° to 35° in any wall.
