Macroscale Elastic Coefficients for Concrete with Reinforcements Under Axial and Shear Loading - 22089

For composite materials of concrete and reinforcement steel bars, to increase the strength, steel bars of equal amount are added in both the compression and tension zones. In this study, the elastic coefficients are calculated by solving boundary-value problems (bvp's) - elastostatic problems, induced by strains on the macroscale. The bvp's are solved numerically by using 3-D quadratic finite elements. The bars used in the analysis are assumed to be of circular cross-section with constant area without ribs. In this study, specifically a normal strain condition in the direction normal to the cross-section and a shear strain case in the horizontal plane when viewed from the front on the macroscale are chosen to calculate displacements on the microscale. By using the microscale results, the effective elastic coefficients on the macroscale are determined. Under shear strain on the macroscale, it is shown that the results obtained by homogenization theory adopted in this study are a little less than those by the volume fraction averaged values. Under shear strain on the macroscale, it is seen that the effective elastic coefficients of the composite material appear to be quite the same as the volume fraction averaged ones. (authors)