Numerical Modeling of Stress-Strain State of a Deep Beam

Abstract

The article presents calculation results for model elastic problem of defining stress-strain state of a deep beam preformed in 3D and 2D statements with the use of ANSYS software package. Geometric relations are taken in the form of Cauchy equations. The purpose of the study is to assess error in the results obtained for the two statements and to draw a conclusion on the possibility of using 2D statement for the deep beam under study. Based on 3D statement calculation results one may observe a short area near the support surface of a deep beam with the maximum load across the entire thickness. In this area the concentration of maximum stress values and maximum linear and angular deformations in the structure material are observed. The area is located on the axis of symmetry of the deep beam near the inner edge of support surface. It is found that the stress intensity values obtained for the two statements have considerable differences in this area, for that reason 3D statement shall be used when performing calculations for the deep beam. This way of solving the problem is illustrative of stress-strain state parameters distribution across the thickness of the structure, which is necessary for its strength evaluation.