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.
Highlights
In publications on solid mechanics the problem of stress-strain state (SSS) calculation for a deep beam is conventionally solved in 2D statement [1-3]
Testing of calculation program was performed by solving a problem for the case of supporting a structure with the entire bottom surface under action of load q, when linear elastic SSS occurs in the deep beam
Based on the performed calculations it was found that the results of a deep beam SSS analysis obtained for 3D statement indicate existence of a short region with the maximum load along the entire thickness of the structure in proximity to the support surface
Summary
In publications on solid mechanics the problem of stress-strain state (SSS) calculation for a deep beam is conventionally solved in 2D statement [1-3] In this case stresses σz,τzx,τzy equal to zero on the sides are neglected inside the beam structure due to smallness of thickness value compared to other parameters. Sinitsyn suggested and implemented an effective technique of finding Airy stress function on the plate boundary by building diagrams for bending moments occurring in the frame having the same configuration as the deep beam form and subjected to the same load. Such technique is called frame analogy method.
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