Abstract
The limiting elastic state of a bar with large curvature under pure bending is considered on the basis of the elasticity theory exact solution. As a criterion for the limiting state, the gradient plasticity condition is used, which determines the yield onset in an inhomogeneous stress state. Analytical expressions for calculating the corresponding stresses are obtained. The results comparison with a simplified solution is given.
Highlights
The theory of strength by its purpose in the calculation of structural elements is aimed at achieving the main goal: ensuring strength and operational safety while reducing material consumption
The problem solution is provided by a numerical comparison of the objectively obtained strength characteristics of the material with the calculated values of the stress state in hazardous sections
This approach does not take into account the possible types of the elements and structures’ real stress state
Summary
The theory of strength by its purpose in the calculation of structural elements is aimed at achieving the main goal: ensuring strength and operational safety while reducing material consumption. The problem solution is provided by a numerical comparison of the objectively obtained strength characteristics of the material with the calculated values of the stress state in hazardous sections. This approach does not take into account the possible types of the elements and structures’ real stress state. The experimental data analysis [1,2,3,4,5] shows that the yield point of the material, determined from experiments on simple tension, does not allow to reliably solve the strength problems with a non-uniform stress distribution. Its application leads to an analytical expression that makes it possible to calculate the corresponding stresses and loads. The authors are not aware of other works leading to the analytical solution
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