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This paper presents an analytic formula for the theoretical stress concentration factor kt for cylindrical tubes with transverse circular holes, loaded in traction or in flexion. The study is based on modern finite element (FEM) techniques, which allow for appreciating with great accuracy the phenomenon of stress concentration. A comparison between the FEM results of this paper and those that were obtained by the existing analytic formulas shows the need of an update, as some discrepancies may be noticed. Our results are the fruit of a wide campaign of numerical FEM simulations that have been conducted analyzing numerous geometric configurations of the tube. Moreover, these configurations are defined in a wider two-dimensional (2-D) domain than the one valid for previous analytic formulas published in literature. Finally, these FEM results have been approximated with great accuracy by means of a fourth degree double polynomial regression that led to the new analytic formula that is proposed in this paper.

Transverse Circular Holes in Cylindrical Tubes Loaded in Traction and in Flexion: A New Analytical Approximation of the Stress Concentration Factor