On the Stress Concentration Problem of a Circular Shaft with a Semicircular Groove Under Tension : An Application of Green's Functions for Body Force Problems of a Solid Cylinder

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This paper is concerned with the stress concentration problem of an elastic circular shaft with an annular groove of a semicircular form under tension. The problem has been treated by several authors, but is seems that these results do not always agree with one another. In the present problem, the author's results are in fairly good agreement with Sato's results analyzed by F.E.M. and measured by strain gages. It may be also said that the form factors shown in the paper conform to Neuber's results in the case of large radii of a groove compared with the radius of the shaft and also conform to Peterson's results in the case of small radii of a groove. A fundamental principle of the method of solution employed in the paper is to superpose Green's functions for axisymmetric body force problems of a solid circular cylinder. This method can be easily applied to other annular grooves besides a semicircular one treated here.