Tensile Fillet Stresses in Loaded Projections

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Abstract
The loaded projection is an essential feature of practically every machine and structure—the screw thread, gear tooth, and simple cantilever are examples. The strength frequently depends on the fillets connecting the projection to its base, and hence the maximum tensile fillet stress may be a critical factor. Existing fillet stress formulae give accurate results over only a narrow range of projection shapes. In this paper an empirical formula is advanced which agrees well with experiment over a wide range of projection shapes, and which provides a powerful method of determining the strongest shape of projection for any given purpose, the procedure being demonstrated for the derivation of a series of screw thread forms having greatest strength.

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