On the Optimum Shape of a Fillet in a Flat Bar with Restrictions

Designing the transition from one given cross-section to another given cross-section in a bar such that stress concentrations become the least possible is a problem of considerable engineering importance. Good results have been obtained in a number of experimental investigations by means of photoelastic tests [1], and it has been demonstrated that stress concentrations can be totally avoided provided the fillet is sufficiently long. In agreement with this, Neuber [2, 3] has recently shown theoretically that the tangential edge stresses are constant for a flat bar in tension with a particular exponential variation of the height of the cross-section.