The Flexural Centre or Centre of Shear

This paper reviews work on the flexural centre of elastic cantilever beams and contains a number of hitherto unpublished results, including a formula giving the position of the flexural centre in terms of the Prandtl torsional stress function.

The appearance of the note by Jacobs has prompted the preparation of a review of this subject which is all the more desirable as several of the investigations made shortly before the 1939-45 War were never published and others, although published, seem to be in danger of being overlooked. The present paper contains a number of hitherto unpublished results. The question of nomenclature is worthy of mention since general agreement is lacking. Some of the names used are flexural centre, centre of flexure, elastic centrum and centre of shear but a complete search of the literature would probably lead to the discovery of yet other names. The terms “centre of shear” and “elastic centrum” seem vague and fail to indicate that the point referred to has any special relation to flexure. We shall here use the name “flexural centre” exclusively.