60. Application of the Trefftz Circle of Inertia to the Analysis of Aircraft Weights Data
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Paper
Abstract
It is shown in any elementary analytical geometry book that the cross-product term may be removed from any 2nd degree equation in two variables (equation of a conic section) by a suitable rotation of the axes. The same mathematics is used to find, the (mutually perpendicular) planes of zero shear in a two-dimensional stress distribution and, with engineers, the Mohr Circle of stress commonly takes the place of the mathematics in this application. Also the same mathematics is used to find thy principal axes of a plane area as in the analysis of the ‘unsymmetrical bending’ of a beam. For this application, Trefftz invented a graphical construction which I think should be ca1led the Trefftz inertia circle.
