Solution of the three forces problem in the case of two forces being mutually orthogonal

The present paper delivers some new numerical and exact solutions of the three forces problem that is one of fundamental problems of Michell’s truss theory. The present problem is to find the lightest fully stressed truss transmitting three self-equilibrated co-planar forces. In this study, we limit our considerations to the case of two forces being mutually orthogonal. The aim of this paper is to classify possible layouts of optimal trusses depending on the position of the applied lateral point load (the positions of the other two forces are fixed, which however does not restrict the scope of the study). The exact analytical solutions are obtained with a great help of numerical solutions that enable proper prediction of the optimal layouts.

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Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).