Abstract
The kern of a section is the region in which a compressive point load may be applied without producing any tensile stress on the cross section. Ten theorems describing the characters of the kern of a general cross section are derived. Three types of cross sections are considered: simply connected, multiply connected, and disconnected. It is shown how to obtain the kern of a multiply-connected or disconnected cross section using an auxiliary simply-connected section. Qualitative shapes of the kerns of some cross sections, with known numerically calculated kerns, are obtained using the derived theorems. Kern ratio is defined and its boundedness is discussed. The kern ratio of regular polygonal sections are obtained as a function of the number of vertices and its minimum and maximum are calculated. The paper ends with an analytical derivation of the kern of a general cross section with some examples.
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