On the kern of a general cross section

The kern of a section is the region in which a compressive point load may b e applied without producing any tensile stress on the cross section. Ten th eorems describing the characters of the kern of a general cross section are derived. Three types of cross sections are considered: simply connected, m ultiply connected, and disconnected. It is shown how to obtain the kern of a multiply-connected or disconnected cross section using an auxiliary simpl y-connected section. Qualitative shapes of the kerns of some cross sections , with known numerically calculated kerns, are obtained using the derived t heorems. Kern ratio is defined and its boundedness is discussed. The kern r atio of regular polygonal sections are obtained as a function of the number of vertices and its minimum and maximum are calculated. The paper ends wit h an analytical derivation of the kern bf a general cross section with some examples. (C) 2000 Elsevier Science Ltd. All rights reserved.