On the kern of a general cross section

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 de®ned 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 example