Louis Turcotte

Determining the kern for a compression member of general cross-section

Abstract The region within which axial loads may be applied to a compression member without inducing tension anywhere in the cross-section, commonly called the ‘kern’, is studied. A general solution is developed for arbitrary polygons. A microcomputer program giving numerical and graphical results is presented. To determine the kern, the program requires only the vertex coordinates which are necessary to describe the polygonal cross-section. Geometries containing curved boundaries can be analyzed by replacing the curved boundary with a suitable set of line segments. Several example geometrics are presented, including standard structural shapes, a cross-section with a hole, a cross-section with disconnected areas, and a cross-section with a curved boundary.