The kern of non-homogeneous cross sections

The state of stresses in non-homogeneous bars due to eccentric axial loads is examined. The governing formulae are written in coordinate free invariant forms by means of vector and tensor algebra. The concepts of centric and eccentric axial loads for non-homogeneous bars are introduced. A general solution is developed to obtain the kern of cross section of arbitrary shape. Examples show how the results derived can be applied to determine the kern of a given inhomogeneous cross section.