Geometric properties for the design of unusual member cross-sections in bending

This short communication presents a series of general geometric properties of unusually-shaped member cross-sections. A skeleton derivation of the most important properties is presented and a method is illustrated for constructing more complex cross-sections. The focus is on the cross-sectional area, centroid and second moment of area, used in classical engineering design for bending. The shapes presented include circular and elliptical segments, sectors and arcs, semiellipses, superellipses, and combinations thereof. The superellipse allows a vast range of novel cross-sections to be described analytically and is a powerful mathematical tool for the analysis of unusual curved shapes. The equations are presented as composites of their geometric components so as to facilitate practising engineers in their implementation as programmed functions or subroutines.