Abstract
A simple bending theory applies when bending takes place about an axis that is perpendicular to a plane of symmetry. If such an axis is drawn through the centroid of a section, and another mutually perpendicular axis is drawn to it through the centroid, then these axes become principal axes. Thus, a plane of symmetry is automatically a principal axis. This chapter explains the mathematical derivation of unsymmetrical bending. All plane sections, whether they have an axis of symmetry or not, have two perpendicular axes about which the product second moment of area is zero. Principal axes are thus, defined as the axes about which the product second moment of area is zero. Simple bending can be taken as bending that takes place about a principal axis, moments being applied in a plane parallel to one such axis. In general, however, moments are applied about a convenient axis in the cross section; the plane containing the applied moment may not be parallel to a principal axis. Such cases are termed “unsymmetrical” or “asymmetrical” bending.
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