As will have been noted from the last chapter, the theory of bending of beams seems always to have given some difficulty. The first key requirement of statics, that there should be no net thrust across a cross-section in pure bending, was recognized in the eighteenth century; but it was only in 1826 that Navier stated explicitly that as a consequence the neutral axis must pass through the centre of gravity of the cross-section. However, even Navier was not aware of the consequences of a second statical requirement; moments of the forces acting on a cross-section lead to the notion of principal axes of bending. Thus Navier gave wrong expressions for the bending of a rectangular cross-section about an axis not parallel to one of its sides, and it fell to Saint-Venant in his 1864 edition of Navier to discuss fully the question of principal second moments of area.

Saint-Venant extended his analysis to cover non-linear behaviour of the material, but confined his work in this connexion to symmetrical cross-sections. The elastic/perfectly plastic material is a special case of Saint-Venant's more general material, and the plastic bending problem was considered separately by Ewing (1899). Ewing again discussed only the rectangular section bent about a principal axis, and indeed most of the modern standard texts on plastic theory do not treat the unsymmetrical problem. Brown (1967) seems to be the first to have recorded the general features of plastic unsymmetrical bending.