1. Introduction. In recent years a good deal of progress has been made in obtaining solutions to practical problems concerned with reinforcement optimization of what, in practice, might be reinforced concrete or other fibre reinforced composites in bending (1). Almost all the solutions have been obtained using a linear expression relating bending moment to the amount of fibre required. In what follows a non-linear expression will be adopted; the expression is obtained by including the next term in a parameter series expansion.