A paper presented recently by Professor J. F. Baker has shown the essential simplicity and economy of the plastic method of design of rigid framed steel structures. The method has been supported by results from tests both on miniaturee and on full-scale framess, and in view of the ease with which it can be applied, it is thought to be of interest to publish results of a theoretical investigation into the material consumption of such frames. In fact, an earlier paper* has dealt with the problem of the exact determination of cross-sections in order that minimum weight design might be achieved; however, the solutions were derived by means of sets of linear inequalities for the quantities required, involving heavy computational labour. The present paper
abandons the idea of obtaining exact solutions; instead, it is shown that upper and lower bounds may be found for the minimum material consumption, and that these bounds may be made sufficiently narrow for practical purposes.