Plastic design of structural frames for minimum weight has been the subject of several papers. In these the weight per unit length of a structural member has been assumed to be proportional to its fully plastic moment, although the effect of deviations from this simple relationship has occasionally been examined qualitatively. This paper is concerned with the minimum-weight design of frames under the assumption that the unit weight of a structural member is proportional to the α-th power of its fully plastic moment, the positive exponent, a, being smaller than unity. For α = 2/3, a chart is developed that gives, at a glance, the minimum-weight design for various geometries and loading conditions of a portal frame.
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William Prager (1958) studied this question.