Optimum Design of Multistory Multispan Frames for Prescribed Elastic Compliance∗

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Abstract
This paper presents an analytical method for minimum cost design of regular rectangular building frames for constrained elastic compliance. The method, consisting of a semi-inverse method and a design region extension procedure, is illustrated by two classes of exact solutions. It is shown that the relative story displacements are almost uniformly distributed in an optimally designed frame with almost uniform story heights and that the solutions enable one to calculate all maximum member-end stresses from member-end curvatures. It is suggested that the proposed design formulas may be utilized for design problems, subject to relative story displacement and stress constraints. Since these solutions are shown to be dependent upon the nature of the prescribed minimum stiffnesses, a method of finding a practically reasonable set of minimum stiffnesses is also presented.

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