Inverse Design of Frames for Specified Second-Order Bending Strains

Abstract

A new inverse design method for frames has been presented by means of an inverse formulation including frame stability effects. Elastic building frames in non-earthquake-prone areas, designed primarily for light horizontal wind loads, are considered. Governing equations based on the well-known second-order slope-deflection equations are derived for fundamental problems for a set of specified member-end fiber bending strains, as a target performance. An explicit expression for the solution stiffnesses is obtained for a hybrid-inverse problem. Further consideration is given for a class where the member stiffness set is determined only by a strain mode such as for a frame consisting of columns under central compression. It is demonstrated that the strain mode of an entire multistory frame can be synthesized by overlapping of the strain modes of decomposed unit frames. The design formulas for the simple models in this paper not only have disclosed the essential characteristics of design solutions but also play the role of initial backbone solutions in the neighborhood of which perturbed solutions can be derived for problems under more practical conditions.