Selection of arbitrarily scaled cross-sections in bending stiffness design

Abstract

Performance indices can be used to model the relative structural efficiency of different cross-sectional shapes. Performance indices have been previously defined mainly for structural cross-sections that are scaled proportionally in size. This paper extends the method of performance indices by allowing scaling of cross-sections in any direction. A novel feature of the method described in this paper is the inclusion of the space envelope as a design parameter. The first part of the paper gives a derivation of the general solution for the performance index. The second part presents a graphical selection procedure and discusses the efficiency limits of cross-sections due to buckling instability. It concludes with a case study to demonstrate the method.