828. Shape Factors for Structural Weight Prediction and Optimization

Paper

Abstract

The primary objectives of this paper were twofold. First, to develop a means whereby structural members requiring a given area moment of inertia could be solved rapidly and, where possible, in an explicit manner rather than by ‘cut-and-try’ or other iterative methods. Secondly, to provide a means of determining optimum structural configurations. These objectives were determined by the requirements for performing structural weight prediction and optimization functions. The objectives were achieved and made compatible with each other through the parametric approach developed herein. The approach utilized in this paper was to parameterize the shape factors, which relate area moment of inertia to cross sectional area, as a function of the ratio of the areas of the elements composing the structural cross section. Parameters of secondary importance in determining the value of the shape factors were eliminated in order to simplify the equations to the point whereby the aforementioned objectives could be attained with a relatively small sacrifice in precision. Shape factors which relate area moment of inertia to cross sectional area are presented for hat sections, box sections, Z-sections, I-sections, T-sections, angles, channel sections, and circular sections. Equations for the shape factors were derived and optimized. Design graphs, which expedite the utilization of the shape factors, are presented. The design graphs are also valuable in directing the designer towards a rational comprehension of the parameters which determine an optimum design and the sensitivity of structural efficiency to variations in these parameters. Considerations affecting the proper application of the equations and design curves are discussed. Sample problems are presented to illustrate how the information contained herein may be conveniently and effectively utilized.