Structural efficiency maps for beams subjected to bending

Abstract

The structural efficiency of different cross-sections subjected to bending is considered in this paper. An envelope efficiency parameter, λ, is defined in terms of two shape transformers, A and 1. These transformers describe the relative ratio of the area and the second moment of area of the cross-sectional shape with respect to a rectangular envelope surrounding the shape. It is shown in a structural efficiency map that the mass efficiency of all cross-sectional shapes subjected to bending is bounded by two limiting curves. One limit curve represents cross-sections with material as far as possible from the neutral axis, the other limit curve is for cross-sections with material close to the neutral axis. The application of the map to two practical cases is also considered, together with scaling of the rectangular envelope.