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.

Keywords

structural efficiency optimal shape shape selection

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