A general solution to the material performance index for bending strength design

This paper presents a general solution to the material performance index for the bending strength design of beams. In general, the performance index for strength design is ρfq/ρ where σf is the material strength, ρ is the material density and q is a function of the direction of scaling. Previous studies have only solved q for three particular cases: proportional scaling of width and height (q = 2/3), constrained height (q = 1) and constrained width (q = 1/2). This paper presents a general solution to the exponent q for any arbitrary direction of scaling. The index is used to produce performance maps that rank relative material performance for particular design cases. The performance index and the performance maps are applied to a design case study.