Abstract
This paper uses a rapidity convergent series to establish the shapes giving minimum cross-sectional area for a convex section subjected to minimum constraints on second moment of area about an arbitrary centroidal axis and on torsional rigidity. In the formulation, some properties of the solution established by earlier workers are assumed. The results give upper bounds on the minimum area which are lower than those previously available and extend solutions to the full range of design parameters. The convexity constraint becomes active for ratios of torsional to bending stiffness of 1.575 and lower.
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