On optimum tin-walled closed cross section

This paper deals with the problem of finding a minimum area thin-walled closed cross section with pre- scribed constant thickness and flexural rigidity. The cross sectionis supposed to be double symmetrical with respect to the Cartesianreference system(x0y),where 0 isthe centroid of the cross section, and subjected to a bending moment M. The vector M is taken to be non-coincident with the x or y axis. This means that to represent the flexural rigidity both Ixand Iymoments of inertia are required. The func- tion describing the centerline of the thin-walled closed cross section is taken as unknown. The solution of this problem shows that such a centerline is an ellipse.