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The octahedron family of tensegrity structures is presented in this research. The octahedron and the expanded octahedron (well-known tensegrities in the literature) are the first and second components of the family. A new tensegrity is presented: the double-expanded octahedron. This new tensegrity form was obtained following the connectivity pattern of the octahedron family presented in this work. The values of the force densities or force:length ratios that satisfy the minimum required rank deficiency of the force density matrix were computed analytically. Two types of solutions are obtained: full and folded forms. Results show that each lower member of the octahedron family is a folded form of a superior member of this family. Several examples are shown.

In order to design a steel member subjected to a bending moment and an axial load, there are an infinite number of possible solutions I-or H-steel cross-sections, the doubly-symmetric solution being just one of them. This paper presents a procedure to obtain the optimal steel cross-section from the infinite number of possible solutions. The process is based on the Reinforcement Sizing Diagrams employed in reinforced concrete strength design. The procedure looks for any type of solution regarding compact or non-compact steel sections. All aspects related to local instabilities will be taken into account, as well as special considerations in order to address the global instabilities associated with the slenderness of the steel element. N EdExternal axial load applied to the section

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